A Novelty Approach of Static odeling using Controllers for Voltage Stability Analysis B. Radha adhavi 1, Cholleti Sriram 2 1 Assistant Professor, EEE Department, Brilliant Group of Institutions, Hyderabad, Telangana, India 2 Assistant Professor, EEE Department, Guru Nanak Institute of Technology, Hyderabad, Telangana, India 1 madhavibendapudi@gmail.com, 2 cholletisriram6@gmail.com Abstract: Voltage stability is the ability of a power system to maintain steady voltages at all buses in the system under normal operating conditions, after being subjected to a disturbance. If the bus does not maintain the steady state value, is called the voltage instability that may result in the form of a disruptive fall or rise of voltages of few buses. Power System modeling is a technique used to model the power system and necessary for voltage stability studies. In this paper, analyzed the modeling parameters of various loads for voltage stability studies using a novelty approach of Cat Swarm Optimization Technique and performed static load modeling study. The accuracy of the results of voltage stability are directly related to the load models used in this analysis. The effectiveness of the proposed method is demonstrated through quantitative studies on standard IEEE 14 bus system using different static load models. The method is analyzed using Continuation power flow routine. A technology with a combination of heuristic approach is applied to give a solution for the problem in this paper. Keywords: Cat Swarm Optimization, Controllers, Static odeling, Voltage Stability. 14 I. INTRODUCTION Power System Stability is a very complex subject that has been challenging the power system engineers in the past two decades. Due to the continuous expansion of power systems to cater the needs of growing population, power system stability problems are considered a continuous and fascinating area of study [1]. When a bulk power transmission network is operated close to the voltage stability limit, it becomes difficult to control the reactive power demand for that system.voltage stability is of major concern in power systems stability. ain reason for the cause of voltage instability is the sag in reactive power at various locations in an interconnected power system. Voltage Stability is a problem related to power systems which are heavily loaded, faulted or have a shortage of reactive power. The problem of voltage stability concerns the whole power system, although it usually has a large involvement in one critical area of the power system. Voltage stability is concerned with the ability of a power system to maintain steady voltages at all buses in the system under normal operating conditions, and after being subjected to a disturbance. Instability that may occurs in the form of a progressive fall or rise of voltage of some buses. The Possible outcome of voltage instability results in loss of integrity of the power system [2]. Power System modelling is a technique used to model the power system and essential for stability assessments. In this project we are trying to analyse modelling parameter inputs to loads for voltage stability studies. Different load models would greatly affect voltage stability aspect of an interconnected power system. We are using continuation power flow to simulate PV curves to analyse the effects of different load models and compare the results [10].To analyse the maximum loading parameter and bus voltage magnitude profile aspects, we are modelling the power system with different types of loads. The effects of these loads are studied for various conditions. A solution is given to mitigate the harmful effects on the voltage stability criterion on the power system using controllers and Heuristic approach. The paper [6] uses continuation power flow to simulate P-V curves to analyse the effects of different load models and system operating constrains on power system static voltage stability. This paper also presents a new contingency parameterization continuation power flow model for faulty steady analysis and the accuracy and correctness of the results of voltage stability are directly related to the load models used in analysis. Optimization techniques find a variety of use in many fields. As Artificial intelligence techniques are improving day by day, the use of these techniques in power systems is playing an important role for the optimal location of controllers. We are using Cat Swarm Optimization (CSO) to identify the location and size of controllers [10].The simulation study and analysis is performed on IEEE 14 bus network. The outline of the paper is as follows: Section II discusses about different types of load models. Section III discusses about Controllers. Section IV presents a new approach i.e Cat Swarm Optimization Section V discusses about IEEE 14 bus system and software used and Section VI presents case study, test results and discussions of the proposed approach and section VII concludes the paper. II. POWER SYSTE LOAD ODELLING Power System odelling is a technique used to model the power system and essential for stability assessments. Accurate modelling of loads continues to be a difficult task due to several factors, for examples, lack of precise information on the composition of the
