Simultaneous placement of electric vehicle charging station and DG units in urban area using novel enhanced antlion optimizer

Abstract

The electric vehicle market has surged the consideration of charging station requirements in the commercial and residential areas of the urban regions. The addition of charging stations at the existing power network introduces a greater challenge on voltage stability and losses. The effect of the charging station can be addressed through the optimal integration of Distributed Generation (DG) units into the network. The improper placement of DG units can jeopardize the network stability. These issues are addressed by optimal placement of DG units and charging stations in the network to improve voltage, reduce transmission loss and maximize the charging station capacity. Here the objectives are considered as a multi-objective problem and solved using an enhanced Ant-lion optimization algorithm. The proposed method is implemented and tested over IEEE – 33, 69 and 94 radial bus system in MATLAB R2020a version. In IEEE – 33 bus system, the total loss reduction of 67.63% and the minimum voltage of 0.981 is attained with 2909.2 kW of DG and 1770.7 kW of charging station. The voltage stability index is improved to 0.92. The efficacy of the proposed method is evaluated through comparison with existing methods such as Genetic Algorithm (GA) with VRP method, Harris Hawks Optimization (HHO) and Particle Swarm Optimization (PSO). It is evident that the proposed method gives improved performance than other methods.

Keywords

Charging stations distributed power generation optimization renewable energy sources smart grids

1 Introduction

The electric grid provides an efficient infrastructure to exchange the remotely generated power to widespread loads. This primary vertical system has drawbacks in performance efficiency and reliability standards. The power system is made smarter to cope–up with the modernizing world. Thus, the power system is converted into the horizontal structure by introducing the Distributed Generation (DG) into the power system.

The introduction of DG and electric transportation transforms the standard grid into a smart grid. The DG units are placed nearer to the load centres which improves the system voltage profile, stability and also reduces the system losses, provided that they are positioned and sized appropriately [26].

A significant step in reducing greenhouse gas emission from the transportation sector is achieved by introducing Electric Vehicles (EV). As the transportation sector is getting more electrified the excess demand due to EV charging will further push the grid to the verge of its stability limits. In making electric transportation real, the electrical grid should be well developed to adopt new load and various generation models to meet the volatility in EV load and Renewable based generation [21]. So, the additional challenge of placing and sizing the charging stations for EV is considered along with the DG optimization.

A brief survey in the area of charging station and Distributed generation integration into power network with various techniques is carried out. EVCS and PV are integrated into the commercial area using PSO for line loss reduction and minimizing voltage deviation [10, 19]. EVCS is placed considering network constraints and economical aspects through PSO [6] similarly with the Krill herd algorithm [2]. In [28] the charging station and capacitor bank are placed in a radial distribution network using a Genetic Algorithm (GA). Also, [3] GA addresses the parking lot cost reduction.

A multi-objective problem of DG and CS placement is addressed with the Differential Evolution (DE) algorithm in [20]. A CPLEX simulator is used to find the location and capacity of the charging station for minimizing the investment and operation cost in [17]. Based on the charging time and Demand Response Programme (DRP) [15] the charging station and energy storage system is placed using the PSO method for maximizing the benefit of distribution companies and charging stations owners. A Fast-Charging Station (FCS) is placed in a residential grid for reducing the charging cost and power loss ensuring security constraints employing Ant Colony Optimization (ACO) [23]. In the work [14] a multi-objective model for placing a charging station is solved using the cross-entropy method. A Smart Load Management system is proposed for effective EV charging in the residential network for achieving peak load shaving and energy conservation in [4].

Experiment on operating EVCS and DG in the network with Constant voltage and constant power mode is made in achieving the reduced power loss [16, 18]. In [8] the effort on reducing the stress and power quality issues on power network due to EV charging through DG integration. The maximum number of PV and wind-based DG units are integrated along with EVCS and minimized the total network loss [5, 22]. In another work [13] reducing the energy purchase cost of the DC micro-grid in presence of an EV charging station, PV generation and storage system with the help of NSGA-II is described.

