A hybrid shuffled frog leaping algorithm and intelligent water drops optimization for efficiency maximization in smart microgrids considering EV energy storage state of health

Abstract

To reduce fossil fuel consumption, carbon dioxide emissions, and greenhouse gas emissions, countries all over the world have been gradually directing their attention toward the development and application of microgrids (MGs) that run on renewable energy sources. The MG concept has been gaining increased interest, particularly with respect to distribution systems. On the other hand MGs are equipped with new technologies such as plug-in electric vehicles (PEVs) and plug-in hybrid electric vehicles, which have become viable alternatives to traditional combustion-engine cars. In this paper the novel optimization method for efficiency maximization in smart MGs in the presence of demand response, was proposed. This method combines a hybrid shuffled frog leaping algorithm (SFLA) and intelligent water drop optimization. In this situation, the EV energy storage system (ESS) state of health (SOH) model was considered to adjust the ESS temperature set point. SFLA is a new member of intelligent algorithms and a new member in the family of memetic algorithms. For this purpose, simulation results were made in MATLAB software environment to demonstrate the effectiveness of the proposed methodology. In order to verify proposed algorithm, simulations were made along with some conventional optimization methods. The results show that the proposed optimization method, can effectively improve the performance of MG power flow, when it is compared with other methods.

Keywords

Shuffled frog leaping algorithm (SFLA)intelligent water drops (IWD) optimization energy storage system (ESS)plug-in electric vehicles (PEVs)microgrids (MGs)renewable energy state of health (SOH)

1 Introduction

Motivated by environmental concerns, exacerbation of energy crisis, global warming and energy efficiency, the penetration of distributed generation (DG) from renewable resources is rapidly increased as small generators units connected to distribution grids. Among various types of renewable energy sources, wind and solar energy is the most rapidly growing one due to its attractive features such as efficiency and economic merit.

The microgrid (MG) concept has been gaining more attention worldwide, particularly for the distribution system, because MG not only provides a solution to manage local generations and loads as a single grid-level entity, but also this is an effective tool to aggregate and integrate smaller renewable energy generations and connect to the utility grid at a single point of interconnection. Furthermore, it has the potential to improve overall system efficiency, power quality, and energy surety for critical loads. MG is required to have the ability to operate interconnected with the main grid or isolated (which may be intentional or un-intentional), but in both the conditions MG must operate autonomously stable [1]. Isolated MGs have limited generation capacity and introducing new loads might lead to a demand-supply balance problem, and consequently a blackout or load shedding, so power supply and consumption is a key requirement of the MG management [2]. Unfortunately, the inherent significant uncertainty of renewable power presents a great challenge to achieve this balance. In view of this, in a MG, it is highly desirable to compensate the variation of wind power by some other means. The recent popularity of plug-in electric vehicles (PEVs) and plug-in hybrid electric vehicles (PHEVs) have offered the possibility to address this issue.

PEVs are rapidly gaining widespread use thanks to the possibility they offer of reducing reliance on and cost of fuel and improving quality of life for their users, so PEVs are significantly expected to be installed in the customer side [5 –10]. In this situation, various PEVs [3] have been developed during the past years. PEV fleets include a number of batteries connected to the grid during the periods when the vehicles are parked (for a few hours at a time) and required to reach specified energy levels at specific hours of the day (e.g., at the vehicle departure time). In order to improve the charging and discharging performance of PEV batteries, super-capacitors are connected in parallel with the batteries. In this context, the grid to vehicle (G2V) [4] and vehicle to grid (V2G) technologies [5] could be usefully exploited; in fact, if the charging process of PEVs is appropriately managed, for instance by an aggregator [6], PEV storages can be considered either as flexible loads (in G2V modes only) or distributed energy storage systems (ESSs) (in V2G modes).

Optimal PEVs power management for minimizing energy loss in a large-scale penetration of PEVs is a nontrivial task due to the large number of control variables. Therefore, some unrealistic assumptions (i.e., the size of power system and number of PEVs are assumed to be small) are made in order to simplify the problem in all previous studies. On the other hand, if smart charging strategies are implemented, PEVs could smooth the load curve by increasing demand in valley hours. They are also leading to a better utilization of system resources and contribute to a more efficient integration of intermittent renewable energy sources (RES) generation by offering storage capabilities to power systems [7].

There are many works in the literature focused on the technical definition and control of V2G systems. Modeling PEV, reducing distribution system loss, and designing infrastructure network for smart charging concepts have been independently introduced in [8] and [9]. In [10, 11], the economic dispatching of PEVs in the power system with high wind power penetration was studied. The objective in [10] was to minimizing the total generation cost of the whole system, while in [11], the objective was to achieve the minimum energy costs of PEVs. Ref. [12] analyzes the potential for regulation service supply by V2G in electricity markets and develops a decision support model for optimal bidding to the wholesale market. In some papers, significant effort has been devoted to reduce PHEV battery charging impacts through managing these loads [13, 14]. The charging impacts of PHEVs on the power distribution networks have been introduced in the literatures and have been widely investigated [15]. In Ref. [16], the progression of V2G aggregators for frequency regulation is proposed. In [17] topologies are presented to optimize charging time for V2G. Theoretical analyses for the integration of renewable generation using V2G can be found in [18]. In [19], a method for energy exchange between grids and EVs along with optimal scheduling in a smart parking has been presented. In these papers, uncertainties for renewable generation have not been taken into account. Ref. [20] proposed an algorithm for tracking the load frequency control signals by groups of PHEVs. A coordinated charging control issues for EVs in V2G mode at the residential transformer level is investigated in [21]. In [22], hierarchical control algorithms were proposed to integrate the PEV charging and wind power scheduling, with the goal of maintaining the frequency of the power system. In [23], the problem of coordination between wind and PEV in a MG to optimize the energy dispatch is examined. In order to reduce both the number of PHEVs and frequency fluctuation, smoothing of wind power production by pitch angle control and PHEV control using a model predictive control method proposed in [24]. Regarding the presence of electric vehicles, in [25] a multi-objective approach is proposed aimed at achieving optimal operation of a MG. Reference [26] presented comprehensive control of responsive loads at house area network for smart MG autonomous operation.

On the other hand all of the optimization methods can be potentially used in order to maximize the whole efficiency of MG. The shuffled frog leaping algorithm (SFLA) is a memetic meta-heuristic which is originally proposed in [27]. For combinatorial optimization problems. The concept of the SFLA is based on observing, imitating, and modeling the social behavior of a group of frogs when they search for the location of a rich source of food. Due to its effectiveness and suitability, the SFLA has been successfully applied to solve many power system optimization problems such as transient stability improvement of a grid-connected wind farm [28], unit commitment problem [29], harmonic distortion minimization in inverter systems [30], power system damping [31], optimal switch placement in a distribution system [32], and optimal reactive power dispatch [33].

