Power system security enhancement through effective allocation, control and integration of demand response program and FACTS devices

Transcription

1 Power system security enhancement through effective allocation, control and integration of demand response program and FACTS devices By Ashkan Yousefi This thesis is presented for the degree of Doctor of philosophy of The University of Western Australia Energy Systems Centre School of Electrical, Electronics and Computer Engineering 2013

2 ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my supervisor and my co-supervisor, Dr Herbert H.C. Iu and Dr Tyrone Fernando, for providing the opportunity to undertake this research, along with their excellent guidance and constant support. I would like to thank the staff at the Energy Systems Centre for their assistance and the use of the facilities of the centre. I would like to express my love to my family for their unconditional love and encouragement during my study. Finally, I would like to express my special appreciation to the University of the Western Australia for providing the SIRF scholarship. 1

3 ABSTRACT This thesis is devoted to the development of a new approach for using the FACTS devices and demand response programs to improve the power system security and reliability. The key objectives of the research reported in this thesis are: -Optimal allocation of demand response program -Optimal allocation of FACTS devices -Congestion management in transmission lines using demand response program -Congestion management in transmission lines by effective integration of FACTS and dispatchable demand response program -Facilitating large penetration of wind power generation into the system by effective utilisation of dispatchable demand response program To be able to cover the above objectives, the thesis first developed a method to find the optimal location of static var compensator (SVC) and thyristor control series compensator (TCSC). A multi-objective optimisation is developed and optimised using non-dominated genetic algorithm to find the optimum location for installing the FACTS devices in the network. In SVC allocation, the objective function covers minimising the SVC installation cost, voltage deviation, maximising the load ability of the transmission lines and minimising the active power loss. In the case of TCSC allocation, the objectives are minimising the investment cost, maximising the loadability of transmission system and minimising the transmission active power loss. To optimise the proposed multi-objective functions non-dominated sorting genetic algorithm which is one of the well-developed member of evolutionary algorithm methods is selected. After determining the optimal location and sizes of SVC and TCSC in the electricity network, a multi-objective approach is applied to find the optimum location for 2

4 dispatchable demand response program. In this case, maximising the available transmission capacity, minimising the expected energy not supplied, minimising the active power loss and minimising the total DR capacity in the network are considered as objectives for allocation of demand response program. After successful allocation of SVC, TCSC and demand response program an approach for transmission lines congestion management is proposed by effective participation of demand response program. In the next step, the congestion management algorithm is developed using effective combination of FACTS and demand response program. A formulation for coordinating both FACTS device controllers and demand responses through constrained optimization is proposed to achieve congestion management in the transmission lines with minimum cost. This coordination can enhance the power system security and provide an effective tool for system operator to mitigate the congestion in transmission lines during high peak demand or major contingencies in the system. In the final step of the research, the role of demand response program in providing the support for the large integration of renewable energy into the electricity network is investigated. 3

5 LIST OF PRINCIPAL SYMBOLS V Θ U α Xtcr System voltage magnitudes System phase angles System Control variables Delay angle which is calculated based on the applied voltage to the TCR Effective reactance of the thyristor controlled reactor at the nominal frequency XL Vhsvc Vsvcref asvc Isvc Bsvcmax Bscvmin g 2 k Reactance of the reactor at the nominal frequency High voltage node for the SVC Voltage reference value for the SVC Slope reactance of the SVC SVC current Maximum susceptance of the SVC Minimum susceptance of the SVC Index indicating violation of line flow limits s i Total power flow in transmission line i s i max L The maximum limit for the line i Total number of transmission lines V n k The voltage magnitude at load bus n in operating condition k k V refn N Y sl,i The nominal or reference voltage at bus n The number of buses in the transmission network The element (sl, i) of the nodal admittance matrix of the power system k E V k Vector function of system Vector of system voltage magnitudes Vector of system phase angle 4 θ k

6 u k V i k k Y i,j Vector of control variables in operating condition k Nodal voltage at node i in operating condition k Element (i, j) of the network nodal admittance matrix in operating condition k P i SP Specified active power load demand at node i V i k Voltage magnitude at node i k V i max g i min g i max G i m Y sl,i P Di Q Di 0 P Di 0 Q Di Maximum voltage allowable value in operating condition k Minimum value obtained for the objective functions Maximum value obtained for the objective functions Selected values for multi objective optimisation Element (sl, i) of the admittance matrix of the power system Real load in load area Reactive load in load area Original real load demands at bus i in the load area Original real load demands at bus i in the load area V i Voltage magnitudes at bus i Gij Bij δ ij N EPNS j T j Y sl,i Real part of the ijth element of bus admittance matrix Imaginary parts of the ijth element of bus admittance matrix Voltage angle difference between bus i and bus j The total number of load loss events in a year Expected power not supplied in the jth event Duration of the outage in the jth event Element (sl, i) of the admittance matrix of the power system P Gi The real power generation at bus i 5

7 V i Voltage magnitudes δ ij Voltage angle difference between bus i and bus j TDRP Total DR programs capacity DRP The amount of load participating in the demand response at the nth load bus TB E D 0 D Total number of load buses with demand response programs Elasticity of the demand Initial demand value (MWh) Demand value (MWh) Electricity price ($/MWh) 0 Initial electricity price ($/MWh) LR() t fin() t Reduction level requested from the aggregator Penalty for not responding to aggregator request LRmax () t Maximum value agreed in the contract between the aggregator and DR participants B( L( t )) Customer revenue for using Lt () Et () 0 () t P redi Elasticity of the load Market price prior to demand response implementation Power provided by responsive demand i max P Gj, l Maximum power block l offered by generator N red Number of responsive demands N L Number of lines 6

8 N Gj Number of blocks offered by generator j f r Pr j Pr l CO( RI ) Risk coefficient Outage probability of generator j Outage of line l probability The function represents the risk. up P Gj Increment in the schedule of generator j down P Gj Decrement in the schedule of generator j down P redi Decrement in the schedule of responsible demand i up r j Price offered by generator j to increase its schedule down r j Price offered by generator j to decrease its schedule P Dik Power block k that demand i is willing to buy at price Dik Dik Price offered by demand i to buy power block k Gjl Price offered by generator j to sell power block l P Gjl Power block l that generator j is willing to sell at price Gjl P fd The fixed load based on demand forecasting. P Dik Power block k that demand i is willing to buy at price Dik Dik Price offered by demand i to buy power block k Gjl Price offered by generator j to sell power block l P Gjl Power block l that generator j is willing to sell at price Gjl P fd Fixed load based on demand forecasting 7

9 E m (.) LE m (.) F(.) Emission function of a unit Slope of segment m in a linearized emission curve Fuel cost function of a unit ME (.) Number of segments for the piecewise linearized fuel cost curve MF (.) Number of segments for the piecewise linearized fuel cost curve P (.) Hourly generation of a unit LG m P m (.) q m (.) u(.) RUP i RAD i SPI () t TIU TIC Slope of segment m in linearized fuel cost curve Generation of segment m in a linearized fuel cost curve Generation of segment m in a linearized emission curve Unit status indicator where 1 means on and 0 means off Ramping up limit of a unit Ramping down limit of a unit Total amount of spinning reserve Number of hours a unit has been on at the start of the scheduling period Number of hours a unit has been off at the start of the scheduling period HT (.) Number of hours a unit needs to remain on if it is on at the beginning of the scheduling period LU(.) Minimum up time of a unit LT (.) Minimum down time of a unit Dm ( i, t ) Power block that demand i is willing to buy at the price of m( it, ) 8

10 GLOSSARY FACTS TCSC SVC EENS ATC DR NSGA ISO EPRI TCR TSC MOV STATCOM UPFC TCVR SSSC TCPAR TCPST FERC DLC DB EDRP CAP A/S Flexible alternating current transmission system Thyristor Controlled Series Capacitor Static VAR compensator Expected Energy Not Supplied Available Transmission Capacity Demand Response Non dominating sorting algorithtm Independent System Operator Electric Power Research Institute Thyristor controlled reactor Thyristor switched capacitors Metal Oxide Varistor Static Synchronous Compensator Unified Power Flow Controller Thyristor Controlled voltage regulator Static Synchronous Series Compensator Thyristor controlled phase angle reactor Thyristor Controlled Phase Shifting Transformer Federal Energy Regulatory Commission Direct load control Demand Bidding Emergency Demand Response Program Capacity market program Ancillary-services market program 9

11 TOU CPP RTP CAISO ERCOT LaaR IEA NYISO DASR FERC MOGA OPF NERC TTC TRM CBM ETC RPF CPF SCOPF DSM NAS Time of Use Critical Peak Pricing Real Time Pricing California Independent System Operator Electric Reliability Council of Texas Loads Acting as a Resource Program International Energy Agency New York Independent System Operator Day-ahead scheduling reserve Federal Energy Regulatory Commission Multi Objective Genetic Algorithm Optimal Power Flow North American Electric Reliability Council Total Transfer Capability Transmission Reliability Margin Capacity Benefit Margin Existing Transmission Commitments Repeated power flow Continuation Power Flow Security constrained optimal power flow Demand Side Management Natrium Sulfur 10

12 Contents Chapter Objectives Outline of the thesis Contributions of the thesis Publications Chapter 2 Steady-state models of flexible AC transmission system devices Basic Mechanisms of Compensation Power system stability Power system static security Steady-state models of power system elements Power system nodal formulation Modelling of the FACTS devices Static VAr compensator (SVC) Thyristor controlled series compensator (TCSC) Applications of FACTS devices in power system The role of FACTS for congestion management Chapter 3 Demand response program Definition of demand response program Benefits of DR programs Demand response in electricity market Different types of demand management programs Incentive-based demand response programs Time-based programs Applications of demand response programs for power system planning and operation

13 3.5.1 The role of DR programs for transmission line planning The role of DR for providing ancillary services Review of demand response programs in electricity markets Electric Reliability Council of Texas California ISO (CAISO) PJM Interconnection New York ISO (NYISO) Summary of the demand response program in the U.S. electricity market Chapter 4 Multi-objective approach for optimal allocation of FACTS devices FACTS allocation overview Problem formulation Cost Loadability index Voltage deviation index Active power losses Equality constraints Inequality constraints Multi-objective optimisation Implementation of NSGA-II method Initial population Fitness evaluation Iterative process Selection of final solution Numerical Studies TCSC allocation Objective function formulation for TCSC allocation Numerical results for TCSC placement

14 4.6.3 Conclusion Chapter 5 Multi-objective demand response allocation Problem formulation Expected energy not supplied (EENS) Active power loss Available transmission capacity Total DR programs capacity Equality constraints Inequality constraints Variables and their representation Fitness evaluation Iterative process Selection of final solution Numerical Studies Conclusion Chapter 6 Congestion management using demand response program Congestion management Preventive congestion management methods Corrective congestion management methods Modelling demand response program Auction-based market clearing Congestion management by generation and demand re-dispatch Numerical studies Conclusion Chapter 7 Hybrid approach for congestion management using combination of demand response and FACTS devices Introduction

15 7.2 Problem formulation Congestion management formulation Numerical studies Conclusion Chapter 8 Facilitating large integration of wind power generation through effective utilisation of demand response program Introduction Problem formulation Market clearing formulation Representative study Conclusion Chapter 9 Conclusions

16 List of Figures: Fig. 2.1: Typical SVC connection Fig. 2.2: Thyristor controlled reactor Fig. 2.3: Typical VAr compensator Fig. 2.4: SVC schematic diagram Fig. 2.5: V-I characteristic of the SVC Fig. 2.6: Schematic diagram of the TCSC Fig. 2.7: The reactance versus delta angle characteristic of the TCSC Fig. 2.8: Typical V-I characteristics for a single-module TCSC Fig. 2.9: The correlation between TCSC reactance and line current Fig. 2.10: Typical V-I capability characteristics for TCSC with two modules Fig. 2.11: Typical X-I capability characteristics for a typical TCSC with two modules 40 Fig. 2.12: Effective FACTS devices for voltage control Fig. 2.13: Effective FACTS devices for reactance and angle Fig. 3.1: Time-based and Incentive-based Demand Response Programs 53 Fig. 4.1: NSGA II procedure 69 Fig. 4.2: Representation of a power system and the sample string for SVC locations and sizes Fig. 4.3: The selection procedure for optimal allocation of the SVC Fig. 4.4: IEEE 14 bus test system Fig. 4.5: Flowchart of the proposed algorithm Fig. 4.6: IEEE 30 bus test system Fig. 5.1: Representation of sample power system and string for DR locations and sizes Fig. 5.2: Flowchart of the proposed algorithm Fig. 5.3: Single line diagram of the IEEE 30 bus test system Fig. 6.1: The elasticity of the typical elastic and inelastic load 110 Fig. 6.2: Linear representation of price versus quantity Fig. 6.3: Non-linear representation of price versus quantity Fig. 6.4: IEEE 30-bus system Fig. 6.5: The load curve before and after DR program implementation Fig. 6.6: Total cost of market operation in three scenarios of demands ($/hour) Fig. 7.1: Typical demand response offer to the market

17 Fig. 7.2: Two step market clearing procedure Fig. 7.3: IEEE 30-bus system Fig. 8.1: Load profile and wind generation in CAISO 139 Fig. 8.2: Approximated cost function by the piecewise blocks Fig. 8.3: Typical price-quantity offer package of the DR aggregator Fig. 8.4: Summary of the market clearing procedure with demand response and NAS battery Fig. 8.5: Load profile before and after DR implementation

18 List of Tables: Table 2.1: FACTS devices and their applications Table 2.2: Various type of FACTS and their applications Table 3.1: Provided spining reserve by demand side resources in different markets across the U.S 56 Table 3.2: Summary of active demand response programs for providing spinning reserve in ERCOT Table 3.3: Summary of demand response programs for providing non-spinning reserve Table 3.4: Comparison of the conventional generators and demand response programs in providing ancillary services Table 3.5: Utility companies with active DLC program Table 4.1: Three contingencies in IEEE 14 bus network 76 Table 4.2: The installation cost, location and size of the SVCs Table 4.3: The comparison between active power loss before and after SVC installation Table 4.4: The comparison between voltage deviation index before and after SVC installation Table 4.5: The comparison between loadability index of transmission lines before and after SVC installation Table 4.6: Selected severe contingencies in the IEEE 30 bus system Table 4.7: The locations and sizes of the TCSC based on the optimisation outcome Table 4.8: The comparison of active-power loss before and after TCSC installation Table 4.9: The security margin comparison before and after TCSC installation Table 4.10: The ATC comparison before and after TCSC installation Table 5.1: Selected buses and the amount of DR programs 102 Table 5.2: The comparison between active-power loss before and after DR implementation Table 5.3: The comparison between EENS before and after DR implementation Table 5.4: The comparison between ATC before and after DR implementation Table 6.1: Loads in three scenarios of demand 117 Table 6.2: Load demands due to various incentives and penalties Table 6.3: The auction results for generators

