Optimal Power Flow Calculation for Unbalanced Distribution Grids

Transcription

1 Power Systems P L Laboratory Stefanie Aebi Optimal Power Flow Calculation for Unbalanced Distribution Grids Semester Project PSL EEH Power Systems Laboratory ETH Zurich Examiner: Prof. Dr. Gabriela Hug Supervisor: MSc Stavros Karagiannopoulos Zurich, June 28, 2017

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3 Abstract New developments in distribution grids including the increased penetration of distributed energy resources require the distribution system operator to apply new planning and operating schemes for cost-effective and secure power supply. This paper proposes a centralized approach for the operational planning of unbalanced active distribution grids based on [1], where the algorithm of [1] has been extended to 3-phase unbalanced operation. Optimal set-points of distributed energy resources are determined with a multi-period optimal power flow algorithm. An exact power flow computation to ensure feasibility of the resulting flows is then done using a backward-forward sweep method as proposed by [2]. The resulting planning scheme is applied to and demonstrated on a low-voltage distribution network model. We see that the efficient use of active control measures helps maintaining currents and voltages under acceptable thresholds. In this thesis, we compare the symmetrical 1-phase case against the 3-phase representation in order to identify differences in the control usage arising from the 3-phase coupling. iii

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5 Acknowledgements My special thanks go to Stavros Karagiannopoulos who has supervised this project, spent a lot of time helping me to find algorithm bugs, supported me with his specialist knowledge and motivated and challenged me throughout this project. I m really greatful for your support! v

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7 Contents List of Acronyms ix 1 Introduction Motivation: New Developments in Distribution Grids Employed Algorithm Main Contributions Power Flow Calculations in DNs Characteristics of Distribution Grids Backward Forward Sweep Method Case Study I: Power Flow Calculations in DNs Case Study Setup Results Multi-Period PF results Optimal Power Flow Calculations in DNs Optimal Power Flow Fundamentals Objective Function Power Balance Constraints Power Quality Constraints OPF Calculation Specifications in this Project Case Study II: OPF Results Discussion Conclusion 21 vii

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9 List of Acronyms DG DER DSO OPF BFS DN RPC APC Distribution Grid Distributed Energy Resource Distribution System Operator Optimal Power Flow Backward-Forward Sweep Distribution Network Reactive Power Control Active Power Curtailment YALMIP Yet Another Linear Matrix Inequality Parser PF BIBC BCBV LV OLTC BESS Power Flow Bus Injection to Branch Current [matrix] Branch Current to Bus Voltage [matrix] Low Voltage On Load Tap Changer Battery Energy Storage System ix

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11 Chapter 1 Introduction 1.1 Motivation: New Developments in Distribution Grids The increasing share of distributed energy resources (DERs) in the electricity distribution network (DN) constitutes new challenges as well as new opportunities. Intermittent renewable energy generators and other DERs lead to intensified power flow (PF) variability, and thus, constantly changing operating conditions [1]. On the other hand, controllable DERs represent new sources of flexibility by providing ancillary services such as reactive power control (RPC) [3] and active power curtailment (APC) [4], whereof RPC is usually preferred to APC for the treatment of voltage or congestion problems because it usually incurs lower cost [1]. These new developments in DNs require the distribution system operator (DSO) to apply new planning and operating schemes to ensure optimal cost-effectiveness and security of supply. This project focuses on optimal power flow calculations for balanced and unbalanced distribution grids. 1.2 Employed Algorithm In this project, a centralized scheme for the operational planning of active DNs was developed, extending [1] to unbalanced operating situations. At the core of the proposed algorithm lies a multi-period centralized optimal power flow (OPF) calculation, employing optimization under consideration of system-wide information. In a first step, a multi-period OPF algorithm is used to compute the optimal set-points of controllable DERs. To reduce computational burden, this is approximated based on the first step of a backward-forward sweep (BFS) algorithm. In a second step, an iterative power flow computation based on BFS is run until convergence to determine the solution state, and thus, ensure feasibility of the resulting power flows and tractability of the algorithm. The resulting operational planning scheme 1

12 2 CHAPTER 1. INTRODUCTION is tested on the Cigre European low-voltage distribution network [6]. 1.3 Main Contributions A centralized scheme for the operational planning of active distribution grids has been proposed in [1]. This project extends the algorithm used by [1] to unbalanced operating conditions, which is usually the case in distribution networks. Furthermore, this paper uses a case study in order to investigate the system behaviour under balanced and unbalanced loading operations.