In this paper, authors have developed a new algorithm based on hybridization of SFLA and intelligent water drops (IWD) optimization, for efficiency maximization in smart MGs. The most distinguished benefit of SFLA is its fast convergence speed. In the other hand, there is a gap in this algorithm when it is unable to find an improved set of variables. In such cases, a new set of variables is randomly generated which may be worse than the previous one. This drawback is eliminated by diverting to another optimization method instead of generating a random set of variables. In other words, whenever the SFLA could not generate a better set of variables, an auxiliary optimization method will be invoked to generate a new set of variables. In this context, IWD algorithm is employed as the auxiliary optimization method to improve the SFLA performance. IWD algorithm is a new swarm-based optimization algorithm inspired by observing natural water drops that flow in rivers [34]. In this situation, proposed algorithm used to optimize the selected multi-objective function. Also, optimization is implemented with consideration for the state of health (SOH) of a PEV energy storage system.

The rest of this paper is organized as follows. Section 2 introduces the configuration of MG, in Section 3, MG elements (i.e., battery, PEVs, photovoltaic (PV) and wind turbines (WTs)) are modeled. In Sections 4 and 5, objective function and proposed optimization method were presented respectively. In Section 6, typical MG with and without proposed optimization method considering SOH of PEV ESS is discussed due to simulation results and finally Section 7 concludes this paper.

2 The microgrid under study

PEV fleets include a number of batteries connected to the grid during the periods when the vehicles are parked and required to reach specified energy levels at specific hours of the day. The PEV aggregator is responsible for the charging of its vehicles on the basis of the drivers’ needs. In fact, the optimal coordination and control of the power transferred to/from each PEV enables the exchange of power among MGs with several benefits, such as the maximization of the self-consumption, the optimization of locally used RES production and the improvement of the global stability of the grid. On the other hand, the presence of PEVs with high power rating in isolated MG and the implementation of DR makes the generation scheduling problem more complex. Clearly, this requires a central management of MG energy consumption and production, dealing also with mobility needs; so, the MG is regulated and dispatched by the central control unit (CCN) to accommodate the power supply of distributed WTs and PVs to the power consumption of EVs and their chargers, BSS, interruptible loads users, and other load demands. In this situation based on drivers’ typical behavior, the aggregator is able to forecast its vehicles’ expected requirements and sends this information to the CCN (i.e., arrival and departure time of its vehicles, energy requests, and availability during this period). The CCN is also able to control the reactive power of DG units when they are connected to the grid through power converters. According to the proposed optimization, a set of constraints is integrated in the operation strategy in order to limit the battery temperature and therefore preserve the lifetime of the storage systems. The constraints differ depending on the use of the battery. As an example, the lifetime is preserved by imposing a limited number of charging/discharging cycles and a maximum depth of discharge. The system structure is depicted in Fig. 1.

Fig.1

Physical configuration of the MG under study.

3 System modeling

In this section, mathematical models along with the dynamic models are described for parts of MG system, which consists of PEV with lithium-ion (Li-ion) battery bank, PV panels, WTs and DC-DC converters.

3.1 Electric vehicle

The most important aspects of the EV modelling are the battery performance (efficiency and temperature) together with user needs. The EV battery life depends on the charging-discharging cycles.

The current flowing into the battery is determined based on the charging voltage and the internal impedance of the battery [35]. The most common method of SOC calculation that also has been selected in this study is Coulomb-counting (Equations 1 and 2). $\begin{matrix} SOC & = & {SOC}_{0} + \frac{1}{C_{n}} \int_{t_{0}}^{t} | I | dt \\ During Charging \end{matrix}$ (1) $\begin{matrix} SOC & = & {SOC}_{0} - \frac{1}{C_{n}} \int_{0}^{t} | I | dt \\ During Discharging \end{matrix}$ (2)

This method needs an accurate measurement of battery current (I) and also knowing the initial value of SOC (SOC ₀).

Between the minimum SOC and a certain limit (a), the discharging power is limited by a linear function depending on the punctual SOC. Considering λ _w as a set of periods where the EV w ∈ W is plugged to the charging point. Equations (3–5) define the power bounds for both of the charging and discharging processes: $\begin{matrix} 0 \leq P_{EV} (t, w) & \leq & {\bar{P}}_{EV} (w) \times x_{EV} (t, w), \\ charging mode, \forall t \in λ_{w} \end{matrix}$ (3) $\begin{matrix} 0 \leq P_{EV} (t, w) & \leq & {\bar{P}}_{EV} (w) \times (1 - x_{EV} (t, w)), \\ discharging mode, \forall t \in λ_{w} \end{matrix}$ (4) $\begin{matrix} P_{EV} (t, w) & \leq & ({\bar{P}}_{EV} (w) / a) \times SOC (t - 1, w), \\ discharging mode, \forall t \in λ_{w} \end{matrix}$ (5)

Where P _EV (t, w) is charging/discharging rate of the EV [kW], ${\bar{P}}_{EV} (w)$ is the maximum instantaneous power for the EV [kW], x _EV (t, w) is power flow direction in the EV battery, which model as binary variables expressing the charging/discharging status of the battery of the associated EV: ${\begin{matrix} x_{EV} (t, w) = 1, \\ if the EV w \in W is charging in period t \in λ_{w} \\ x_{EV} (t, w) = 0, otherwise \end{matrix}$ (6)

Considering R _EV (w) as the energy required by the vehicle while it is not connected i.e., the energy that will be used by the vehicle in the periods t ∈ T. This demand affects to the state of charge SOC (t, w), let be defined as:

$\begin{matrix} P_{EV} (t, w) \\ = {\begin{matrix} (β P_{EV, ch} (t, w) - \frac{P_{EV, dis} (t, w)}{η}) & Δ t ift \in λ_{w} \\ R_{EV} (w) & if t \in T \end{matrix} \end{matrix}$ (7)

Where, P _EV,ch (t, w) is the charging rate of the EV [kW], P _EV,dis (t, w) is the discharging rate of the EV [kW], β is the charge efficiency [% ], η is the discharge efficiency [% ] and Δt is the duration of the time intervals.

Then, the state of charge must be limited by: ${SOC}_{min} (t, w) \leq SOC (t, w) \leq {SOC}_{max} (t, w)$ (8)

Where, SOC _max (t, w) is the maximum SOC for the EV and time interval [% ] and SOC _min (t, w) is the minimum SOC for each EV and time interval [% ].

