Multi-periods distribution feeder reconfiguration at the presence of distributed generation through economic assessment using a new modified PSO algorithm

Abstract

Over the past few years, distribution system operators try their best in order to obtain the well-balanced distribution systems to reduce the power loss, decrease the operation cost and improve the reliability indices. This paper presents an efficient method to solve the multi-periods distribution feeder reconfiguration (DFR) with respect to the presence of Distributed Generators (DGs). Most studies so far have investigated reconfiguration problem as a single period problem considering a fixed level of load. However, in this study, time-varying characteristics of load profiles and line failure rates are considered. The proposed framework formulates and studies the direct and implied costs of power supply, reliability, energy loss, and switching operations, simultaneously. By considering these conditions to the DFR problem, the number of decision variables is significantly increased and the problem becomes more complicated than before. To this end a new modified particle swarm optimization (PSO) algorithm, compatible with the multi-periods problems, is presented. In the proposed algorithm, the costs of individual periods and the total cost are considered simultaneously in order to update the particles. To evaluate the performance of the proposed method, the results are compared with the original one. A typical distribution test system is used to demonstrate the performance of the proposed approach.

Keywords

Distribution feeder reconfiguration distributed generation reliability particle swarm optimization algorithm

1 Introduction

In recent years, the distribution networks experience a sharp increase in load demand on account of the extensive growth of the utilities. Besides, with the advent of deregulation in the power industry, there is a greater focus on managing the network assets efficiently rather than reinforcing the network’s capacity. Electric utility distribution companies (DISCOs) intend to improve their profits and reduce the investment risk to meet the growth demands in their territories while keeping their customers’ bills affordable. DISCO planners try their best in order to implement new planning strategies for their network in order to meet the load growth economically and serve their customers with a reliable electricity supply. These goals can be reached by doing DFR and considering new technologies such as DG.

A literature survey reveals that various optimization techniques have been used for solving DFR problem, and most of them are established upon heuristic search techniques. The research works in this area can be categorized in two major groups: i) the papers didn’t consider the impact of DGs on DFR problem i.e. [1 –9] and ii) the articles which evaluated the presence performance of DGs on DFR problem [10 –13]. Although there is a vast body of research on the DFR problem, little attention has been paid to the consideration of DGs influence on DFR problem. Ashisa et al. proposed an AIS-ACO hybrid approach for multi objective DFR problem [1]. Raju and Bijwe presented an approach based on sensitivity and heuristics for loss reconfiguration of distribution system [2]. Assadian et al. presented a guaranteed convergence PSO in cooperation with graph theory to distribution network reconfiguration in order to save energy [3]. Falaghi et al. utilized ant colony optimization-based method for placement of sectionalizing switches in distribution networks using a fuzzy multi-objective approach [4]. Mendoza et al. proposed a new methodology for minimal loss reconfiguration using GA with the help of fundamental loops [5]. They have utilized loop vectors to ensure the generation of feasible individuals, but this approach fails to search the isolation of principal interior nodes of the distribution networks and therefore requires mesh checks. Abdelaziz et al. presented a modified Tabu search algorithm for distribution system reconfiguration [6]; also they proposed a modified particle swarm optimization for distribution system reconfiguration [7]. Swarnkar et al. proposed a new codification for various meta-heuristic techniques to solve the reconfiguration problem of distribution networks [8]. Their proposed codification was based upon the fundamentals of graph theory which not only restricts the search space but also avoids tedious mesh checks. Wang and Cheng proposed a plant growth simulation algorithm for configuration of large distribution systems [9]. In recent years, deregulation and liberalization of energy market, increasing petroleum fuel prices, technical benefits and associated environmental concerns have attracted the attention of researchers to incorporate DGs in distribution system. Narimani et al. proposed a new approach on the basis of gravitational search algorithm to solve the DFR problem considering DGs [10]. Nasiraghdam et al. presented a novel multi-objective artificial bee colony algorithm to solve the DFR problem and hybrid DGs sizing [11]. Franco et al. modeled the problem of DFR considering the presence of DGs as a mixed-integer linear programming (MILP) problem and solved it with MILP solvers [12]. In [13], Wu et al. suggested an ACO algorithm to solve the multi-objective DFR problem with consideration of DGs in order to obtain the optimal power loss and load balance of radial networks.