13 Chapter 2 Power Flow Calculations in DNs 2.1 Characteristics of Distribution Grids It is well-known that power distribution systems are significantly different from transmission systems. They are usually radial or weakly meshed, show high R/X ratios and are operated multiphase and unbalanced. Moreover, DNs contain increasing shares of distributed loads and generation [5]. All these factors make traditional power flow methods, e.g. based on Newton Raphson method, inappropriate for distribution grids due to poor convergence features. However, various methods making use of the specific characteristics of distribution grids have been proposed and can be summed into three groups: network reduction methods, backward/forward sweep methods and fast decoupled methods [5]. The algorithm proposed in this project builds upon a direct backward/forward sweep procedure based on [2], which solves PF exploiting the radial DN topology. 2.2 Backward Forward Sweep Method A backward forward sweep method (BFS), in short terms, is carried out by iteratively sweeping the network and updating the variables at each iteration. A rough summary of the algorithm is given in Algorithm 1. 3

14 4 CHAPTER 2. POWER FLOW CALCULATIONS IN DNS Algorithm 1: Main steps of BFS, based on [2], taken from [1] Input: BIBC, BCBV, P inj, Q inj, V slack Output: Ibranch k, V bus k 1: initialize: k = 1, Vbus k = 1 0 2: do ( ) 3: Backward sweep: Iinj k = (Pinj +jq inj ) 4: I k branch = BIBC Ik inj V k bus 5: Forward sweep: V k+1 = BCBV Ibranch k 6: V k+1 bus = V slack + V k+1 7: Update ( iteration: k+ = ) 1 8: while max Vbus k k 1 Vbus η 9: return Ibranch k, V bus k The Bus Injection to Branch Current matrix (BIBC) is a matrix capturing the network topology and the Branch Current to Bus Voltage matrix (BCBV) the complex line impedances. The algorithm proposed by [2] was expanded to 3-phase systems in order to account for imbalances; BIBC thus in our case contains 3x3 identity matrices and BCBV is made of 3x3 complex impedance matrices. During the backward sweep, current injections at all buses are calculated and then used to compute branch currents. These branch currents are then used in the forward sweep to determine the voltage drops over all branches and thus update the bus voltages. 2.3 Case Study I: Power Flow Calculations in DNs Case Study Setup The methods suggested in this project are demonstrated on a benchmark system proposed in [6]. CIGRE benchmark systems form a common basis of test systems for the analysis and validation of new methods and techniques tackling the integration of DERs and Smart Grid technology in the power system [6]. In this project, the proposed algorithm was applied to the CIGRE European low-voltage distribution network, which is depicted in Fig All network parameters were taken from [6]. The grid consists of 18 branches and 19 buses, including loads at buses 12, 16, 17, 18 and 19. In this project, the case of a system with a small battery storage at node 16 and PV generation at nodes 12, 16, 18 and 19 with a share of 30% each on the load was studied for a worst-case summer day. The applied load was balanced over all phases, however the algorithm is also supposed to work under unbalanced loading conditions.

