Optimal location of FACTS devices in a power system solved by a hybrid approach

Nonlinear Analysis 65 (2006) 2094–2102 www.elsevier.com/locate/na

Optimal location of FACTS devices in a power system solved by a hybrid approach J. Baskaran a,∗ , V. Palanisamy b,1 a Electrical Department, Government College of Engineering, Anna University, Salem-636011, Tamil Nadu, India b Government College of Technology, Coimbatore, Tamil Nadu, India

Abstract In this paper, a non-traditional optimization technique, a Micro-Genetic Algorithm (MGA) is conjunction with Fuzzy Logic (FL), is used to optimize the various process parameters involved in the introduction of FACTS devices in a power system. The various parameters taken into consideration were the location of the devices, their type, and their rated value. The simulation was performed on a 30-bus power system with various types of FACTS controllers, modeled for steady state studies. The optimization results are compared to the solution given by another search method. This comparison confirms the efficiency of the proposed method, which makes it promising for solving combinatorial problems of FACTS device location in a power system network. c 2006 Elsevier Ltd. All rights reserved. 

1. Introduction In a power system network, the transmission interconnection is essential for power delivery, apart from pooling power plants and load centers in order to minimize the total power generation capacity and fuel cost. Advantages of interconnections are diversity of loads, availability of sources, and as regards fuel price in order to supply electricity to the loads at minimum cost with a required reliability. By deregulation of electricity markets, the traditional concepts and practices of power systems have been changed. This leads to Flexible AC Transmission Systems (FACTS) such as Thyristor Controlled Series Compensations (TCSC), Thyristor Controlled Phase Angle ∗ Corresponding author.

E-mail addresses: [email protected] (J. Baskaran), [email protected] (V. Palanisamy). 1 Principal, Government College of Technology, Coimbatore, Tamil Nadu, India. c 2006 Elsevier Ltd. All rights reserved. 0362-546X/$ - see front matter  doi:10.1016/j.na.2005.11.052

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

2095

Regulators (TCPAR), Unified Power Flow Controllers (UPFC) and Static Var Compensators (SVC). These devices control the power flows in the network, reducing the flow in heavily loaded lines, thereby resulting in an increase loadability, low system losses, improved stability of the network and reduced cost of production [2–4,6]. It is more important to ascertain the location of these devices because of their significant costs. Jerbex et al. [15] provides an idea regarding the optimal locations of FACTS device, without considering the investment cost of FACTS devices and their impact on the generation cost. Cai et al. [13] later studied the optimal location considering the generation cost of the power plants and the investment cost of the devices. The main objective of this paper is to develop an algorithm for finding and choosing the optimal location of FACTS devices, based on power loss reduction, which is to be maximized. The different types of FACTS device and their different locations have different advantages. For the proposed objective function, the suitable types of FACTS devices, their location, and their rated values must be determined simultaneously. This combinatorial analysis problem is solved by a hybrid method. This paper is organized as follows. Following the introduction, different FACTS device mathematical models are described in Section 2. Then in Section 3, objective functions are described. In Section 4, the proposed method for optimal location of FACTS devices is discussed in detail. The simulation results are given in Section 5. Finally, a brief conclusion appears in Section 6. 2. Mathematical model of a FACTS device 2.1. FACTS device In an interconnected power system network, power flows obey Kirchhoff’s laws. The resistance of the transmission line is small compared to the reactance. Also the transverse conductance is close to zero. The active power transmitted by a line between the buses i and j may be approximated by the following relationships: Pi j = (Vi V j / X i j ) sin δi j where Vi and V j are voltages at buses i and j ; X i j are reactances of the line; δi j is the angle between Vi and V j . Under the normal operating conditions for a high voltage line, the voltage Vi = V j and δi j is small. The active power flow coupled with δi j and the reactive power flow are linked to the difference Vi − V j . The control of X i j acts on both active and reactive power flows. The different types of FACTS device have been chosen and located optimally in order to control the power flows in the power system network. The reactance of the line can be changed by TCSC. TCPAR varies the phase angle between the two terminal voltages and SVC can be used to control the reactive power. UPFC is the most powerful and versatile device, which controls the line reactance, terminal voltage, and the phase angle between the buses. In this paper, four different typical FACTS devices have been selected: TCSC, TCPAR, SVC and UPFC. Their block diagrams are shown in Fig. 1. The below mentioned FACTS controllers can be applied to control the power flow by changing the parameters of the power systems, so that the power flow can be optimized.