Quadratic programming is adopted in [11, 24] reducing the network loss and voltage deviation by demand forecasting with the effect of charging Plug-in Hybrid Electric Vehicles (PHEV). A load density method based on EVCS sizing is done and a model of the vehicle to the grid is presented in [32]. A hybrid Artificial Bee Colony (ABC) and Firefly Algorithm is utilized in optimal charging of PHEV [1, 31]. DG placement is addressed with ALO in [12].

Based on the above review on the works that have been carried on charging station placement and Distributed generation placement in the distribution network, we could identify the need and complexity of the problem statement. In this work, we have contributed to the existing literature in two parts. Firstly, finding the maximum possible charging points that can be provided with the allotted capacity to accommodate more vehicles at a time, secondly, this complex problem is achieved through a novel heuristic approach with enhancement.

This paper is organized with the introduction in the first section followed by a problem statement in the second section and modelling of Ant-lion optimization with differential learning scheme in the third section. In the fourth section, the results are discussed and finally, the conclusion of this work is presented.

2 Problem formulation

The integration of Charging Station (CS) and DG units introduced excess network power loss and voltage fluctuations. The focus of the research work is to formulate a non-linear problem comprising of network loss reduction, improves voltage stability and increase the charging station capacity allocation. The objective function is expressed as a weighted sum multi objective problem. The optimal placement of DG and Charging Station (CS) with appropriate size is the motive of the research. Mathematical modelling of the system is done to analyze its characteristics and performance.

2.1 PV modelling

A photovoltaic module will have a large number of solar cells interconnected inside a structure. V-I characteristic of the PV cell is calculated and its power production is determined. The model has a photovoltaic cell that generates current, drop-in diode and series resistance. The current produced by the PV cell is given by: $I = I_{L} - I_{D}$ (1)

The Shockley equation gives the diode current: $I_{D} = I_{0} [exp (\frac{q (V + {IR}_{S})}{γ {kT}_{C}}) - 1]$ (2)

The diode current is related to the saturation diode current I₀ and output voltage V; form factor γ; series resistance of the cell R_S; electric charge q; Boltzman’s constant k and module temperature T_C. $I = I_{L -} I_{0} [exp (\frac{q (V + {IR}_{S})}{γ {kT}_{C}}) - 1]$ (3)

2.2 Wind power modelling

A wind turbine produces electricity by extracting power from the wind flow. The wind power will lift and rotates the turbine blade and the generator connected to it. To know the power that can be produced by the wind generator is given by: $P_{Wind Turbine} = C_{p} P_{air} = C_{p} \times \frac{1}{2} ρ {Av}^{3}$ (4)

where ρ is the air density approximately 1.225 kg/m3, A is the swept area of the rotor (m2), v is the wind velocity (m/s) and C_p is the power coefficient which gives the power conversion figure from air to the turbine, which will not be more than 59.3%.

2.3 Electric vehicles and EV charging station

The electric vehicle utilizes batteries to store electric energy and use it to make a tractive effect through electric motors. The introduction of EV increases the power demand of the network due to its battery charging. The EV can be exploited to get ancillary services and power back to the grid during peak load condition.

At the power network, during the charging of electric vehicles, the electric vehicles are considered as the static power load. Based on the power and current relationship, an EV load at the network is given by the equation, $i_{k} = \sum_{k} i_{p, k} = \sum_{k} \frac{P_{k}^{EV}}{V_{k}}$ (5)

From the above static load modelling of electric vehicle, similar to power flow calculation, current i_p,k is the total current drawn together by its downstream electric loads. where, I_k is current at k^th charging station, V_k is voltage at at k^th charging point, P_k is the EV – power demand of the k^th electric vehicle.

The charging stations play a significant role in the energy trade between vehicles and the grid. The proper operation of the charging station will give in great influence on energy market operation and critical decisions.

2.4 Objective function

The objective function framed will reduce the power loss, improve the voltage stability index and increase the possible size of the charging station. The objective function is considered as multi-objective and formulated using a weighted sum approach $min (f) = w_{1} f_{1} + w_{2} f_{2} + w_{3} f_{3}$ (6)

w₁, w₂ and w₃ are used to show the weights assigned to the functions and their sum is equal to one.

