Power system reconfiguration and loss minimization for a distribution systems using “Catfish PSO” algorithm

Abstract

One of the very important ways to save electrical energy in the distribution system is network reconfiguration for loss reduction. Distribution networks are built as interconnected mesh networks; however, they are arranged to be radial in operation. The distribution feeder reconfiguration is to find a radial operating structure that optimizes network performance while satisfying operating constraints. The change in network configuration is performed by opening sectionalizing (normally closed) and closing tie (normally opened) switches of the network. These switches are changed in such a way that the radial structure of networks is maintained, all of the loads are energized, power loss is reduced, power quality is enhanced, and system security is increased. Distribution feeder reconfiguration is a complex nonlinear combinatorial problem since the status of the switches is non-differentiable. This paper proposes a new evolutionary algorithm (EA) for solving the distribution feeder reconfiguration (DFR) problem for a 33-bus and a 16-bus sample network, which effectively ensures the loss minimization.

Keywords

distribution system reconfiguration (DFR) / power loss reduction / catfish particle swarm optimization (catfish PSO) / radial structure

Introduction

The primary concern in a power industry is the consumer satisfaction and service reliability and continuity. The power distribution system is a field which is still having enormous scope for research and improvement. Faults are one of the important parameters in a power system, because of which 100% of efficiency cannot be guaranteed. Distribution system reconfiguration is a process of maintaining power balance and continuity of supply after removing the faulted portion. The main aim of reconfiguration is to restore the supply to as many loads as possible along with supply constraints. Although these loads are in good condition, they are unable to receive power due to fault. Hence the aim is to restore maximum possible loads taking various factors into consideration like system continuity, radiality, power loss, voltage magnitude, etc.

With the help of monitoring and control functions in an automated distribution system, fault location and isolation of a faulty section in real time is made possible [ 1]. But, service restoration to the non-faulted-out-of-service area in real time poses a real challenge. In recent years, fast restoration strategies have been developed to reduce the inconvenience to the user during such interruptions [ 2]. Still there has been considerable scope for research in service restoration through distribution feeder reconfiguration. In this section, the above problem is formulated as a nonlinear optimization problem where power loss is minimized subject to security and operational constraints. The test results obtained from a sample distribution network suggest that the catfish particle swarm optimization (catfish PSO) approach is better than the results obtained by other methods.

The distribution feeder reconfiguration problem can be formulated as a nonlinear optimization problem, and many optimizing techniques have been used to find the optimal solutions. Based on the characteristics of distribution network, some modifications are done so that the radial structure is retained and searching requirement is reduced.

All optimization problems in the steady-state analysis of power systems aim at minimizing or maximizing an objective function. Traditional methods like Gauss-Siedel method and operations research methods are used to solve linear, continuous, and differential objective functions. To solve nonlinear objective functions, evolutionary algorithms came into existence. The evolutionary algorithms, random and stochastic, are used for optimization of nonlinear problems. One of the recently proposed evolutionary algorithms is the catfish PSO algorithm.

It is known that distribution networks are built as interconnected meshed networks, while in operation they are arranged into a radial tree structure. A distribution network is divided into subsystems of radial feeders equipped by a number of sectionalizing switches and tie switches [ 3]. The power system can be operated more reliably by changing the configuration of the network. A number of algorithms including mathematical programming and artificial intelligent methods, such as, refined genetic algorithms (RGAs), ant colony search (ACS), heuristic approach (HA), adaptive genetic algorithms (AGAs) and honey-bee mating optimization (HBMO) [ 4] have been proposed to reconfigure distribution feeders with the objective of minimizing real power losses while avoiding transformer and feeder overloads and inadequate voltages. Of these evolutionary algorithms (EAs), the recently proposed algorithm is catfish PSO implemented on 16-bus [ 5] and 33-bus [ 6] test systems, whose test results obtained confirm that it produces better results compared to the results obtained by other methods.

Load flow or power flow program computes the voltage magnitude and angle at each bus in a power system under balanced three phase steady-state operating conditions. Once they are calculated, real and reactive power flows for all equipment interconnecting the buses are computed. The load flow analysis is implemented on 16-bus and 33-bus test systems. The objective function in this case is the loss reduction [ 7]. By using compensation techniques and using catfish PSO the losses are reduced in the system.