19 Table 6.4: The auction results for generators and responsible demands Table 6.5: Generator increment and decrement to release the congestion Table 6.6: Generators and Responsible demands increment and decrement to release the congestion Table 7.1: Load demand with power factor Table 7.2: selected buses for Demand response implementation Table 7.3: selected buses for demand response implementation Table 7.4: Facts devices data Table 7.5: The Auction Results for Generators participated in electricity market Table 7.6: Generation increment and decrement for all generators due to congestion management (MW) Table 7.7: demand response contribution for congestion management (MW) Table 7.8: Total cost of market operation and redispatch cost in different scenarios and system states Table 8. 1: Cost function and generation limit for conventional generators in IEEE 57 bus system 146 Table 8.2: The pollution cost function for IEEE 57 bus generators Table 8.3: Cost function and generation limit for conventional generators in IEEE 30 bus Table 8.4: The pollution cost function for generators in IEEE 30 bus Table 8.5: Self and cross elasticity values Table 8.6: Demand side resources contribution for three different participation levels in IEEE 57 bus system Table 8.7: Conventional generators contribution for three different participation levels in IEEE 57 bus system Table 8.8: Demand side resources contribution for three different participation levels in IEEE 30 bus system Table 8.9: Conventional generators contribution for three different participation levels in IEEE 30 bus system Table 8.10: Total Market Cost for different demand side participation level in Table 8.11: Total Market Cost for different demand side participation level in

20 Chapter 1 Many countries around the world are introducing programs aimed at reducing the emissions produced by the power plants and increasing the utilization of renewable generation. Among different types of renewable energy technologies, wind power is expected to be one of the most popular types of renewable in the near future [1]. However, high penetration of wind power can introduce new challenges and reduce the power system security [2-7]. Some of the major challenges which arise as a result of large integration of renewable generation are summarised as follows: Lack of wind power and demand correlation Congestion in transmission lines Impacts on transient stability of the system Protection system maloperation in distribution networks Addressing these issues require considerable research on the identified problems. This thesis focuses on lack of correlation between the demand and the wind power generation as well as transmission congestion management in power systems. A comprehensive approach is proposed to address these issues by effective utilisation of 19

21 FACTS devices and demand response programs. In this research, a day ahead network constrained market clearing formulation is developed in which demand side resources can participate in the market in addition to the conventional generators. In the next step, an integrated approach using combination of FACTS and dispatchable demand response program is proposed to provide additional flexibility for system operator to maintain the system security during peak demand or major contingencies in the network. To be able to achieve this goal, potential barriers are determined and required milestones are identified. Summary of the achieved milestones are reported in the following: In the first step, different types of demand response programs and its application for the power system operation are reviewed and the summary of the literature review is presented. In the next step, various types of flexible AC transmission system devices and their applications for power system are reviewed through extensive literature review. As part of this step, the steady state model of popular FACTS devices including thyristor controlled series compensator (TCSC) and the static var compensator (SVC) are presented which used for FACTS simulation in later stages of this research. In the next step, a multi-objective algorithm is developed for optimum allocation of TCSC and SVC in the electricity network. The TCSC allocation considers four objectives including power loss reduction, investment cost minimisation, security margin improvement and available transmission capacity enhancement. Another multi-objective allocation problem is also developed for SVC allocation that considers network active-power loss, capital cost of SVCs and system voltage deviation as the main objectives for optimisation. The outcomes of the proposed algorithm can 20

22 determine the optimum location and sizes of the TCSC and SVC in the electricity network. The next stage of the thesis is dedicated to optimum allocation of demand response program. As different factors are involved for effective allocation of demand response program, a multi-objective optimisation is formulated which considers expected energy not supplied (EENS), active power loss, available transmission capacity (ATC) and total DR programs capacity as the main objectives for demand response program allocation. In addition, the demand response elasticity based model is developed by adding incentive and penalty factors to the existing mathematical model to provide additional control for the market operator to have two factors to control the capacity of responsive demands. These additional control factors can provide an opportunity for system operator to encourage demand response program participants at specific load nodes that has a considerable impact on the power system security enhancement. In the next stage, an integrated approach is developed using combination of FACTS and event-driven dispatchable demand response program to manage the congestion in the transmission lines during the peak periods or major contingencies in the network. A constrained optimisation is developed as part of this stage for effective coordination of FACTS and demand side resources. The final part of the thesis focuses on the role of demand side resources in enabling the power system for large integration of renewable energy especially the wind power generation. A day-ahead network-constrained market clearing formulation is proposed in which dispatchable demand side resources can reduce the need for ramping up/down services by conventional generators. This approach can provide a cost 21

23 effective solution for operation of power system with large amount of renewable energy and enhance the system security and reliability. The presented methods in this thesis can provide additional tool for system operator to maintain the power system security in electricity networks with large integration of renewable energy. 1.1 Objectives a) Developing a mathematical model for demand response program b) Developing a comprehensive multi-objective approach for demand response program allocation c) Determining the optimal size and location of static var compensator in the electricity network through multi-objective approach d) Determining optimal location and sizes of TCSC in the electricity network by using multi-objective optimisation e) Proposing an integrated approach for transmission congestion management through effective combination of demand response program and FACTS devices f) Proposing a comprehensive approach to mitigate the lack of correlation between power system load profile and wind power generation using demand response programs in electricity networks with high penetration of wind power generation 1.2 Outline of the thesis This thesis is organised in nine chapters. Starting with the background and scope of the research, the first chapter presents the objectives, outline and the contributions of the thesis. Chapter 2 focuses on general overview of the previously reported steady-state models for FACTS devices. In this chapter, a comprehensive review for the FACTS devices and their applications in power system operation are presented. In Chapter 3, a comprehensive overview of the demand response programs is presented and reviewed. The successful experiments of demand response programs in different 22

24 countries are also reviewed in this chapter. Chapter 2 and 3 provide a foundation for the subsequent chapters. Chapter 4 develops a multi-objective approach to find the optimal allocation of SVC and TCSC in the electricity network. This Chapter presents a comprehensive approach to find optimum locations and sizes of TCSCs (Thyristor controlled Series Compensator) and static var compensator (SVC) in the power system. The approach comprises two main parts. In the first part, a mixed continuous-discrete multi-objective optimization problem is formulated in which TCSCs locations and sizes are the variables. The second part develops an optimization method based on NSGA II (Nondominated Sorting Genetic Algorithm) to solve the problem. Non-dominated sorting genetic algorithm (NSGA II) is used for determining the optimal location of TCSCs. This is done by considering power loss reduction, investment cost minimisation, security margin improvement and available transmission capacity enhancement in the allocation objectives. A similar multi-objective approach is also used for optimum allocation of SVC with considering network active-power loss, capital cost of SVCs and system voltage deviation. In chapter 5 is developed a comprehensive solution for optimal allocation of the demand response programs in the electricity network. The outcomes of this chapter can determine the optimum amount and the location of the demand response programs in the electricity network. An approach for optimally selecting the locations of DR programs in the network together with their capacities to achieve the maximum technical benefits from the programs is proposed. The method is based on the constrained optimization of multi-objective function formed in terms of the expected energy not supplied (EENS), active power loss, available transmission capacity (ATC) and total DR programs capacity. This multi-objective function is then optimised based on a heuristic method to find the amount and locations of DR programs. The presented approach is a general one in principle and can be customised and extended to design DR programs with technical and economic objectives other than those considered in this research. Chapter 6 develops a method for transmission line congestion management using demand side approach. In the proposed method, a non-linear mathematical model for 23

25 incentive-based event-driven demand response program is used for modelling demand side resources. A coordination process between the generators, demand response participants and independent system operator is proposed to release the congestion in the electricity network. In addition, to evaluate the effectiveness of the proposed method in contingency condition, critical contingencies are identified and considered to verify the effectiveness of the proposed approach in the contingency condition. A hybrid approach is proposed in chapter 7 for transmission lines congestion management in a restructured market environment using combination of dispatchable demand response (DR) program and flexible alternating current transmission system (FACTS) devices. A two-step market clearing procedure is formulated which conventional generators and demand side resources can bid to the market. In the first step, generation companies bid to the market for maximizing their profit, and the ISO clears the market based on social welfare maximisation. Network constraints including those related to congestion management are presented in the second step of the marketclearing procedure. A re-dispatch formulation for the second step is developed using mixed integer optimisation technique in which demand responses and FACTS device controllers are optimally coordinated with conventional generators. A day-ahead network-constrained market clearing formulation is presented in chapter eight that considers a combination of conventional generators and demand side resources. The proposed approach can provide flexible load profile and reduce the need for ramp up/down services by the conventional generators. This method can potentially facilitate large penetration of renewable generation by shifting the wind power generation from the off-peak periods to the high-peak hours. The proposed approach can mitigate some of the challenges that arise because of large-scale wind power penetration into the electricity network. The overall conclusion in chapter 9 summarises the main features and advances of the research reported in this thesis. 24

26 1.3 Contributions of the thesis 1. Development of a comprehensive multi-objective approach for demand response programs allocation 2. Optimum allocation of static var compensator (SVC) in the electricity network to minimise the investment cost, voltage deviation, the active power loss and also maximising the transmission system loadability 3. Optimal allocation of TCSC in the electricity network to minimise the investment cost, the active power loss and maximise the loadability of transmission lines 4. Development of a non-linear incentive based demand response model by adding penalty and incentive factors which can potentially increase the control of the market operator on amount and availability of demand side resources 5. Proposal of an integrated approach for transmission congestion management through effective combination of demand response program and FACTS devices 6. Proposal of a comprehensive approach to mitigate the lack of correlation between power system load and wind power generation in electricity networks with high penetration of renewable energy 1.4 Publications This thesis is supported by eight publications as follows: 1- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando, An Approach for Providing Spinning Reserve using Demand Response Program, International Journal of Electrical Power and Energy Systems, 2013 (under review). 2- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando and Hieu Trinh, An Approach for Wind Power Integration Using Demand Side Resources, IEEE Transactions on Sustainable Energy, vol.4, no.4, pp.917,924, Oct Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando, Optimum Scheduling of Spinning Reserve by Integration of Demand Response Program, AJEEE: Australian Journal of Electrical & Electronics Engineering, Volume 10 Issue 2 (2013). 4- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando, Optimal locations and sizes of static var compensators using NSGA II, AJEEE: Australian Journal of Electrical & Electronics Engineering, Volume 10 Issue 3 (2013). 5- A. Yousefi, T. T. Nguyen, H. Zareipour, and O. P. Malik, "Congestion management using demand response and FACTS devices," International Journal of Electrical Power and Energy Systems, vol. 37, pp ,

27 6- T. T. Nguyen and Ashkan Yousefi, "Demand side solution for transmission congestion relief in competitive environment," International Review on Modeling and Simulations, vol. 4, pp , T. T. Nguyen and Ashkan Yousefi, "Multi-objective demand response allocation in restructured energy market," in Innovative Smart Grid Technologies (ISGT), 2011 IEEE PES, 2011, pp T. T. Nguyen and Ashkan Yousefi, "Multi-objective approach for optimal location of TCSC using NSGA II," in Power System Technology (POWERCON), 2010 International Conference on, 2010, pp

28 Chapter 2 Steady-state models of flexible AC transmission system devices Demand growth together with the requirement for providing transmission access for generation companies leads to the need for transmission system reinforcement or expansion. However, practical constraints, which arise from environmental consideration and investment decision in competitive electricity markets, can prevent, or defer the construction of new transmission lines. Consequently, the transmission system capacity would not be adequate to meet the requirements related to demand growth. With limited capacity, transmission congestion can arise, depending on the demand and /or contingency. To certain extent, FACTS devices can enhance the transmission capacity of the existing system without the need for additional transmission lines. With FACTS device installation, transmission congestion can be eliminated or mitigated [8-10]. The effectiveness of FACTS devices needs detailed evaluation based on system simulation. In the context of dispatch and congestion management in electricity market, FACTS devices are represented in terms of steady-state models in a single-phase equivalent form[11]. Although, there has been some research on representing stability constraints in dispatch calculations, using dynamic models [12, 13], the focus of the thesis is on steady-state operation. The steady-state FACTS devices models are in the 27

29 form that directly augments the steady-state power network model to a set of equations and inequalities for use in dispatch calculation together with congestion evaluation and management. This chapter reviews the FACTS devices operating principles and control objectives based on which the FACTS models are explained[14]. 2.1 Basic Mechanisms of Compensation Transmission line capacity is usually limited by some factors including thermal limit of transmission lines, power system security and system stability. These limitation factors are briefly reviewed in the following section Power system stability Power system stability is the capability of a power system, for a specific initial operating condition, to recover a state of operating equilibrium after a system disturbance and/or contingency, with most system variables bounded so that the entire system remains intact [15]. Generally, stability margin is reduced during high peak periods. Stability would be lost if the system loading exceeds its upper limit which depends mainly on the type of disturbance Power system static security The other major factor in limiting the transmission line capacity is referred to as power system static security. The power system should be managed in a way that satisfies the static security criteria, which are specified in terms of voltage limitations and maximum transmission capacity of the transmission lines in steady-state operating condition[16]. 2.2 Steady-state models of power system elements Modelling each individual components or items of plant in the system is a major milestone in power system analysis. In power system studies, different models are used for different studies. For the purpose of this thesis, the steady state model will be 28