2096

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

Fig. 1. Block diagram of the FACTS controllers considered; (a) TCSC, (b) UPFC, (c) TCPAR, (d) SVC.

2.2. Mathematical models The power-injected model is a good model for a FACTS controller because it will handle them well in a load–flow computation problem. Since, this method will not destroy the existing impedance matrix z, it would be easy to implement in load–flow programs. In fact, the injected power model is convenient and sufficient for a power system with a FACTS controller. Mathematical models of the FACTS controller are developed mainly to perform steady state research. The TCSC, TCPAR, SVC and UPFC are modeled using the power injection method [1, 4,11,12]. Furthermore, the TCSC, TCPAR, SVC and UPFC mathematical models are integrated into the model of the transmission line. Fig. 1 shows a simple transmission line; the parameters are connected between bus i and bus j . The voltages and angles at the buses i and j are Vi , δi and V j , δ j respectively. The real and reactive power flows between the buses i and j can be written as the real and reactive power flows between the buses i and j as Pi j = Vi2 G i j − Vi V j × [G i j cos δi j + Bi j sin δi j ] Q i j = −Vi2 (Bi j + Bsh ) − Vi V j × [G i j sin δi j − Bi j cos δi j ] where the δi j = δi − δ j ; similarly, the real and reactive power flows between the buses j and i are P j i = V j2 G i j − Vi V j × [G i j cos δi j − Bi j sin δi j ] Q j i = −V j2 (Bi j + Bsh ) + Vi V j × [G i j sin δi j + Bi j cos δi j ]. TCSC. The model of a transmission line with TCSC connected between the buses i and j is as shown in Fig. 1; the change in the line flow is due to series reactance. The real and reactive power injection at buses i and j (Pic , P j c and Q ic , Q j c ) can be expressed as in [11]. The TCSC has a working range between −0.7X i j and 0.2X i j [2,3], where X i j is the reactance of the transmission line, where the TCSC is installed; X t CSC = Rv × 0.45 − 0.25. TCPAR. The voltage angle between the buses i and j can be regulated by TCPAR; the model of a TCPAR with a transmission line is as shown in Fig. 1. The injected real and reactive powers at

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

2097

buses i and j having the phase shifter are expressed in [11]. The working range of the TCPAR is between −5◦ and +5◦ . ϕTCPAR = Rv × 5 (deg). UPFC. A series inserted voltage and the phase angle of the inserted voltage can be modeled as the effect of UPFC on the network. The inserted voltage has a maximum magnitude of 0.1 Vm , where Vm is rated voltage of the transmission line, where the UPFC is connected. It is connected to the system through two coupling transformers [7,13]. The real and reactive powers injected at buses i and j can be expressed as in [13]. The working range of the UPFC is between −180◦ and +180◦. ϕUPFC = Rv × 180 (deg). SVC. The primary purpose of SVC is usually to control voltages at weak points in a network. This may be installed at the mid-point of the transmission line. At the given limit, the reactive power output of the SVC can be expressed as in [4,1,7]. The working range of the SVC is between −100M var and +100M var. The SVC has been considered as a reactive power source with the above limit. Q SVC = Rv × 100(M var). The exact loss formula of a system having N buses is [15] Pltc =

N
N


[α j k (Pi P j + Q j Q k ) + β j k (Q j Pk − P j Q k )]

J =1 K =1

where P j , Pk and Q j , Q k , respectively, are the real and reactive powers injected at bus j and α j k , β j k are the loss coefficients defined by α j k = (R j k /V j Vk ) cos(δ j − δk ) β j k = (R j k /V j Vk ) sin(δ j − δk ) where R j k is the real part of the j kth element of the [Zbus] matrix. If FACTS devices are used one at a time, the total loss can be written as follows [9]: Plk = Pltc − [Pic + P j c ]. Pic , P j c are injected real powers. 3. Objective function The aims of this, with the help of a FACTS device, is to ensure the quality of the power supply to the consumer, without overloaded lines and with an acceptable voltage level. The optimal location of FACTS devices problem is to increase as much as possible the capacity of the network, i.e. the loadability. In this work, the FACTS device has been considered for reducing the power loss. The objective function is Min

