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Optimal Location and Initial Parameter Settings of Multiple TCSCs for Reactive Power Planning Using Genetic Algorithms Narayana Prasad Padhy

Abdel-Moamen M. A

Abstract—In this paper, a genetic algorithms based optimal reactive power planning model incorporating FACTS devices has been presented. Optimal placement of multiple FACTS devices will naturally control the overall reactive power requirements. But the mathematical complexity and hence the solution time increases for reactive power planning of large power networks with multiple FACTS devices. To obtain a feasible and suboptimal solution for reactive power planning, optimal location of FACTS devices and its parameters have been determined using simple genetic algorithms. Genetic algorithm, performed on two parameters: the optimal location of the devices and their control parameter and then the fitness function has been determined using Quasi-Newton algorithm based optimal power flows for minimization of reactive power losses and generations. The performance of the proposed algorithm has been tested for IEEE-30 systems with multiple TCSC devices. It has also been observed that the proposed algorithm can be applied to larger systems and do not suffer with computational difficulties. Index Terms— FACTS devices, TCSC, Newton’s Optimal Power Flow and Genetic Algorithms.

I. INTRODUCTION

O

PTIMAL Power Flow (OPF) for reactive power planning is a static nonlinear programming problem aimed at scheduling the controls of the power system in a manner that optimizes a certain objective function while satisfying a set of physical and operational constraints imposed by equipment limitations and security requirements. OPF was born in 1962 [1] and took a long time to become a successful algorithm that could be applied in every days use. Over the last three decades, many successful OPF techniques have been developed [2-4] such as, the generalized reduced gradient method, successive linear programming solution, successive quadratic programming, the Newton method, the P-Q decomposition approach, the Interior Point Method Narayana Prasad Padhy is currently with the Department of Electrical Engineering, Indian Institute of Technology, Roorkee – 247667, India ([email protected] )

B. J. Praveen Kumar

(IPM), Genetic Algorithm (GA), Evolutionary Programming etc. In the present day deregulated environment scenario, the main objective of the pool has to dispatch both real and reactive power requirements of the heavily loaded customers and encourage only those bidders leads maximum social benefits. Due to cheap power sale based on real power cost characteristics leads to shortage in reactive power requirements and hence loss of stability in the system. So it is equally important to develop a suitable algorithm for optimization of reactive power requirement. Further, reactive power optimization has gained more importance due to exploitation of power generating sources at remote places and inclusion of FACTS devices in the transmission networks in the system. As power transfers grows, the power system can become increasingly more difficult to operate, and the system becomes more insecure with unscheduled power flows and higher losses. In this context, as well as the rapid development of self-commutated semiconductor devices, have made it possible to design power electronic equipments. These equipments are well known as Flexible AC Transmission Systems (FACTS)-devices, and introduced in 1988 by Hingorani [5]. The objective of FACTS devices is to bring a system under control and to transmit power as ordered by the control centers, it also allows increasing the usable transmission capacity to its maximum thermal limits. By Using FACTS devices it is possible to control the phase angle, the voltage magnitude at chosen buses and /or line impedances of a transmission system. Power flow is electronically controlled and it flows as ordered by control center and consequently the cost and losses will be optimized. It has been observed that installation of FACTS devices increases the network’s controllability. But the existing conventional OPF algorithms have to be modified such that power system analysis is possible for modern power industry with FACTS devices. For last two decades researchers developed new algorithms and models for power flow and optimal power flow incorporating FACTS devices, so that cheap power can be made available to the customers without violating system constraints. Still research is in progress to meet the present day congestion management problem with help of FACTS devices efficiently. Various algorithms have been reported to