load, changing of load composition with time delay and week, seasons, weather, through time and more[4]. Electric utility analysts and their management require evidence of the benefits of improved load representation in order to justify the effort and expense of collecting and processing load data, as well as to modify computer program load models. The interest in load modelling has been continuously increasing in the last years, and power system load has become a new research area in power systems stability. Several studies have shown the critical effect of load representation in voltage stability studies, and therefore the need of finding more accurate load models than the traditionally used ones. A. Static odelling: These models express the active and reactive powers, at any instant of time, as a function of the bus voltage magnitude and frequency. Common static load models for active and reactive power are expressed in a polynomial or an exponential form, and can include, if it is necessary, a frequency dependence term[6],the static load models have been used for a long time for both purposes, to represent static load components, such as resistive and lighting loads, but also to approximate dynamic components. A brief description of static load models is given below. B. Zip or Polynomial odel: The static characteristics of the load can be classified into constant power, constant current and constant impedance load, depending on the power relation to the voltage. For a constant impedance load, the power dependence on voltage is quadratic, for a constant current it is linear, and for a constant power, the power is independent of changes in voltage [6]. C. Constant Impedance odel: In this model, active and reactive power injections at a given load bus vary directly with the square of nodal voltage magnitude. This model is also called constant admittance model. P = f (v 2 ) (1) Examples for constant impedance loads are residential loads such as refrigerators and washing machines and lighting loads such as bulbs etc. D. Constant Current odel: In this model, the active and reactive power injections at a given load bus vary directly with the nodal voltage magnitude. P = f(v) (2) Examples for constant current load are transistors, transducers and incandescent lamps e.t.c. E. Constant Power odel: 15 Here, the power of load bus is assumed to be constant and does not vary with nodal voltage magnitude. P = k (3) where k is constant Its active and reactive power models are given below: P = P 0 [a(u/u 0 )2 + b p (U/U 0 ) +c p ] (4) Q = Q 0 [a q (U/U 0 )2 + b q (U/U 0 ) +c q ] (5) Where Q 0, P 0 are power consumed by load at referent voltage, then we can get the following equations: a p + b p + c p = a q +b q +c q = 1 (6) Through changing the coefficients, we may realize a host of ZIP loads. Examples for constant power loads are switching regulators, industrial loads such as motor loads with constant speed etc. F. Exponential odel: In exponential load model the active and reactive power injections of load bus are related to bus voltage through exponential function. P = P 0 (U/U 0 )α (7) Q = Q 0 (U/U 0 )β (8) Where: U 0 is referenced or rated voltage, P 0, Q 0 are powers consumed in rated voltage and indexes α, β change according to different load types. The following three load models are vital: Constant impedance model (Z ), when α=β=2; Constant current model (I ), when α=β=1; and Constant power model (P ), when α=β=0. G. Frequency Dependent odel: A static load model which includes frequency dependence is called a frequency dependent load. This is usually represented by multiplying either a polynomial or exponential load model by a factor including the frequency deviation and the frequency sensitivity parameter. The factor is usually in the following form: 1 + a f (f - f 0 )] (9) where f is the frequency of the bus voltage, f0 is the rated frequency, and a f is the frequency sensitivity parameter of the model. Examples for frequency dependent loads are refrigerators, freezers, air conditioners, water heaters, pumps and ovens. H. Voltage Dependent odel: A voltage dependent load is an electrical device whose power consumption varies with the voltage being supplied to it. Examples for voltage dependent loads are the most common types of incandescent lamps are standard tungsten filament, tungsten halogen and reflector lamps and motor loads.