In order to evaluate the battery pack temperature, the lumped capacitance battery thermal model which initially developed at national renewable energy laboratory (NREL) has been used [36]. The governing formulas as explained in [37] are as follow. Figure 2 shows the configuration of battery thermal design and analysis. $H_{d} = (T_{ess} - T_{air}) / R_{eff}$ (9) $R_{eff} = 1 / (h γ) + t / (k γ)$ (10) $h = {\begin{matrix} a {(\frac{m / ρ A}{5})}^{b} & T_{ess} > T_{ess - set} \\ 4 & T_{ess} > T_{ess - set} \end{matrix}$ (11) $T_{S} = T_{amb} + 0.5 H_{d} / (r_{air} C_{p, air})$ (12) $p_{l, ess} = η_{c} R_{int} I^{2}$ (13) $T_{ess} = \int_{0}^{t} \frac{H_{d} - p_{l, ess}}{m_{Batt} C_{p, Batt}} dt$ (14)

Where H _d is heat dissipate, T _s is surrounding temperature (°C), T _ess is energy storage system temperature (°C), R _eff is effective thermal resistance, T _amb is ambient temperature (°C), r _air is air flow rate, C _p,air is air heat capacity, m _Batt is battery mass, C _Batt is battery heat capacity, h is heat transfer coefficient, K is heat conductivity coefficient, a, b is battery pack geometry constants, A is area of battery pack (m ³), ρ is air density, t, γ is battery pack related parameters value, P _r is request power of battery pack (w), P _l,ess is battery power loss (w) and η _c is columbic efficiency.

Fig.2

Configuration of the battery thermal analysis.

In this situation, temperature limit for battery pack is: $T_{ess} \leq T_{ess}^{max}$ (15)

Where, $T_{ess}^{max}$ is the maximum temperature allotted for battery pack.

3.2 DC/DC converters model

The MG contains some DC/DC boost converters for PV modules and wind system. The role of the DC/DC converter is converting the input voltage to a proper level in order to be feed to the DC bus. In a boost convertor, output voltage is larger than input voltage and they are related by Equation (16) [38]. $V_{o} = (1 / (1 - D)) V_{i}, D is duty cycle$ (16)

3.3 PV model

The following constraints are associated with the PV storages:

PV storage energy balance:

$\begin{matrix} E_{St} (i, t) \\ = E_{st} (i, t - 1) + (η_{St, C} (i) \times P_{St, C} (i, t) \times Δ t) \\ - (\frac{1}{η_{St, D} (i)} \times P_{St, D} (i, t) \times Δ t) \end{matrix}$ (17)

Where, E _St (i, t) is the energy stored in PV storage connected to bus i at hour t [kWh], P _St,C (i, t) is the power charge of PV storage connected to bus i at hour t [kW], P _St,D (i, t) is the power discharge of PV storage connected to bus i at hour t [kW], η _St,C (i) is the charging efficiency of PV storage connected to bus i, η _St,D (i) is the discharging efficiency of PV storage connected to bus i and Δt is the duration of the time intervals.

PV storage charge/discharge rates:

P_{St, C / D} (i, t) \leq P_{St, C / D}^{max} (i)

(18)

Where, $P_{St, C / D}^{max} (i)$ is the maximum power charge/ discharge of PV storage connected to bus i [kW].

PV storage capacity limits:

E_{St}^{min} (i) \leq E_{St} (i, t) \leq E_{St}^{max} (i)

(19)

Where, $E_{St}^{max} (i)$ is the maximum energy capacity of PV storage connected to bus i [kWh] and $E_{St}^{min} (i)$ is the minimum energy capacity of PV storage connected to bus i [kWh].

3.4 WT model

The model employed to calculate the power generated by WT as a function of wind speed is given below [39]:

$\begin{matrix} P_{WT} \\ = {\begin{matrix} 0 & 0 < V < V_{ci} \\ (A . V^{2} + B . V + C) * P_{rate} & V_{ci} \leq V \leq V_{r} \\ P_{rate} & V_{r} \leq V \leq V_{co} \\ 0 & V_{co} \leq V \leq \infty \end{matrix} \end{matrix}$ (20)

Where P _rate is the rated power of WT, V _ci and V _co are the cut-in and cut-out wind speed and the A, B and C coefficients are specified in the Plant’s datasheet provided by the manufacturer.

Equation (21) models the operational bounds for the wind resources in each period t ∈ T: $0 \leq P_{w} (t) \leq {\bar{P}}_{w} (t) \forall t \in T$ (21)

Where, P _w (t) is the wind generation [kW] and ${\bar{P}}_{w} (t)$ is the maximum available wind power [kW].

3.5 MPPT for PV system

The MPPT not only enables an increase in the power delivered from the PV module to the load, but

also enhances the operating lifetime of the PV system. A variety of MPPT methods have been developed and implemented, such as the neural network method [40] and incremental conductance method [41], to control PV arrays to ensure maximum utilization efficiency. In this paper, in order to achieve maximum power point, methods article [42] is applied.

3.6 MPPT for wind system

MPPT is an essential requirement to maximize the utility of the natural wind energy and consequently the economics of the whole wind system. There are various methods of implementing MPPT for the wind imitation platform and mostly driven by a controllable DC motor. In this paper the method which proposed in paper [43], used for wind power system which that adopts direct power control of DC motor together with decoupled vector control of the permanent magnet synchronous generator (PMSG) rotor speed.

4 Objective function

The objective function imposed on MG is divided into five objectives (see Equation (22)). Under this circumstance, the power of PHEVs at each time step are considered as control variables. Therefore, the first objective is aimed at improving the energy efficiency of the grid by minimizing power losses. The price of charging PEVs ( $π_{t}^{C}$ ) is assumed to be based on the price [44].

From PEV customer’s point of view, minimizing the cost of charging the PEVs is the second objective. This objective can be utilized by the MG system operator to study the impact of PEV charging on the system, expecting rational behavior of customers. The third objective represents the fear of running out of energy before the destination has been reached, by means of a penalty parameter, the possible policies of this range anxiety effect.

$\begin{matrix} fobj & = & min {(α \sum_{t = 1}^{T} \sum_{i = 1}^{N} \sum_{j = 1}^{N} Y_{ij} [v_{i, t}^{2} + v_{j, t}^{2} - 2 v_{i, t} v_{j, t} cos (δ_{j, t} - δ_{i, t})]) \\ + (β \sum_{t = 1}^{M} \sum_{t = 1}^{T} P_{i, t}^{PEV} π_{t}^{C}) + (γ \sum_{w \in W} \sum_{t \in λ_{w}} ({Pen}_{w} - {Pen}_{w} {SOC}_{t, w}) {Cap}_{w})} \end{matrix}$ (22)subjected to:

PEV	Equations (3–8, 15)
PV generation	Equations (17–19)
WTs generation	Equation (21)
Voltage magnitude constraints of nodes (with and without DG) at each time stage	V _min (i, t) ≤ V (i, t) ≤ V _max (i, t)
Active power output (with and without DG)	P _min (i, t) ≤ P (i, t) ≤ P _max (i, t)
Thermal limits of lines	$T_{l} (i, t) \leq T_{l}^{max} (i, t)$

Where, Y _ij is admittance between bus-i and bus-j [PU], Pen _w is the penalty associated with the EV range anxiety [$/kWh], Cap _w is the battery capacity of the EV [kWh], ${Cost}_{i, t}^{PV}$ is the cost of generating electricity with PV generation system connected to bus at hour [$] and ${Cost}_{i, t}^{W}$ is the cost of generating electricity with wind generation system connected to bus i at hour t [$].