Here f₁ gives the power loss in the network obtained from the power flow solution after DG and CS placement. The expression for f₁ s given as $f_{1} = \sum_{\begin{matrix} i = 2 \\ j = 2 \end{matrix}}^{n_{b}} (P_{g_{i}} - P_{d_{i}} - V_{i} V_{j} Y_{ij} cos (δ_{i} - δ_{j} + θ_{ij}))$ (7)

The f₂ gives the inverse of the minimum available stability index of the network and is given as below and the expression for calculating the VSI for each bus is given in equation (8). $\begin{matrix} f_{2} = \frac{1}{\min {VSI}} \\ VSI (k) = {| V_{i} |}^{4} - 4 {(P_{k} . X_{ik} - Q_{k} . R_{ik})}^{2} \\ - 4 (P_{k} . R_{ik} - Q_{k} . X_{ik}) . {| V_{i} |}^{2} \end{matrix}$ (8)

The term f₃ a charging station capacity index will maximize the size of the adopting charging station into the network and is given below: $f_{3} = \frac{1}{({CS}_{1} + {CS}_{2})}$ (9)

Where CS1 and CS2 stands for the capacity of the charging stations 1 & 2 respectively.

2.4.1 Power balance constraint

The DG inserted into the network should meet the power balance constraint $\begin{matrix} \sum_{i = 1}^{N_{b}} P_{g_{i}} + P_{{DG}_{i}} - P_{d_{i}} - P_{{CS}_{i}} \\ - V_{i} \sum_{j = 1}^{N_{b}} V_{j} Y_{ij} cos (δ_{i} - δ_{j} - θ_{ij}) = 0 \\ \sum_{i = 1}^{N_{b}} Q_{g_{i}} + Q_{{DG}_{i}} - Q_{d_{i}} - Q_{{CS}_{i}} \\ - V_{i} \sum_{j = 1}^{N_{b}} V_{j} Y_{ij} sin (δ_{i} - δ_{j} - θ_{ij}) = 0 \end{matrix}$ (10)

2.4.2 Voltage limits

The voltage magnitude are restricted within the limits and given by (11) $V_{i}^{\min} ⩽ V_{i} ⩽ V_{i}^{\max}$ (11)

2.4.3 Thermal profile

The distribution lines have their own operation limits based on their design $| S_{i} | ⩽ | S_{i}^{\max} | i = 1, \dots, N_{l}$ (12)

2.4.4 DG capacity constraint

The DG capacity is inherently limited by the energy resources at any given location; it is necessary to constrain capacity between the maximum and the minimum levels. $P_{dgi}^{\min} ⩽ P_{dgi} ⩽ P_{dgi}^{\max}$ (13)

2.4.5 Charging station size constraint

The CS capacity is limited by network adaptability and reliability and stability limit of the network. The minimal requirement of CS capacity is that to charge the average number of EV vehicles available for charging in a day. $P_{CSi}^{\min} ⩽ P_{CSi} ⩽ P_{CSi}^{\max}$ (14)

3 Ant Lion optimizer with differential learning scheme

Recently, in [27] a nature inspired population-based Ant Lion Optimization algorithm (ALO) is given by Seyedeli Mirjaliti. He has developed this algorithm based on antlion life phase of larva and adult. The hunting and reproduction are formulated to give as an ALO algorithm.

An ant-lion larva digs a cone-shaped hole in soil by moving along a circular path and throwing out the soil by its massive jaw. The size of the trap depends on the hungry level of the ant-lion and moon size. If the hungry level or moon size is more, then trap size is more and vice versa. After digging the trap, the larvae hide at the bottom of the cone and waits for prey (ant) to be trapped in the hole. Once the ant lion realizes that prey is in the trap, it tries to catch it. If the trapped ant is consumed, the antlion will expel the waste and reconstruct the hole as initial.

This ALO is unlike other gradient search method, it has a free search capability through its random antlion selection and random walk of ants in the search region. The steps of ALO algorithm are explained in following sections.

