Optimal Reactive Power Planning By Using Evolutionary Engineering Essay

This paper presents a methodology for solving Optimal Reactive Power Planning (ORPP) problem by using Evolutionary Programming (EP) Optimization Technique in order to improve the voltage stability and minimize the losses in the power system. This study has developed the Evolutionary Programming (EP) Optimization Technique using MATLAB software. The study tested two fitness functions namely total loss minimization and the voltage stability improvement in power system with two different mutation technique. Comparison in the results obtained was made in order to determine the best fitness function and the best mutation technique to be used for solving ORPP and hence the voltage stability is improved. The proposed technique was tested on the IEEE 26 bus reliability test system.

Keywords:

Optimal Reactive Power Planning (ORPP), Voltage Stability Improvement, Evolutionary Programming (EP)

I. INTRODUCTION

In general, the problem of optimal reactive power planning (ORPP) can be defined as to determine the amount and location of shunt reactive power compensation devices needed for minimum cost while keeping an adequate voltage profile. The ORPP is one of the most challenging problems since objective functions, the operation cost and the investment cost of new reactive power sources, should be minimized simultaneously [1].

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Transmission loss can be minimised by performing reactive power planning which involves optimisation process. The ORPP is a large-scale nonlinear optimization problem with a large number of variables and uncertain parameters. Various mathematical optimization algorithms have been developed for the ORPP, which in most cases; use nonlinear [2], linear [3], or mixed integer programming [4], and decomposition methods [5-8]. However, these conventional techniques are known to converge to a local optimal solution rather than the global one for problems such as ORPP which have many local minima.

Recently, evolutionary algorithms (EAs) have been used for optimization; in particular both the genetic algorithm and evo1ution programming have been used in the ORPP problem. The EA is a powerful optimization technique analogous to the natural selection process in genetics. It is useful especially when other optimization methods fail in finding the optimal solution [1]. Evolutionary Programming (EP) optimization technique is recently applied in solving electric power system optimization problems. It is part of the Evolutionary Algorithm (EA) optimization techniques under the artificial intelligence hierarchy. Optimization is an important issue in power system operation and planning particularly in the area of voltage stability studies [9]. In this study, EP engine was initially developed to implement the optimisation process considering two mutation techniques, each with two different objective functions. Comparative studies performed in this study aimed to identify the most suitable mutation technique with the best objective function for minimising transmission loss in power system and also improving the voltage stability. The parameters for this problem are: generated reactive power (Qg), injected reactive power (Qinj) and transformer tap (T). Validation on the effectiveness of the proposed technique was conducted on the IEEE-26 reliability test system.

Figure 1: The IEEE 26 bus test system

II. OBJECTIVES

The two objective functions of this study are:

To obtain the total loss minimization

To improve the voltage stability

Where: Total_Loss is total loss minimization

LQNmax is voltage stability improvement

III. BACKGROUND STUDIES

A. Optimal Reactive Power Planning (ORPP)

Optimal Reactive Power Planning (ORPP) is a sub-problem of Optimal Power Flow solution which has been widely used in power system operation and planning to determine the optimal control parameter settings, in order to minimize or maximize the desired objective function while satisfying a set of system's constraint. Reactive Power Planning (RPP) involves in optimizing the transformer tap setting, injection of reactive power at generator and load bus so as to fulfill the objective function. Since the OPF approach is commonly concerned with the security and economic operation of the power system, Economic Dispatch (ED) technique is also adopted in RPP scheme. The value of active power generated by the generator is also adjusted in the approach. [11]

ORPP is a nonlinear programming problem which has the following mathematical formulation:

Maximize or minimize

f(x, u) (3)

subject to

g(x, u) =0 (4)

hmin ≤ h(x, u) ≥ hmax (5)

where u is the vector of control variables and x is the vector of dependent variables. f(x, u) is the objective function, while g(x, u) is the nodal power constraints with hmin ≤ h(x, u) ≥ hmax are the inequality constraints of the dependent and independent variables.