5 Methodology

5.1 Shuffled frog leaping algorithm (SFLA)

The SFLA is a real coded population based meta-heuristic optimization method that evolves through the time loops in the form of memetic evolution. This algorithm, mimics the memetic evolution of a different groups which have different cultures of frogs when seeking for the location that has the maximum amount of available food, in the other word, Each frog improves its position according to the information from itself and other members of the group during the search for food. In this situation number of memetic evolution steps defined firstly, then ideas are passed among memeplexes in a shuffling process. A shuffling strategy allows to move toward a locality to a globality optimum. Both of the local search and shuffling process continues until the required convergence criteria are achieved. In essence, this algorithm

combines the benefits of the local search tool of the PSO [45] and mixing information from Parallel Local Searches to move toward a global solution [46]. PSO is an evolutionary optimization method which is based on the metaphor of social interaction and communication such as bird flocking and fish schooling.

In the SFLA, the frog position is the candidate solution. The initial population of F virtual frogs are randomly generated within the feasible search space at the beginning of the algorithm, so each frog is correlated with a position vector, X _i = [x _i1, x _i2, …, x _iN], where N is the number of decision variables. The frogs are sorted in a descending order according to their fitness. As illustrated in Fig. 3, in this procedure, each frog moves to each memeplex, so, the first frog moves to the first memeplex, the second frog moves to the second memeplex and the mth frog moves to the mth memeplex, then (m + 1) ^th frog goes back to the first memeplex and so on [3]. Therefore, the whole population is divided into m memeplexes, each including n frogs (F = m × n).

Fig.3

Movement of frogs.

In each memeplex, the frogs position with the best and worst fitnesses are represented as X _b and X _w, respectively. Moreover, the frog position with the global best fitness is recorded as X _g [27].

The local exploration is implemented in each submemeplex, thus, a memetic evolution is applied to improve only the worst frog in each cycle and changes its position by leaping action; the leaping step is computed by Equation 23 and the worst frog’s new position is determined by Equation 24. $\begin{matrix} Step (i + 1) \\ = {\begin{matrix} min {int [{Rand}^{i} (X_{b}^{i} - X_{w}^{i})], {Step}_{max}}, for positive step \\ max {int [{Rand}^{i} (X_{b}^{i} - X_{w}^{i})], - {Step}_{max}}, for negative step \end{matrix} \end{matrix}$ (23) $X_{w}^{i + 1} = X_{w}^{i} + Step (i + 1)$ (24)

Where step (i + 1) denotes the updated step size of the shuffled frog-leaping, Int means rounding, step _max is the allowed maximum step size to be adopted by a frog after being affected, rand is a random number in the range [0,1], i is the evolution generation or iteration number.

After updating, if the solution $X_{w}^{i + 1}$ is better than the original worst performance solution PW in the submemplex, $X_{w}^{i}$ will be replaced by $X_{w}^{i + 1}$ . Otherwise, use $X_{g}^{i}$ instead of $X_{b}^{i}$ to carry out the updating strategy (23) and (24) repeatedly. If there is still no improvement, randomly generate a new feasible solution to replace $X_{w}^{i}$ with Equation 25. The calculations continue for a specific number of iterations. Then, all frogs are shuffled for global information exchange. The shuffling process and local exploration continue until a pre-specified convergence criterion is satisfied. $X_{w}^{i + 1} = {Bound}_{Min} + int [{Bound}_{Max} - {Bound}_{Min}]$ (25)

Where Bound _Max and Bound _Min are the maximum and minimum boundaries of frogs’ feasible location, respectively.

5.2 Intelligent water drops (IWD)

The IWD algorithm is a population based optimization algorithm which, mimics the dynamic process of river systems and the actions that water drops do in the rivers. This algorithm is inspired by the observation of natural water flow in the rivers formed by a swarm of water drops [34].

Depending on the force of the gravity and terrain covered, the swarm of water drops fined their own way to the lakes or oceans. However, being blocked by different kinds of obstacles and constraints, there exist lots of twists and turns in the real path of the river. During this movement, the water drops have to face with two important parameters such the amount of soil it carries and the velocity at which it movies; the more the velocity, the greater the amount of soil carried. So, the path with least amounts of soil will be more likely to be used by other water drops. In this situation, by mimicking the features of water drops and obstacles of the environment, the IWD algorithm uses a population of water drops to construct paths and obtain the optimal or near-optimal path among all these paths over time.

The steps of IWD algorithm scheme in each iteration might be outlined as follows.

Step 1. Graph representation of search space: every water drop finds an optimal path by traversing the search space of the given problem and then modifies the environment in which it is flowing. First of all, set t = 0 and the graph of the problem is given to the algorithm, then, search for showing construction that is suitable for IWD to seek given problem solutions. The searching space of the problem is shown in Fig. 4. All possible capacity values in m location are represented by the states in the searching space in correspondence to m stage.

Fig.4

Searching space of the problem.

Step 2. Initialization of static parameters: in this step, different static parameters values of algorithm will be set. In this context, the best path is denoted by TS _B which is still unknown and its objective function value is initially set to infinity (q (TS _B) = ∞). Number of iterations and number of IWDs (NIWD) depend on the problem, determined by the user with a positive number. Global update parameter is set with positive number between zero and one. In addition, the initial soil on each edge of graph is denoted by the constant InitSoil such that the soil of the edge between every two nodes i and j is set by soil (i, j) = InitSoil. Initial velocity variable for each IWD with InitVel value is initialized. Both parameters InitSoil and InitVel are user selected and they should be tuned experimentally for the application. Here, InitSoil = 10000 and InitVel = 200.

Step 3. Initialization of dynamic parameters: the velocity of each IWD is set to InitVel whereas the initial soil of each IWD is set to zero.

Step 4. Spread the IWD randomly on edges in search space as their first visited nodes.

Step 5. For each IWD, using roulette wheel mechanism select randomly the visited node to include the nodes just visited.

Step 6. Repeat steps following step (a–d) for those IWD with partial solutions.

a. for each IWD, select randomly the next node to build a solution (path) which does not violate any constraints of the problem and is not in the visited node states, V _C (IWD), as it will be described according to the probability $P_{i}^{I} WD (j) :$ $P_{i}^{IWD} (j) = \frac{f (soil (i, j))}{\sum_{K \notin V_{c} (IWD)} f (soil (i, n))}$ (26)Such that: $f (soil (i, j)) = \frac{1}{ε + g (soil (i, j))}$ (27)

$\begin{matrix} g (soil (i, j)) \\ = {\begin{matrix} soil (i, j) & if \min_{l \notin V_{C} (IWD)} soil (i, l) \geq 0 \\ soil (i, j) & - \min_{l \notin V_{C} (IWD)} soil (i, l); else \end{matrix} \end{matrix}$ (28)

Then add the newly visited node j to the state V _C (IWD) . Where, ε is a small positive number to prevent a possible division by zero in the function f (.) and soil (i, j) refers to the amount of soil within the local path between nodes i and j.

