**4. Optimization of V2G services for RE integration**

#### **4.1. Optimization techniques for V2G services**

Mathematical modeling of systems allows for variable change while trying to maintain a maximization or minimization of a criterion or many criteria. This modeling allows for experimental change without potential risks to the actual system. Finding an optimal middle ground between maximized efficiency and minimized cost is achievable through mathemat‐ ical modeling using various optimization techniques and functions. The different techniques are summarized in the following sections.

#### *4.1.1. Classical optimization techniques*

Classical techniques are utilized when the optimization function is a continuous and/or differentiable function. The solutions of optimization are found using differential calculus. The most utilized types of classical models are: linear programming (LP), nonlinear programming (NLP), dynamic programming (DP), mixed-integer programming (MIP), stochastic program‐ ming (SP), convex programming (CP), and analytical modeling (AM).

## *4.1.2. Metaheuristic optimization techniques*

Metaheuristic optimization techniques find, generate, or select a heuristic in this case a method of searching for an optimization strategy that may provide the best solution to the optimization problem with nonderivative, noncontinuous objective functions These metaheuristic methods sample from a much larger sample set to find a solution that best fits the entire set. It is based off of random operators to find the best solution to the set of variables faster than iterative or simple heuristics. The common types of metaheuristic techniques are: genetic algorithms (GA), particle-swarm optimization (PSO), ant colony optimization (ACO), simulated annealing (SA), and Tabu search [3].

### *4.1.3. Hybrid optimization techniques*

Hybrid optimization techniques are techniques that combine two or more of the previously described methods, either classical or metaheuristic. Typically, they combine iterative ap‐ proaches to heuristic solutions.

## **4.2. Optimization objectives**

The focus on optimization for V2G services are cost, efficiency, and emission optimization. Through the use of the optimization techniques listed above, significant gains can be made toward producing the most efficient and cost-effective EVs, maximizing V2G interactions, and improving smart grid technologies and power generation and distribution.

#### *4.2.1. Cost optimization*

Cost optimization is focused on minimizing the costs of interaction between EVs and RES providers through the smart grid. Providers wish to reduce costs and maximize profit while EV owners wish to minimize the cost of charging and vehicle maintenance [3].

## *4.2.1.1. Operational cost minimization*

Operational costs and their minimization are crucial for all market participants including the generation, transmission, and distribution providers and users [3]. **Table 1** summarizes the related research works, their objective functions, techniques in use for optimization, and their main findings.


(NLP), dynamic programming (DP), mixed-integer programming (MIP), stochastic program‐

Metaheuristic optimization techniques find, generate, or select a heuristic in this case a method of searching for an optimization strategy that may provide the best solution to the optimization problem with nonderivative, noncontinuous objective functions These metaheuristic methods sample from a much larger sample set to find a solution that best fits the entire set. It is based off of random operators to find the best solution to the set of variables faster than iterative or simple heuristics. The common types of metaheuristic techniques are: genetic algorithms (GA), particle-swarm optimization (PSO), ant colony optimization (ACO), simulated annealing (SA),

Hybrid optimization techniques are techniques that combine two or more of the previously described methods, either classical or metaheuristic. Typically, they combine iterative ap‐

The focus on optimization for V2G services are cost, efficiency, and emission optimization. Through the use of the optimization techniques listed above, significant gains can be made toward producing the most efficient and cost-effective EVs, maximizing V2G interactions, and

Cost optimization is focused on minimizing the costs of interaction between EVs and RES providers through the smart grid. Providers wish to reduce costs and maximize profit while

Operational costs and their minimization are crucial for all market participants including the generation, transmission, and distribution providers and users [3]. **Table 1** summarizes the related research works, their objective functions, techniques in use for optimization, and

improving smart grid technologies and power generation and distribution.

EV owners wish to minimize the cost of charging and vehicle maintenance [3].

ming (SP), convex programming (CP), and analytical modeling (AM).

*4.1.2. Metaheuristic optimization techniques*

158 Modeling and Simulation for Electric Vehicle Applications

and Tabu search [3].

