Effect of plug-in electric vehicles demand on the renewable micro-grids

Abstract

This paper assesses the effect of appearance of plug-in electric vehicles (PHEVs) on the management of Micro-Grids (MGs) considering different charging schemes. The MG includes different renewable sources such as Wind Turbine (WT), Fuel Cell (FC), Micro Turbine (MT) and Photovoltaics (PVs) as well as battery as the storage device. In order to make the analysis practical, different classes of PHEVs and chargers are included in the proposed problem. The optimization framework tries to optimize the total MG cost when considering several operational and security constraints. In order to solve the problem optimally, a new modification method based on bat algorithm (BA) is employed. In addition, a new modification method is introduced for the BA to reduce the possibility of trapping in local optima. The simulation results show the satisfying performance of the proposed method for managing the MG with high penetration level of PHEVs.

Keywords

Plug-in Hybrid Electric Vehicles (PHEVs)Renewable Micro-Grid storage device Modified Bat Algorithm (MBA)

Nomenclature

AER

All-Electric Range is the maximum distance which a PHEV can travel on the battery

B_Gi (t)

The bid of ith DG at time t

B_Sj (t)

The jth storage device bid at time t

BF ₁

Factor indicating the mutual benefit to the organism X _i

B_Grid (t)

Utility bid at time t

C _bat

Battery capacity of PHEV

Daily driven mile of PHEV

maxDOD

Maximum depth of discharge in PHEV battery

Mutual _ Vector

The relationship characteristic between organism X _i and X _j

Number of the state variables

N _g

Number of generating units

N _s

Number of storage devices

N _L

Total number of load levels

N _PHEV

Total number of PHEVs

Rate of PHEV charger

P _g

Vector including the power generation of all power units

P_G,i (t)

Active power production of ith power unit

P_G,i,min (t)

Minimum active power production of ith power unit at t

P_G,i,max (t)

Maximum active power production of ith power unit at t

P_s,j,min (t)

Minimum active power production of jth storage device at t

P_s,j,max (t)

Maximum active power production of jth storage device

P_Grid,min (t)

Minimum active power production of the grid at t

P_Grid,max (t)

Maximum active power production of the grid at t

P_L,k (t)

The amount of kth load value at time t

P _PHEV,l

The amount of lth PHEV power consumption at time t

P _{charge/P_discharge}

Permitted rate of charge/discharge during a finite time period (Δt)

P _{charge,max/P_{discharge,max}}

Maximum permitted rate of charge/discharge during a finite each time period (Δt)

rand

Random generator operator

fre _i

Frequency of ith bat

S _Sj(t)

Start-up/Shut down cost of jth storage device at time t

S _Gi(t)

Start-up/Shut down cost of ith DG at time t

S _Grid(t)

Active power bought (sold) from (to) the utility at time t

SOC

State of the charge in PHEV battery

t _start

Charging start time of PHEV

t _D

Charging duration of PHEV

Number of time intervals

u _i(t)

State of the ith unit denoting ON/OFF statuses

U _g

Vector including ONN/OFF statuses of all power units

W _ess(t)

Amount of stored energy inside the battery at time t

W _{ess,max/W_ess,min}

Maximum/Minimum stored energy inside the battery

State variables vector

X _i

ith bat

X _gbest

Best bat

efficiency of PHEV charger

η _{charge/η_discharge}

Battery efficiency during charge/discharge period

σ/μ

Log-normal pdf parameters for PHEV smart charging

σ_m/μ_m

Log-normal pdf parameters for PHEV daily mileage

f _min

Minimum frequency of each bat

f _max

Maximum frequency of each bat

Random number in the range of [0,1]

v _i

Velocity of ith bat

r _i

Frequency Rate of ith bat

A _i

Frequency loudness of ith bat

X _gbest

Best bat in the population

A _min

Minimum frequency loudness of each bat

Round

Math round operator

ψ _{1,…, ψ₄}

Random values in the range [0,1]

Random number in the range of [−1,1]

Constant parameter of the BA

M _D

Column-wise average of the bat population

T _F

Random integer equals 1 or 2

1 Introduction

According to the recent demands from the growing concerns of the people, the renewable energy sources (RESs) have been introduced by the power engineers and researchers [1 –3]. Some of the benefits of RESs can be named as fast installation, higher power quality, less pollution and increased energy efficiency. In addition, the nearness of RESs to the consumers reduces the network power losses, T & D feeder contingencies and the failure time of the feeders [4, 5]. Along with these benefits, the appearance of RESs creates new challenges for the network which part of it is discussed in the form of MG. A MG is a collection of distributed generations (DGs) and electrical loads with interconnection of the main grid [6]. One of the most significant aspects of the MG is optimal operation and management that has attracted the attention of many researchers.