solve power flow and optimal power flow (OPF) for power systems equipment with various FACTS devices. New control variables and control objective equations are usually added in conventional power flow equations. Several papers have reported the OPF incorporating FACTS devices. Noroozian and Andersson [6] have proposed a method for solving the power flow control problem incorporating FACTS devices based on decomposition and locally measurable variables. Taranto et al. [7] have proposed a decomposition method for representing FACTS devices in optimal power flow (OPF) model. The proposed approach was first proposed to solve the optimal active power flow dispatch problem incorporating FACTS devices. This methodology is based on mathematical decomposition and network compensation techniques. This method can deal with the representation of series compensators and phase shifters, but this method did not consider the specified line flow constraints. Hiyama, et al. [8], presented an application of a fuzzy logic control scheme for TCSC module to enhance overall stability of electric power systems and also to increase the maximum power transmission through the existing AC transmission lines. Gotham and Heydt [9] presented the modeling of FACTS devices for power flow studies and the role of that modeling in the study of FACTS devices. Also they proposed a simultaneous method to solve the combined set of power flow equation and FACTS control equations. Chung et.al., [10] described a method to incorporate the power flow control using FACTS for the optimal active power flow problem. Povh [11] presented that FACTS controller can essentially improve long-distance ac transmission. This technology has been extended by a large number of further FACTS elements, which can be effectively used for load flow control in power systems. Ambriz-Perez et al [12] solved the OPF incorporating FACTS devices using Newton’s method, leading to highly robust iterative solutions. Fuerte et al [13] proposed simultaneous methods to solve the combined set of power flow equations and FACTS control equations. Lu and Abur [14] presented a systematic procedure to place and operate TCSCs in a power system. First the “Single Contingency Sensitivity (SCS)” criterion for a given branch flow is defined. This criterion is then used to develop a branch’s prioritizing index in order to rank branches for possible placement of TCSCs. Finally, optimal settings for TCSC parameters are determined for important contingencies. Billinton et al [15] presented power system reliability enhancement using a TCSC. Chung and Li [16] presented an improved genetic algorithm (GA) to solve optimal power flow (OPF) problems in power system with FACTS. In the solution process, GA coupled with full AC power flow, selects the best regulation to minimize the total generation fuel cost and keep the power flows within their secure limits. The optimization process with GA is presented with case study examples of a IEEE test system to demonstrate its feasibility and effectiveness. The proposed model for ractive power planning algorithms incorporating TCSC devices is capable of handling multiple TCSC devices and also independent of the system size. The algorithm uses Quasi-Newton optimization [17] for

fitness function calculations and due to which the mathematical complexity has been reduced drastically without compromising optimality. Placement of TCSC’s in an optimal location is decided based on different factors such as loss reduction, improvement in stability margin etc. Due to high cost of these FACTS devices, it is important to decide their optimal placement to meet the desired objective. II. PROBLEM FORMULATION 1. Proposed Solution Scheme In the first step, GA handles a combinatorial nature of the problem because here the optimal location of the TCSCs is a problem of combinatorial analysis. The GA selects both the location and initial value of α, the firing angle of the thyristor in TCSC and passes both for fitness function calculation. The optimization method used in OPF is a Quasi-Newton method with line search algorithm for constraint optimization. Optimization toolbox in MATLAB4.1 has been used for optimization at the simulation level [26]. 2. Description of Genetic Algorithm Used The genetic algorithm (GA) used in the proposed algorithm is a simple version where three operators were used: reproduction, crossover and mutation. The reproduction consists of the selection and the process of copying the genetic information of the individuals to create a new population. The crossover is the genetic information exchange of two strings that are selected from the population at random with a crossover probability fixed at 0.7. Mutation is the process of random alteration of the value of the string position with a mutation probability fixed at 0.001. The goal of the genetic algorithm is to find the best locations of a given number of FACTS devices in accordance with a defined criterion. A configuration of NF FACTS devices is defined with two parameters: the location of the devices and their parameters. An individual string used in genetic algorithm is represented with two substrings. The length of the first substring is nl where as the second substring is Na (gene length). The first substring corresponds to the optimal location of the FACTS devices. It contains 1’s and 0’s of length nl, no. of lines in the system. 1 represents that FACTS device is present and 0 represents that FACTS device is not present. The bit number from the left gives the line in which FACTS device is located or not. Hence the length of first substring is kept equal to number of lines in the system. The second substring of the individual represents the parameter values of the TCSC device (α), in the proposed model the substring represent as many values of α equal to the number of devices available in the first string. The length of this substring is taken as Na*NF. Where, Na is the gene length for encoding the value of α in binary form and NF is the number of FACTS devices to be located in the system. Then evaluate the objective function(as per the equation 3.1) for each individual strings generated. The population size is the number of individual strings generated and it is taken as 200 in this work.. Stopping criteria is set by maximum number of generations had been attained

is Voltage magnitude at bus i is power angle

or not. If so, stop the program and take the best individual and its fitness function.