*4.1.3. Hybrid optimization techniques*

proaches to heuristic solutions.

**4.2. Optimization objectives**

*4.2.1. Cost optimization*

their main findings.

*4.2.1.1. Operational cost minimization*

[24] min {*l <sup>k</sup>* },{*zk* } ∑ *k pB T l <sup>k</sup>* <sup>+</sup> *<sup>ρ</sup>* <sup>2</sup> | |*l <sup>k</sup>* − *zk* | | <sup>2</sup> <sup>2</sup> <sup>+</sup> *<sup>C</sup>*<sup>2</sup> *<sup>f</sup>* 0(<sup>∑</sup> *k*

is the energy bid of the utility at hour *t*.

*zk* is the auxiliary variable; *pB* is the base price; *l <sup>k</sup>* is the

*zk* )

*k*th user load; *ρ* is the quadratic coefficient for augmented

Classical (NLP) Demand curve can be flattened after numerical examples of optimization



**Table 1.** Optimization of V2G services for minimizing operational cost.

PEV fleet.

**Reference Objective function(s) Optimi-**

Lagrangian; *C*2 is the coefficient for fluctuation price; *f*0 is

*<sup>i</sup>* is the generator group; *t* is the time intervals; *Hi*,*t* is the

*ni*,*<sup>t</sup>* <sup>+</sup>∑ *j*=1

*J*

*pi*, *<sup>j</sup>*,*<sup>t</sup>Bi*, *<sup>j</sup>*)

is the marginal cost of segment *j*

is the no-load cost of

the variance of aggregated demand load.

(*n*) + (*Ai*

of the group *i*'s cost function; *ni*,*t* is the integer of

is the output for segment *j* of group *i* at time *t*.

CHP + ∑ *N i*=1 ∑ *T h* =1 *Costi*,*<sup>h</sup> b*

*SC* \**e ph* \* *gridh*

*e ph* \* *gridh*

CHP is the cost of electricity production by CHP

PV is the total operation cost of PV

buy and *gridh*

sell are the

Metaheu-ristic (PSO)

sell)}

purchased and sold electricity from/to the upstream network; *e ph* is the electricity price at hour *h* in the upstream network; *SC* is the sell coefficient; *N* is the number of buses; *T* is the number of intervals (hour).

*TC* =*Wc* ×(*Fuel* + *Start* −*Up*)

(*Pi* (*t*))

*Wc*(*FCi*

(*t* −1)))

buy)

*<sup>b</sup>* is the cost of heat production by the

[25]

min *n*,*p* ∑ *t*=1

*T* ∑ *i*=1

[26] min{*Cost* −*Revenue*}

={(∑ *N i*=1 ∑ *T h* =1 *Costi*,*<sup>h</sup>*

+∑ *N i*=1 ∑ *T h* =1 *Costi*,*<sup>h</sup>* PV + ∑ *T h* =1

−( ∑ *T h* =1

*Costi*,*<sup>h</sup>*

[27, 28] min *Ii* (*t*),*NV* <sup>2</sup>*G*(*t*)

systems; *Costi*,*<sup>h</sup>*

boilers; *Costi*,*<sup>h</sup>*

+*We* × *Emission*

*ECi* (*Pi* (*t*)) *Ii* (*t*))}

={*E*( ∑ *s*∈*S* ∑ *i*=1 *N* ∑ *t*=1 *H*

+*We*(*ψ<sup>i</sup>*

+*SCi* (1− *Ii*

generation systems; *gridh*

*N*

160 Modeling and Simulation for Electric Vehicle Applications

one unit of group *i*; *Bi*, *<sup>j</sup>*

commitment decisions; *pi*, *<sup>j</sup>*,*<sup>t</sup>*

*Hi*,*<sup>t</sup>*

start-up cost of group *i* at time *t*; *Ai*

**zation technique** **Findings**

can substantially reduce the cost of supplying additional EV demand due to lowered usage of peak generators, avoiding

wind/solar curtailment, reduce carbon emission and associated costs, and reduce thermal generator start-up

times.

