Power Flow Control incorporating TCSC using Differential Evolution

Power Flow Control incorporating TCSC using Differential Evolution

Abhishek Bhardwaj

Thapar University, Patiala

Manbir Kaur, Member IET

Thapar University, Patiala

Abstract Optimal power flow aims to optimize the generation cost, active power loss via optimal adjustment of power system control variables, while at the same time satisfying various equality and inequality constraints. In recent years FACTS devices have made the power systems operation more flexible and secure. In this paper, the focus is to obtain the optimal solution using differential evolution, when thyristor controlled series capacitors (TCSC) are used at fixed location in the system. The proposed strategy is tested on IEEE 14 bus system and load flow is carried out with Newton Raphson method. The results obtained are compared for the system with and without TCSC. and shows improvement in results.

Index Terms Differential Evolution, Generator Fuel Cost FACTS, Optimal power flow.

1. INTRODUCTION

   As power industry is moving to a competitive market, its operation is strongly influenced. Optimization methods have been widely used in power system operation, analysis and planning. One of the most significant application is optimal power flow (OPF). So when we consider the case of power system operation and planning, Optimal Power Flow (OPF) plays an important role. The OPF mainly aims to optimize the selected objective function such as fuel cost, active power loss via optimal adjustment of power system control variables, keeping the equality and inequality constraints in limit. Equality constraints are basically the power flow equations, while inequality constraints are the limits on control variables and control variable includes the generator active powers, the generator bus voltage magnitudes, the transformer tap settings and reactive power of VAR sources. Mathematically, OPF is modelled as a nonlinear programming (NLP) problem, which usually minimizes the total generating unit fuel cost and total load bus voltage deviation from a specified point subject to a set of equality and inequality constraints and thus losses can be reduced to a significant amount by keeping the equality and inequality constraints in limit. Now as the demand for the power transfer increases, the power system becomes increasingly more difficult to operate and insecure with unscheduled power flows and thus handling the losses. Rapid development of self-commutated semiconductor devices has made it possible to design power electronic equipment. This equipment is well known aslexible AC Transmission System (FACTS) which has been introduced by Hingorani [1] in

   1988. FACTS Technology is concerned with the management

   through the system can significantly improve the performance of the power system. So, as discussed earlier OPF is modelled as a nonlinear programming (NLP) problem and when we incorporated FACTS in it and considered as a control variable, it becomes even more nonlinear and complex. Various researchers developed algorithms to solve optimal power flow incorporating FACTS devices. T.S.Chung et al. [2] presented a Hybrid Genetic Algorithm (GA) method to solve OPF incorporating FACTS devices. GA is integrated with conventional OPF to select the best control parameters to minimize the total generation fuel cost and keep the power flows within the security limits. TCPS and TCSC are modeled. The proposed method was applied on modified IEEE 14 bus system and it converged in a few iterations. L.J.Cai et al. [3] proposed optimal choice and allocation of FACTS devices in multi-machine power systems using genetic algorithm. The objective is to achieve the power system economic generation allocation and dispatch in deregulated electricity market. The locations of the FACTS devices, their types and ratings are optimized simultaneously. UPFC, TCSC, TCPST and SVC are modeled and their investment costs are also considered.

   The remaining part of the paper is organized as follows. Section II presents the modeling of TCSC. Section III represents the problem formulation of OPF using TCSC. Section IV gives the brief idea about Differential Evolution. Section V gives overview of proposed algorithm. Implementation of DE to solve OPF problem incorporating TCSC and results is presented in Section VI. Finally conclusion is drawn in Section VII.