15 2.3. CASE STUDY I: POWER FLOW CALCULATIONS IN DNS 5 Figure 2.1: CIGRE European low-voltage distribution network [6] Results A BFS PF calculation was applied to the Cigre LV grid without control. Fig. 2.2 and 2.3 show the resulting voltage magnitudes and angles at all buses of the system. For a comparison, the states calculated by [1] for 1-phase balanced operation (using self-impedances only and symmetrical components) are plotted next to the full 3-phase BFS results. It can be observed that the two approaches yield very similar results regarding the voltage magnitudes, yet differ substantially concerning the voltage angles. The 3-phase BFS results in slightly lower voltage magnitudes as an effect of phase interference (mutual impedance) leading to higher overall impedances. It can be shown that the algorithm results in exactly the same PF results for 3-phase calculation as it does for 1-phase calculation, if the mutual impedances (i.e. the off-diagonal elements in the line impedance matrices) are left out (Fig. 2.4). This implies that phase interference is responsible for the differences observed between the 3-phase and 1-phase calculation and - since these differences are not negligible - must be considered if the assumption of having balanced loading is not realistic Multi-Period PF results The voltage and current magnitude evolution over a period of 24 hours is depicted in Fig Regarding the PV injections, we consider the worst summer day in order to investigate the control behavior under high solar radiation. It can easily be seen that for the given worst-case scenario, the system experiences severe overvoltages (up to 10%) and thermal overloadings. This calls for active control measures, which will be considered in the next chapter.

16 6 CHAPTER 2. POWER FLOW CALCULATIONS IN DNS voltage magnitude [p.u.] BFS 1-phase Matpower bus (a) Voltage magnitudes, 1-phase, according to [1] voltage magnitude [p.u.] BFS phase A-B BFS phase B-C BFS phase C-A bus (b) Voltage magnitudes, 3-phase Figure 2.2: Voltage magnitudes at all the buses for a symmetrical singlephase (top) and a 3-phase (bottom) representation

17 2.3. CASE STUDY I: POWER FLOW CALCULATIONS IN DNS 7 voltage angle [deg] BFS 1-phase Matpower bus (a) Voltage angles, 1-phase, according to [1] voltage angle [deg] BFS phase A-B BFS phase B-C BFS phase C-A bus (b) Voltage angles, 3 phases Figure 2.3: Voltage angles at all the buses for a symmetrical single-phase (top) and a 3-phase (bottom) representation

18 8 CHAPTER 2. POWER FLOW CALCULATIONS IN DNS voltage magnitude [p.u.] BFS phase A-B BFS phase B-C BFS phase C-A 1-phase reference bus (a) Voltage magnitudes, 1 phase and 3 phase without phase interference voltage angle [deg] BFS phase A-B BFS phase B-C BFS phase C-A 1-phase reference bus (b) Voltage angle, 1phase and 3 phases without phase interference Figure 2.4: Voltage magnitudes and angles at all the buses, considering all three phases but without mutual interference, compared to the 1-phase reference of [1]

19 2.3. CASE STUDY I: POWER FLOW CALCULATIONS IN DNS node time [h] (a) Voltage magnitudes (p.u.) 150 thermal loading [%] branch (b) Thermal loadings Figure 2.5: Voltage magnitudes and thermal loadings for an uncontrolled 1-phase system, based on [1]

20 10 CHAPTER 2. POWER FLOW CALCULATIONS IN DNS

21 Chapter 3 Optimal Power Flow Calculations in DNs To make sure that the network constraints are not violated, the system needs to be controlled. Optimal Power Flow (OPF) is a widely used tool in this context. In this project, an Optimal Power Flow algorithm for unbalanced distribution grids was set up and investigated. The algorithm is an extension of [1] and basically consists of two main steps processed in an iterative manner: First, a multi-period OPF is run to calculate optimal set-points of DERs in the system. Second, an iterative PF computation using BFS (as described in Chapter 2) is run until convergence to determine the solution states of the system (Fig. 3.1). What has been modified as compared to [1] is that 3 phases have been considered in the PF computation, making the algorithm applicable to unbalanced loading. 3.1 Optimal Power Flow Fundamentals Optimal Power Flow is a powerful tool which is used to calculate DERs optimal set-points in the context of this project. It works on the optimization of an objective function under given constraints. Usually, the objective is a cost function and to be minimized: min u c(x, u) where u is the control vector (i.e., the DERs set-points) and x is the state vector (i.e. the bus voltage magnitudes and angles). The control vector u is optimized over the objective function Objective Function In our case, the cost function is based on cost of APC and RPC, which are assumed to account for the overall cost of DER control to guarantee a safe 11