PV (photovoltaic) generation systems coupled with PV storage systems in IMGs (industrial microgrid) could have positive effects on their scheduling solution and minimizing the overall cost.

PSO was utilized to generate a successful schedule considering the stochastic nature of renewable energies, load and GVs in a smart grid. Valid

Classical (NLP) The introduction of

Classical (MILP) Controlled charging



**Table 2.** Optimization of V2G services for minimizing generation cost.

#### *4.2.1.2. Generation cost optimization*

**Reference Objective function Optimi-**

*u*1 is the electricity generation; *u*2 is the scheduling of wind power; *C*energy is the cost of electricity generation; *C*reserve,*<sup>s</sup>* is the reserve scheduling; *C*reserve,*<sup>d</sup>* is the expected reserve

is the scheduling of conventional reserve (MW); *Rd* is the expected dispatch of conventional reserve (MW).

{*C*energy(*u*1) + *C*reserve,*s*(*Rs*)

[30] min

[31]

*u*1,*u*<sup>2</sup> ∑ *T t*=1

+*C*reserve,*<sup>d</sup>* (*Rd* )}

162 Modeling and Simulation for Electric Vehicle Applications

dispatch; *Rs*

min *PGi* (*t*) .*PL <sup>j</sup>* (*t*) ,*EV Bj* (0) ,*ΔE* ∑ *t*=*i*

by load *Lj*

[32] min *E* |*Ctotal* |

+ ∑ *i*=1 *Nw Cw*,*u*,*<sup>i</sup>* (*Ws*,*<sup>i</sup>* , *Wi* ) + ∑ *i*=1 *Nw Cw*,*o*,*<sup>i</sup>* (*Ws*,*<sup>i</sup>* , *Wi* )

+∑ *i*=1 *Ne Ce*,*<sup>i</sup>* (*Pe*,*s*,*<sup>i</sup>* ) + ∑ *i*=1 *Ne Ce*,*u*,*<sup>i</sup>* (*Pe*,*<sup>i</sup>* , *Pe*,*s*,*<sup>i</sup>* )

+∑ *i*=1 *Ne Ce*,*o*,*<sup>i</sup>* (*Pe*,*<sup>i</sup>* , *Pe*,*s*,*<sup>i</sup>* )

*C*total= ∑ *i*=1 *Nc Ci* (*Ps*,*<sup>i</sup>* ) + ∑ *i*=1 *Nw Cw*,*<sup>i</sup>* (*Ws*,*<sup>i</sup>* )

*PGi*

*T* ∑ *i nGi* ⋅*PGi* (*t*)

marginal cost of generator *Gi*

aggregation of virtual batteries.

; *EV Bj*

is the power produced by generator *Gi*

battery; Δ*E* is the shift in the energy content of the

; *PL <sup>j</sup>*

is the energy content of the virtual

; *nGi* is the

is the power consumed

**zation technique** 

Hybrid (Classical and scenario method)

Hybrid (Interior point based PSO)

**Findings** 

value of fully exploring the synergy between PEV and wind power using a three-level controller; with the top-level minimizing

generation costs, midlevel allotting charging time and power based on battery SOC, and bottom-level using real-time feedback to attempt grid frequency synchronization.

Compared to a pure cost-optimizing strategy, part of the charging has to be moved from the night to more expensive hours to reduce the SOC swing. This leaves enough flexibility to compensate the forecast error.

By studying the statistical properties of charging and discharging EVs along with formulating a power system economic dispatch model, which takes into account impacts of EVs and wind

Classical (DP) Demonstrated the

Generation cost optimization is crucial to both power distributors, charging station operators, and the EV owners. Interactions between EVs and RESs through the smart grid are at the center of intensive research. Maximizing the profit for distributors, minimizing cost of operation/ generation, and the cost of ownership and charging of EV is crucial with the proliferation of green energy [3]. **Table 2** summarizes the related research works, their objective functions, techniques in use for optimization, and their main findings.