b. as illustratd in Equation (29), the velocity of the IWD denoted by v _IWD (t) is updated by the amount of soil (soil (i, j)) between the two locations i and j. $v_{IWD} (t + 1) = v_{IWD} (t) + \partial / (σ + δ {soil}^{2} (i, j))$ (29)

Where v _IWD (t + 1) is the updated velocity of the IWD, ∂, σ and δ are IWD velocity updating parameters which set by 1, 0.01 and 1, respectively.

c. The amount of decreased soil from each edge depends on velocity of IWDs and heuristic functions according to following equations. $Δ soil (i, j) = \frac{α}{β + γ . {time}^{2} (i, j, v_{IWD} (t + 1))}$ (30)Such that: $time (i, j, v_{IWD} (t + 1)) = \frac{HUD (j)}{(v_{IWD} (t + 1)}$ (31)

Where the heuristic undesirability HUD (j) is defined appropriated for the given problem, α, β and γ are IWD soil updating parameters which set by 1, 0.01 and 1, respectively.

d. for each IWD, update the soil (i, j) of the path node i to node j traversed by that IWD and also update the soil that the IWD carries soil _IWD, by: $soil (i, j) = (1 - ρ_{n}) . soil (i, j) - ρ_{n} Δ soil (i, j)$ (32) ${soil}_{IWD} = {soil}_{IWD} + Δ soil (i, j)$ (33)

Where ρ _n is the local soil updating parameter, which is a small positive number less than one, is set as ρ _n = 0.9.

Step 7. Find the iteration best solution, S _B, from all the solutions, S _IWD, that can be calculated by, $S_{B} = \arg \underset{\forall S_{IWD}}{max q} (S_{IWD})$ (34)

Where function q(.) gives the quality of the solution.

Step 8. At this step, soil of traveled edges by the best IWD of the current iteration to be updated, according to Equation (35).

$\begin{matrix} soil (i, j) = (1 + ρ_{IWD}) . soil (i, j) \\ - ρ_{IWD} \frac{1}{N_{B} - 1} {soil}_{B}^{IWD} \forall (i, j) \in S_{B} \end{matrix}$ (35)

Where, N _B is the number of nodes in the solution S _B, ρ _IWD is the global soil updating parameter, which is chosen from [0, 1] which is set as ρ _IWD = 0.9.

Step 9. Update the total best solution TS _B. Using the current iteration best solution S _B. by, ${TS}_{B} = {\begin{matrix} {TS}_{B} & q ({TS}_{B}) \geq q (S_{B}) \\ S_{B} & otherwise \end{matrix}$ (36)

Step 10. If one of the stopping criteria is satisfied then stop, else go to step 2, so at the end, the algorithm stops with the total-best solution TS _B.

5.3 SFLA-IWD algorithm

As illustrated in Section 5.1 (SFLA algorithm), when evaluating worst frog position in each cycle (using (23), (24)) and changing its position by leaping action, does not lead to a better frog than the worst frog, it will be replaced with a new randomly generated frog. This replacement may cause a worst frog than the current frog. So, it is inferred that, behind the benefit of SFLA (fast convergence speed), there is a gap in this algorithm when it is unable to find an improved set of variables. In the other word, In the SFLA, updating of worst fitness is limited in the line segment between its current position and the position of best fitness, and the Xw could not jump over the Xb. Thus in SFLA local search space is restricted during each memplex evolution procedure and best frog has a less chance of evolution. This may lead to the improper learning process and results in prematured convergence. Because of this, the algorithm may be trapped to local optimum easily.

To prevent such problem and increase the capability of local search of SFLA, an auxiliary optimization method is invoked to generate a new set of variables. In this context, instead of generating a random set of variables, IWD algorithm is employed, so, the worst frog of current memeplex will be replaced with the output of IWD algorithm. Figure 5 illustrates the flowchart of the proposed algorithm. In this situation proposed algorithm iteratively updates position of the frog until user-defined number of generations are generated and last converges to the optimal solution.

Fig.5

Flowchart of the proposed algorithm.

6 Simulation results and discussion

The model proposed in Section 4 has been tested on a modified version of distribution system consist of three IEEE 33-bus radial distribution system given in [47] (see Fig. 6). For each aria, in different places, three kind of renewable energies (PV, wind and PV+wind) are considered as a DG capacity. Total active and reactive loads of each aria are same which considered, 3.72 MW and 2.30 MVar, respectively. The capacity of the system is S_base = 100 MVA and V_base = 12.66 kV. In this situation, the numerical results are organized and the MG model is tested with and without consideration of proposed algorithm.

Fig.6

Configuration of the MG under study.

General input data

It should be noted that the purpose of 55-h scheduling is to evaluate the performance of the proposed method in each areas, this planning horizon ranges from 0:00 h of a given day up to 7.00 h of the second day. Nevertheless, in practical analysis, the method can be extended to weekly, monthly or yearly analysis with similar method. In fact, there are no limitations or changes in the problem and solution structure by extending the time window of the analysis. The estimated hourly load demand of the test system for a 55-h period is shown in Fig. 7.

Fig.7

Hourly load demand.

Two renewable technologies are also considered: wind turbines and photovoltaic (PV) cells. It is worth mentioning that the proposed formulation is general enough to straightforwardly include other renewable technologies such as biomass or CSP (concentrating solar power) units. Observe that, in this study, the considered renewable sources constitute the 45.9% of the total installed capacity. The offering prices of wind and PV units are assumed to be equal to zero. In all scenarios, PV and WT available outputs are fully exploited.

This is a forcing and encouraging policy for supporting WT and PV since these devices have to generate after the first time capital investment. It is assumed that the wind speed and solar irradiance forecasts for areas of each aggregators are different from the ones for areas of the other aggregators.

The hourly wind speeds information for each area is shown in Fig. 8. All wind turbines installed in the test system are of the same type and of 1 MW, with cut-in speed of 5 m/s and cut-out speed of 25 m/s with nominal speed of 16 m/s. eleven 50 kW PV systems are installed in the test system; each of them is composed of 5*10 kW solar PV panels with 22.8% [48]. The average hourly solar irradiance is shown in Fig. 9.

Fig.8

Hourly wind speeds information.

Fig.9

Average hourly solar irradiance.

For this study, each PEV has an actual energy consumption of 0.18 kW/km and is equipped with a 22 kWh battery pack according to Yoshita PEV [49] (see Fig. 10). This vehicle has been built by our team and currently is under development. The efficiencies of the charger and the battery are 0.964 and 0.93, respectively. Thus, the efficiencies of charging and discharging processes are both considered to be 0.9. The charging voltage and the peak power transfer rate values depend on the technical characteristics of the charge coupler. For simplicity, the study assumes that PEVs are charged under a charging voltage of 230 V and a peak power transfer rate of 7.2 kW. The daily distance driven by PEVs is characterized using the expected daily driving distance from Yoshita PEV (see Ref. [49]). Also, the other driving patterns (expecting from rational behavior of customers) consists of trip duration of each type of customer, SOC, size and start and end time of their trip were extracted from statistical analysis in a real town, which represented in Table 1.