30 discussed in more details. There are different levels for presenting power system and its components in the steady-state mode. If the focus is on system operating unbalances, then phase variable models are required in the analysis and evaluation for most of the steady-state system studies. The system voltage and current variables are represented by positive-phase sequence, and the system elements are modelled based on single-phase equivalent in positive sequence [11]. 2.3 Power system nodal formulation This model is developed on the key assumption that the network operates in steady-state mode at the supply frequency, and the voltages and the currents are represented in phasor forms. This allows the system elements to be modelled by their impedances/admitances at the supply frequency. Based on balanced operating condition, the system elements are represented by a single-phase equivalents expressed in the positive-phase sequence. The network model, which is combined with nodal operating constraints at individual load nodes and generator nodes, are converted to set of nonlinear equations. Inequality constraints are used for considering generator reactivepower limits and transformer tap position ranges. They are given in the following in a compact form. The power system nodal formulation can be explained in a compact form as per equation (2.1). f( V, θ, u) 0 (2. 1) where f is a function of V, θ and u which is explained in a vector form; System voltage magnitudes and phase angles are explained by V and θ Control variables are summarised in vector u The control variables in (2.1) are the control signals of the controlling tools such as offnominal tap position of a load-tap-changing transformer (LTC). In addition to these equality constrains, there are other inequality constrains that can be considered for power flow calculations. These inequalities constrains are summarised and presented in a short form as follows: 29

31 h( V, θ, u) 0 (2. 2) In (2.2), h is a vector function of V, θ and u. 2.4 Modelling of the FACTS devices The flexible AC transmission systems which is known as FACTS are power electronic devices are used for improving the efficiency and enhancing the controllability of the electricity network. The FACTS devices were introduced for the first time by the Electric Power Research Institute (EPRI) to improve the controllability on the power system and enhancing the dynamic response of the power system elements. The major benefits of the FACTS for power system can be summarized as increasing the control on the voltage nodes and the power flow in electricity network [14]. In addition, these power electronic devices have considerable effects on improving the dynamic responses of the power system which is not a main focus of this research. This section reviews two of the popular FACTS devices which are the static VAr compensator (SVC) and thyristor-controlled series compensator (TCSC) [11] [14] Static VAr compensator (SVC) The first SVCs were installed for compensation of large fluctuating caused by large industrial loads, such as switching of large motors in factories. Later, the SVC applications are focused on voltage improvement and increasing the control on transmission lines [17]. The SVC is made of advanced power electronic tools and used for providing shunt compensation in the network. Fig. 2.1 explains the typical SVC structure and its main components. 30

32 High-voltage bus Transformer Low-voltage bus Thyristor switched capacitors Harmonic Filter Controlled reactor Fig. 2.1: Typical SVC connection In many cases, the SVC is connected to the transmission network through coupling step-up transformer. At the low-voltage side of the transformer, three types of elements are connected, including fixed harmonic filters, thyristor switched capacitors and thyristor controlled reactor [14]. The brief review of each item is presented as follows: Thyristor controlled reactor (TCR): A schematic diagram of the single-phase TCR, including the thyristor pair and the reactor is shown in Fig XL Fig. 2.2: Thyristor controlled reactor The controlled switching of the thyristors combined with the linear reactor enables the effective supply-frequency for TCR, which is a function of the delay angle, to 31

33 change continuously from the predefined reactance value of the reactor to the value that the thyristor operates on fully non-conducting mode [11, 14]. The effective value of the TCR is shown in equation (2.3): where π X tcr ( ) X L (2. 3) π sin2 α is the delay angle which is calculated based on the applied voltage to the TCR, and can varies from π 0 2 ; Xtcr is the effective reactance of the thyristor controlled reactor at the nominal frequency; XL is the reactance of the reactor at the nominal frequency Thyristor switched capacitors (TSCs): TSC has the ability to provide inductive and capacitive output for the network Fixed harmonic filters: The filters can provide low-impedance paths and capacitive compensation for harmonic currents generated from the TCR. Variation of the thyristor firing angle α yield to the TCR reactance change that eventually changes the effective reactance of the SVC. In other words, the SVC can change from the capacitive mode to the reactive one by changing the firing angle. Schematic diagram of an SVC is shown in Fig The SVC generally considered as a device that can provide a capacitive or inductive mode by either generating or absorbing the reactive power. 32

34 Transmission line XL C Fig. 2.3: Typical VAr compensator Generally, the SVC is not connected directly to the transmission lines and a coupling transformer is required for connecting an SVC to the high voltage level. Fig 2.4 demonstrates an SVC connection to the high voltage line. Vhsvc High voltage line Isvc Coupling transformer Vlsvc SVC Fig. 2.4: SVC schematic diagram V-I characteristic of the steady-state operational mode of the SVC is shown in Fig A steady-state model for the SVC should be able to reproduce the above characteristic. 33

35 Fig. 2.5: V-I characteristic of the SVC Based on this explanation the voltage magnitude at the high-voltage side can be explained as per equation (2.4): Vhsvc Vsvcref asvci svc (2. 4) where Vhsvc and Vsvcref are high-voltage node and the reference value for the SVC respectively; asvc is the SVC slope reactance Isvc is the SVC current The SVC current phasor can be considered as possible reactive power contribution by ignoring the active-power loss of the SVC. If the current lags the voltage by 90, the SVC operates in inductive mode. The SVC runs in a capacitive mode when the voltage and the current angle is 90 lead. Based on V-I characteristics in Fig. 2.5, It can be seen that the operating constraints of the SVC depends on its susceptance. The SVC susceptance is explained in equation (2.5). B I svc svc (2. 5) Vhsvc 34

36 Based on V-I characteristics of Fig. 2.5, the SVC operating constraints can also be explained based on its susceptance as per equation (2.6). B svc min Bsvc Bsvcmax (2. 6) where Bsvcmax and Bscvmin are the maximum and minimum susceptance of the SVC, respectively. The control ability of the SVC is valid just between these operating limits [14] Thyristor controlled series compensator (TCSC) The other FACTS device that is used for improving the power system efficiency is thyristor controlled series compensator. The TCSC is connected in series to the transmission lines and it has a crutial role in improving the loadability of the transmission line. TCSC can have a significant contribution for power system stability improvement and have a noticeable effect on enhancing the power transfer capability. Fig. 2.6 demonstrates a typical TCSC [14, 18]: MOV XC XL Fig. 2.6: Schematic diagram of the TCSC TCSC can be modelled by capacitors connected in series with a transmission line. TCSC is able to reduce the transmission line impedance and facilitate the transfer of additional power via the existing transmission lines. In addition, TCSC is able to enhance the loadability of the transmission lines and improve the voltage profile. In other words, TCSC can be used as an effective tool to enhance the security of the power system. The main elements of the TCSC are a series capacitor that is connected in parallel with a TCR. In addition to these a metal-oxide varistor (MOV) is connected in parallel with the series capacitor play a role of protection. In Fig. 2.6, the reactance of the series capacitor and the reactor of the TCR are denoted by XC and XL, respectively. 35

37 Basically, TCSC has three operation modes which can be useful in different operational condition [19]: Bypassed-thyristor mode: In this mode, the TCSC acts as a combination of parallel capacitor and reactor. The net reactance of the TCSC can be calculated by X bypass which is explained in equation (2.7). X bypass XLXC X X L C (2. 7) If the TCSC is operated in the inductive mode, the XL value can varies in the following range: 0 XL XC (2. 8) Blocked-thyristor mode: The TCSC is controlled to block the current through TCR branch, and acts as a fixedseries capacitor Partially conducting thyristor mode: In this mode which is the most controllable mode in comparison to other modes, the firing angles of the TCSC can vary in a range to shift the TCSC from the capacitive mode to the inductive mode or vice versa. In the partially conducting thyristor mode, the effective reactance of the TCSC is calculated based on parallel circuit consisting of a fixed capacitive reactance, XC, and a variable inductive reactance, Xtcr(α) [14]. The effective reactance of the TCSC can be calculated as per equation (2.9): X X X ( ) ( C tcr t csc ) (2. 9) X tcr ( ) X C Fig. 2.7 demonstrates the correlation between effective reactance and the firing angle of the TCSC. In Fig. 2.7, δ Lmax and δ Cmax are the delay angle limits in the inductive and capacitive areas. The delay angle between δ Lmax to δ Cmax is not permitted, and XLmax 36

38 and XCmax are maximum limits of the inductive and capacitive reactance modes of the TCSC. Xtcsc Inductive area 0 L max XLmax Operation inhibited L max C max Xbypas 0 L max C max π/2 XC Xcmax Capacitive area C max / 2 Fig. 2.7: The reactance versus delta angle characteristic of the TCSC The other constraint on the operation of a TCSC is imposed by MOV, which limits the TCSC operation in the inductive zone. 37

39 (Inductive area) (Capacitive area) Voltage 0 Maximum firing Firing limitation (delay) MOV protection level Harmonic limitation Full Thyristor conduction Maximum thyristor current Current Fig. 2.8: Typical V-I characteristics for a single-module TCSC Continuous operation Transient operation in long-term Transient operation in short-term Fig. 2.8 [14, 20, 21] shows a V-I characteristics of the typical TCSC. This characteristic is derived based on different constrains in TCSC operation such as thyristor delay angle and voltage limits. Fig. 2.9 shows the operational constraints of the TCSC in terms of the relationship between reactance and lines current [20]. As it is shown, the voltage compensation can be achieved because of changes in compensating impedance. The TCSC limitation is dynamic, and it varies based on reactance boundaries as shown in Fig It is necessary to note that reactance boundaries are not fixed values and could be change based on transmission line currents [14, 22]. 38

40 The other limitation in the operation of the TCSC is a gap in the control range between block reactance and the bypass reactance that are denoted by XC and Xbypass respectively. Capacitive area Reactance 1 Inductive area X 0 bypass X C 0 Imax current Fig. 2.9: The correlation between TCSC reactance and line current One of the alternatives to bypass this gap is to split the TCSC operation into multiple sections which each of which section can simulate the TCSC for both inductive and capacitive modes [23]. Figs.2.10 shows the V-I characteristics of the typical TCSC. Fig shows the reactance versus the line current for the operation of the TCSC. As it can be seen, the operational boundary of the TCSC can be limited if the current increases in the transmission lines. The dependency of operational range of TCSC to the transmission line currents is demonstrated in Fig

41 Inductive area Capacitive area Voltage 0 Current Fig. 2.10: Typical V-I capability characteristics for TCSC with two modules Both TCSC modules operate in a capacitive region One TCSC module operates in a capacitive region, the other one in an inductive region Both TCSC modules operate in an inductive region Capacitive area Inductive area Reactance 0 Imax Current Fig. 2.11: Typical X-I capability characteristics for a typical TCSC with two modules Both TCSC modules operate in a capacitive region One TCSC module operates in a capacitive region, the other in an inductive region Both TCSC modules operate in an inductive region 40

42 As it is shown, the transition between the capacitive and inductive zone can be smoother by increasing the number of modules [11, 14, 24]. The following table summarises and compares different FACTS devices and the general applications of each type. Table 2.1: FACTS devices and their applications Type of FACTS Static VAr Compensator (SVC) Thyristor-controlled series compensator (TCSC) Unified Power flow Controller (UPFC) Features Reactive power compensation, Voltage control Power control, voltage control, series impedance control, transient stability Power control, voltage control, reactive power compensation, transient stability In the next section, application of each type of FACTS devices and practical experiments in using FACTS devices and practical experiments at restructured electricity network are presented and discussed [25]. 2.5 Applications of FACTS devices in power system FACTS devices are generally divided into two broad groups from controlling the active power transfer capability of the transmission lines. First group of FACTS as presented in Fig 2.12 can be used for voltage control such as SVC, static synchronous compensator (STATCOM), Unified Power Flow Controller (UPFC) and Thyristor Controlled voltage regulator (TCVR). The second group of FACTS as presented in Fig 2.13 can be used for controlling line reactance and angle such as TCSC, static synchronous series compensator (SSSC), UPFC, Thyristor controlled phase angle reactor (TCPAR) and Thyristor Controlled Phase Shifting Transformer (TCPST). 41

43 Fig. 2.12: Effective FACTS devices for voltage control Fig. 2.13: Effective FACTS devices for reactance and angle 42

44 Table 2.2 summarise the main application of various FACTS devices in the electricity network. This table also categorises FACTS devices based on major impacts of each group on power system. Principle Series compensation Shunt compensation Load flow control Table 2.2: Various type of FACTS and their applications Type of FACTS Devices FSC (fixed series compensator) TPSC (Thyristor protected series compensator) TCSC (Thyristor controlled series compensator) SVC (Static var compensator) STATCOM (Static synchronous compensator) UPFC (Unified Power flow controller) Major effects on the power Load flow system stability Power quality The role of FACTS for congestion management As mentioned in previous sections, the congestion is one of the major problems for both vertically integrated and deregulated power systems. In vertically integrated systems the duration, place and type of congestion were determined before generator dispatch. However, in the electricity market, the congestion problem is more complicated and many uncertainties might affect the congestion problem in the system. The congestion in the restructured environments has serious impacts on the electricity market performance such as [26-29]: Preventing new contracts in the market Market Power in some parts of the network 43

45 Load shedding The majority of the researches related to FACTS devices for congestion management. Some of the research focused on operation cost minimisation using FACTS devices. In [30-43], the FACTS device allocation and its effects for minimising the cost of operation is considered. The main aims of these researches are cost minimisation by improving the available transmission capacity and congestion relief. The major differences of these researches can be summarised into four different areas: Different kind of markets (pool, bilateral and hybrid) Different type of FACTS devices Different optimisation methods In [44-50] the available transmission capacity (ATC) maximisation is considered. In [10], the FACTS devices are used for congestion management and also the cost allocation of each market participant for providing the capital cost of FACTS devices are considered. Most of the papers in congestion management section consider the thermal limits of the transmission lines and the role of FACTS for improving the load ability of transmission system. However, in [51] the voltage profile and the transmission line load ability enhancement considered simultaneously. In [52], the location marginal price minimisation is considered as an objective function for congestion management. In [53-55] the congestion management is considered and the number and size of the FACTS devices are optimised to satisfy the proposed object. In [56], the effect of FACTS devices in minimising the cost of locational marginal price is presented. In [57], the economic studies for European electricity network are implemented to analyse the effects of FACTS devices for transmission line enhancement. The results of these studies confirm that FACTS devices can be a feasible solution for congestion management in midterm. 44

46 Chapter 3 program Demand response The aim of this chapter is to introduce demand response (DR) programs and have a brief overview on each time-based and incentive-based programs. This chapter covers the following topics: Definition of demand response program Different types of demand management programs The role of DR in power system operation The role of demand response in electricity market 3.1 Definition of demand response program Demand response program is defined as changes in electricity consumers demand in response to price signals or incentives, which are offered by utilities or market operators [58]. In some electricity markets, DR programs are defined as changes in electricity consumption by retail customers from their normal load in response to electricity price 45