#### *4.2.1.3. Profit/benefit optimization*

By maximizing the profit for generators/providers, or the benefits for providing energy, the effects are felt by the supply chain through aggregators, charging stations, etc. down to the EV owners. Optimization is referenced from the viewpoint of increasing investments in RESs or electricity delivery management. **Table 3** summarizes the related research works, their objective functions, techniques in use for optimization, and their main findings.

#### *4.2.1.4. Charging cost optimization*

Minimizing costs is crucial to both distributors and EV owners. Ensuring that the costs stay low on the distribution side ensures that costs stay low on the consumer side. Maximizing the synergy between stochastic RES generation and EV charging loads is the key to minimizing the costs surrounding EVs [3]. **Table 4** summarizes the related research works, their objective functions, techniques in use for optimization, and their main findings.



**Table 3.** Optimization of V2G services for maximizing profits/benefits.

green energy [3]. **Table 2** summarizes the related research works, their objective functions,

By maximizing the profit for generators/providers, or the benefits for providing energy, the effects are felt by the supply chain through aggregators, charging stations, etc. down to the EV owners. Optimization is referenced from the viewpoint of increasing investments in RESs or electricity delivery management. **Table 3** summarizes the related research works, their

Minimizing costs is crucial to both distributors and EV owners. Ensuring that the costs stay low on the distribution side ensures that costs stay low on the consumer side. Maximizing the synergy between stochastic RES generation and EV charging loads is the key to minimizing the costs surrounding EVs [3]. **Table 4** summarizes the related research works, their objective

> **zation technique**

**Findings**

can maximize profits by optimizing the schedule of supply to the grid based on the wind energy production and the available storage.

Classical (Iterative LP) VPP formed with EVs

Classical (SP) A stochastic-based

framework is proposed for smart grid operators to determine optimal charging control of EVs and energy purchasing to

objective functions, techniques in use for optimization, and their main findings.

functions, techniques in use for optimization, and their main findings.

(*n*) *x*(*n*) + *d*(*n*)

(*n*) is the wholesale price of electricity.

(*ξ*)} }

is the

is the

**Reference Objective function Optimi-**

*x* is the energy supplied directly to the grid; *b* is the energy transferred to the batteries; *d* is the energy

the batteries; *y* is the needed storage capacity; *g* is the energy transferred to the batteries as payment; *P*() is the

raised by the virtual power plant (VPP) from the

*c <sup>h</sup>* ⋅ *y <sup>h</sup>*

(*ξ*)−*q <sup>h</sup>* ⋅*v <sup>h</sup>* \*

*<sup>h</sup>* is the allocation of energy to EV *i* for hour *h; yh*

per energy unit at which energy is charged to the EVs during hour *h* by the aggregator; *c <sup>h</sup>* is the price of bulk

amount of purchased bulk energy for hour *h; ph*

techniques in use for optimization, and their main findings.

*4.2.1.3. Profit/benefit optimization*

164 Modeling and Simulation for Electric Vehicle Applications

*4.2.1.4. Charging cost optimization*

[35]

max *x*,*b*,*d*,*y*,*g* *P*(*x*, *d*)= ∑

transferred from

revenues

electricity sold at market; *pe*

> *u* −{∑ *h p <sup>h</sup>* ∑ *i xi <sup>h</sup>* −∑ *h*

*xi*

price

−*Eξ*∑ *h*

{*r <sup>h</sup>* (*ξ*) ⋅ *z <sup>h</sup>* \*

[36] min

*n*=0 *N* −1 *p e*


**Table 4.** Optimization of V2G services for minimizing EVs' charging cost.

#### *4.2.1.5. Other cost-related optimization*

Other cost-related optimizations include minimizing overall costs related to system lifetime, transmission, materials and resources, upgrades, losses, and renewable imbalances [3]. **Table 5** summarizes the related research works, their objective functions, techniques in use for optimization, and their main findings.

### *4.2.2. Efficiency optimization*

**Reference Objective function Optimi-**

)*QEV* ,*<sup>t</sup>* + *βQEV* ,*<sup>t</sup>* 2

charging rate of vehicle *i* out of a total number of vehicles

*Qg*(*t*)(1 <sup>+</sup> *<sup>η</sup>*

*xg*(*t*) is the control variable; *V* is a parameter that is used to tune the tradeoff between cost and queue backlog

*γ*(*t*) is the electricity price at time *t; y*(*t*) is an auxiliary variable; *Qg*(*t*) the total charging tasks in timeslot *t* of *g*

*Pt* ×*SPt*)

is the starting hour of charge/discharge for the PEV; *tb* is the ending hour of charge/discharge for the PEV.

 are the total purchases and sales of the aggregator; *α, β* are variables linearly relating price to load.

**Table 4.** Optimization of V2G services for minimizing EVs' charging cost.

is the virtual queue; *Rg* is the max charging time; *η* is a constant to adjust the growth rate of the virtual

> *t*=*t a*

*EC* is the energy costs of the PEV; *Pt*

discharge power at hour *t; SPt*

*αqt* + *βqt* 2 *t b* *Rg*

) + *Zg*(*t*) *xg*(*t*)

is the charge/

is the spot hour price at

*<sup>N</sup>* is the time-dependent network tariff; *α<sup>t</sup>*

*ui,t* is the optimization variable representing the

baseline electricity price at time *t; QEV,t* is the extra

2 is the

*g*=1 *G*

[39]

[40]

[41]

[42]

min *ui*,*t* ∑ *t*=1 *Nt* (*Ct <sup>N</sup>* <sup>+</sup> *<sup>α</sup><sup>t</sup>*

the

demand

min *xg*(*t*)

growth;

queue.

hour *t; ta*

min ∑ *t*=1 *T*

*qt*

queues; *Zg*(*t*)

min (*EC*)=min (∑

of the EVs; *βQEV* ,*<sup>t</sup>*

EV-dependent part.

*Vγ*(*t*)*y*(*t*)−∑

166 Modeling and Simulation for Electric Vehicle Applications

at time *t*; *Ct*

**zation technique**

scheme)

Classical (Rolling horizon optimization

Classical (Lyapunov optimization)

Classical (Sequential

Classical (Quadratic

progra mming)

quadratic programming)

is

**Findings**

An analysis of EVcaused distribution network congestion management is presented and a mathematical model of optimization is proposed.

A stochastic

optimization problem is formulated to describe the queuing problem for EV charging requests and minimize the time average cost of using other energy sources when renewable sources are unable to meet demand.

The optimization method presented has shown that PEV charging/discharging during optimal spot market times minimize energy costs on low windgenerated power

days.

This paper offers to aggregators a framework of optimizing charging and discharging of EV fleets given driving patterns and spot market prices.

The efficient utilization of renewables can reduce the use of fossil energy quite substantially. This can elicit several benefits including air pollution reduction and cost savings for consum‐ ers. The efficiency-related optimization objectives in regards to EVs interactions with RESs are maximizing RES utilization, optimizing energy dispatch, optimizing energy management, minimizing power loss, and minimizing energy loss. Sections 4.2.2.1 and 4.2.2.2 provide details regarding the efficiency-related optimization works for EVs interacting with RESs.



**Table 5.** Optimization of V2G services for minimizing costs.

#### *4.2.2.1. RES utilization maximization*

**Reference Objective function Optimi-**

*a, b, c* are cost coefficients; *P*Conv(*t*) is the

168 Modeling and Simulation for Electric Vehicle Applications

[46] min {*C*Pen. + *C*V2G −*R*V2G}

*C*Pen.

[47]

imbalances;

is the revenue for V2G services.

min ∑ *k*=1 *K C*Pen . (*tk* )

generation of the conventional generator at time *t*.

is the penalty cost for wind power

*C*pen is the penalty cost for PV power imbalances;

*K* is the number of time steps.

