Medium Voltage Distribution Network Reconfiguration Considering Reactive Power Compensation

International Journal of Energy and Power (IJEP) Volume 4, 2015 www.ijep.org doi: 10.14355/ijep.2015.04.012

Medium Voltage Distribution Network Reconfiguration Considering Reactive Power Compensation Xiaorong Li1, Shunxin Li1, Dapeng Liang1, Anjia Mao2, Zixia Pei2, Lanlan Chen2 Economy & Technology Research Institute of SGCC JIBEI, North China Electric Power University lxr_xr@163.com

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Abstract A new method of distribution network configuration, including reactive power optimization is proposed in this paper. This method is based on the similarity of the configuration and reactive power optimization both in modelling and the algorithm.

The paper takes the reactive power compensation capacity as a load change in distribution network configuration, and combines the two chromosomes of compensation and configuration together. The global optimal solution of minimizing the net loss is obtained using GA (Genetic Algorithm). Owe to the relevance of the two factors, the conclusion of this paper is more convincible. In the end, the results of the IEEE‐33 system demonstrate the method’s effectiveness.

Keywords Distribution Network Configuration; Reactive Power Compensation; Loss Reduction; GA

Introduction The power distribution network interlinks the power transmission network and connects to power users, undertaking the task of electricity distribution. For a long time, the focus of the power grid construction in China is mainly concentrated in the highly technical transmission network, which plays a key role in the power supply and the safety and stability of the power operation. However, little attention is paid to the 10 KV (or below) terminal distribution network, which is relatively simple‐structured and has less impact on the whole power grid. Because of that, the distribution network loss rate is generally on the high side and thus it seriously affects the economic operation of power system and is not conducive to energy conservation and emission reduction.

The fundamental measure to save energy and reduce loss is supposed to innovate the technology of the distribution network, such as the replacement of wires of large wire diameter and low resistance or the replacement of transformers of low loss. Nevertheless, it is in fact not a good choice considering the cost of investment and construction period. Hence, on the basis of the existing distribution network, using network reconfiguration and reactive compensation measures to optimize the operation of the distribution network, has become one of the main measures to reduce losses in current distribution network [1]. Network reconfiguration changes the combination of the circuit breaker status to optimize the path of the user’s power supply. Common algorithms mainly include the optimal flow algorithm [2], branch exchange method [3], dynamic programming algorithm [4], artificial intelligence algorithm [5‐6] as well as the combination of the above methods [7], etc. For example, a hybrid algorithm, proposed in [7], has higher computational efficiency, combining genetic algorithm and particle swarm optimization algorithm. Similar to network reconfiguration, reactive power optimization regulates the reactive voltage by adjusting the capacity of the reactive power compensation device, aiming to reduce grid loss and increase the rate of qualified voltage. The algorithms for reactive power optimization mainly include linear programming [8], nonlinear programming [9], mixed integer programming [10], and artificial intelligence algorithms [11], and so on. The method, proposed in [11], of which solve the reactive power optimization of power systemutilizing local random search application particle swarm optimization (LRS ‐ PSO) algorithm, can get better convergence and higher quality of the solution. Genetic algorithm of the artificial intelligence algorithm, due to simple and easy encoding, does not require the objective function of good mathematical properties, take the elite reserved strategy into account, and is in theory a kind of global convergence

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of the algorithm. Therefore, it has been widely used in different aspects of power system.

At present, most of the researches on measures to reduce power lossof thedistribution network, such asnetwork reconfiguration and reactive optimization are studied separately. There are a few researches, considering the influence of both of the two loss reduction measures. One example, studied in [13], is to reconstruct the network and then use the alternate iteration method of reactive power compensation. Another example, proposed in [14], introduces alternating iterative algorithm based on electrical dissection information, of which has high computing speed and good convergence performance. Though, these algorithms are searching another local optimal solution based on a local optimal solution and thus it is very likely that the result wonʹt be the global optimal solution.

Seeing that the distribution network reconfiguration and reactive power optimization, whether in the establishment of the model are based on the research of genetic algorithm, has a certain similarity, the paper presents the medium voltage distribution network reconfiguration method considering reactive power compensation. The paper takes reactive power compensation capacity of the uncompensated position as the variation of load in the power distribution network reconfiguration, comprehensive analysing the influence of the two factors on the distribution network line loss. Therefore, the result is the globally optimal. The method has better reference value than considering distribution network reconstruction or the reactive power optimization separately. At he end of the paper, we present an example based on IEEE‐33 to prove the effectiveness of the method.

Mathematical ModelLing The mathematical example of distribution network reconfiguration is usually stated as the pattern, as shown in (1).

