Abstract
The appearance of Plug-in Electric Vehicles (PEVs) in the electric grids is providing new opportunities when some new challenges are also created. Technically, PEVs are movable loads that can benefit to both owners and utilities in case of using Vehicle-to-Grid (V2G) technology. Therefore, this article aims to investigate the Distribution Feeder Reconfiguration (DFR) effect to optimally manage PEV performance in a probabilistic framework. The proposed stochastic framework will capture the uncertainties of location of PEVs as well as driving pattern and battery State-of-Charge (SOC). In addition, a new self-adaptive evolutionary swarm algorithm based on Social Spider Optimization (SSO) algorithm is proposed that will search the problem space globally. The simulation results on the IEEE standard test system shows the high performance of the proposed method.
Keywords
Nomenclature
Hourly energy price/ loss cost/ V2G price. Cartesian distance to closest/best individual. Energy for PEVs in fleet v to drive at time t. Available energy in batteries of fleet v at time t. Initial/final energy in PEV fleet v. Min/max energy in batteries of PEV fleet v. Objective value of ith/best/worst individual. Iteration counter. Maximum number of iterations. Lvy flight function. Weighted mean of male spiders in the colony. Number of individuals which select a strategy. Population size. Number of female/male spiders in the colony. Total number of PEVs. Number of control variables. Hourly/max imported power from upstream grid. Hourly active power loss of network. Charging/discharging capacity of PEV fleet v. Min/max charging capacity of PEV fleet v. Min/max discharging capacity of PEV fleet v. Charge/discharge power rate of PEV fleet v at time t. Hourly injected active/reactive power at bus i. Attraction threshold. Normalized selection probability of sth strategy. Mating region. Hourly/max apparent power flow between bus i and j
Set of modification strategies. Success factor of ith individual. Planning horizon. Time in which SOC is set to a specific value. Status of grid connection of fleet v at time t. Indicator of fleet v in charge/ greaterthan discharge/idle mode. Upper/lower bound of jth control variable. Voltage magnitude/phase of bus i at hour t. Minimum/maximum voltage at bus i. Weight of ith/closest/best/closest female individual. Position of closest spider/closest female spider. Position of ith/best/randomly selected individual. Position of ith female/dominant male/non-dominant male spider. Improved new individual based on mutation process. ith test individual generated in modification strategy. Magnitude/phase of impedance between bus i and j. ith random number between [0, 1].
Introduction
Plug-in Electric Vehicles (PEVs) are new technologies with promising advantages that have attained much popularity in the recent years. The mobile characteristic of PEVs will also germinate new constraints and challenges for the electric grid to supply the loads with high reliability. In other words, the high penetration of these devices in the system requires the preparation subscriptions in the basics of the grid. Some of these challenges can be named as congestion on transmission and distribution lines, proliferation in energy loss, reducing the reliability and power quality [1–4]. According to the statistics, the charging hours of most of electric vehicles and the peak load hours meet at the same time [5]. In order to deal with this issue, the Vehicle- to-Grid (V2G) technology can be employed to minimize the unwanted impacts of PEVs. V2G represents a scheme where power can be traded to the network by plugging an idle PEV to the system. As a result, the energy can be transferred between different locations in the grid without using the traditional power flow rules [6–9].
One of the precious strategies that can be affected by the appearance of PEVs is distribution feeder reconfiguration. DFR is defined as the process of changing the topology of the radial networks using some pre-determined normally open and closed switches. During this reconfiguration, the radial structure of the network should be preserved and all operation limits should be preserved [10]. Some of the main benefits of using DFR can be named as loss reduction, cost reduction, voltage enhancement and load balance increment. In the area of DFR, some of the most well-known methods can be named as Artificial Neural Network (ANN) [11], optimum flow pattern [12], graph theory [13], brute-force approach [14], heuristic techniques [15], Genetic Algorithms (GA) [16–18], expert systems [19], and Particle Swarm Optimization (PSO) [20, 21]. Some other targets like enhancing load balance [22], voltage deviation [23] emission [24, 25] and reliability indices [26, 27] are discussed too. In [28], the DFR strategy is solved considering the charging demand of PEVs. Here, the uncertainty of PEVs and the V2G technology are both ignored in the analysis. In [29], the effects of plug-in hybrid electric vehicles are assessed on the DFR strategy considering different penetration levels. In [30], a new smart framework is devised to model the PEVs charging demand in the distribution system and total cost of supplying the load demand. In [31], the effects of PEVs on the reliability of the distribution systems are addressed completely.