**Table 5.** Optimization of V2G services for minimizing costs.

*C*V2G is the cost for V2G services; *R*V2G

**zation technique**

Hybrid (GAbased Monte Carlo simulation (MCS))

Hybrid (PSObased Monte Carlo simulation (MCS))

**Findings**

resources.

The proposed optimization provides collaboration between wind participants and EV aggregators to minimize the sum of the penalty cost associated with wind power imbalances and V2G expenses associated with purchased energy, battery degradation and capital costs as well as increasing the EVs' revenues and incentives.

This paper proposes a coordinated charging/ discharging scheme to optimally utilize V2G capacities of EVs to minimize the penalty cost for PV power

under-/

overproduction.

(EMS) that allows distributors a more economical means of incorporating wind resources and EV storage solutions into existing generation

The excessive power generated by RESs can be stored in batteries of the EV fleets and DC-link capacitors in specialized charging stations to supply the necessary power through V2G infrastructure when the renewable energy generation is insufficient to meet load demands. An optimization strategy is required to coordinate the EVs' charging/discharging with RESs uncertainties to maximize the use of renewable generation. **Table 6** summarizes the related research works, their objective functions, techniques in use for optimization, and their main findings.




**Table 6.** Optimization of V2G services for maximizing RES utilization.

#### *4.2.2.2. Other efficiency-related optimization*

**Reference Objective function Optimi-**

(*C*start,*<sup>n</sup>* + (*PCn*(*PTUn*)

*C*tot(*t*) is the total production cost; *C*start,*<sup>n</sup>* is the startup cost

*PCn* is the production cost of unit n; *Cems,n* is the CO2

*NTU*

[50]

[51]

*C*tot(*t*)=min( ∑

of unit *n;*

emission

*J u*˜\* (*x*0)=

*u*˜\*

[52] min

*xt <sup>k</sup>* {∑*<sup>t</sup>*=1 *<sup>T</sup> Ct*

cost of unit *n; PTUn*

is the output power of unit

max *<sup>u</sup>*˜ <sup>∈</sup>*<sup>U</sup> <sup>J</sup> <sup>u</sup>*˜(*x*0)

*<sup>J</sup> <sup>u</sup>*˜(*x*0)=lim*<sup>T</sup>* <sup>→</sup>*<sup>∞</sup>*

*n; t*int is the time period share in an hour.

1 *<sup>T</sup> E*{*∫* 0 *T*

(∑*<sup>k</sup>* =1 *<sup>K</sup> xt*

subscribers that aid in balancing; *xt*

*Ct*(.) is the imbalance cost; *Dt*

is the energy demand of subscriber *k* during time slot *t*.

*r*(*x*(*t*), *a*(*t*))d*t*}

is the optimal charging policy; *r*(*x*(*t*), *a*(*t*)) is the

*<sup>k</sup>* ) + ∑*<sup>k</sup>* =1

*<sup>K</sup>* ∑*<sup>t</sup>*=1 *<sup>T</sup> Dt k* (*xt k* )}

*k*

*<sup>k</sup>* (.) is the disutility of the

reward for the action *a*(*t*) taken in a state *x*(*t*).

+*Cems*,*n*(*PTUn*).*t*int)

170 Modeling and Simulation for Electric Vehicle Applications

*n*=1 *NTU*

is the number of thermal units;

**zation technique** **Findings**

strategy to fully supply the EVs' charging load by RESs within a microgrid composing of a photovoltaic plant, a thermal unit, battery energy storage systems, and electric vehicle charging

stations.

developed an optimal charging policy strategy to maximize renewable energy utilization within preexisting distribution

infrastructure despite stochastic generation

The authors proposed an optimal distributed algorithm to balance the synergy of

smartgrid interactions between RES supply and EV charging

potential.

demand.