3.1 Random walk of ant

Ants search their food with free walk and is given by equation, $\begin{matrix} X_{RW} (t) = [0, cumsum (2 r (t_{1}) - 1), cumsum (2 r (t_{2}) - 1) \\ , \dots, cumsum (2 r (t_{n}) - 1)] \end{matrix}$ (15)

Where X_RW is the random walk of ants, is the cumulative sum, n is the maximum number of iterations, t represents the step of random walk, and r(t) is a stochastic function defined as follows, $r (t) = {\begin{matrix} 1 if rand > 0.5 \\ 0 if rand ⩽ 0.5 \end{matrix}$ (16)

Where ‘rand’ will generate a random decimal from 0 to 1. A min-max normalization procedure is followed in restricting the random walk of ants within the boundary, the model is expressed as, $X_{m}^{t} = \frac{(X_{m}^{t} - a_{m}) \times (d_{m} - c_{m}^{t})}{(b_{m}^{t} - a_{m})} + c_{m}$ (17) where a_m b_m are minimum and maximum of the random walk of ants $c_{m}^{t}$ , $d_{m}^{t}$ represents the minimum and maximum m^th variable at t^th iteration.

3.2 Trapping in Ant-lion’s Traps

The following equations describe the effect of ant-lions traps on random walks of ant, $c_{m}^{t} = {Antlion}_{j}^{t} + c^{t}$ (18) $d_{m}^{t} = {Antlion}_{j}^{t} + d^{t}$ (19)

Where c^t is the minimum of all variables at t^th iteration, d^t indicates the vector including the maximum of all variables at t^th iteration $c_{m}^{t}$ is the minimum of all variables for mth ant, $d_{m}^{t}$ is the maximum of all variables for mth ant, and ${Antlion}_{j}^{t}$ shows the position of the selected j^th ant-lion at t^th iteration

3.3 Building traps

The ALO employs the roulette wheel operator for selecting ant lion based on their fitness during optimization. This mechanism gives more chance for ant-lions to traps prey.

3.4 Sliding ants towards ant-lion

According to the mechanisms above, ant-lions can build traps proportional to their fitness, and the ants move near the centre of the pit. Once ant-lions catch an ant in a trap, they will shoot the sand outward in the middle of the trap. This mechanism can be mathematically modelled as follow, $c^{t} = \frac{c^{t}}{I}$ (20) $d^{t} = \frac{d^{t}}{I}$ (21)

Where $I = 1 + 100^{w} \frac{t}{T}$ which is a ratio, c^t is the minimum of all variables at t^th iteration and d^t indicates the vector including the maximum of all variables at t^th iteration. W is a constant, whose value is given as: $W = {\begin{matrix} 2 if t > 0.1 T \\ 3 if t > 0.5 T \\ \begin{matrix} 4 if t > 0.75 T \\ 5 if t > 0.9 T \\ 6 if t > 0.95 T \end{matrix} \end{matrix}$ (22)

Here t is the current iteration, and T is the maximum number of iterations.

3.5 Catching prey and re-building the pit

The last phase of hunting occurs when an ant reaches the bottom of the pit and is trapped in the ant-lion’s jaw. After this stage, the ant-lion pulls the ant inside the sand and consumes its body. If the fitness of ant is greater than antlion, the antlion will update its position to that ant and increase the probability for new hunt. ${Antlion}_{j}^{t} = {Ant}_{m}^{t} iff ({Ant}_{m}^{t}) > f ({Antlion}_{j}^{t})$ (23)

Where t shows the current iteration, ${Antlion}_{j}^{t}$ shows the position of selected j^th ant-lion at t^th iteration and ${Ant}_{m}^{t}$ indicates the position of m^th ant at t^th iteration.

3.6 Elitism

Elitism is an important characteristic in heuristic algorithm, which is adopted to preserve the best solution obtained in every iteration. Here the elitism is performed for the top 5% of the population attained through random walk of around antlions using Rowlett wheel method and given by the equation, ${Ant}_{m}^{t} = \frac{R_{A}^{t} + R_{E}^{t}}{2}$ (24)

Where $R_{A}^{t}$ the random walk around the ant-lion is selected by the roulette wheel at t^th iteration $R_{E}^{t}$ is the random walk around the elite at t^th iteration and ${Ant}_{m}^{t}$ indicates the position of m^th and at t^th iteration.

The performance of ALO algorithm depends on the problem size and are subjected to premature convergence. To enhance the performance we have adopted a new method for population initialization. The detailed procedure is followed in the sections.