N

Pli2  Qli2

i 1

U i2

min f   ki Pli   ki Ri

(1)

When considering loss reduction as the target, the mathematical model of reactive power optimization of the distribution network is commonly stated as the pattern, as shown in (2).

N

m

n

i 1

i 1

i 1

min f  w1  Pli  w2  Qci  w3   U i  (2) 2

Where N, m and n denote the branch number, the node number of reactive power compensation and the total node number respectively. Pli represents the active power loss of the i line, ki represents the state of switch (1 for opening and 0 for closing) and Ri represents the resistance of the branch i. Pli is the active power of the i line and Qli is the reactive power of theithline. Ui is the voltages at the node i, U i is the voltage variation and Qci is the

reactive compensation at the node i.w1, w2 and w3 represent the weight coefficient.

As mentioned above, we choose joint distribution network loss as the model of distribution network reconfiguration considering the reactive power compensation, as shown in (3).

N

Pli2  Qli2

i 1

U i2

min f   ki Pli   ki Ri

(3)

It should be noted that Qli represents the reactive power after the compensation. And then we take the two optimization objectives after the reactive power optimization model as inequality constraints.

The power flow equations become the equality constraints of the optimization, as shown in (4). n   Pi  U i j1U j Gij cos ij  Bij sin ij (4)  n Qi  Qci  U i  U j Gij sin ij  Bij cos ij  j 1









Pi and Qi represent the active and reactive power injected in node i, Ui and Uj denote the voltage magnitude at node i and jrespectively. Gij and Bijare the conductance and susceptance of branch connecting node iand node j.  ij

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represents voltage phase angle difference between node i and j.

The inequality constraints represent operating limits on voltage magnitudes, compensation and complex power. U i min  U i  U i max  Qc min  Qci  Qc max S  S j max  j

 i  1, 2, , n    (5)  j  1, 2, , l 

U i min and U i max denote the lower and the upper bound. Qc min and Qc max denote the lower limit and the upper limit

of compensation. S j and S j max represent the complex power across the feeder line and the maximum permissible power respectively. l and n denote the branch number and the node number respectively. In addition, there are following constraints to meet when reconfiguring the distribution network: one is that distribution network must meet the requirements of the load, and there can be no island. Another one is that after reconfiguration the distribution network must become radial.

Genetic Algorithm Considering Network Reconfiguration of the Reactive Power Compensation Genetic algorithm renders the objective function of solving the problem corresponding to the fitness of the individual, that is to say, the bigger fitness means closer to the optimal solution and also has a higher chance of heredity to the next generation. Crossover and mutation can obtain new excellent individuals, and maintain the diversity of the genetic algorithm group. Finally, we can find the optimal solution of this problem via repeated iterations Establish the Fitness Function To ensure the fitness function F constantly greater than zero and as large as possible, we simply need to take the objective function as the reciprocal of the fitness function, shown in (6).

F

1 (6) Pli2  Qli2  ki Ri U i2

Encode Chromosomes This paper uses the binary encoding. We have presented a chromosome as an array of integers, where the position of each element indicates the state of switches and the length is the sum of the switches. In reactive power optimization, chromosome can be expressed as a vector, i.e. [G1,G2,…,Gi,…,Gm]. Where m is the total number of nodes required for reactive power compensation in the network. Giisbinary string whose length iski. when converted to decimal, it also represents the number of nodes which need to be compensated.Binary encoding just needs to cover themaximumcompensation at the node.For example, suppose the node here needs to install 5 groups of compensation deviceat most.Since 23>5>22, we choose 3 as the value of k. Jointing chromosomes of reconfiguration and reactive power optimization together, we can obtain chromosomes of the network reconfiguration considering the reactive power compensation, as shown in (7).

1, 0,1...0,1, G1 , G 2 ,..., Gi ,..., G m  (7) Selection of the Crossover Rate and the Mutationrate Since compensation gene segments are appended to the chromosomal gene ofreconfiguration, the length of the chromosome in genetic algorithm increases, extending the search space of the algorithm and thus affecting the search efficiency of the algorithm.In order to improve the search performance of the algorithm, the crossover rate and mutation rate can be properly optimized.

In the initial iterations, most of the chromosomes are constituted of a pool of random solutions. We need to find a higher crossover rate to guarantee the search speed of the algorithm., but in the later iterations, individuals tend to be the optimal solution and if using the high crossover rate, the good genes may be destroyed. Though, the

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crossover rate can’t be assigned a value too low to affect the genetic search speed. Hence, we should modify in real time the crossover rate Pc according to the good level(that is,the fitness)of the individuals of the population in the iterations. This paper chooses the formula, as shown in (8).  Pcs F (n)   , Pc  Pcb  F (m)  F (n)   n F (n)   , Pc  Pcb (8) Pc   Pcs  (0)  F   Pcb Pc  Pcb 

N and m denote the number of iterations and the first iteration number for F (n)   respectively, Pcs represents the highest crossover rate and Pcb represents the lowest crossover rate. We define  as the step size parameter of the decreasing of the crossover rate and ε as the bounds of the fitness variation when decreasing the crossover rate, representing the fitness variation between the maximum and the minimum of the initial population ,the population of the nth iteration and the population of the mth iteration. Since the crossover rate value ranges from 0.4 to 0.9 [15], PCS and PCB belong to 0.4 to 0.9.