B. Evolutionary Programming (EP)

EP is one of the popular techniques which fall under the Evolutionary Computation in Artificial Intelligence (AI) hierarchy and increasingly applied for solving power system optimization problem in recent years. A new population is formed from an existing population through the use of a mutation operator. This operator produces a new solution by perturbing each component of an existing solution by a random amount. The degree of optimality is measured by the fitness, which can be defined as the objective function of the problem [12].

Through the use of a ranking scheme, the candidate solutions in each population were sorted in ascending order according to the number of the best population. The best population form a resultant population is referred as the next generation.

The ranking scheme must have more optimal solutions which has a greater chance of survival than the poorer solutions. It is a stochastic optimization strategy, which based on the mechanics of natural selections-mutation, competition and evolution. This technique stressed on the behavioural linkage between parents and their offspring. In general, EP consists of 3 major steps which briefly discussed as follow [12], [13]:

i. Initialization

The initial population of μ individuals consists of (xi, ƞi), ˅i € {1, 2,…μ} are generated randomly based on its limit, whereby xi denotes the control variable and ƞi is the strategic parameter with respect to xi. The fitness is calculated for each individual based on its objective function, f(xi).

ii. Mutation

a) First Mutation Technique

Each parent (xi, ƞi), i=1,…, μ, creates a single offspring (x'i, ƞ'i), where xi' and ƞi' are given by:

x'i (j) = xi (j) + Æž'i (j) Nj (0, 1) (6)

Æži (j) = Æži (j) exp (Ï„' N (0, 1) + Ï„ Nj (0, 1)) (7)

and

Ï„ = ((2(n) ½) ½)-1 (8)

Ï„'= ((2n) ½)-1 (9)

xi (j), xi'(j), Æži(j) and Æži'(j) are the j-th component of the vectors xi, xi', Æži and Æži' respectively. N(0,1) represents a normally distributed one-dimensional random number with mean zero and standard deviation 1. Nj(0,1) denotes that the random number is generated anew for each value of j. Subsequently, the fitness is calculated for each offspring.

b) Proposed Mutation Technique

The proposed mutation rule was inspired by neural network back propagation learning. The following three equations are employed for perturbing the parents to generate their offspring:

In these equations, xij [k] [k] is the jth variable of an ith individual at the kth generation. The learning rate, ƞ, and the momentum rate, α, are real-valued constants that are determined empirically. |.| denotes an absolute value and N represents the normal distribution. Δxij [k] is the amount of change in an individual, which is proportional to the temporal error, and it drives the individual to evolve close to the best individual at the next generation.

It may be viewed as a tendency of the other individuals to take after or emulate the best individual in the current generation. sxij [k] is the evolution tendency or momentum of previous evolution.

It accumulates evolution information and tends to accelerate convergence when the evolution trajectory is moving in a consistent direction [14]. The best individual is mutated only by the momentum. This expands the exploitation range and increases the possibility for escaping from local minima. acci[k] in (10) is defined as follows.

acci[k] = 1; if the current update has improved cost,

0; otherwise. (10)

iii. Combination and Selection

In combination stage, the union of parents and offspring are ranked in ascending or descending order according to its fitness and purpose of the optimisation. Hence, the top μ individuals are selected to be parents for the next generation.

The process of mutation, combination and selection are repeated until the stopping criterion is met. In this paper, the stopping criterion is taken to be the convergence of fitness value.

IV. METHODOLOGY

Figure 3 explained the overall methodology for the evolutionary programming optimization technique to solve ORPP. The produced offspring vector must satisfy and consider the constraints as at the initialization. The main concept of EP is the mutation process.

Then continues with learning about the MATLAB software and tested the IEEE 26-Bus Test System to observe initial values which are total power loss, initial minimum and maximum voltages and the initial line stability index (LQP & LQN). These initial values have been taken by considering the unstable transmission lines in the test system (IEEE 26-BUS).

The unstable line means the line stability index value is close to 1.00. The unstable voltage is when the value is not within the range of (0.90≤V≤1.10).