22 12 CHAPTER 3. OPTIMAL POWER FLOW CALCULATIONS IN DNS Figure 3.1: Proposed operational planning scheme, based on [1] grid, and on the network losses [1]. For a multi-period OPF, the objective function is summed over the entire time horizon N hor and over all buses N bus and branches N branch : N hor min u t=1 N bus (c T P P curt,j,t + c T Q Q ctrl,j,t ) + j=1 N branch i=1 c T P P loss,i,t t where P curt,j,t is the curtailed active power at node j and time t and Q ctrl,j,t the reactive power support, c T P and ct Q represent the cost of curtailing active power and supplying reactive power, respectively. Reactive power control is usually the preferred option. P loss,i,t accounts for the power losses in branch i at time t Power Balance Constraints Power balance constraints create a relation between injected and withdrawn powers from the network. They are set up for both active and reactive power: P f inj,j,t = P f gen,j,t P f charge flex.load,j,t (PB,j,t P discharge B,j,t ) Q f inj,j,t = Qf gen,j,t P f flex.load,j,t tan(arcos(pf)) where P f inj,j,t is the flexible power injected at node j and time t, P f gen,j,t describes generated power, P f flex.load,j,t consumed power and P B the power charged to or discharged from a battery, respectively. The reactive power

23 3.2. CASE STUDY II: OPF 13 balance is based on flexibly generated reactive power (Q f gen,j,t ) and consumed reactive power, which is determined from consumed active power via the power factor Power Quality Constraints Power quality constraints make sure the system parameters stay within acceptable limits. These usually comprise voltage and current constraints: V min V bus,j,t V max V slack = 1, θ 1 = 0 I br,i,t I i,max where V bus,j,t is the voltage magnitude at bus j and node t, V min and V max are given voltage constraints, V slack and θ 1 are the reference voltages at the slack bus and I br,i,t is the current magnitude in branch i at time t, limited by a maximal branch current I i,max. In addition to the constraints mentioned above, there can also be further constraints such as on load tap changer (OLTC) constraints, controllable load constraints, battery energy storage system (BESS) constraints etc. [1] OPF Calculation Specifications in this Project Optimal Power Flow typically considers the full, non-linear AC power flow equations. If the inter-temporal constraints that come with active measures such as BESS and controllable loads and the integer variables of OLTC and controllable loads are considered as well, the problem can easily get computationally very intensive [1]. To avoid that within the context of this project, the full PF equations within the OPF problem are approximated with a single BFS iteration. After the OPF solution, which determines optimal DERs set-points, an exact BFS power flow computation under these set-points returns the precise solution state of the system. 3.2 Case Study II: OPF Results Using the same setup as presented in section and employing the algorithm introduced in Chapter 3 and depicted in Fig. 3.1, the results illustrated in Fig were obtained. Comparing these results to the case without control (shown in Fig. 2.5),

24 14 CHAPTER 3. OPTIMAL POWER FLOW CALCULATIONS IN DNS node time [h] (a) Voltage magnitudes (p.u.), 1 phase with control node time [h] (b) Voltage magnitudes (p.u.), 3 phases with control Figure 3.2: Voltage magnitudes after OPF-BFS at all the buses for a symmetrical single-phase (top) and a 3-phase (bottom) representation

25 3.2. CASE STUDY II: OPF node time [h] (a) Reactive power generation (%), 1 phase node time [h] (b) Reactive power generation (%), 3 phases Figure 3.3: Reactive power control in form of reactive power generation at all the buses for a symmetrical single-phase (top) and a 3-phase (bottom) representation

26 16 CHAPTER 3. OPTIMAL POWER FLOW CALCULATIONS IN DNS node time [h] (a) PV curtailment (%), 1 phase node time [h] (b) PV curtailment (%), 3 phases Figure 3.4: Active power control in form of PV curtailment at all the buses for a symmetrical single-phase (top) and a 3-phase (bottom) representation

