# Providing a Novel Approach Based on Decomposition for Congestion Management considering EVCSs, Wind Farms, and DLC

Authors: Mohammad Hasan Nikkhah; Mahdi Samadi; Mohammad Ebrahim Hajiabadi; Hossein Lotfi
Journal: International Journal of Energy Research
 (2023)

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## Abstract

The acceptance of renewable energy sources and electric vehicle charging stations (EVCSs) around the world is growing, which changes the network’s congestion. From the operator’s perspective, congestion management is essential for network reliability despite increased demand. Additionally, it is among the most crucial elements in preventing network market power. Therefore, the items affecting the congestion changes of network lines, in particular, congested lines, are important for the operator. In this paper, using an analytical method and structural decomposition, the impact of wind farms, EVCSs, and demand response to changes in network line congestion in various cases has been investigated. In addition, some indices have been proposed to evaluate the ability of each item to change the congestion at low and peak loads. The proposed method has been implemented on the IEEE standard 24-bus network, and the results have been analyzed. This method is an effective tool for the network operator to predict the state of the network due to changes in items.


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## Body

## 1. Introduction

### 1.1. Motivation

Nowadays, the use of renewable energy has attracted the attention of many countries due to the reduction of environmental pollution [1–2]. In this regard, the amount of line congestion changed for the placement of renewable energies in the network is important from the operator’s point of view. So that with the increase in demand over time, network lines become congested [3]. On the other hand, the network operator seeks to balance the network load between low and peak load by load shedding and by using incentive plans that affect the changes in the flow of lines [4–6]. Fast and effective congestion management (CM) is inevitable in today’s competitive electricity markets, so its incorrect management causes a lack of network reliability [7]. The purpose of this paper is to evaluate the impact of electric vehicle charging stations (EVCSs), wind farms, and demand response (DR) on changes in the congestion of network lines using an analytical method and structural decomposition. Determining the contribution of each item gives an effective signal to the network operator to predict the future of the network.


### 1.2. Literature Review

One of the important issues for maintaining the security and reliability of the network is CM [8]. When overload appears on network lines, network congestion occurs [9]. Many studies have been done in the field of CM from different aspects. A comparison has been made between nodal, regional, and discriminatory pricing in public networks with transmission constraints [10]. In reference [11], two methods of the highest locational marginal price (LMP) and LMP difference have been used to locate distributed generation (DG) from the point of view of CM. To place DGs for CM in Reference [12], two methods of LMP and congestion rent were used. Diallo et al. proposed a new approach using LMP analysis and the Lagrange function to manage transmission congestion and maximize social welfare [13]. The expansion of the network to manage network congestion has been investigated in reference [14]. Also, an index to encourage customers to participate in the DR plan based on the size of their participation has been investigated. If the network congestion is ignored, there is a possibility of network shutdown. Many factors affect the changes in network congestion, but the impact of items such as EVCSs and wind farms has been discussed in a few articles.There are a few articles on the impact of EVCSs on the congestion of network lines. For instance, a quadratic optimization problem based on the charging cost of electric vehicles (EVs) with congestion constraints is presented in references [15, 16]. Also, in reference [17], CM is presented with a new strategy due to the introduction of EVs into the network, in which the overall cost is optimized by an optimization problem in two modes: grid-to-vehicle (G2V) and vehicle-to-grid (V2G). A CM method caused by EVs using partial Lagrange decomposition is presented in reference [18], which considers two states of charging and discharging. In reference [19], in order to balance between congestion and operating costs, an optimization algorithm is presented for analysis by an optimization method. In reference [20], the optimization problem is formulated with the aim of reducing the final cost and reducing congestion. So, EVs act as a network load in G2V mode and as a generation unit in V2G mode. In addition, many articles on the optimal placement of EVCS have been reviewed from different aspects, so that the number of EVs in the specified area can be predicted [21]. Also, in reference [22], the problem of placement of charging stations (CSs) is formulated, and four solution methods are proposed to deal with the problem of placement of EVCSs. Andrews et al. presented an optimization model to determine the location of EVs based on the Chicago and Seattle data [23]. Liu et al. have initially identified the optimal locations of EVCSs using a two-stage screening method. Also, using a mathematical model, they identified the most optimal sizing for EVs [24]. Lam et al. formulated the problem of locating EVCSs by considering the reduction of the total cost based on an efficient algorithm [25]. Zhenghui et al. presented a new model for locating CSs with constant volume with the aim of minimizing investment and user costs [26]. Sadeghi-Barzani et al. proposed a mixed-integer nonlinear optimization method for locating fast CSs. Also, a suggested index for the effect of network reliability on the location and size of the CS to reduce the charging cost is provided [27]. Eisel et al. presented a method for considering customer preferences for the location problem of EVCSs [28]. A method for addressing V2G techniques for congestion management difficulties is brought out in reference [29], in which power distribution variables are employed to calculate how much energy a certain EV should give to ease congestion on a line. Reference [30] has looked into a probabilistic model to lessen the likelihood of line congestion and voltage violations in a smart grid located in a radial distribution network despite the uncertainty of electric vehicles and renewable resources. In order to relieve congestion in low voltage networks, reference [31] suggests a centralized control algorithm that regulates EV charging stations. In reference [32], a novel method for figuring out the ideal size of Emergency Demand Response Programs (EDRP) and Plug-in Hybrid Electrical Vehicle (PHEV) parking lots is suggested in order to alleviate transfer congestion in an affordable manner. As mentioned, few articles have been presented in the field of the impact of EVCSs on the congestion of lines, which do not consider variable charging and discharging. In this regard, one of the goals of this paper is to examine the effect of variable charging and discharging of EVs on the congestion of network lines.The expansion of wind farms is one of the items influencing the variations in line congestion and the reduction of unit generation costs [33, 34]. Actually, a few articles have investigated the effects of wind farms on the changes in grid line congestion by considering wind speed instability. An approach based on LMP for the impact of wind energy on line congestion is investigated in reference [35], and CM problems due to wind farm integration are discussed. One of the most important problems of wind power farms is the instability of wind speed, which causes instability in practical applications [36–42]. To overcome this problem, Dursun et al. used a wind energy storage system based on Turkey’s electricity needs [43]. When the ramping rates of power plants are taken into account, a thorough investigation of the dynamic interactions between wind energy curtailment and an energy storage system (ESS) becomes necessary to address transmission congestion management [44]. Since the effect of wind speed has an effect on the generation power of wind farms and causes the instability of generation power, the effect of wind speed has been investigated in a few articles in the field of wind farms. Hence, one of the goals of this paper is to investigate the impact of wind farms on the congestion of grid lines by considering the variable wind speed.DR programs are one way to resolve congestion. One of the influential items for correcting the network load curve is the DR programs, which are usually implemented during peak consumption hours to reduce generation costs [45]. For example, in references [46, 47], the effects of DR on cost reduction and load curve modification are presented. Also, a method for the most conservative load model was selected for load estimation. The authors have considered the DR program in reference [48] based on the incentive that consumers reduce their consumption during peak hours. Also, an index is provided to encourage users to participate in DR. The direct load control (DLC) method (as one of the DR methods) was implemented in the emergency situation on the test network, which was a suitable tool to improve congestion [49]. A unique hybrid IGDT-based system, referred to as SIGDT in reference [50], is presented for corrective transmission congestion management in the presence of a sizable number of uncertain wind farms, demand response companies, and conventional producing units. Reference [51] suggests a bilevel optimization model to resolve congestion management in order to identify the best DR buses for CM in the day-ahead market, taking into account the uncertainty of wind power. It is natural that these plans to improve the consumption pattern and increase reliability affect the congestion of lines, and the effects of these plans are considered in this paper. In Table 1, the comparison between the presented paper and previous works has been examined from different aspects.Table 1
Comparison of previous works and the proposed paper.
Ref.MethodObjective functionTransmission network constraintProposing indexConsidering uncertainlyEnergy resourcesDemand responseEVCSWind farm15Quadratic programming problemMinimizing charging cost✓××✓××16Quadratic programming problemCost-optimal profile of the aggregated energy demand✓××✓××17Gradient boosting regression tree method (GBM)Minimizing overall cost✓××✓××20Random forest method (RFM)Reducing congestion and total charging cost×××✓××27Genetic algorithm techniqueOptimal placing and sizing of the fast charging stations✓✓×✓××34Artificial bee colony algorithm and particle swarm optimization methodReducing congestion management✓×××✓×35Generalized modelMaximizing social benefit✓×××✓×44Comprehensive analysis of the dynamic interactionsReducing operational costs✓×✓×✓×50Novel hybrid scenario-IGDT-based frameworkCorrective transmission congestion management✓×✓×✓✓51Proposing new algorithmReducing congestion✓×✓×✓✓Our researchQuadratic programming problem (decomposition)Congestion assessment✓✓✓✓✓✓


### 1.3. Contribution

As mentioned, a few articles have been presented in the field of the impact of renewable energy, such as the impact of wind farms and EVCSs on changes in line congestion. The main goal and innovation of this paper is to evaluate the impact of EVCS and wind farms, as well as the impact of DLC (one of the incentive plans to encourage users to participate in this plan), on the changes in network line congestion using a powerful analytical method. So, according to this proposed method, there is no need to perform multiple power flows to determine the share of the items, and only by performing the market-clearing problem once can the contribution of all items to the changes in line congestion be determined. This method has been used in references52–58 to evaluate collusion and market power and other topics, which has accurately determined the share of each user. The general framework of the proposed method in this paper is as follows, as shown in Figure 1:
(i)
Determining the most optimal locations in terms of changes in the line flow for installing EVCSs, consider two conditions: low load and peak load(ii)
Calculating the optimal effect of EVCSs on changes in the lines’ congestion at low load (G2V) and peak load (G2V)(iii)
Calculating the effect of wind farms on changes in congestion in low and peak load(iv)
Calculating the impact of DLC on changes in low and peak load congestion(v)
Calculation of the effect of the combination of the mentioned items in different modes under low and peak load(vi)
Definition of indices (calculation of the impact of all items on line congestion)(vii)
There is no need to perform multiple power flows to determine the items affecting the congestion of network linesFigure 1
General framework of proposed method.