Vi δij

3. Fitness Function Calculations Now the OPF formulation has been modified with the variable parameters of TCSC devices and the fitness function(F) is redefined to minimize the reactive power requirement, and at the same time, some constraints, including entire power flow equations, generation limits, voltage ranges, line transfer capability and TCSC impedance etc., has to be satisfied. The fitness function for reactive power planning can be formulated as:

xtcsci is reactance of TCSC as a function of α

nl

k =1

is thyristor firing angle. III NUMERICAL RESULTS

The effectiveness of proposed approach has been illustrated using the IEEE 30 bus test systems. 2

1

ng

nl

min F = ∑ QLk + ∑ PLk + ∑ Qgn k =1

α

(3.1)

n =1

5

TCSC TCSC

3

where,

TCSC

6

13

Subject to: Equality constraints

∑V V Y (x ) cos(δ +γ −γ ) = 0 (3.2) + ∑ V V Y ( x ) sin (δ + γ − γ ) = 0 (3.3)

12

r

N

i

TCSC

8

4

Pgi − Pdi −

7

t csc

j ij

ij

j

16

10

17

28

11

9

i

j =1

Q gi − Q di

N

r

i

j

ij

t csc

ij

j

14

18

19

20

21

22

27

30

i

j =1

Inequality constraints min gi

P

15

≤ Pgi ≤ P

∀i ∈ NG

(3.4)

∀i ∈ NG

(3.5)

∀i ∈ NT

(3.6)

∀i ∈ N

(3.7)

max gi

Q gimin ≤ Qgi ≤ Q gimax

Ti

min

≤ Ti ≤ Ti

Vi

min

≤ Vi ≤ Vi

max max

δ ij min ≤ δ ij ≤ δ ij max

∀i ∈ N

MVAimin ≤ MVAi ≤ MVAimax min xt csci min i

α

≤

max xt csci ≤ xt csci max i i

≤α ≤α

∀i ∈ NB

∀i ∈ NTCSC

(3.8) (3.9)

∀i ∈ NTCSC

where F is the objective function PLK is the real power loss in the kth line QLK is the reactive power loss in the kth line Qgn is the reactive power generation nl is number of lines in the system. nb is number of buses in the system. ng is number of generators in the system. N is set of bus indices; NT is set of transformer indices; NG is set of generation bus indices; NTCSC is set of TCSC indices; NB is set of branch indices; Yij and θij are magnitude and phase angle of element in admittance matrix; Pgi is Real power generation at bus i Qgi is Reactive Power generation at bus i Pdi is Real Power load at bus i Qdi is Reactive power load at bus i Ti is tapping ratio at transformer i

23

26

24 25

29

Fig. 1. The IEEE 30-bus system a. IEEE 30-Bus System Cases studies for IEEE 30 bus system [20] shown in Fig. 1. have been carried out to determine the effectiveness of the proposed model. The system has 6 generation, 4 LTC transformers, and 41 transmission lines. TCSC device has been installed on different branches one by one based on the optimal power flows and further the model has been applied to multiple FACTS devices (two and three). The objective function (Fval) taken from Eq. 3.1 with reactive power generation, real and reactive power losses are solved conventionally(shown in Fig.2) by locating TCSC in each and every line. The optimal location, which is the location at which Fval is minimum, can be found as 16th line. That means locating the TCSC in 16th line gives best optimum value. Thus by conventional method the optimal location of TCSC is the 16th line for 30 bus system. We can also observe that for different initial values of α, the OPF converges to different optimal values, and for some initial values of α, it diverges giving worst solutions. Hence the initial value of α play an important role in the process of optimization due to its complex non linearity. Fig. 3. shows the variation in the objective function versus different initial values of α. The Newton Raphson load flow solutions of IEEE 30 bus system are tabulated in Table 1 and Table 2. OPF without

FACTS devices has also been solved and optimal solutions are tabulated in Table. 1 and Table 2.

Fig. 3. Objective function versus initial value of α Table 1. Real Power Generation, Reactive Power Generations and Thyristor angle α Obtained Using Proposed Algorithm with Multiple TCSC IEEE 30 BUS

Load flow

OPF without TCSC

Pg1

25.9

50.0

Pg2

60.9

26.0

Pg13

37.0

50.0

Pg22

21.5

24.7

Pg23

19.2

20.7

Pg27

26.9

19.8

Qg1

-1.0

-2.7

Qg2

32.0

32.3

Qg13

11.3

32.2

Qg22

39.5

12.1

Qg23

7.9

10.1

Qg27

10.5

12.4

Fig. 2. Objective function versus TCSC location Now in the proposed approach GA providing both the location and initial value of α is implemented and the solutions are tabulated in the Table 2 for one, two and three TCSC. The voltage profile of the proposed algorithms with one, two and three FACT devices shows the maximum improvement over classical load flows and OPF without FACT device solutions. Above and all the reactive power requirement and the system losses are reduced. The OPF with genetic algorithm, which uses its natural search algorithm, selects both optimal location of the devices and its parameters enhance the performance of proposed model.