Most of presented papers so far have implemented reconfiguration methods for fixed level of power demand whereas this assumptions lead to suboptimal solution. Operational experiences have shown that many influences in distribution operations, such as load profiles, failure rates and service restoration times, have time-varying characteristics. Therefore, to enhance distribution service reliability and operation efficiency, these factors should be considered in operation planning. In [14], network reconfiguration and capacitor allocation are implemented for loss reduction using mixed integer nonlinear programming (MINLP) method. The proposed method considers the daily load curve represented by a given number of load levels; however, it does not consider switching costs. Ref. [15], is one of the few researches which considers time-varying nature of loads and switching costs during reconfiguration process. The objective function consists of loss cost, outage cost and switching costs. In this method annual load curve is divided into multi-periods load levels and the feeder configuration of each load level is optimized using binary particle swarm optimization method. Disadvantage of this method is that configuration of each load level is achieved based on load profile in that period and switching cost from configuration in previous period network. Therefore, only network configuration in the previous period is considered in determination of one period and configurations of other periods are not considered, whiles, one switching have impact on reliability and loss of multiple periods. Also, in [16], a two stage method is presented to determine annual feeder reconfiguration scheme considering switching costs and time-varying variables such as load profiles. In the first stage of the proposed method, to obtain effective configurations, optimal configuration for each day of year is determined independently using harmony search algorithm (HSA) and graph theory. After determination of effective configurations for the network, in the second stage, year is divided into multi equal periods, and dynamic programming algorithm (DPA) is used to find the optimum annual reconfigurationscheme.

Nowadays due to rise of fuel prices and consequently rise in electricity power generation cost, it is crucial to find away in order to generate electricity power with minimum cost while satisfying technical and security aspects of the network. In this regard operation cost has been considered in the objective function in this paper. Furthermore with expansion of power network and increase of power electricity demand, it is important to keep the power losses in acceptable range or reduce it. To this end the cost of power losses has been added to the objective function of the proposed approach. Also, it is a true fact that consumers would be very pleased to do their activities with no interruption of electricity. Hence they expect fewer power supply faults and as shorter (short as possible) duration of these interruptions in power demands. In the other hand power supply companies have identical aims due to money losses. There are many formulations in relation to power system reliability and availability, one of them is Energy Not Supplied which is considered in the objective function in this paper. The main objective is to give the network owners incentives to plan, operate and maintain their networks in a socio-economic optimal way, since they have to pay fine for energy not supplied hours, and thereby provide a socio-economic optimal level of reliability.

The problem is proposed as a multi-periods (monthly) DFR, which has a large search space. Therefore, conventional algorithms may not achieve acceptable results, and it is crucial to solve it with a special accurate method. To this end, a modified PSO algorithm is used to be compatible with the proposed multi-periods problem.

The highlighting characteristic features of this paper can be summarized as follow:

The DFR problem is implemented in the multi-periods environment regarding time-varying characteristics of load profiles and reliability data.

The objective function is formulated considering power supply cost, reliability (ENS) cost, power losses cost and switching operations cost, simultaneously.

A Modified PSO algorithm is proposed to solve the problem.

The performance and potential of the proposed approach is effectively validated with numerical results.

The remainder of this paper is conducted as follows: Section 2 presents problem formulations. In section 3, the solution strategy is explained. Section 4 is devoted to present the application examples. Finally, conclusion of the paper is drawn in Section 5.

2 Problem formulation

The total cost model considered as the objective function, consist of four main components: power supply cost, reliability cost, power losses cost and switching operations cost. The mathematical models of these functions as well as the related decision variables and the constraints are proposed in the subsequent subsections:

2.1 Objective function

Cost of power supply

Mathematical model of electrical power supply cost for monthly periods during a year is as follows: $\begin{matrix} Cost_P = {Cost}_{DG} + {Cost}_{sub} = \dots \\ \sum_{n = 1}^{N_{DG}} (K_{n} \times \sqrt{P_{{DG}_{I} NS, n}}) + \dots \\ \sum_{m = 1}^{12} (\sum_{n = 1}^{N_{DG}} (P_{DG, n}^{m} \times {price}_{DG, n}) + P_{Sub}^{m} \times {price}_{Sub}) \times t^{m} \end{matrix}$ (1)

