Reactive Power Optimization of Wind Farm based on Improved Genetic Algorithm

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Energy Procedia

Energy Procedia 00 (2011)14000–000 Energy Procedia (2012) 1362 – 1367 www.elsevier.com/locate/procedia

2011 2nd International Conference on Advances in Energy Engineering (ICAEE 2011)

Reactive Power Optimization of Wind Farm based on Improved Genetic Algorithm Xiang-jun Zenga, Jin Taob, Ping Zhangc, Hui Pana and Yuan-yuan Wanga a

School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, 410076, China; b China electric power research institute, Beijing, 102200, China; c JiaXing HaiNing Power Supply Buerau, ZheJiang, 314400, China

Abstract Reactive power optimization plays a significant role in the operation of wind farm grid intern connection to maintaining voltage stability and system reliability. Genetic algorithm (GA) is an efficient method which can be applied in reactive power optimization to reduce power loss and improve power quality. However, traditional GA has some defects, such as slow convergence and prematurity. For improvement, the paper modified decoding method, genetic operators, crossover and mutation probability, iteration stopping criterion based on the theory of Catastrophism. A reactive power optimization techniques based on improved genetic algorithm (IGA) of wind farm is such presented. Simulation results for Chinese Mongolia Huitengliang Power Plant show that the proposed method has satisfied global performance, high convergence speed and stable convergence performance, so it is suitable to solve the optimal reactive power planning.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee © 2011 Published by Elsevier Ltd. Selectioninand/or responsibility of [name organizer] of 2nd International Conference on Advances Energypeer-review Engineeringunder (ICAEE). Keywords: improved genetic algorithm, reactive power optimization, wind farm.

1. Introduction With the rapid development of wind power technology and national policies on the renewable energy sources, wind energy has been widely used in power generation. However, the large-scale wind farm grid interconnection will have a great influences on the system reliability and the stable operation in the power system for two reasons: (1) The areas where possesses rich wind sources, that can be used to make largescale development of the wind generation, are generally in the terminal of the network, where the power grid structure is weak; (2) The wind energy is an unstable and random energy, so active power output changes along with the wind speed. The most serious problem is that the voltage quality on local power grid within or close to wind farm decreases seriously, since the grid interconnection will cause the Xiang-jun Zeng is with School of Electrical & Information Engineering, Changsha University of Science and Technology, Hunan Province, 410076, P. R. China (Tel:86-0731-85258300; E-mail: [email protected])

1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE). doi:10.1016/j.egypro.2011.12.1102

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fluctuation of the reactive power and then influences the system voltage or even cause the collapse of entire power system. The reactive power optimization of power system is the most efficient method to decrease the loss on power network and maintain the voltage level of the power grid by reasonable allocation of reactive sources and rational compensation of reactive load. For decades, many electric power experts have made a great research on the reactive power optimization and carried out many methods. Reference [1] introduces tabu search (TS), which has a strong ability of global optimization, can be arranged for the operation, and has the potential of online decision-making . However, it is difficult to adjust parameters and the result is greatly affected by the randomly generated initial solution. Genetic/Tabu search hybrid algorithm is proposed in [2], combines the advantages of two algorithms, in spite of that, it is difficult to achieve is obvious. The paper improved decoding method, genetic operators and iteration stopping criterion of the traditional GA [3-4]. A novel improved GA based on catastrophic genetic algorithm, which is suitable for reactive power optimization, was proposed. In addition, grouping decimal integer encoding [5], tournament selection, adjacent mutation and the operation of the disaster are discussed. This method is suitable to the actual situation and can get the optimal solution quickly. 2. Model of Wind Farm Reactive Power Optimization The reactive power optimization is a nonlinear optimal problem, for its multivariable and multiconstraints [6], it can be described as follows: 2.1. Objective function Reactive power optimization objective function includes technical performance indicators and key economic indicators, and there are differences between two objective due to the optimize focus. In this paper, the objective function is loss minimum for the reactive power compensation capacity and network losses. NR

NC

i =1

j =1

min F = ∑ α Ri QRi + ∑ α Cj QCj + Cτ maxPS

(1)

α Ri : The inductive reactive power compensation per capacity of node i; QRi : The inductive reactive power compensation capacity of node i;

N R : The inductive

node number of the power network;

The capacitive reactive power compensation per capacity of node j;

α Cj :

QCj : The capacitive reactive power

compensation capacity of node j; N C : The capacitive node number of the power network; C : The price of active power loss; PS : The active power loss. τ max : The time of the maximum load loss; 2.2. Equality constraint The equality constraints of each node are as follows: N

PGi − PGi = Ui ∑U j (Gij cosδij + Bij sinδij )

(2)

j =1

N

QGi + QCi − QLi − QRi = U i ∑U j (Gij sin δ ij − Bij cosδ ij ) j =1

(3)