47 change, or to incentive payments. These programs are designed to reduce lower electricity usage at times of high wholesale market price or to maintain the power system security and reliability[59]. 3.2 Benefits of DR programs The main advantages of DR programs are those of optimising the utilisation of the existing power network and deferring / avoiding network expansion, and this goal can be achieved if the customers [60] : a) Reduce the electricity consumption during high price periods and participate in demand management programs b) Invest in advanced energy-efficient tools to reduce their consumption In addition, demand response has influence on pricing interactions between customers and suppliers in connecting the retail and wholesale markets in the deregulated market environment. Policy makers in most of the major electricity markets in the U.S modifying the rules to allow large electricity consumers to participate in the wholesale electricity market[61]. 3.3 Demand response in electricity market In the fully developed electricity market, both supply and demand sides have an active role in the wholesale and retail electricity market. In the current wholesale market, demand side does not have a considerable role, and market operators try to develop new rules to increase demand-side participation and deploy these market based tools to improve the economical and technical performance of the electricity market [62]. The result of study by Federal Energy Regulatory Commission (FERC) showed that shifting 46

48 five to eight percent of electricity demand to off-peak hours in the U.S. could save up to $15 billion a year [58]. The result of research by the federal energy regulatory commission confirmed that 3-5 percent of annual U.S. peak load can be reduced through implementation of demand response program and this reduction could potentially leads to significant improvement in market efficiency [63]. Another study conducted by the New England independent system operator showed that there are two ways to respond to the escalating electricity demand. The first is to reduce demand, and the second is to develop new supply sources. As a result of complex environmental policies, the electricity sector cannot significantly expand the conventional generators and increase the transmission capacity by adding new infrastructure. Therefore, many utilities and market operators focus on the first option to postpone constructing new power plants and transmission lines. 3.4 Different types of demand management programs Basically, DR programs are classified into two broad sections which are: a) Incentive-based demand response programs: Incentive-based demand response programs are categorised into different subsections including: Direct load control Demand bidding Emergency demand response programs Capacity market programs 47

49 Ancillary-services market programs b) Time-based demand response programs: Time-of-use Critical-peak pricing Real-time pricing Incentive-based demand response programs are structured to lower the electricity consumption during system peak load periods or system emergency cases such as contingencies. Customers who participate in incentive-based demand response programs receive reduced electricity tariff or separate incentives for load reduction or shifting their demand. The incentive-based programs can be triggered for either reliability or economic reasons [59, 64]. The second category of demand response program is focused on time-based programs. Different types of time-based rates are currently in operation all over the world. Timebased programs are designed to reduce the system load in peak hours and transferring the electricity consumption from the peak periods to the off-peak hours. The brief review of each sub-group can be found in the following section Incentive-based demand response programs These programs do not rely on natural responses of customers to price change, which are not easy to predict. Incentive-based demand response programs can provide an effective tool for electric utilities and/or market operators to enhance reliability and improve the electricity market efficiency. The incentive-based demand response programs are briefly reviewed in the following section. 48

50 Direct load control (DLC) Direct load control (DLC) is a well-known program in various electricity markets in which a system operator is able to shut down customer s electrical equipment in a short notice. DLC program is typically triggered during or after contingency in the electricity network. DLC has been in operation for at least a decade in different electricity systems around the world and its effectiveness on improving the power system operation is proven in various electricity markets [58] [65] Interruptible/Curtailable (I/C) Participated electricity customers in interruptible/curtailable service rates receive a discounted rate or credit to reduce their load during system contingencies. If customers do not curtail, they can be penalised. It is necessary to note that I/C program is different from emergency demand response program and capacity program. These programs are offered by utility company and load serving entity to apply the load reduction when necessary and participated customers must comply with utility company request [58] Emergency demand response program (EDRP) Participants in emergency demand response program is developed as a market based tool. Emergency demand response program receive credit for demand reduction during contingencies or high peak periods. In this program participants are not penalised for not responding to the market operator invoke for load reduction [59]. New York independent system operator introduced an emergency demand response program to provide flexibility for system operator in emergency situations [66]. 49

51 Capacity market program (CAP) In capacity-market program, participants sign a contract to provide pre-specified load reductions in emergency cases, and if they do not respond to the request, they have to pay the predefined penalty. Capacity market program is considered as an insurance for power system. Participants in capacity market program have to provide the required facilities to confirm that the claimed reduction is achievable for at least four hours[67]. Capacity market program has been successfully in operation in New York since 2002 and played an effective role in electricity network restoration after the August 14, 2003, blackout. The other successful example of this category is implemented in ISO New England and had considerable effect on preventing blackout in the U.S southwest connection during the summer 2005 [58] Demand bidding program (DB) Demand bidding program encourages large electricity customers to reduce their load at the prespecified amount that they offered to the market. These programs enabled the system operator to control the electricity price during emergency cases. If customer bids are accepted, the offered capacity will be dispatched, and the participants shall reduce their load to the prespecified amount. DB program is an attractive option for customers because they have the opportunity to receive higher payments for load reduction during high electricity market price [68] Ancillary service program (AS) The last category of incentive-based demand response is ancillary-service program. Ancillary service programs allow customers to participate in operating reserve market to 50

52 provide their available capacity for the spinning reserve market. If their bids are accepted, participants receive the market clearing price to provide standby capacity for the system operator. If the load reduction is requested by the market operator the additional credit which is equals to the spot electricity market price will be paid to the AS provider. The participants in this program shall be equipped with on line communication channels to connect to the control centre to adjust their load in emergency condition such as rapid load change or major contingency in the network. The typical loads which are able to participate in AS program are large industrial processes loads that can reduce their loads quickly without any stress on equipment. California Independent System Operator (CAISO) and Electric Reliability Council of Texas (ERCOT) are the leaders in implementing ancillary services program. One example for ancillary service participant in CAISO market is large water pumps operated by California Department of Water Resources. Another example from ancillary services category that is already in operation is Loads Acting as a Resource (LaaR) program. The minimum requirements for LaaR program participants are the load monitoring system and real-time control facilities [67, 69] Time-based programs The second major group of demand response programs are dedicated to the time-based programs. After electricity industry restructuring, market operators developed programs to promote active participation of electricity customers in the electricity market. Time-based programs can connect and link the wholesale and retail market. In fact, these programs can reflect the variation of electricity price change in wholesale market. Three major time based programs are time-of-use (TOU), critical peak pricing (CPP) 51

53 and real-time pricing (RTP). Brief review of these programs are presented in the following section [70] Time-of-use rates Time-of-use (TOU) program was initially designed for residential customers. Significant number of customers in the U.S adopted some types of TOU rates in various electricity markets. TOU rates and intervals varies based on the time of the year and geographic locations [71] Critical peak pricing Critical peak pricing (CPP) is a program that is designed to trigger load reduction during system contingencies or very high electricity price. The load reduction for participants in CPP are triggered in a limited number of days [72] Real-time pricing (RTP) This program is able to reflect the electricity price variations in the wholesale electricity market to the retail customers. The first real time pricing program was introduced in California to improve the reliability of the power system. According to the study conducted by the national grid in the U.S, more than 70 utilities in North America offer RTP on either a pilot or approved programs [58, 73]. DR programs are divided into two main categories and different subsections, which are presented in Fig

54 Time of Use (TOU) Time - based programs Real Time Pricing (RTP) Critical Peak Pricing(CPP) Demad Response (DR) programs Direct Load Control (DLC) Interruptible/Curtailable (I/C) Services Demand Bidding /Buy Back (DB) Incentive - based programs Emergency Demand Response Program (EDRP) Capacity Market Program (CAP) Ancillary Service (A/S) Markets Fig. 3.1: Time-based and Incentive-based Demand Response Programs 53

55 3.5 Applications of demand response programs for power system planning and operation In the strategic plan of the International Energy Agency (IEA) for , demand side activities are considered as the preferred option in all energy policy decisions, because of its potential benefits including enhancing the power system reliability, security and emission reduction [74]. Demand response program can have significant role for power system operation and need to be considered as an effective tool in power system planning. Prior to electricity industry deregulation, most regions in the United States designed generation and transmission expansion plans solely based on conventional resources. However, deregulation in electricity industry during 1990s in most parts of the U.S such as California and the state of New York encouraged the policy makers to choose integrated resource planning to use variety of resources including demand response programs[75, 76]. The NYISO (New York Independent System Operator) has introduced the SCR (Special Case Resources) program and utilize it during reserve shortage cases [66]. The PJM interconnection developed the day-ahead scheduling reserve (DASR) market and is intended to provide incentives for demand resources to provide day-ahead scheduling reserves [77]. The Electric Reliability Council of Texas (ERCOT) introduced the load acting as a resource (LAAR) program, which allows customers who satisfy certain performance requirements to provide operating reserve [69]. The ISO New England started the real-time DR program in 2005, which requires customers to commit mandatory load reductions on a predefined triggers from the ISO [63]. 54

56 3.5.1 The role of DR programs for transmission line planning Demand response programs have a significant potential to defer installation of new transmission lines to increase the available transmission capacity during peak periods. The significant positive impacts of demand response programs in increasing the available transmission capacity and congestion management in the transmission lines are addressed in the literature [60, 78-82] The role of DR for providing ancillary services Demand response programs also have significant potential to provide ancillary services such as spinning reserve for the electricity network. Participants in this program have to be able to reduce their load in emergency cases and be equipped with specific communication and control facilities to interrupt the load. It is essential to note that, providing local spinning reserve that is distributed in the electricity network can enhance the reliability level of the power system. Table 3.1 summarise some of the major ancillary services that is provided by demand response program in electricity markets across the U.S. 55

57 Table 3.1: Provided spining reserve by demand side resources in different markets across the U.S [58] Non- Non- Market Non- Regulation Spinning Spinning Spinning Name Spinning Long Term Replacement ISO-NE N/A N/A DR active DR active N/A NYISO N/A DR active DR active DR active N/A PJM DR active DR active DR active N/A N/A MISO N/A N/A N/A DR active N/A ERCOT N/A DR active DR active DR active DR active CAISO N/A DR active DR active DR active N/A As it is shown in Table 3.1, demand response program has permitted to participate in non-spinning and slower reserve services in most markets. 3.6 Review of demand response programs in electricity markets In recent years, technology development in control, communications, and metering result in considerable expansion in demand response programs in various electricity markets in the U.S. and other countries. This section reviews some of the implemented DR programs in major electricity markets around the world [58] Electric Reliability Council of Texas Electric Reliability Council of Texas (ERCOT) responsible to increase the reliability of electricity network in the state of Texas. ERCOT was established in 2001 based on combining 10 control areas into one single control area. In ERCOT, DR programs are allowed to provide spinning reserve and non-spinning reserve services. According to the 56

58 statistics, ERCOT is integrated 1100 MW of demand side resources for providing the spinning reserve in the market. This approach helped the market operator to prevent the blackout in Table summarises active demand response programs in ERCOT [58, 69]. Table 3.2: Summary of active demand response programs for providing spinning reserve in ERCOT Program type Provided services The minimum requirements Voluntary load response Curtailment or reduction in response to Market Price Metering and/or curtailment technology. Load Acting as a Resource (LaaR) ERCOT Ancillary Services (AS) Advance metering Curtailment technology. Table 3.3: Summary of demand response programs for providing non-spinning reserve Type of Service Metering Participants benefits Response time Telemetry Market clearing price in Non-Spinning & non-spinning reserve Reserve advanced market and energy when Within 30 minutes metering invoked Telemetry Market clearing price in Replacement & Negotiable with replacement market and Reserve advanced Market operator energy when invoked metering Negotiable Voluntary Load with Negotiable with Market-clearing price Response Market Market operator operator 57

59 Table 3.4: Comparison of the conventional generators and demand response programs in providing ancillary services Type of Service Regulation Down Regulation Up Spinning Reserve Nonspinning Reserve Replacement Generation Resources Load with response capability within 10 minutes Active Active Active Active Active N/A N/A Active Active Active California ISO (CAISO) The California market operator has one of the most advanced demand response programs, and it is one of the leading independent system operators to promote demand side participation. In CAISO electricity market, demand response programs varies from residential air conditioning systems to large water pumps with 80,000 horsepower. The California market operator strategic plan aims to reduce five percent of power system peak by the use of demand side resources[67] PJM Interconnection PJM Interconnection is one of the major market operators in the U.S and provides electricity to approximately 51 million people in 13 states. The PJM has a peak demand of 135,000 MW, which equals to approximately 16 percent of the total US/Canadian 58

60 demand. PJM market has a comprehensive program to enhance the reliability of transmission system by providing distributed spinning reserve and other reliability services using demand response program [77] New York ISO (NYISO) NYISO is responsible to monitor the reliability level of electricity network and manages 10,775 miles of transmission system in the state of New York. NYISO has initiated a program to enhance the reliability of the electricity network by integrating demand side resources. The NYISO deployed 1,750 MW of demand side resources to provide spinning reserve for the electricity network [83]. 3.7 Summary of the demand response program in the U.S. electricity market The result of the study by Federal Energy Regulatory Commission (FERC) summarised the active DR programs in various electricity markets in the U.S [58]. Table 3.5 summarise the direct load control participants in industrial level in the U.S electricity market. 59

61 Table 3.5: Utility companies with active DLC program Name of Utility Number of participants in DLC Florida Power and Light Progress Energy Florida Detroid Edison Baltimore Gas and Electric Northern State Power Duke Power Southern California Edison Public Service Electric & Gas Dairyland Power Cooperative Sacramento Municipal Utility District As it is shown in Table 3.5, the Florida Power and Light Company has the highest number of customers enrolled in DLC program in comparison with other utilities based on the study results by federal energy regulatory commission [84]. 60

62 Chapter 4 Multi-objective approach for optimal allocation of FACTS devices This chapter focuses on finding an optimal location and sizes of FACTS devices. The proposed approach is applied to two types of FACTS devices including SVC and TCSC. In the first part, SVC allocation is considered, and in the next step the optimal location of TCSC is investigated and discussed. As part of the FACTS device allocation, a comprehensive literature review is conducted and in the next step, the multi-objective problem is formulated. Later, an optimisation technique is applied to the developed multi-objective FACTS device allocation to determine the optimum amount and the number of FACTS devices. The proposed method is verified using standard IEEE networks. 61

