Abstract
The emergence of dispersed generation, smart grids, and deregulated electricity markets has increased the focus on enhancing the performance of distribution systems. This paper proposes a method to reduce the energy loss and improve the reliability of distribution systems by performing distribution network reconfiguration (DNR) and distributed generator (DG) allocation. In this study, the intermittent nature of renewable-based DGs and the load profile are considered using a probabilistic method. The study investigates different annual plans based on the seasonal power profiles of DGs and the load to minimize the combined cost function of annual energy loss and annual energy not served. The proposed method is implemented using the firefly algorithm (FA), which is one of the meta-heuristic optimization algorithms. Several case studies are investigated using the IEEE 33-bus distribution system to highlight the effectiveness of the method.
RECENTLY, the deregulation of the electricity markets and the emergence of renewable-based distributed generators (DGs) have gained significant interest. Consequently, local utilities must pay more attention to the efficient planning and operation of the distribution system. Several techno-economical aspects should be considered in the planning and operation of the distribution system while integrating DGs. The technical aspects include protection coordination [
These aspects are considered as the motivation by some researchers to develop the methods that can ensure the efficient planning and operation of the distribution system. One of these methods is the distribution network reconfiguration (DNR). The DNR is performed by changing the status of the system sectionalizing and tie switches. Accordingly, the distribution network configuration is adjusted to achieve specific objectives. Some of these objectives are energy loss minimization [
Recently, some studies suggested performing simultaneous DNR and DG allocation to enhance the performance of the distribution system [
However, none of those mentioned studies considered the intermittency in the output power of renewable-based DGs or the different annual load profiles. In [
The studies in [
Note: ✕ means covered; means in the presence of DGs without optimal DG allocation; Obj1 means energy loss; Obj2 means reliability; Obj3 means power quality; Obj4 means load balance; Obj5 means voltage stability; Obj6 means system operation cost; U1 means load uncertainty; and U2 means output power uncertainty of DGs.
In addition, few studies proposed simultaneous DNR and DG allocation while considering the intermittency in the output power of renewable-based DGs and the different annual load profiles. Moreover, these studies proposed simultaneous DNR and DG allocation during the study period. However, none of the aforementioned studies investigated the possibility of simultaneous DNR and DG allocation while investigating the impact of further reconfiguration for the distribution system on a seasonal basis. Hence, the main contributions of this paper can be summarized as follows.
1) Developing different annual plans by performing simultaneous DNR and DG allocation based on a specific season and then performing further DNR for the remaining seasons.
2) Modeling the uncertainties of different types of renewable-based DGs and loads using a probabilistic method.
3) Improving the performance of the distribution system by reducing the energy loss and enhancing the system reliability.
It is well known that the generation from renewable-based DGs and the system demand is subjected to seasonal variations. In this study, the sizes and locations of DGs are kept fixed once the optimal DG allocation is achieved; however, the DNR is investigated each season. Therefore, the proposed strategy is based on developing different annual plans considering the four seasons of the year. Hence, the plan providing the best performance of the distribution system is to be chosen. To achieve this task, the proposed strategy is divided into two phases.
1) Phase 1 aims to perform simultaneous DNR and DG allocation for the four seasons of the year independently to find the optimal network configuration and the optimal size and location of DGs based on the data of each season. The output of this phase provides four planning options at the beginning of the study period.
2) In phase 2, each planning option is used to complete the annual plans by performing additional seasonal DNRs for the remaining seasons, e.g., an annual plan x consists of simultaneous DNR and DG allocation based on the winter season data and this is followed by further DNRs for the three remaining seasons. Hence, the annual plans are developed, and the system operator can choose the best plan for the whole year. The flow chart of the proposed strategy is shown in