Fig.10

Yoshita PEV.

Table 1

PEVs movement information

Area	Number of PEV	Available Time	Primary SOC (%) in the first hour of the work day
1	120	6:00–13:00 &	10%	SOC < 50
		18:00–23:00	30%	50 < SOC < 80
			30%	80 < SOC < 90
			20%	90 < SOC < 100
			10%	SOC = 100
2	80	6:00–24:00	10%	SOC < 50
			30%	50 < SOC < 80
			30%	80 < SOC < 90
			20%	90 < SOC < 100
			10%	SOC = 100
3	160	9:00–14:00 &	15%	SOC < 40
		17:00:24:00	20%	40 < SOC < 70
			40%	70 < SOC < 90
			20%	90 < SOC < 100
			5%	SOC = 100

The PEVs are configured as an agglomeration of several distributed parking sites within a large area, which, their locations are determined by various scenarios. The stations are equipped with two charging plat-forms –400 V/32A–24 kW-3 phase for normal (2:30 h) charging, and 400 V/63A–43kW-3 phase for fast (25 min) charging.

Comparison and discussion

In this paper, in order to minimize both energy loss and operating cost of charging the PEVs, a new hybrid algorithm for finding the location and capacity of PEVs was proposed. In this way, the load profiles of the network at each loading point are obtained by integrating the loads of customer and the connected PHEVs using MATLAB software. Then, general algebraic modeling system tool is used for solving the optimization problems. Six proposed scenarios are considered for simulations conducted in this investigation corresponding to different charging strategies of PEVs, along with an extra reference scenario without PEV. In this way, the MG under study is analyzed according to the flowchart as shown in Fig. 2 which identified as scenario 3. In order to verify proposed algorithm, the significance of the paper approach against conventional algorithms (genetic algorithm (GA), IWD optimization method and SFLA) can be discussed as following scenarios. It must be noted than in scenario 2–6 all PHEVs operating both in G2V and in V2G modes.

Scenario 1: No PHEV connected to the network.

Scenario 2: The scenario with unmanaged charging of PEVs.

Scenario 3: The scenario with managed charging of PEVs base on proposed hybrid optimization (population size: IWD = 80, SFLA = 110).

Scenario 4: The scenario based on managed charging of PHEVs using IWD optimization method (population size: 110).

Scenario 5: The scenario based on managed charging of PHEVs using SFLA optimization method (population size: 130).

Scenario 6: The scenario based on managed charging of PHEVs using GA optimization method (population size: 60, Binary mutation, normalized geometric selection, cross over: Simple Xover, Algorithm termination: Maximum number of generation (60)).

Since the main aim of the proposed optimization is to lower the total loss of system, As a result, scenario 3 (PEVs operating both in G2V and in V2G modes together which they are sited and sized with proposed optimization method) must represent the most favorable charging strategy of PEVs. In this situation, the scenario which modeling charge/discharge program of PEVs for each area is extracted (see Fig. 11). It must be considered that, all PEVs are forced to be totally charged at the end of the charging period defined for each PEVs. According to the second part of the objective function (cost minimization objective), it is obvious that EVs discharging when power demand is high. Also, this proses is carried out during the high electricity prices hours. On the other hand, charging them back when the peak is over during the low electricity prices hours. Furthermore as shown in Fig. 12, charging and discharging amounts of each PEVs are related to consumption growth. It is obvious that renewables should be utilized as much as possible.

Fig.11

Modeling charge/discharge program of PEVs.

Fig.12

Relation between charging and discharging amounts of each PEVs and consumption growth.

Figure 13 shows the average active power of all 33 buses of area 1 for the proposed scenarios along with scenarios 2, 5 and 6 during the time under study.

Fig.13

Average active power: a) scenario 2: unmanaged charging of PEVs, b) scenario 3: proposed algorithm, c) scenario 6: genetic algorithm, d) scnario 5: shuffled frog leaping algorithm.

From this figure, it can be observed that when EVs are in charging mode on distribution substation without any management, load profile belonging to scenario 2 confront the greatest peak as compared to the other scenarios and can leads to the greater evening peak. As PEVs can operate both in G2V and in V2G modes in scenarios 3–6, active power value during peak hours is lower as compared to scenario 1.

According to Fig. 13(b), proposed algorithm compared with other smart charging strategies (scenarios 2–6), leads to a decrease in active power demand in peak hours, so leads to an increase in demand in off-peak hours. Also in scenario 3, the active power of all substation is lower compared to the all scenarios.

In other words, managed charging and discharging of PHEVs is one of the DR approaches which can flatten the load profile out and minimize network energy loss.

To investigate how energy loss quantities may be affected depending on charging of PHEVs, the calculation is further performed for different size and places of PHEVs which determine by each scenarios. The network energy loss for the time under study, without presence of PEVs is equal to 121.12 KWh.

According to Table 2, it is discernible that the energy loss resulting from network operation over the time under study is within the range of 93.70–127.14 MWh for various size and places of PEVs which are determined with each scenarios. The most discernible point in Table 2 is that without smart charging of PHEVs, i.e., scenario 2, there is a unpredictable increase in the network energy loss value, as compared to other scenarios. This increase is in proportion to PEVs location and size.

Table 2

Comparison of simulation results of 33-bus system

Scenario	Item	Area1	Area2	Area3
Scenario 1: no PHEV connected to the network	PEVs parking location	–	–	–
	Total PEVs size	–	–	–
	Real power loss (kW)	121.26	114.96	127.14
	% Real power loss reduction	–	–	–
	V_min (p.u)	0.9134	0.9216	0.9169
	Total PEVs charging cost	–	–	–
Scenario 2: unmanaged charging of PEVs	PEVs parking location	uncertain	uncertain	uncertain
	Total PEVs size (KW)	1944	1296	2592
	Real power loss (kW)	114.1	108.40	119.51
	% Real power loss reduction	5.9	5.7	6
	V_min (p.u)	0.9234	0.9214	0.9287
	Total PEVs charging cost ($)	7935	6710	8560
Scenario 3: proposed algorithm	PEVs parking location	13, 16, 32	18, 30, 32	11, 29, 30
	Total PEVs size (KW)	1944	1296	2592
	Real power loss (kW)	98.05	93.70	101.73
	% Real power loss reduction	19.14	18.49	19.98
	V_min (p.u)	0.9725	0.9695	0.9785
	Total PEVs charging cost ($)	6457	5940	7125
Scenario 4: intelligent water drops algorithm	PEVs parking location	11, 18, 14	11, 13, 30	14, 16, 29
	Total PEVs size (KW)	1944	1296	2592
	Real power loss (kW)	105.61	100.36	110.48
	% Real power loss reduction	12.9	12.7	13.1
	V_min (p.u)	0.9436	0.9382	0.9475
	Total PEVs charging cost($)	7230	6342	7996
Scenario 5: shuffled frog leaping algorithm	PEVs parking location	9, 18, 29	9, 11, 33	9, 14, 29
	Total PEVs size (KW)	1944	1296	2592
	Real power loss (kW)	106.83	102.33	111.5
	% Real power loss reduction	11.9	10.98	12.3
	V_min (p.u)	0.9412	0.9324	0.9435
	Total PEVs charging cost ($)	7145	6240	7925
Scenario 6: genetic algorithm	PEVs parking location	8, 29, 32	8, 11, 30	8, 13, 32
	Total PEVs size (KW)	1944	1296	2592
	Real power loss (kW)	103.13	98.46	107.57
	% Real power loss reduction	14.95	14.35	15.39
	V_min (p.u)	0.9642	0.9598	0.9684
	Total PEVs charging cost ($)	6951	6445	7829