F(u), P L(V, δ, S) =

N


Plk

(1)

i=1

Subject to

f (b, v) = 0,

f 1(s) < m1,

f 2(v) < m2

2098

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

where u is a set of parameters that indicate the location, devices and rated values. Plk is the power loss difference between the cases without FACTS devices and with FACTS devices in a power system network. f (b, v) are conventional power flow equations; f 1(s) < m1 and f 2(v) < m2 are inequality constraints for FACTS devices and conventional power flows. The FACTS device can be used to change the power system parameters. These parameters give different results for the objective function (1). Also the various FACTS device locations, rated values and types have influences on the objective function. The above mentioned parameters are very difficult to optimize simultaneously by conventional optimization methods. To solve this type of combinatorial problem, the micro-genetic algorithm with fuzzy logic is proposed. The proposed methods are well developed and utilized effectively for this work, for which C computer codes are developed and simulated. 4. Micro-genetic algorithm A GA (genetic algorithm) is based on the global searches technique and the mechanisms of natural selection and genetics; GAs can search for several possible solutions simultaneously. A simple genetic algorithm is constituted by a random creation of an initial population and a cycle of three stages, namely: • evaluation of each chromosome, • chromosome selection for reproduction, • creation of a new population; this includes crossover and mutation. Each time this cycle is completed, it is said that a generation has occurred. The disadvantage of GAs is the high processing time consumption due to their evolutionary concept, based on random processes that cause the algorithm to be quite slow. However different methods are available for reducing the processing time; one of the methods, known as the micro-genetic algorithm approach, reduces the processing time considerably [7,10]. Most GAs produce poor results when populations are small because of insufficient information about the problem and convergence to a local optimum being obtained. Population size generally varies from 20 to 250 individuals. In general a Micro-Genetic Algorithm (MGA) can work with small populations (nearly 5 to 10 individuals) and this reduces the processing time. The frequent reproductions occurring inside a small population, where the desirable genetic characteristic emerges quickly, also avoid the mutation process because after a certain number of generations, the best chromosomes are maintained and the remaining ones are randomly selected generated ones. Accordingly, some numbers of individuals are selected for such a group, in which they are randomly coupled. Then, the grouping is repeated and individuals are selected to form couples to begin the crossover. The above work can be summarized in a flowchart. 4.1. Fuzzy logic In 1965, Zadeh proposed fuzzy logic; it has been effectively utilized in many fields of knowledge for solving control and optimization problems. In the power system area, it has been used in stability studies, load frequency control, unit commitment, and reactive compensation in distribution networks and other areas. The combination of fuzzy logic and the micro-genetic algorithm produces very good results, as presented in [5,8]. Further, it reduces the computation time also. In fuzzy logic, one looks for the main variables that control the decisions to be taken and also quantifies their values as regards relevance level. According to previously obtained information,

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

2099

(a) Bus voltage (p.u.).

(b) Power loss (p.u.). Fig. 2. Input relationship function. (a) Bus voltage. (b) Power loss.

Fig. 3. FACTS allocation.

the relationship function is established, rules are established and actions necessary to obtain a solution are determined. In this paper, rules are established for determining the advantage of having the FACTS device in the right location, or not. The bus voltage (BV) and power loss (PL) are the fuzzy variables; they are functions of each bus, used to verify where the FACTS devices are located. PL can be calculated for each bus; it indicates the sensitivity of the power loss reduction function as expressed in Eq. (1). It is essential for FACTS device location. Here, the fuzzy variable relationship functions are the same as in [6] (see Fig. 2). Those variables indicate lack of FACTS devices in the power system network and determine the allocation sensibility degree of each bus, as shown in Fig. 3. The fuzzy rules are established by considering first two extreme situations: (1) low bus voltage and high MPL, where FACTS devices are essential;