A continuous curve in Fig.1 describes the variation trend of the discrete crossover rate.

Pc

Pcs

Pcb

m

n

Fig.1 CURVE OF CROSS‐RATE

The optimal value range of the cross‐rate is from 0.001 to 0.1 [15]. To guarantee the diversity of the population in the initial iteration, mutation rate should not be too low. In the later iterations, the population tends to appear the same chromosomes and the crossover may occur in the two same chromosomes, consequently making no sense to cross. In addition, upon the occurrence of a succession of generations of the same optimal chromosome, the algorithm easily falls into a local optimum situation. So we need to further increase the mutation rate. The paper sets the initial mutation rate 0.05.If the chromosome is still the same after five successions of generations, we set the rate 0.1.

Main Steps of the Algorithm 1. Set the chromosome coding length L,the population size N0, the evolution number of the largest population NG,the mutation rate Pm and the crossover rate Pc,etc.

2. Generate the initial population X0 of the size N0, and fix the infeasible solution.Set the genetic number T=1.

3. Calculate the network power flow, and get the fitness of chromosomes.

4. Go on genetic operation, and sort it.

5. Determine whether achieves the convergence condition, if so, output the first individual of the population. If not, then T = T + 1, turn to step (3).

Numerical Simulation The paper is based on the platform MATLAB, and calculate on the node system of IEEE‐33, as shown in Fig.2. The system contains 37 branches among whichthere are 5 tie switch branches. The voltage reference is 12.66 KV and the power reference is 10MW. The initial total load of the net is 4084.26 + j2547.32kVA. Set the parameter PCS, PCB, the size of the population and the iteration number as 0.9, 0.5, 20 and 40,respectively.

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Fig.2 IEEE‐33 NODE DISTRIBUTION NETWORK

The nodes of the compensation in this example are derived from article [16], covering the node 30, node 8 and node 14. The article applies the adaptive genetic algorithm to the network for reactive power optimization. The comparison of the result after compensation between the example and article [16] is shown in Tab.1 and Tab. 2.

From the Tab.1 and Tab.2, we can get the idea that the paper’s compensation is lower and the loss reduction rate is higher than article [16].

The hybrid intelligent algorithm, presented in [7], is to reconfigure the networkindependently. We compare our configuration result with the article, as shown in Tab. 3.

TAB.1 COMPARISON OF REACTIVE POWER COMPENSATION (KVA)

the Node number

Article [16]

The paper

30

930

920

8

300

280

14

390

240

TAB.2 COMPARISON OF NETWORK LOSS AFTER OPTIMIZATION

Article [16]

The paper

Optimize before (p.u.)

0.0203

0.0203

Optimize after (p.u.)

0.0147

0.0095

Loss reduction rate

0.2737

0.5320

TAB.3 COMPARISON OF DISTRIBUTION NETWORK CONFIGURATION

Article [7]

The Paper

Open branch collection

7|9|14|32|37

7|9|14|32|36

Net loss before reconfiguration (p.u.)

0.0207

0.0203

Net loss after reconfiguration (p.u.)

0.0142

0.0095

Loss reduction rate

0.3149

0.5320

From the Tab.3, we can get the idea that there is little difference in the reconfiguration network between the paper and the article [7].

Conclusion And Prospect This paper takes into account reactive power compensation in the algorithm of the distribution network configuration.With the two methods of loss reduction optimizing at the same time, relative to alternate iteration, the optimal solution has the global convergence.Moreover, since the algorithm of the paper is equivalent to improve the load quality when configuring the network and shape the network structure, the algorithm comparing to optimize separately obtains a better optimization effect. The final example proves the feasibility and superiority of the method.

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In this paper, we splice the chromosomes of reconfiguration and compensation together when encoding. Though, to a large extent it ensures the global convergence of the optimal solution, it has also spun the search space of the solution and lower the search speed of the optimal solution. Hence, in future,we could consider the further enhancement of the algorithm to increase the computational efficiency.

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XiaorongLi: (1977‐), female. Senior engineer, main research direction, power system planning, analysis and control of power system.

Shunxin Li: (1978‐), female. Senior engineer, main research direction, power system planning, analysis and control of power system.

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