3.7 Population randomization: RCO based population generation

The search agents initially generated in population-based optimization algorithms will have a greater influence on finding the better result. As the search agents give more information regarding the search area, they need to carefully distribute it all over the search space. This sort of initialization will collect more information regarding the search space and helps in updating the search agent in attaining the solution rapidly.

3.7.1 The pseudocode of the proposed population initialization algorithm (RCO)

Sinusoidal Iterator based population generation for ‘n’ numbers $x_{i + 1} = sin (π x_{i}), i = 1, 2, \dots, n$

Population generation for ‘n’ numbers using Opposition based Mechanism ${OP}_{i, j} = a_{j} + b_{j} - P_{i, j}, i = 1, 2, \dots, n; j = 1, 2, \dots, N_{v} .$

Where, N_v is the problem dimension, and a_j, b_j are boundaries of variables. i.e x_j ∈ [a_j, b_j].

From the combined ‘2n’ populations a randomly chosen three individuals produce a member through QI. $r_{i} = \frac{1}{2} \cdot \frac{(b^{2} - c^{2}) \times f (a) + (c^{2} - a^{2}) \times f (b) + (a^{2} - b^{2}) \times f (c)}{(b - c) \times f (a) + (c - a) \times f (b) + (a - c) \times f (c)}$

Where i = 1, 2, ... , 2n., a, b, c are the variables picked from ‘2n’ population and its corresponding fitness are given by f(a), f(b), f(c). The initial population for the ALO algorithm is taken form r_i. A new RCO based population initialization adopted to initially generate the search agents distributed equally in all areas of search region [29].This wide-explored population generation is obtained in three steps: first, the population is generated using chaotic sinusoidal iterator, and in a second step the opposition mechanism is adopted and finally, a direct search procedure of Quadratic Interpolation (QI) method is chosen to select the diverse population from combining the population of previous stages. The pseudo-code of this algorithm is presented below:

3.8 ALO with differential learning (DL) scheme

The ALO learning scheme is inclusive of all the fitness of the ant and ant-lions populations. The ant-lions with the least fitness are learned from the direct update with the neighbor parameters. This may have a negative impact on overlooked regions in the search area. To overcome this issue the differential learning scheme of updating the few worst candidates with the best ant-lions without any probability constraints. The pseudo-code for the proposed update process is presented here.

3.8.1 Pseudocode for DL scheme

Take H_w, w ∈ H_if search agents with least fitness value, w is taken with the probability of ρ = 0.5.

Choose H_w, w = n, n - 1, n - 2, … listed with lower fitness rank.

w is accepted when U (0.1)> ρ

Compute $\begin{matrix} H_{w} = H_{w} + δ (H_{r 1} - H_{r 2}) + (1 - δ) (H_{r 3} - H_{r 4}) \\ δ = U (0.1) and r 1, r 2, r 3, r 4 \in U (1, \frac{n}{2}) \end{matrix}$

The best candidates are taken for updates

The candidates with least fitness are updated with step 2 by differential learning scheme randomly to cover at least 30% of its population. The flowchart for the enhanced antlion optimizer is given in Fig. 1.

Fig. 1

Flowchart of Enhanced ALO algorithm.

Performance analysis of proposed enhanced Antlion algorithm is compared with the existing Antlion algorithm by implementing over two test functions T₁ and T₂.

$T_{1} (x) = \sum_{i = 1}^{n - 1} [100 {(x_{i + 1} - x_{i}^{2})}^{2} + {(x_{i} - 1)}^{2}]$ (25) $T_{2} (x) = \sum_{i = 1}^{n} [x_{i}^{2} - 10 cos (2 π x_{i}) + 10]$ (26)

The population size for the system is set as 100 and the number of iteration is limited to 300. The top 5% of the results are preserved as elite for each iteration. The DL scheme has updated the new population through elite results and made some remarkable convergence characteristics. The proposed method is compared with the existing Antlion algorithm [7] and given in Table 1. The effectiveness of the proposed algorithm is revealed by Table 1.

