Optimal Distribution Systems Reconfiguration for ...

Optimal Distribution Systems Reconfiguration for Short Circuit Level Reduction using PSO Algorithm Ali Parizad

H.R. Baghaee

Amirnaser Yazdani

G.B. Gharehpetian

Graduate Student Member, IEEE, Iran University of Science and Technology (IUST), Tehran, Iran. [email protected]

Member, IEEE, EE Department at Amirkabir University of Technology (AUT), Tehran, Iran. [email protected]

Senior Member, IEEE, Ryerson University, Toronto, Canada [email protected]

Senior Member, IEEE, EE Department at Amirkabir University of Technology (AUT), Tehran, Iran. [email protected]

Abstract— Power distribution systems are developing continuously and, consequently, the available short-circuit levels may exceed the ratings of the switchgear. One of the efficient methods of alleviating short-circuit currents is the reconfiguration. Network reconfiguration refers to the opening and closing of switches in a distribution system so that the network topology and, consequently, power flow from the substation to the consumers are changed. Distribution feeder reconfiguration (DFR) is a complex nonlinear combinatorial problem since the status of the switches is non-differentiable. This paper presents a new efficient algorithm for DFR, based on particle swarm optimization (PSO) algorithm, in order to minimize the short-circuit level. The numerical results of the porposed algorithm tested on the IEEE 83-Bus distribution system model reveals the feasibility, authenticity, and efficiency of the proposed PSO-based optimal reconfiguration algorithm. Keywords— Depth First Search, Distribution Networks, Particle Swarm Optimization, Reconfiguration, short circuit level

I.

INTRODUCTION

Distribution networks are crucial parts of the electrical power system, since they provide the final connection between a utility’s bulk transmission network and its customers. In distribution networks, switches are used for different applications [1]-[5]. They are commonly planned to isolate a fault, improve system reliability, reduce short-circuit level, restore the system, reconfigure system topology, restore the network, and reduce losses [6]-[10]. The majority of research on distribution network reconfiguration has concentrated on the minimization of losses. Thus, the network can be reconfigured depending on the characteristics of its loads, in order to reduce the active power losses. This can be achieved by changing the status of the existing sectionalizing and tie switches [12]-[13]. Thus far, various methods have been investigated for determining the optimal reconfiguration of a distribution network [13]-[26]. Merlin et al. 1975 described a branch and bound type method for minimizing losses [13]. In 1988, Civanlar et al. discussed the problem of reducing power losses in distribution feeders through feeder reconfiguration

[14]. In the study performed by Civanlar in [14], the feeder reconfiguration has been implemented by opening/closing of tie and sectionalizing switches. Shirmohamadi et al. [15], developed a heuristic method based on the idea presented in [13]. In this kind of study, convergence to the optimum solution and the independence of the final solution from the initial status of the network switches are guaranteed, and also some major drawbacks of the method proposed in [13] are avoided. Loss reduction via branch exchange approach by Backward/Forward Power Flow method was implemented in [16]. Heuristics methods were implemented to find the optimal solution with high computational speeds. In [17], simulated annealing (SA) and tabu search algorithms hav beeen used for loss reduction of distribution systems by automatic sectionalizing switch operation in large scale distribution systems. The implementation of SA is responsible for excessive computational time requirements. In contrast, Tabu search attempts to determine a better solution, but convergence cannot be guaranteed. Genetic algorithm (GA) is more likely to obtain the global optimal solution and takes less time in comparison to heuristic search methods. Radha et al. [18], presented an improved method based on a modified GA with real valued genes and an adaptive mutation rate in order to minimize the system power loss through distribution network reconfiguration (DNRC). Other algorithms such as ant colony, differential evolution, harmony search, and particle swarm have been employed for solving problems in network reconfiguration of distribution systems [19]-[22]. In [23], plant growth simulation algorithm (PGSA) has been used for nonlinear programing problems in reconfiguration of radial networks, and it can handle both objective functions and constraints. Multi-objective distribution feeder reconfiguration based on modified honey bee mating optimization (MHBMO) approach for loss reduction has been presented in [24]. In [25], a method has been proposed for improving the reliability of distribution systems using the reconfiguration, by defining a cost function that takes active power losses into consideration. In [26], a path-based mixed integer quadratic programming (MIQP) formulation of distribution feeder reconfiguration

(DFR) has been proposed for loss minimization and reliability enhancement. Most of the published work in the area of DFR are related to power loss reduction, voltage profile improvement, and load balancing. Besides these benefits, network reconfiguration can also reduce short-circuit levels and therefore prevent lossng of protection settings. This advantage of DFR has not been sufficiently addressed by the prior research. Thus, this paper is focused on the problem of reconfiguration for the purpose of reducing short-circuit levels in distribution networks. It is difficult to solve this problem by traditional linear or nonlinear programming methods, due to its nonlinear and nondifferentiable characteristics. Therefore, PSO algorithm (which has been previously used in [27] for distribution network reconfiguration), which is essentially a meta-heuristic numerical optimization tool, is used for finding the optimum solution for the entire distribution system. Thus, the proposed PSO-based algorithm has been implemented in MATLAB programming environment. Simulation results reveal that the proposed PSO-based optimization algorithm can find the optimal solution for the DNRC problem with a high degree of accuracy and authenticity. The next section briefly describes the problem formulation. The proposed optimization algorithm is described in Sections III. Simulation results are presented in Section VI. Finally, Section VII is devoted to conclusions. II.