Where, Cost_DG and Cost_Sub are the power supply costs of DG units and substation, respectively. t^m is the time of mth monthly period. N_DG is the number of DGs. $P_{DG, n}^{m}$ , $P_{Sub}^{m}$ , price_DG,n and price_Sub are the output powers and the energy prices of the nth DG unit and the substation in mth monthly period, respectively. Also, P_{DG_INS,n} and K_n are the installation capacity and an empirical coefficient for the nth DG unit, respectively.

Cost of power losses

Minimizing the active power losses is an important issue in DFR problem which is considered in most of the previous works. Power losses cause an extra energy consumption which is supplied and not sold. Therefore, its cost should be calculated and added to the total cost as follows: $Cost_Loss = \sum_{m = 1}^{12} \sum_{b = 1}^{N_{b r c h}} (R_{b} \times {| I_{b}^{m} |}^{2}) \times t^{m} \times p r i c e_{s u b}$ (2) where, R_b is the resistance of the bth branch, $I_{b}^{m}$ is the magnitude of current for the bth branch in mth monthly period, and N_brch is the number of branches in the network.

Cost of switching operations

By considering the costs of maintenance, switching operations, switch surge and switch lifetime, this study assumes switching operation cost to be a certain percentage of a sectionalizer’s installation cost. The total annual switching cost is calculated by: $Cost_S w = \sum_{m = 2}^{12} \sum_{s = 1}^{N_{S w}} | S w_{s}^{m} - S w_{s}^{m - 1} | \times {price}_{S w}$ (3)

Where, $S w_{s}^{m}$ is the state of sth switch in mth monthly period, with 0 and 1 corresponding to open and close states, respectively. N_Sw is the total number of switches, and price_Sw is the switching operation cost.

Cost of reliability

The customer service interruption cost is evaluated based on the Energy Not Supplied (ENS) index. Energy Not Supplied (ENS) has not been considered too much in literatures, so it is explained in this section. In this regard consider a distribution network with N_B nodes (N_B > 1) and node 1 as the source of this network. Assume that all nodes except the source have an active power $P_{bi}^{m}$ [kW], bi∈ { 2, …, N_B }, in mth monthly period. The value of ENS at each node can be calculated in terms of the reliability parameters of the distribution network [17]. To this end, a distribution branch between nodes bi and bj is associated with the following parameters: a failure rate $λ_{bi, bj}^{m}$ ([fail/km-month]), an average reparation time t_bi,bj ([h/fail]), and a line length, d_bi,bj ([km]). The reparation time is the time that passed to reestablish the service to a faulty zone after the failure has been fixed. Assume that every distribution branch incorporates a sectionalizing device on it in which, when a network reconfiguration process is triggered, such devices can be acted to change the network topology. In accordance with [17], the ENS at the node bi can be calculated as: ${ENS}_{bi} = \sum_{m = 1}^{12} (P_{bi}^{m} \times \sum_{bi, bj \in V, bj \neq bi} (U_{bj, bi}^{m}))$ (4)

Where, V ={ 1, …, N_B } is the bunch of nodes in distribution network, $U_{bj, bi}^{m}$ is the service unavailability related to the reparation time of all upstream branches connecting the node bi in mth monthly period. It is worthwhile to note that the summation in (4) has to be understood as the sum of all the unavailability related to the bith node. The unavailability $U_{bj, bi}^{m}$ is defined as follows: $U_{bj, bi}^{m} = λ_{bj, bi}^{m} \times d_{bj, bi} \times t_{bj, bi}$ (5)

The ENS of the whole distribution network is computed as the summation of all nodes except the node 1, as follows: $ENS = \sum_{bi = 2}^{N_{B}} {ENS}_{bi}$ (6)

And, the cost of customer service interruption is calculated by: $Cost_E NS = \sum_{bi = 2}^{N_{B}} {ENS}_{bi} \times {price}_{ENS, bi}$ (7)

Where, price_ENS,bi is the cost associated with ENS_bi (the cost paid by the utility to customer bi as penalty), dollars per kWh.

