Enhancing Voltage, Reliability, and Demand Balance via Combined Model of Distributed Generation Allocation and Distribution System Reconfiguration

. Te present study attempts to deal with two problems: optimal allocation of distribution generations (DGs) and reconfguration of a distribution system to satisfy several multiobjectives including smoothing the voltage profle, minimizing the cost of reliability, and balancing the amount of load on the end-user side. Tese problems are merged into one single optimization problem with the aforementioned objective functions. Te problem type is mixed-integer nonlinear programming (MINLP) and is subject to various limitations imposed by, for example, the operating status of DGs, demand equilibrium, bus voltages, and power passing on the distribution lines. Moreover, the paper adopts particle swarm optimization to fnd a solution to the MINLP problem under study. Te test system was implemented in the MATLAB environment to validate the capability of the suggested approach.


Introduction
Installation of automatic and remotely controlled switches provides many benefts for the distribution system. In medium voltage distribution networks, automatic switches are used to clear transient faults, isolate faults, manage the network structure, and thus increase system reliability. Tese switches play an essential role in distribution networks, and for this reason, the confguration of switches is a key factor in system design. Application of these switches enhances system reliability, reduces undistributed energy, and, as a result, increases the income of distribution companies. On the other hand, since the price of these switches is signifcantly high, their adoption should be economically justifed for electricity distribution companies. Another issue that should be considered is network load balancing. In distribution networks, due to the random and nonsimultaneous behavior of single-phase customers, load imbalance has a dynamic and time-varying nature. A useful method to detect load imbalance at any moment according to load changes during the day and reduced it to an acceptable extent is the adoption of active power compensation devices and also the limitation of power fow through the lines, which can be solved by placing distributed generations (DGs) across the distribution network or using the distribution network reconfguration strategy. Furthermore, the use of DGs and distribution network reconfguration provides various capabilities in improving the technical indices of the network such as voltage profle, reliability, and balancing the network even in critical conditions such as load growth.
Various solutions to compensate for the negative efects of load growth have been carried out in most research pieces. One of these solutions is the reconfguration or rearrangement of the distribution network by power switches [1,2]. In this method, based on [1,2], by determining the appropriate status of power switches and by establishing closed loops in the network, reconfguration causes loads to be fed from points closer to power generation sources. Tis has resulted in reduced network losses, less line congestion, improved voltage profle, and much fewer outages. Fewer outages result in improved reliability of the distribution network. In addition to the reconfguration of the distribution network, some references such as [3,4] have considered the presence of DGs in the problem of reconfguration of the distribution network. Based on the results of these references, it can be seen that the proper management of DGs is a suitable help along with the reconfguration of the distribution network to improve network indices. It should also be noted that, in a network, the number of DGs is limited. Terefore, many references suggest the optimal placement of these sources in the distribution network [5,6]. In [7], a model based on EMTP software is presented for three-phase transient analysis and smart grid reconfguration. Te networks in this reference are divided into subnetworks to increase reliability. Te simulation results in this reference have been compared with real transient events, which have proven the suitability of the proposed method of this reference. Studies [7] show that to avoid problems such as lack of coordination of protective relays and incorrect installation of equipment, steady state analysis along with time domain analysis is important before implementing the principles of a smart grid. In [7], the ant colony algorithm is used to reduce losses and balance the load for the radial distribution system. Tis method is derived from ant colonies and has the advantage of parallel search and can fnd the optimal solution. By comparing the distribution system in the absence and presence of DGs, it is found that DGs improve reliability and reduce losses. Comparing the results of ant colony analysis with the genetic algorithm in [8] shows the superiority of the ant colony method. In [9], the ant colony algorithm was used for the optimal confguration of the feeder, the optimal placement of the capacitors, and the combination of these two problems. Tis algorithm has found the optimal solution by using the behavior of ants. Distribution system confguration based on several objectives such as load balancing, voltage changes, and loss minimization as well as taking into account line current constraints using the fuzzy method is presented in [10]. In this reference, using heuristic rules to optimize performance and better operation, communication switches, and reducing computation time was adopted.