Table 1

Performance comparison of Enhanced ALO with ALO

Function	Algorithm	Dimension	Search space	Best value	Worst value	Mean value	Saturated iteration
T1	ALO	10	[-200 200]	5.321e-7	250.75	18.551	60
	Enhanced ALO	10	[-200 200]	2.642e-9	11.32	0.682	27
T2	ALO	10	[-300 300]	0.0562	42.8	10.6	71
	Enhanced ALO	10	[-300 300]	0.0214	2.32	0.154	32

4 Results and discussion

The Proposed simultaneous allocation of RES and EVCS is carried out in various networks to find the effectiveness of the approach. Urban test systems IEEE 33-bus, IEEE 69-bus and IEEE 94-bus were adopted to implement the method and simulate to find the results. Three different cases of DG insertion has been considered. In case 1 DG with only real power output is inserted, in case 2 DG with combined load power factor is inserted. While in case 3, DG with effective power factor method [29] is inserted. Here the charging infrastructure is installed with the maximum possible capacity the network could adopt along with DG implementation.

4.1 Test system 1: IEEE 33-bus system

The test system is a 33-bus radial distribution with a total load of 3.715 MW, 2.3 MVar, 33 bus and 32 branches as shown in Fig. 2. The network has a real and reactive loss at the base case is 0.211 MW and 0.143 MVar.

Fig. 2

Single line diagram of IEEE 33 bus system.

The proposed work is implemented, and the effectiveness of the approach is found and compared with the other methods. The DG is inserted with a different power factor ratio, and the charging station is considered without discharging capability to find the network robustness. The capacity of the distributed generation units at both the location and charging station size chosen at the two locations with its respective loss for all the three cases is given in Fig. 3.

Fig. 3

DG units, CS size and loss for test system 1.

The charging slot’s that could be provided for a particular charging station capacity is calculated and presented in Table 2. Here the slow, medium, fast and rapid charging slots for every CS capacity are calculated based on its standard capacity ratings of 3 kW, 7 kW, 43 kW, and 125 kW respectively. In Table 3 the result for simultaneous allocation of DG in the IEEE 33-bus system is given with three power factor cases. The loss reduction with the three cases is given and the result shows the superiority with case three.

Table 2

Charging slot allotment for CS size in the 33-bus system

Case	CS Position	CS Size (kW)	Number of electric vehicles
			Slow	Medium	Fast/Rapid
Case 1	7	995.2	331	142	23/8
	4	190.4	63	27	4/1
Case 2	20	619.1	206	88	14/5
	19	1190.8	397	170	28/10
Case 3	2	1134.5	378	162	26/9
	21	636.2	212	91	15/5

Table 3

Results of proposed work for IEEE 33-bus system

Scenario	DG location	DG size (kW)	Power loss (kW)			Mini. Voltage
			P	Q	Total
Case 1	30	1474.0	154.1	106.91	187.6	0.978
	13	1988.3
Case 2	29	2817.1	88.6	68.62	112.1	0.983
	9	831.5
Case 3	8	1630.8	53.9	41.87	68.3	0.981
	31	1278.4

This shows that case 3 with effective power factor adopted DG units providing nominal power and distributes even load through the charging station into the network and gives better loss reduction than other methods.

The voltage profile after optimal placement of the DG and CS into the IEEE-33 bus system for all three cases is compared with the base case voltage profile and shown in Fig. 4.

Fig. 4

Voltage profile comparison for test system 1.

The improvement in voltage profile is witnessed with the comparison of voltage deviations in the respective cases given in the result Table 3. A minimum voltage of 0.9811 is obtained through effective power factor model which proves to better approach when compared with other p.f. models. The convergence graph for all three case with the proposed model is given in Fig. 5. The fitness value is given y axis and its iteration count is given in x axis. The convergence for all three cases are consistent.

Fig. 5

Convergence graph comparison for test system 1.

4.2 Test system 2: IEEE 69-bus system

The IEEE 69-bus system is a radial network with 68 branches and 3801.9 KW real power load and 2704.1 KVAr reactive load. The DG and CS placement is placed to reduce system loss and adopt the maximum possible charging station size. As the charging station size gets increased the number of vehicles slots for charging is increased. This in future will be helpful for network support during two-way power transaction.