Note that, in this work, DGs can be support the costumers to decrease the ENS. To this end, in all monthly period, the installation capacity of DGs should be considered, not their output power. Therefore, the maximum output powers of DGs during year (as their installation capacity) have been used to calculate ENS in all monthly period.

More information about this objective function can be achieved in [10, 18].

Finally, the objective function of the proposed problem is to minimize the total cost as follow: $\begin{matrix} TC = \dots \\ \min (Cost_P + Cost_L oss + Cost_S w + Cost_E NS) \end{matrix}$ (8)

2.2 Decision variable

The decision variables of the proposed optimization problem are defined as follows: $X = [\begin{matrix} \bar{S_{O}} & \bar{P_{DG}} \end{matrix}]$ (9) $S_{O} = [\begin{matrix} S_{O, 1}^{1} & \dots & S_{O, N_{So}}^{1} \\ ⋮ & ⋮ \\ S_{O, 1}^{12} & \dots & S_{O, N_{So}}^{12} \end{matrix}]$ (10) $P_{DG} = [\begin{matrix} P_{DG, 1}^{1} & \dots & P_{DG, N_{DG}}^{1} \\ ⋮ & ⋮ \\ P_{DG, 1}^{12} & \dots & P_{DG, N_{DG}}^{12} \end{matrix}]$ (11)

Where, $\bar{S_{O}}$ is the list of switch numbers which should be open to have a radial structure network in each monthly period, and $\bar{P_{DG}}$ is the list of output powers of DGs in each monthly period. Also, N_So is the number of switches which should be open.

2.3 Constraints

The problem is subjected to the following constraints:

Voltage limits of buses

v_{bi}^{min} \leq v_{bi} \leq v_{bi}^{max}

(12)

Where, v_bi , $v_{bi}^{min}$ and $v_{bi}^{max}$ , are the magnitude, allowable higher and lower values of voltage at nodebi.

DG technical constraints

Since the capacity of DG units is different depending on type and operation conditions, it is necessary to constrain the capacity within the permissible levels. $P_{DG, n} \leq P_{DG, n}^{max}$ (13)

Where, $P_{DG, n}^{max}$ is the maximum allowable capacity of nth DG unit.

Branch flow limits

The power flow over the lines is limited based on the capacity of lines: $S_{b} \leq | S_{max, b} |$ (14)

Where, S_b and S_max,b are the power flow amount of the bth branch and its maximum allowable power flow.

Radial structure of the distribution network

To have easier protection of the network, it is assumed that the structure of distribution networks should be kept in radial structure.

It is notable that the “death penalty” method is used in this paper to consider constraints in the optimization. In this method, the constraints are included in the objective function with a penalty factor, called DP. If all constraints are satisfied, DP will be zero. Otherwise, DP is set as a large number and is added to the objective function to exclude the relevant solution from the search space.

3 Solution method

In this paper, a modified PSO algorithm is used to be compatible with the proposed multi-objective problem. In the multi-periods optimization problems compared to the single-period ones, the number of decision variables is significantly increased. For example, in the proposed problem, they will be twelve times more. Therefore, simultaneous (not sequential) optimization of all periods causes the problem space to be complicated and very large. As a result, conventional algorithms and methods may not achieve acceptable results. The original PSO and the Modified method are presented in the subsequent subsections.

3.1 Overview of original PSO

PSO is an evolutionary optimization method. The method is developed through a simulation of simplified social models [19 –24]. The features of the method are described in the following.

The method is based on movement of such organisms in a bird flock or fish school.

The PSO concept is simple. The method has 2 steps, first calculates the velocity of particle and then updates the particle position. So, the computation time is fast and occupies little memory.

According to researches on bird flocking, birds find food by flocking. It can be seen that the information obtains jointly in flocking. Or assume a human group. The behavior of each individual is in accordance with behavior pattern of the group such as custom or experience of each individual.

PSO can be developed through simulation of bird flocking in a two-dimensional area. The position of each individual is expressed by XY axis position and the velocity is represented by v_x (the velocity along x axis) and v_y (the velocity along y axis). Modification of each agent (individual) is understood by its position and velocity information.