Table 2. Reactive Power Losses, Reactive Power Generations, Real Power Losses and Thyristor Firing Angle α Obtained Using Proposed Algorithm with Multiple TCSC Firing angle α, of TCSC

IEEE 30 BUS

Obje ctive Func tion

Q loss Mvar

Q genr Mvar

P loss MW

Lin e

Load Flow

111. 84

8.99

100.41

2.44

--

--

105. 46

6.75

96.54

2.16

--

--

104. 49

5.35

96.69

2.43

16

56.30

100. 37

3.90

95.46

2.37

10 12

48.73 131.61

99.4 1

1.77

95.15

2.49

12 15 16

91.34 0.87 67.97

OPF With out TCSC GA 1 TCSC GA 2 TCSC GA 3 TCSC

IV CONCLUSION A algorithm algorithm for reactive power planning based on the optimal placement of TCSC in modern power systems has been proposed in this research paper. With the above proposal it is possible for utility to place multiple TCSCs in

the transmission line such that proper reactive power planning can be achieved with minimum system losses and reactive power generation. The OPF with and without FACTS devices not only reduce the system loss but improves the voltage profile at all the buses in the system. It has also been observed that proposed algorithm is also suitable for large systems with multiple FACTS devices, and the results so obtained are found to be encouraging. V REFERENCES [1] Carpentier J., “Contribution a l’étude du Dispatching Economique,” Bulletin de la Société. Française des Electriciena, Ser. 8 Vol. 3, pp. 431–447, August 1962. [2] Huneault M. and Galiana F.D.:”A Survey of the Optimal Power Flow Literature,” IEEE transactions on Power Systems, Vol. 6, N0.2, pp. 762-770, May 1991. [3] Wood A.J. and Wollenberg B.F. “Power Generation, Operation, and Control”, John Wiley and Sons, New York, 1996. [4] Momoh JA, Elhawary ME., Adapa R, “A Review of Selected Optimal Power Flow Literature to 1993, Part I, Part II, IEEE transactions on Power Systems Vol.14, No. 1,pp.96-111, Feb.99 [5] Hingorani N.G. “Power Electronics in Electrical utilities: Role of Power Electronics in Future Power Systems”, Proceedings of the IEEE Vol. 76 No. 4, pp.481-482, April 1988. [6] Noroozian M. Angquist L., Ghandhari M., Andersson G. “Improving Power System Dynamics by Series-Connected FACTS Devices”, IEEE Transactions on Power Delivery, vol. 12, No. 4, pp.1635-1641, October 1997. [7] Taranto G.N., Pinto L.M.VG., Pereira MVF.,“Representation of FACTS Devices in Power System Economic Dispatch”,IEEE transactions on Power Systems vol.7, No. 2, pp.572-576, Mary92. [8] Hiyama,T. et al. “Coordinated Fuzzy Logic Control for Series Capacitor Modules and PSS to Enhance Stability of Power System”, IEEE Transactions on Power Delivery vol.10, No. 2, 1098-1104 April. 1995. [9] Gotham D.J. and Heydt G.T.,: “Power Flow Control and Power Flow Studies for Systems with FACTS Devices,” IEEE transactions on Power System vol.13, No. 1, pp. 60-65 Feb.1998. [10] Ge S.Y. and Chung T.S. “Optimal Active Power Flow Incorporating FACTS Devices with Power Flow Control Constraints”, Electrical Power& Energy Systems vol.20, No. 5, pp.321-326 May. 1998. [11] Dusan Povh:, ”Use of HVDC and FACTS”, Proceedings of the IEEE, vol. 88, No. 2, pp. 235-245, February 2000. [12] Ambriz-Perez H., Acha E., Fuerte-Esquivel C.R.: “Advaced SVC Model for Newton-Raphson Load Flow and Newton Optimal Power Flow Studies” IEEE transactions on Power Systems, vol. 15, N0.1, pp.129-136, February 2000. [13] Fuerte CR., Acha E., Tan SG., Rico JJ.:“Efficient Object Oriented Power Systems Software for the Analysis of LargeScale Networks Containing FACTS-Controlled Branches” IEEE transactions on Power Systems, vol. 13, N0.2, pp.464-472, May 1998. [14] Lu Yunqiang and Abur Ali,: “Improving System Static Security via Optimal Placement of Thyrister Controlled Series Capacitor (TCSC)”, IEEE, PES, WM, Columbus, Ohio, USA., Jan. 2001. [15] Billinton R., Firuzabad M.F., Faried S.O. “Power System Reliability Enhancement using a thyristor Controlled Series Capacitor”, IEEE transactions on Power Systems vol.14, No. 1, pp.369-374, February. 1999. [16] Chung T.S., Li Y.Z. “A Hybrid GA Approach for OPF with Consideration of FACTS Devices”, IEEE Power Engineering Review, vol. 21, N0.2, pp. 47-50, February 2001.