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N : The number assembles of node in the network; PGi , PLi : The active power generation and load of

node i, respectively; QGi , QLi : The reactive power generation and load of node i, respectively; QCi , QRi :The capacitive and inductive reactive power compensation capacity of node i, respectively; Gij , B ij :The conductance and susceptance between node i and j; δ ij : The phase-angle difference of the

voltage value between node i and j. 2.3. Inequality constraint

Control variable constraint:

State variable constraint:

U Gi⋅min ≤ U Gi ≤ U Gi⋅max , i = 1,2,⋅ ⋅ ⋅, N G QGi⋅min ≤Q Ri ≤ Q Ri⋅max,i = 1,2,⋅ ⋅ ⋅, N R

(5)

QCj⋅min ≤ QCj ≤ QCj ⋅max, j = 1,2,⋅ ⋅ ⋅, N C

(6)

(4)

Ttk ⋅min ≤ Ttk ≤ Ttk ⋅max , k = 1,2,⋅ ⋅ ⋅, N t

(7)

QGi⋅min ≤ QGi ≤ QGi⋅max , j = 1,2,⋅ ⋅ ⋅, N G U Dj ⋅min ≤ U Dj ≤ U Dj ⋅max , j = 1,2,⋅ ⋅ ⋅, N D

(8)

q Bl ⋅min ≤ qBl ≤ qBl ⋅max, l = 1,2,⋅ ⋅ ⋅, N B U Gi : The voltage value of generator i;

(9) (10)

U Gi⋅min ,U Gi⋅max :The minimum and maximum voltage value of

generator I, respectively; QRi : The inductive reactive power compensation of generator i; QRi⋅min , QRi⋅max : The minimum and maximum inductive reactive power compensation capacity of generator i, respectively; QCi : The capacitive reactive power compensation capacity of node i; Ttk : The locating of the tap changer of transformer; Ttk ⋅min,Ttk ⋅max : The lower, upper bound values of the tap changer, respectively; QGi : The reactive power generation of generator i; U Dj : The voltage value of load node j; U Dj⋅min ,U Dj⋅max : The minimum and maximum voltage value of load node j, respectively; q Bl : The reactive power flow of branch l; q Bl⋅min , q Bl⋅max : The minimum and maximum reactive power flow of branch l, respectively; N G : The number of generator; N R : The number of node for inductive reactive power compensation; N C : The number of node for capacitive reactive power compensation; N t : The number of adjustable taps transformers; N D : The number of load point; N B : The number of branches. 3. Application of IGA for Reactive Power Optimization of Wind Farm Based on the concept of catastrophe [7], population diversity can be achieved by retaining the best offspring and regenerating the population, population size can be regulated, and the computational time can be reduced. 3.1. Scheme for population size selection by catastrophe

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The solution steps of the IGA are shown in Fig.1. (1) Initialize the requirements and set number of “catastrophe”; (2) Come into being out the initial race; (3) Begin Operate the genetic evolution; (4) Record the maximum and the minimum adaptation value individual in the Reading in the original data of the wind population; (5)Carry out the catastrophe and preserve the farm and the parameters of GA current optimal solution while the difference between the maximum and the minimum adaptation value individual is Choosing the position of the reactive smaller than a threshold, and return to step(3); Otherwise, power take the next step. 3.2. Optimizing encoding method

Using the transformer tap and the reactive compensation capacity as the controlling variable , which will be decimal coded then saving the coding to the two dimensional array

Integer coding, comparing with binary coding, is adapted to the problem with discrete control variables which can be expressed by an integer gene. It can reduce the length of coding string enormously, so the memory space needed is less. In addition, genetic operational efficiency is improved [8]. Decimal integer coding makes the solution space of original problem mapping to the strand spaces of decimal integer, then crossover and mutation, finally, restore its phenotype to go along fit evaluation through decoding process.

Using the coding as the chromosome and using the random way to make out the initial population

Making the fitness function

Making the operation of the crossover and the mutation

Obtaining the actual value by the requerying

3.3. Operator

Calculating everyone ’s individual investment , networkloss , voltage level and getting the adaptive value

Reserved operator was introduced in this paper in order to ensure finding the global optimal solution. That is, some optimal or suboptimal individuals of parent, which only replaced by better species, were selected instead of offspring. It can be proved that the present method has good capability to obtain global optimal solution with the chance of 100%, in mathematics.

Y

Whether meeting the demand of the disaster ?

Whether meeting the demand of the evolution?