Regarding the above concept, an optimization technique is described as follows: bird flocking optimizes a certain objective function. Each agent i has information about its best value so far (pbest) and its XY position (p_i). Furthermore, each agent knows its best value in the group (gbest) among pbest. Each agent tries to adapt its position using the following information:

the current position vector p_i = [p_xi, p_yi],

the current velocity vector v_i = [v_xi, v_yi],

the distance between the current position and pbest, introduced as (pbest_i - p_i), and

the distance between the current position and gbest, introduced as (gbest_i - p_i).

The modification is expressed by the concept of velocity. The velocity of each agent is modified by the following equation: $\begin{matrix} v_{i}^{k + 1} = w . v_{i}^{k} + c_{1} . rand . ({pbest}_{i} - p_{i}^{k}) + \dots \\ c_{2} . rand . (gbest - p_{i}^{k}) \end{matrix}$ (15)

Where, $v_{i}^{k}$ is the velocity of agent i at iteration k, w is the adaptive inertia weight linearly adapted to decrease from w_max = 0.9 to w_min =0.4, such that w = w_max - [(w_max - w_min)/number of iterations] * current iteration number, c_j are the accelerating coefficients within the range [4] which are conventionally set to a fixed value of 2, rand is random number between 0 and 1, $p_{i}^{k}$ is the current position of agent i at iteration k, pbest_i is the pbest of agent i, and gbest is the gbest of the group.

By using the above equation, the velocity which gets close to pbest and gbest, obtains. The current position (searching point in space point) can be modified as follows: $p_{i}^{k + 1} = p_{i}^{k} + v_{i}^{k}$ (16)

3.2 Modified method

As mentioned, in the original PSO, in each iteration, the particles move to pbest and gbest. In the multi-periods problems, the solution of pbest and gbest may not be more efficient in some periods, and cause the particles to be misguided. This affects extremely the ability of the algorithm to find the global optimal solution. Therefore, in addition to the value of objective function for total periods (annual), the values of objective function in each period (monthly) should be considered in the optimization process. To this end, the original PSO algorithm is modified considering following point:

Both monthly and annual values of objective functions are calculated.

The values of pbest_i are calculated and updated for each period, separately. Indeed, the monthly (not annual) values of objective functions are used to update pbest_i.

The value of gbest is calculated and updated annually, similar to the conventional PSO method.

Therefore, equation of (15) is changed as follows: $\begin{matrix} v_{i}^{k + 1} = w . v_{i}^{k} + c_{1} . rand . ({pbest}_{i}^{m} - p_{i}^{k}) + \dots \\ c_{2} . rand . (gbest - p_{i}^{k}) \end{matrix}$ (17)

Where, ${pbest}_{i}^{m}$ is the pbest of agent i, considering mth monthly period.

4 Numerical results

The proposed problem is studies on a distribution network from Taiwan Power Company (TPC) that is shown in Fig. 1. As seen, three types of feeders, with different time-varying characteristics of load profiles and reliability data, have been considered for this network. Table 1 shows the essential data for this test system, and more information is available in [25].

Also, Tables 2 and 3 present the considered coefficients for monthly variations of peak loads and the service unavailability (U) in different types of feeders, respectively. This test system consists of four DGs at buses #6, #12, #16 and #31, and their maximum output powers are 1000 kW. The energy prices of the substation and DG units are 0.065625$/kWh and 0.044$/kWh respectively. K_n for all DG units is set to $3000. Switching cost is $203 for each switching [15]. And the cost associated with ENS is firstly set to 10$/kWh; however it is changed in thesimulation.

At first, the proposed algorithm, in the previous section, should be evaluated in comparison with original particle swarm optimization.

4.1 Performance evaluation of the presented algorithm

As mentioned earlier, the proposed algorithm has been modified to be compatible with multi-periods optimization problems. Therefore, to compare the performance of the proposed modified PSO algorithm with the original one, the presented framework is solved considering different number of periods (months) with both algorithms. Indeed, the presented DFR problem, with the aim of reducing costs Equation 8, is initially solved for the first month by both algorithms. Then, the number of months increases to 2, 4, 8, and 12, to evaluate ability of the algorithms for obtaining the optimal solutions.