[17] Sun I David, Ashley Bruce, Bewer Brian, Hughes Art, Tinney E. William,:”Optimal Power Flow by Newton Approach”, IEEE transactions on Power Apparatus and Systems vol.PAS 103, No. 10, pp.2864-2875, October 1984. [18] Abdel-Moamen, M. A.; Padhy, N.P. “Newton-Raphson TCSC Model for Power Flow Solution of Practical Power Networks” IEEE PES, SM, Vol: 3, pp: 1488 -1493, 2002 [19] Alsac O. and Stott B.:”Optimal Power Flow with Steady-State Security”, IEEE transactions on Power Apparatus and Systems, Vol. PAS- 93, No. 3, pp.745-751, May/June 1974. [20] Power Systems Test Case, The University of Washington Archive, http://www.ee.washington.edu/research/pstca/, 2000. [21] Lee, K. Y. and Yang, F. F. , “Optimal Reactive Power Planning Using Evolutionary Algorithms : A Comparative Study for Evolutionary Programming, Evolutionary Strategy, Genetic Algorithm and Linear Programming”, IEEE Transactions on power systems, Vol. 13, No. 1, Feb-1998, pp : 101-108. [22] Carpentier, J., “Optimal power flow – a survey”, International Journal on Electric Power and Energy Systems, Vol. 1, No. 1, 1979, pp : 3-15. [23] Huneault, M., Galiana, F. D., “A Survey of Optimal Power Flow Literature”, IEEE Transactions on power systems, Vol. 6, No. 2, 1991, pp : 762-770. [24] Hingorani, N. G., “Flexible AC Transmission” IEEE spectrum, April-1993, Vol. 30, No. 4, pp : 40-45. [25] Stephane Gerbex, Rachid Cherkaoui, and Alain J. Germond, “Optimal Location of Multi-Type Facts Devices in a Power System by Means of Genetic Algorithms”, IEEE Transactions on power systems, Vol. 16, No. 3, Aug-2001, pp : 537-544. [26] “Optimization Toolbox for use with MATLAB”, users guide Version 2, PDF-Document, www.mathworks.com. [27] Alberto J. Urdaneta, Juan. F. Gomez, Elmer Sorrentino, “A Hybrid Genetic Algorithm for Reactive Power Planning based upon Successive Linear Programming”, IEEE Transactions on power systems, Vol. 14, No. 4, Nov-1999, pp : 1292-1297. [28] Preecha Preedavichit, Srivastava, S. C., “Optimal Reactive Power Dispatch Considering FACTS Devices”, Electric power system research, Vol. 46, 1998, pp : 251-257. [29] M. H. Haque, “Optimal Location of Shunt FACTS Devices in Long Transmission Lines”, IEE Proceedings Generation, Transmission and Distribution, Vol. 147, No. 4, July-2000, pp : 218-222. [30] D. E. Goldberg, “Genetic Algorithms in Search Optimization and Machine Learning” Addison-Wesley Publishing Company, Inc., 1989.

VI BIOGRAPHIES Narayana Prasad Padhy received the Degree in Electrical Engineering and Masters Degree in Power Systems Engineering with Distinction in 1990 and 1993, respectively. He received the Ph.D., Degree in Electrical Engineering from Anna University, Chennai, India in 1997. Then he joined Birla Institute of Technology & Science(BITS) as an Assistant Professor, Electrical Engineering Department in 1997. Currently, he is Assistant Professor in the Department of Electrical Engineering, Indian Institute of Technology, Roorkee. He taught course in Basic Electrical Engineering, Power Systems and Artificial Intelligence. His field of interest is Power System Privatization, Restructuring and Deregulation, Artificial Intelligence Applications to Power System Operation and Optimization Problems, Unit Commitment, Power System Wheeling and FACTS.