In [7], authors proposed a MG with different RESs and then devised a planning method to minimize the total expenses of the MG. A new agent-based approach was introduced in [8] to increase the flexibility of a photovoltaic (PV) based MG incorporating the battery energy storage. A new method based on linear optimization was proposed in [9] to operate a renewable MG considering the On/OFF status of the MG in the connected mode. A seven-day planning strategy was introduced in [10] to manage a MG in the deterministic framework. In [11], a price-based approach was devised to optimize the MG total cost in the connected mode with the main grid. A three-phase solution based on forecasting, storage and optimization was introduced in [12] to solve the MG using the well-known genetic algorithm (GA). The unit commitment of the RESs and DGs in the MG was assessed in [13] for minimizing the total cost of supplying the MG load. With the purpose of considering the life of battery, authors in [14] studied a typical MG and reduced its total expanses. A hybrid wind turbine (WT) and PV based Mg was studied in [15]. Here a linear solution was introduced for optimizing the MG generation cost. As it can be seen, these researches have focused on the optimal operation of the MGs which shows its significance in the research area. Nevertheless, there is little attention paid to the effect of electric vehicles (EVs) on the Mg operation.

The appearance of EVs was caused by the same reason as that of the renewable energy sources; that means concerns over the pollutions of fossil fuels. Since pure electric battery can not be a reliable choice for passing long distances, plug-in hybrid electric vehicles (PHEVs) were introduced later [16]. The recent surveys show the widespread popularity of the PHEVs in the industrial countries [17, 18]. According to this issue, this paper tries to address the effect of charging of PHEVs on the optimal operation of the renewable MGs. In this way, three different charging schemes of uncontrolled, controlled and smart charging are considered in the analysis. Since the total charging behavior of PHEVs is uncertain, then proper probability density functions (PDFs) are defined to model this uncertainty. Monte Carlo Simulation (MCS) is used as the stochastic method for modeling these uncertainties. According to the high complexity of the optimization problem, bat algorithm (BA) with a new modification method is used as the optimizer. BA mimics the behavior of bat animals to find their prey without eyes depending on the echolocation process [19]. The proposed modification method makes use of two new improvisation stages that will equip BA to escape from the several local optima of the problem. In short, the main contributions of the paper are as follows: 1) Considering the charging demand of PHEVs on the renewable Micro-Grids, 2) Utilization of the BA for solving the optimal operation of MG with the high penetration of PHEVs and 3) Introducing a new modification method for BA to improve the search ability of the algorithm. Finally, the satisfying performance of the proposed method is shown on a typical MG with different RESs.

2 Problem formulation

As mentioned before, the most significant target of a MG is to minimize its total costs when supplying the electrical demands of the consumers. The objectives and constraints are discussed in this section.

2.1 Objective function

The cost function includes the cost of power generation by the up-stream grid, DGs, RESs, battery as well as the cost of switching On/Off the DGs as follows [6]:

$\begin{matrix} Min f (X) = \sum_{t = 1}^{T} {Cost}^{t} = \\ \sum_{t = 1}^{T} {\sum_{i = 1}^{N_{g}} [u_{i} (t) p_{Gi} (t) B_{Gi} (t) + S_{Gi} | u_{i} (t) - u_{i} (t - 1) |] \\ + \sum_{j = 1}^{N_{s}} [u_{j} (t) p_{sj} (t) B_{sj} (t) + S_{sj} | u_{j} (t) - u_{j} (t - 1) |] \\ + p_{Grid} (t) B_{Grid} (t)} \end{matrix}$ (1) where X is the system variable victor incorporating the output power of DGs, up-stream grid and batteries as well as their On/Off status [6]: $\begin{matrix} X & = & [P_{g}, U_{g}]_{1 \times 2 nT}; n = N_{g} + N_{s} + 1 \\ P_{g} & = & [P_{G}, P_{s}] \\ P_{G} & = & [P_{G, 1}, P_{G, 2}, \dots, P_{G, N_{g}}] \\ P_{s} & = & [P_{s, 1}, P_{s, 2}, \dots, P_{s, N_{s}}] \\ P_{G, i} & = & [P_{G, i} (1), P_{G, i} (2), \dots, P_{G, i} (T)]; i = 1, 2, \dots, N_{g} + 1 \\ P_{s, j} & = & [P_{s, j} (1), P_{s, j} (2), \dots, P_{s, j} (T)]; j = 1, 2, \dots, N_{s} \\ U_{g} & = & [u_{1}, u_{2}, \dots, u_{n}], \\ u_{k} & = & [u_{k} (1), u_{k} (2), \dots, u_{k} (T)]; k = 1, 2, \dots, n \end{matrix}$ (2)