The number of particles and iterations for both algorithms are set to 1000 and 200, respectively. Also, the problem is solved 20 times in all cases, and the best ones are selected. Obtained results are shown in Fig. 2.

This figure demonstrates that, with the increasing number of months, the total cost is proportionally increased. Considering one month (single period) will result the same values for both method. Since, Equations 15 and 17 are not different in this case. However, with the increasing number of months, ability of the original PSO in searching the optimal solution is reduced. As can be seen, when the number of months reaches to 8 and 12, the percentage difference of the obtained solutions for two methods is significantly increased. In 12 months, the total cost of the original PSO is 13.1% more than the value calculated by the proposed method, which is absolutely not acceptable. In the proposed modified PSO, with considering monthly costs in addition to the annual cost for moving the particles, the ability of finding the optimal solution is significantly enhanced.

4.2 Sensitivity analysis

Sensitivity analyses are proposed before presenting the final optimization results, in order to see how each component of the objective function contributes to the total cost and how they vary with the DGs penetration. In this section, the network is considered according to its original configuration, and DGs are installed on the mentioned locations and the active output power of DGs is varied from 0 to 100% of total load, continuously and simultaneously. Note that the term “penetration” used here actually represents the ratio of DGs output powers to the maximum load level. Also, the reliability penalty (cost associated with ENS) is firstly considered equal to 10$/kWh for loss of load.

Figure 3 shows the power utility’s yearly expenses related to reliability, power losses, and power supply (by DG units and substation), with respect to the DGs penetration. The cost associated with power losses can be considered relatively small. We can see that as the DGs penetration increases, the power losses reduce to a minimum value, and then starts to increase. Indeed, the presence of DGs can reduce the power losses; however, their size should be properly determined.

The main contributions to the total utility expenses are made by the reliability cost and the power supply cost. Simulation results show that the reliability cost decreases as the sizes of DGs increases. This outcome is quite obvious since the bigger the DG sizes, the more chance for customers to be supplied during a system failure. The DG capital investment and operation costs increase, and the substation cost decreases together with the rising of the DG sizes. The sum of those is the power supply cost which has not a uniform behavior.

Consequently, the trend for total cost, which is the most important factor in the optimization process, reaches a number of local minimums with increase in the level of DGs penetration. It’s shown that, when the DGs rated at 88% penetration is applied in the system, the total payment from the utility is found to be the lowest. For this particular case, we can see that the DG size is quite high when there are high line fault rates or when the reliability penalty is high.

As we notice from the previous study, the reliability penalty has a great impact on the overall result of the optimization process. To verify this finding, simulations were carried out to obtain total cost versus DGs penetration for different prices of load outage, ranging from $0 to $10 per kWh outage. Table 4 present the obtained optimal DGs penetration with respect to different reliability penalties. Also, in Fig. 4, the variations of total cost curve regarding different reliability penalties (values from $5 to $9 per kWh outage) are depicted. As can be seen, the optimal DGs penetration reduces considerably as the reliability price decreases. It can be explained as follows: In Fig. 3, it was observed that the curve of reliability cost is descending. Therefore, when the reliability cost decreases, the total cost reaches to its global minimum in a lower level of DGs penetration. In the curves of Fig. 4, with decreasing the reliability prices, one of the local minimums with lower level of DGs penetration becomes global. Also, in Table 4, it can be seen that, the optimal penetration of DGs has not changed for the reliability price values from $0 to $5 and from $9 to $12 per kWh outage.

Depending on how critical the customer loads are, different rates of penalty for outage can be applied. For example, a loss of an industrial load or hospital will result in much greater costs compared to that of a residential load. Thus, types of load, which directly affect the reliability penalty, are of great importance in the optimization of the DG design and needed to be assessed with much care.

4.3 Final optimization results

In order to better illustrate the performance of the proposed multi-periods DFR framework, five cases are considered as follows:

Case 1: Original configuration, regardless of time-varying characteristics for load profiles and reliability data (all coefficients in Tables 2 and 3 are set to unity).

Case 2: Original configuration, regarding time-varying characteristics for load profiles and reliability data.

Case 3: Original configuration, at the presence of DGs, regarding time-varying characteristics for load profiles and reliability data.