III. CONTROLLERS Introducing controllers is the most effective way for utilities to improve the voltage profile and voltage stability margin of the system. The devices that are used are Thyristor Controlled Series Compensator (TCSC), whereas VSI are the Static Var Compensator (STATCO), the Static Synchronous Source Series Compensator (SSSC) and the Unified Power Flow Controller (UPFC). Each model is described by a set of differential algebraic equations: X c = f c (X c, X s, V, θ, u) (10) X s = f s (X c, X s, V, θ) (11) P = g p (X c, X s, V, θ) ; Q = g p (X c, X s, V, θ) (12) (SA) etc. Some of these optimization algorithms were developed based on swarm intelligence. Cat Swarm Optimization (CSO), the algorithm, is motivated from PSO and ACO. According to the literatures, PSO with weighting factor usually finds the better solution faster than the pure PSO, but according to the experimental results, Cat Swarm Optimization (CSO) presents even much better performance [11]. Via observing the behavior of creatures, we may get some idea for solving the Optimization problems. By studying the behavior of ants achieves ACO, and with examining the movements of the flocking gulls realizes PSO. Through inspecting the behavior of cat, we present Cat Swarm Optimization (CSO) algorithm. Where X c are the control system variables, X s are the controlled state variables (e.g. firing angles), and the algebraic variables V and θ are the voltage amplitudes and phases at the buses at which the components are connected, they are vectors in case of series components. Finally, the variables u represents the input control Parameters, such as reference voltages or reference power flows. Shunt components, i.e. SVCs, STATCOs and UPFCs, require a PV generator to be properly initialized. In the case of UPFCs, the PV generator must be placed at the sending end bus. SVC, TCSC, STATCO, SSSC and UPFC models have an additional stabilizing signal V pod which is the output of the Power Oscillation Damper. The controller used in the paper is UPFC (Unified power flow controller). A. Unified Power Flow Controller: The UPFC is a combination of an STATCO and an SSSC, sharing a common dc link as shown in figure 2. The UPFC can control both the active and reactive power flow in the line. It provides independently controllable shunt reactive compensation [8]. The UPFC is a two-port circuit (in series with a transmission line and parallel with a bus bar). The series voltage source and the shunt current source are defined as follows: v S = (v p + v q ) ejφ = r V k e jγ (13) i SH = (i p + i q ) e j θ k (14) IV. Fig. 1. UPFC Controller CAT SWAR OPTIIZATION In the field of optimization, many algorithms were being proposed recent years, e.g. Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), and Simulated Annealing Fig. 2. Flow Chart of Cat Swarm Opimization V. IEEE 14 BUS SYSTE AND SOFTWARE The block diagram of IEEE 14 bus network and the components used in the network shown in the figure. There are 6 load buses and for these load buses static and dynamic loads are connected for modeling, the remaining buses are generator buses and one slack bus. It consists of five synchronous machines with IEEE type-1 exciters, three of which are synchronous compensators used only for reactive power support. There are 11 loads in the system totalling 259 W and 81.4 VAR. The dynamic data for the generators exciters was selected from past. Automatic voltage regulator, turbine governor, power system stabilizer controllers were also added to the system, as shown in Figure, to study their effect in the system and their interactions. 16
Fig. 3. IEEE 14 Bus System PSAT is a ATLAB toolbox for electric power system analysis and control. PSAT includes power flow, continuation power flow, optimal power flow, small signal stability analysis and time domain simulation. All operations can be assessed by means of graphical user interfaces (GUIs) and a Simulink-based library provides a user friendly tool for network design [3]. VI. RESULTS AND DISCUSSIONS A. Voltage Stability Analysis using Static odels: Bus No Table I. Bus Voltages for Different s V(p.u) V(p.u) V(p.u) V(p.u) ZIP load Vol Dep Freq Dep Exp Rec Bus 1 1.0566 1.0566 1.0572 1.057 Bus 2 0.8926 0.8892 0.91956 0.9117 Bus 3 0.7593 0.7409 0.76727 0.7522 Bus 4 0.7375 0.7409 0.81655 0.8035 Bus 5 0.7621 0.7676 0.84161 0.8298 Bus 6 0.8192 0.8363 0.94378 0.9328 Bus 7 0.7897 0.8022 0.91208 0.8994 Bus 8 0.9351 0.943 1.0099 1.0024 Bus 9 0.7291 0.7459 0.89255 0.8773 Bus 10 0.7239 0.7423 0.89501 0.8796 Bus 11 0.7611 0.7796 0.91591 0.9023 Bus 12 0.7733 0.794 0.92785 0.915 Bus 13 0.756 0.7781 0.92092 0.9072 Bus 14 0.6882 0.7135 0.88901 0.8722 From the above table we can observe, the voltages at the marked buses are less, so we considered these buses as weakest buses and controllers are incorporated at these specified buses for each load to achieve the objective function for load modeling. B. Voltage Stability Analysis using Controllers: 1) Zip : profile and maximum loading parameter for zip load when 3 UPFC S are used in the location 14-13, 5-4, and 14-9. Bus No. Table II. Bus Voltages for Zip V(p.u) (with ZIP without V(p.u) (with ZIP with 1 1.0566 1.0556 2 0.89264 0.89264 3 0.75932 0.7788 4 0.73748 1.045 5 0.76214 0.9483 6 0.81924 0.99631 7 0.78969 1.051 8 0.93511 1.0826 9 0.72905 1.0451 10 0.72392 1.0066 11 0.76108 0.9881 12 0.77332 0.96501 13 0.75599 0.97184 14 0.68821 1.0955 2) Voltage Dependent : 2.653 4.0333 profile and maximum loading parameter for VD load when 3 UPFC S are used in the location 14-13, 5-4, and 14-9. Bus No. Table III. Bus Voltages for VD V(p.u) (with VD without V(p.u) (with VD with 1 1.0566 1.0556 2 0.88923 0.88478 17