The charging station size for the respective positions was chosen based on the objective and its effects are analyzed in the perspective of voltage and loss profile improvements. Table 4 gives the charging slot counts that can be facilitated for the corresponding mode of charger for the respective charging station capacity allotted.

Table 4
Charging slot allotment for CS size in the 69-bus system

Case CS position CS size (kW) Number of electric vehicles

Slow Medium Fast/Rapid

Case 1 28 607.7 202 87 14/5

49 1289.5 430 184 30/10

Case 2 40 427.5 142 61 10/3

06 2297.3 766 328 53/19

Case 3 37 790.9 263.6 113 18/7

47 430.4 143 61 10/4

Case	CS position	CS size (kW)	Number of electric vehicles
Case 1	28	607.7	202	87	14/5
	49	1289.5	430	184	30/10
Case 2	40	427.5	142	61	10/3
	06	2297.3	766	328	53/19
Case 3	37	790.9	263.6	113	18/7
	47	430.4	143	61	10/4

The results obtained by optimal allocation of DG units in the 69-bus radial bus system are presented in Table 5. With its corresponding real, reactive and total power loss the voltage deviation from the nominal value is presented to emphasize the effectiveness of the proposed Ant-Lion optimization approach with differential learning. The voltage profile of the network operated with the integrated distributed generation and charging station demand for the respective cases are presented in distinct plots in Fig. 6. The voltage improvements in the valley and maintaining the recommended voltage range in other healthy buses is made perfectly with all three cases. In Fig. 7 the capacity of the two DG units and two charging station size is pictured with its corresponding total power loss for all three cases.

Table 5

Results of proposed work for IEEE 69-bus system

Scenario	DG location	DG size (kW)	Power loss (kW)			Minimum voltage
			Real	Reactive	Total
Case 1	61	2102.2	99.83	65.54	119.43	0.9908
	11	1749.7
Case 2	63	2247.4	44.61	24.95	51.12	0.9939
	27	998.8
Case 3	62	2557.0	18.86	13.44	23.17	0.9942
	15	812.7

Fig. 6

Voltage profile comparison for test system 2.

Fig. 7

DG units, CS size and loss for IEEE 69 bus system.

From Table 5 the various location of DG size can be seen for a different scenario of the 69-bus system. In case 1 the location of DG is identified as 30, 13 with size 1474 kW and 1988.4 kW. The total loss obtained is 187.56 kW. In case 2 the total loss is obtained as 112.03 kW by locating DG at position 29 and 9 with the size of 2817.1 kW and 831.5 kW. A minimum loss of 68.26 kW is obtained in case 3 with DG size of 1630.8 kW, 1278.4 kW in 8,31 locations. The complex problem of simultaneous allocation of two DG units and two charging station with optimal locations and its effective capacity is made faster by this method. In respect of demonstrating the efficacy of this approach, the convergence graph is plotted against iteration and fitness value in Fig. 8.

Fig. 8

Convergence plot for IEEE 69 bus system.

4.3 Test system 3: IEEE 94-bus system

The IEEE 94-bus system is a radial system that has 93 branches with a real power load of 4797 KW and a reactive power load of 2323.9 KVAr. This is a large distribution network with various load types and characteristics, the vast option for DG and CS placement makes the search area larger. The power factor of the distributed generating units integrated into the network will play a major role in controlling the power flow and voltage profile enhancement.

Table 6 gives the charging slot counts for the IEEE 94-bus system that can be facilitated for the corresponding mode of charger for the respective charging station capacity allotted. In Table 7 the locations of DG is shown. This gives a clear idea of parameter allocation for obtaining the objective and its contribution to improving the network profile.