Fig. 1 Flow chart of proposed strategy.
In the proposed strategy, the temporal historical load power and weather data related to DGs are used to build a probabilistic model for the demand and generation of the distribution system. The weather data related to DGs are mainly the solar irradiance for PV systems and wind speed for WTs.
The obtained data are converted into a probabilistic model representing each season, which is then used in the optimization algorithm. This model is based on multi-state variables [
The PV system modeling starts by obtaining the historical solar irradiance over several years at the candidate locations. The full range of solar irradiance values is divided into Np PV states, where each PV state represents a specific range of solar irradiance. Furthermore, the solar irradiance data are separated into four seasons so that each season can be represented by a probabilistic 24-hour day. Each hour in this day contains the probabilities corresponding to each PV state, which is obtained from the historical data. The output power corresponding to each PV state, using the model in [
The probabilistic model for the output power of WTs is built from the historical wind speed data at the candidate locations. The full range of wind speed is divided into Nw WT states, where each WT state represents a range of the wind speed. Moreover, the wind speed data are separated into four seasons; each season is represented by a probabilistic 24-hour day. Each hour in this day contains the probabilities corresponding to each WT state. The output power corresponding to each WT state is calculated at the mid-value of this state using the output power curve of the WT.
After calculating the output power of each WT state, a 1×Nw vector Aw containing these power is formed. Also, a 24×Nw seasonal probability matrix Mw is formed, where each element of this matrix Pbw corresponds to the probability of a certain WT state at a specific hour.
The load model (LM) is built using the way similar to the PV system and WT models. The historical load data are collected at the same candidate locations. The full range of the load data is divided into Nl LM states, which are stored in a 1×Nl vector Al containing the output power of each LM state. Also, a 24-hour seasonal probability matrix Ml is formed, where each element of this matrix Pbl corresponds to the probability of a certain LM state at a specific hour.
Finally, a combined 24×NT probability matrix is formed for each season, where NT is the total number of the combined states and is obtained by:
(1) |
The probability matrix contains the seasonal combined probability of different combined states corresponding to the PV systems, WTs, and the load. This matrix is formed by multiplying each probability element of the matrix with the corresponding row of the matrix and matrix at a specific hour as follows.
(2) |
where is the combined probability at hour k with combined state h; and , , and are the probabilities at hour k with state h of the PV, WT, and load, respectively.

Fig. 2 Probabilistic modeling process of DGs and load.
In general, the energy loss is affected by the network configuration and the sizes/locations of DGs in the distribution system [
1) In fault analysis, once the optimal network configuration is achieved based on the optimal system reliability, no further DNR is performed, and the open switches remain unchanged.
2) In fault analysis, each DG is kept connected to its local bus if it has sufficient active/reactive power to supply its local load.
The objective of the optimization problem is to perform optimal DNR and DG allocation in order to minimize the seasonal combined cost of energy loss and energy not served CT, which is expressed as:
(3) |
(5) |
(6) |
where CL is the seasonal cost of the energy loss, which is calculated by summing the probabilistic cost of the energy loss of branch z at hour with combined state for Nd season days; CR is the seasonal cost of the energy not served, which is calculated by summing the probabilistic cost of the energy not served of bus i at hour with combined state for Nd season days; is a binary variable representing the decision of each branch, which equals to 1 if the branch is connected and 0 otherwise; is the set of candidate locations where the DGs are installed; is the number of modules of each DG at each candidate location in the network; nbr is the total number of branches; is the unit cost of the system power loss; is the current of branch z at hour with combined state , which is obtained from the optimal power flow analysis; Rz is the resistance of branch z; is the time step; is the expected failure time of bus i at hour with combined state , which is investigated to check whether the DGs have sufficient power to supply the bus demand or not; nb is the total number of buses; is the unit cost of the energy not served of bus i at hour with combined state ; and are the active and reactive output power from modules stored in Aw and Ap, respectively; and are the active and reactive power of the load stored in Al, respectively; SWz is the switching time of branch z; is the failure rate of branch z; nbru is the number of the upstream branches connecting bus i to the substation; nbrd is the number of the branches connecting bus i to the remaining downstream buses; and REPz is the repair time of branch z.
The following constraints are considered in the optimization problem.
(7) |
(8) |
where is the binary status of the branch connecting bus i and bus j; and are the voltage magnitudes of buses i and j at hour with combined state , respectively; is the admittance magnitude of branch ij; is the admittance angle of branch ij; and is the power angle between bus i and bus j at hour with combined state .
(9) |
where Vmin and Vmax are the minimum and maximum acceptable bus voltages, respectively.
(11) |
The network radiality constraint for a distribution system composed of nb buses ensures that only branches must be connected for each configuration. In addition, there are four conditions that are utilized to guarantee that (11) gets feasible (i.e., radial) configurations for the distribution system [
The firefly algorithm (FA), one of the modern metaheuristic techniques [
(12) |