### 1.4. Paper Organization

This paper is divided into five general categories. The presentation of the basic formulas related to the topic is discussed in Section2. Then, the formulas of the proposed method and proposed indices are examined in Section 3. The results of the proposed method are analyzed in Section 4. Finally, the conclusion of the paper is examined in the final part which is the Section 5.


## 1.1. Motivation

Nowadays, the use of renewable energy has attracted the attention of many countries due to the reduction of environmental pollution [1–2]. In this regard, the amount of line congestion changed for the placement of renewable energies in the network is important from the operator’s point of view. So that with the increase in demand over time, network lines become congested [3]. On the other hand, the network operator seeks to balance the network load between low and peak load by load shedding and by using incentive plans that affect the changes in the flow of lines [4–6]. Fast and effective congestion management (CM) is inevitable in today’s competitive electricity markets, so its incorrect management causes a lack of network reliability [7]. The purpose of this paper is to evaluate the impact of electric vehicle charging stations (EVCSs), wind farms, and demand response (DR) on changes in the congestion of network lines using an analytical method and structural decomposition. Determining the contribution of each item gives an effective signal to the network operator to predict the future of the network.


## 1.2. Literature Review

One of the important issues for maintaining the security and reliability of the network is CM [8]. When overload appears on network lines, network congestion occurs [9]. Many studies have been done in the field of CM from different aspects. A comparison has been made between nodal, regional, and discriminatory pricing in public networks with transmission constraints [10]. In reference [11], two methods of the highest locational marginal price (LMP) and LMP difference have been used to locate distributed generation (DG) from the point of view of CM. To place DGs for CM in Reference [12], two methods of LMP and congestion rent were used. Diallo et al. proposed a new approach using LMP analysis and the Lagrange function to manage transmission congestion and maximize social welfare [13]. The expansion of the network to manage network congestion has been investigated in reference [14]. Also, an index to encourage customers to participate in the DR plan based on the size of their participation has been investigated. If the network congestion is ignored, there is a possibility of network shutdown. Many factors affect the changes in network congestion, but the impact of items such as EVCSs and wind farms has been discussed in a few articles.There are a few articles on the impact of EVCSs on the congestion of network lines. For instance, a quadratic optimization problem based on the charging cost of electric vehicles (EVs) with congestion constraints is presented in references [15, 16]. Also, in reference [17], CM is presented with a new strategy due to the introduction of EVs into the network, in which the overall cost is optimized by an optimization problem in two modes: grid-to-vehicle (G2V) and vehicle-to-grid (V2G). A CM method caused by EVs using partial Lagrange decomposition is presented in reference [18], which considers two states of charging and discharging. In reference [19], in order to balance between congestion and operating costs, an optimization algorithm is presented for analysis by an optimization method. In reference [20], the optimization problem is formulated with the aim of reducing the final cost and reducing congestion. So, EVs act as a network load in G2V mode and as a generation unit in V2G mode. In addition, many articles on the optimal placement of EVCS have been reviewed from different aspects, so that the number of EVs in the specified area can be predicted [21]. Also, in reference [22], the problem of placement of charging stations (CSs) is formulated, and four solution methods are proposed to deal with the problem of placement of EVCSs. Andrews et al. presented an optimization model to determine the location of EVs based on the Chicago and Seattle data [23]. Liu et al. have initially identified the optimal locations of EVCSs using a two-stage screening method. Also, using a mathematical model, they identified the most optimal sizing for EVs [24]. Lam et al. formulated the problem of locating EVCSs by considering the reduction of the total cost based on an efficient algorithm [25]. Zhenghui et al. presented a new model for locating CSs with constant volume with the aim of minimizing investment and user costs [26]. Sadeghi-Barzani et al. proposed a mixed-integer nonlinear optimization method for locating fast CSs. Also, a suggested index for the effect of network reliability on the location and size of the CS to reduce the charging cost is provided [27]. Eisel et al. presented a method for considering customer preferences for the location problem of EVCSs [28]. A method for addressing V2G techniques for congestion management difficulties is brought out in reference [29], in which power distribution variables are employed to calculate how much energy a certain EV should give to ease congestion on a line. Reference [30] has looked into a probabilistic model to lessen the likelihood of line congestion and voltage violations in a smart grid located in a radial distribution network despite the uncertainty of electric vehicles and renewable resources. In order to relieve congestion in low voltage networks, reference [31] suggests a centralized control algorithm that regulates EV charging stations. In reference [32], a novel method for figuring out the ideal size of Emergency Demand Response Programs (EDRP) and Plug-in Hybrid Electrical Vehicle (PHEV) parking lots is suggested in order to alleviate transfer congestion in an affordable manner. As mentioned, few articles have been presented in the field of the impact of EVCSs on the congestion of lines, which do not consider variable charging and discharging. In this regard, one of the goals of this paper is to examine the effect of variable charging and discharging of EVs on the congestion of network lines.The expansion of wind farms is one of the items influencing the variations in line congestion and the reduction of unit generation costs [33, 34]. Actually, a few articles have investigated the effects of wind farms on the changes in grid line congestion by considering wind speed instability. An approach based on LMP for the impact of wind energy on line congestion is investigated in reference [35], and CM problems due to wind farm integration are discussed. One of the most important problems of wind power farms is the instability of wind speed, which causes instability in practical applications [36–42]. To overcome this problem, Dursun et al. used a wind energy storage system based on Turkey’s electricity needs [43]. When the ramping rates of power plants are taken into account, a thorough investigation of the dynamic interactions between wind energy curtailment and an energy storage system (ESS) becomes necessary to address transmission congestion management [44]. Since the effect of wind speed has an effect on the generation power of wind farms and causes the instability of generation power, the effect of wind speed has been investigated in a few articles in the field of wind farms. Hence, one of the goals of this paper is to investigate the impact of wind farms on the congestion of grid lines by considering the variable wind speed.DR programs are one way to resolve congestion. One of the influential items for correcting the network load curve is the DR programs, which are usually implemented during peak consumption hours to reduce generation costs [45]. For example, in references [46, 47], the effects of DR on cost reduction and load curve modification are presented. Also, a method for the most conservative load model was selected for load estimation. The authors have considered the DR program in reference [48] based on the incentive that consumers reduce their consumption during peak hours. Also, an index is provided to encourage users to participate in DR. The direct load control (DLC) method (as one of the DR methods) was implemented in the emergency situation on the test network, which was a suitable tool to improve congestion [49]. A unique hybrid IGDT-based system, referred to as SIGDT in reference [50], is presented for corrective transmission congestion management in the presence of a sizable number of uncertain wind farms, demand response companies, and conventional producing units. Reference [51] suggests a bilevel optimization model to resolve congestion management in order to identify the best DR buses for CM in the day-ahead market, taking into account the uncertainty of wind power. It is natural that these plans to improve the consumption pattern and increase reliability affect the congestion of lines, and the effects of these plans are considered in this paper. In Table 1, the comparison between the presented paper and previous works has been examined from different aspects.Table 1
Comparison of previous works and the proposed paper.
Ref.MethodObjective functionTransmission network constraintProposing indexConsidering uncertainlyEnergy resourcesDemand responseEVCSWind farm15Quadratic programming problemMinimizing charging cost✓××✓××16Quadratic programming problemCost-optimal profile of the aggregated energy demand✓××✓××17Gradient boosting regression tree method (GBM)Minimizing overall cost✓××✓××20Random forest method (RFM)Reducing congestion and total charging cost×××✓××27Genetic algorithm techniqueOptimal placing and sizing of the fast charging stations✓✓×✓××34Artificial bee colony algorithm and particle swarm optimization methodReducing congestion management✓×××✓×35Generalized modelMaximizing social benefit✓×××✓×44Comprehensive analysis of the dynamic interactionsReducing operational costs✓×✓×✓×50Novel hybrid scenario-IGDT-based frameworkCorrective transmission congestion management✓×✓×✓✓51Proposing new algorithmReducing congestion✓×✓×✓✓Our researchQuadratic programming problem (decomposition)Congestion assessment✓✓✓✓✓✓


## 1.3. Contribution

As mentioned, a few articles have been presented in the field of the impact of renewable energy, such as the impact of wind farms and EVCSs on changes in line congestion. The main goal and innovation of this paper is to evaluate the impact of EVCS and wind farms, as well as the impact of DLC (one of the incentive plans to encourage users to participate in this plan), on the changes in network line congestion using a powerful analytical method. So, according to this proposed method, there is no need to perform multiple power flows to determine the share of the items, and only by performing the market-clearing problem once can the contribution of all items to the changes in line congestion be determined. This method has been used in references52–58 to evaluate collusion and market power and other topics, which has accurately determined the share of each user. The general framework of the proposed method in this paper is as follows, as shown in Figure 1:
(i)
Determining the most optimal locations in terms of changes in the line flow for installing EVCSs, consider two conditions: low load and peak load(ii)
Calculating the optimal effect of EVCSs on changes in the lines’ congestion at low load (G2V) and peak load (G2V)(iii)
Calculating the effect of wind farms on changes in congestion in low and peak load(iv)
Calculating the impact of DLC on changes in low and peak load congestion(v)
Calculation of the effect of the combination of the mentioned items in different modes under low and peak load(vi)
Definition of indices (calculation of the impact of all items on line congestion)(vii)
There is no need to perform multiple power flows to determine the items affecting the congestion of network linesFigure 1
General framework of proposed method.


## 1.4. Paper Organization

This paper is divided into five general categories. The presentation of the basic formulas related to the topic is discussed in Section2. Then, the formulas of the proposed method and proposed indices are examined in Section 3. The results of the proposed method are analyzed in Section 4. Finally, the conclusion of the paper is examined in the final part which is the Section 5.