2.2 Constraints

2.2.1 Power generation and demand equation

The most significant constraint is the balance between the load and generation as follows:

$\begin{matrix} \sum_{i = 1}^{N_{g}} P_{G, i} (t) + \sum_{j = 1}^{Ns} P_{s, j} (t) + P_{Grid} (t) \\ = \sum_{k = 1}^{N_{L}} P_{L, k} (t) + \sum_{l = 1}^{N_{PHEV}} P_{PHEV, l} (t) \end{matrix}$ (3)

2.2.2 Generation limits

Each power unit can produce in the pre-defined limited ranges of capacity: $\begin{matrix} P_{Gi, min} (t) \leq P_{Gi} (t) \leq P_{Gi, max} (t) \\ P_{grid, min} (t) \leq P_{Grid} (t) \leq P_{grid, max} (t) \\ P_{sj, min} (t) \leq P_{sj} (t) \leq P_{sj, max} (t) \end{matrix}$ (4)

2.2.3 Battery and Charger Performance Limits

The battery can discharge limited to its stored energy in the last hours as well as the charging rate as below: $\begin{matrix} W_{ess} (t) = W_{ess} (t - 1) + η_{charge} P_{charge} Δ t \\ - \frac{1}{η_{discharge}} P_{discharge} Δ t \\ {\begin{matrix} W_{ess, min} \leq W_{ess} (t) \leq W_{ess, max} \\ P_{charge} (t) \leq P_{charge, max} \\ P_{discharge} (t) \leq P_{discharge, max} \end{matrix} \end{matrix}$ (5)

3 PHEV model

The increasing concern regarding the fossil fuel emission is changing the tendency from the traditional combustion engines to the new electric vehicles based on electric batteries. From the view of the electric companies, PHEVs are dispersed mobile loads that can make severe problems if not optimally managed in the scheduling programs. In fact, the charging demand topography of PEVs may alter during the daily operation of the power system. This issue can become troublesome when generally the amount of energy drawn from the MG is more than the injected power to the MG. In order to model the charging demand of PHEVs, several factors should be considered including: state of charge (SOC), type of EVs, type of chargers, charging time and the length of charging for each PHEV. In order to reach a more accurate and practical formulation, three different charging schemes are defined in this section:

Uncontrolled charging: this charging models the behavior of those PHEV owners that will charge their car as soon as they reach to the home. This model simulates a rectangular PDF with a small length of charging as follows [20]: $\begin{matrix} f (t_{start}) = \frac{1}{b - a} a \leq t_{start} \leq b a = 18, b = 19 \end{matrix}$ (6) where a and b are the PDF parameter.

Controlled charging: This charging model simulates the behavior of those PHEV owners that prefer to charge their car at the off-peak hours generally at 9 pm as follows [20]: $\begin{matrix} f (t_{start}) = \frac{1}{b - a} a \leq t_{start} \leq b a = 21, b = 24 \end{matrix}$ (7)

Smart charging: The smart charging scheme simulates the most intelligent charging strategy that can be controlled by the main grid controller, here the MG central control (MGCC). This charging pattern will shift the charging time to low-cost hours or the time at which the MG has extra capacity as follows [20]: $\begin{matrix} f (t_{start}) = \frac{1}{σ \sqrt{2 π}} e^{(- \frac{1}{2} (\frac{t_{start} - μ}{σ})^{2})} & μ = 1, σ = 3 \end{matrix}$ (8) where σ and μ are the normal PDF parameters. Each of the above charging schemes determines the charging time. But the length of the charging is determined using the below equation: $t_{D} = \frac{C_{bat} \times (1 - SOC) \times MaxDOD}{η \times P}$ (9)

In the above equation, the battery Charger rate (P) can be found by the charger type and the charger efficiency (η) which is defined by their level as shown in Table 1. It is worth noting that charging level 1 and 2 are for the household usages and Level 3 chargers are for businesses and mass transits.