It should be noted that scenario 3 seems to have the most advantageous impact on the network energy loss reduction. In fact, as illustrated in Table 2 by comparing the information relating to scenario 3, with other scenario, it can be inferred that smart managing of PEVs location and size with proposed algorithm, has significant effect on MG energy loss (network energy loss reduces down to 19.98 percent).

Table 2 compares the information calculated by all scenarios. This table shows that the proposed method provided the lowest (best) values of Real power loss in all areas. As a result, the energy loss reduction is estimated to be in the range of 0%–19.98% for the network under study (see Fig. 14). For the best locations and size of PEVs which are possible with proposed algorithm, network energy loss can be reduced up to 19.98%. In compared to scenario 1, this reduction stems from the fact that active power in peak hours and over a day with best location and size can be injected by PEVs in smart charging scenarios. Similar results can be acquired by applying the proposed methodology to any given network, if the required data are available. Comparison between proposed hybrid optimization with some other optimization strategy in field of real power loss and total PEVs charging cost, are also shown in Fig. 14.

Fig.14

Comparison between proposed hybrid optimization with some other optimization strategy.

The hypervolume indicator was originally proposed and employed in Ref. [50] to numerically compare the outcomes of different multi objective optimization problem. In this way, to obtain better insight on how proposed algorithm converges to the pareto optimal front, we run each algorithm for a maximum of 1000 fitness evaluations and calculate the hypervolume values of the pareto approximation sets in each generation.

To visualize the convergence speed, we show the results in Fig. 15, where the horizontal axis denotes the number of fitness evaluations and the vertical axis records the hypervolume values with different algorithms. It is obvious from Fig. 15 that proposed algorithm is superior to the other three algorithms in that it quickly converges to reach the maximum hypervolume values.

Fig.15

Hypervolume values of the algorithms over 1000 fitness function evaluations.

In other words, proposed algorithm is more computationally efficient to reach pareto approximation sets with a certain quality compared with other algorithms for a constant number of fitness evaluations. These results indicate the benefits of proposed optimization method as an evolutionary scheme compared with other conventional optimization methods.

7 Conclusion

The MG concept has been gaining more attention worldwide, particularly for the distribution system, so it is necessary to improve overall system efficiency, power quality, and energy surety for critical loads. In this situation, this paper proposed the novel optimization method using hybrid SFLA and IWD optimization for efficiency maximization in smart MG considering SOH of PEV energy storage system. Behind the benefit of SFLA (fast convergence speed), there is a gap in this algorithm when it is unable to find an improved set of variables. To prevent such problem and increase the capability of local search of SFLA, an auxiliary optimization method is invoked to generate a new set of variables. In this context, instead of generating a random set of variables, IWD algorithm is employed. The purpose of the MG under study, consists of PV panels, WTs, PEV (which Li-ion battery pack is used as ESS) and DC-DC converters. The results showed that the proposed optimization method compared to other methods, can effectively improve the performance of MG power control and follow a desired output power value in accordance with the renewable energy scheduling instruction with a smooth power for the grid.

References

Lasseter

R.H.

and Piagi

, Extended microgrid using (DER) distributed energy resources, in Proc IEEE PES Gen Meeting, Tampa, FL, USA, 2007, pp. 1–5.

Kim

, et al., Cooperative control strategy of energy storage system and microsources for stabilizing the microgrid during islanded operation, IEEE Trans Power Electron 25(12) (2010), 3037–3048.

Emadi

, Lee

Y.J.

and Rajashekara

, Power electronics and motor drives in electric, hybrid electric, and plug-in hybrid electric vehicles, IEEE Trans Power Electron 55(6) (2008), 2237–2245.

Quinn

, Zimmerle

and T.H.

, An evaluation of state-of-charge limitations and actuation signal energy content on plug-in hybrid electric vehicle, vehicle-to-grid reliability, and economics, IEEE Transaction on Smart Grid 3(1) (2012), 483–491.

Kempton

and Tomic

, Vehicle-to-grid power fundamentals: Calculating capacity and net revenue, Journal of Power Sources 144(1) (2005), 268–279.

Damiano

, Gatto

, Marongiu

, Porru

and Serpi

, Vehicleto- grid technology: State-of-the-art and future scenarios, Journal of Energy and Power Engineering 8(1) (2014), 152–165.

Lopes

J.A.P.

, Almeida

P.M.R.

and Soares

F.J.

, Identifying management procedures to deal with connection of electric vehicles in the grid, IEEE Power Tech, Romania, 2009.

Tae-Kyung

, Bareket

, Gordon

and Filipi

Z.S.

, Stochastic modeling for studies of real-world PHEV usage: Driving schedule and daily temporal distributions, IEEE Trans Veh Technol 61(4) (2012), 1493–1502.

Grahn

, Munkhammar

, Widen

, Alvehag

and Soder

, PHEV home-charging model based on residential activity patterns, IEEE Trans Power Syst 28(3) (2013), 2507–2515.

10.

Zhao

, Wen

and Dong

, Optimal dispatch of electric vehicles and wind power using enhanced particle swarm optimization, IEEE Trans Ind Informat 8(4) (2012), 889–899.

11.

, Su

, Chen

and Bak-Jensen

, Optimal operation of plug-in electric vehicles in power systems with high wind power penetrations, IEEE Trans Sustain Energy 4(3) (2013), 577–585.

12.

Caramanis

and Foster

J.M.

, Management of electric vehicle charging to mitigate renewable generation intermittency and distribution network congestion, In: Joint 48th IEEE Conference on Decision and Control, 2009.

13.

Pieltain Fernández

, Román

T.G.S.

, Cossent

, Domingo

C.M.

and Friìas

, Assessment of the impact of plug-in electric vehicles on distribution networks, IEEE Trans Power Syst 26(1) (2011), 206–213.

14.

Sekyung

, Soohee

and Sezaki

, Development of an optimal vehicle-to-grid aggregator for frequency regulation, IEEE Trans Smart Grid 1(1) (2010), 65–72.

15.

Shafiee

, Fotuhi-Firuzabad

and Rastegar

, Investigating the impacts of plug-in hybrid electric vehicles on power distribution systems, IEEE Trans Smart Grid 4(3) (2013), 1351–1360.

16.

