discharging of grid-enabled electric vehicles for predictability enhancement of PV generation

Electric Power Systems Research 117 (2014) 134–142

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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Optimal charging/discharging of grid-enabled electric vehicles for predictability enhancement of PV generation M. Ghofrani a,∗ , A. Arabali b , M. Ghayekhloo c a b c

School of Science, Technology, Engineering and Mathematics (STEM), University of Washington, Bothell, United States Department of Electrical and Biomedical Engineering, University of Nevada, Reno, United States Department of Electrical and Computer Engineering, Science and Research Branch, Islamic Azad University, Qazvin, Iran

a r t i c l e

i n f o

Article history: Received 10 June 2014 Received in revised form 5 August 2014 Accepted 10 August 2014 Keywords: Battery storage Collaborative strategy Coordinated charging/discharging Electric vehicles Monte Carlo simulation Vehicle-to-grid

a b s t r a c t This paper proposes a collaborative strategy between the photovoltaic (PV) participants and electric vehicle (EV) owners to reduce the forecast uncertainties and improve the predictability of PV power. The PV generation is predicted using an auto regressive moving average (ARMA) time series model. Fuzzy C-means (FCM) clustering is used to group the EVs into fleets with similar daily driving patterns. Uncertainties of the PV power and stochastic nature of driving patterns are characterized by a Monte Carlo simulation (MCS) technique. A particle swarm optimization (PSO) algorithm is developed to optimally use the vehicle-to-grid (V2G) capacities of EVs and minimize the penalty cost for PV power imbalances between the predicted power and actual output. The proposed method provides a coordinated charging/discharging scheme to realize the full potential of V2G services and increase the revenues and incentives for both PV producers and EV drivers. An economic model is developed to include the V2G expenses and revenues to provide a complete picture of the cost–benefit analysis. The proposed model is used to evaluate the economic feasibility of V2G services for PV power integration. © 2014 Elsevier B.V. All rights reserved.

1. Introduction The expected widespread adoption of plug-in hybrid electric vehicles (PHEVs) along with increasing penetrations of renewable energy generation mandated by renewable portfolio standards (RPS) provide an opportunity to develop a sustainable integrated electricity and transportation system. This offers several benefits such as emission reduction, cost savings and reduced petroleum dependency. The revenues are further expanded for grid-enabled vehicles (GEVs) where their vehicle-to-grid (V2G) capabilities provide several services including load smoothing, energy and ancillary services as well as support for renewable integration. A coordinated charging/discharging strategy is required to realize full potential of V2G benefits. This would expand economic incentives and enhance drivers’ participation in V2G services. The high penetration of intermittent renewable resources increases the need for a smart scheduling strategy as power system uncertainties increase significantly. This is particularly true for photovoltaic (PV) power

∗ Corresponding author at: UWBB Room 227, 18807 Beardslee Blvd, Bothell, WA 98011, United States. Tel.: +1 425 352 3224; fax: +1 425 352 3775. E-mail address: [email protected] (M. Ghofrani). http://dx.doi.org/10.1016/j.epsr.2014.08.007 0378-7796/© 2014 Elsevier B.V. All rights reserved.

systems where the generation fluctuations exhibit a major challenge for PV integration. Thermal generating units are proposed to provide the additional reserve capacity and energy services required to minimize the PV power intermittency [1,2]. The increase in reserve capacity requires reducing generation form the lower-cost units to accommodate the more flexible units which provide the reserves. This results in an uneconomic dispatch which increases the cost of PV integration and decreases the efficiency of power systems [2]. In addition, the response time of the thermal units may not be fast enough to mitigate the variability of PV generation. Moreover, the additional spinning reserves call for more online units which increase the maintenance requirements of the system [2]. These deficiencies necessitate the need for an alternative to thermal units for PV integration. Several references used energy storage technologies to compensate for PV power uncertainties [3–6]. The rapid-response characteristic of battery energy storage systems (BESS) enables them to mitigate the fast fluctuations of PV generation. In addition, market-oriented applications provide economic benefits for the integrated PV-BESS power system. These applications include time-shifting, leveling and hedging against forecast uncertainties. The economic benefit is particularly significant for the hedging application. This is true for energy markets where the penalties associated with PV power imbalances increase PV

M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142

Nomenclature Apv Cb Cc Cac CV2G Cd Ce Cpe Cpen d db Eb Ed Gbestb H0 K Lc Let Lyr m n p Pc Pd Ppv PAPV PSPV Pcmax Pdmax