According to the above explanations, the role of the DFR strategy on the PEV penetration is not yet analyzed completely. In response to this need, this paper tries to investigate the simultaneous effect of DFR strategy and the PEV charging and discharging periods. In this way, a new stochastic framework is devised to model the uncertainties of energy price, active/reactive load demand and PEV charging and discharging demand using Monte Carlo simulation (MCS). Since the proposed problem is a complex and nonlinear optimization problem, it requires a powerful optimization algorithm to be solved optimally. Here we make use of the Social Spider Optimization (MSSO) algorithm with a new modification method to response to this issue. SSO is a swarm population based optimization algorithm that mimics the mating behavior of spiders [32]. Finally, the proposed stochastic method is implemented on the IEEE 69-bus distribution test system to examine its feasibility and satisfying performance. In summary, the main contributions of the paper can be named as 1) modeling of large scale PEV integration as mobile distributed load and storages 2) assessing the impact of DFR on the PEV penetration level, 3) introduction of a new intelligent method based on SSO to solve the problem and 4) introduction of a new modification method for SSO to increase its ability in the optimizationapplications.
Proposed stochastic problem
PEV Fleet in the network
PEVs are movable probabilistic sources and consumers in distribution grid. Therefore, some expectations should be made to calculate and governor the impression of a large quantity of PEVs in the system. In this way, we assume that there are two main trips in each day. The short 10 minutes trips are disregarded in the analysis. It is clear that these short intervals can also be considered without any issue. PEVs are intended to activate their daily shuttle with 100% State-of-Charge (SOC) at the beginning of the day. Also, the maximum DOD is considered to be 20% SOC [36, 37, 36, 37].
Problem formulation
Optimal feeder reconfiguration lessens the distribution feeder losses, poise load influence and increase system safety by relocating consumers from one feeder to the other. This is done by the use of some sectionalizing and some tie switches that are considered before the strategy. These switches are generally remotely controlled. In the proposed formulation, DFR aims to minimize the total network costs when meeting some security and operation constraints as below:
The total network cost (1) involves three components. The first term signifies the price of managed power with upstream grid thru network substations. The second part is the cost of active power losses. The last part is the operation cost associated with the combined PEVs which relies on the sum of vehicles and charging/discharging energy. The restrictions (2)–(14) assurance a safe optimal power flow and besides radial construction of system for each hour of programming time horizon. Equation (2) denotes ac power flow constrictions for the network and bus voltage bounds are painstaking in (3). The volume of power exchange at upstream system source ideas is controlled by (4) and distribution feeder limits is embodied in (5). In (6), the structure of the system topology is bound to be radial as the most essential imperative in the DFR.
In this article, the central closed loops of the structure are employed to examine the radial framework of the grid topology. It is noticed that every primary circle incorporates a tie switch and comparing segment switches that can frame a circle. To hold an outspread system structure, every time that a tie switch is shut, stand out sectionalizing switch is opened in that circle. Mathematical statements (7)–(14) show PEV limitations. The hourly charge/discharge/shiftless conditions of navies are set in (7). PEVs can interchange power with the network whereas they are in non-operational style and linked to the grid. The limit specifies existence of PEV fleet v in the charging station at time t. After a PEV fleet is linked to the net, the amassed battery can be shiftless (neither charging nor discharging), pull power from the system, or insert power to the system. The expanse of this power exchange with the grid is limited by equations (8)–(9). The hourly energy equilibrium in PEV batteries is satisfied in (10) and the energy capacity edge of each fleet is offered in (11)–(13). As said previously, it is supposed that the SOC is 100% when a PEV fleet is leaving the station in the chief journey at the beginning of day. Equation (14) is planned to regard this assumption.
As it was told before, PEV charge/discharge outline inclines to be extremely uncertain. PEV energy consumption shapes and the number of PEVs in a fleet are signified by shortened normal distribution functions wherein the unpleasant values are the forecasts and the standard deviations are percentages of the mean values [1]. We make use of the Monte Carlo simulation (MCS) to model the uncertainties of the problem.
Original optimization algorithm
Originally, SSO was introduced to show the performance of spiders in their mating process. SSO algorithm was first suggested by Cuevas et al. [32] in 2012 for exhibiting the helpful performance of social spiders in a colony. In this procedure, a group of spiders is produced haphazardly with N
F
and N
M
female and male. The population size matches the amount of male and female spiders i.e. N
p
= N
F
+ N
M
. Meanwhile the populace of social spiders is extremely female-biased, made up 65% –90% of the population. After the diplomacies are designed a weight (w
i
) is elected to each spider in keeping with the best (f
b
) and the worst (f
w
) values as below:
The collaborating performance of females which causes their position tuning in each rehearsal is then executed as below:
Here, both striking and disgusting relations of ith female spider are surrounded by positive and negative symbols, correspondingly. Male participants, with a weight value above the middle drive the dominant set and others to non-dominant set. The location of dominant males is informs as:
As argued formerly, main male spiders entice nearby female spiders and the non-dominant ones are fascinated to the prejudiced mean of the male populace as:
Finally, the mating process is done between the dominant males and female spiders:
A new phase is added to original SSO to enforce adaptive progress to the algorithm by incorporating two different modification strategies which are devised based on mutative approaches and Lvy flight [38].The new phase is modeled such that each spider selects the best strategy adaptively based on its probability. The superior strategies perform will get higher possibility to be picked in the next iteration. The strategies are described at below.