2100

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

Table 1 Fuzzy rules Voltage → Power loss ↓

Low

Medium low

Medium

Medium high

High

Low Medium low Medium Medium high High

Medium low Medium Medium Medium high High

Medium low Medium low Medium Medium high Medium high

Low Medium low Medium low Medium Medium

Low Low Low Medium low Medium low

Low Low Low Low Medium low

(2) high voltage and low PL, where FACTS device low attribute. The fuzzy rules are evaluated and listed in Table 1. 4.2. Hybrid method For this study, two stages are proposed. In the first stage fuzzy logic is applied to reduce the search space. The second stage follows a micro-genetic algorithm which works only with previously known buses. The hybrid method consists of the following steps. (1) Calculate the bus voltages and power considering a power system without FACTS devices. (2) Determine the bus voltage (BV) defined for each bus and the power loss (PL). (3) Apply fuzzy logic to determine the subgroup of buses in which the FACTS device locations have more advantages. (4) On the basis of the subgroup, randomly generate a P size population and go to step 6. (5) On the basis of the subgroup, randomly generate a P − 1 size population. (6) Determine the fitness function of each chromosome. (7) Carry out the crossover operation. (8) Calculate the fitness function value of the new chromosome. (9) Repeat steps 7 and 8 until the best chromosome is reached; print the best chromosome and discard the others. (10) Repeat steps 5 to 9 n times; the best individual is obtained after m consecutive generations. 5. Simulation results The power flow studies are carried out with the help of the AU Power software package. The simulation was carried out on an IEEE 30 Bus test system. It consists of 30 buses, 41 lines; generators are modeled as PV-nodes, loads are modeled as PQ-nodes; the line is modeled using the classical scheme. The modified IEEE 30 bus test system is used to verify the effectiveness of the proposed algorithm, whose line and load data can be found in [14]. The initial value of n facts , which indicates the number of FACTS devices to be simulated, is defined as 4: TCSC is 1, TCPAR is 2, UPFC is 3 and SVC is 4. The total number of generations is 200 and there are 16 individuals in each generation with crossover and mutation rates of 70% and 5% respectively. In the proposed optimization study for considering the power system network, the different types of FACTS device and their optimal locations allow reduction of the total real power losses. The solutions found by the hybrid method clearly indicate more locations; also the power loss reduction is efficient compared to the genetic algorithm (GA) and genetic algorithm with fuzzy logic (FGA) cases, as shown in Table A.1 in the Appendix.

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

2101

6. Conclusion In this paper, a proposed hybrid method is found to be more efficient for solving for the locations of a given number of FACTS devices in a power system; their type and rated values are simultaneously optimized. Four different types of device are simulated: TCSC, TCPAR, UPFC and SVC. The reduction of overall system real power loss significantly improves the system performance. This method reduces the search space and decreases the execution time; also it changes to reach the global optimal location. The hybrid approach results may have merit when compared to solutions obtained from other search methods (non-traditional methods). Future research may focus on the impact of the hybrid approach. Hybrid approaches deserve future investigation as well. The simulation results clearly indicate the efficiency of the proposed algorithm; also it simultaneously optimizes the location, type and rated values of the devices. This algorithm is suitable for searching for several possible solutions simultaneously. Further, this algorithm is practical and easy to implement into the power system. Appendix Table A.1 Locations of FACTS devices of different types Hybrid method Line Device Rated value

1 3 4 5 6 8 9 11 14 15 18 19 20 22 24 26 30 32 34 35 36 37 41

3 1 4 1 4 3 3 3 1 1 1 2 3 2 4 3 2 3 1 3 3 2 4

105.12◦ −0.812 0.0521 −1.002 0.826 48.23◦ −22.78◦ 62.12◦ −0.127 0.212 0.201 24.21 168 2.317 0.891 1.620◦ −0.945 33.12◦ −0.732 26.21◦ 2.72◦ −0.761 0.321