27 3.2. CASE STUDY II: OPF 17 both currents and voltages are brought under acceptable thresholds using active measures. Fig show the voltage magnitude, APC and RPC profiles over all nodes and hours for the specified worst-case day. The figures cannot be interpreted separately because of their cross-dependencies (i.e., control measures influence voltage magnitudes and vice versa). Furthermore, in each figure the 3-phase results obtained in this project are plotted together with the 1- phase reference following the algorithm of [1]. The resulting patterns show clear similarities for 1-phase and 3-phase, however with some non-negligible differences. These will be discussed in the following Discussion During the problematic hours 9-18, voltages rise up to 1.04 p.u. (which is the upper voltage constraint) both for 1-phase (according to [1]) and 3-phase OPF-BFS computation. Highest voltages are experienced at PV nodes and nodes close to PV injection. The 3-phase OPF shows voltages dropping below 0.8 p.u. at certain nodes at night. This is an effect of the 3-times higher total load applied in the 3-phase calculation. In order to better observe the critical hours, every phase in the 3-phase system was loaded with the same load as was the single phase in 1-phase calculation. At hours where PV infeed is low, this leads to significantly higher voltage drops and thus a voltage constraint relaxation has been performed in order to still get a feasible result. In real system operation, however, undervoltages of that degree are not tolerable and this issue would need to be addressed. Apart from the lower voltage constraint, 1-phase computation and 3-phase computation yield similar but not equal results for the different nodes. Even the three phases amongst each other don t show uniform results but usually slightly lower voltages on phase b-c than on phases a-b and c-a. The phase differences have to do with the line impedance matrix, which contains equal impedances for phases a-b and c-a but different self- and mutual impedances in relation with phase b-c (figure 3.5). Comparing 1-phase results to 3-phase results, it can be observed between hours 9-18 that the voltages lie around the same value, phases a-b and c-a being a bit higher than the 1-phase voltage and phase b-c a bit lower. The lower voltage on phase b-c stands in connection with some heavy PVcurtailment at node 19 mostly on phase b-c, which might reduce the voltage on that phase over the whole system. The most significant difference between the 1-phase and the 3-phase results lies with node 12, where 1-phase computation gets to substantially lower voltages than 3-phase. This is an effect of the higher degree of PV curtailment at node 12 with 1-phase OPF (Fig. 3.4 (a)). Reactive Power Control is generated at all PV nodes, i.e. nodes 12, 16,

28 18 CHAPTER 3. OPTIMAL POWER FLOW CALCULATIONS IN DNS (a) line impedance matrices, 1- phase (b) line impedance matrices, 3-phase Figure 3.5: Line impedance matrices used in the 1-phase (left) and 3-phase (right) calculation. The two impedance matrices per system correspond to two different line types. 18 and 19. During the hours experiencing overvoltages, RPC is mostly fully exploited both for 1-phase and 3-phase OPF-BFS. This is due to the fact that RPC is economically preferred to APC, so that APC is only applied if RPC is not sufficient to control the voltage. Fig. 3.3 and 3.4 nicely show that RPC is used during the problematic hours 9-18 (3-phase) or (1-phase). APC is rolled out one hour later, when RPC is already fully exploited but PV infeed still rises, and it is stopped again an hour before RPC because in that hour 18 (3-phase) or 17 (1-phase), RPC can make up for the overvoltages on its own. During the hours with little reactive power generation, that is the transition hours, there is only RPC on phases a-b and c-a and none on phase b-c. Since voltages are also lower on phase b-c, it can be assumed that this is an effect of phase interference and that, apparently, phase interference works mostly for the benefit of b-c. Comparing 1-phase results to 3-phase results, 1-phase OPF-BFS results in less RPC because reactive power compensation starts later and ends earlier. This, however, is simply due to voltages being generally lower at hours 9 and 18 with 1-phase computation. 1-phase OPF-BFS resulted in excessive APC at node 12 during the afternoon hours while curtailing only a little percentage at nodes 16 and 18 and none at all at node 19. With 3-phase OPF, these differences are levelled out a bit more: PV at nodes 12, 16, 18 and 19 are all curtailed to a rather small degree, and not in every phase uniformely. As has been observed previously, phase b-c shows a different pattern than the other two phases, resulting in slightly less curtailment at all nodes apart from node 19, where there is heavy curtailment in phase b-c, accounting for many of the phase differences observed hitherto. The fact that there is significantly more APC at node 12 in the 1-phase calculation than in the 3-phase system explains the lower voltages at node 12 observed for 1-phase before. As has also been mentioned, APC generally takes place when RPC is fully exploited, and is peaking at hours