Regarding the battery capacity, the class of PHEVs should be known. Table 2 shows different classes of PHEVs along with their market share [20]. The images of some of these cars are shown in Fig. 1. Using the MinC _bat and MaxC _bat from Table 2, the mean and standard deviation of the PDFs are calculated as follows:

$\begin{matrix} μ_{C_{bat}} = \frac{{MinC}_{bat} + {MaxC}_{bat}}{2} \\ σ_{C_{bat}} = \frac{{MaxC}_{bat} - {MinC}_{bat}}{4} \end{matrix}$ (10)

The last term in (9) is the SOC of the batteries that is a function of the daily travel distances of PHEVs. Therefore, first the average daily driven distance for the PHEVs is calculated: $\begin{matrix} f (m) = \frac{1}{m σ_{m} \sqrt{2 π}} e^{\frac{- (ln (m) - μ_{m})^{2}}{{2 σ}_{m^{2}}}} & m > 0 \end{matrix}$ (11)

Technically, different PHEVs belong to four classes of PHEV-20, PHEV-30, PHEV-40 and PHEV-60 wherein the last numbers shows the All-Electric Range (AER) parameter. Therefore, the SOC is calculated as follows: $SOC = {\begin{matrix} 0 & m > AER \\ \frac{AER - m}{AER} \times 100 % & m \leq AER \end{matrix}$ (12)

4 Optimization based on modified BA

This section describes the proposed modified BA for solving the proposed problem.

4.1 The original BA

BA was first developed by the researchers in 2008 to mimic the search behavior of bats for the food in the dark nights using the echolocation process. This process helps bats to distinguish between food and prey in the dark area using the echo of the signals that they have sent to the air previously. Figure 2 shows the echolocation process. In comparison to other algorithms such HS [21], FA [22 –24], TLBO [25, 26], CA [27] and HBMO [28 –30]; BA is simpler and has more applicable and useful optimizers for searching both local and global spaces. It is shown in the literature that BA can solve both continuous and discrete optimization problems. BA works using three ideas of 1) all bats use the echolocation mechanism to understand the distance; 2) each bat X _i flies randomly with the velocity v _i producing frequency f _i, wavelength λ and loudness A ₀ and 3) the loudness of the signal of the bat changes from a large value of A ₀ to a minimum value of A _min.

BA makes use of an initial random population of bats to solve any optimization problem. Each bat is a promising solution for the problem in hand. After calculating the cost objective function for the bats, the population should be improved. The best bat in the population is called X _gbest. Now the positions of the bats are improved as follows: $\begin{matrix} {fre}_{i} = f_{min} + (f_{max} - f_{min}) β \\ v_{i}^{k + 1} = v_{i}^{k} + (X_{i}^{k} - X_{gbest}) {fre}_{i} \\ X_{i}^{k + 1} = X_{i}^{k} + v_{i}^{k + 1} \end{matrix}$ (13)

With the aim of simulating a random walk around each bat, a random number (θ) is generated. If θ is bigger than $r_{m}^{k}$ , a new solution is generated as follows: $X_{new} = X_{old} + ɛ A^{k}$ (14)

On the other hand, if the random value θ is smaller than $r_{m}^{k}$ , a new solution is generated randomly in the feasible region (X _new). This new bat is accepted if the below two criteria are satisfied: $& [f (X_{i}) < f (X_{gbest})]$ (15)

It may be worthy to mention that $A_{i}^{k}$ and $r_{i}^{k}$ are updated after each iteration using the below adaptive formulations: $\begin{matrix} A_{i}^{k + 1} = α A_{i}^{k} \\ r_{i}^{k + 1} = r_{i}^{0} [1 - exp (- γ k)] \end{matrix}$ (16)