63 4.1 FACTS allocation overview With the worldwide restructuring and deregulation of power systems, sufficient transmission capacity and reliable operation have become more valuable for both system planners and operators. Building new transmission circuits to enhance the transmission capacity of a network is very expensive, time consuming and many constraints have to be satisfied for new transmission lines development. As a result, there is a significantly increased potential for the application of FACTS devices due to their flexibility and relatively lower costs in power system security enhancement. It has been generally acknowledged that the effectiveness of FACTS in providing voltage and reactive power flow control functions depend importantly on their locations and ratings. The problem of determining the optimal locations and sizes of FACTS is a nonlinear and complex problem [85]. To identify the buses at which FACTS should be located is a combinatorial problem with discrete variables. There are several methods to find optimal locations of FACTS devices in both vertically integrated and unbundled power systems. There have been various optimisation methods previously proposed to solve the FACTs device allocation problem where only a limited number of objectives is included [86]. In general, optimal FACTS device allocation problem is to determine the optimal sizes and locations of new FACTS devices in order to optimise a set of objective functions subject to a range of operating constraints. According to the characteristics of FACTS devices, various criteria have been considered in allocation problem. Some of the reported objectives are: long term voltage stability enhancement [87, 88], network loadability enhancement [89], loss reduction, voltage profile improvement [90], and overall system cost minimisation. Each of the above mentioned objectives improves power system network operation. 62

64 However, improvement in one objective does not guarantee the same improvement in the others. For instance, satisfying the voltage magnitude constraint might not meet the power flow security constraints. Therefore, none of the mentioned technical objectives can be neglected in FACTS device allocation. On the other hand, allocation of the FACTS devices based on one or more technical objectives without considering the economic objective expressed in terms of cost of FACTS devices are not a practical one. Consequently, both technical and economic objectives should be represented in formulating the FACTS device allocation problem. In previous efforts, to achieve the mentioned goals, some simplifications have been made. In [91], a multi-objective genetic algorithm (MOGA) approach has been implemented for FACTS device allocation, in which only two objectives have been considered for optimisation including line overload and voltage violation, and these objectives have been combined to form a single objective function. A key problem in multi-objective function optimisation is to select the optimal solution that is non-inferior one often referred to as Pareto optimal solution. There have been proposed optimisation procedures based on GA by which Pareto optimal solution is obtained. In [91], a genetic algorithm referred to as NSGA (nondominated sorting genetic algorithm) was proposed in which a new selection operator was developed, and chooses only non-inferior solutions in the search. Subsequent development led to its improvement [91]. The NSGA II, which has better algorithm for ranking incomparison with NSGA, is used for solving a multi-objective optimization problem to find the locations and sizing of 63

65 FACTS. The objective functions to be optimised in this problem formulation are network active-power loss, capital cost of FACTS, voltage deviation and loadability. These objective functions are to be optimised subject to sets of equality and inequality constraints, which include the power flow equations and operating limits. The solution to the multi-objective constrained optimisation problem determines the optimal locations, and sizing of the SVCs. In the following section, the mathematical concept of multi-objective allocation of SVC is discussed. Four groups of objective functions are considered in this research. 4.2 Problem formulation Cost In general, the cost of each SVC can be expressed in terms of a nonlinear function of its reactive-power rating. If the cost of the ith SVC is denoted by f i (q i ) where q i is the reactive power rating of the SVC, then the total cost function to be minimised is: T 1 i1 g (4. 1) f i ( q i ) where T is the number of SVCs. For example, a cost function of an SVC in a quadratic form which can be expressed as follows[92]: where a, b and c are constants. 2 f ( q ) aq bq c (4. 2) i i i i Loadability index The severity of the system loading under normal and contingency cases can be described by a line power flow index as follows: 64

66 g k L f k ( s ) 2 2 i i 1 where g k 2 is the index indicating violation of line flow limits, and f ( s ) k 2 i (4. 3) is a function defined as follows[93]: 1; if s k max i s i f k 2 (s i ) = { exp (λ 1- s i k s max ) ; if s k max i > s i i (4. 4) where s i is the total power flow in transmission line i ; s max i the maximum limit for the line i, and λ is a small positive constant. Superscript (k) indicates operating condition including normal condition and contingencies. The notation L in (4.3) is the total number of transmission lines Voltage deviation index To have a good voltage performance, the voltage deviation from each load bus must be made as small as possible. The voltage deviation index to be minimised can be expressed as follows: k k 2 V N k 3 n Vrefn n1 g (4. 5) where V k k n is the voltage magnitude at load bus n in operating condition k and V refn the nominal or reference voltage at bus n. N is the number of buses in the transmission is network and n is the node identifier, i.e. n 1,..., N Active power losses Minimising the active-power loss is equivalent to minimising the slack node activepower. Active-power at the slack node,p sl, is expressed as : 65

67 * g4 Psl Re Vsl Ysl, i Vi (4. 6) i where Y sl,i is the element (sl, i) of the nodal admittance matrix of the power system. It is noted that the active-power loss minimisation is considered only for the base case Equality constraints Equality constraints consist of power flow equations applied for individual power network nodes, which is written in a compact form as follows: E k k k k V,θ, u 0 (4. 7) where k E is a vector function; V k and θ k are the vectors of system voltage magnitudes and phase angles, and u k is the vector of control variables in operating condition k such as generator excitation control and SVC reference signals. An example for active-power equation at a load node is given in the following: * k k k sp ReVi Yi,j.Vj Pi 0 (4. 8) j where V k i is the nodal voltage at node i in operating condition k. Y k i,j is element (i, j) of the network nodal admittance matrix in operating condition k. P i SP is the specified active-power load demand at node i. In addition to above equality constraints, the optimisation is subject to inequality constraints that are described as follows Inequality constraints In general, the inequality constraints can be written in the compact form: h k ( V k, θ k, u k ) 0 (4. 9) 66

68 where h k is in general a nonlinear vector function relating to operating conditions such as power flow constraints, generator reactive power and controllers limits: An example for inequality constraint is that of voltage magnitude constraint: V k i k V 0 (4. 10) i max where V k k i and V i max are voltage magnitude at node i and its maximum allowable value in operating condition k respectively. 4.3 Multi-objective optimisation Many real-world problems involve simultaneous optimisation of several objective functions. Generally, these functions are non-commensurable, and often represent conflicting objectives. Multi-objective optimisation with such conflicting objective functions gives rise to a set of optimal solutions, instead of one optimal solution. The reason for the multiple optimal solutions is that no one can be considered better than any other with respect to all objective functions. One of the optimal solutions is known as the Pareto-optimal solution. The definition of Pareto optimal or Pareto nondominated solution is explained through an example in the following: A multi-objective optimisation problem is stated as per equation (4.11). Minimise F(x) = (f 1 (x),, f m (x)) (4. 11) Subject to a set of equality and/or inequality constraints In a multi-objective minimisation problem, a feasible solution denoted by vector X is said to be non-dominated if and only if, for any other vector denoted by Y, every single objective function value determined by vector X is less than or at most equal to that determined by vector Y, and at least one of the objective functions determined by vector X is less than the corresponding objective function determined by vector Y. A Pareto- 67

69 optimal solution cannot be improved with respect to any objective without worsening at least one other objective. In this research, the NSGA-II [94], which incorporates the concept of Pareto optimality into its search algorithms,and can find optimal trade-offs among the multiple conflicting objectives simultaneously, has been implemented and applied to solve the FACTS device allocation problem. 4.4 Implementation of NSGA-II method The basic idea of the NSGA II algorithm is to subdivide the population in each generation into a number of subsets referred to as fronts, which are ranked in terms of levels. Each level consists of some members, and based on ranking method, the whole population is divided to various levels. For each front, there is one non-dominated solution, which satisfies Pareto optimality condition. In this way, for the entire population, there is a set of non-dominated solutions derived from the individual fronts. In the second generation starting from the initial population, these ranked fronts are then reproduced through crossover and mutation operators. Individual elements in the fronts with a high level in the ranking have a high probability of being selected for reproduction. The solutions in the first level front are assigned the highest priority, and then those in the second level and so forth. The crossover and mutation procedures are the same as those used in GA. Fig. 4.1 shows the procedure of one NSGA II iteration. In the first step the population is divided into two sections and after first iteration the off springs are ranked into various groups, first three fronts in the ranking are selected, and the algorithm is continued up to satisfaction of stoping criteria. 68

70 Fig. 4.1: NSGA II procedure Initial population The multi-objective optimisation with NSGA II algorithm in common with the variables of the optimisation problem to be coded as a string of binary digits of finite length. The variables representing the SVCs locations and sizing are grouped into a string with the structure shown in Fig The first part of the structure is for the coding of the SVCs locations. Each gene in this part is associated with a node in the power system. The gene value of 1 means that the node has an SVC, and the gene value of 0 corresponds to the node having no SVC. The number of nodes determines the length of the first part in the power system. The second part of the structure comprises a number of blocks of binary numbers. Each block is associated with a node in the power system that represents the reactive-power rating of the SVC connected to the node. The number of blocks in the second part is the number of nodes in the power system. The length in each block is determined by the maximum power rating and accuracy required. Fig. 4.2 shows a power system and a sample string for SVC locations and sizing. 69

71 Fig. 4.2: Representation of a power system and the sample string for SVC locations and sizes Fitness evaluation The fronts are formed from the current population using an iterative process described in the following. In forming the first front, the entire population is considered from which the first non-dominated solution is identified. The second member of the first front is then selected from the reduced population in which the first non-dominated solution is excluded. The second member is the non-dominated solution belonging to the reduced population. The process is repeated for a finite number (based on the size of the case study) of times to form level-1 front. The same procedure is then applied to form level-2 front from the remaining population where level-1 front individuals are excluded. Successive fronts with lower ranks are constructed iteratively. 70

72 Individual fronts are assigned fitness values accordingly to their levels. Level-1 front has the largest fitness value. Lower fronts are then assigned smaller fitness values. Having formed the fronts together with their fitness values, it is required to assign fitness value for each member of each front. The requirement in this fitness value assignment is to maintain diversity. This means that the fitness value distribution over the individuals in each front is a non-uniform one. Various schemes can be designed to form the distribution of fitness values. For example, the present research implements a scheme based on a clustering algorithm which will assign low fitness values to the individuals in close proximity to one another as measured by the norms of the differences between the vectors representing these individuals[91]. The assignment of fitness values for the individuals in each front also takes account of the fitness value of the front so that the lowest fitness value of an individual in a front will still be greater than that of another individual in a front with a lower rank Iterative process The population is reproduced according to the fitness values. Since individuals in the first front have the highest fitness values, they always get more copies than the rest of the population. The efficiency of NSGA lies in the way by which a mapping from objective function values to fitness values of individuals in a population is achieved using the Pareto optimal criteria. In principle, the method can be applied to any number of objective functions encountered in a constrained optimisation problem. The flow chart of the proposed algorithm is shown in Fig Either reaching the maximum number of allowed iterations or finding no other new non-dominated solution in a predefined number of successive iterations has been considered as the termination criterion. The key aspect in the flowchart of Fig.4.3 is the application of the OPF 71

73 (optimal power flow) for evaluation of individual objective functions, which are essential to the NSGA II procedure. The input to the OPF in terms of SVCs sizes and locations are those given in each possible solution vector in individual iteration. Outputs of this step will be used to rank possible solutions in different fronts. Then, a new population will be reproduced from the individuals with fitness values above a specified threshold. Finally, a max-min approach is used to determine the best compromising solution Selection of final solution The final solution will be one of the vectors in the front with level 1 in the population of the last generation. An obvious choice for the final solution is that which satisfies the Pareto optimality condition. However, the system planners can have the flexibility of selecting a solution in level-1 front, which deviates from the Pareto optimality condition in meeting their practical planning requirements and conditions. The system planners can formulate criteria based on which the most suitable solution is selected. In this research, a min-max approach is used to select the suitable locations and sizes of SVCs. Each possible solution in the front with level 1 has an associated vector of values of objective functions that can be normalised using the following expressions[93]: G 1 m = g 1m -g 1min g 1 max -g 1min G 2 m = g 2m -g 2min g 2 max -g 2min G 3 m = g 3m -g 3min g 3 max -g 3min (4. 12) (4. 13) (4. 14) G 4 m = g 4m -g 4min g 4 max -g 4min (4. 15) 72

74 Where g 1 min, g 2min, g 3min and g 4min are the minimum values, and g 1 max, g 2max, g 3max and g 4max are the maximum values obtained for the objective functions. G 1 m, G 2m, G 3m and G are selected values for multi objective optimisation. 4m The notation m is the identifier of an element in the front. It is noted that the result of this normalisation shows the level of contentment for each objective function. Afterwards, a min-max approach, summarised in (4.16), is applied to select the final multi-objective SVCs placement and sizing. k k Min Max G1 m G2 m, G3 m, G4 m, (4. 16) 73

75 Fig. 4.3: The selection procedure for optimal allocation of the SVC 74

76 4.5 Numerical Studies The modified IEEE 14-bus test system has been used to demonstrate the application of the proposed formulation and evaluate the effectiveness of the NSGA II in solving the SVC allocation problem. Fig. 4.4 shows the single line diagram of the test system. The information related to lines, transformers, generators, synchronous condensers, network peak load in normal condition, and lines power rating of the test system can be found in [70]. Fig. 4.4: IEEE 14 bus test system It is required that contingencies are to be taken into account in determining the optimal SVC allocation in relation to maintaining system security following the loss of one or more transmission circuits. In the present study, the loss of only one transmission line in each contingency is considered. In this research, three line outage as per Table 4.1 is considered and ranked based their impacts on loss of load in IEEE 14 bus test system. 75

77 Table 4.1: Three contingencies in IEEE 14 bus network Line Number The goal of this section is to find the best locations and sizes of SVCs which are previously described. The optimisation is to be carried out with respect to two parameters: location and size. The optimal locations of SVCs is considered as a discrete decision variable, where all load buses except those which have a generator and synchronous compensator are candidates to be the optimal locations of SVCs. The problem is formulated as a multi objective optimisation considering the cost, voltage deviation index, power loss and loadability index. Here, these objectives are optimised at the same time, using NSGA II. In this study, the max-min method is applied to find, among possible solutions, the most suitable one. The number of SVCs to be installed in the network as found from the solution of the optimisation problem is two with their optimal places and sizes given in Table 4.2. To be able to achieve the presented results in Table 4.2, the optimisation is conducted with respect to two parameters: location and size. The optimal location of SVC is considered as a discrete decision variable, where all load buses except those which have generator and synchronous compensator are candidates to be the optimal location of SVC. The problem is formulated as a multi objective optimisation considering the minimisation of cost, voltage deviation index, power loss and maximisation of powerflow security. Here, these objectives are optimised at the same time, using NSGA II which has been described in section