29 3.2. CASE STUDY II: OPF 19 What seems to have no influence on the (over-)voltages is the BESS installed at node 16. That is simply due to the fact that the battery has a small capacity of only 2.7kWh and it reaches its maximal state of charge at hour 8 already. To make sure the differences in the results of 1-phase and 3-phase OPF-BFS don t base on algorithm disparities but on the different character of 1-phase symmetrical components and 3-phase unbalanced systems, a test run with self-impedances in the impedance matrices only has been performed, just as what has been done for the BFS only in Fig The resulting patterns are plotted in Fig The results are completely identical.

30 20 CHAPTER 3. OPTIMAL POWER FLOW CALCULATIONS IN DNS node time [h] (a) Voltage magnitudes (p.u.), 1-phase calculation according to [1] node time [h] (b) Voltage magnitudes (p.u.), 3-phase calculation without phase interference Figure 3.6: Voltage magnitudes at all the buses and hours, considering all three phases but without mutual interference (no off-diagonal elements in the impedance matrix), compared to the 1-phase reference of [1]

31 Chapter 4 Conclusion This paper proposes a multi-period optimal power flow algorithm for unbalanced distribution grids, using the backward-forward sweep technique. It provides an approach to efficiently use system controls in order to stabilize system operation and can thus be used in the operational planning of distribution networks. This in turn enables a more efficient use of infrastructure because operational control measures replace network reinforcement for congestion relaxation to a certain degree [7]. The suggested algorithm has been applied to a Cigre benchmark system [6] and the most important results presented in the case study. The patterns and relationships of voltages, reactive power control and activer power curtailment over the whole system and a worst-case summer day are discussed and compared with the results obtained by a 1-phase symmetrical calculation as has been proposed by [1]. It can be seen that the results show some non-negligible differences due to phase-interference. Future work would need to take into consideration more constraints and elaborate on algorithm performance. 21

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33 Bibliography [1] S. Karagiannopoulos, L. Roald, P. Aristidou, and G. Hug, Operational Planning of Active Distribution Grids under Uncertainty, [2] J. H. Teng, A direct approach for distribution system load flow solutions, IEEE Transactions on Power Delivery, vol. 18, no. 3, pp , [3] P. Kotsampopoulos, N. Hatziargyriou, B. Bletterie, and G. Lauss, Review, analysis and recommendations on recent guidelines for the provision of ancillary services by Distributed Generation, Intelligent Energy Systems (IWIES), 2013 IEEE International Workshop on, pp , [4] R. Tonkoski, L. A. C. Lopes, and T. H. M. El-Fouly, Coordinated active power curtailment of grid connected PV inverters for overvoltage prevention, IEEE Transactions on Sustainable Energy, vol. 2, no. 2, pp , [5] G. Hug, Power System Analysis, lecture notes, ETH Zurich, [6] K. Strunz, E. Abbasi, C. Abbey, C. Andrieau, F. Gao, T. Gaunt, A. Gole, N. Hatziargiou, and R. Iravani, Benchmark Systems for Network Integration of Renewable and Distributed Energy Resources, CIGRE, Task Force C6.04, no. 273, pp. 4-6, [7] S. Karagiannopoulos, P. Aristidou, and G. Hug, Hybrid approach for planning and operating active distribution grids, IET Generation, Transmission & Distribution, pp. 1-23, Feb