Classical (LP) The authors

Classical (Convex optimi-zation– quadratic) progr-

amming

Classical (MIP) This paper suggests a

Other efficiency-related optimizations include minimizing imported electricity [54], mini‐ mizing power loss [55], minimizing loss energy, and optimizing energy management [56], etc. Table 7 below summarizes the related research works, their objective functions, techni‐ ques in use for optimization, and their main findings.



wind is the

**Table 7.** Optimization of V2G services for improving efficiency.

power scenario *Sc*wind

obtained from garage *j* at time *t*; *P*GA*<sup>R</sup> <sup>j</sup>*,*t*,*<sup>S</sup> <sup>c</sup>*

power input/output for garage *j* at time *t* and under wind

## *4.2.3. Emission optimization*

**Reference Objective function Optimi-**

*i*∈*N*DG

, 0)) <sup>+</sup>∑ *i*∈*N* max

*f*1 is the power losses of *N*-bus distribution system; *f*<sup>2</sup> is the error between rated voltage (1 p.u) and

*V* is the voltage; *N*DG is the total number of system

*wind* )

is the price of energy

is the price of energy

wind is the

wind) *π*(*Sc*wind) is the probability/weight of wind scenario *Sc*wind; *Sc*wind is the index of wind power scenarios

obtained from dispatch-able generating unit *i* at time *t*;

generating unit *i* at time *t* and under wind power scenario *Sc*wind; *C*grid,*t* is the price of energy obtained from the main grid at time *t*; *P*grid,*t* is the power input/output for

power input/output for garage *j* at time *t* and under wind

is the power output from dispatch able

max |, 0)

*π*(*Sc*wind)

(max(*Vi* −*Vi*

max , 0)

[55] *<sup>F</sup>* =min ( *<sup>f</sup>* <sup>1</sup> <sup>+</sup> *<sup>f</sup>* 2) <sup>+</sup> ∑

+( |*Si* | − | *Si*

voltage of each bus;

min <sup>−</sup>*Vi*

172 Modeling and Simulation for Electric Vehicle Applications

+max(*Vi*

suppliers.

Min *<sup>C</sup>* <sup>=</sup> ∑

*I*

+*C*grid,*<sup>t</sup>*.(*P*grid,*t*)

*C*GA*<sup>R</sup> <sup>j</sup>*,*<sup>t</sup>* . (*P*GA*<sup>R</sup> <sup>j</sup>*,*t*,*<sup>S</sup> <sup>c</sup>*

∑ *t*=0

<sup>+</sup>∑ *j*=1

*J*

*P*DG*Ui*,*t*,*<sup>S</sup> <sup>c</sup>*

*N* −1 ∑ *i*=1

*Sc*wind

*C*DG*Ui*,*<sup>t</sup>* . (*P*DG*Ui*,*t*,*<sup>S</sup> <sup>c</sup>*

running from 1 to *H*; *C*DG*Ui*,*<sup>t</sup>*

the main grid at time *t; CGAR j,t*

obtained from garage *j* at time *t*; *P*GA*<sup>R</sup> <sup>j</sup>*,*t*,*<sup>S</sup> <sup>c</sup>*

**Table 7.** Optimization of V2G services for improving efficiency.

wind

power scenario *Sc*wind

*H*

[56]

**zation technique**

Metahe-uristic (GA)

**Findings**

overall distribution performance, reducing

charging times and related costs.

The focus of this paper is on improving the "smart parking lot," with a primary goal of efficiently reducing power losses through improving voltage profiles and optimized scheduling of EV fleet charging during peak and nonpeak hours.

provided in this paper assesses the ability of V2G systems to provide power support to conventional grid operations, including small electric energy systems (SEESs).

Classical (LP) The practical model

Emission reduction is one of the most important objectives of EVs' adoption for transportation. This objective can be further satisfied through interactions between EVs and RESs. V2G implementation plays a key role in this scenario to decrease the power utility costs and protect the environment. Related research works include references [27] and [28] of **Table 1**, reference [43] of **Table 5**, and reference [57] whose objective function, optimization technique, and its main finding is provided in **Table 8**.


**Table 8.** Optimization of V2G services for reducing emission.