Figure 3: The flow chart for the EP optimization technique

The EP program was developed and the analysis of the result is tested based on objective function of the project such as minimize total loss and the voltage stability improvement. Then, the program has been run for five times for each type of objective function. Finally, this project has been concluded and the report has been written.

A. Development of EP for Optimal Reactive Power Planning

The optimal reactive power planning problems has been tested on the IEEE 26 bus test system.

The two objective functions tested are:

Fitness1 = Total_Loss;

Fitness2 = LQNmax;

To find the solution of the problem, the parameters d were decided. The parameters were:

Reactive Power of Generator Bus

Table 1 shows the parameters and size of reactive power of generation bus. There are five generator buses in IEEE 26-bus test system: Bus 2, 3, 4, 5 and 26. The size of each bus is as below.

Table 1: Parameters and size of reactive power of generator bus

Parameter

Bus

Size (MVar)

Qg2

2

0 to 50

Qg3

3

0 to 40

Qg4

4

0 to 35

Qg5

5

0 to 30

Qg26

26

0 to 20

2. Injected Reactive Power to the Bus

Table 2 shows the parameters and size of injected reactive power to the bus. It shows that there is nine buses have been injected by reactive power. The buses are as below. The unit of the injected reactive power is in MVar.

Table 2: Parameters and size of injected reactive power to the bus

Parameter

Bus

Size (MVar)

C1

1

0 to 9

C4

4

0 to 9

C5

5

0 to 9

C6

6

0 to 9

C9

9

0 to 9

C11

11

0 to 9

C12

12

0 to 9

C15

15

0 to 9

C19

19

0 to 9

3. Transformer Tap at the Transmission Line

Table 3 shows the parameters and size of transformer tap at transmission line. It shows that there is seven transformer tap change at transmission line in IEEE 26-bus test system. The size of each transformer tap is (0.9 to 1.2).

Table 3: Parameters and size of transformer tap at the transmission line

Parameter

Line

Size (p.u)

T1

2-3

0.9 to 1.2

T2

2-13

0.9 to 1.2

T3

3-13

0.9 to 1.2

T4

4-8

0.9 to 1.2

T5

4-12

0.9 to 1.2

T6

6-19

0.9 to 1.2

T7

7-9

0.9 to 1.2

The EP process is initialization, mutation, rank and selection and convergence test.

4.1.1 Initialization

Initial population of size 20 is formed by a set of randomly generated actual value. Each member is tested using equation (12) - (17) as below. Equations (12) - (16) are the generation constraints. The bus voltage limits in equation (17) are stated in order to avoid any violation to the system operation. The total loss limit in equation (18) is stated in order to avoid the losses greater than the initial values.

0MVar ≤ Qg2 ≤ 50MVar (12)

0MVar ≤ Qg3 ≤ 40MVar (13)

0MVar ≤ Qg4 ≤ 35MVar (14)

0MVar ≤ Qg5 ≤ 30MVar (15)

0MVar ≤ Qg26 ≤ 20MVar (16)

0.90V ≤│V│≤ 1.10V (17)

Total Losses ≤ 16 (18)

The generated random numbers must be smaller than the initial solution set in order to make sure that fitness will be improved. Only the member that satisfy the constraints are included in the initial population set.

4.1.2 Mutation

Mutation is a method to execute the random number to produce offspring. An offspring vector Li' is created from each parent vector by adding Gaussian random with zero mean and standard deviation.

4.1.3 Rank and Selection

The offspring populations generated form mutation process is merged with the parent populations. The selection process is to generate a new 20 populations based on the objective function of total losses minimization and the voltage stability improvement.

All of members were sorted in ascending order to produce the best twenty or the strongest twenty populations for next generation.

4.1.4 Convergence test

The stopping criteria in order to obtain the optimal solution are by looking at the difference in maximum fitness and minimum fitness which must less then certain values. If not achieved, the process will be repeated until it converged.