Table 6
Charging slot allotment for CS size in the 94-bus system

Case CS position CS size (kW) Number of electric vehicles

Slow Medium Fast/Rapid

Case 1 08 908 303 130 21/7

02 1624.2 541 232 38/13

Case 2 03 1568 523 224 36/12

46 931.1 310 133 22/7

Case 3 10 1444.4 481 206 33/12

01 1386.9 462 198 32/11

Case	CS position	CS size (kW)	Number of electric vehicles
Case 1	08	908	303	130	21/7
	02	1624.2	541	232	38/13
Case 2	03	1568	523	224	36/12
	46	931.1	310	133	22/7
Case 3	10	1444.4	481	206	33/12
	01	1386.9	462	198	32/11

Table 7

Results of proposed work for IEEE 94-bus system

Scenario	DG location	DG size (kW)	Power loss (kW)			Minimum voltage
			Real	Reactive	Total
Case 1	83	1159.2	150.8	175.8	231.6	0.936
	13	3021.7
Case 2	20	2284.6	119.2	116.1	166.4	0.967
	14	2339.5
Case 3	20	1546.2	112.4	122.2	166.1	0.964
	13	3054

The respective voltage values at each bus for different power factor case of DG operation is plotted along with base case voltage profile in Fig. 9 to witness the effectiveness in voltage profile improvement. The loss obtained with all the cases with its DG and CS size parameters presented for comparisons in the bar chart format in Fig. 10.

Fig. 9

Voltage profile comparison for test system 3.

Fig. 10

DG units, CS size and loss for IEEE 94 bus system.

The voltage improvement in the network is one of the major considerations for network security and power flow management. The convergence for this large system is time-consuming as the search area is more and there is a chance of local convergence. The proposed method outperforms in these hard circumstances and finds the global optimal fitness and gives the accurate result. The convergence curve of the proposed work is plotted against the iteration in Fig. 11.

Fig. 11

Convergence plot for IEEE 94 bus system.

The superiority of the proposed enhanced Ant-lion optimizer is proven by comparing the output parameters with other existing optimization approaches like Genetic Algorithm (GA) with VRP method, Harris Hawks Optimization (HHO) and Particle Swarm Optimization (PSO). The IEEE-33 bus system with the best case 3 is selected for the comparison and presented in Table 8. In IEEE – 33 bus system, the total loss reduction is 68.26 kW which comparatively lesser than other methods, the minimum voltage of 0.981 is attained with 2909.2 kW of DG and 1770.7 kW of charging station. The voltage stability index (VSI) is improved to 0.92.

Table 8

Comparison of proposed work with existing work-IEEE 33 bus system

Parameter/Work	No. of DG	DG location	DG size (kW)	No. of CS	CS location	CS size (kW)	VSI	Power loss (kW)	V_min
Proposed (Case 3)	2	8, 31	2909.2	2	2, 21	1770.7	0.92	68.26	0.981
HHO [25]	2	13,24	2388.6	2	2,19	2149	0.8872	74.012	0.93
GA with VRP method [9]	–	–	–	2	2, 19	3000	0.347	230	0.807
PSO [30]	2	9,28	5150.5	2	22,25	3674	0.423	418	0.812

5 Conclusion

The requirement for the charging station with adequate capacity is increasing due to higher rate of electric vehicles adoption in recent years. However the capacity addition of charging stations and Distributed Generation (DG) units in the existing network results in voltage volatility and increase losses. In this research work, the problem is formulated to optimally allocate maximum size of charging station and DG units at appropriate locations. This multi-objective problem with more search parameters is optimally solved using proposed enhanced antlion optimizer. The proposed method is tested over IEEE – 33, 69 and 94 radial bus systems. IEEE-69 bus system, the system arrived with minimum power loss of 23.17 kW, the minimum voltage of 0.994 for the DG capacity of 3369.7 kW and 1221.3 kW of charging station. Similarly, with IEEE-94 bus system, the minimum power loss of 166.1 kW, the minimum voltage of 0.964 for the DG capacity of 4592.2 kW and 2831.3 kW of charging station is attained. The results of the best case i.e. case 3 from IEEE-33 bus system has been taken and compared with other works solved through Genetic Algorithm (GA) with VRP method, Harris Hawks Optimization (HHO) and Particle Swarm Optimization (PSO). It is identified that the total loss reduction is 68.26 kW with the minimum voltage of 0.981 is achieved for the installed DG capacity of 2909.2 kW and 1770.7 kW of charging station. The voltage stability index is improved to 0.92. From the results, it is understand that the proposed method offers the better performance than other methods. The study on the stochastic nature of both energy sources and loads will be the future scope of the present research work.

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