% power loss reduction 0.891 3.23 11.210 8.12 0.926 1.99 0.7128 6.20 6.21 2.8167 6.72 48.23 14.956 48.72 83.71 9.816 22.81 6.012 0.891 3.217 10.931 11.70 21.72

FGA Line Device Rated value

1 4 5 8 9 12 15 18 19 21 22 26 30 32 34 36 38 39 41

3 4 1 3 3 3 3 1 2 3 2 3 2 1 3 3 3 1 4

98.55◦ 0.0699 −0.1766 37.69◦ −15.66◦ −28.56◦ 28.78◦ 0.1848 22.005◦ 11.88◦ 2.210◦ 183.47◦ −0.8145 0.0864 136.54◦ 1.620◦ 18.252◦ 0.0743 0.4499

% power loss reduction 0.212 0.9438 0.7728 0.5335 0.445 2.067 1.7128 6.20 41.987 2.8167 47.198 0.4236 14.956 2.067 21.928 9.816 40.89 8.574 19.003

GA Line Device Rated value

3 5 9 10 11 14 20 22 24 25 35

1 1 3 1 3 1 3 2 4 1 3

−0.4322 −0.4345 −117.08◦ 0.2589 53.69◦ 0.1213 177.7◦ 2.20◦ 0.919 0.2385 22.518◦

% power loss reduction 2.0 0.5 0.67 1.28 3.69 3.83 2.452 76.126 86.98 1.327 2.317

References [1] B.A. Desouza, et al., Microgenetic algorithm and fuzzy logic applied to the optimal placement of capacitor banks in distribution networks, IEEE Trans. 19 (2004) 942–947.

2102

J. Baskaran, V. Palanisamy / Nonlinear Analysis 65 (2006) 2094–2102

[2] D.J. Gotham, G.T. Heydt, Power flow control and power flow studies for system with FACTS devices, IEEE Trans. Power Syst. 13 (1) (1998). [3] D.E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley Publishing Company, Inc., 1989. [4] F.D. Galiana, K. Almeida, M. Doussaint, J. Griffin, D. Atanackovic, Assessment and control of the impact of FACTS devices on power system performance, IEEE Trans. Power Syst. 11 (4) (1996). [5] F. Herrera, M. Lozano, Adaptive genetic operators based on co-evolution with fuzzy behaviours, IEEE Trans. Evol. Comput. 5 (2001) 149–165. [6] G.H. Hingorani, Flexible AC transmission system, IEEE Spectrum (1993). [7] H.C. Leung, T.S. Chung, Optimal power flow with a versatile FACTS controller by genetic algorithm approach, in: Proceedings of the 5th International Conference on Advances in Power System Control, Operation and Management, APSCOM 2000, October 2000, pp. 178–183. [8] I.O. Elgard, Electric Energy System Theory—An Introduction, McGraw-Hill Inc., New York, 1971. [9] J. Baskaran, V. Palanisamy, Genetic algorithm based optimal location of FACTS device in a power system network, in: International Conference and Exposition on AISTech 2005 at Charlotte Convention Center, NC, vol. 2, 2005, pp. 854–864. [10] J. Baskaran, V. Palanisamy, Micro-genetic algorithm based optimal location of FACTS device in a power system network, J. Comput. Sci. 1 (2) (2005) 89–94. [11] K.S. Verma, S.N. Singh, H.O. Gupda, Location of unified power flow controller for congestion management, Electr. Power Syst. Res. 58 (2001) 89–96. [12] K. Habur, D. Oleary, FACTS—flexible AC transmission system for cost effective and reliable transmission of electrical energy, http://www.siemenstd.com/transSys/pdf/costEffectiveReliabTrans.pdf. [13] L.J. Cai, I. Erlich, Optimal choice and allocation of FACTS devices using genetic algorithms, IEEE Trans. Power Syst. (2002) 1–6. [14] P. Preedavichit, S.C. Srivastava, Optimal reactive power dispatch considering FACTS devices, Electr. Power Res. 48 (1995) 251–257. [15] S. Gerbex, R. Cherkaoui, A.J. Germond, Optimal location of multi-type FACTS devices in a power system by means of genetic algorithm, IEEE Trans. Power Syst. 16 (2001) 537–544.