Te literature review presented in [1][2][3][4][5][6][7][8][9][10] reveals a gap in research regarding the concurrent advancement of economic and technical metrics. Te studies [1,2] focused solely on enhancing the operational status of the network, while those in [3,4] solely addressed improving its reliability status. It is important to acknowledge that a network comprises distinct technical and economic indices, and enhancing the performance of one index does not necessarily ensure the enhancement of another. In order to enhance the reliability of the network, it is imperative that the local resources situated within the network introduce a substantial amount of active power into the system. However, this matter exhibits a direct correlation with the escalation of losses and overvoltage within the network. Consequently, it is imperative to concurrently simulate multiple indices within the optimal network performance framework. Te operational status of a network is characterized by several indicators, including the voltage profle, distribution substation and line capacity release, and network balance. However, a limited number of studies have reported on the concurrent enhancement of these metrics. Furthermore, there exist several potential remedies to enhance the technical and economic condition of the network. Several prior studies in the research background have incorporated the implementation and management of DGs within the network. Te network reconfguration program has been utilized in previous studies. However, there has been limited research on the implementation of multiple solutions within a network. It is anticipated that the concurrent utilization of multiple solutions will enhance the economic and technical state of the network to a greater extent than their singular usage [11][12][13][14][15][16][17][18][19].
To compensate of the research gaps, this paper proposes the mathematical model of the problem of optimal placement of DGs along with the reconfguration of the distribution network to improve voltage profle, reliability, and load balancing in the distribution network. It is worth mentioning that the mentioned problem is in the form of an optimization problem whose objective function is to minimize the voltage deviation from the desired value, minimize the cost of reliability (the cost of expected energy not-supplied (EENS)), and minimize the consumption of energy. Terefore, it is expected that the voltage profle of the test network is fat. Also, the amount of EENS should be low, so the cost of reliability will be reduced. Finally, by minimizing the cost of energy, it is expected that the distribution of energy among consumers will be in such a way as to avoid high costs. Moreover, the mentioned problem has network limitations, limitations of network indices such as the voltage and power fow of the lines, the relationships governing DGs, load balancing, and items corresponding to the proposed problem. It should be noted that by presenting the constraint of load balancing, the loads are expected to be symmetrically distributed in the three phases of the system. Te presented problem will be a mixed-integer nonlinear programming (MINLP) problem and using the mathematical rules to solve the proposed problem is cumbersome; therefore, it is expected that the execution time of solving the problem will be very high. Hence, in this paper, the evolutionary algorithm of particle swarm optimization (PSO) is used to solve the mentioned problem because the proposed algorithm has a low population and fewer repetitions of the solution, which will increase the speed of solving the problem.
Upon conducting a comparative analysis of the research background and the proposed plan, several innovative elements can be identifed for the latter: (i) Simultaneous modeling and improvement of economic, operation, and reliability indices in the distribution network (ii) Modeling and enhancing several diferent indices of distribution network operation, such as improving the voltage profle, releasing the capacity of the distribution substation, and balancing the network (iii) Simultaneous use of DG planning-operation and distribution network reconfguration plan in upgrading the technical and economic indices of the distribution network In the following, Section 2 presents the formulation of scheme, and the solution method is expressed in Section 3. Numerical results obtained from diferent case studies are explained in Section 4, and fnally, conclusion is presented in Section 5.
Te mathematical model of the problem of placement of DGs in the distribution network and reconfguration of the network is as follows, the objective function is expressed in equation (1), and the constraints of the problem are mentioned in equations (2) to (13): ������������������ � International Transactions on Electrical Energy Systems 3 Te objective function of the proposed problem is stated in (1), which has three parts. Te frst part is related to the minimization of the voltage deviation from the desired value, where the term V ref expresses the desired value of the voltage magnitude [59]. Te second part also shows the cost of energy supplied by the distribution network substation and DGs. Finally, the third part refers to the cost of reliability [60]. It should be noted that all parts of the objective function are normalized and all items are in percentage form. Terefore, there is no need to defne the weight for each part of the objective function to normalize the computational unit, and also, the mentioned function was multiobjective, and by normalizing it, the objective function was expressed as a single objective. Te limitations of AC power fow are also mentioned in equations (2) to (6), which include the balance of active and reactive power in each bus given in (2) and (3), the active and reactive powers fow through the lines given in (4) and (5), and voltage angle in the slack bus is given in equation (6) [59,61,62]. It is worth mentioning that the terms P G and Q G are related to the power of the substation to the consumers, which is assumed to exist only in the slack bus. Terefore, the values of P G and Q G in other buses are equal to zero [59].