Pbestib PF PTC

q rd Rb RV2G SOC Sk SOCmin SOCmax Uib Vib w Xj ˛1 ˛2  1 , 2  c d PV j k  k ϕi

area for the photovoltaic array capital cost for the EV battery capital cost for V2G service annualized capital cost for V2G service cost for V2G service cost of equipment degradation due to V2G service cost per energy unit discharged through V2G cost of purchased energy for V2G service penalty cost for wind power imbalances discount rate self-discharge rate for the EV battery capacity of the EV battery discharging energy of the EV battery vector of global best position attained among all particles in the swarm at the bth iteration extra-terrestrial radiation on a horizontal surface number of time steps battery lifetime in cycles battery lifetime in energy throughput battery lifetime in years order of the AR model order of the MA model parameter in the functional form for the k(kt ) charging power of the EV battery discharging power of the EV battery PV power actual PV power scheduled PV power power rating for charging power rating for discharging vector of best position attained by the ith particle at the bth iteration penalty factor for the PV power deviations production tax credit for renewable electricity production parameter in the functional form for the k(kt ) ratio, diffuse radiation in hour/diffuse in day geometric factor, the ratio of beam radiation on the tilted surface to that on a horizontal surface revenue for V2G service state of charge of the EV battery simulated clearness index minimum capacity of the EV battery maximum capacity of the EV battery a-dimensional vector for the position of the ith particle at the bth iteration a-dimensional vector for the velocity of the ith particle at the bth iteration inertia weight jth stochastic input variable cognitive parameter for PSO social parameter for PSO random numbers uniformly distributed within [0,1] roundtrip efficiency of the EV battery charging efficiency of the EV battery discharging efficiency of the EV battery efficiency for the PV generation moving average coefficient of the ARMA model mean of the clearness index reflectance of the ground standard deviation of the clearness index autoregressive coefficient of the ARMA model

135

integration costs [3]. An efficient hedging strategy minimizes deviations of the scheduled PV generation from the actual PV power and provides economic incentives by optimal charging/discharging of energy storage systems. Reference [4] introduces a BESS-based control method to level out the PV power fluctuations. Sizing of hybrid photovoltaic-energy storage systems were investigated in [5,6] where the optimal design is calculated for the islanding operation without considering the market opportunities. EVs can potentially provide an appropriate solution for PV integration as an alternative to other storage technologies [7,8]. The relatively lower capital cost of power systems with EVs and the low incremental cost of adding V2G capability to an EV justify the economic advantage of EVs over bulk energy storage systems [9,10]. In addition, EVs can be used to support the grid as distributed energy storage units which provide technical advantages over the centralized storage systems. These advantages include transmission and distribution upgrade deferral, transmission congestion relief and better utilization of renewable generation [11,12]. The practices proposed in the literature are concerned with the operation of power systems with EVs. Power system operation with EV aggregation requires the participation of different resources including conventional generation and V2G capacities to provide operating reserves and ancillary services. The operating reserve requirements are significantly reduced if the PV producers follow their cleared schedules more accurately. This can be provided by a collaborative strategy between the PV producers and EV owners to mitigate the effects of uncertainty and enhance the predictability of PV power. The utilization of PV power is increased as a result which reduces the penalty costs for PV power under-/over-production. This also increases the revenues for PV participants and provides economic incentives for EV owners to participate in V2G services. To the best of our knowledge, the collaboration of PV producers and EV owners to enhance the dispatchability of PV power and increase their participation in V2G services has not been addressed in the literature. Hence, there is a need for a stochastic framework to optimally utilize V2G services for the hedging application. The demand for the EV grid services is more obvious for the higher penetrations of intermittent renewable resources that require greater attention to the load management. This paper proposes a stochastic framework to optimally use V2G capacities of EVs and enhance the dispatchability of PV power. A PSO-based MCS is developed to provide a collaborative scheme between the PV producers and EV owners to encourage EVs’ participation in V2G services. The proposed framework increases revenues for PV producers by minimizing the penalty cost for PV power deviations. It also provides economic incentives for EV owners by selling the V2G energy and increasing the utilization of renewable generation. In addition, the V2G potential for PV power integration is fully realized in this paper when compared to earlier studies which emphasized the operation perspective. Section 2 explains the ARMA model for solar irradiance and the battery and economic models for the EVs. The clustering of EVs, PSO and MCS are also described in this section. Section 3 provides the simulation results as well as the cost–benefit analysis. Conclusions are presented in Section 4.

2. Methodology 2.1. Time-series model for PV generation This paper uses an ARMA time series model to forecast the PV power generation. A mth-order AR nth-order MA model characterizes uncertainties of the solar irradiance and PV

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M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142 Table 1 EV specifications [17,18].

generation [13]: yt =

m 

ϕi yt−i +

i=1

n 

j εt−j

(1)

j=1

where εt is the white noise with zero mean, zero autocorrelation and a variance of  2 . The autoregressive and moving average coefficients are estimated using a least square approach. The estimation minimizes the sum of the squares of the residuals, i.e. the differences between the clearness index measurements and model outputs. The randomly generated value of εt and the previous values of y and ε are used to provide a time series representation for y. The clearness index is simulated by shifting and scaling the time series (yt ) using the mean and standard deviation of the historical data [14]: Skt = kt + ykt · kt

(2)

The simulated clearness index (Skt ) is then used to stochastically model the solar irradiance. The clearness index (kt ) is defined as the quotient of the irradiance on a flat level, It (kW/m2 ), and the extraterrestrial solar irradiance, It (kW/m2 ) [15]: It Io

kt =

(3)