2. MODELLING OF TCSC

   Transmission lines are invariably represented by equivalent parameters and is located as lumped component in the entwork. The series compensator Thyristor controlled Series Compensator (TCSC) is a static capacitor/ reactor with impedance XC. Fig. 1 shows a transmission line incorporating a TCSC. [4][5] between bus nodes i and j and updated admittance between nodes i and j will be expressed as in equation (1):

   = – =( + j ) – ( + j ) ..(1)

   of active and reactive power to improve the performance of

   electrical networks and thus minimizing the losses. FACTS includes various types of series and shunt type VAR

   =

   2 + 2

   ;

   = –

   2 + 2

   compensators. Series and shunt VAR compensators have the

   =

   rij +

   ; =

   capability to change the performance characteristics of electrical networks. In both of them, the reactive power

   2 +

   + )2

   2 +

   + )2

   Figure 1: Equivalent circuit of a line with TCSC

   With the addition of TCSC in the line between bus i and bus j of a general power system, the new system admittance matrix Ybus can be updated as:

   Ybus= Ybus + A (2)

   0	0	0 0	0	0
   0		0 0		0
   0	0	0 0	0	0
   A=
   0	0	0 0	0	0
   0		0 0		0
   0	0	0 0	0	0

   0	0	0 0	0	0
   0		0 0		0
   0	0	0 0	0	0
   A=
   0	0	0 0	0	0
   0		0 0		0
   0	0	0 0	0	0

   s

3. PROBLEM FORMULATION

   The objective function of power flow problem is the minimization of total generation cost. Power flow equations in the OPF problem incorporating flexible ac transmission system is expressed as follows:

   Reactive power generation at bus i

   Real power demand at bus i

   Reactive power demand at bus i

   ijmagnitude of ijth element in bus x

   ij angle of ijth element in bus admittance matrix

   Vi voltage magnitude at bus i

   j phase angle at bus j

   reactance of TCSC i

   set of generator bus indexes

   set of bus indexes having reactive power source

   set of bus indexes

   set of transmission line indexes

   set of TCSC

   , , , , cost coefficient of generator i,

4. DIFFERENTIAL EVOLUTION

   Differential Evolution (DE) is an evolutionary algorithm originally proposed by Price and Storn [6] for optimization problems over a continuous domain. DE is exceptionally simple, significantly faster and robust. The basic idea of DE is to adapt the search during the evolutionary process. Differential Evolution (DE) is a parallel direct search method and selectes the optimal solution from D dimension population. The initial vector population is chosen randomly defioned over the parameter space. The perturbation is assumed as large at the start of evolution. At the start of the evolution, the perturbations are large since parent populations are far away from each other. Over the evolution process the population converges to a small region and the perturbations adaptively become small. As a result, the evolutionary algorithm performs a global exploratory search during the early stages of the

   + + 2 + | }|

   evolutionary process and local exploitation during the mature

   =1

   Subject to

   =1

   =1

   ij cos ij + i j = 0

   stage of the search. In DE the fittest of an offspring competes one-to-one with that of corresponding parent which is different from other evolutionary algorithms. This one-to-one competition gives rise to faster convergence rate. The

   ………(4)

   =1

   =1

   ij sin ij + i j = 0

   optimization process in DE is carried out with three basic operations: mutation, crossover and selection. The DE algorithm is described as follows:

   =1

   =1

   =1

   =1

   .(5)

   .(6)

   (7)

   1. Initialization

      The initial population X with population size of Np is initialized randomly such that X=[N1, N2, N3…………..NNP]. Each solution is given by Nn =[Pn1,Pn2,Pn3,………PnN](where n

      (8)

      = 1, 2 … Np ,N is the number of real power generations in the

      problem and Np is the Number of population). The variables shall bound within their upper and lower limits. Let the nth

      ….(9)

      component of the mth population members may be initialized

      as

      …..(10)

      0 = + 0,1 ( ).(10)

      where,

      Where is the upper bound of the nth variable of the problem , is the lower bound of the nth variable of the

      Real power generation at bus i,

      problem, rand (0,1) is a uniformly distributed number within

      the limits(0,1), 0 is the initial nth variable of the mth population.

   2. Mutation

      Mutant population is generated. Among the DE variants used

      buses and series capacitors of TCSC. The ith parent vector is as follows:

      = [ 1 … . . . , 1 . . . , . . 1 . . ,

      ……… . ].