Te limitation of the network indices is given in equations (7)-(9), which, respectively, express the limitation of the voltage magnitude of the buses [63,64], the limitation of the power fow through the lines, and the limitation of the transmission power of the distribution network substation [59]. It should be noted that (8) refers to the limitation of the power fow on the lines. Terefore, this limitation makes load balancing possible in the feeders and phases of the system because this equation does not allow the power to pass beyond the allowed limit of the lines. Hence, according to the objective function and this limitation, power fow through the feeders is in a balanced state concerning each other. In other words, the power in one feeder or phase is not higher or lower than the other feeder or phase, and the power is distributed evenly among the feeders [59]. Also, the limitation of power generation by DGs is mentioned in (10) [65][66][67][68][69][70]. Te proposed scheme assumes that the network data, such as the load, do not considerably change in the planning horizon. In other words, the load data is assumed the same for diferent days and years. So, similar to (10), the DG size variable (SDG max ) is considered time-independent. Under such conditions, the planning range is not taken into account. However, in the proposed scheme, the location of DGs for all operating hours is identical.
It is worth mentioning that in this paper, the network structure is assumed to be radial, which can be investigated by the main closed loops of the system. It should be noted that the main loops include tie and sectionalizing switches in each loop. Terefore, the number of main loops is calculated based on (11). Finally, (12) calculates the amount of EENS of the entire distribution network, which is equal to the sum of loads not-supplied [60]. In addition, the three-phase system load balancing constraint is expressed in (13). It should be noted that in this equation, the distance between the voltages of the phases should be less than the permissible limit so that in this case, the loads are placed symmetrically and balanced in the three-phase system. To check the state of load balance in diferent phases, constraint (13) has been used. In this constraint, to establish balance in the three-phase system, the distance and voltage of diferent phases should be minimal because if the load in all three phases is close to each other, constraint (13) will be valid. Terefore, this constraint was used to check the load balance situation. It is worth mentioning that the proposed problem has decision variables, which in the abovementioned problem, the decision variables include the following: (i) Te variables of the on/of states of the tie and sectionalizing switches that are controlled remotely and these variables are displayed with the terms SW k,t and Tie k,t . Also, these variables are binary and have two values of zero and one. (ii) Te variable of the location of DGs in the distribution network, which is denoted by dg j . Also, this variable is binary, which has two values of zero and one [70]. (iii) Te active and reactive power variables of DGs are expressed by the terms P DG and Q DG . Also, these variables are continuous [70].
Terefore, the vector of decision variables (X) corresponds to the above explanation as follows: Te decision variable is the independent variable whose value determines the status of other variables.

Solution Method Based on PSO
Te problem presented in this section is an MINLP, and the use of mathematical rules to solve the proposed problem is very cumbersome and challenging. Terefore, it is expected that the execution time of solving the problem is very high. Hence, in this paper, the PSO is used to solve the mentioned problem because the proposed algorithm has a low population and fewer iterations of the solution, which will increase the speed of solving the problem [71]. To start the PSO algorithm, a certain number of populations are defned for each variable. Ten, for each variable and each population, a random value is calculated within the range of variable changes. In the next step, the ftness function is calculated according to each population. It is worth mentioning that the ftness function is the objective function of the proposed problem. Te next step is to calculate the best point, which is defned as the optimal point of the ftness function, and the variables of this point are displayed by x best . To move towards the optimal point, the particle moves towards the new point with a specifc speed, so in this section, it is necessary to calculate the new speed and position of the particle, which can be calculated from (15) and (16), respectively [72].
In (15), the terms C 1 , C 2 , and w are known as the setting parameters of the PSO. In other words, by changing these parameters, the mentioned algorithm can provide more suitable capabilities in solving the problem at one point of these parameters. Generally, based on experience, the appropriate values of C 1 and C 2 are 2 and 2, respectively. Also, the value of w decreases in proportion to the increase in the repetition of solving the problem so that in the initial iteration, it has a value close to one and in the higher iterations, its value becomes smaller [72]. Also, based on this equation, it can be seen that the speed of each particle is calculated based on the diference between the position of the particle and the desired position. Finally, the new position of the particle is calculated in (16). Te next step is to calculate the ftness function for the new positions of the particle and examine the convergence conditions. It is worth mentioning that the steps are updated until the convergence point is extracted.