3.4. Adopting changeable crossover rate and mutational rate

N

Out put the results The end

Fig. 1. Solution steps of the IGA

In the prophase of the genetic iterative, in order to insure the calculation process advanced steadily, the crossover rate should be larger, while the mutational rate should be smaller. But in later iteration, the chromosome among its group tends towards stability, and is easy to fall in local optimum. The calculation formulas of changeable crossover rate and mutational rate are as follows: ⎛ Δu ⎞ ⎜⎜ − N ⎟⎟ c ⎠

Pc(k ) = Pc(0 ) − (Pc(0 ) − Pc⋅min )⋅ e⎝

Pm(k ) = Pm(0 ) − (Pm⋅max − Pm(0 ) ) ⋅ e

⎛ Δu ⎜⎜ − ⎝ Nm

(11) ⎞ ⎟⎟ ⎠

(12)

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k: The iteration number; Δu : The difference between the highest and lowest value of the adaptive function in the k − 1 iteration; pm⋅max =0.1; N c = N m = 20 . 3.5. Calculating of the adaptive value Using the objective function as the adaptive value: 3 F fitness = Fobject = max⎛⎜ ∑ϖ i μ (Fi )⎞⎟ ⎝ i =1 ⎠ The solution steps of the IGA are shown on fig.1.

(13)

4. Analysis of Examples

Wind farms in Inner Mongolia own 200 wind turbines. They are divided into 20 groups, and each group has 10 turbines. The total installed capacity up to 300MW. The wind turbine boosts to 35KV with box-type transformer T2, then through 20 35kV transmission lines together to the substation which has two main components of the 220kV transformer step-up substation. The wind farm model has 403 nodes, due to its complexity and limited space [9], just 42 nodes of them were chosen. To consider the loss of cable lines, SVC is installed in the nodes for simulation. Based on the above mentioned, MATLAB simulation was applied in this paper [10]. Through the calculation of the wind farm inside network, the optimal reactive compensation can be solved. Reference power SB is 100MW, reference voltage UB is 220kV, and the highest reactive investment is 500 million. Encode the SVC and on-load tap changer. The largest code is 50, and the largest number of disaster is 100.

Fig. 2. The model of the wind farm with 42 nodes Table.1. Compared results of reactive power optimization between tga and iga Project Traditional Genetic Algorithm Improved Genetic Algorithm

Investment of reactive power compensation (million Yuan) 338 336

The system loss(kW) V=4m/s

V=8m/s

V=12m/s

1872 1731

2480 2292

3129 2892

Table 1 shows the compared result of reactive power optimization between TGA and IGA. The improved Genetic Algorithm reduced the network loss and investment of compensation equipment, which is better than Traditional Genetic Algorithm. Table 2 shows the voltage level of 10 nodes out of 42 nodes.

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Reactive power compensation is helpful in reducing network loss in wind farm as well as improving the voltage level. Table. 2. Voltage of node

node numbering 1 2 3 4 5 6 7 8 9 10

Voltage(Per-Unit Value) Before Compensation 0.977 0.977 0.976 0.976 0.974 0.974 0.975 0.974 0.972 0.970

After compensation 0.994 0.994 0.993 0.993 0.992 0.991 0.992 0.991 0.990 0.989

5. Conclusion

Genetic algorithm (GA) can be applied in reactive power optimization. However, Traditional Genetic Algorithms has some drawbacks, such as slow convergence and prematurely. Based on the catastrophic genetic algorithm, an improved genetic algorithm (IGA) for reactive power optimization of wind farm approach is presented. Results show the proposed method is rationality and validity. References [1] Yu-tian Liu, Li Ma. Reactive power optimization based on tabu search approach. Automation Of Electric Power Systems 24 (2) (2000) 61-64(in chinese). [2] Ling Li, Xiang-jun Zeng, Ping Zhang. Wind farms reactive power optimization using genetic/tabu hybrid algorithm. International Conference on Intelligent Computation Technology and Automation, 2008, pp. 1272-1276. [3] Chang-chun Cai, Xiao-qun Ding, Bin Wang. Application of chaos simulation annealing in power system reactive optimization. High Voltage Engineering, 34 (3) (2008) 578-582(in chinese). [4] S.Sundhararajan, A. Pahwa. Optimal selection of capacitors for radial distribution systems using a genetic algorithm. IEEE Trans. Power Systems, 9 (3) (1994) 1499-1507. [5] Xiao-ping Wang, Li-ming Cao. Genetic Algorithm: theory and software used to achieve. Xi'an University of Electronic Science and Technology, press, Xi'an , China, 2002(in chinese). [6] Xin-yin Xiong, Yao-wu Wu. Genetic algorithm and its application in power system. Huazhong University of Science and Technology, press, Wu han, China, 2000(in chinese). [7] Jun-yong Zhang, Xia Ren, Hong-mei Zhong. The active power optizimation based on the catastrophe of GA. power system automation, 2002, 26(23):29-32(in chinese) [8] Wu-jun Zhang, Jian-feng Ye, Wei-jie Liang. Multiple objective reactive power optimization based on improved genetic algorithm. Power System Technology, 28(11) (2004) 67-71(in chinese). [9] Wiik J, Gjerde J O, Gjengedal T. Steady state power system issues when planning large wind farms. IEEE Power Engineering Society Winter Meeting, 2002, pp. 657-661. [10] Ying-jie Lei, Shan-wen Zhang. The box and the application of the MATLAB Genetic Algorithm. Xi'an University of Electronic Science and Technology, press, Wu han, Ching, 2006(in chinese).

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