      1

      for mutation in DE, the addition of the weighted difference vector between the two population members to the third member is adopted in this approach. Here three different members namely Xr1 ,Xr2 and Xr3 are chosen from the current population .Then the difference between any two of these members is scaled by a scalar number F, which is then added to the third member. The value of F is usually in between 0.4 and 1. The Mutation operation using the difference between two randomly selected individuals may cause the mutant individual to escape from the search domain. If an optimized variable for the mutant individual is outside of the domain search, then this variable is replaced by its lower bound or its

      upper bound so that each individual can be restricted to remain within the search domain. mth member of the donor vector Vn(t) is expressed as

      (+1) = 1 + 2 3 (12)

   3. Crossover

      . A new population is created by suitably combining the parent population and the mutant population. The process of crossover is based on the CR which is in between (0,1). Binomial crossover scheme is used which is performed on all D variables and can be expressed as:

      () = () if rand (0, 1) < CR

      () = () else

      where () is the child which is obtained after crossover operation where m = 1,2, … Np, n = 1,2, ….. D. Here, rand ensures that the newly generated vector is different for both

      () and () .

   4. Selection

   After calculating the objective function F(t) using D number of variables for using initial and crossover population , a new population with the least objective function ( minimum fuel cost) is formed foSr the next generation. This is given by

   X ( t+1 ) = () if f( () ) f( ()) X ( t+1 ) = () if f( ()) > f ( ())

   The process is repeated until the maximum number of

   generations or no improvement is seen in the real power generation cost after many generations. The global optimum searching capability and the convergence speed of DE are very sensitive to the choice of control parameters NP, F and CR. The crossover rate CR is between [0.3, 0.9].

5. PROCEDURAL STEPS

   Step 1.Intailse the population for decision variables of power system namely: real power generation of the generating units excluding slack bus, voltage magnitude and phase angle of the

   Step 2: Run NewtonRaphson load flow for each parent vector pi. The reactive power generations, transmission loss, slack bus generations and line flows are determined. Cost of generation is calculated for each parent vector pi.

   Step 2. Perform mutation for each target vector.

   Step 3. Perform crossover for each target vector and create a trial vector.

   Step 4. Perform selection for each target vector, by comparing its cost with that of the trial vector. The vector that has lesser cost of the two would survive for the next generation.

   Step5. Stop if the maximum number of generations is reached otherwise go to Step 2.

6. RESULTS AND DISCUSSIONS

   The effectiveness of the proposed algorithm is tested on IEEE 14-bus system. Two branches, (2, 3), (6, 8) are selected and TCSC are installed. Limits of the series capacitors size are taken in such a manner that the ratio of maximum series capacitors limit to line reactor is equal or more than 50% . The results obtained are tabulated in table 1. The values of TCSC capacitances obtained are presented in table 2.

   Table 1: Comparison of Results

   Cost($/h)

   Generator (MW)	Power Generation with TCSC using DE	Power Generation without TCSC using DE	Power Generation Using Conventional Load flow method
   P1	162.81	162.30	232.60
   P2	34.95	61.03	40
   P3	26.10	21.56	0
   P4	20.81	13.82	0
   P5	22.58	10.00	0
   746.2312	754.7656	801.0287
   Losses(MW)	8.2542	9.711	13.600

   Table 2 Values of TCSC obtained from DE

   Position of TCSC	Capacitance values in pu
   23	0.0826
   68	0.0090

   Table 3 represents the comparison of conventional load flow solution for bus voltages and phase angles of modified IEEE 14 bus system with and without TCSC.

   Table 3: bus Voltage magnitudes and Phase angles

   Fig. 2 and Fig. 3 represents the generation cost with and without TCSC respectively.

   780

   775

   cost $/Mwh

   cost $/Mwh

   770

   765

   760

   755

   750

7. CONCLUSIONS

. In this study, differential evolution is successfully implemented to minimize the generator fuel cost in optimal power flow control with TCSC keeping the equality and inequality constraints in limits. Differential evolution achieves better solution on modified IEEE 14-bus system with TCSC fixed at the given locations. The results has been compared with conventional load flow method and OPF using DE without TCSC and it is concluded that the generator fuel cost reduces significantly and losses are also less when we use TCSC with DE as compared to other two.

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   775

   770

   cost $/Mwh

   cost $/Mwh

   765

   760

   755

   750

   0 50 100 150

   iteration

   Figure 2. Cost Reduction using DE without TCSC

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