## 2. Problem Formulation

The basic mathematical formulas related to the subject of this paper are based on quadratic programming. Therefore, to express the proposed model, it is necessary to first introduce the assumed basic concepts. The general form of quadratic programming is given by(1)Min12XT.H.X+FT.X,SubjecttoAeq.X=Beq:Λ,A.X≤B:Ω,LB≤X≤UB:Τ−,Τ+.After solving the optimization function, optimal values, minimum, and maximum, as well as Lagrange coefficients are calculated. Therefore, according to Equation (2), all parameters are divided into three parts:
(2)X=XminXmaxXmrg,LB=LBminLBmaxLBmrg,UB=UBminUBmaxUBmrg,Τ−=Τmin−Τmax−Τmrg−,Τ+=Τmin+Τmax+Τmrg+,F=FminFmaxFmrg.Similarly, in Equation (3) for matrix Aeq, we have
(3)Aeq=AmineqAmaxeqAmrgeq.Therefore, the Lagrange function for solving the problem is as follows:(4)LX,Λ,Ω,Γ=12XT.H.X+FT.X+ΛT.Aeq.X−Beq+ΩT.A.X−B+Γmin−T.LBmin−Xmin+Γmax+T.Xmax−UBmax.The following lemma is used to calculate the effect of each variable on the changes of the function.Lemma 1.
“For the QP problem (1) with a Lagrangian function (4), the output of the optimization including marginal variables and Lagrangian multipliers can be decomposed as the matrix form (5) into structural factors of the QP problem.”According to Lemma1, the general form of the coefficient matrix to calculate the effect of variables on the desired variables is in accordance with
(5)XmrgΛΩ=C11C12C13C14C15C21C22C23C24C25C31C32C33C34C35FmrgLBminUBmaxBeqB.The proof of Lemma1 is provided in reference [55].The objective function of the market with equation and inequality constraints is given in(6)MinPG,PL∑i=1Ngai.Pgi+12bi.Pgi2,MG.PG−ML.PL=PD:LMP,Pl−θa−θbxab−1=0,PGMin≤PG≤PGMax,−PLMax≤PL≤PLMax.The output of the optimization problem, including line flows, LMP of the buses, and the generation power of the units, is obtained by performing the market-clearing problem on the test network. According to the results, generators that generate power at their maximum capacity are known as cheap generators (CGs), while generators that generate power at their minimum capacity are known as expensive generators (EGs), as well as generators that generate power between their minimum and maximum capacity are known as marginal units (MGs).


## 3. Proposed Method

Based on the proposed method, the flow of lines and the coefficients affecting it can be formulated as follows:(7)Flow=φflowNl×Nt.QNt×1⇒dFlow=φflowNl×Nt.dQNt×1,dFlow=φmrgflow⏟Nl×Nmrgφexflow⏟Nl×Nexφchflow⏟Nl×NchφPdflow⏟Nl×Nbφclflow⏟Nl×Ncl.damrgdPGMindPGMaxdPDdPLMax.In general, five factors affect the changes in the flow of network lines, which include MGs, EGs, CGs, network load, and congested lines. MGs have an effect on the changes in the flow of network lines due to their bid price. While EGs and CGs affect the changes in line flow by changing their minimum and maximum generation capacity, the two final factors influencing the flow of network lines are network load and congested lines. So the network load affects the flow changes of the lines by increasing their power consumption, and the congested lines are affected by changing their maximum capacity. Also, according to Equation (8), network lines are divided into two categories: normal lines and congested lines.
(8)CL=FlowlFlowlmax≥α⇒Flowl≥α×Flowlmax.A line whose ratio of passing flow to its capacity is greater thanα is called a congested line and other network lines that do not include this condition are called normal lines. In the following, the impact of EVCSs, wind farms, and DLC on low and peak load will be investigated. In this paper, EVCSs are referred to as “grid loads” and wind farms as “CGs”.


### 3.1. Formulation of Electric Vehicle Charging Stations

As mentioned, EVCSs in the network act as sources of load in low load. In other words, flow is injected from the grid to the vehicle (G2V). This transaction is the opposite of peak load, and the flow is transferred from the vehicle to the grid (V2G) so that the network can respond to consumers in peak load. Therefore, the matrix of effective network load coefficients on network lines is defined as follows:(9)φPdflow=Ψ1,1flow⋯Ψ1,bflow⋯Ψ1,Nbflow⋮⋱⋮⋱⋮Ψl,1flow⋯Ψl,bflow⋯Ψl,Nbflow⋮⋱⋮⋱⋮ΨNl,1flow⋯ΨNl,bflow⋯ΨNl,NbflowNl×Nb,whichΨl,bflow is the effect factor of the load placed in the bus b on the flow of the line l. On the other hand, the total number of EVCS positions in the network with Nb bus and Nv stations is as follows:
(10)Nc=NbNv,1≤Nv≤Nb.AndSc indicates the placement of stations in case c.
(11)Sc≜Loc1c,⋯,Locvc,⋯,LocNvc∀c,1≤v≤Nv,c=1,2,⋯,Nc,Locvc∈1,2,⋯,Nb.After determining the location of the stations in the network, the matrix of their influence coefficients on the changes in the flow of the lines is determined using(12)φNvflow≜φPdflowSc=ΨLoc1cflowNl×1⋯ΨLocvcflowNl×1⋯ΨLocNvcflowNl×1=Ψ1,Loc1cflow⋯Ψ1,Locvcflow⋯Ψ1,LocNvcflow⋮⋱⋮⋱⋮Ψl,Loc1cflow⋯Ψl,Locvcflow⋯Ψl,LocNvcflow⋮⋱⋮⋱⋮ΨNl,Loc1cflow⋯ΨNl,Locvcflow⋯ΨNl,LocNvcflowNl×Nv,which isΨl,Locvcflow the coefficient of influence of the EVCS v on the flow of the line l in case c. By placing EVCSs on the network, the network load changes by the matrix dPLoadEV. This change is applied to the dQ matrix
(13)dQ=000dPLoad⏟1×Nb01×NtT,which these load changes in the buses where the CSs are located are equal toωavgb∈Scand the load changes in the buses where the charging stations are not located are equal to zero. b∉Sc(14)Inwhich:dPLoadEVb=0b∉ScdPLoadEVbb∈Sc.Finally, by applying the fluctuations of the stations in terms of power consumption to get closer to the real conditions, the matrix of network load changes caused by the CSs is as follows:(15)dPLoadEVc=ωv1Nv×1⋯ωvqNv×1⋯ωvNqNv×1c,ωvq∈ωvavg±ϒv.After determining the matrix of network load changes caused by CSs, the calculation of line flow changes in two states, G2V and V2G, will be done.


#### 3.1.1. The Effect of EVCSs on Line Flow in Low Load (G2V Mode)

In low load, EVCSs act as network loads. Therefore, the flow changes of network lines caused by EVCSs in casec per Nq sample is defined as follows:
(16)dFlowcvNl×Nq=φNvflowNl×Nv.dPLoadEVcNv×Nq.Then, by averaging the samples of changes in load power consumption caused by EVCSs, the effect of EVCSs in casec is defined as follows.
(17)EEALc,lG2V=∑q=1NqdFlowcvNq,∀c.Next, the impact of EVCSs on the flow of network lines at peak load will be discussed.


#### 3.1.2. The Effect of EVCSs on Line Flow in Peak Load (V2G Mode)

At peak load, EVCSs act like generation units. In other words, they inject power into the grid. Therefore, the matrix of the effective coefficients of the EVCSs is multiplied by the negative and the flow changes of the network lines caused by the EVCSs perNq sample in the case c are as follows:
(18)dFlowcvNl×Nq=−φNvflowNl×Nv.dPLoadEVcNv×Nq.Similarly, by calculating the average of sampleNq in the V2G mode, the effect of the EVCSs in the case c is calculated.
(19)EEALc,lV2G=∑q=1NqdFlowcvNq,∀c.After calculating the effects of EVCSs in both low and peak load, the overall impact of the stations on the network is defined as follows.(20)EEALc,lρ=EEALc,lG2V+ρ.EEALc,lV2G,ρ=0,0.1,⋯,1,whichρ is the return power of EVs to the stations.Also, the proposed method is able to detect the location of the EVCSs in the most optimal case, which is analyzed in the results section.


### 3.2. The Effect of Wind Farms on Variation of Line Flows

Wind farms are considered among the CGs in the grid due to their low prices. In this regard, the matrix of the effective coefficients of the CGs affecting the changes in the flow of the grid lines is defined as follows:(21)φchflow=Ψ1,1flow⋯Ψ1,chiflow⋯Ψ1,Nchflow⋮⋱⋮⋱⋮Ψl,1flow⋯Ψl,chiflow⋯Ψl,Nchflow⋮⋱⋮⋱⋮ΨNl,1flow⋯ΨNl,chiflow⋯ΨNl,NchflowNl×Nch,whichΨl,chiflow is the effect factor of the CG i on the flow of the line l. Depending on the placement of wind farms in the network, the matrix of the effective coefficients of wind farms is proposed in
(22)φNwflow=φchflowLocw=Ψ1,1flow⋯Ψ1,wflow⋯Ψ1,Nwflow⋮⋱⋮⋱⋮Ψl,1flow⋯Ψl,wflow⋯Ψl,Nwflow⋮⋱⋮⋱⋮ΨNl,1flow⋯ΨNl,wflow⋯ΨNl,NwflowNl×Nw,Nw≤Nch,which Ψl,wflow is the effect factor of wind farm w on the flow of the line l. Therefore, the changes in generation power due to the presence of wind farms in the network are defined as follows:
(23)dQ=00dPΓMax⏟1×Nch001×NtT.aSo these power changes are applied to the buses where the wind farms are located, and in other buses, the changes are equal to zero.(24)Inwhich:dPGMaxchi=0chi∉chwdPGWchichi∈chw.Due to the variable wind speed and variable generation power of wind farms, their generation power is considered with different samples.(25)dPGW=ωw1Nw×1⋯ωwqNw×1⋯ωwNqNw×1,ωwq∈ωwavg±ϒw.Therefore, the changes in the flow of grid lines per sampleNq caused by wind farms are as follows:
(26)dFlowwNl×Nq=τ.φNwflowNl×Nw.dPGWNw×Nq.Finally, the impact of the wind farm on the network flow changes is calculated as follows:(27)EEWLl=∑q=1NqdFlowwNq.Therefore, the amount of flow changes and the congestion of grid lines can be calculated for the presence of wind farms using the proposed method. It is natural that the effects of wind farms are different at low and peak load. So that the matrix of the effective coefficients of the wind farm changes with the flow changes of the grid lines. In the following, the impact of DR in network peak load on changes in line congestion will be investigated.


### 3.3. The Effect of Demand Response on Variation of Line Flows

Demand response means the ability of customers to improve the energy consumption pattern to reach appropriate prices and improve network reliability. In this regard, based on references [59–61], load shifting from peak load to low load is formulated as follows, if possible
(28)Lt¯=Pt∈ΩLt+At∈ψ,where
(29)A=λ∑t∈ΩLt−PN.In other words, the network operator leads consumers to reduce consumption during peak periods. Instead, with incentive schemes, it encourages them to increase consumption during low load to improve the consumption load pattern. At peak load, the network operator encourages users to reduce consumption with incentive plans. Suppose the network load at peak load is equal toPT. Therefore, by using incentive plans, a percentage of a network load is reduced in peak load and added to low load. So, we have
(30)TP=ξ×PT,0<ξ≤1,whichξ is a coefficient of the total load at peak load. TP is the amount of load that is reduced during this time and is added to the time of low load. It is natural that the matrix of load reduction coefficients influencing the changes in line flow in peak load is different from the matrix of coefficients in low load. If the matrix of coefficients in peak load is φPd.peakflow, we have
(31)dFlowDLCpeak=−TPNb.φPd,peakflow.dPLoad.The negative sign in Equation (31) is due to the load reduction during peak load. After reducing the load during the peak load, the flow changes of the network lines in the low load caused by the increase in the load during the peak load are defined in
(32)dFlowDLClow=β×TPNb.φPd,lowflow.dPLoad,0≤β≤1.The load added to the low load can be the total load removed from the peak load or a certain ratio of that load, which is defined byβ. Therefore, according to the proposed method, the amount of change in the flow of grid lines is calculated for the purpose of applying direct load control planning. In the following, the proposed indices will be presented.


### 3.4. Proposed Indices

In this section, to evaluate the items influencing the changes in the flow of lines, two indices are proposed in Table2:Table 2
Proposed indices.
IndexDefinitionEAFlowEffect of all items on line flows in low loadEAFpeakEffect of all items on line flows in peak loadIn fact, the impact coefficients of EVCSs, wind farms, and DLC are provided by two indices in.(33)EAFlow=∑l=1Nl∑EVCSΨl,EVCSlow.PEVCS+∑bΨl,blow.PDLC+∑wΨl,wlow.PwFlowllow=∑l=1Nl∑EVCSΨl,EVCSlow.PEVCSFlowllow⏟EAFEVCSlow+∑l=1Nl∑bΨl,blow.PDLCFlowllow⏟EAFDLClow+∑l=1Nl∑wΨl,wlow.PwFlowllow⏟EAFwindlow,EAFpeak=∑l=1Nl∑EVCSΨl,EVCSpeak.PEVCSFlowlpeak⏟EAFEVCSpeak+∑l=1Nl∑bΨl,bpeak.PDLCFlowlpeak⏟EAFDLCpeak+∑l=1Nl∑wΨl,wpeak.PwFlowlpeak⏟EAFwindpeak.In other words, the index related to each item is determined in low and peak load. In the following, the results of the proposed method will be presented.


## 3.1. Formulation of Electric Vehicle Charging Stations

As mentioned, EVCSs in the network act as sources of load in low load. In other words, flow is injected from the grid to the vehicle (G2V). This transaction is the opposite of peak load, and the flow is transferred from the vehicle to the grid (V2G) so that the network can respond to consumers in peak load. Therefore, the matrix of effective network load coefficients on network lines is defined as follows:(9)φPdflow=Ψ1,1flow⋯Ψ1,bflow⋯Ψ1,Nbflow⋮⋱⋮⋱⋮Ψl,1flow⋯Ψl,bflow⋯Ψl,Nbflow⋮⋱⋮⋱⋮ΨNl,1flow⋯ΨNl,bflow⋯ΨNl,NbflowNl×Nb,whichΨl,bflow is the effect factor of the load placed in the bus b on the flow of the line l. On the other hand, the total number of EVCS positions in the network with Nb bus and Nv stations is as follows:
(10)Nc=NbNv,1≤Nv≤Nb.AndSc indicates the placement of stations in case c.
(11)Sc≜Loc1c,⋯,Locvc,⋯,LocNvc∀c,1≤v≤Nv,c=1,2,⋯,Nc,Locvc∈1,2,⋯,Nb.After determining the location of the stations in the network, the matrix of their influence coefficients on the changes in the flow of the lines is determined using(12)φNvflow≜φPdflowSc=ΨLoc1cflowNl×1⋯ΨLocvcflowNl×1⋯ΨLocNvcflowNl×1=Ψ1,Loc1cflow⋯Ψ1,Locvcflow⋯Ψ1,LocNvcflow⋮⋱⋮⋱⋮Ψl,Loc1cflow⋯Ψl,Locvcflow⋯Ψl,LocNvcflow⋮⋱⋮⋱⋮ΨNl,Loc1cflow⋯ΨNl,Locvcflow⋯ΨNl,LocNvcflowNl×Nv,which isΨl,Locvcflow the coefficient of influence of the EVCS v on the flow of the line l in case c. By placing EVCSs on the network, the network load changes by the matrix dPLoadEV. This change is applied to the dQ matrix
(13)dQ=000dPLoad⏟1×Nb01×NtT,which these load changes in the buses where the CSs are located are equal toωavgb∈Scand the load changes in the buses where the charging stations are not located are equal to zero. b∉Sc(14)Inwhich:dPLoadEVb=0b∉ScdPLoadEVbb∈Sc.Finally, by applying the fluctuations of the stations in terms of power consumption to get closer to the real conditions, the matrix of network load changes caused by the CSs is as follows:(15)dPLoadEVc=ωv1Nv×1⋯ωvqNv×1⋯ωvNqNv×1c,ωvq∈ωvavg±ϒv.After determining the matrix of network load changes caused by CSs, the calculation of line flow changes in two states, G2V and V2G, will be done.


### 3.1.1. The Effect of EVCSs on Line Flow in Low Load (G2V Mode)

In low load, EVCSs act as network loads. Therefore, the flow changes of network lines caused by EVCSs in casec per Nq sample is defined as follows:
(16)dFlowcvNl×Nq=φNvflowNl×Nv.dPLoadEVcNv×Nq.Then, by averaging the samples of changes in load power consumption caused by EVCSs, the effect of EVCSs in casec is defined as follows.
(17)EEALc,lG2V=∑q=1NqdFlowcvNq,∀c.Next, the impact of EVCSs on the flow of network lines at peak load will be discussed.


### 3.1.2. The Effect of EVCSs on Line Flow in Peak Load (V2G Mode)

At peak load, EVCSs act like generation units. In other words, they inject power into the grid. Therefore, the matrix of the effective coefficients of the EVCSs is multiplied by the negative and the flow changes of the network lines caused by the EVCSs perNq sample in the case c are as follows:
(18)dFlowcvNl×Nq=−φNvflowNl×Nv.dPLoadEVcNv×Nq.Similarly, by calculating the average of sampleNq in the V2G mode, the effect of the EVCSs in the case c is calculated.
(19)EEALc,lV2G=∑q=1NqdFlowcvNq,∀c.After calculating the effects of EVCSs in both low and peak load, the overall impact of the stations on the network is defined as follows.(20)EEALc,lρ=EEALc,lG2V+ρ.EEALc,lV2G,ρ=0,0.1,⋯,1,whichρ is the return power of EVs to the stations.Also, the proposed method is able to detect the location of the EVCSs in the most optimal case, which is analyzed in the results section.


## 3.1.1. The Effect of EVCSs on Line Flow in Low Load (G2V Mode)

In low load, EVCSs act as network loads. Therefore, the flow changes of network lines caused by EVCSs in casec per Nq sample is defined as follows:
(16)dFlowcvNl×Nq=φNvflowNl×Nv.dPLoadEVcNv×Nq.Then, by averaging the samples of changes in load power consumption caused by EVCSs, the effect of EVCSs in casec is defined as follows.
(17)EEALc,lG2V=∑q=1NqdFlowcvNq,∀c.Next, the impact of EVCSs on the flow of network lines at peak load will be discussed.


## 3.1.2. The Effect of EVCSs on Line Flow in Peak Load (V2G Mode)

At peak load, EVCSs act like generation units. In other words, they inject power into the grid. Therefore, the matrix of the effective coefficients of the EVCSs is multiplied by the negative and the flow changes of the network lines caused by the EVCSs perNq sample in the case c are as follows:
(18)dFlowcvNl×Nq=−φNvflowNl×Nv.dPLoadEVcNv×Nq.Similarly, by calculating the average of sampleNq in the V2G mode, the effect of the EVCSs in the case c is calculated.
(19)EEALc,lV2G=∑q=1NqdFlowcvNq,∀c.After calculating the effects of EVCSs in both low and peak load, the overall impact of the stations on the network is defined as follows.(20)EEALc,lρ=EEALc,lG2V+ρ.EEALc,lV2G,ρ=0,0.1,⋯,1,whichρ is the return power of EVs to the stations.Also, the proposed method is able to detect the location of the EVCSs in the most optimal case, which is analyzed in the results section.


## 3.2. The Effect of Wind Farms on Variation of Line Flows

Wind farms are considered among the CGs in the grid due to their low prices. In this regard, the matrix of the effective coefficients of the CGs affecting the changes in the flow of the grid lines is defined as follows:(21)φchflow=Ψ1,1flow⋯Ψ1,chiflow⋯Ψ1,Nchflow⋮⋱⋮⋱⋮Ψl,1flow⋯Ψl,chiflow⋯Ψl,Nchflow⋮⋱⋮⋱⋮ΨNl,1flow⋯ΨNl,chiflow⋯ΨNl,NchflowNl×Nch,whichΨl,chiflow is the effect factor of the CG i on the flow of the line l. Depending on the placement of wind farms in the network, the matrix of the effective coefficients of wind farms is proposed in
(22)φNwflow=φchflowLocw=Ψ1,1flow⋯Ψ1,wflow⋯Ψ1,Nwflow⋮⋱⋮⋱⋮Ψl,1flow⋯Ψl,wflow⋯Ψl,Nwflow⋮⋱⋮⋱⋮ΨNl,1flow⋯ΨNl,wflow⋯ΨNl,NwflowNl×Nw,Nw≤Nch,which Ψl,wflow is the effect factor of wind farm w on the flow of the line l. Therefore, the changes in generation power due to the presence of wind farms in the network are defined as follows:
(23)dQ=00dPΓMax⏟1×Nch001×NtT.aSo these power changes are applied to the buses where the wind farms are located, and in other buses, the changes are equal to zero.(24)Inwhich:dPGMaxchi=0chi∉chwdPGWchichi∈chw.Due to the variable wind speed and variable generation power of wind farms, their generation power is considered with different samples.(25)dPGW=ωw1Nw×1⋯ωwqNw×1⋯ωwNqNw×1,ωwq∈ωwavg±ϒw.Therefore, the changes in the flow of grid lines per sampleNq caused by wind farms are as follows:
(26)dFlowwNl×Nq=τ.φNwflowNl×Nw.dPGWNw×Nq.Finally, the impact of the wind farm on the network flow changes is calculated as follows:(27)EEWLl=∑q=1NqdFlowwNq.Therefore, the amount of flow changes and the congestion of grid lines can be calculated for the presence of wind farms using the proposed method. It is natural that the effects of wind farms are different at low and peak load. So that the matrix of the effective coefficients of the wind farm changes with the flow changes of the grid lines. In the following, the impact of DR in network peak load on changes in line congestion will be investigated.


## 3.3. The Effect of Demand Response on Variation of Line Flows

Demand response means the ability of customers to improve the energy consumption pattern to reach appropriate prices and improve network reliability. In this regard, based on references [59–61], load shifting from peak load to low load is formulated as follows, if possible
(28)Lt¯=Pt∈ΩLt+At∈ψ,where
(29)A=λ∑t∈ΩLt−PN.In other words, the network operator leads consumers to reduce consumption during peak periods. Instead, with incentive schemes, it encourages them to increase consumption during low load to improve the consumption load pattern. At peak load, the network operator encourages users to reduce consumption with incentive plans. Suppose the network load at peak load is equal toPT. Therefore, by using incentive plans, a percentage of a network load is reduced in peak load and added to low load. So, we have
(30)TP=ξ×PT,0<ξ≤1,whichξ is a coefficient of the total load at peak load. TP is the amount of load that is reduced during this time and is added to the time of low load. It is natural that the matrix of load reduction coefficients influencing the changes in line flow in peak load is different from the matrix of coefficients in low load. If the matrix of coefficients in peak load is φPd.peakflow, we have
(31)dFlowDLCpeak=−TPNb.φPd,peakflow.dPLoad.The negative sign in Equation (31) is due to the load reduction during peak load. After reducing the load during the peak load, the flow changes of the network lines in the low load caused by the increase in the load during the peak load are defined in
(32)dFlowDLClow=β×TPNb.φPd,lowflow.dPLoad,0≤β≤1.The load added to the low load can be the total load removed from the peak load or a certain ratio of that load, which is defined byβ. Therefore, according to the proposed method, the amount of change in the flow of grid lines is calculated for the purpose of applying direct load control planning. In the following, the proposed indices will be presented.


## 3.4. Proposed Indices

In this section, to evaluate the items influencing the changes in the flow of lines, two indices are proposed in Table2:Table 2
Proposed indices.
IndexDefinitionEAFlowEffect of all items on line flows in low loadEAFpeakEffect of all items on line flows in peak loadIn fact, the impact coefficients of EVCSs, wind farms, and DLC are provided by two indices in.(33)EAFlow=∑l=1Nl∑EVCSΨl,EVCSlow.PEVCS+∑bΨl,blow.PDLC+∑wΨl,wlow.PwFlowllow=∑l=1Nl∑EVCSΨl,EVCSlow.PEVCSFlowllow⏟EAFEVCSlow+∑l=1Nl∑bΨl,blow.PDLCFlowllow⏟EAFDLClow+∑l=1Nl∑wΨl,wlow.PwFlowllow⏟EAFwindlow,EAFpeak=∑l=1Nl∑EVCSΨl,EVCSpeak.PEVCSFlowlpeak⏟EAFEVCSpeak+∑l=1Nl∑bΨl,bpeak.PDLCFlowlpeak⏟EAFDLCpeak+∑l=1Nl∑wΨl,wpeak.PwFlowlpeak⏟EAFwindpeak.In other words, the index related to each item is determined in low and peak load. In the following, the results of the proposed method will be presented.


## 4. Case Study

According to Table3, the proposed method has been implemented in several scenarios on the IEEE 24-bus network [62] and is shown in Figure 2. The basic scenario, as the first scenario, examines the number of congested lines in the basic mode of the network. Each scenario includes the low and peak load of the network.Table 3
Classification of scenarios.
Basic scenarioLoading network lines in basic mode (low/peak load)Scenario 1Network line loading considering only EVCS (low/peak load)Scenario 2Network line loading considering only DLC (low/peak load)Scenario 3Network line loading considering only wind farms (low/peak load)Scenario 4Network line loading considering the combination of EVCSs and DLC (low/peak load)Scenario 5Network line loading considering the combination of EVCSs and wind farms (low/peak load)Scenario 6Network line loading considering the combination of DLC and wind farms (low/peak load)Scenario 7Network line loading considering EVCSs and DLC and wind farms (low/peak load)Figure 2
The IEEE 24-bus network.


### 4.1. Loading Network Lines in Basic Mode (Basic Scenario)

First, the condition of the network lines in terms of congestion in the basic case is determined in the basic scenario. In this paper, according to Equation (8), a congested line is known if the ratio of the line flow to its capacity is greater than 0.8. (α =0.8) Also, the lines that do not have this condition are called “normal” network lines. The loading status of network lines at low network load is presented in Figure 3. So, the congestion of line No.30 is equal to 0.92, which is considered a congested line. Also, the congestion of line No.28 is equal to its capacity and is equal to 1.Figure 3
Congested lines in Basic scenario (Low load).It is normal that the number of congested lines in the network is higher in network peak load. According to Figure4, apart from two lines No. 10 and No. 23, the number of congested lines increases to 5. Also, lines No. 15, 16, 18, and 27 are close to the congestion condition.Figure 4
Congested lines in Basic scenario (Peak load).The purpose of the paper is to evaluate congestion management by adding items such as EVCSs, wind farms, and DLC and to investigate the changes in line congestion.


### 4.2. Network Line Loading considering Only EVCS (Scenario 1)

Line loading changes as EVCSs are added to the network. One of the important items in the optimal change of line congestion is the optimal placement of EVCSs. The proposed method is able to determine the most suitable location for the EVCSs in addition to calculating the effect of the EVCSs on the congestion of the lines. In this paper, four EVCSs are considered for installing the network (Nv =4). Therefore, the total number of placement states of EVCSs in the network to achieve the most optimal state is equal to:(34)Nc=Nb=24Nv=4=10626.The effect of four EVCSs on grid lines in G2V and V2G modes for all placement cases is shown in Figure5.Figure 5
Flow changes in network lines caused by the EVCSs in G2V/V2G modes.Furthermore, the return power of EVs to the station is assumed to be 50% (ρ =0.5). Therefore, the best and worst locations of EVCSs considering their impact at low and peak load are shown in Figure 6. According to the figure, buses No. 15, 16, 21, and 22 are the optimal places to install EVCSs and buses No. 1, 2, 6, and 7 are the worst places in terms of network flow.Figure 6
Locating the optimal and worst EVCSs in the 24-bus network (ρ=0.5).The location of EVCSs can depend on the amount of return power of EVs. In other words, the location of the stations can be changed by changing the return power of the EVs. In this paper, the return power value is considered equal to 0.5. After determining the optimal place to install four EVCSs, the effect of the stations on the changes in the loading of network lines at low and peak load is shown as a percentage in Figure7.Figure 7
Line loading changes due to scenario 1 (%).According to Figure7, the highest percentage of influence of four EVCSs to improve the loading of the lines is better at the peak load of the network than at low load. So, in peak load, the percentage of changes to improve loading is 4.28% on line No. 24. This value is equal to 2.49% on line No. 29 when under low load. The loading of line No. 28 increases by 4.40% in peak load of the network due to the addition of four EVCSs to the network. Whereas, this value is equal to 2.89% in low load on line No.30. The decomposition of the values obtained from each EVCS is presented precisely in terms of percentage in Table 4.Table 4
The share of each EVCS on the specified lines (%).
ConditionLineEVCS 1(bus 15)EVCS 2(bus 16)EVCS 3(bus 21)EVCS 4(bus 22)TotalLow load29-1.138-1.7420.3950.000-2.49300.057-0.0042.8310.0002.89Peak load24-2.290-0.002-0.802-1.187-4.28280.5350.0002.1371.7234.40In the following, the effect of DLC on the loading of network lines will be investigated as scenario 2.


### 4.3. Network Line Loading considering Only DLC (Scenario 2)

Direct load control has a significant impact on congestion management to modify the network load pattern. In this paper, the total load coefficient at peak load is assumed to be 10% (ξ=0.1). Also, it is assumed that the entire value is transferred to the low load (β=1). As a result, Figure 8 shows the number of network line loading changes caused by the use of DLC in network peak load. It can be inferred that the loading of the lines at peak load is reduced by the application of DLC. Considering that a percentage of the load has been reduced from the network, it is natural that the loading of most lines will decrease. For example, the loading of lines No. 3, 4, 5, and 20 is significantly reduced. Also, the loading of line No. 18, which is close to 0.8, is reduced by applying DLC. In addition, the loading of congested lines No. 11 and 17 has decreased.Figure 8
Line loading changes due to scenario 2 (peak load).On the other hand, the reduced load at peak load is added to the low load. Therefore, it is natural that the loading of more lines will increase during this period. The amount of network line loading changes in low load due to the DLC program is presented in Figure9. One of the most important results of this figure is the addition of two normal lines to congested lines. Lines No.10 and No.23, which were normal network lines at low load, have been converted into congested network lines with values of 0.87 and 0.81, respectively. Also, the loading of line No.7 is close to 0.8 due to the addition of load to the network. The loading of line No. 30, which is considered one of the congested lines in the period of low load, increases and finally reaches 0.98.Figure 9
Line loading changes due to scenario 2 (low load).Therefore, it can be seen that DLC plays a significant role in changing the loading of lines. Another influential item is wind farms, which will be discussed further.


### 4.4. Network Line Loading considering Only Wind Farms (Scenario 3)

Another item influencing the loading of grid lines is wind farms. In this paper, two wind farms are considered, so that wind farm No.1 is located on bus No.15 and wind farm No.2 is located on bus No.18, and 10 wind turbines are considered in each wind farm (τ=10). Therefore, Figures 10 and 11 show the impact of wind farms on the flow changes of grid lines at low and peak load.Figure 10
Line flow changes due to scenario 3 (low load).Figure 11
Line flow changes due to scenario 3 (peak load).The effect of wind farms on line No. 11 is different in the two modes of low and peak load. So, in the period of low load, only wind farm No. 1 affects line No. 11, which reduces the flow of this line by 10 MW, and wind farm No. 2 does not affect the changes in the flow of this line. However, two wind farms have different effects on peak load, so that wind farm No. 1 increases the flow of line No. 11 and wind farm No. 2 decreases the flow of this line. Finally, the flow of line No. 11 increases by 4.20 MW. The flow of line No. 22 decreases by 4.43 MW due to the presence of wind farms in the low load, but this value is positive and insignificant in the peak load. In general, the effect of wind farms at low and peak load on the flow changes of network lines is negative.Therefore, based on the proposed method, the effect of each item is investigated separately on the network lines. In the following, the effects of the items are investigated simultaneously.


### 4.5. Network Line Loading considering the Combination of EVCSs and DLC (Scenario 4)

In scenario 4, the effect of EVCSs and DLC simultaneously on the flow of network lines at low and peak load is presented in Figure12. The greatest effect of these two items on the flow of line No.21 is in the period of low load, with a value of 107.47 MW, so that the change caused by DLC is equal to 105.08 MW and the change caused by EVCSs is equal to 2.38 MW on line No.21. Also, the most optimal effect of these two items in the low load is on the flow of line No. 29 with a value of -82.16 MW. This value is equal to -91.16 MW on line No.24 in peak load.Figure 12
Variation of line flow due to scenario 4 (MW).On the other hand, the two items (EVCSs and DLC) do not affect the flow of line No.10 at the peak load due to the congestion of the line, but at the low load they increase the flow of this line by 32.02 MW, of which 31.81 MW is caused by DLC and 0.26 MW is caused by EVCSs. Similarly, the flow of line No.28 does not change because it is quite congested at low load. At peak load, its flow increases by 83.87 MW, of which 61.88 MW is due to DLC and 21.98 MW is due to EVCSs.


### 4.6. Network Line Loading considering the Combination of EVCSs and Wind Farms (Scenario 5)

Similarly, the effect of two items (EVCSs and wind farms) simultaneously on low and peak load is presented in Figure13. The most optimal effects of these two items in low and peak load are on lines No. 29 and No. 24, respectively, with values of -10.28 MW and -21.70 MW. Also, the most positive effect on the flow of lines during low load and peak load periods is on lines No. 30 and No. 28, respectively, with values of 14.37 MW and 22.06 MW.Figure 13
Variation of line flow due to scenario 5 (MW).The exact contribution of each EVCS and each wind farm in terms of low load and peak load in scenario 5 is presented in Table5. Since line No. 28 is completely congested at low load, none of the items affect its flow changes. By determining the most influential item on the specified lines in Table 5, it can be concluded that EVCS 1, which is located on bus No. 15 and line No. 24, is connected to this bus, and therefore has the greatest impact on changes in the flow of line No. 24 in low and peak load.Table 5
The exact contribution of each item in scenario 5 (MW).
ConditionLineEVCSsWind farmsTotalEVCS 1(bus 15)EVCS 2(bus 16)EVCS 3(bus 21)EVCS 4(bus 22)Wind farm 1(bus 15)Wind farm 2(bus 18)Low load24-9.2300.7153.2170.0001.1510.560-3.58280.0000.0000.0000.0000.0000.0000.00029-5.690-8.7141.978-0.0031.4900.660-10.28300.289-0.02214.1590.000-0.036-0.02014.37Peak load24-11.453-0.011-4.014-5.937-0.4800.190-21.70282.6760.00210.6898.6180.110-0.04022.06290.0700.0190.0370.0450.850-0.3400.68302.3110.002-3.7228.4120.100-0.0407.06On the other hand, in low network load, the EVCS acts as a network load. In this regard, EVCS 2, which is located on bus No. 16 and line No. 29 is connected to this bus, therefore has the greatest impact on the flow changes of line No. 29 with a value of -8.714 MW in low network load. However, wind farm No. 1 has the greatest impact, with a value of 0.85 MW on the flow changes of line No. 29 in peak load. Similarly, the contribution of each item can be determined for all network lines, which is a suitable tool for the network operator.


### 4.7. Network Line Loading considering the Combination of DLC and Wind Farms (Scenario 6)

The effect of combining the two items (wind farms and DLC) on the power changes of grid lines is shown in Figure14. These two items have the greatest impact in low and peak load, with 99.41 MW and 61.95 MW on lines 21 and 28, respectively. The effect of these two items in low load on line No.28 is zero due to its congestion. Also, the most optimal impact in low and peak load is on lines No. 29 and No. 24, respectively, with values of -67.58 MW and -70.03 MW.Figure 14
Variation of line flow due to scenario 6 (MW).In the following, the impact of all these items on the changes in network line loading will be investigated.


### 4.8. Network Line Loading considering EVCSs, DLC, and Wind Farms (Scenario 7)

In scenario 7, as the last case, the impact of all items on the loading changes of network lines is presented. It can be clearly deduced that in low load, as it is shown in Figure15, most of the lines have increased loading and the loading of fewer lines has decreased. Among the effects of this scenario, we can point out the addition of two lines, No. 10 and No. 23, to the congested lines of the network, which in the basic scenario are considered normal lines. The effect of the total items on the loading of line No. 10 is 0.18, which has caused congestion in this line. Also, the loading of line No. 23 has increased by 0.13 compared to the basic scenario. In addition, line No. 30, which was one of the congested lines in the basic scenario, has been loaded to its capacity by applying scenario 7. On the other hand, some lines are close to the limit of condensation. For instance, the loading of lines No. 7 and No. 8 has increased to 0.78 and 0.75, respectively, by applying this scenario.Figure 15
Variation of line loading due to scenario 7 (low load).The effect of each item in this scenario on the changes in the loading of network lines is shown in Figure16. It can be concluded that wind farms have reduced the loading of grid lines at low load. Instead, DLC has had the opposite effect of wind farms on most lines. Due to the fact that a certain amount of network load is added to the network’s low load using the DLC program, it is natural to increase the loading on most network lines.Figure 16
Decomposition of variation of line loading due to scenario 7 in low load (%).Also, the effect of all items on the loading of network lines at peak load is shown in Figure17, where it can be deduced that some lines have decreased loading. The main cause of this incident is the application of the DLC program at peak load when a certain part of the network load has been reduced and transferred to the low load. Therefore, DLC has a negative effect on the loading of most lines, as shown in Figure 18. In other words, it reduces the loading of these lines. Due to the insignificant effect of wind farms and charging stations on load control, load control can be decisive in changing the density of the network. Due to the insignificant effect of wind farms and EVCSs on DLC, it can be decisive in changing the congestion of the network.Figure 17
Variation of line loading due to scenario 7 (peak load).Figure 18
Decomposition of variation of line loading due to scenario 7 in peak load (%).


### 4.9. Proposed Indices

In general, the results of two indices to detect the ability to change the loading of lines in percentage are presented in Table6. Each of the indices includes three indices caused by the items affecting the changes in the status of network lines. The DLC has a greater effect among the other two items in low and peak load, therefore it can be deduced that it plays a significant role in the changes in line loading. Finally, the overall impact of all items in low and peak load on each of the network lines has been determined, which gives a good view to the network operator for decision making. It can be clearly concluded that the effect of the total index (EAF) is positive on most lines at low load and negative on most lines at peak load because DLC has a significant effect among other factors in determining the total index.Table 6
The effect of each index on the loading changes of each line (%).
LineConditionLow loadPeak loadTotalEAFEVCSlowEAFDLClowEAFwindlowEAFEVCSpeakEAFDLCpeakEAFwindpeakEAFlowEAFpeak1-0.1673.724-0.2240.1505.591-0.0483.3325.6922-0.34813.043-0.465-0.369-15.5300.08112.229-15.81830.1804.2520.2410.012-21.565-0.0044.674-21.55640.0535.2370.070-0.067-18.4830.0155.361-18.53650.1144.6090.1530.000-13.5710.0004.876-13.5716-0.7401.616-0.9900.5424.256-0.121-0.1134.6777-0.47612.351-0.6360.3992.719-0.08911.2383.02980.05318.8090.0700.0674.912-0.01518.9334.96490.18017.8230.241-0.0127.9930.00418.2467.985100.11418.1800.1530.0000.0000.00018.4480.000110.00013.571-5.7140.283-4.9042.3997.857-2.22212-0.05015.477-2.924-0.095-3.591-1.21012.501-4.895130.05011.665-2.789-0.188-5.077-1.1898.926-6.45514-0.0208.341-0.370-0.122-3.184-0.2347.951-3.540150.34511.888-0.445-0.127-4.037-0.24911.788-4.41416-0.10711.623-0.486-0.041-1.904-0.25211.029-2.197170.25815.169-0.561-0.046-2.757-0.26714.866-3.071180.52210.3800.223-0.131-13.571-0.38811.125-14.09019-0.62410.341-0.9080.0004.7500.0008.8094.750200.0065.3790.329-0.123-12.368-0.3665.715-12.858210.47621.016-1.134-0.0162.182-0.04720.3592.120220.52820.510-1.4470.0509.2430.15019.5919.44323-0.62415.091-0.9080.0000.0000.00013.5590.00024-1.059-13.1130.343-4.283-13.949-0.058-13.830-18.290250.7793.133-0.0830.8013.312-0.0073.8304.106260.7793.133-0.0830.8013.312-0.0073.8304.10627-0.38114.631-0.5090.319-2.575-0.07113.740-2.327280.0000.0000.0004.39812.3760.0130.00016.78729-2.485-13.9460.4290.035-2.8240.103-16.002-2.687302.8857.034-0.0101.4015.2860.0129.9086.698310.114-2.2840.010-0.0032.3400.002-2.1582.33932-0.836-6.7410.077-0.8000.2680.006-7.500-0.52633-0.836-6.7410.077-0.8000.2680.006-7.500-0.52634-1.242-9.3480.214-0.017-0.963-0.052-10.376-1.03235-1.242-9.3480.214-0.017-0.963-0.052-10.376-1.03236-1.242-11.7230.214-0.017-3.338-0.052-12.751-3.40737-1.242-11.7230.214-0.017-3.338-0.052-12.751-3.40738-0.114-2.465-0.0100.0032.410-0.002-2.5912.411


### 4.10. Sensitivity Analyses

The amount of return power (ρ) of EVs, which can have a different effect on the network, is one of the factors affecting line congestion. The effect of all four EVCSs on the changes in the total flow of the network for different return powers in the optimal and worst cases is presented in Table 7. Also, another feature of return power is the ability to change the location of EVCSs, which can change the location of the EVCS depending on its value.Table 7
The overall effect of EVCSs on changes in network flow for differentρ (MW).
ρ=0.3ρ=0.4ρ=0.5ρ=0.6ρ=0.7Optimal-6.23-6.21-6.18-6.18-6.15Worst14.1914.1814.1214.1314.12In addition, the amount of added load (ξ) in low-load applications can have a significant effect on changes in line congestion. Figure 19 depicts the value of the EAF index for the amount of different load added in low load, which increases the number of changes in network line congestion.Figure 19
The effect of DLC on the EAF index for differentξ.


## 4.1. Loading Network Lines in Basic Mode (Basic Scenario)

First, the condition of the network lines in terms of congestion in the basic case is determined in the basic scenario. In this paper, according to Equation (8), a congested line is known if the ratio of the line flow to its capacity is greater than 0.8. (α =0.8) Also, the lines that do not have this condition are called “normal” network lines. The loading status of network lines at low network load is presented in Figure 3. So, the congestion of line No.30 is equal to 0.92, which is considered a congested line. Also, the congestion of line No.28 is equal to its capacity and is equal to 1.Figure 3
Congested lines in Basic scenario (Low load).It is normal that the number of congested lines in the network is higher in network peak load. According to Figure4, apart from two lines No. 10 and No. 23, the number of congested lines increases to 5. Also, lines No. 15, 16, 18, and 27 are close to the congestion condition.Figure 4
Congested lines in Basic scenario (Peak load).The purpose of the paper is to evaluate congestion management by adding items such as EVCSs, wind farms, and DLC and to investigate the changes in line congestion.


## 4.2. Network Line Loading considering Only EVCS (Scenario 1)

Line loading changes as EVCSs are added to the network. One of the important items in the optimal change of line congestion is the optimal placement of EVCSs. The proposed method is able to determine the most suitable location for the EVCSs in addition to calculating the effect of the EVCSs on the congestion of the lines. In this paper, four EVCSs are considered for installing the network (Nv =4). Therefore, the total number of placement states of EVCSs in the network to achieve the most optimal state is equal to:(34)Nc=Nb=24Nv=4=10626.The effect of four EVCSs on grid lines in G2V and V2G modes for all placement cases is shown in Figure5.Figure 5
Flow changes in network lines caused by the EVCSs in G2V/V2G modes.Furthermore, the return power of EVs to the station is assumed to be 50% (ρ =0.5). Therefore, the best and worst locations of EVCSs considering their impact at low and peak load are shown in Figure 6. According to the figure, buses No. 15, 16, 21, and 22 are the optimal places to install EVCSs and buses No. 1, 2, 6, and 7 are the worst places in terms of network flow.Figure 6
Locating the optimal and worst EVCSs in the 24-bus network (ρ=0.5).The location of EVCSs can depend on the amount of return power of EVs. In other words, the location of the stations can be changed by changing the return power of the EVs. In this paper, the return power value is considered equal to 0.5. After determining the optimal place to install four EVCSs, the effect of the stations on the changes in the loading of network lines at low and peak load is shown as a percentage in Figure7.Figure 7
Line loading changes due to scenario 1 (%).According to Figure7, the highest percentage of influence of four EVCSs to improve the loading of the lines is better at the peak load of the network than at low load. So, in peak load, the percentage of changes to improve loading is 4.28% on line No. 24. This value is equal to 2.49% on line No. 29 when under low load. The loading of line No. 28 increases by 4.40% in peak load of the network due to the addition of four EVCSs to the network. Whereas, this value is equal to 2.89% in low load on line No.30. The decomposition of the values obtained from each EVCS is presented precisely in terms of percentage in Table 4.Table 4
The share of each EVCS on the specified lines (%).
ConditionLineEVCS 1(bus 15)EVCS 2(bus 16)EVCS 3(bus 21)EVCS 4(bus 22)TotalLow load29-1.138-1.7420.3950.000-2.49300.057-0.0042.8310.0002.89Peak load24-2.290-0.002-0.802-1.187-4.28280.5350.0002.1371.7234.40In the following, the effect of DLC on the loading of network lines will be investigated as scenario 2.


## 4.3. Network Line Loading considering Only DLC (Scenario 2)

Direct load control has a significant impact on congestion management to modify the network load pattern. In this paper, the total load coefficient at peak load is assumed to be 10% (ξ=0.1). Also, it is assumed that the entire value is transferred to the low load (β=1). As a result, Figure 8 shows the number of network line loading changes caused by the use of DLC in network peak load. It can be inferred that the loading of the lines at peak load is reduced by the application of DLC. Considering that a percentage of the load has been reduced from the network, it is natural that the loading of most lines will decrease. For example, the loading of lines No. 3, 4, 5, and 20 is significantly reduced. Also, the loading of line No. 18, which is close to 0.8, is reduced by applying DLC. In addition, the loading of congested lines No. 11 and 17 has decreased.Figure 8
Line loading changes due to scenario 2 (peak load).On the other hand, the reduced load at peak load is added to the low load. Therefore, it is natural that the loading of more lines will increase during this period. The amount of network line loading changes in low load due to the DLC program is presented in Figure9. One of the most important results of this figure is the addition of two normal lines to congested lines. Lines No.10 and No.23, which were normal network lines at low load, have been converted into congested network lines with values of 0.87 and 0.81, respectively. Also, the loading of line No.7 is close to 0.8 due to the addition of load to the network. The loading of line No. 30, which is considered one of the congested lines in the period of low load, increases and finally reaches 0.98.Figure 9
Line loading changes due to scenario 2 (low load).Therefore, it can be seen that DLC plays a significant role in changing the loading of lines. Another influential item is wind farms, which will be discussed further.


## 4.4. Network Line Loading considering Only Wind Farms (Scenario 3)

Another item influencing the loading of grid lines is wind farms. In this paper, two wind farms are considered, so that wind farm No.1 is located on bus No.15 and wind farm No.2 is located on bus No.18, and 10 wind turbines are considered in each wind farm (τ=10). Therefore, Figures 10 and 11 show the impact of wind farms on the flow changes of grid lines at low and peak load.Figure 10
Line flow changes due to scenario 3 (low load).Figure 11
Line flow changes due to scenario 3 (peak load).The effect of wind farms on line No. 11 is different in the two modes of low and peak load. So, in the period of low load, only wind farm No. 1 affects line No. 11, which reduces the flow of this line by 10 MW, and wind farm No. 2 does not affect the changes in the flow of this line. However, two wind farms have different effects on peak load, so that wind farm No. 1 increases the flow of line No. 11 and wind farm No. 2 decreases the flow of this line. Finally, the flow of line No. 11 increases by 4.20 MW. The flow of line No. 22 decreases by 4.43 MW due to the presence of wind farms in the low load, but this value is positive and insignificant in the peak load. In general, the effect of wind farms at low and peak load on the flow changes of network lines is negative.Therefore, based on the proposed method, the effect of each item is investigated separately on the network lines. In the following, the effects of the items are investigated simultaneously.


## 4.5. Network Line Loading considering the Combination of EVCSs and DLC (Scenario 4)

In scenario 4, the effect of EVCSs and DLC simultaneously on the flow of network lines at low and peak load is presented in Figure12. The greatest effect of these two items on the flow of line No.21 is in the period of low load, with a value of 107.47 MW, so that the change caused by DLC is equal to 105.08 MW and the change caused by EVCSs is equal to 2.38 MW on line No.21. Also, the most optimal effect of these two items in the low load is on the flow of line No. 29 with a value of -82.16 MW. This value is equal to -91.16 MW on line No.24 in peak load.Figure 12
Variation of line flow due to scenario 4 (MW).On the other hand, the two items (EVCSs and DLC) do not affect the flow of line No.10 at the peak load due to the congestion of the line, but at the low load they increase the flow of this line by 32.02 MW, of which 31.81 MW is caused by DLC and 0.26 MW is caused by EVCSs. Similarly, the flow of line No.28 does not change because it is quite congested at low load. At peak load, its flow increases by 83.87 MW, of which 61.88 MW is due to DLC and 21.98 MW is due to EVCSs.