Problem Data.
Te proposed problem is implemented on the 69-bus radial distribution network, whose structure is shown in Figure 1 and its specifcations are presented in [1]. In this fgure, the switches are normally open, which are indicated by dashed lines. It should be noted that the meaning of normally open is that the switches are open in normal network conditions and these switches are connected in critical network conditions. It is worth mentioning that the amount of active and reactive load of network buses for the frst phase at the peak load hour (20 : 00) is equal to one-third of the load presented in [61] and the load of the second phase is 2% of the load of the frst phase, and the load of the third phase is 2% less than the load of the frst phase. Also, the amount of active and reactive load of buses in other hours is obtained by multiplying the active and reactive load of the peak hour and the load factor curve [72][73][74][75][76][77][78][79][80][81][82][83][84]. It should be noted that the load factor curve is in the form of Figure 2 [59]. Te price of electrical energy is shown in Figure 3, and based on this fgure, the price of energy includes three periods of time such as the period of cheap price, average price, and expensive price, and each period according to Figure 2 is, respectively, overlapping with of-peak, medium, and peak periods.
It should be noted that the minimum and maximum voltage magnitudes considered are equal to 0.9 and 1.05 per unit (p.u.), respectively. Moreover, the reliability price represents a penalty price, which according to [60] should be several times the price of electrical energy. Terefore, in this paper, this price is assumed to be about 10 times the price of electrical energy. Moreover, the basic power and voltage for the said network are equal to 1 MVA and 12.66 kV. Finally, it should be said that in this paper, three-phase microturbinetype DGs are used, each of which has a capacity of 0.3 MVA. Also, the maximum distance between the voltages of the phases is considered 0.005 p.u.

Results.
In this section, the results of the reconfguration of the distribution network and the optimal placement of DGs in the distribution network are expressed. In other words, this section includes all the variables and equations of the proposed problem (1) to (14). In addition, several different studies are carried out to analyze network indices and reliability in this section, which are as follows: (i) Case I: Performing power fow in the distribution network of the test case (there is no switching in this case and it is the basic case) (ii) Case II: Reconfguring the network to minimize voltage deviation from the desired value, energy cost, and reliability in the test network (iii) Case III: Optimal planning and operation of DG1 to DG6 and reconfguring the network to minimize voltage deviation from the desired value, energy cost, and reliability in the test network Te diferent results of this section on the network indices are shown in Figure 4 and 5, which, respectively, represent the daily curve of the apparent power received by the distribution network from the upstream grid (seen from bus one which is assumed to be connected to the upstream grid) and the voltage profle of the distribution network is at peak hour or 20 : 00 for the frst phase. It should be noted that in Figure 4, the expression S max represents the maximum capacity of the distribution network. According to Figure 4, the 69-bus distribution network in Case I for the hours 18:00 to 22:00 has more apparent power than its limit, but in the other case, the time interval for the mentioned case has decreased. Te distribution network in Case II for hours International Transactions on Electrical Energy Systems 19:00 to 22:00 has more apparent power than its allowed limit. However, in the third case, the apparent power of the distribution network is less than its allowed limit at all hours. In Case I, there was no switching and DGs, but in Case II, there was switching, and in Case III, there is switching and DGs. Terefore, it can be said that network reconfguration using switching will lead to the more optimal distribution of power in the distribution network, and the use of DG units along with network reconfguration will reduce the level of power demand from the upstream grid. Figure 5 shows the voltage profle of the 69-bus distribution network for the peak hour in the frst phase. Based on this fgure, the voltage drop in Case I for buses 57 to 65 is more severe than for other buses. Terefore, due to the frst part of the objective function (1) (minimizing the voltage deviation from the desired value), in the second case, the switching in the  network is such that all the switches are closed, and in Case III, all the switches are closed and DGs are placed in bus 57 to 65 and 27. Terefore, according to Figure 5, it can be seen that distribution network reconfguration by using the switching of diferent switches at the network level and the greater number of DGs in the network will increase the network voltage towards 1 p.u. so that the voltage profle is directed to a smoother shape. Table 1 tabulates the results of load imbalance. It is worth mentioning that in cases I and II, the distance between the bus voltages is more than the permissible limit, i.e., 0.005. Nevertheless, in Case III, the distance between bus voltages is less than the permissible limit. Terefore, it can be seen that