Mathematical formulation of problem

This paper is aimed at finding a way for load balancing through feeder reconfiguration so that stability and reliability of the distribution network could be enhanced. The objective of this optimization problem can be expressed by the minimization of the power loss as

(1) \mathrm{\Delta }P=\mathrm{Re}\left\{\mathrm{2}{\displaystyle \sum _{i=\mathrm{1}}^n\left(E_m-E_n\right)}\right\}+R_{\mathrm{line}}{{\displaystyle \sum _{i=\mathrm{1}}^n\left|I_i\right|}}^{\mathrm{2}},

subject to

1) No feeder section can be left out of service.

2) Radial network structure must be always retained:

(2) \phi \left(i\right)=\mathrm{0}

3) Bus voltage magnitude should be strictly restricted between the upper and lower limits:

(3) E_{\min }\le E\le E_{\max }\mathrm{,}

where \mathrm{\Delta }P is the net power loss, E_m is the voltage at node with higher potential, E_n is the voltage at the node with a lower potential, R_{\mathrm{line}} is the resistance of the line, and I_i is the current in the line.

Equation (1) corresponds to the objective function to be optimized and represents the total real power loss of the distribution system. Equation (2) deals with the radial topology constraint. It ensures the radial structure of the ith candidate topology. Equation (3) considers voltage constraints for each node of the system. In this study, the feeder switching status and consequently, the network configuration [ 8] are adjusted to keep the losses at a minimum in the area [ 9]. I_i is the current flowing through sectionalizing switches in the simplified model. The above objective function is also solved by the traditional mathematical programming method.

Catfish PSO algorithm

The catfish effect derived its name from an effect that Norwegian fishermen observed. If the fishermen could keep a higher percentage of their sardines alive when they arrived at the port, they stood to make more profit. The sardines were confined in small holding tanks which deprived them of their exercise during the transportation back to the port. Therefore, only a few sardines were usually alive upon returning to the port, with the majority having died halfway during their journey. However, some fishermen discovered that the majority of the sardines could be kept alive if a small number of catfish was introduced into the holding tank. The catfish, a different species of sardines, swarm around their new environment and stimulated movement in the school (swarm) of sardines. This stimulation made the sardines nervous of the catfish, and accelerated the swim of the sardines. This stimulated movement kept the sardines alive for a longer period. This effect was also used in the management of human resources in the workplace. A competition was introduced into a group of individuals by eliminating the worst performing individuals and replacing them with newly hired employees. The fear of being eliminated stimulated renewed motivation in this group of employees.

PSO, a population-based stochastic optimization technique, was developed by Eberhart and Kennedy in 1995 inspired by simulating the social behavior of organisms. PSO was employed to effectively solve the optimization problem in various areas, e.g. function optimization [ 10], fuzzy system control [ 11], parameter optimization [ 12], artificial neural network training [ 13], job shop scheduling problem [ 14], among other areas where genetic algorithms can be applied to. PSO showed promising performance on nonlinear function optimization and has received much attention [ 15]. However, PSO exhibited poor local search capabilities [ 16] and often led to premature convergence, especially in complex multi-peak search problems [ 17]. To overcome these disadvantages of PSO, many improvements were proposed. Shi and Eberhart [9] proposed a linearly decreasing weight particle swarm optimization (LDWPSO), in which a linearly decreasing inertia factor was introduced into the velocity update equation of the original PSO. The performance of LDWPSO was significantly improved over the original PSO, as LDWPSO effectively balanced the global and local search abilities of the swarm.

To overcome the disadvantages (premature convergence, especially in complex multi-peak search problems) of PSO, the catfish PSO was proposed in this paper, in which the catfish effect was applied to improve the performance of the LDWPSO algorithm. The LDWPSO was chosen to demonstrate the effectiveness of the catfish particle, because LDWPSO was the most representative method among the improved PSO methods [ 9]. The catfish effect was the result of the introduction of new particles into the search space (“catfish particles”), which replaced the particles with the worst fitness by the initialized value at extreme points of the search space when the fitness of the global best particle was not improved for a certain number of consecutive iterations. This resulted in further opportunities of finding better solutions for the swarm by guiding the whole swarm to promising new regions of the search space. In the PSO, w_{\max } is 0.9, w_{\min } is 0.4 and {\max }_{\mathrm{iter}} is the maximum number of allowed iterations.

The motivation for developing the catfish PSO was derived from the observation of the interaction between sardines and catfish. Analogous to the effect described above, the introduced catfish particles stimulated a renewed search by the “sardine” particles. In other words the “catfish” particles led the “sardine” particles which were trapped in a local optimum into a new region of the search space, and thus to potentially better particle solutions. The particles, generations, search space and the catfish particles of the catfish PSO are analogous to the sardines, the transportation process, the fish tank and the catfish of the Norwegian fishermen, respectively. In the catfish PSO, a particle swarm is randomly initialized in the first step, with the particles distributed over a D-dimensional searching space. Each particle is updated by the following two values. The first one, called p_{\mathrm{best}i} , is the best solution (fitness) it has achieved so far. The other value, tracked by the PSO, is the global best value g_best obtained so far by all particles in the population. The position and velocity of each particle are updated according to Eqs. (2)–(3). If the distance between g_best and the surrounding particles is small, each particle is considered a part of the cluster around g_best and will only move a very small distance in the next generation. To avoid this premature convergence, catfish particles are introduced. The catfish particles replace some of particles with the worst fitness value of the entire swarm. The catfish PSO process is graphically illustrated in Fig. 1 for the two-dimensional Rastrigrin function. The diamond sign denotes the optimal solution. It is seen from Fig. 1 that almost all particles converge near g_best after a certain period of time. If the g_best value does not improved for a number of consecutive iterations (five iterations has been adopted as a threshold value), it is considered stuck in a local optimum. Under such circumstances, some of the particles with the worst fitness value W are removed, but their p_best is still retained. In Fig. 1(b), the current p_best position of the worst of the particles (indicated by W) is shown as W-p_best. After the particles W are removed, an equal number of catfish particles, in this case C are introduced into the swarm. Its p_best values (C-p_best) is identical to W-p_best of the particles that have been removed (Fig. 1(c)). At the beginning, the catfish particles have no velocity \left(v_{\mathrm{id}}^{\mathrm{old}}=\mathrm{0}\right) . They are randomly positioned at the extreme points of the search space, i.e. the positions (min, min), (min, max), (max, min) or (max, max) in the two-dimensional function, and stimulate a renewed search process for all particles of the swarm. Each catfish particle will update its positions by following its own p_best and the g_best value. In Eqs. (2) and (3), the parameters r₁ and r₂ are the key factors affecting the updating vector of a catfish particle if v_{\mathrm{id}}^{\mathrm{old}}=\mathrm{0} and c = 2. The size of the catfish particle search area is dependent on the position of its p_best and the velocities of itself and g_best position. If r₁>r₂, the catfish particles will be drown closer to the position of p_best after updating. If r₁<r₂ however, it will be drown closer to g_best. The distance covered by the catfish particle when it updates is directly proportional to r₁ and r₂. Therefore, the potential search area of a catfish particle can be plotted with the x_{\mathrm{id}}^{\mathrm{old}} , p_best and g_best given according to Eqs. (1) and (2). In Fig. 1, q (square box) denotes the potential search angle of catfish particles C. The green lines indicate the border of the potential search area of catfish particles C that have started at the positions (max, max).

By positioning the catfish particles at extreme points of the search space, the potential search area of the catfish particle is maximized. The probability of finding a better solution also increases when the potential search area of the catfish particle is maximized. Consequently, introducing the catfish particles at extreme points of the search space is the ideal choice. Figure 1(d) and (e) show how the introduced catfish particles update their position within the positional search area via Eqs. (2) and (3), and how they guide the g_best particle, whom the other particles follow, to new, promising regions of the search space. Finally, the particles converge around g_best when a stopping criterion is met (Fig. 1(f)), i.e. an optimal solution is found. As shown in Fig. 1, the region of swarm activity is constantly changing and the swarm makes continuous progress. The relatively small number of catfish particles guides the entire search process, and influences the entire swarm. The reason for the introduction of catfish particles at extreme positions in the search space is simple: it maximizes the potential search area.

Steps for implementing catfish PSO for loss reduction

01: Begin

02:ƒ Randomly initialize 20 swarms of voltages (particles) ƒ€ƒat the 33 buses

03: ƒwhile (number of iterations= 30)

04:ƒƒ Evaluate fitness or power loss for each set of ƒƒƒvoltages

05: ƒƒ forn = 1 to number of particles (5 sets of voltages)

06: ƒƒƒFind p_best

07: ƒƒƒFind g_best

08: ƒƒƒfor d = 1 to dimension of particle swarm (33).

09: ƒƒƒƒƒƒupdate the position of particles by ƒƒƒƒƒƒƒstandard equations

10: ƒƒƒnext d

11: ƒƒ next n

12: ƒƒ if fitness of g_best is the same 5 times then

13:ƒƒƒ Sort the particle swarm via fitness from best to ƒƒƒƒ€worst

14:ƒƒƒ for n = few of N number of particles (all 33-ƒƒƒƒ bus voltages)

15: ƒƒƒƒfor d = 1 dimension of particle swarm

16: Randomly select extreme points at max or min of the ƒ€€search space

17: ƒƒƒƒƒReset the velocity to 0

18: ƒƒƒƒnext d

19: ƒƒƒnext n

20: ƒƒ end if

21: ƒƒUpdate the inertia weight (initial= 0.9, final= ƒƒƒƒ0.4) value by Eq. (3)

22: ƒnext generation until stopping criterion

23: end

Tables 1 and 2 are respectively the line data for 33- and 16-bus test system. Figures 2 and 3 are respectively the 33- and 16-bus radial distribution system.

Results and comparisons

Tables 3 and 4 give the power loss results with various switch statuses of the 16-bus and 33-bus test system.

Tables 5 and 6 show the comparison of the results obtained by the catfish PSO with the results obtained using other methods for the 16- and 33-bus test systems.

For assumed series fault at bus 14 in the 33-bus system, and at bus 11 in the 16-bus system, Tables 3 and 4 present the results obtained by using catfish PSO. It is observed that the power loss is minimum when switches 7, 11, 14, 28, 32 are turned on for the 33-bus system and 5, 4, 11 are turned on for the 16-bus system. If the configuration changes, the power loss will increase. The power loss is calculated using catfish PSO with various switch statuses and listed in Tables 3 and 4. The proposed method is compared with the methods proposed by BFOA [ 6], Shrimohammadi et al [ 3], Zhu [ 4], Bouhouras and Labridis [ 7], Gomes et al. [ 8], Wu et al [ 18], Martin and Gil [ 19], Gomes et al. [ 2], Goswami & Basu [ 21], ACSA and various other prevalent methods for the same 16-bus and 33-bus test system. For effective comparison, the results of the proposed method along with other methods are tabulated in Tables 5 and 6. Here the power loss is minimized by 3.35% and 4.49% respectively compared with the result as mentioned in other methods. In the initial configuration, the power losses are 202.71 kW and 511.41 kW but after reconfiguration using proposed method, the power loss is 131.228 kW and 145.14 kW which is much less compared with other methods. Approximately a power loss of 35.26% and 12.95% is minimized as compared with the original configuration. So the proposed method is highly suitable for restoration and reconfiguration [ 21, 22].

Figures 4 and 5 demonstrate the convergence characteristics of power-losswith 30 and 25 iterations.

Conclusions

The catfish PSO algorithm was proposed in this paper to configure the distribution network to keep the load balance so that the power loss was minimum. The problem was formulated as a nonlinear optimization problem with an objective function of minimizing power loss subject to security constraints. The test results indicated that using the catfish PSO method, the feeder reconfiguration problem [ 23, 24] could be solved efficiently and the power loss was minimized effectively by reconfiguring the system. The fast and effective convergence of this approach proves that it is a highly suitable technique to use in service restoration procedures of distribution automation system.

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