3 0.74094 0.77537 4 0.74086 1.045 5 0.76757 0.9484 6 0.83625 0.99748 7 0.80221 1.0516 8 0.94304 1.083 9 0.74587 1.046 10 0.74231 1.0079 11 0.77959 0.98957 12 0.79402 0.96743 13 0.77805 0.97331 14 0.71354 1.0972 3) Frequency Dependent : 18 2.7571 4.0401 profile and maximum loading parameter for FD load when 3 UPFC S are used in the location 04-05, 14-09, and 09-10. Bus No. Table IV. Bus Voltages for FD V(p.u) (with FD without V(p.u) (with FD with 1 1.0572 1.0588 2 0.91956 0.95597 3 0.76727 0.65951 4 0.81655 1.045 5 0.84161 1.0332 6 0.94378 0.99559 7 0.91208 1.0955 8 1.0099 1.1084 9 0.89255 1.118 10 0.89501 1.045 11 0.91591 1.0138 12 0.92785 0.96621 13 0.92092 0.98549 14 0.88901 1.045 4) Exponential Recovery : 3.1718 4.6352 profile and maximum loading parameter for ER load when 3 UPFC S are used in the location 04-05, 14-09, and 09-10. Bus No. Table V. Bus Voltages for ER V(p.u) (with ER without V(p.u) (with ER with 01 1.057 1.0588 02 0.91165 0.95654 03 0.75224 0.66297 04 0.80345 1.045 05 0.82977 1.0332 06 0.93282 0.99575 07 0.89938 1.0967 08 1.0024 1.1091 09 0.87733 1.1207 10 0.87959 1.045 11 0.90226 1.0134 12 0.91496 0.96541 13 0.90724 0.98542 14 0.87218 1.045 5) Consolidated Result: Table VI. Bus Voltages for Different s 3.14 4.6347 s Zip Voltage Dependent Frequency Dependent Exponential Recovery out out out out Bus 04 0.7375 1.0450 0.7409 1.0450 0.8166 1.0450 0.8035 1.0450 Bus 05 0.7621 0.9483 0.7676 0.9484 0.8416 1.0332 0.8298 1.0332 Bus 09 0.7291 1.0451 0.7459 1.0460 0.8926 1.1180 0.8773 1.1207 Bus 10 0.7239 1.0066 0.7423 1.0079 0.8950 1.0450 0.8796 1.0450 Bus 13 0.7560 0.9718 0.7781 0.9733 0.9209 0.9855 0.9072 0.9854 Bus 14 0.6882 1.0955 0.7135 1.0972 0.8890 1.0450 0.8722 1.0450
L.P 2.6530 4.0333 2.7571 4.0401 3.1718 4.6352 3.1400 4.6347 VII. CONCLUSION World Academy of Science, Engineering and Technology 2009. This paper presented here gives a study and analysis of different static load models by using continuous power flow method for voltage stability analysis. The different load models show an impact of instability in the system for which a solution is given using controllers. A method is also presented to determine the optimal location and size of controllers to enhance the power system voltage stability. This method is based on cat swarm optimization (CSO). This algorithm was found to be easy in implementing in comparison with earlier AI techniques. It is capable of finding multiple optimal solutions to the constrained multi objective problem, giving more flexibility to make the final decision about the location of the controllers. The maximum loading parameter, bus voltage profile improvement and size of controller are employed as the measure of power system performance in optimization algorithm. On conclusion, paper presents an advanced technique to address stability issues in large power systems, which consist of various loads. Also CSO algorithm as compared with PSO has a significant advantage, by giving better solutions with less computational effort when applied with controllers. 19 VIII. REFERENCES [1] Wen Zing Adeline Chan, Power System odelling, The School of Information Technology and Electrical Engineering, The University of Queensland, Oct 2003. [2] Voltage Stability of Power systems concepts, Analytical Tools and Industry Experience, IEEE Committee Vol.IEEE/PES 93TH0358-2-PWR 1990. [3] Cheng-Hong Gu, Qian Ai, Jiayi Wu, A Study of Effect of Different Static odels and System Operating Constrains on Static Voltage Stability, Proceedings of the 5th Wseas/IASE Int. Conf. on Systems Theory and Scientific Computation, alta, September 15-17, 2005 pp(44-49). [4] Sameh Kamel ena Kodsi, Claudio A. Canizares, odelling and Simulation of IEEE 14 Bus System with Controllers, Technical Report 2003. [5] Alok Kumar ohanty, Amar Kumar Barik, Power System Stability Improvement Using Controllers, International Journal of odern Engineering Research (IJER), Vol.1, Issue.2, pp-666-672, ISSN: 2249-6645. [6] ehrdad Ahmadi Kamarposhti, ostafa Alinezhad, Comparison of SVC and STATCO in Static Voltage Stability argin Enhancement, [7] ehmet B, Keskin, Continuation Power Flow and Voltage Stability in Power Systems, A Thesis Submitted to the Graduate School of Natural and Applied Sciences of iddle East Technical University. [8] Jong-Ching Hwang, Jung-Chin Chen, J.S. Pan, CSO and PSO to Solve Optimal Contract Capacity for High Tension Customers, Department of Electrical Engineering National Kaohsiung University of Applied Sciences Kaohsiung, Taiwan, Department of Industrial anagement National Pingtung University of Science and Technology. [9] Kalaiselvan. G, Lavanya.A, Natrajan, Enhancing the Performance of Watermarking Based on Cat Swarm Optimization ethod, IEEE-International Conference on Recent Trends in Information Technology, ICRTIT 2011, IT, Anna University, Chennai. June 3-5, 2011.