Case 4: Single reconfiguration form original, at the presence of DGs, regarding time-varying characteristics for load profiles and reliability data.

Case 5: Multi-periods reconfiguration, at the presence of DGs, regarding time-varying characteristics for load profiles and reliability data.

In all cases, the reliability penalty is considered equal to 10$/kWh for loss of load. Table 5 presents annual total costs and its components using different reconfiguration cases. The following observations can be concluded, regarding the results:

For the original configuration without considering time-varying effect (case 1), the total annual cost is $3,773,200. With considering time-varying effect (case 2), the total annual cost increases to $3,897,150. In these two cases, the cost of power supply has not changed considerably, since the load average is constant. However, the cost of power losses and ENS are changed. This result indicates that ignoring time-varying characteristics of load and reliability data will affect the final solutions.

In case 3, with the presence of DGs, despite an increased power losses, the total cost is significantly decreased (to 2,802,940), due to the substantial improving of ENS.

Considering single reconfiguration at the presence of DGs for a whole year (case 4), all cost components is reduced, compared to previous cases. Therefore, the annual total cost of $2,305,020 is achievable.

Comparing the obtained results of the fifth case and previous ones in Table 5 denotes that it is necessary to solve the proposed problem as a multi-periods framework, to have an optimum solution. As it can be seen multiple reconfigurations at the presence of DGs results total cost of $2,025,763. In this case, both the cost of power losses and ENS are significantly reduced, and compensate the extra switching cost.

Decision variables of the different reconfiguration cases are presented in Table 6. In case 5, depending on the monthly conditions, related configurations have been efficiently determined, and the number of switching operations during a year have been reduced as much as possible. Considering a high reliability penalty (10$/kWh for loss of load), the output powers of DGs have been close to their upper limit. In June, July, and August, all DGs have their maximum output powers, due to high power consumption and high service unavailability. The obtained results seem reasonable, that is, when feeder loads, and feeder failure rates are changed due to seasonal changes, the proposed procedure would manage how to supply the feeders.

5 Conclusion

A secure multi-periods optimization framework has been presented in this paper for network reconfiguration at the presence of DGs. The proposed objective function estimate the annual costs of a distribution company related to power supply, switching operations, power losses and service unavailability. To this end, time-varying effects of the loads and line failure rates are considered. The aforementioned conditions cause the problem becomes more complicated than before and it needs to be solved with a special precise algorithm. Therefore a modified particle swarm optimization algorithm, compatible with the multi-periods problems, is proposed. Obtained results indicate a considerable improvement in the proposed algorithm compared to the original one. Also, results show that the reliability cost can have a great impact on the total utility expenses, and in cases highly critical loads are present (which means the reliability penalty is high), a higher penetration of the DGs is required to provide the power supply.

References

Ashisa

, Sanjoy

and Anil

, An AIS-ACO hybrid approach for multi-objective distribution system reconfiguration, IEEE Trans Power Syst22(3) (2007), 1101–1111.

Raju

G.K.V.

, Bijwe

P.R.

and An efficient algorithm for loss reconfiguration of distribution system based on sensitivity and heuristics, IEEE Trans Power Syst23(3) (2008), 1280–1287.

Assadian

, Farsangi

M.M.

and Nezamabadi-pour

, GCPSO in cooperation with graph theory to distribution network reconfiguration for energy saving, Energy Convers Manage51(3) (2010), 418–427.

Falaghi

, Haghifam

M.R.

and Singh

, Ant colony optimization-based method for placement of sectionalizing switches in distribution networks using a fuzzy multi-objective approach, IEEE Trans Power Deliv24(1) (2009), 268–276.

Mendoza

, Lopez

, Morales

, Lopez

, Dessante

and Moraga

, Minimal loss reconfiguration using genetic algorithms with restricted population and addressed operators: Real application, IEEE Trans Power Syst21(2) (2006), 948–954.

Abdelaziz

A.Y.

, Mohamed

F.M.

, Mekhamer

S.F.

and Badr

M.A.L.

, Distribution system reconfiguration using a modified tabu search algorithm, Electr Power Syst Res80(8) (2010), 943–953.

Abdelaziz

A.Y.

, Mohamed

F.M.

