ABSTRACT
Plug-in hybrid electric vehicle (PHEV) optimization is an emerging field which is increasingly being implemented in many charging infrastructures on a global scale� A near-comprehensive understanding of smart charging is crucial for the large participation of PHEVs� Proper charging can reassure PHEV users, lessen their “range anxiety,” and switch into the new green vehicle revolution with less carbon-dioxide emissions� In this chapter, the authors present swarm intelligence-based optimizations to optimize the smart charging of PHEVs in charging infrastructures�
Recent studies on renewable technologies for the transportation sector are gaining much attention among various research groups� As a result, PHEVs have a bright future because of their charge storage system and smart charging facilities from customary grid system� Several researchers have proven that significant reductions in greenhouse gas emissions and reduced dependence on oil could be accomplished by electrification of the transport sector (Caramanis & Foster, 2009)� Future transportation sector will depend much on the advancement of this emerging field of vehicle optimization� Indeed, the adoption of hybrid electric vehicles (HEVs) has brought significant market success over the past decade� Vehicles can be classified into three groups: internal combustion engine vehicles (ICEVs), HEVs, and all-electric vehicles (AEVs) (Tie & Tan, 2013)� PHEVs which have been very recently introduced promise to boost up the overall fuel efficiency by holding a higher-capacity battery system, which can be directly charged from conventional power grid system that helps the vehicles to operate continuously in “all-electric-range” (AER)� AEVs are a kind of transport that uses electric power as the only source to run the system� PHEVs with a connection to the smart grid can own all of these strategies� Hence, the widely extended adoption of PHEVs might play a significant role in the alternative energy integration into traditional grid systems (Lund & Kempton, 2008)� There is a need for efficient mechanisms and algorithms for smart grid technologies in order to solve highly diverse problems such as energy management, cost reduction, efficient charging station, and so on, with different objectives and system constraints (Hota, Juvvanapudi, & Bajpai, 2014)�
According to statistics of the Electric Power Research Institute (EPRI), about 62% of the entire US vehicles will comprise PHEVs within the year 2050 (Soares et al�, 2013)� Moreover, there is an increasing demand to implement this technology
on the electric grid system� Large numbers of PHEVs have the capability to make threats to the stability of the power system� For example, in order to avoid disturbance when several thousand PHEVs are introduced into the system over a small period, the load on the power grid will need to be managed very carefully� One of the main targets is to facilitate proper communication between the power grid and the PHEV� For the maximization of customer contentment and minimization of burdens on the grid, a complicated control appliance will need to be addressed in order to govern multiple battery loads from a number of PHEVs properly (Su & Chow, 2012a)� The total demand pattern will also have an important impact on the electricity production due to differences in the needs of the PHEVs parked in the deck at a certain time (Su & Chow, 2011)� Proper management can ensure strain minimization of the grid and enhance the transmission and generation of electric power supply� The control of PHEV charging depending on the locations can be classified into two groups: household charging and public charging� The proposed optimization focuses on the public charging station for plug-in vehicles because most of the PHEV charging is expected to take place in public charging locations (Su & Chow, 2012a)� Wide penetration of PHEVs in the market depends on a well-organized charging infrastructure� The power demand from this new load will put extra stress on the traditional power grid (Morrow, Karner, & Francfort, 2008)� As a result, a good number of PHEV charging stations with suitable facilities are essential to be built for recharging electric vehicles (EVs); for this some strategies have been proposed by the researchers (Mayfield, 2012)� Charging stations are needed to be built at workplaces, markets/shopping malls, and home� Boyle (2007) proposed the necessity of building new smart charging stations with effective communication among utilities along with substation control infrastructure in view of grid stability and proper energy utilization� Furthermore, ample energy storage, cost minimization, quality of services (QoS), and intelligent charging stations for optimal power are underway (Hess et al�, 2012)� In this wake, numerous techniques and methods were proposed for deployment of PHEV charging stations (Li, Sahinoglu, Tao, & Teo, 2010)�
One of the main targets is to facilitate proper interaction between the power grid and the PHEV� For the maximization of customer satisfaction and minimization of burdens on the grid, a complicated control mechanism will need to be addressed in order to govern multiple battery loads from a number of PHEVs appropriately (Su & Chow, 2012b)� Charging infrastructures are essential in order to facilitate the large-scale penetration of PHEVs� Different computational intelligence-based methods have been used by some researchers for charging station optimization of PHEVs� Most of them applied traditional methods which are needed to be improved further�
Swarm intelligence came from the mimicking of living colonies such as those of ants, birds, and fish in nature, which show unparalleled excellence in swarm behavior rather than being single in food seeking or nest building� Drawing inspiration from this, researchers designed many algorithms simulating colony living, such as ant colony algorithm, particle swarm optimization (PSO) algorithm, artificial bee colony (ABC) algorithm, and gravitational search algorithm, which show excellent performance in dealing with complex optimization problems (Jia-Zhao, Yu-Xiang, & Yin-Sheng, 2012)� The intrinsic characteristics of all the population-based
metaheuristic algorithms such as PSO and accelerated particle swarm optimization (APSO) are to maintain a good compromise between exploration and exploitation in order to solve the complex optimization problems (Rahman, Vasant, Singh, & Abdullah-Al-Wadud, 2014b)�
PSO is based on two fundamental disciplines: social science and computer science� In addition, PSO uses the swarm intelligence concept, which is the property of a system, whereby the collective behaviors of unsophisticated agents that are interacting locally with their environment create coherent global functional patterns� PSO algorithm has been successfully used for solving many problems related to power systems (del Valle, Venayagamoorthy, Mohagheghi, Hernandez, & Harley, 2008) such as voltage security, optimal power flow, power system operation and planning, dynamic security, power quality, unit commitment, reactive power control, capacitor placement, and optimizing controller parameters�
Moreover, APSO-based optimizations have already been studied by the researchers for optimal design of substation grounding grid, nonconvex optimization (Ganesan, Vasant, & Elamvazuthy, 2012), performance analysis of radar waveform, design of frame structures, dual channel speech enhancement (Prajna, Rao, Reddy, & Maheswari, 2014), synthesis gas production, and a faster path planner (Mohamed, Lee, Hsu, & Nath, 2012)�
The performance of a PHEV depends on proper consumption of electric power which is solely affected by the battery state-of-charge (SoC)� In PHEVs, a key parameter is the SoC of the battery as it is a measure of the amount of electrical energy stored in it� It is analogous to a fuel gauge on a conventional internal combustion (IC) car (Chiasson & Vairamohan, 2005)� SoC determination becomes a progressively dynamic issue in all the areas that include a battery� Previous operation policies made use of voltage limits only to guard the battery against deep discharge and overcharge� Currently, battery operation is changing to what could rather be called battery management than simply protection� For this improved battery control, the battery SoC is a key factor indeed (Piller, Perrin, & Jossen, 2001)�
A charging station is one way that the operator of an electrical power grid can adapt energy production to energy consumption, both of which can vary randomly over time� Basically, PHEVs in a charging station are charged during times when production exceeds consumption and are discharged at times when consumption exceeds production� There is a need of in-depth study on maximization of average SoC in order to facilitate intelligent energy allocation for PHEVs in a charging station�
The purpose of this chapter is to optimize SoC, with respect to total cost, charging time, and present SoC� Two swarm intelligence-based methods, PSO and APSO, were applied for solving the optimization problem�
The idea behind smart charging is to charge the vehicle when it is most favorable, which could be when electricity price and demand are lowest and when there is excess capacity (Su & Chow, 2012b)�
Suppose, there is a charging station with the capacity of total power P� Total N numbers of PHEVs need to be served in a day (24 h)� The proposed system should allow PHEVs to leave the charging station before their expected leaving time for making the system more effective� It is worth mentioning that each PHEV is regarded to be plugged-in to the charging station once� The main aim is to allocate power intelligently for each PHEV coming to the charging station� The SoC is the main parameter which needs to be maximized in order to allocate power efficiently� For this, the fitness function considered in this chapter is the maximization of average SoC and thus allocate energy for PHEVs at the next time step� The constraints considered are: charging time, present SoC, and price of the energy (Rahman, Vasant, Singh, & Abdullah-Al-Wadud, 2014a)�
The fitness function is defined as
∑= +J k w k kMax ( ) ( )SoC ( 1)i i
(3�1)
( )=w k f C k T k D k( ) ( ), ( ), ( )i i i ir, r, (3�2)
( )= − ⋅C k k C( ) 1 SoC ( )i i ir, (3�3)
where Cr,i(k) is the battery capacity (remaining) needed to be filled for i number of PHEVs at time step k; Ci is the battery capacity (rated) of the i number of PHEVs; remaining time for charging a particular PHEV at time step k is articulated as Tr,i(k); the price difference between the real-time energy price and the price that a specific customer at the i number of PHEV charger is willing to pay at time step k is presented by Di(k); wi(k) is the charging weighting term of the i number of PHEVs at time step k (a function of charging time, present SoC, and price of the energy); SoCi(k + 1) is the SoC of the i number of PHEVs at time step k + 1�
Here, the weighting term indicates a bonus proportional to the attributes of a specific PHEV� For example, if a PHEV has a lower initial SoC and less charging time (remaining), but the driver is willing to pay a higher price, the system will provide more power to this particular PHEV battery charger:
[ ]α + +w k C k D k T k( ) ( ) ( ) 1/ ( )i i i ir, r, (3�4) The charging current is also assumed to be constant over Δt�
( ) ( ) ( )+ − ⋅ = = ∆k k Q I k tSoC 1 SoC Capi i i i i (3�5)
( ) ( ) ( )+ = + ∆k k I k tSoC 1 SoC /Capi i i i(3�6) where the sample time Δt is defined by the charging station operators, and Ii(k) is the charging current over Δt�
The battery model is regarded as a capacitor circuit, where Ci is the capacitance of battery (Farad)� The model is defined as
⋅ =C dV
(3�7)
Therefore, over a small time interval, one can assume the change of voltage to be linear,
( ) ( )⋅ + − ∆ =C V k V k t I1 /i i i i (3�8)
( ) ( )+ − = ∆V k V k I t C1 /i i i i(3�9)
As the decision variable used here is the allocated power to the PHEVs, by replacing Ii(k) with Pi(k) the objective function finally becomes:
+ = + ∆
⋅ ⋅
∆ + +
k k P k t
C P k t C
V k V k SoC ( 1) SoC ( ) ( )
0.5 2 ( ) ( ) ( ) i i
(3�10)
Power obtained from the utility (Putility) and the maximum power (Pi,max) absorbed by a specific PHEV are the primary energy constraints being considered in this chapter� The overall charging efficiency of a particular charging station is described by η� From the system point of view, charging efficiency is supposed to be constant at any given time step� Maximum battery SoC limit for the i number of PHEVs is SoCi,max� When SoCi reaches the values close to SoCi,max, the i number of battery charger shifts to a standby mode� The SoC ramp rate is confined within limits by the constraint ΔSoCmax� The overall control system has changed the state when (i) system utility data updates; (ii) a new PHEV is plugged in; and (iii) time period Δt has periodically passed�
Table 3�1 shows all the objective function parameters that were tuned for performing the optimization� There are totally three kinds of parameters: fixed, variables, and constraints� Total charging time is fixed to 20 min and charging station efficiency is assumed to be 0�9� The values are retrieved from various literatures (Hota et al�, 2014)� Moreover, SoC is in the range of 0�2-0�8 (Chang, 2013)�
PSO is an evolutionary computation technique which is proposed by Eberhart and Yuhui (2001)� The PSO is inspired from social behavior of birds flocking� It uses a number of particles (candidate solutions) which fly around in the search space to find the best solution� Meanwhile, they all look at the best particle (best solution) in their
paths� In other words, particles consider their own best solutions as well as the best solution that has been found so far�
A PSO system begins with a primary initial population of random individuals and signifies solutions of problems, to which are allocated random velocities� Each particle in a PSO should consider the current position, the current velocity, the distance to pbest, and the distance to gbest to modify its position� PSO was mathematically modeled as follows:
( ) ( )= ω + ⋅ ⋅ − + ⋅ ⋅ −+V v c x c xrand pbest rand gbestit it it it1 1 2 (3�11) = +
Generally speaking, the principal steps in PSO can be summarized as follows:
1� Generate a group of random solutions (particles) in the feasible region� Since we normally have very little information about the global optima, these particles are scattered over the search space as uniformly as possible�
2� Evaluate the distance between the new solution and the desired solution based on a fitness function�
3� Compare the fitness value at the current iteration with previous best, and update the individual best (pbest) and group best (gbest)�
4� Update the velocities of the particles� 5� Update the positions of the particles� 6� Repeat steps 2−5 until the maximum number of iterations or the minimum
error criteria are met�
TABLE 3.1 Parameter Settings of the Objective Function
Here vi t is the velocity of particle i at iteration t and w is a weighting function usually
used as follows:
ω = ω −
− ωw
max (3�13)
3.3.1.1 Selecting PSO Parameters Appropriate values for ωmin and wmax are 0�4 and 0�9� Appropriate value range for c1 and c2 is 1 to 2, but 2 is most appropriate in many cases� rand is a random number between 0 and 1, xi
t is the current position of particle i at iteration t, pbesti is the pbest of agent i at iteration t, and gbest is the best solution so far� The parameter settings for PSO are demonstrated in Table 3�2� Total size of the swarm is 100 and PSO inertia is taken as 0�9� PSO is also fairly immune to the size and nonlinear nature of the objective function being considered� The algorithm does not converge with less iterations, while more iterations increase computation complexity; so the maximum iterations are 100�
The main advantage of PSO is its simplicity, while being capable of delivering accurate results consistently� It is fast and also very flexible, being applicable to a wide range of problems, with limited computational requirements (Eberhart & Yuhui, 2001)� For these reasons, the present work focuses on metaheuristics optimization approaches, namely PSO applied in order to optimize the SoC for charging PHEVs�
The system initially has a population of random selective solutions� Each potential solution is called a particle� Each particle is given a random velocity and is flown through the problem space� The particles have memory and each particle keeps track of its previous best position (called the pbest) and its corresponding fitness� There exist a number of pbest for the respective particles in the swarm and the particle with greatest fitness is called the global best (gbest) of the swarm� The basic concept of the PSO technique lies in accelerating each particle toward its pbest and gbest locations, with a random weighted acceleration at each time step (Ganesan, Vasant, & Elamvazuthy, 2012)�
TABLE 3.2 PSO Parameter Settings
Algorithm 1: Particle Swarm Optimization
Step 1: Particle’s position and velocity initialization� Step 2: Particle’s velocity update� Step 3: Particle’s position update in two stages� Step 4: Particle’s best-known position “pbest” update� Step 5: Swarm’s best-known position “gbest” update� Step 6: Set new population = current population� Step 7: If the termination conditions are satisfied halt and print solutions, else
go to step 2�
In APSO, each member of the population is called a particle and the population is called a swarm� Starting with a randomly initialized population and moving in randomly chosen directions, each particle moves through the searching space and remembers the best earlier positions, velocity, and accelerations of itself and its neighbors� Particles of a swarm communicate good position, velocity, and acceleration to each other as well as dynamically adjust their own position, velocity, and acceleration derived from the best position of all particles� The next step starts when all particles have been shifted� Finally, all particles are inclined to fly toward better positions over the searching process until the swarm moves close to an optimum of the fitness function�
The standard PSO uses both the current global best and the pbest� The reason of using the pbest is mainly to increase the diversity in the quality solutions; however, this diversity can be simulated using some randomness� Subsequently, there is no convincing reason for using the pbest, unless the optimization problem of interest is multimodal and highly nonlinear�
It is worth pointing out that there is no need to deal with initialization of velocity vectors� Therefore, the APSO is much simpler� Compared with many PSO variants, the APSO uses only two parameters, and the mechanism is simple to understand� In APSO, for the optimization we have considered three parameters-position, velocity, and acceleration-for each swarm particle, whereas in PSO only two parameters-position and velocity-are considered for each particle� Here in this algorithm the swarms are in the random sequence and rand positions are generated� From these positions, the velocity and acceleration are generated�
The outline of APSO is given below:
Algorithm 2: Accelerated Particle Swarm Optimization
Step 1: Generation of primary population� Step 2: Random initialization of initial position and velocity� Step 3: Evaluate particle velocity� Step 4: Evaluate particle position in single step�
Step 5: Actual position of each particle� Step 6: Set new population = current population� Step 7: If the termination conditions are satisfied halt and print solutions, else
go to step 2�
A simplified version which could accelerate the convergence of the algorithm is to use the global best only� Thus, in the APSO, the velocity vector is generated by a simpler formula where randn is drawn from (0,1) to replace the second term� The update of the position is simply like Equation 3�15�
( )= + α ⋅ + β ⋅ −+V V t g xrandn( )it it it1 * (3�14) where randn is drawn from N (0,1) and the update of the position is like the standard PSO method� In order to increase the convergence even further, the update of the position can be written in a single step, as
= − β + β ⋅ + α+x x g r(1 )it it1 * (3�15)
3.3.2.1 Selecting APSO Parameters In our simulation we use
α = 0.7 t (3�16)
The typical values for this accelerated PSO are α ≈ 0�1-0�4 and β ≈ 0�1-0�7; however, α ≈ 0�2 and β ≈ 0�5 are recommended (Mohamed et al�, 2012)� In general, any evolutionary search algorithm shows improved performance with a relatively larger population� However, a very large population will cost more in terms of fitness function evaluations without producing significant improvements� In this simulation, the population size is set to 100� Total 30 independent runs were performed with 100 iterations each time� The parameter settings for APSO are demonstrated in Table 3�3�
TABLE 3.3 APSO Parameter Settings
The PSO and APSO algorithms were applied to find out global best fitness of the objective function� All the simulations were run on a Core™ i5-3470M CPU@ 3�20 GHz processor, 4�00 GB RAM and MATLAB R2013a�
Table 3�4 summarizes the simulation results for 50, 100, 500, and 1000 PHEVs, respectively, for finding the maximum fitness value of objective function J(k)� In order to evaluate the performance and show the efficiency and superiority of the proposed algorithm, we ran each scenario total 30 times� So it can be concluded that APSO outperformed PSO in terms of average best fitness� Starting from 50 numbers of PHEVs up to 1000 PHEVs, APSO shows better fitness value than PSO�
Table 3�5 shows the computational time requirement for APSO and PSO methods� As the number of PHEVs increased from 100 to 500 and 1000, APSO technique showed better result than standard PSO method in terms of computational time�
It can be apparently seen that although the algorithm has been set to run for maximum 100 iterations, the fitness value converges after 10 iterations and becomes stable� So, there is an early convergence which may cause the fitness function to trap into local minima� This can be avoided by increasing the size of swarm; hence the computational time will also be increased� As a result, a trade-off should be taken into consideration between the proper convergence and computational time (Rahman, Vasant, Singh, & Abdullah-Al-Wadud, 2014c)�
For solving this particular optimization problem, we faced some issues which will be discussed in this section�
TABLE 3.4 Average Best Fitness for APSO and PSO
TABLE 3.5 Computational Time for APSO and PSO
Although APSO needs more parameter tuning compared to standard PSO method, when the number of PHEVs increases, APSO takes less time than PSO� This characteristic makes APSO very efficient to solve this particular optimization problem� In APSO, the velocity vector ensures local exploitation capability� Moreover, the disadvantage of APSO is that it suffers early convergences in primary stages�
The advantages of PSO algorithm:
1� The algorithm is simple, with less adjustable parameters and being easy to implement�
2� The random initialization of population has strong global search ability, which is similar to genetic algorithm (GA)�
3� It uses the evaluation function to measure the individual searching speed� 4� It has strong scalability�
The disadvantages of PSO algorithm:
1� The algorithm cannot make full use of the feedback information in the system�
2� Its ability to solve combinatorial optimization problems is not strong� 3� It is easy for this algorithm to obtain local optimal solution�
The advantages of APSO algorithm:
1� Very efficient in terms of solving the particular fitness function� 2� The velocity vector is generated by a simpler formula� 3� Update of the position can be written in a single step� 4� Local exploitation ability to find good solutions�
The disadvantages of APSO algorithm:
1� Suffers from early convergence in the primary stages� 2� α and β parameters have effects on the algorithm performance and no fixed
value can ensure higher fitness values�
Finally, from Figure 3�1, we come to a conclusion that APSO performs better than PSO in terms of average best fitness for up to 1000 PHEVs�
For real-life glitches, the computational cost of a full evaluation of the fitness function can easily become the dominant computational cost� This computational cost can have the effect of making the time for the swarm to converge sluggishly� In this APSO method, the computational cost is moderate as compared to standard PSO method because of using acceleration factors, α and β�
Since an iterative method computes successive approximations to the solution of a system, stopping criteria are needed to determine when to stop the iteration� The maximum number of iterations was set to 100 for this optimization�
The robustness of the algorithm is tested in terms of the variability of the final solutions from each set of experiments� APSO algorithm is not too robust as the maximum, average, and minimum fitness values show different values for different number of PHEVs� Tuning the parameters such as α and β will improve the robustness of this optimization which is beyond the scope of this research�
Computational complexity refers to the different problems encountered in solving an optimization algorithm, such as premature convergence, high computational time, trapping in local optima, incapability of reaching global optima/minima, and so on� In our optimization problem, we encounter premature convergences� Moreover, if the size of swarm is very small, then the algorithm traps in local minima� In order to avoid this, we started our simulation using standard swarm size which is 100� In future, more swarm sizes will be considered in order to find a global solution�
This paragraph encapsulates the review results and suggests future directions of optimization techniques and procedures� The specific research field is relatively new and possible future perspectives have to be emphasized, so that new techniques can be realized�
Optimization techniques such as evolutionary algorithms, direct search methods, and other heuristic methods should be introduced in order to avoid the calculation of function derivatives� Multiobjective capability should also be provided for multicriteria optimization problems� The future optimization tools should be capable of performing parallel processing evaluations on the same computer by using modern multicore processor technology or to distribute the calculations to a cluster of computers� Such ability will substantially improve the simulation runtime� Advanced controlling mechanisms are necessary for allocating sufficient energy to a particular charging station in order to facilitate large-scale PHEV penetration in upcoming years� The future optimization tools should have the capability of stable convergence and thus provide a good solution to the desired fitness functions� Exploration and exploitation of the search space are essential in order to get desired solution within acceptable computation time� Finally, optimization of charging station needs proper assortment of available resources as well as efficient available technique implementation� Possible characteristics of the future optimization tools are given below�
3.7.1.1 Ant Colony Optimization (ACO) Ant colony optimization (ACO), introduced by Dorigo in his doctoral dissertation, is a class of optimization algorithms modeled on the actions of an ant colony� ACO is a probabilistic technique useful in problems that deal with finding better paths through graphs� Artificial “ants” simulation agents locate optimal solutions by moving through a parameter space representing all possible solutions (Dorigo, 2006)� Natural ants lay down pheromones directing each other to resources while exploring their environment� The simulated “ants” similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions� For solving this highly nonlinear fitness function, ACO method can be applied in order to achieve high fitness value and also less computation time� This method is a member of swarm intelligence (SI) group� So, similar results are expected for PSO and APSO� Researchers should apply this method for solving charging problem of PHEVs and find the outcomes with extensive comparison with other swarm intelligence-based methods�
3.7.1.2 ABC Optimization ABC algorithm is one of the most recently introduced swarm-based algorithms� ABC simulates the intelligent foraging behavior of a honeybee swarm (Karaboga & Basturk, 2007)� In the ABC model, the colony consists of three groups of bees: employed bees, onlookers, and scouts� It is assumed that there is only one artificial employed bee for each food source� In other words, the number of employed bees in the colony is equal to the number of food sources around the hive� Employed bees go to their food source and come back to the hive and dance on this area� The employed bees whose food source has been abandoned become scouts and start searching for finding a new food source� Onlookers watch the dances of employed bees and choose food sources depending on dances� In ABC, a population-based algorithm, the position of a food source represents a possible solution to the optimization problem and
the nectar amount of a food source corresponds to the quality (fitness) of the associated solution� The number of the employed bees is equal to the number of solutions in the population� Future studies for solving smart charging problem of PHEVs should involve the ABC optimization technique�
Demand side management (DSM) is defined by the Department of Energy (DOE) as, “changes in electric usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized�” Therefore, the DSM programs should be incorporated into the existing Intelligent Energy Management System (iEMS) model in order to avoid voltage sag and blackout and to maximize the commercial benefits� In addition, this underutilized capacity could effectively power a national fleet of PHEVs with little need to increase the energy delivery capacity of the existing grid infrastructure (Gerkensmeyer, Kintner-Meyer, & DeSteese, 2010)�
Considering the effects of cost and performance on the marketability of PHEVs, the fitness function is defined to minimize drivetrain cost and driving performance requirements are selected as constraints to ensure that the vehicle performance is not sacrificed during the optimization� The battery is the key component within an EV which determines its overall capital cost and performance� Therefore, the task of determining the cost-effectiveness of EVs is predominantly one of identifying the future trajectory of battery cost and performance� To meet power requirements, batteries have lower discharge power at low SoC and lower charge power at high SoC� To reduce safety risks, limiting the maximum SoC avoids overcharge situations�
In this chapter, APSO-based optimization was performed in order to allocate power optimally to each of the PHEVs entering into the charging station� A sophisticated controller will need to be designed in order to allocate power to PHEVs appropriately� For this wake, the applied algorithm in this chapter is a step toward real-life implementation of such a controller for PHEV charging infrastructures� Here, four different numbers of PHEVs were considered for MATLAB simulation and then obtained results were compared with PSO in terms of average best fitness and computational time� The success of the electrification of transportation sector solely depends on charging infrastructure� Only proper charging control and infrastructure management can assure the larger penetration of PHEVs� The researchers should try to develop efficient control mechanisms for charging infrastructure in order to facilitate upcoming PHEVs penetration in highways� In future, more vehicles should be considered for intelligent power allocation strategy as well as hybrid versions of PSO should be applied to ensure higher fitness value and low computational time�
