Electrical vehicles impact on unbalanced distribution networks considering different loads and energy prices

Abstract

The expansion of distributed generation and erratic loads create many challenges for electricity distribution networks (DN), like grid congestion and load unbalance. Technological advances in recent years have made the use of electric vehicles (EVs) more economical and justified for network connection. The use of smart EVs in the network scale, in addition to the peak shedding, if it is used in a single phase, it can also lead to the improvement of load unbalance. This paper proposes an energy and cost management model for the appropriate and distributed deployment of single phase EVs in distribution networks to provide network support for a DN including renewable resources. By connecting or disconnecting single-phase smart EVs to the DN, unbalanced loads in this network will be balanced as much as possible. To evaluate the proposed model, a network of 13 buses has been used, and the calculations of these energy costs have been measured during 24 h by two types of household and industrial loads. These loads are unbalanced in the DN and single-phase EVs have the ability to improve the unbalanced load of the DN. Also, the energy price is variable during the day and depends on the peak load. From the sensitivity analysis and with the relative increase or decrease of load, load change effects on the cost of each DN per-unit power have been measured and compared with the presence or absence of single-phase smart EVs to obtain more practical results. According to this paper, the use of EVs, in addition to improving the load of the DN, greatly reduces the costs of DN.

Highlights

• •The use of smart EVs in the network scale, in addition to the peak shedding, if it is used in a single phase, it can also lead to the improvement of load unbalance.
• •Proposes an energy and cost management model for the appropriate and distributed deployment of EVs in distribution networks to provide network support for a DN rich in renewable resources.
• •A 13-bus network has been used to evaluate the proposed model and according to the costs imposed on DN, the calculations of these energy costs will be measured during 24 h by two types of household and industrial loads.
• •The energy price is variable during the day and depends on the peak load.
• •From the sensitivity analysis and with the relative increase or decrease of load, load change effects on the cost of each DN per-unit power will be measured and will be compared with the presence or absence of single-phase smart EVs to obtain more practical results.

Nomenclature

ABBREVIATIONS:
Ab	Explain
DN	Distribution Network
PV	Photovoltaic
ITR	Interruption
SC	Scenario
LT	Load Type
BESS	Battery Energy Storage System
CPL	Cost Per Load
LTF	Load Type Factor
Ab.	Explain
WT	Wind Turbine
UBL	Unbalanced-Load
PF	Power Fluctuation
EP	Energy Price
EV	Electrical Vehicle
DNO	DN Operator
DG	Distributed Generation

Symbols:

Symbol	Explain	Symbol	Explain	Symbol	Explain
P	Active Power	Q	Reactive Power	|V|	Voltage Magnitude
θ	Voltage Angle	G	Conductance	B	Susceptance
r	Resistance	x	Reactance	J	Jacobian Matrix
PG	Generation Power	PL	Load Power	FP	BESS Final Power
CTotal	Overall Cost of DN	CUBL	Unbalanced-Load Cost	CITR	Interruption Cost
CPF	Power Fluctuations Cost	Sc	Scenario Number	t	Hour
b	DN Bus Number	NBus	Total Number of Buses	K	Penalty Factor
EP	Energy Price at t	Ph	Phases a, b, and c	mPG	Minimum PG
MPG	Maximum PG	CPL	Cost Per Load of DN	LT	Load Type

1. Introduction

In distribution networks (DN) that include renewable sources, interruption and fluctuations in power generation are high. These power fluctuations and interruption will lead to damage to the network and lack of proper response in the load. Now the networks are also facing an unbalanced phenomenon. This imbalance will lead to the rotation of power between three phases and the loss of energy and the increase of losses. For this purpose, in unbalanced networks, load and network balancing is one of the goals of experts. In this paper, an attempt is made to consider load imbalance in a network that absorbs power from wind turbine (WT) and photovoltaic (PV) renewable sources, and in addition, electric vehicles (EVs) are used to balance single-phase lines.

Reference [1] investigates the imbalance in AC and DC loads in a micro-grid DN connected to hybrid sources. According to this authority, generation and consumption management has been carried out under separate conditions from the grid and also connected to the infinite grid. It has also balanced the unbalanced loads by connecting to the infinite network and has used load shedding to reduce costs in this network.

Based on [2], the performance of the network under unbalanced loads and in the presence of wind turbines and in the conditions where the network works as an island has been investigated. According to this reference, by simulating a network in island mode in MATLAB, it has dealt with energy management in the presence of wind turbines and with unbalanced load conditions.

In reference [3], unbalanced load of three-phase network is managed in the grid by the electric load transfer index. This review is also done in a DN.

The expansion of renewable generation that are distributed in the network create many challenges for the electricity DNs. Storage technology advances in recent years have made BESS more economical than the past, and for this reason, these equipment are used in the network. Also, the distributed BESS can act as a factor for more penetration of renewable energies in the DN [4]. This reference obtains the most optimal mode for the placement and size of batteries. This situation is obtained according to the cost of batteries, operation, maintenance, etc.

By having correct energy management programs in micro-grids, the use of renewable energy increases and reliability and flexibility in DNs are improved. While micro-grids operate automatically, coordination between micro-grids and DN operators will help improve economics and reliability. Also, load response is a decentralized energy management framework for micro-grids. Now, the unbalanced performance of the DN and micro-grids, as well as the uncertainty in the operation of micro-grids, demand management and renewable energy have been investigated in Ref. [5].

According to Ref. [5], each micro-grid operator has communication with the DNO to manage consumption and production. DNO plans resources considering the possible islanding of micro-grids in the DN. Since micro-grids operate automatically, the proposed framework will exchange limited data between DNOs and micro-grid operators. According to this procedure, it will be tried to control the network in the best way by taking into account the correct response of the load and the uncertainties in the renewable energy.

The technologies with low carbon deployment such as EVs and photovoltaic is increasing according to their advantages. Also, in the case of residential loads, rapid integration imposes many technical problems on grid operators. A sensitivity analysis with the aim of determining the impact of these technologies on unbalanced low voltage residential loads has been carried out in Ref. [6]. According to this reference, the effect of different powers has been taken into account and then the results have been evaluated using different technical indicators.

In [7], an optimal technique for the penetration capacity and the optimal location of the BESS of WT for charging/discharging the battery is proposed. The proposed method will use moderate power loads to discharging or charging of the battery. WT is completely used to charge the battery. The proposed method is implemented on the 37-bus unbalanced distribution system. The results of this procedure indicate that the proposed method leads to the improvement of several performance objectives in DN through the optimal coordination of BESS.

Reference [8] deals with the BESS optimal allocation in radial DN to reduce energy costs and regulate bus voltage. According to this reference, a hierarchical model is presented with the objective of optimal configuration (such as location, number, size) of batteries.

The final configuration of BESS is based on the minimization of the cost of life cycle, which considers the cost of investment, the residual value of the BESS, and the operating cost of the system. Voltage regulation targets are modeled as constraints. The proposed method significantly reduces the computational burden and determines the most effective buses to reduce the voltage fluctuation. This optimal allocation method is affected for 15-bus and 69-bus IEEE modified distribution network.

According to Ref. [9], in recent years, the BESS has been considered as a suitable procedure to reduce wind power frequencies. According to this reference, the optimal capacity and location of the wind-influenced BESS, and the BESS charge/discharge dispatches are determined using the Inheritance Competitive Congestion Optimization (ICSO) algorithm to improve the function of the unbalanced system with respect to technical problems. This procedure uses the average feeder load as a decision criterion for battery discharging or charging.

According to Ref. [10], BESS can perform well to overcome the challenges of renewable energy, especially in the field of smart grid. In Ref. [10], the wind power penetration and optimal BESS location, and BESS charge/discharge dispatches are determined using the ICSO algorithm to improve of the unbalanced system. The proposed method is evaluated on IEEE 37. The results enhance the various performance objectives of the DN by optimally battery transmissions coordination.

A modified Archimedes algorithm for optimizing EVs in DNs is described in Ref. [11]. According to this reference, the parameters of voltage stability index (VSI), power loss and voltage deviation are included. Also, according to Ref. [12], the size of EVs in a DN that has benefited from the production of renewable resources has been evaluated. In the meantime, by considering the random changes in the renewable source, this model has been implemented.

In [13], to increase the power of renewable energy, real-time charging system has been used in EV. To implement this procedure, PV and wind turbine have been used. Also, according to Ref. [14], the predictive control procedure was used in unbalanced and balanced DNs, and according to that, the utilization of the accumulated reactive power in the network capabilities of EV chargers was done in real time. According to this reference, prediction information is shared in a peer-to-peer (P2P) manner to realize asynchronous broadcast in DN.

An optimized multi-objective timed DN method is described in Ref. [15]. This method takes into account the charging of electric vehicles and in addition to reducing the cost of operating the network, it also improves the amount of PV consumption. According to Ref. [16], the method of predicting the numerical values of the wind speed has been used to improve the operation of the wind turbine and reduce the fluctuation of its output power as well as increase its energy.

An approximate linear three-phase power flow model for an artificial DN considering the load model and PV has been proposed by Ref. [17]. The proposed method is not limited to radial topology and can handle branches with high R/X ratio.

The planning of a real DN with the aim of integrating EVs and considering the effects of charging EVs with coordinated and uncoordinated charging patterns for 30 and 100 % EV penetration is considered in Ref. [22]. The proposed method in Ref. [23] can also increase the profitability of EVs. According to this reference, real measurement data is included in the model.

Reference [24] proposes a new approach for optimal coordination of directional overcurrent relays (DOCRs) to achieve minimum operating time and optimal regulation considering the connection of EVs to grid. According to Ref. [25], innovative algorithms have been proposed to minimize the total working time of relays and in the form of scenarios considered in vehicle-to-grid and grid-to-vehicle modes to increase network reliability.

The reduction of wind turbine power output in micro-grid with the voltage level of the DN by the fuzzy controller has also been evaluated in Ref. [26].

According to the contents and literature review, Table (1) shows the aspects and innovations expressed in the relevant references as well as the present paper. According to this table, considering 1 and 3 phase load, load balance improving and Variable energy price are the innovations of this paper, which are going to be stated below.

Table 1.

Compare the proposed method and previous methods.

No.	Aspect	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]	[11]	[12]	[13]	[14]	[15]	[16]	This paper
1	Unbalanced load	✓	✓	✓	✓	✓	✓	✓		✓	✓							✓
2	Renewable energy				✓	✓	✓	✓		✓	✓		✓	✓		✓	✓	✓
3	Energy storage system				✓	✓	✓	✓	✓	✓	✓						✓	✓
4	Distribution system	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
5	Electrical vehicle						✓					✓	✓	✓	✓	✓		✓
6	P2P														✓
7	Predictive control													✓	✓		✓
8	Demand side management					✓		✓					✓	✓				✓
9	1 and 3 phase load																	✓
10	Improved load balance																	✓
11	Variable energy price																	✓

The main contributions of this article are summarized as follows.

• •The EV loads are considered intelligent and the network loads are available as single phase and three phase.
• •The DN loads are considered unbalanced, and according to this, the operation of the DN is managed according to the intelligent single-phase loads. Based on this and comparing the cost of the DN, the difference between the presence and absence of single-phase EV loads is determined.
• •By applying different load types and also different energy prices during the day, comprehensive results of the DN are obtained and sensitivity analysis is also included.

In this paper, first the power DN model is stated and its mathematical relationships are briefly explained. Then, the proposed methodology of the paper is explained in detail and the costs of the DN, including the cost of load unbalance, interruption of power generation, and power fluctuations are explained in the form of scenarios of EVs and types of household and industrial loads. In the following, a case study including the 13 bus IEEE DN and the specifications are presented. Then the simulation results and discussion on its outputs are given. At the end, the conclusion of the paper is stated.

2. Distrubution network model

A three-phase network model should be considered to model an unbalanced DN. Based on this, the active-reactive power injected in phase “a” of ith bus can be presented as equations (1), (2), respectively, and these relationships are non-linear.

To model a DN with unbalanced loads, a three-phase distribution network should be modeled. The active and reactive power of this DN can be expressed as equations (1), (2). As can be seen, these equations are non-linear. So, by stating the following assumptions, these equations can be expressed in a linear form.

• •Angle difference between the connected basses is small.
• •Magnitude of the voltage is close to 1 per-unit.

$$P_i^a=V_i^a\sum _j^N\sum _b^{a-c}{V}_j^b\left(G_{ij}^{ab}\cos \left({\theta }_{ij}^{ab}\right)+B_{ij}^{ab}\sin \left({\theta }_{ij}^{ab}\right)\right)$$ (1)

$$Q_i^a=V_i^a\sum _j^N\sum _b^{a-c}{V}_j^b\left(G_{ij}^{ab}\sin \left({\theta }_{ij}^{ab}\right)-B_{ij}^{ab}\cos \left({\theta }_{ij}^{ab}\right)\right)$$ (2)

where N is the number of buses. Therefore, equation (3) is applied.

$$V_k\left(V_k-V_j\right)\approx \left(V_k-V_j\right)$$ (3)

Where k and j are kth and jth bus number in DN. Based on this, equations (1), (2) are rearranged in matrix form, according to equation (4). This equation expresses the active-reactive power injection in each phase of each bus.

$$\left[\begin{array}{c}{P}^a\\ P^b\\ P^c\\ Q^a\\ Q^b\\ Q^c\end{array}\right]=\left[\begin{array}{cccccc}{J}_{PV}^{aa}& J_{PV}^{ab}& J_{PV}^{ac}& J_{P\theta }^{aa}& J_{P\theta }^{ab}& J_{P\theta }^{ac}\\ J_{PV}^{ba}& J_{PV}^{bb}& J_{PV}^{bc}& J_{P\theta }^{ba}& J_{P\theta }^{bb}& J_{P\theta }^{bc}\\ J_{PV}^{ca}& J_{PV}^{cb}& J_{PV}^{cc}& J_{P\theta }^{ca}& J_{P\theta }^{cb}& J_{P\theta }^{cc}\\ J_{QV}^{aa}& J_{QV}^{ab}& J_{QV}^{ac}& J_{Q\theta }^{aa}& J_{Q\theta }^{ab}& J_{Q\theta }^{ac}\\ J_{QV}^{ba}& J_{QV}^{bb}& J_{QV}^{bc}& J_{Q\theta }^{ba}& J_{Q\theta }^{bb}& J_{Q\theta }^{bc}\\ J_{QV}^{ca}& J_{QV}^{cb}& J_{QV}^{cc}& J_{Q\theta }^{ca}& J_{Q\theta }^{cb}& J_{Q\theta }^{cc}\end{array}\right]\left[\begin{array}{c}{V}^a\\ V^b\\ V^c\\ {\theta }^a\\ {\theta }^b\\ {\theta }^c\end{array}\right]$$ (4)

As can be seen from equation (5), the power injected in a phase (P^a,b,c) is related to the active power of the load connected to the phase.

As can be seen in equation (5), the Jacobean matrix is N × N (N = (bus number) × 3). This matrix depends on the impedances in DN. Therefore, this matrix is constant for a given system configuration.

$$P^{a,b,c}=P{L}^{a,b,c}-P{G}^{a,b,c}+F{P}^{a,b,c}$$ (5)

Equations (6), (7), (8) provide three entry examples of matrix. Equation (4) determines magnitudes and angles of all phases and buses voltage.

$$J_{QV}^{aa}=-B^{aa}$$ (6)

$$J_{PT}^{ca}=-\left(\frac{-\sqrt{3}}{2}\times G^{ca}+\frac{-1}{2}\times B^{ca}\right)$$ (7)

$$J_{QV}^{cb}=-\left(\frac{-\sqrt{3}}{2}\times G^{cb}+\frac{1}{2}\times B^{cb}\right)$$ (8)

Then, the transmitted power between the connected nodes is obtained by equation (9) whose format is for each phase and these equations are proposed in detail in Ref. [18].

$$L_{ij}^a\approx \frac{r_{ij}^a{x}_{ij}^a}{{r_{ij}^a}^2+{x_{ij}^a}^2}\frac{V_i^a-V_j^a}{x_{ij}^a}+\frac{{x_{ij}^a}^2}{{r_{ij}^a}^2+{x_{ij}^a}^2}\frac{{\theta }_i^a-{\theta }_j^a}{x_{ij}^a}$$ (9)

• 3.METHODOLOGY

According to the paper purpose, it is necessary to define a function in which all the parameters related to DN costs are taken into account in order to make appropriate decisions related to the state of the DN. For this purpose, the following situations are stated.

• •Unbalanced load (UBL)
• •Interruption (ITR)
• •Power fluctuation (PF)
• •Electrical vehicle (EV)
• •Load type (LT)

In the following, each of the above situations are explained in detail and the cost equations that each of them will have on the DN is explained. It should be noted that the above values and costs are obtained after obtaining the simulation results.

Also, unbalanced load, interruption and power fluctuation determine the total cost of the DN and electrical vehicle and load type are expressed as scenarios proposed in the DN. The schematic of this procedure is shown in Fig. (1).

Fig. 1.

Schematic of proposed methodology.

The relationships of each of these situations and scenarios are explained in section (3.5).

2.1. Total cost of DN

The total cost of the DN can be expressed as equation (10):

$$C_{Total}^{Sc}=\sum _{t=1}^{24}{C}_{UBL,t}^{Sc}+C_{ITR,t}^{Sc}+C_{PF,t}^{Sc},Sc=1,2,\dots ,6$$ (10)

Based on the above equation, C_Total expresses the overall cost of the DN, C_UBL expresses the unbalanced-load cost, C_ITR expresses the interruption cost, C_PF expresses the power fluctuations cost, Sc expresses the scenario number and t expresses the hour of energy management in the DN during 24 h a day.

2.2. UNBALANCED-LOAD cost of DN

The unbalanced-load cost of the DN can be expressed as equation (11):

$$C_{UBL,t}^{Sc}=\sum _{b=1}^{N_{Bus}}\left[MP{L}_{b,t}^{Ph,Sc}-mP{L}_{b,t}^{Ph,Sc}\right]\times K\times E{P}_t,Ph=a,b,c$$ (11)

Based on the above equation, C_UBL expresses the unbalanced-load cost, b indicates the DN bus number, N_Bus indicates the total number of DN buses, K indicates the penalty factor, EP indicates the energy price at t, and Ph indicates phases a, b, and c on the unbalanced load side.

Also, MLP and mLP are the maximum and minimum load power among each of a, b and c phases, respectively, which are expressed in equation (11-a) and (11-b), respectively.

$$MP{L}_{b,t}^{Ph,Sc}=\max \left(P{L}_{b,t}^{Ph,Sc}{|}_{Ph=a},P{L}_{b,t}^{Ph,Sc}{|}_{Ph=b},P{L}_{b,t}^{Ph,Sc}{|}_{Ph=c}\right)$$ (11a)

$$mP{L}_{b,t}^{Ph,Sc}=\min \left(P{L}_{b,t}^{Ph,Sc}{|}_{Ph=a},P{L}_{b,t}^{Ph,Sc}{|}_{Ph=b},P{L}_{b,t}^{Ph,Sc}{|}_{Ph=c}\right)$$ (11b)

According to the above relationships, PL expresses the load power in each of a, b and c phases.

2.3. Interruption cost of DN

The interruption cost of the DN can be expressed as equation (12):

$$C_{ITR,t}^{Sc}=\left[\sum _{b=1}^{N_{Bus}}\sum _{Ph=a}^{c}P{L}_{b,t}^{Ph,\text{Sc}}-\sum _{b=1}^{N_{Bus}}mP{G}_{b,t}^{Sc}\right]\times K\times E{P}_t$$ (12)

Based on the above equation, C_UC expresses the interruption cost, PL expresses the load power in each phases and mPG expresses the minimum power generation in 1 h of the considered interval in the simulation. This value is expressed as equation (12-a).

$$mP{G}_{b,t}^{Sc}=\min \left(P{G}_b^{Sc}{|}_{\left(t\right)-\left(t+1\right)}\right)$$ (12a)

According to the above equation, PG represents the power generation during 1 h of simulation. This period is considered between t and t+1.

2.4. POWER-FLUCTUATION cost of DN

The power fluctuation cost of the DN can be expressed as equation (13):

$$C_{\text{PF},t}^{Sc}=\left[\sum _{b=1}^{N_{Bus}}MP{G}_{\mathrm{b},t}^{Sc}-\sum _{b=1}^{N_{Bus}}mP{G}_{\mathrm{b},t}^{Sc}\right]\times K\times E{P}_t$$ (13)

Based on the above equation, C_PF expresses the power fluctuation cost and MPG and mPG express the maximum/minimum power generation in 1 h of considered interval in the simulation, respectively. These value are expressed as equation (13-a) and (13-b), respectively.

$$MP{G}_{b,t}^{Sc}=\max \left(P{G}_b^{Sc}{|}_{\left(t\right)-\left(t+1\right)}\right)$$ (13a)

$$mP{G}_{b,t}^{Sc}=\min \left(P{G}_b^{Sc}{|}_{\left(t\right)-\left(t+1\right)}\right)$$ (13b)

2.5. DECISION-MAKING scenarios of DN

As mentioned, in this paper, various scenarios are presented to improve energy management in the DN and make appropriate decisions for load and generation management. Table (2) shows these scenarios related to the load side of the DN (electric vehicle and load type). According to this table, there are two modes for the electric vehicle (on-off) and three modes for the load type (load type 1- load type 2- sum of load types 1 and 2), which are combined together and form six different scenarios.

Table 2.

Decision-making scenarios.

Scenario	EV	LT
Sc_1	Off	1
Sc_2	Off	2
Sc_3	On	1
Sc_4	On	2
Sc_5	Off	1 + 2
Sc_6	On	1 + 2

Based on this, regarding the two parameters affecting these six scenarios.

• •Electric vehicles (EVs) are used with the purpose of load balancing. In other words, although the presence of EVs in scenarios 3, 4 and 6 will increase the amount of consumption on the load side, this presence will balance the load and improve the situation of the load side in the DN.
• •Two load types (LTs) have been considered, which due to the different energy prices at different hours of the day, these two LTs will show the state of DN management in different modes.

2.6. Cost per load of DN

Finally, in this section, the cost of each kW of DN is obtained. This value determines the DN cost per unit of electricity generation. In other words, the total cost for the generation of each unit of power is determined, and with this work, a better comparison is made between six scenarios. This transformation is expressed in equation (14).

$$CP{L}^{Sc}=\frac{C_{Total}^{Sc}}{Loa{d}_{Total}^{Sc}},Sc=1,2,\dots ,6$$ (14)

According to the above relation, CPL represents the cost per load of DN in the desired scenario. Load represents the total load of the DN in the same scenario and expressed in equation (14-a).

$$Loa{d}_{Total}^{Sc}=mean\left(LT\right)\times \sum _{b=1}^{N_{Bus}}\sum _{Ph=a}^{c}P{L}_{b,t}^{Ph,\text{Sc}}$$ (14a)

Where PL expresses the load power in each of a, b and c phases and LT expresses load type of each scenario which is averaged in the whole scenario.

3. Case study

The DN specifications, unbalanced loads, balanced loads, energy price and load type are stated in this section.

3.1. DN specification

To analyze the proposed model in this paper, an IEEE 13-bus distribution system according to Ref. [19] is used. This system illustrates an unbalanced network. Also, only the transformer on the infinite network side is considered and all voltage regulators are neglected. In addition, the effect of BESSs is neglected and this effect is included in the renewable resources themselves. Hence, reactive power exchanges between DN and BESS and vice versa, are assumed to be negligible.

A single line diagram of the network in illustrated in Fig. (2). Detailed system specifications can be found in Refs. [19,20]. Also, DGs, i.e. solar PV and WT, are included in the buses in Fig. (2). The power of WT and PV is considered to be 50 kW.

Fig. 2.

Modified IEEE 13-bus unbalanced DN.

The synthesized information for daily load profiles in different buses is presented in the following to achieve the purpose of this paper [21]. Based on this, the peak load power (in kW) and unbalanced in each bus is shown in Table (3).

Table 3.

Unbalanced loads.

Load number	Load Power of each Phase (kW)
	A	B	C
Load 1	0	230	0
Load 2	280	0	300
Load 3	660	620	620
Load 4	0	0	170
Load 5	402	451	672
Load 6	485	68	290
Load 7	128	0	0
Load 8	410	410	405

According to Fig. (2), if EVs are used in this network, these EVs can be placed on all bus loads. Also, the following assumptions are valid in connection with these EVs.

• •These EVs will be added in all bus loads and are considered as single phase.
• •These EVs will be smart added to the network.
• •The placement of these EVs will eliminate the load unbalance. In other words, these EVs will be added to the phases that have less load power and all three phases will be placed in the peak load and balanced.

So, the peak load power (in kW) and balanced in each bus is shown in Table (4).

Table 4.

Balanced loads by EV.

Load number	Load Power of each Phase (kW)
	A	B	C
Load 1	230	230	230
Load 2	300	300	300
Load 3	660	660	660
Load 4	170	170	170
Load 5	672	672	672
Load 6	485	485	485
Load 7	128	128	128
Load 8	410	410	410

Also, as seen in Fig. (2), the DN has two renewable energy (wind turbine and photovoltaic) and one infinite network. The voltage level of the DN is 254 V and its frequency is 50 Hz. The information related to wind turbine and photovoltaic system are shown in Table 5, Table 6, respectively. Noted that the power produced by these sources is considered as three balanced phases.

Table 5.

Wind turbine specifications.

Parameter	Value
Nominal Wind Speed	11 m/s
Cut-in Speed	3 m/s
Cut-out Speed	25 m/s
Wind Speed	11 m/s
Generator Type	Fix Speed
Output Power	1000 kVA

Table 6.

Photovoltaic turbine specifications.

Parameter	Value
Irradiance	1000 W/m2
Temperature	25oC
ISC	2.02 A
VOC	86.8 V
Im	1.93 A
Vm	70.4 V
Output Power	500 kVA

3.2. ENERGY-PRICE specification

The average of energy price (EP) is shown in Fig. (3). This value is adopted in the year according to the data obtained from 2020. As can be seen, the value of this index is changing during one day, and during peak hours, the EP consumption is higher than during off-peak hours. These values have an impact on the cost of the DN. In other words, if the load of the DN is high during peak hours, the cost of the DN will increase. It should be noted that the penalty factor is considered equal to 1 in this paper.

Fig. 3.

Hourly prices in this study.

3.3. LOAD-TYPE specification

Normalized load profiles for one day is shown in Fig. (4) in two categorize. These normalized values are multiplied by the loads stated in Table 3, Table 4. According to this figure, it can be seen that the major difference between these two load types (LTs) is their peak moments. In other words, LT 1 is a household load, while load LT 2 is a commercial load, which reached its peak value at 6 p.m. Also, the average values in LT 2 are higher than the average values of LT 1. The difference between these two LTs, along with the difference in EP shown in Fig. (3), will make interesting points that is mentioned in the following sections.

Fig. 4.

Normalized load profiles in two categorize.

4. Results and discussion

Results of this paper are analyzed and discussed in this section. Accordingly, first decision-making scenarios of DN analysis and then CPL analysis are stated. In the rest, the sensitivity analysis is given to confirm the obtained results.

4.1. DECISION-MAKING scenarios analysis

Based on the simulation of the 13-buses DN and the application of the two LT and also according to the stated scenarios, the C_Total of the DN in all six scenarios during a period of 24 h in one day is shown in Fig. (5) (Scenarios 1, 2, 3, 4, 5, and 6 are shown in Fig. (5-a), (5-b), (5-c), (5-d), (5-e), and (5-f), respectively).

Fig. 5.

Cost of DN in 24 h in (a) scenario_1 (b) scenario_2 (c) scenario_3 (d) scenario_4 (e) scenario_5 (f) scenario_6.

So, the following results can be discussed.

• •The maximum cost of the DN in scenarios 2 and 4 is much higher than scenarios 1 and 3, and the reason for this is that the amount of peak LT 2 coincides with the maximum EP in the same hours of the day.
• •The maximum amount of cost in scenarios 1 and 3 is ahead of scenarios 2 and 4, which is because the peak load is ahead in scenarios 1 and 3.
• •The cost of energy in scenarios 1 and 3 is smoother than scenarios 2 and 4, which shows that household loads are far better than commercial loads.
• •The cost of scenarios 5 and 6 is higher than the first four scenarios, which was completely predictable due to the increase in network load. The same issue shows that the overall cost of DN may be misleading, because if the load increases and the cost also increases, this point will not be considered negative and the cost of each unit of load should be obtained as per-unit.

Now, if the total cost of DN is calculated in each scenario, Fig. (6) is obtained. According to this figure, the C_Totaol has been expressed in all six scenarios and compared with each other. The values of the vertical axis in this figure are in $.

Fig. 6.

C_Total of each scenario.

According to this figure, the following results can be discussed.

• •It can be seen that in general, DN costs in LT 1 are more than 100 $ per day less than DN costs in LT 2.
• •In both load types of LT 1 and LT 2 and sum of them, DN costs have been reduced by placing the load of EVs on the load side and balancing the phases.
• •The difference in the cost of the DN is not much if there are EVs or not, because the presence of EVs in the DN will be an additional load on the DN and will increase the network load. However, with this placement, DN costs have also decreased.

4.2. CPL analysis

To check the per-unit of the above values each unit of load power in DN, it is necessary to specify Load_Total^Sc in each scenario. This value is obtained according to (14-a) and is shown in Table (7).