the reconfguration along with the optimal placement of DGs in the network will balance the load in the three-phase system. Table 2 shows the results of switching in cases II and III. As can be observed, all the switches placed in the 69-bus distribution network are in the closed mode, which is a mode to improve reliability, energy cost, and voltage deviation. Table 3 provides the results of the optimal placement of DGs in Case III. As can be seen, DGs are distributed in buses 57 to 65 and a DG is placed in bus 27. Since the voltage profle will be smoother, the reliability will be improved and the energy cost will be lower. In addition, Figures 6 and 7, respectively, illustrate the daily curve of total active and reactive power injected into the distribution network in Case III. As can be seen, based on these fgures, DGs have allocated their maximum capacity for active power injection and a very low amount of their capacity has been allocated for reactive power injection in the distribution network. Tis is because the objective function of the problem has three parts: minimization of energy cost, minimization of reliability cost, and minimization of voltage deviation. Now, although injecting the active power of DGs into the distribution network will improve all three cases, injecting the reactive power of DGs into the distribution network will enhance the network voltage. Table 4 examines the results of diferent study cases for the reliability index. According to Table 4, the value of reliability indices for Cases I and II is not zero, but in Case III, these values are zero. In other words, it can be said that the reconfguration of the 69-bus distribution network alone is not able to improve the reliability of the said distribution network. However, in the presence of a signifcant number of DGs, in addition to the problem of network reconfguration, it can improve reliability and make its indicators zero.

. Conclusion
In this paper, the problem of optimal placement of DGs along with distribution network reconfguration to improve the voltage profle, reliability, and load balancing in the distribution network was stated. Te mentioned problem is in the form of an optimization problem whose objective function is to minimize the voltage deviation from the desired value, minimize the cost of reliability (the cost of EENS), and minimize energy consumption. Also, the problem is subject to network limitations, network indices' limitations such as voltage and power fow of lines, relationships governing DGs, load balancing limitations, and items corresponding to the proposed problem. In this problem, by establishing the load balancing limit, it is expected that the load on each phase will be within the normal limit and will not exceed its permitted limits. Terefore, load balancing in this proposed problem was expressed as a constraint. It should be noted that the presented problem was in the form of MINLP and was solved using PSO evolutionary algorithm. Finally, the following general results have been extracted based on the numerical results obtained from diferent study cases: (i) Improving the voltage profle or reducing the amount of voltage drop in the distribution network with the presence of more DGs and their energy management (ii) Improving the reliability or reducing the EENS index in the distribution network with the presence of more DGs and their energy management (iii) Balancing the load in the three-phase system in the distribution network with the presence of more DGs and their energy management (iv) Enhancing the voltage profle or reducing the amount of voltage drop in the distribution network with the ability to reconfgure the network by using diferent switches (v) Slight improvement of reliability or slight reduction of the EENS index in the distribution network with the ability to reconfgure the network by using diferent switches (vi) Balancing the three-phase system in the distribution network with the ability to reconfgure the network using diferent switches.
In the proposed plan for planning distributed generations, load changes were not included in the planning horizon. But the load curve is diferent for diferent days. Also, the consumption growth rate is diferent in diferent years. Terefore, there is a possibility that there will be load changes in the planning horizon. So, the proposed plan according to this issue was included as a future work.

Nomenclature i:
Bus index j: Bus index t: Time step index k: Switch index ref: Reference or slack bus p: Phase index φ i : Set of buses φ t : Set of time steps φ k : Set of switches φ p : Set of phases P G : Active power transmitted by the distribution network substation (placed on the slack bus) towards the consumption load (p.u) P DG : Active power generation by DGs (p.u.) P L : Active power fow through the lines (p.u.) Q G : Reactive power transmitted by the distribution network substation (placed on the slack bus) towards the consumption load (p.u.) Q DG : Reactive power generation by DGs (p.u.) Q L : Reactive power fow through the lines (p.u.) V: Voltage magnitude (p.u.) Θ: Voltage angle (rad) I D : Active load not-supplied (p.u.) EENS: Expected energy not-supplied (p.u.) N L : Number of main loops V ref : Voltage magnitude of the slack bus that is assumed the desirable value (p.u.)

Data Availability
Te data used to support the fndings of this study are available from the corresponding author upon reasonable request.