Han

, Han

and Sezaki

, Development of an optimal vehicle-to-grid aggregator for frequency regulation, IEEE Trans Smart Grid 2010 1(1) (2010), 65–72.

17.

Rotering

and Ilic

, Optimal charge control of plug-in hybrid electric vehicles in deregulated electricity markets, IEEE Trans Power Syst 26 (2011), 1021–1029.

18.

Kempton

and Tomic

, Vehicle to grid power implementation: From stabilizing the grid to supporting large scale renewable energy, Journal of Power Sources 144 (2005), 280–294.

19.

Honarmand

, Zakariazadeh

and Jadid

, Optimal scheduling of electric vehicles in an intelligent parking lot considering vehicle-to-grid concept and battery condition, Jornal of Energy 65 (2014), 572–579.

20.

Galus

M.D.

, Koch

and Andersson

, Provision of load frequency control by phevs, controllable loads, and a cogeneration unit, IEEE Trans of Ind Elec 58 (2011), 4568–4582.

21.

Geng

, Mills

J.K.

and Sun

, Two-stage charging strategy for plug-in electric vehicles at the residential transformer level, IEEE Trans of Smart Grid 4 (2013), 1442–1452.

22.

Kennel

and Gorges

, Energy management for smart grids with electric vehicles based on hierarchical MPC, IEEE Trans Ind Inf 9(3) (2013), 1528–1537.

23.

, Yang

, Bao

and Yan

, Coordinated energy dispatching in microgrid with wind power generation and plug-in electric vehicles, IEEE Trans Smart Grid 4(3) (2013), 1453–1463.

24.

Pahasa

and Ngamroo

, Coordinated control of wind turbine blade pitch angle and PHEVs using MPCs for load frequency control of microgrid, IEEE System Journal 10(1) (2016), 97–105.

25.

Khorramdel

, Khorramdel

, Aghaei

, Heidari

and Agelidis

V.G.

, Voltage security considerations in optimal operation of BEVs/PHEVs integrated microgrids, IEEE Trans Smart Grid 6(4) (2015), 1575–1587.

26.

Afrakhte

, Bayat

and Bayat

, Energy management system for smart house with multi-sources using PI-CA controller, IEEE Conference on Renewable Energy & Distributed Generation (ICREDG), 2017.

27.

Eusuff

and Lansey

, Optimization of water distribution network design using the shuffled frog leaping algorithm, Journal of Water Resources Planning and Management 129(3) (2003), 210–225.

28.

Hasanien

H.M.

, Shuffled frog leaping algorithm-based static synchronous compensator for transient stability improvement of a gridconnected wind farm, IET Renew Power Gener 8(6) (2014), 722–730.

29.

Ebrahimi

, Hosseinian

and Gharehpetian

, Unit commitment problem solution using shuffled frog leaping algorithm, IEEE Trans P Syst 26 (2011), 573–581.

30.

Alimardani

, Mazaheri

, Abdi

and Hosseinian

S.H.

, Modified shuffled frog-leaping algorithm in company with neural networks for harmonic distortion minimization in real-time control applications of programmed pulse-width modulation inverters, IET Power Electron 4(8) (2011), 943–950.

31.

Bijami

, Askari

and Farsangi

M.M.

, Design of stabilizing signals for power system damping using generalized predictive control optimized by a new hybrid shuffled frog leaping algorithm, IET Gener Transmiss Distrib 6(10) (2012), 1036–1045.

32.

Goroohi Sardou

, Banejad

, Hooshmand

and Dastfan

, Modified shuffled frog leaping algorithm for optimal switch placement in distribution automation system using a multi-objective fuzzy approach, IET Gener Transmiss Distrib 6(6) (2012), 493–502.

33.

Khorsandi

, Alimardani

, Vahidi

and Hosseinian

S.H.

, Hybrid shuffled frog leaping algorithm and nelder-mead simplex search for optimal reactive power dispatch, IET Gener Transmiss Distrib 5(2) (2011), 249–256.

34.

Shah-Hosseini

, The intelligent water drops algorithm: A nature inspired swarm-based optimization algorithm, Int Bio-Inspired Comput 1 (2010), 71–79.

35.

Rand

D.A.J.

, Woods

and Dell

R.M.

, Batteries for Electric Vehicles, Research Studies Ltd, 1998, pp. 125–230.

36.

Pesaran

A.A.

, Vlahinos

and Burch

S.D.

, Thermal performance of EV and HEV battery modules and packs, in Proceedings of the 14th Internal Electric Vehicle Symposium, Orlando, Fla, USA, 1997.

37.

Rao

and Wang

, A review of power battery thermal energy management, Journal of Renewable and Sustainable Energy Reviews 15 (2011), 4554–4571.

38.

Rashid

M.H.

, Power Electronics: Circuits, Devices & Applications, Pearson Education, Edition 4, 2013.

39.

Billinton

and Bai

, Generating capacity adequacy associated with wind energy, IEEE Transactions on Energy Conversion 19(13) (2004), 641–646.

40.

Hiyama

, Kouzuma

and Imakubo

, Identification of optimal operating point of PV modules using neural network for real time maximum power tracking control, IEEE Trans Energy Convers 10 (1995), 360–367.

41.

Wasynzczuk

, Dynamic behavior of a class of photovoltaic power systems, IEEE Trans Power App Syst PAS-102(9) (1983), 3031–3037.

42.

Moradi

M.H.

, Tousi

S.M.R.

, Nemati

and Sadat Basir

and Shalavi

, A robust hybrid method for maximum power point tracking in photovoltaic systems, Journal of Solar Energy 94 (2013), 266–276.

43.

Han

and Chen

, A novel control strategy of wind turbine MPPT implementation for direct-drive PMSG wind generation imitation platform, IEEE 6th International P Elec and Motion Control Conference, 2009, pp. 2255–2259.

44.

Time of Use (TOU) price in Ontraio. [Online]. Available: http://www.ontario-hydro.com/current.

45.

Kennedy

and Eberhart

, Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks IEEE Service Center, NJ, 1995, pp. 1942–1948.

46.

Duan

Q.Y.

, Gupta

V.K.

and Sorooshian

, Shuffled complex evolution approach for effective and efficient global minimization, Journal of Optimization Theory and Applications 76(3) (1993), 501–521.

47.

Baran

M.E.

and Wu

F.F.

, Optimal sizing of capacitor placed on radial distribution systems, IEEE Trans Power Deliv 4(1) (1989), 735–743.

48.

Sunpower solar panels [Online], “”, https://us.sunpower.com/blog/2016/06/26/sunpower-solar-module-verified-241-percent-efficient/.

49.

Hatami

, Tousi

M.R.

, Bayat

and Bayat

, Power management strategy for hybrid vehicle using a three-port bidirectional DC-DC converter, 23rd Iranian Conference on Electrical Engineering (ICEE), 2015, pp. 1498–1503.

50.

Zitzler

and Thiele

, Multiobjective evolutionary algorithms, A comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation 3(4) (1999), 257–271.