Fig. 1. a) Tree Search Strategy, b) Depth First Search

PROBLEM FORMULATION

The topography of the power system network is continuously changing as the new power plants are constructed and power consumption increases. One of the effects of this growth is the increment in short circuit level of the power systems. These fault currents can cause thermal and mechanical stresses and may damage the equipment. Consistent to this issue, the control and reduction of short circuit level is a key factor in power systems. One solution to reduce the risk of increasing short circuit levels (SCL) is to upgrade the protection equipment in order to keep fault currents within the equipment capacity. Also, other techniques such as splitting the network, installing fault current limiter, change the neutral earth policy and etc. can be applied. In this paper, distribution system reconfiguration is used to reduce SCL. A. Objective Function th Short circuit level in i bus is defined as: (1) Vi 2 ( p.u ) Z i ( p.u ) where, Vi is prefault voltage at ith bus, and Zi is the equivalent impedance seen from ith bus. In order to reduce short circuit level and also keep voltage profile in acceptable range, the following multi-objective function is defined. (2) n  n SCLnew 

SCLipu =

  i Obj.Func. : α   ( ) 2  + β   (Vi − 1)2  + χ old  i =1   i =1 SCLi 

Fig. 2. Depth First Search Flowchart New

where, SCCi is short circuit level after reconfiguration, SCCiOld is short circuit level before reconfiguration, Vi is the voltage magnitude in ith bus, and N is the number of buses. The

first term in objective function is related to short circuit level reduction and the second term refers to voltage profile improvement index. Also, α , β , γ are weighting factors that

are slected arbitrarily. In this paper, a backward/ forward sweep-based load flow is used to solve power-flow problem [28]. However, for the distribution systems including distributed enrgy resources, the newly reported techniques are more efficient [29]-[35]. B. Depth First Search (DFS) Generally, a tree search starts at the root and explores nodes from there, looking for a goal node which satisfies certain conditions, depending on the problem. For some problems, any goal node is acceptable (N or J in Fig. 1(a)); In other problems, a minimum-depth goal node, i.e. a goal node nearest the root like only J in Fig. 1(a), is acceptable. Depth-First Search (DFS) is way of traversing graphs, which is closely related to preorder traversal of a tree. it explores a path all the way to a leaf before backtracking and exploring another path. For example, as shown in Fig. 1(b) after searching A, then B, then D, the search backtracks and tries another path from B. In this case, nodes are explored in the order A, B, D, E, H, L, M, N, I, O, P, C, F, G, J, K, Q and N will be found before J [36]. The representation of DFS algorithm is shown in Fig. 2. According to this flowchart, at each step, the stack contains some nodes from each of a number of levels. DFS visits all the nodes reachable from v in depth-first order method. Typically, distribution systems are operated as radial network. In this case, all of the loads are fed and there is no meshed network in system. In this study, DFS method is used to determine whether network is operated as radial or meshed system. In general, a graph is composed of edges E and vertices V that link the nodes together. A graph G is often denoted G= (V, E). An electrical network graph is a graph G (V, E) such that each element vi∈V is either a substation, transformer, or consuming unit of a real power network. There is an edge ei, j = (vi, vj) ∈ E between two nodes, if there is a physical line (cable) connecting directly the elements represented by vi and vj. III. PARTICLE SWARM OPTIMIZATION In recent years, efficient and effective stochastic optimization algorithms have been developed to solve varios engineering problems. Dissimilar to the traditional stochastic search algorithms, evolutionary computation techniques exploit a set of potential solutions, namely a population, and detect the optimal solution through cooperation and competition among the individuals of the population. These techniques often detect optimal solution in difficult optimization problems faster than traditional methods [37]. Essentially, PSO has been inspired by the swarming behavior of animals, and human social behavior. In recent years, various researches strongly confirmed the abilities of this newly proposed optimization technique [37]-[38], e.g. fast convergence, finding global optimum in presence of several local optima, simple programming and adaptability with constrained problems. Some new variations such as variable inertia coefficient, constriction factor, deflection, repulsion, stretching, maximum velocity limit, parallel optimization, and mutation have been

Fig. 3. Concept of PSO algorithm.