Among the above strategies, one with higher probability will be selected. Using the above formulations, the best successful strategy will be utilized to train each particle in the swarm in an adaptive way as described in [26].
The pseudo code for the RWM is depicted in Fig. 1.
This section will examine the performance of the proposed method on the 69-bus IEEE distribution test system [19]. This network contains 5 normally open switches and 68 normally closed switches. Figure 2 shows the single line illustration of the grid wherein the normal open switches are shown by dotted lines. Each time that a normal open switch is closed, a loop is formed which should be omitted. Moreover, it is assumed that there is a main breaker in the main feeder with a sectionalizer at the launch of each line. The network is supplying total active and reactive loads 2142 kW and 1500 kVar, correspondingly. Figure 3 shows the cumulative load value of the network during 24 hours. The network initial losses is 250 kW and the maximum voltage deviation of buses is 0.09079 pu. Table 1 shows the hourly energy price which is sold/bought. As it is seen from Fig. 2, the network has five PEV fleets with different driving patterns. Tables 2 and 3 shows the characteristics of each travel in the network. The algorithm has 35 initial swarm with the termination criterion of 200.
So as to explain the usefulness of the planned way, three dissimilar cases are defined: (I) without PEV, (II) without DFR and III) with DFR and PEVs.
In the first part of the simulations, the search ability of the MSSO is investigated. The results of single-objective optimization of the proposed method are shown in Table 4. The use of DFR has resulted in about 55.7 percent reduction in the power losses which is a notable value. According to the results, the proposed MSSO could reach the best optimal solution that is attained by the other methods. This reduction in the power losses is done by preserving the voltage value of buses in the pre-determined levels. The network total costs before and after reconfiguration are shown in Table 5. From these results, the high capability of DFR in reducing the costs are deduced easily.
In the second part of the simulations, the PEVs are considered in the network neglecting the DFR strategy. The uncertainties of PEVs are modeled using MCS. The number of scenarios is assumed to be 1000 for sufficient modeling of uncertainty. The main goal is to reach the optimal scheduling for the charge or discharge of PEVs at each hour of the day. The simulation results are shown in Table 6.
Table 6 comprehends the anticipated cost of the network at each hour before and after applying DFR to the network. As it can be seen from these results, the network cost is higher at peak load hours and vice versa. Also, the use of DFR could reduce the network costs at most of hours of the day suitably. In the hours that the network costs are not reduced, the PEVs are either charged which means incremental costs. From the operation point of view, the change in the network topology has been as the result of power exchange between the PEV fleets and the upstream grid. In general, the DFR strategy could reduce the system total costs suitably. Finally, Table 7 shows the amount of power exchange with the main grid. The positive values means charging and the negative values means discharging. Note it that PEVs can provide new opportunities for transferring energy between different buses when meeting the maximum thermal transfer ability of the feeders. Fleet 3 departs from bus 1 in the morning fully charged and returns in the evening with charge of 21% . This event can be interpreted as a transfer of energy from bus 1 to bus 27 by fleet 3.
In order to better compare the performance of the proposed method, Table 8 shows the results of optimization by a number of different methods. Here, the simulation results for the cost minimization through the DFR strategy and in the presence of PEV fleets are shown. The results are repeated for 20 trails and the results of the best solution, the worst solution and average value are provided comparatively. Also, the mean CPU time are provided. According to these results, the proposed MSSO could reach the best solution with higher robustness. Also, from the CPU time, the less computational effort of the algorithm can be deduced easily.
Conclusion
In this article, a smart stochastic structure is offered for mechanization of smart networks with the high dispersion of PEVs in the conveyance market. The target is to minimize the total network costs through optimal scheduling of charge and discharge hours of PEVs and control of some normally and closed switches. The simulation results on the IEEE test system shows that the mobile PEVs can be considered as new opportunities in the system for transferring energy among buses without obeying the traditional load flow equations. In addition, it was seen that DFR strategy can reduce the total network costs at each hour greatly. From the optimization point of view, the proposed MSSO could reach the optimal values more successfully than the other popular methods in the area.