## 4.6. Network Line Loading considering the Combination of EVCSs and Wind Farms (Scenario 5)

Similarly, the effect of two items (EVCSs and wind farms) simultaneously on low and peak load is presented in Figure13. The most optimal effects of these two items in low and peak load are on lines No. 29 and No. 24, respectively, with values of -10.28 MW and -21.70 MW. Also, the most positive effect on the flow of lines during low load and peak load periods is on lines No. 30 and No. 28, respectively, with values of 14.37 MW and 22.06 MW.Figure 13
Variation of line flow due to scenario 5 (MW).The exact contribution of each EVCS and each wind farm in terms of low load and peak load in scenario 5 is presented in Table5. Since line No. 28 is completely congested at low load, none of the items affect its flow changes. By determining the most influential item on the specified lines in Table 5, it can be concluded that EVCS 1, which is located on bus No. 15 and line No. 24, is connected to this bus, and therefore has the greatest impact on changes in the flow of line No. 24 in low and peak load.Table 5
The exact contribution of each item in scenario 5 (MW).
ConditionLineEVCSsWind farmsTotalEVCS 1(bus 15)EVCS 2(bus 16)EVCS 3(bus 21)EVCS 4(bus 22)Wind farm 1(bus 15)Wind farm 2(bus 18)Low load24-9.2300.7153.2170.0001.1510.560-3.58280.0000.0000.0000.0000.0000.0000.00029-5.690-8.7141.978-0.0031.4900.660-10.28300.289-0.02214.1590.000-0.036-0.02014.37Peak load24-11.453-0.011-4.014-5.937-0.4800.190-21.70282.6760.00210.6898.6180.110-0.04022.06290.0700.0190.0370.0450.850-0.3400.68302.3110.002-3.7228.4120.100-0.0407.06On the other hand, in low network load, the EVCS acts as a network load. In this regard, EVCS 2, which is located on bus No. 16 and line No. 29 is connected to this bus, therefore has the greatest impact on the flow changes of line No. 29 with a value of -8.714 MW in low network load. However, wind farm No. 1 has the greatest impact, with a value of 0.85 MW on the flow changes of line No. 29 in peak load. Similarly, the contribution of each item can be determined for all network lines, which is a suitable tool for the network operator.


## 4.7. Network Line Loading considering the Combination of DLC and Wind Farms (Scenario 6)

The effect of combining the two items (wind farms and DLC) on the power changes of grid lines is shown in Figure14. These two items have the greatest impact in low and peak load, with 99.41 MW and 61.95 MW on lines 21 and 28, respectively. The effect of these two items in low load on line No.28 is zero due to its congestion. Also, the most optimal impact in low and peak load is on lines No. 29 and No. 24, respectively, with values of -67.58 MW and -70.03 MW.Figure 14
Variation of line flow due to scenario 6 (MW).In the following, the impact of all these items on the changes in network line loading will be investigated.


## 4.8. Network Line Loading considering EVCSs, DLC, and Wind Farms (Scenario 7)

In scenario 7, as the last case, the impact of all items on the loading changes of network lines is presented. It can be clearly deduced that in low load, as it is shown in Figure15, most of the lines have increased loading and the loading of fewer lines has decreased. Among the effects of this scenario, we can point out the addition of two lines, No. 10 and No. 23, to the congested lines of the network, which in the basic scenario are considered normal lines. The effect of the total items on the loading of line No. 10 is 0.18, which has caused congestion in this line. Also, the loading of line No. 23 has increased by 0.13 compared to the basic scenario. In addition, line No. 30, which was one of the congested lines in the basic scenario, has been loaded to its capacity by applying scenario 7. On the other hand, some lines are close to the limit of condensation. For instance, the loading of lines No. 7 and No. 8 has increased to 0.78 and 0.75, respectively, by applying this scenario.Figure 15
Variation of line loading due to scenario 7 (low load).The effect of each item in this scenario on the changes in the loading of network lines is shown in Figure16. It can be concluded that wind farms have reduced the loading of grid lines at low load. Instead, DLC has had the opposite effect of wind farms on most lines. Due to the fact that a certain amount of network load is added to the network’s low load using the DLC program, it is natural to increase the loading on most network lines.Figure 16
Decomposition of variation of line loading due to scenario 7 in low load (%).Also, the effect of all items on the loading of network lines at peak load is shown in Figure17, where it can be deduced that some lines have decreased loading. The main cause of this incident is the application of the DLC program at peak load when a certain part of the network load has been reduced and transferred to the low load. Therefore, DLC has a negative effect on the loading of most lines, as shown in Figure 18. In other words, it reduces the loading of these lines. Due to the insignificant effect of wind farms and charging stations on load control, load control can be decisive in changing the density of the network. Due to the insignificant effect of wind farms and EVCSs on DLC, it can be decisive in changing the congestion of the network.Figure 17
Variation of line loading due to scenario 7 (peak load).Figure 18
Decomposition of variation of line loading due to scenario 7 in peak load (%).


## 4.9. Proposed Indices

In general, the results of two indices to detect the ability to change the loading of lines in percentage are presented in Table6. Each of the indices includes three indices caused by the items affecting the changes in the status of network lines. The DLC has a greater effect among the other two items in low and peak load, therefore it can be deduced that it plays a significant role in the changes in line loading. Finally, the overall impact of all items in low and peak load on each of the network lines has been determined, which gives a good view to the network operator for decision making. It can be clearly concluded that the effect of the total index (EAF) is positive on most lines at low load and negative on most lines at peak load because DLC has a significant effect among other factors in determining the total index.Table 6
The effect of each index on the loading changes of each line (%).
LineConditionLow loadPeak loadTotalEAFEVCSlowEAFDLClowEAFwindlowEAFEVCSpeakEAFDLCpeakEAFwindpeakEAFlowEAFpeak1-0.1673.724-0.2240.1505.591-0.0483.3325.6922-0.34813.043-0.465-0.369-15.5300.08112.229-15.81830.1804.2520.2410.012-21.565-0.0044.674-21.55640.0535.2370.070-0.067-18.4830.0155.361-18.53650.1144.6090.1530.000-13.5710.0004.876-13.5716-0.7401.616-0.9900.5424.256-0.121-0.1134.6777-0.47612.351-0.6360.3992.719-0.08911.2383.02980.05318.8090.0700.0674.912-0.01518.9334.96490.18017.8230.241-0.0127.9930.00418.2467.985100.11418.1800.1530.0000.0000.00018.4480.000110.00013.571-5.7140.283-4.9042.3997.857-2.22212-0.05015.477-2.924-0.095-3.591-1.21012.501-4.895130.05011.665-2.789-0.188-5.077-1.1898.926-6.45514-0.0208.341-0.370-0.122-3.184-0.2347.951-3.540150.34511.888-0.445-0.127-4.037-0.24911.788-4.41416-0.10711.623-0.486-0.041-1.904-0.25211.029-2.197170.25815.169-0.561-0.046-2.757-0.26714.866-3.071180.52210.3800.223-0.131-13.571-0.38811.125-14.09019-0.62410.341-0.9080.0004.7500.0008.8094.750200.0065.3790.329-0.123-12.368-0.3665.715-12.858210.47621.016-1.134-0.0162.182-0.04720.3592.120220.52820.510-1.4470.0509.2430.15019.5919.44323-0.62415.091-0.9080.0000.0000.00013.5590.00024-1.059-13.1130.343-4.283-13.949-0.058-13.830-18.290250.7793.133-0.0830.8013.312-0.0073.8304.106260.7793.133-0.0830.8013.312-0.0073.8304.10627-0.38114.631-0.5090.319-2.575-0.07113.740-2.327280.0000.0000.0004.39812.3760.0130.00016.78729-2.485-13.9460.4290.035-2.8240.103-16.002-2.687302.8857.034-0.0101.4015.2860.0129.9086.698310.114-2.2840.010-0.0032.3400.002-2.1582.33932-0.836-6.7410.077-0.8000.2680.006-7.500-0.52633-0.836-6.7410.077-0.8000.2680.006-7.500-0.52634-1.242-9.3480.214-0.017-0.963-0.052-10.376-1.03235-1.242-9.3480.214-0.017-0.963-0.052-10.376-1.03236-1.242-11.7230.214-0.017-3.338-0.052-12.751-3.40737-1.242-11.7230.214-0.017-3.338-0.052-12.751-3.40738-0.114-2.465-0.0100.0032.410-0.002-2.5912.411


## 4.10. Sensitivity Analyses

The amount of return power (ρ) of EVs, which can have a different effect on the network, is one of the factors affecting line congestion. The effect of all four EVCSs on the changes in the total flow of the network for different return powers in the optimal and worst cases is presented in Table 7. Also, another feature of return power is the ability to change the location of EVCSs, which can change the location of the EVCS depending on its value.Table 7
The overall effect of EVCSs on changes in network flow for differentρ (MW).
ρ=0.3ρ=0.4ρ=0.5ρ=0.6ρ=0.7Optimal-6.23-6.21-6.18-6.18-6.15Worst14.1914.1814.1214.1314.12In addition, the amount of added load (ξ) in low-load applications can have a significant effect on changes in line congestion. Figure 19 depicts the value of the EAF index for the amount of different load added in low load, which increases the number of changes in network line congestion.Figure 19
The effect of DLC on the EAF index for differentξ.


## 5. Conclusion

Congestion management is one of the critical factors from the point of view of the network operator, so that neglecting this issue may result in network outage and uncertainly. Therefore, identifying the items affecting the changes in network line loading is essential for the network operator, which can increase the reliability of the network and prevent network blackouts. In this paper, first, by using an analytical method and structural decomposition, the most optimal location of EVCSs is determined from the aspect of loading the lines by considering low and peak load. Then, the contribution of the items (EVCSs, wind farms, and DLC) to the loading of network lines, especially congested network lines, is investigated separately. Among the important results obtained, the following can be mentioned:(i)
Among the influencing items, DLC has the greatest impact on the loading of network lines at low load, so that the number of congested lines increases in this state and the loading of the entire network lines increases by 15.36% compared with the basic scenario(ii)
The effect of these items in different modes, including a combination of two items (DLC and EVCS/DLC and wind farms/EVCSs and wind farms), and three items on network lines, is presented(iii)
The highest share of the index presented in low load is, respectively, on lines 21, 8, 10, and 9 with values of 20.35%, 18.93%, 18.44%, and 18.24%. While in peak mode, the share of the presented index is, respectively, on lines 28, 24, 4, and 3 with the values of 16.78%, -18.29%, -18.53%, and -21.55%.(iv)
The contribution of each factor to the indices is examined, and DLC had the largest contribution to these indices(v)
Finally, the most effective scenarios among the proposed scenarios in terms of the worst and best impacts on network flow changes in low load conditions are scenario 2 and scenario 5, respectively, with values of 577.60 MW and -75.22 MW. The worst and best impacts in high load conditions are scenario 1 and scenario 6, respectively, with values of 8.72 MW and -191.12 MWThe proposed method could be a suitable tool for network operators’ decision-making and forecasting. Congestion on a line in this way can cause the phenomenon of congestion rent, and as a result, the users pay the congestion fee. Therefore, determining the contribution of each factor by the proposed method can give an effective signal to the network operator.



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*Source: 1363377-2023-02-03.xml*