Fig. 4. Single-line diagram for IEEE 83-buses network

proposed to enhance convergence speed and accuracy of the PSO algorithm [39]. PSO is a population-based algorithm that exploits a population of individuals to probe a promising region of the search space. In this context, the population is called ‘swarm’ and the individuals are called ‘particles’. Each particle moves with an adaptable velocity within the search space and retains in its memory the best position it ever encountered. The global variant of PSO, the best position ever attained by all individuals of the swarm, is communicated to all the particles. The general principles for the PSO algorithm are stated as follows [38]-[39]: th Suppose that the search space is n-dimensional, then the i particle can be represented by a n-dimensional vector,

X i = [ xi1 , xi 2 ,..., xin ]

T

, and

velocity Vi = [ vi1 , vi 2 ,..., vin ]

T

where i = 1, 2,3..., N and N is the size of population. In PSO, particle i remembers the best position it visited so far, referred to as Pi = [ pi1 , pi 2 ,..., pin ]T , and the best position of the best particle in the swarm is referred as G = [ g1 , g i 2 ,..., g n ]T . Each

particle i adjusts its position in next iteration t + 1 with respect to the following equations [37]-[38]: (3) Vi (t + 1) = ω (t )Vi (t ) + c1r1 ( Pi (t ) − X i (t ))

+c2 r2 (Gi (t ) − X i (t ))

RESULTS OF THE PSO ALGORITHM.

Obj. Function Minimum Optimal Value

Obj. Function Maximum Optimal Value

Mean of Optimal Resulted values

Standard Deviation of Optimal Resulted values

0.9612

0.9703

0.9632

0.0241

(4)

IV. SIMULATION RESULTS

The proposed method for reducing of SCL and simultaneously maintain voltage profile in allowable range through reconfiguration, using PSO optimization method have been implemented in MATLAB 2016. The IEEE 83-bus distribution network is chosen to illustrate the effectiveness of this combinational optimization problem [40]. The single-line diagram for 83-buses test system is shown in Fig. 4. This system consists of 13 tie switches, 85 sectionalizing switches, 11 feeders and operates in 11.4 KV voltage level. The parameters of the study system and PSO algorithm have been provided in [40] and [38]-[39], respectively. The result of running PSO algorithm (10 times) are provided in Table I. The open switches before reconfigurations are: 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96. And the opened switches after reconfigurateion are: 96, 41, 34, 29, 25, 20, 15, 18, 13, 87, 43, 7, 1. Fig. 5 shows the trend of the convergence of the proposed algorithm in different iterations. Also, voltage profile of the study system before and after optimal reconfiguration is illustrated in Fig. 6. Also, in order to see the capability of the proposed optimal reconfiguration algorithm in decreasing the fault level of the system, the ratio of the SCC of buses after optimal reconfiguarion to the SCC of system before optimal reconfiguration is illustrated in Fig. 7. Simulation results indicate that after optimal reconfiguration using the proposed algorithm, voltage profile of the system is improved and fault level of the buses are decreased. Consequently, the distribution system security is improved.

1.5 Objective Function

Objective Function

1.4

1.3

1.2

1.1

1

0.9

0

50

100

150 200 Iteration Number

250

300

350

Fig. 5. Trend of the convergence of the proposed algorithm in different iterations.

1.04 After optimal DNRC Before opptimal DNRC 1.02

Voltage Magnitude (pu)

where, ω (t ) is inertia coefficient which gradually decreases from 1 at first iteration to a small magnitude about zero on a straight line. χ is constriction factor which is used to limit velocity, here χ = 0.7 .c1 and c2 denote the cognitive and social parameters respectively, here both of them are set to 2. r1 and r2 are random real numbers drawn from uniformly distributed interval [0,1]. The inertia coefficient in (3) is employed to manipulate the impact of the previous history of velocities on the current velocity. Therefore, ω (t ) resolves the tradeoff between the global and local exploration ability of the swarm. A large inertia coefficient encourages the global exploration while a small one promotes local exploration. Experimental results suggest that it is preferable to initialize it to a large value, giving priority to global exploration of search space, and gradually decreasing as to obtain a refined solution [39]. Fig. 3 shows the concept of particle swarm optimization formulation.

1

0.98

0.96

0.94

0.92

0.9 10

20

30

40 Bus Number

50

60

70

80

Fig. 6. Voltage profile of Study System before and after optimal Reconfiguration. 0

-10

SCC,new / SCC,old

-20 SCC,new / SCC,old (%)

X i (t + 1) = X i (t ) + χVi (t + 1)

TABLE I.

-30

-40

-50

-60

-70 10

20

30

40 Bus Number

50

60

70

80

Fig. 7. Ratio of SCC of buses after optimal reconfiguarion to the SCC of system before optimal reconfiguration.

Finally, it should be noted that installation of distributed energy resources affects the fault level of the system. The extention of the proposed method for distribution systems including distributed energy resources is the subject of feauture research of the authors.

V.

CONCLUSION

In this paper, a new algorithm was proposed for optimal reconfiguration of distributeion networks in order to reduce short circuit level and also keep voltage profile in acceptable range, simultaneously. Since it is a multi-objective problem, it is difficult to solve by traditional programming methods, due to its nonlinear and no differential characteristics. Accordingly, particle swarm optimization algorithm is used to find optimum solution for network reconfiguration problem. This algorithm can effectively ensure the convergence and speed up the calculation. To find distribution system topology (radial/ meshed network) first depth search method is used. The proposed approach was implemented on IEEE 83-bus and simulation results confirmed that implementing the proposed technique not only reduces short circuit level, but also maintains voltage profile level in acceptable range.

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