78 In this study, two sets of initial population and number of iterations are considered and compared. First set considers the initial population of 200 and the maximum number of iterations of 100. The initial population of 150 and the maximum iteration of 200 are also considered for the second set. The Probabilities of mutation and crossover operators are set to 0.1 and 0.6, respectively. To select the best multi-objective solution, the max-min method is applied to find among possible solutions, the most suitable one. The number of SVCs to be installed in the network as found from the solution of the optimisation problem is two with their optimal places and sizes given in Table 4.2. Table 4.2: The installation cost, location and size of the SVCs Cost of SVC installation(u.s $) SVC locations Bus 9 and Bus 14 SVC size (MVAr) 18MVAr and 14 MVAr Comparison between the objective functions in normal and contingency states before the SVC installation and those after the SVC installation is summarised in Tables Comparison between the objective functions both in normal and contingency states before the SVC installation and those after the SVC installation is summarised in Tables It can be seen that the active power loss, voltage deviation index and powerflow security are improved by optimal locations and sizes of SVCs in the network. Sensitivity studies have also been performed with various values for the parameters of NSGA II algorithm. These studies indicate that improvements in the objective functions, if there are any, are minimal in comparison with those in Tables As it can be seen, the voltage deviation index can be improved by 36.93% during line

79 outage. In addition, optimal allocation of SVC can reduce transmission active power loss by 5.63% during Line 1-5 outage. Table 4.3: The comparison between active power loss before and after SVC installation Transmission Loss before SVC installation No contingency MW Line 1-2 outage MW Line 1-5 outage MW Line 2-3 outage MW Transmission Loss after SVC installation No contingency MW Line 1-2 outage MW Line 1-5 outage MW Line 2-3 outage MW Table 4.4: The comparison between voltage deviation index before and after SVC installation Before SVC installation No contingency Line 1-2 outage Line 1-5 outage Line 2-3 outage After SVC installation No contingency Line 1-2 outage Line 1-5 outage Line 2-3 outage

80 Table 4.5: The comparison between loadability index of transmission lines before and after SVC installation Before SVC installation Line 1-2 outage Line 1-5 outage Line 2-3 outage After SVC installation Line 1-2 outage Line 1-5 outage Line 2-3 outage It can be seen that the active power loss, voltage deviation index and power-flow security are improved by optimal locations and sizes of SVCs in the network. 4.6 TCSC allocation It has been generally acknowledged that the effectiveness of TCSCs depends importantly on their locations and sizes. The problem of determining the optimal locations and sizes of TCSCs is a nonlinear and complex one. To identify the lines in which TCSCs should be located is a combinatorial problem with discrete variables. There are several methods to find optimal locations of TCSC devices in both vertically integrated and unbundled power systems. There have been various optimization methods previously proposed to solve the TCSC device allocation problem where only a limited number of objectives is included. In general, optimal TCSC allocation problem is to determine the optimal sizes and locations of new installed TCSC devices in order to optimize a set of objective functions subject to a range of operating constraints. According to the characteristics of TCSC devices, various criteria have been 79

81 considered in allocation problem. Some of the reported objectives are: network load ability enhancement [92], ATC enhancement, congestion management [90], loss reduction, and economic factors which minimised the overall system cost function [95]. In [96], a multi-objective genetic algorithm (MOGA) approach has been implemented for TCSC allocation, in which only two objectives have been considered including line overload and voltage violation reduction, and these objectives have been combined to form a single objective function. The combination causes some problems such as: the possible benefits of TCSC devices being not fully utilized. Against the above background, the present research proposes to apply an optimisation procedure based on NSGA II (Non-dominated Sorting Genetic Algorithm) [91]. The objective functions which are considered in the TCSC allocation problems are power loss, investment cost, loadability index and available transmission capacity [97] Objective function formulation for TCSC allocation In this section, the mathematical concept of multi-objective allocation of TCSCs is presented. The four groups of objective functions will be considered in this research as explained in the following: Cost In general, the cost of each TCSC can be expressed in terms of a nonlinear function of its capacity in MVAr. However, TCSC is supposed to carry rated transmission line current. Its rating will be decided by maximum current carrying capacity of a transmission line. As a result, the size of TCSC will be directly proportional to its 80

82 reactance limit. The cost of the ith TCSC is denoted by f i (s i ) where s i is the rating of the TCSC in MVAr. The total cost function to be minimised is: T g 1 = i=1 f i (s i ) (4. 17) where T is the number of TCSCs. For example, a cost function of an TCSC in a quadratic form is: Where a, b and c are constants. f i (s i ) = as i 2 + bs i + c (4. 18) Line flow limit index The severity of the system loading under normal and contingency cases can be described by a line power flow index as follows: g k L 2 = i=1 f k 2 (s i ) (4. 19) where g 2 k is the factor indicating violation of line flow limits, and f 2 k (s i ) is a function which defined as follows: 1; if s k max i s i f k 2 (s i ) = { exp (β 1 s i k s i max ) ; if s k max i > s i (4. 20) where s i is the total power flow in transmission line i ; s max i the maximum limit for the line i, and β is a small positive constant. Superscript (k) indicates operating condition, including normal condition and contingencies. The notation L in (4.19) is the total number of transmission lines Active Power Losses Minimising the active-power loss is equivalent to minimising the slack node activepower. Active-power at the slack node,p sl, is expressed as per equation (4.21). 81

83 g 4 = P sl = Re {V sl [ i Y sl,i. V i ] } (4. 21) where Y sl,i is the element (sl, i) of the admittance matrix of the power system. It is noted that the active-power loss minimisation is considered only for the base case Available transmission capacity Available transmission capacity (ATC) was defined by North American Electric Reliability Council (NERC) as a measure of the available transfer capability in transmission network. Adequate ATC is required to ensure all power transactions to be achieved successfully. Calculation of ATC involves four components: total transfer capability (TTC), transmission reliability margin (TRM), capacity benefit margin (CBM), and existing transmission commitments (ETC). Mathematically, available transmission capacity can be formulated as per equation (4.22) [93]: ATC = TTC TRM CBM ETC (4. 22) where TTC refers to the maximum power which can be transferred from one power control area to other areas (source/sink), which cause no thermal overloads, voltage limit violations or voltage collapse. TRM is the amount of transmission capability necessary to ensure that the interconnected system is secure under a reasonable range of uncertainty. Furthermore, CBM is the amount of the transmission transfer capability which is reserved by load serving entities in order to ensure access to generation via interconnected systems considering generation reliability requirements and finally ETC is the existing transmission commitment. TTC is commonly used as the basis for the evaluation of ATC because other components are either known for a giving operating condition or specified by the power company. Therefore, maximising the ATC in (4.22) is equivalent to maximising the following: TTC ETC (4. 23) 82

84 Several methods have been developed for TTC calculation. These approaches can be classified in three groups as follows: i) Repeated power flow (RPF) method; ii) Continuation power flow (CPF) method; iii) Security constrained optimal power flow (SCOPF) method. In this research, RPF method is used to evaluate TTC in IEEE 30 bus test system. Repeated power flow (RPF) method enables the increase in the transfer of power by increasing the load with uniform power factor at every load bus in the load area (sink) and increasing the injected real power at generator buses in the generation area (source) in incremental steps until the power flow calculation fails to converge or when the power flow and/or voltage solution violates their specified operating limits. The mathematical formulation of TTC using RPF can be expressed as follows: Maximize λ at following equations P Di = P 0 Di. (1 + λ. K Di ) (4. 24) 0 Q Di = Q Di. (1 + λ. K Di ) (4. 25) where P Di (real load in load area) and Q Di (reactive load in load area) and P 0 0 Di, Q Di original real and reactive load demands at bus i in the load area and K Di is a constant used to specify the change rate in the load as λ varies [93]. Subject to: n P Gi P Di j=1 V i. V j (G ij cos δ ij + B ij sin δ ij ) = 0 (4. 26) n Q Gi Q Di j=1 V i. V j (G ij sin δ ij B ij cos δ ij ) = 0 (4. 27) are Vi min Vi Vi max (4. 28) S ij S ij max (4. 29) Qgen i min Qgen i Qgen i max (4. 30) 83

85 where λ is scalar parameter representing the increase in the area s load or generation. λ = 0 corresponds to the base case,and λ = λ max corresponds to the maximum transfer; V i, V j are voltage magnitudes at bus i and j; Gij; Bij are real and imaginary parts of the ijth element of bus admittance matrix; δ ij is voltage angle difference between bus i and bus j,and S ij is apparent power flow in line ij ; Qgen i is generator reactive power. TTC level in each case (normal or contingency) is calculated as per equation (4.31): 0 TTC P (λ ) P (4. 31) Di jsinkarea max Di j SinkArea where P (λ ) Di j SinkArea max is the sum of the loads in the sink area when λ = λ max,and P jsinkarea 0 Di is the sum of the loads in the sink area when λ = 0. The equality and in equality constraints such as power flow constraints, generator reactive power and controller limits are similar to the SVC allocation which explained previously. Summary of the optimisation procedure for TCSC allocation is presented in Fig

86 Generating first population (set of possible solutions) Iteration=1 Determine TCSC Determine Determine Determine cost Power loss ATC Line flow limit Non-dominated sorting, Assignment of fitness value to each solution Reproduction, Crossover, Mutation, Generating a set of off spring Determine TCSC Determine Determine Determine cost Power loss ATC Line flow limit Non-dominated sorting, Assignment of fitness value to each solution Choosing solutions for the new population Iteration=Iteration+1 NO Termination Criteria? Set of non-dominated solutions YES Decision Making Analysis Final Solution Fig. 4.5: Flowchart of the proposed algorithm 85

87 4.6.2 Numerical results for TCSC placement The IEEE 30-bus test system selected to demonstrate the application of the proposed formulation and evaluate the effectiveness of the NSGA II in solving the TCSC allocation problem. This test system was selected for TCSC placement exercise because of higher number of generators and load buses as well as capability to be divided into generation and load area. Fig. 4.6 shows the single line diagram of the test system with the red line divide the IEEE 30 bus to into two parts i.e. generation and load area. The information related to lines, transformers, generators, synchronous condensers, network peak load in normal condition, and lines maximum powers of the test system are based on the IEEE 30 bus test system[24, 70]. Fig. 4.6: IEEE 30 bus test system 86

88 A contingency analysis is carried out to show the effectiveness of the method during the contingency condition and to emphasis on benefits of optimal allocation of TCSC in the network. Three contingencies are selected and listed in Table 4.6. Table 4.6: Selected severe contingencies in the IEEE 30 bus system Contingency number Line The main goal of this section is to find the best locations and sizes of TCSCs which optimise all objective functions as described in previous parts. The optimisation is made on two parameters: location and size. The locations of TCSCs are considered as discrete decision variables. The problem is formulated as multi objective optimisation considering the minimisation of cost, active power loss, security margin improvement and ATC enhancement. Values in Table 4.7 present the optimal places and sizes of TCSCs to be installed. Table 4.7: The locations and sizes of the TCSC based on the optimisation outcome NO TCSC location TCSC size (MVAr) 1 Line Line Comparison between security margin, active power loss, and ATC in the normal and contingency situation before and after TCSC installation is summarised in Table 4.8 to Table It can be seen that the active power loss, security margin and ATC of the network are improved considerably. 87

89 Table 4.8: The comparison of active-power loss before and after TCSC installation Transmission Loss before TCSC installation No contingency MW Line 4-12 outage MW Line 6-10 outage MW Line outage MW Transmission Loss after TCSC installation No contingency MW Line 4-12 outage MW Line 6-10 outage MW Line outage MW Table 4.9: The security margin comparison before and after TCSC installation Line flow limit before TCSC installation Line 4-12 outage Line 6-10 outage Line outage Line flow limit after TCSC installation Line 4-12 outage Line 6-10 outage Line outage Table 4.10: The ATC comparison before and after TCSC installation ATC before TCSC installation No contingency MW Line 4-12 outage MW Line 6-10 outage MW Line outage MW ATC after TCSC installation No contingency MW Line 4-12 outage MW Line 6-10 outage MW Line outage MW 88

90 4.6.3 Conclusion In this chapter, an approach has been proposed to determine the optimal sizes and locations of SVC and TCSC, based on a multi-objective function. In this method, the allocation problem has been formulated according to various technical and economical considerations such as voltage deviation, active power loss and installation cost. Also, in contrast to previous research, the cost objective function has been considered, besides other objectives, to reach a cost-effective and practical solution. In addition, NSGA II method which has been utilised to find the optimal solution has been found to be robust, and offer good convergence property in achieving the solution. The results confirm that the optimal allocation of SVC and TCSC can play a considerable role in improving the performance of the network in terms of lowering the active power loss and increasing the security margin of the network. 89

91 Chapter 5 Multi-objective demand response allocation With the continued increase in the demand for the electrical energy and lack of enough transmission capacity, power system security has become an issue of increased importance in power system operation. To meet the load demand in a power system and satisfy the stability and reliability criteria, both the existing transmission lines and generation units must be utilised more efficiently, or new lines and generation units should be added to the existing system. The latter is often costly and impractical. The reason is that building a new power line or generator in many countries is a time consuming process and sometimes an impossible task, due to environmental problems. Therefore, the first alternative i.e. maximising system utilisation provides an economically and technically attractive solution to power system security problem. The integrated use of demand and supply side resources can be a solution for enhancing the utilisation factor in the electricity network. In addition, reliability enhancement and power system security improvement could be achieved by effective utilisation of 90