Fig. 3 Implementation of FA in proposed method.
where is the position of the best firefly; is the position of the current firefly; rtw is the cartesian distance between firefly t and firefly w; is the attractiveness when ; is the light absorption coefficient; is a random coefficient; and is a random number generator uniformly distributed in [0, 1].
The effectiveness of applying the FA to the proposed method is investigated and it is compared with other optimization algorithms. This is done by performing simultaneous DNR and DG allocation under peak load and DG generation conditions. Then, the implementation of annual plans considering the uncertainties in the output power of DGs and the load is investigated. The proposed method is tested on the 12.66 kV IEEE 33-bus distribution system with a peak demand of 3.7 MW and 2.3 Mvar. The operation power factor of all DGs is set to be 0.85 lag [
In this case, the FA is benchmarked with different optimization algorithms, including harmony search algorithm (HSA) [
The minimization of the power loss is considered as the main objective of this case, similar to the studies in [
Note: the numbers in the () represent the bus number.
The results show that the FA achieves the better power loss reduction for the studied distribution system under peak load and DG generation conditions compared with the other algorithms.
For this case, the solar irradiance and wind speed data are obtained for two years during the interval of 2012-2014 [
The solar irradiance data are divided into 10 states () starting from 0.05 kW/

Fig. 4 Hourly solar irradiance data in winter during 2-year study period.

Fig. 5 Output power curve of WT.

Fig. 6 Hourly wind speed data in winter during 2-year study period.

Fig. 7 Per unit load data.
The probability of each hourly load is considered to be unity. The reliability parameters and energy loss cost of this case are presented in

Fig. 8 Energy not served cost.
In this case, five different annual plans are presented described as follows.
1) Plan 1: performing simultaneous DNR and DG allocation based on the data of winter followed by performing DNR for each of the remaining seasons.
2) Plan 2: performing simultaneous DNR and DG allocation for the data of spring followed by performing DNR for each of the remaining seasons.
3) Plan 3: performing simultaneous DNR and DG allocation for the data of summer followed by performing DNR for each of the remaining seasons.
4) Plan 4: performing simultaneous DNR and DG allocation for the data of fall followed by performing DNR for each of the remaining seasons.
5) Plan 5: performing simultaneous DNR and DG allocation once for the whole year without performing DNR.
These plans are compared with the base case of the default network configuration and without using any DGs.
To compare the results of different plans, the annual cost reduction is calculated as:
(13) |
where is the annual cost without DNR or DG allocation, i.e., base case; and is the annual cost of each plan.
Note: the numbers in the () represent the bus number.

Fig. 9 Annual cost of each plan.

Fig. 10 Annual cost reduction of each objective plan.
The results demonstrate the positive impact of performing the simultaneous DNR and DG allocation on the cost related to energy loss and reliability. Furthermore, the results show that the results of the annual cost reduction corresponding to plans 1-4, where seasonal DNRs are performed, are significantly higher than that of plan 5. Hence, presenting annual plans based on the seasonal DNRs leads to a significant reduction in the system operation cost. However, performing additional DNR, i.e., monthly or weekly, will add more switching costs and thus affect the overall system operation cost. Moreover, for the studied distribution system, plan 3 provides the highest corresponding to different annual costs compared with those of the other plans. This indicates that for the studied distribution system, performing the simultaneous DNR and DG allocation based on the season with the higher demand, i.e., summer, followed by performing DNR for the remaining seasons, leads to a higher reduction of the combined cost.
The daily voltage profile based on the season is investigated as well, where the voltage of each node is multiplied by its corresponding probability resulting in a probabilistic daily voltage.

Fig. 11 Probabilistic daily voltage profile for plan 3 in winter.

Fig. 12 Probabilistic daily voltage profile for plan 3 in spring.

Fig. 13 Probabilistic daily voltage profile for plan 3 in summer.

Fig. 14 Probabilistic daily voltage profile for plan 3 in fall.
It can be clearly observed that the proposed method is able to maintain the daily voltage profile within acceptable limits for the studied distribution system for all buses under different loading conditions.
In this study, DNR and DG allocation are used to enhance the performance of distribution systems. The purpose of the study is to develop annual plans that minimize the combined costs of the energy loss and the energy not served related to the system reliability. The proposed method considers the uncertainties in the output power of the DGs and the system demand using a combined probabilistic model. The method is applied to the IEEE 33-bus distribution system using the FA.
The study shows that simultaneous DNR and DG allocation can significantly reduce the combined costs. Moreover, the voltage profile is improved. The study shows that considering the seasonal changes in the network configuration while developing annual plans can lead to better network performance than implementing only the DNR or DG allocation for the whole year. The study also shows that performing simultaneous DNR and DG allocation for the season with the highest demand followed by performing the DNR for the remaining seasons produces the optimal results. Accordingly, it is recommended that the system operators develop different seasonal plans to compare their results before deciding on the optimal sizes/locations of DGs and the network configuration.
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