Table 7.

Load_Total of each scenario.

Scenario	LoadTotal
Sc-1	1670.05
Sc-2	3234.49
Sc-3	2318.74
Sc-4	4490.85
Sc-5	4911.14
Sc-6	6818.76

Next, according to (14), CPL index is measured. As mentioned, this index will also consider the amount of load on the DN and in a way, it will calculate the cost per kilowatt of power generation. Fig. (7) shows this index in six scenarios.

Fig. 7.

CPL of each scenario.

According to this figure, the following results can be discussed.

• •It can be seen that there is not much difference between the costs of LT1 and LT2. Because it is true that the LT2 has more electricity generation costs on the DN, but it should be noted that the amount of this load is also higher than the LT1, and naturally more benefits are obtained.
• •With the increase in load in scenarios 5 and 6, although the overall cost of the DN has increased, the cost of each power unit has decreased significantly.
• •The presence of EVs in this network has greatly reduced the value of CPL index. Because it has caused balance in DN phases. Therefore, it can be said that the presence of these EVs in a smart grid, in addition to consuming more power in the DN and optimal use of the power produced by the sources, will also greatly reduce the cost of DGs.
• •The presence of LT1+LT2 loads in the DN along with the presence of EVs will lead to a significant cost reduction of each power unit.

4.3. Sensitivity analysis

Effect of LT changes on DN cost or DN CPL is discussed in this section. Based on this, by using sensitivity analysis and 20 % change in LT values for each scenario, the results are checked. Fig. (8) shows the results related to 20 % LT changes in scenarios 1–4 during a period of 24 h (0.8 < Load Type Factor (LTF) < 1.2) (Scenarios 1, 2, 3, and 4 are shown in Fig. (8-a), (8-b), (8-c), and (8-d), respectively). So.

• •An increase in LTF steer to an increase in the cost of DN, although this cost increase is not high.
• •Despite the 20 % increase in LT in scenarios 1 and 3, the amount of cost in these two scenarios is still lower than scenarios 2 and 4.
• •Despite the 20 % reduction of LT in scenarios 2 and 4, the amount of cost in these two scenarios is still higher than scenarios 1 and 3.
• •According to the previous two points, getting the LTF values does not have a great overall cost impact on the DN, and the cost of the DN is more influenced by other parameters.

Fig. 8.

Sensitivity analysis DN cost in 24 h in (a) scenario_1 (b) scenario_2 (c) scenario_3 (d) scenario_4.

According to Fig. (9), the effect of sensitivity analysis on CPL is shown. According to this figure.

• •The reduction of CPL in scenarios 2 and 4 is quite evident compared to scenarios 1 and 3, and this indicates that the presence of EVs in the DN will lead to a drastic cost reduction of producing power per-unit.
• •It can also be seen that the relative increase or decrease of LTF in the DN can be ignored in relation to the presence or absence of EVs, and by placing EVs in the DN as a single phase and improving the unbalanced-load of the phases of the DN, it is possible to compensate the production costs of each additional per-unit of power.

Fig. 9.

CPL sensitivity analysis of each scenario.

5. Conclusion

In this paper, smart EVs were used and on a distribution scale to improve the operation of a DN. These EVs were considered as single-phase and in addition to the peak shedding on the load side, it also led to the improvement of load unbalance and finally reduced the costs of the DN. To prove this proposed model, a DN with two types of household and industrial loads was used, as well as taking advantage of the variable energy price during the day. Finally, it was found that the use of EVs, in addition to improving the load on the distribution network side and more efficient consumption of energy produced by DGs, has greatly reduced the costs of power generation in the DN. This cost reduction is stated per-unit of production power in order to make a better comparison between the existing scenarios. Also, by using the sensitivity analysis, it was found that the relative increase or decrease of the load does not have a great cost effect of power of DN, and the presence or absence of single-phase smart EVs in the DN will further reduce the cost of per-unit power.

6. Data AVAILABILITY statement

Data will be made available on request.

CRediT authorship contribution statement

S.M.A.Mousavi Sadat: Writing – original draft, Validation, Software, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. H. Mohammadnezhad Shourkaei: Writing – review & editing, Visualization, Supervision, Project administration. S. Soleymani: Writing – review & editing, Visualization, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.