Where:

Total_Lossmax- Total_Lossmin < 1.0; for the total loss minimization and

LQNmax - LQNmin < 0.05; for the voltage stability improvement

V. RESULTS AND DISCUSSION

An EP optimization technique has been developed in this study and tested on IEEE 26-bus test system. The objective function is to minimize the total power loss and to improve the voltage stability in power system. The program has been developed to find the optimal value of control variables based on each objective functions. However, before this program was run, load flow solution for the IEEE 26-bus test system was obtained to determine the initial values. The initial total power loss and stability index is 18.986 MW and 0.754 respectively.

For each objective function the program was run five times and the results were tabulated in tables according to the objective function. Then the best result for each objective function was selected and tabulated in Table 1 in the Appendix A in order to make a comparison between the two objective functions. According to the result which tabulated in Table 1 in the Appendix A, it was found that EP optimization technique with voltage stability improvement as the objective function give the best result which is total power loss of 14.462 MW and stability index of 0.717. The EP optimization technique with total power loss minimization as the objective function give results 14.987 MW.

The EP optimization technique using proposed mutation rule with voltage stability improvement as objective function, the result - MW and - for the total power loss and stability index respectively.

According Table 4, the total power loss and stability index is 15.534 MW and 0.734 respectively. The result after solve the Optimal Reactive Power Planning (ORPP) is 13.019 MW and 0.699. The percentage reduction for total power loss and stability index after solves the ORPP is 16.19 % and 4.77 %.

Table 4: Comparison results before and after solves the Optimal Reactive Power Planning

Terms

Before

Solve ORPP

After Solve ORPP

Total Power Loss (MW)

15.534

13.019

Stability Index, LQNmax

0.734

0.699

VI. CONCLUSION

An evolutionary programming optimization technique has been developed to optimize the real power of generator bus, the reactive power and transformer tap control variables for minimal total cost of generation, total power loss and voltage stability improvement.

In this paper, the total cost minimization is the best objective function for minimization of total cost, total power loss and stability index is reduced. The percentage reduction for the total cost and total power loss is acceptable. The percentage reduction of stability index is the highest. The percentage reduces for the total cost, total power loss and stability index is 7.77 %, 16.19 % and 4.77 % respectively. This is the acceptable and reasonable percentage reduction as compared to other objective functions. Therefore voltage stability improvement may not have to be the objective function in order to improve the voltage stability condition of a power system in solving the OPF.

VII. FUTURE DEVELOPMENT

For future development, the other optimization techniques are proposed to be implemented in solving the ORPP in order to minimize the total power system losses and especially to improve the voltage stability in larger power system. Further modification should be included to get more accurate results for example using different mutation rules and selection strategies.

VIII. REFERENCES

[1] Kwang. Y. Lee and Frank F. Yang Department of Electrical Engineering The Pennsylvania State University University Park, PA 16802, "Optimal Reactive Power Planning Using Evolutionalry Algorithms: A Comparative Study for Evolutionary Programming, Evolutionary Strategy, Genetic Algorithm, and Linear Programming"; IEEE Transactions on Power Systems, Vol. 13, No. 1, February 1998

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[4] K. Y. Lee, Y. M. Park, and J. L. Oritz, "A united approach to optimal real and reactive power dispatch', IEEE Trans. on Power Appar. and Syst., Vol. PAS-104, pp. 1147-1153, May 1985. [SI K. Y. Lee, J. L. Ortiz, Y. M. Park, andL. G. Pond, "An optimization technique for reactive power planning of subtransmission network under normal operation", IEEE Trans. on Power Syst., Vol. PWRS-1, pp. 153-159, May 1986.

[6] M. K. Mangoli, K. Y. Lee, and Y. M. Park, "Operational real and reactive power control using linear programming", Electric Power Systems Research,[7] M. K. Mangoli, K. Y. Lee, andY. M. Park, "Optimal long-term reactive power planning using decomposition techniques", Electric Power System Research, Vol. 26,

Rana Mukerji, Wendell Neugebauer, Richard P. Ludorf and Armand Catelli, "Evaluation of Wheeling and Non-Utility Generation (NUG) Options using Optimal Power Flows", IEEE Transaction on Power Systems, Vol. 7, No. 1, February 1992.