92 demand side resources. Considerable research has been done on the impacts of demand response on generation and transmission system reliability [98]. However, few researches have focused on the allocation problem. The optimal allocation of DR has a considerable impact on enhancing the electricity network performance. In this research, the DR program is optimally designed to maximise the available transmission capacity (ATC), minimise the expected energy not supplied (EENS), minimise active power loss and minimise the total DR programs capacity. In this study, EENS represents an index of composite system reliability, which is considered as an important network operator s concern. The focus of the current research is that of determining the optimal DR locations and their capacities to optimize specified objectives subject to operating constraints 5.1 Problem formulation As it is mentioned in the previous section, four objective functions are considered in formulating the optimisation problem. The objective functions are those of ATC, expected energy not supplied (EENS), total active power loss and total DR programs capacity. The decision variables in this optimisation problem are locations and the amount of DR programs to optimise the four objective functions. The details of the objective functions are presented in the following: Expected energy not supplied (EENS) The expected energy not supplied is chosen in this research as an index for composite system reliability. The EENS can be calculated by (5.1): N EENS EPNS j. T (5. 1) j1 91 j

93 where N The total number of load loss events in a year EPNS j Expected power not supplied in the jth event. T j Duration of the outage in the jth event. EPNS j is evaluated based on the annual failure rates of the items of power system,the outage of which leads to loss of load supply Active power loss In steady-state operation, there are always the active and reactive-power balances. Minimizing the active-power loss is therefore, equivalent to minimizing the slack node active-power. Active-power at the slack node P sl is expressed as: * P Re. sl Vsl Ysl, i V (5. 2) i i where Y sl,i is the element (sl, i) of the admittance matrix of the power system. To reduce the amount of computation, the base case network configuration and maximum load demand condition are adopted in forming the objective function for active-power loss Available transmission capacity ATC was defined by North American Electric Reliability Council (NERC) as a measure of the transfer capability in transmission network. Adequate ATC is required to ensure that all economic transactions can be successfully achieved. Calculation of ATC involves four components: total transfer capability (TTC), transmission reliability margin (TRM), capacity benefit margin (CBM), and existing transmission commitments (ETC). Mathematically, ATC is defined as: ATC TTC TRM CBM ETC (5. 3) 92

94 In (5.3), TTC refers to the maximum power that can be transferred from generation area to the load area (source/sink), which causes no thermal overloads, voltage limit violations or voltage collapse. TRM is the amount of transmission capability necessary to ensure that the interconnected system is secure under a reasonable range of uncertainty. CBM is the amount of the transmission transfer capability which is reserved by load serving entities in order to ensure access to generation via interconnected systems considering generation reliability requirements, and finally. ETC is the existing transmission commitment. TTC is commonly used as the basis for the evaluation of ATC because other components are either known for a given operating condition or specified by the transmission company. Therefore, maximising the ATC in (5.3) is equivalent to maximising the following equation. TTC ETC (5. 4) Several methods have been developed for TTC calculation. These approaches can be classified in three groups as follows: i) Repeated power flow (RPF) method; ii) Continuation power flow (CPF) method; iii) Security constrained optimal power flow (SCOPF) method. In this research, RPF method is used to evaluate TTC because of ease of implementation and time convergence. The Repeated power flow (RPF) method enables the increase in the transfer of power by increasing the load with uniform power factor at every load bus in the load area (sink) and increasing the injected active power at generator buses in the generation area (source) in incremental steps until the power flow calculation fails to converge or when the power flow and/or voltage solution violates their specified operating limits. The mathematical formulation of TTC using RPF is expressed in the following: 93

95 Maximise λ Subject to: P Gi P Di n G cos B sin 0 ( ) V. V (5. 5) j2 i j ij ij ij ij Q Gi Q Di n G sin B cos 0 ( ) V. V (5. 6) j2 i j ij ij ij ij V Q i min geni min V V (5. 7) i Sij S ij max geni i max geni max (5. 8) Q Q (5. 9) where λ is a scalar parameter representing the increase in the area s load or generation, λ = 0 corresponds to the base case and λ = λ max corresponds to the maximum transfer; P Gi and Q Gi are the real and reactive power generation at bus i ; V i, Vj are voltage magnitudes at bus i and j ; G ij and B ij are real and imaginary parts of the th ij element of bus admittance matrix; δ ij is voltage angle difference between bus i and bus j,and S ij is apparent power flow in line ij ; Qgen i is the reactive power of the th i generator. In the power flow in (5.5) and (5.6), P Di (active load in load area) and Q Di (reactive load in load area) are calculated as: P Q Di Di 0 P.(1. K ) (5. 10) Di Di 0 Q.(1. K ) (5. 11) Di Di where P 0 Di and Q 0 Di are base real and reactive load demands at bus i in the load area,and K Di is a constant used to specify the change rate in the load as λ varies. Inequalities (5.7) and (5.8) impose the voltage limits of the buses and the thermal limits of transmission lines, respectively. The load demands in the source area, if there are any, have their values kept fixed at those in the base case. TTC level in each case (normal or contingency) is calculated as follows: 94

96 jsinkarea TTC ) (5. 12) P Di ( max jsinkarea where P ) is the sum of the loads in the sink area when λ = λ max. In terms of Di ( max generation to meet the demand as specified in (5.10) and (5.11), optimal power flow (OPF) is performed to determine the optimal generation schedule for each iteration. The OPF objective is to minimise the total generation cost, with the assumption that the cost functions for individual generators are specified Total DR programs capacity This objective function is the total DR programs capacity in the power system that is formed as follows: TDRP DRP TB TB TDRP DRP n n 1 (5. 13) Total DR programs capacity The amount of load participating in the demand response at the nth load bus Total number of load buses with demand response programs Equality constraints Equality constraints consist of power flow equations applied for individual power network nodes, which is written in a compact form as follows: V,, u 0 E (5. 14) In (5.14), V k and θ k are the vectors of system voltage magnitudes and phase angles, and u k is the vector of control variables such as generator excitation control. In addition to above equality constraints, the optimisation is subject to inequality constraints that are described in the following section. 95

97 5.1.6 Inequality constraints In general, the inequality constraints can be written in the compact form as follows: V,, u 0 H (5. 15) In (5.15), H is in general a nonlinear function that relates to operating conditions such as power flow constraints, generator reactive power and controllers limits. An example for inequality constraint is that of voltage magnitude constraint: V (5. 16) i V 0 i max In (5.16), V k k i and V i max are voltage magnitude at node i and its maximum allowable respectively 5.2 Variables and their representation The multi-objective optimisation with NSGA II algorithm requires the variables of the optimisation problem to be coded as a string of binary digits of finite length. The variables representing the DR program locations and sizing are grouped into a string with the structure shown in Fig 5.1. The first part of the structure is for the coding of the DR program locations. Each gene in this part is associated with a bus in the power system. The gene value of 1 means in that bus DR program has been implemented. The length of the first part is given by the number of load buses in the power system. The second part of the structure comprises a number of blocks of binary numbers. Each block is associated with a load bus in the power system that represents the size of the DR program assigned to the bus. The length in each block is determined by the maximum amount and accuracy required. 96

98 Fig. 5.1: Representation of sample power system and string for DR locations and sizes Fitness evaluation The fronts are formed from the current population using an iterative process described in the following. In forming the first front, the entire population is considered from which the first non-dominated possible solution is identified. The second possible solution of the first front is then selected from the reduced population in which the first non-dominated possible solution is excluded. The process is repeated for a finite number of times to form level-1 front. The same procedure is then applied to form level- 2 front from the remaining population where level-1 front individuals are excluded. Individual fronts are assigned fitness values accordingly to their levels. Level-1 front has the largest fitness value. Lower fronts are then assigned smaller fitness values. Having formed the fronts together with their fitness values, it is required to assign fitness value for each element of each front. The requirement in this fitness value assignment is to maintain diversity. This means that the fitness value distribution over the individuals in each front is a non-uniform one. Various schemes can be designed to form the distribution of fitness values. For example, the present research implements a 97

99 scheme based on a clustering algorithm that will assign low fitness values for the individuals in close proximity to one another as measured by the norms of the differences between the vectors representing these individuals. The assignment of fitness values for the individuals in each front also takes account of the fitness value of the front so that the lowest fitness value of an individual in a front will still be greater than that of another individual in any other front with a lower rank Iterative process The population is then reproduced according to the fitness values. Since individuals in the first front have the highest fitness values, they always get more copies than the rest of the population. The efficiency of NSGA II lies in the way by which a mapping from objective function values to fitness values of individuals in a population is achieved using the Pareto optimal criteria. In principle, the method can be applied to any number of objective functions encountered in a constrained optimisation problem. The flow chart of the proposed algorithm is shown in Fig Either reaching the maximum number of allowed iterations or finding no other new non-dominated solution in a predefined number of iterations has been considered as the termination criterion. The key aspect in the flowchart of Fig. 5.2 is the essential application of the OPF (optimal power flow) for evaluation of individual objective functions, which are used for the NSGA II procedure. The inputs to the OPF in terms of DR programs sizes and locations are those given in each possible solution vector in individual iteration. Outputs of this step will be used to rank possible solutions in different fronts. Finally, a max-min approach described in the following section is used to determine the compromising solution. 98

100 Fig. 5.2: Flowchart of the proposed algorithm 99

101 5.2.3 Selection of final solution The final solution will be one of the vectors in the front with level 1 in the population of the last generation. An obvious choice for the final solution is that which satisfies the optimality condition. However, the system planners might prefer to have the flexibility of selecting a solution level-1 front that deviates from the Pareto optimality condition in meeting their practical planning requirements and conditions. The system planners can formulate criteria based on which the most practical solution is selected. In the current research, a min-max approach is used to select the suitable locations and sizes of DR programs. Each possible solution in the front with level 1 has an associated vector of values of objective functions that can be normalised using the following expressions: G G G 1m 2m 3m 1m 1min (5. 17) g g 1max 2 max g g 1min 2m 2 min (5. 18) g g 3max g g 2 min 3m 3min (5. 19) g g g g 3min G 4m g g 4m 4 min (5. 20) 4 max g g where g 1 min, g 2min, g 3min and g are the minimum values and 4min 4 min g 1 max, g 2max, g 3max and g 4max are the maximum values obtained for the objective functions. The notation m is the identifier of an element in the front. It is noted that the result of this normalisation shows the level of contentment for each objective function. Afterwards, a min-max approach, summarised in (5.21), is applied to select the final multi-objective DR program placement and sizing. Min Max G1 m G2m, G3m, G4m, (5. 21) 100

102 5.3 Numerical Studies The proposed algorithm has been tested on the modified IEEE-30 bus test system, which has six generator buses, 21 load buses, 41 lines, and four tie-lines as represented in Fig. 5.3 [70]. Fig. 5.3: Single line diagram of the IEEE 30 bus test system It is assumed that all load buses could have DR programs up to 10% of their demand. The design results are shown in Table 5.1 in terms of the buses selected for DR programs together with their sizes. Sensitivity design studies have also been performed with various values for the parameters of NSGA II algorithm. These studies indicate that improvements in the objective functions, if there are any, are minimal in comparison with those in Tables 5.2 to Tables 5.4. Table 5.2 shows the active power loss in the electricity network with and without DR programs. Moreover, three contingencies are also considered to show the effectiveness of the method in the contingency situation. 101

103 In Table 5.3 is summarised the EENS of the network before and after DR implementation, and finally Table 5.4 illustrates the noticeable effect of DR on ATC enhancement in normal and contingency conditions. Table 5.1: Selected buses and the amount of DR programs Bus Number Initial Demand(MW) DR program sizes (MW) Table 5.2: The comparison between active-power loss before and after DR implementation Transmission Loss before DR installation (MW) No contingency Line 4-12 outage Line 6-10 outage Line outage Transmission Loss after DR installation (MW) No contingency Line 4-12 outage Line 6-10 outage Line outage Table 5.3: The comparison between EENS before and after DR implementation EENS before DR installation (MWh) EENS after DR installation (MWh)

104 Table 5.4: The comparison between ATC before and after DR implementation ATC before DR installation (MW) No contingency Line 4-12 outage Line 6-10 outage Line outage ATC after DR installation (MW) No contingency Line 4-12 outage Line 6-10 outage Line outage Conclusion A flexible design procedure based on multi-objective function optimization using NSGA II algorithm has been developed and presented in this chapter for optimally allocating DR programs in terms of their locations and sizes. Network security constraints are included in optimizing the objective functions related to ATC, EENS and active-power loss. The design procedure is a flexible and general one that can be extended in a straightforward manner to incorporate other objective functions including those of an economic nature and constraints encountered in system operation. The effectiveness of the procedure developed and DR programs has been illustrated with a representative design study based on an IEEE 30 bus power system, the results of which confirm the noticeable improvements of the objective functions chosen in the DR program design. 103

105 Chapter 6 Congestion management using demand response program According to North American Electricity Reliability Council (NERC) Operating Policy, demand response (DR) programs are recognised as one of the contingency reserve services. This market based tools are very valuable when the operating margins available to the independent system operator (ISO) reduced considerably with increasing market competition. In addition, demand side management (DSM) strategic plan of International Energy Agency (IEA), for confirms that, demand side activities should be active elements and the first choice in all energy policy decisions designed to create more reliable and more sustainable energy systems. At the moment, different independent system operators (ISOs) in Europe, Oceania and North America are continuing development of a demand response program with the objective of changing electricity demand of large power users. ISOs in different power market around the world try to use DR programs to enhance the security of the power system. 104

106 The role of demand response programs in a restructured power system and its effects in congestion management was addressed in this chapter. In this approach, Day-Ahead Demand Response Program (DADRP) and Interruptible /Curtailable (I/C) loads are modelled based on load elasticity and used to release transmission congestion in a leastcost manner by considering different load scenarios. The present research proposes an integrated framework for congestion management, using DADRP and I/C programs as an effective tools for congestion management. To achieve this goal, a market auction with combining DADRP and I/C programs are designed. 6.1 Congestion management The electricity network is congested when one or some of the transmission lines reached to its maximum limits or the voltage in some buses exceeds its limitations [29]. Although, the congestion problem is not a new problem in the power system, it has become more severe in a restructured market environment. There are different congestion management methods apply in different electricity markets around the world [27, 28]. Generally, these methods can be categorised into two major groups, which are as follows: Preventive congestion management methods Corrective congestion management methods Preventive congestion management methods These methods are applied before finalising the electricity market. The Preventive congestion management methods are categorised into three different sub sections apply for different time lines. The time line for each category varies from short term to long 105

107 term solutions. One of the most popular methods of this group is reserving the transmission line capacity method and is used for bilateral contracts. In the following, different methods for congestion management based on the preventive congestion management methods will be discussed in details [28] Congestion management using the transmission right In this method, transmission line capacity will be assigned to different customers in the market based on six months or 12 months contracts. This method is very effective in electricity markets with considerable bilateral contracts. If the congestion occurs in the market, the system operator priorities customers with reserved transmission capacity. This approach can potentially reduce the probability of congested transmission lines [99] Point to point method In the point to point method some of the nodes are considered as power injection and some nodes are considered as power consumption points. In the next step, maximum transferable power between these two points is calculated and required transfer capacity will be reserved for power transaction [28] Area to area method In this method, the network is divided into different areas then the maximum transferable power between two sections can be calculated with considering the maximum thermal limitations of transmission lines, transformer limitations and voltage stability [28]. 106

108 Congestion management methods based on the ATC The available transmission capacity can be calculated as per equation (6.1) [100]: ATC TTC TRM CBM ETC (6. 1) The TTC equals to the total transfer capacity between two points or two areas in the transmission system. The factors that affect the total transfer capacity (TTC) include thermal limitation of the transmission lines, voltage limitation on buses and the stability limits. The transmission reliability margin (TRM) is a reliability index. This index shows that the power transfer is not exceeded the reliability margin of the line. The other terms which can affect this index are load forecast errors and contingency in the electricity network. The capacity benefit margin (CBM) index is also similar to TRM and considers a security margin for transmission lines. The, existing transmission capacity (ETC) shows the existing transferable power from one area to other or from one point to other point. In this method, the system operator calculates the ATC for different areas and publishes this information before the actual operation time. This information will be published via the specific gateway. In the next step, the system operator recalculate the ATC based on the received information from the market participants. During the transmission congestion the system operator might ask for improving or cancelling some of the contracts to be able to recover the available transmission capacity to the normal level [101] Corrective congestion management methods The corrective congestion management alternatives focuses on eliminating the congestion when occurs during system operation, through online control actions. Some of the usual corrective congestion management methods include, the controlling actions from phase shifters, transformer tap changing, revising the FACTS device reference 107

109 value and generator re-dispatch [8, 39, 40, 102]. Although, the preventive actions can help the system operator to prevent the congestion in transmission lines, the corrective actions have to be applied in some cases such as major generator or transmission line outages or any other major contingency in the system. 6.2 Modelling demand response program In order to analyse the impact of demand response program on load profile characteristics, development of responsive load economic models are necessary. There are several models available to show the relationship between the price and demand. These models can be used for simulating different type of customers such as linear, logarithmic, exponential and hyperbolic [103]. One of the important steps associated with modelling the demand response participants is to determine how the reduced load by participants would be recovered after predefined reduction by the market. Basically, load reductions by DR participants are divided into two categories. Non-transferable loads: Load reduction without recovering it later. For example, lighting load, air conditioning loads are examples of loads which cannot be shifted to another hours. Transferable loads: some types of loads can be rescheduled and shifted as required. Some of industrial processes can be rescheduled and shifted based on request. The Elasticity is defined as the demand sensitivity with respect to the price, and it is explained as follows [103]: D 0 dd E. D dp 0 (6. 2) 108

110 where E Elasticity of the demand D 0 D Initial demand value (MWh) Demand value (MWh) Electricity price ($/MWh) 0 Initial electricity price ($/MWh) Based on this definition if the electricity price increases or if the independent system operator considers incentive payment in some intervals, the electricity customers react to these changes based on equation (6.2). Some types of loads are not capable to be transferred from one period to another. These type of loads known as self elasticity", and it has negative value. In other hand, some loads could be able to shift from the peak period to the off-peak hours known as multi period loads and they have positive elasticity values. The equation (6.3) shows the self and cross elasticity: 0( j) dd() i E( i, j). D ( i) dp( j) 0 E( i, j) 0 if i j, self elasticity E( i, j) 0 if i j, cross elasticity (6. 3) The self and cross elasticity can be explained for each hour of a day with 24 by 24 matrices as per equation (6.4) [64, 104]. d(1) E(1,1) E(1,2) E(1,24) ( 1) d(2) E(2,1) E(2,2) (2) d(3) E( i, j) ( j)... E(23,1)... E(23, j)... E(23,24)... d(24) E(24,1)... E(24, j)... E(24,24) (24) (6. 4) The self elasticity is shown in the diagonal items of this matrix, and the off-diagonal items correspond to the cross elasticity. For instance, Column j of this matrix shows how a change in price during the single period j affects the demand during all other periods. The elasticity for the electricity sector generally varies by a value between -1 and +1. Fig. 6.1 shows the elasticity of inelastic and elastic load and Fig. 6.2 shows the 109

111 elasticity of the typical customers to the price based on linear model. This figure explains the relation between quantity and price for any commodity including the electricity from customer point of view. Fig. 6.1: The elasticity of the typical elastic and inelastic load Fig. 6.2: Linear representation of price versus quantity The equation (6.5) shows the relationship between the price and quantity based on linear function that is shown in Fig ( j) dd() i E( i, j). 0 (6. 5) D0 ( i) dp( j) In the equation (6.5) dd() i dp( j) is constant, which means if the price increases from $1 to $2, it has similar effect on changing from $100 to $101. The non-linear modelling can highlight this difference and leads to the accurate model for elasticity. 110

112 Fig. 6.3: Non-linear representation of price versus quantity Three factors including incentive, penalty and elasticity are considered in this research to form the mathematical model that can be used to form the price quantity offer by the demand response aggregators. The steps for developing the mathematical demand response formulation are explained in the following: The load change at the ith bus arising after load reduction by demand response participants can be expressed as follows: L( t) L0 ( t) L( t) (6. 6) In (6.6), L 0 () t and Lt () are the load at the ith location before and after demand response, respectively. If IN() t is paid as incentive to the customer for each unit of load reduction, the total incentive for participating in DR program will be calculated based on equation (6.7). The incentive amount is a fixed value that is determined by the market operator. The amount of penalty is also assumed to be a fixed amount, and for the purpose of this chapter the penalty is set to be 1.5* IN(t) [79]. P( L( t)) IN( t)[ L ( t) L( t)] (6. 7) 0 If the customers participating in the DR program do not respond to the minimum load reduction as required in the contract, the customers will have to pay the penalty. If the 111

113 reduction level requested from the aggregator and penalty for the same period are denoted by LR() t and fin() t, respectively, then the total penalty TFIN ( L( t)) is calculated as follows: TFIN ( L( t)) fin( t).{ LR( t) [ L ( t) L( t)]} 0 (6. 8) The requested load reduction level, LR() t, is limited to the maximum value LR max () t agreed in the contract between the aggregator and DR participants. If the customer as revenue is considered as calculated as follows: B( L( t)) for using Lt (), the customer net benefit can be In (6.9), () t S ( t) B( L( t)) L( t). ( t) P( L( t)) TFIN ( L( t)) (6. 9) is the price that should be notified or forecasted by the demand response aggregator or demand response participants prior to the day for implementing DR program. To maximize the customer s net benefit, S Lt () in equation (6.9) is set to zero. S( t) B( L( t)) ( t) L( t) P( L( t)) TFIN ( L( t)) 0 L( t) L( t) L( t) L( t) L( t) (6. 10) From (6.10), B( L( t)) ( t) IN( t) fin( t) Lt () (6. 11) In general, various forms of customer revenue function have been proposed for expressing the customer revenue in terms of demand [63, ]. In this paper, an exponential function of demand elasticity as given in [107] is adopted for deriving the optimal demand response: 1 Ei () 0( i) L( i) Li () B( L( i)) B0( L0( i)) Ei ( ) L0 () i (6. 12) In (6.12), Et () is the elasticity of the load and 0 () t is the market price prior to demand response implementation. Differentiating equation (6.12) yields to: 112

114 1 Et () B( L( t)) 0() t L( t) 1 1 L( t) 1 Et ( ) L0 ( t) 1 ( ) 1 Et ( ) 1 0( t). L( t) 1 1 Lt ( ) Et ( ). 1 Et L0( t) L0( t) (6. 13) Simplifying equation (6.13) and substituting into equation (6.11) yields to equation (6.14). 1 ( t) IN( t) fin( t) (1 Et ( ) ). () t E( t) E( t) 1 L t L( t) ( ) 1 Et ( ). L ( t) L ( t) 0 0 (6. 14) Rearranging equation (6.14) leads to: 1 Et () ( t) IN( t) fin( t) L( t) 1 1 0( t) L0( t) 1 Et ( ) (6. 15) The second term of the right hand side of equation (6.15) can be discarded for small amount of elasticity, and finally the demand response model can be achieved as follows: ( t) IN( t) fin( t) L( t) L0 ( t). () t Et () 0 (6. 16) In this research, it is assume that the aggregators submit the offers to the wholesale market on behalf of the demand response participants and NAS battery owners. The demand response formulation in (6.16) is used to form the price-quantity offer package to the market. The aggregated package comprises a number of power blocks each of which with block size and bidding price. The details of the market clearing formulation with considering demand side resources are explained in the following section. 113

115 6.3 Auction-based market clearing Customers can bid their capacity and associated price at which they would be willing to curtail their loads on a day-ahead auction dispatch (DADRP). The market clearing formulation can be presented according to equation (6.17). Min Subject to N N G Gj NreD NDi ND NDi : ( Gj, l. PGj, l ) ( redi, k. PreDi, k ) ( Di, k. PDi, k ) f. CO ( RI) j1 l1 i1 k1 i1 k1 r (6. 17) 0 P 1,..., N (6. 18) max Di, k PDi, k i 1,..., ND, k 0 P P j 1,..., N, 1,..., N (6. 19) max Gj, l Gj, l G l Di Gj u N Gj j l1 NGj NGj min max Gj, l PGj, l u j PGj, l j l1 l1 P 1,..., N G (6. 20) 0 P P i 1,..., N, k 1,..., N (6. 21) max redi, k redi, k red ND NDi N N N i1 k1 Di k red Di i1 k1 redi, k N G Gj P, P P (6. 22) j1 l1 Gj, l redi RI N N R red ( j 1 L L (. Pr ) (1 ) Pr Pr) (. Pr) (1 ) Pr Pr j j j l j l i i i l i l (6. 23) l 1 i 1 l 1 u j,, {0,1} j R, l L, ired (6. 24), j l i j 0,1 j 1 NG u,..., (6. 25) where P Gj, l Power block l that generator j is willing to sell at price Gj, l up to a maximum of max P Gj, l ; P redi, k Power block k that responsive demand i is willing to sell; P redi Power provided by responsive demand I; max P Gj, l Maximum power block l offered by generator ; N red Number of responsive demands; N L Number of lines; NGj Number of blocks offered by generator j; f r Risk coefficient; Pr j outage probability of generator j; Pr l outage of line l probability; CO( RI ) the function represents the risk. The objective function is presented 114

116 in (6.17). The set of constraints are presented in (6.18) to (6.22). The set of constraints (6.18) specifies the sizes of responsible demand bids. Constraint (6.22) states that the production should be equal to the demand balance considering the responsible demands. Equation (6.23) is explaining the risk factor. 6.4 Congestion management by generation and demand re-dispatch The congestion management formulation using demand response and conventional generators are presented as follows: down down up up down down Min : ( r P r P ) ( r P ) (6. 26) jg j Gj j Gj i ired redi Subject to: A down A down PG P P P B ( ) 0 n 1,..., N (6. 27) n G max nm n nm D n n m D n m max nm n nm n P B ( ) P n 1,..., N, m (6. 28) j min Gj A Gj down Gj j max Gj m u P P P u P j 1,..., N (6. 29) down down P P n 1,..., N (6. 30) Gn jg n Gj G n A A PG P n 1,..., N n jg n Gj down down PD P n 1,..., N n id n redi (6. 31) (6. 32) A A PD P n 1,..., N n id n Di (6. 33) The objective function for congestion management is presented in (6.26), and the constraints are presented in (6.27) to (6.33). Where down P Gj up P Gj increment in the schedule of generator j; down decrement in the schedule of generator j; decrement in the P redi schedule of responsible demand I; up rj price offered by generator j to increase its schedule; r down j price offered by generator j to decrease its schedule 115

117 6.5 Numerical studies A case study based on the modified IEEE 30-bus system is presented. Transmission capacity limits of the lines are supposed to be 70% of the values given in [24]. Fig. 6.4: IEEE 30-bus system Three scenarios of the demands are considered; in scenario 1, all the demands are considered to be in their peak value during the 24-hour period. In scenarios 2 and 3, two sets of random numbers are generated for determination of the loads in every load bus. These random numbers are generated by uniform distribution in the range of 0 1 with considering a typical load duration curve. The load demands in three scenarios are presented in Table

118 Table 6.1: Loads in three scenarios of demand Bus Number Scenario 1 Scenario 2 Scenario

119 A typical load curve is selected to test and analyse the effect of DADRP and I/C programs. The load curve is divided into three intervals; low-load period, off-peak period, and peak period. In this study, three values of incentives and penalties are considered for DR programs. The incentive value is assumed to be 30, 40 and 60$/MWh and the penalty value is assumed to be 60, 80 and 110 $/MWh for all customers. The load curves before and after implementation of DR program is presented in Fig. 6.5 for different incentive and penalty values. Fig. 6.5: The load curve before and after DR program implementation In this study, seven high load buses are selected as the candidates for implementing DR programs. These selected buses and the reduction amount are provided in Table

120 Table 6.2: Load demands due to various incentives and penalties Responsible Demand Number Bus Number Initial Demand 30$ /MWh Incentive 60$/MWh Penalty 40$/MWh Incentive 80$/MWh Penalty 60$/MWh Incentive 110$/MWh Penalty The market clearing results for generators and demand response programs are presented in Table 6.3 and Table 6.4. In addition, increment and decrement for generators and demand response programs are shown in Table 6.5 to 6.6. Table 6.3: The auction results for generators Generator Number Bus Number Production (MW)

121 Table 6.4: The auction results for generators and responsible demands Generator Number Bus Number Production (MW) Responsible Bus Number Production(MW) Demand(DADRP) Table 6.5: Generator increment and decrement to release the congestion Generator Bus Without _DR Number Number Decrement Increment

122 Total Cost($) Table 6.6: Generators and Responsible demands increment and decrement to release the congestion Generator Bus With _DADRP Number Number Decrement Increment Responsible Bus Decrement Increment Load Number Number Total cost of market for various scenarios and three load demands are presented and compared in Fig Total Market Cost WITHOUT DR DADRP I/C DADRP+I/C Demand Demand Demand Fig. 6.6: Total cost of market operation in three scenarios of demands ($/hour) 121