, Mekhamer

S.F.

and Badr

M.A.L.

, Distribution systems reconfiguration using a modified particle swarm optimization algorithm, Electr Power Syst Res79(11) (2009), 1521–1530.

Swarnkar

, Gupta

and Niazi

K.R.

, A novel codification for meta-heuristic techniques used in distribution network reconfiguration, Electr Power Syst Res81(7) (2011), 1619–1626.

Wang

and Cheng

H.Z.

, Optimization of network configuration in large distribution systems using plant growth simulation algorithm, IEEE Trans Power Syst23(1) (2008), 119–126.

10.

Narimani

M.R.

, Azizi-Vahed

, Azizipanah-Abarghooee

and Javidsharifi

, Enhanced gravitational search algorithm for multi-objective distribution feeder reconfiguration considering reliability, loss and operational cost, IET Generation Transmission & Distribution8(1) (2013), 1–15.

11.

Nasiraghdam

and Jadid

, Optimal hybrid PV/WT/FC sizing and distribution system reconfiguration using multi-objective artificial bee colony (MOABC) algorithm, Solar Energy86(10) (2012), 3057–3071.

12.

Franco

J.F.

, Rider

M.J.

, Lavorato

and Romero

, A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation, Electr Power Syst Res97 (2013), 51–60.

13.

Y.K.

, Lee

C.Y.

, Liu

L.C.

and Tsai

S.H.

, Study of reconfiguration for the distribution system with distributed generators, IEEE Trans Power Deliv25(3) (2010), 1678–1685.

14.

De Oliveira

L.W.

, Carneiro

Jr. , de Oliveira

E.J

, Pereira

J.L.R

, Silva

I.C

Jr. and Costa

J.S

, Optimal reconfiguration and capacitor allocation in radial distribution systems for energy losses minimization, Int J Electric Power Amp Energy Syst32 (2010), 840–848.

15.

Shih-An

and Chan-Nan

, Distribution feeder scheduling considering variable load profile and outage costs, Power Syst IEEE Trans24 (2009), 652–660.

16.

Shariatkhah

M.-H.

, Haghifam

M.-R.

, Salehi

and Moser

, Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm, International Journal of Electrical Power & Energy Systems41(1) (2012), 1–10.

17.

Endreneyi

, Reliability Modeling in Electric Power Systems, NewYork, Wiley, 1978.

18.

Cárcamo-Gallardo

, García-Santander

and Pezoa

J.E.

, Greedy reconfiguration algorithms for medium-voltage distribution networks, IEEE Trans Power Deliv24(1) (2009), 328–337.

19.

Kennedy

and Eberhart

, Particle swarm optimization, IEEE International Conference on Neural Networks, Piscataway, NJ, 1995, pp. 1942–1948.

20.

Khalghani

M.R.

, Shamsi-nejad

M.A.

and Khooban

M.H.

, Dynamic voltage restorer control using bi-objective optimisation to improve power quality’s indices, Science, Measurement & Technology, IET8(4) (2014), 203–213.

21.

Khooban

M.H.

, Alfi

and Abadi

D.N.M.

, Control of a class of non-linear uncertain chaotic systems via an optimal Type-2 fuzzy proportional integral derivative controller, Science, Measurement & Technology, IET7(1) (2013), 50–58.

22.

Kavousi-Fard

, Niknam

and Khooban

M.H.

, Intelligent stochastic framework to solve the reconfiguration problem from the reliability view, Science Measurement & Technology, IET2014, Accepted for publication. DOI: 10.1049/iet-smt.2013.0106.

23.

Niknam

, Khooban

M.H.

, Kavousifard

and Soltanpour

M.R.

, An optimal type II fuzzy sliding mode control design for a class of nonlinear systems, Nonlinear Dynamics75(1-2) (2014), 73–83.

24.

Khooban

M.H.

, Soltanpour

M.R.

, Abadi

D.N.M.

and Esfahani

, Optimal intelligent control for hvac systems, Journal of Power Technologies92(3) (2012), 192–200.

25.

Baran

M.E.

and Wu

F.F.

, Network reconfiguration in distribution systems for loss reduction and load balancing, IEEE Trans, Power Deliv4(2) (1989), 1401–1407.