[3] Kessel and Glavitsch> "Estimating the Voltage Stability of a Power System", IEEE Transaction on Power Delivery, Vol. PWRD-1, NO. 3, July 1986, pp 346-352.

[4] Jason Yuryevich and Kit Po Wong, "Evolutionary Programming Based Optimal Power Flow Algorithm", IEEE Transaction on Power Systems, Vol. 14, No. 4, November 1999, pp 1245-1250.

[5] A.M. Chebbo, M.R. Irving. M.J.H Collapse Proximity Indicator: Behaviour and Implications", IEE Proceedings -C, Vol. 139, No. 3, May 1992.

[6] Mahmoud Moghavvemi, "New Method for Indicating Voltage Stability Condition in Power System", Proceedings of IEE International Power Engineering Conference, IPEC'97, Singapore, pp. 223-227.

[7] Jason Yuryevich, Student Member IEEE, "Evolutionary Programming Based Optimal Power Flow Algorithm", IEEE Transactions on Power Systems, Vol. 14, No. 4, November 1999.

[8] Salami, M. and Cain, G., "Multiple Genetic Algorithm Processor for The Economic Power Dispatch Problem", Proceeding of the genetic algorithm in engineering systems: Innovations and Applications, Conference Publication No. 414, IEE, 1995, pp 188-193.

[9] I Musirin and T K Abdul Rahman, "On-Line Voltage Stability Index for Voltage Collapse Prediction in Power System," presented at Brunei International Conference on Engineering and Technology 2001 (BICET2001), Brunei. October 2001.

[10] Toro, V.D., "Electric Power System", Prentice Hall, Englewood Cliffs, New Jersey, 1992.

[11] 'What's Evolutionary Programming', http://www.faqs.org/faqs/ai-faq/genetic/part2/section-3.html.

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[13] Slobodan Pajic, Dr Kevin A. Clements, Dr. Paul W. Davis and Dr Alexander E. Emanuel, "Sequential Quadratic Programming Base Contingency Constraint Optimal Power Flow", Degree of Master of Science in Electrical and Computer Engineering, Worcester Polytechnic Institute, April, 29 2003.

[14] Fogel , D.B. : "A comparison of evolutionary programming and genetic algorithms on selected constrained optimization problems", Simulation, June,1995,pp.397-404.

[15] Yao, X., Liu, Y. and Lin, G., (1999) "Evolutionary programming made faster," IEEE Trans. Evolutionary Computation. vol. 3, no. 2, pp. 82-102.

[16] Miller, R.H. and Malinnowski, J.H., "Power System Operation", McGraw-Hill, Inc., 1994.

Appendix A

Table 1: Results of EP Optimization Technique

Objective Function

Control Variables/ Parameters of OPF

Total Cost

($/h)

Total Power Loss

(MW)

Stability Index, LQNmax

Time Taken

(s)

Real Power of Generator Bus (MW)

Injected Reactive Power (Mvar)

Transformer Tap (p.u)

Pg2

Pg3

Pg4

Pg5

Pg26

C1

C4

C5

C6

C9

C11

C12

C15

C19

T1

T2

T3

T4

T5

T6

T7

Total Power Loss Minimization

163.12

281.14

146.07

147.94

92.11

5.95

4.79

0.39

5.39

5.23

1.40

4.23

5.43

3.83

0.96

0.99

1.04

0.96

0.96

0.96

0.91

15449.1

12.132

0.767

11843

Voltage Stability Improvement

110.35

287.28

128.95

163.42

97.14

1.24

1.28

2.36

1.05

2.58

0.76

4.50

2.19

2.39

0.94

1.00

0.96

1.11

1.05

0.90

0.98

15523.1

14.461

0.713

6358