4.2 Modified BA (MBA)

BA has many special features that makes it a very useful technique for solving the complex and hard problems. Some of the main characteristics of BA can be named as simple concept, little adjusting parameters and fast convergence. Nevertheless, in order to improve the performance of this already fine algorithm, we have devised a new two-phase modification method. Each of these methods can improve the position of the bats from a special view. The first modification method is used for increasing the diversity of the bat population. In this way, in each iteration and for each bat X_i, three dissimilar bats X _q1, X _q2, X _q3 are chosen and injected to the below equation to produce a ne mutated solution: $X_{Test 1, i}^{k} = X_{q 1}^{k} + ψ_{2} (X_{q 2}^{k} - X_{q 3}^{k})$ (17) $\begin{matrix} x_{Test 1, i}^{k} = {\begin{matrix} x_{Test 1, i}^{k} if (ψ_{2} \leq ψ_{3}) \\ x_{i}^{k} Else \end{matrix} \\ X_{Test 1}^{k} = [x_{Test 1, 1}^{k}, x_{Test 1, 2}^{k}, \dots, x_{Test 1, n}^{k}] \end{matrix}$ (18) $\begin{matrix} x_{Test 2, i}^{k} = {\begin{matrix} x_{gbest, i}^{k} if (ψ_{3} \leq ψ_{4}) \\ x_{i}^{k} Else \end{matrix} \\ X_{Test 2}^{k} = [x_{Test 2, 1}^{k}, x_{Test 2, 2}^{k}, \dots, x_{Test 2, n}^{k}] \end{matrix}$ (19)

The best test solution among $X_{Test 1, i}^{k}, X_{Test 2, i}^{k} &$ $X_{Test 3, i}^{k}$ is chosen to replace $X_{i}^{k}$ .

The second modification method is a shifting formulation that makes use of the moving idea to change the average of the bat population toward the best bat X _gbest as follows: $\begin{matrix} X_{Test, i}^{k} = X_{i}^{k} + ψ_{1} (X_{gbest}^{k} - T_{F} M_{D}) \\ T_{F} = round (rand + 1) \\ M_{D} = average (popualtion) \end{matrix}$ (20)

5 Simulation results

The proposed problem is examined on a typical MG that includes many different types of RESs, DGs and battery as the storage. This Mg includes one WT, one PV, one fuel cell (FC), one micro turbine (MT) and one battery. Also, the MG is in connection with the mail grid and can decide to either sell or buy power to/from the grid. The single line diagram of the test system is depicted in Fig. 3. The output power of the WT and PV is completely used by the MG. This is a useful policy for supporting the idea of renewable sources. The cost of battery is assumed to be 350 $ as given in [16].

The maximum and minimum capacities of the DGs and RESs as well as the cost of power and shut-down and start up are given in Table 3.

The first part of the simulation is to prove the high search ability of MBA. Therefore, the PHEVs are neglected at this part. Table 4 shows the results of simulation for optimal management of the MG. For better comparison, the results of other methods are also shown in this table comparatively. In order to make a fair comparison, the simulations are repeated for 20 time and the results of the best solution, the worst solution and the average value are evaluated and shown comparatively. According to these results, the proposed MBA has overcome the other methods successfully. In fact, the MBA could reach to a new optimal for the network that was not found by the other methods yet. The optimal output powers of the units corresponding with the best optimal solution of MBA are shown in Table 5. As it can be seen from Table 5, the battery is charged in the first hours of the day to be able to discharge at the later hours.

In the second part of the simulations, the PHEV charging demand is considered in the problem. Therefore, the three charging schemes of uncontrolled, controlled and smart charging are considered in the simulations. Since PHEVs are additional loads for the Mg, we have to increase the maximum power generation of the units to be able to operate the MG. Here we decide to increase the maximum power capacity of the main grid from 30 kW to 120 kW. Table 6 shows the simulation results. According to the results of Table 6, the lowest cost function value belongs to the smart charging of PHEVs. This result shows that smart charging can be a very useful tool in the operator hand. The optimal operating points of the power units for each charging scheme are shown in Tables 7–9. As it can be seen from these tables, the main grid has to increase its power to supply the additional loads of the PHEVs.

6 Conclusion

The main purpose of this paper was to consider the effect of considering the possible charging demand of PHEVs on the optimal operation of the MGs. In this way, three different charging schemes were defined including an uncontrolled, controlled and smart pattern. Also, a new optimization method was introduced to solve the problem properly. The simulation results show the satisfying performance of the MBA in comparison with other methods. Also it was seen that considering the PHEVs in the Mg can affect the operation strategies greatly. Nevertheless the smart charging pattern can be the best solution for reducing the sever effect of the PHEVs on the total cost of the MG.

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