Iˇ is the irradiance inclining with an angle of ˇ with respect to the horizontal plane [16]:





Iˇ = Rb +

1 + cos ˇ − Rb 2



·k+·

1 − cos ˇ 2



· It

(4)

It is a function of H0 , rd and kt as: H0 It = · r · kt 3600 d

(5)

Correlation of the diffuse fraction (k) with the clearness index (kt ) is approximated with a piecewise linear function as follows [16]: k = p − qkt

(6)

1 − cos ˇ Rb +  · 2

Iˇ =

H0 ·rd · · kt − 3600



  +

1 + cos ˇ − Rb 2

1 + cos ˇ − Rb 2







·p



(7)

T=

Rb +  ·

1 − cos ˇ 2

  +

1 + cos ˇ − Rb 2



 · p · rd ·

H0 3600 (8)

 T =

1 + cos ˇ − Rb 2

Li-Ion 24 kWh 100 miles 88.2% 98.0% 6 kW 4h

2.2. Battery model for EV For each time step (tk ), the state of charge (SOC) of the EV battery is updated according to the charging/discharging status. The EV is charged during PV power over-production periods when PAPV (tk ) ≥ PSPV (tk ). It is discharged during PV power underproduction periods when PAPV (tk ) < PSPV (tk ). The SOC is calculated using (11a) and (11b) for charging and discharging, respectively [17]: SOC(tk ) = (1 − db ) · SOC(tk−1 ) + c · tk · Pc (tk )

(11a)

1 SOC(tk ) = (1 − db ) · SOC(tk−1 ) − · tk · Pd (tk ) d

(11b)

The EV is not charged and discharged at the same time, i.e. the status is either charging or discharging. This gives the following constraint: Pc (tk ) = / 0, Pd (tk ) = 0 when PAPV (tk ) ≥ PSPV (tk )

(12a)

Pc (tk ) = 0, Pd (tk ) = / 0 when PAPV (tk ) < PSPV (tk )

(12b)

The maximum, Smax , and minimum, Smin , battery capacity requirements are determined by the size and depth-of-discharge of the battery. The state of charge of the EV battery satisfies the capacity requirements as: SOCmin ≤ SOC(tk ) ≤ SOCmax

∀k ∈ K

Power rating of the EV battery for charging/discharging determines the maximum allowable power for charging/discharging the EV:

· q · rd ·

H0 3600

(9)

(14b)

2.3.1. Economic model for EV The difference between the revenue and costs of the V2G service defines the V2G economic value. The discharged energy is traded at real-time market clearing prices (MCPs) with the revenue given by [19]:

(10)

where the simulated and historical clearness index are used to calculate the scheduled PV power (Pspv ) and actual output (PAPV ), respectively.

(15)

The cost of energy and capital costs are added up to obtain the annual cost of V2G as [19]: CV2G = Ce · Ed + Cac

The PV power output is calculated by: PPV = APV · PV · Iˇ = APV · PV · (T · kt − T  · kt2 )

(14a)

2.3. Economic models

RV2G (tk ) = Pd (tk ) · tk · MCP(tk ) ∀k ∈ K



(13)

The Nissan Leaf is the EV used in this paper. Table 1 provides the characteristics of the EV and the battery in use for the investigation.

H0 · q · rd · · k2 3600 t

= T · kt − T  · kt2 where T and T’ are:

Nissan leaf EV

Battery type and energy All-electric range Charging efficiency Discharging efficiency Level 2 charging Power rating Charge time

  Pc (tk ) ≤ Pcmax ∀k ∈ K   Pd (tk ) ≤ P max ∀k ∈ K d

Iˇ is calculated by substituting (5) and (6) in (4) as follows:



Electric vehicle model

(16)

where Ce is the cost of energy defined as the cost per energy unit discharged through V2G. This includes the purchased energy and battery wear (degradation) costs [19]: Ce =

Cpe + Cd 

(17)

M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142 Table 2 Economic characteristics of the EV battery.

The penalty factors for deviation bands 1, 2 and 3 are given by (24a), (24b) and (24c), respectively [25].



Cost parameters

Value

Comments

 (%) Cb ($)

86.4 7500

Let (kWh)

69,720

Cd ($/kWh) Cc ($)

0.123 1900

Cac ($/year)

266

Roundtrip efficiency 300 ($/kWh)a × 24 kWh + 10 h replacement labor × 30 ($/h) Based on 3500-cycle lifetime at 83% DoD [21] – On-board incremental cost of $400 and wiring upgrade cost of $1500 [19] Based on discount rate of 10% and lifetime of 10 years (d = 10%, Lyr = 10)

a

Based on [20].

(18)

The degradation cost of the EV battery (Cd ) is the ratio of the battery capital cost (Cb ) to the battery lifetime in energy throughput (Let ): Cd =

Cb Let

(19)

where Let is given by: Let = Lc · Eb · DoD

d(1 + d) (1 + d)

Lyr

Lyr +1

1 PAPV (tk ) < PSPV (tk ) ∀k ∈ K 1 PAPV (tk ) > PSPV (tk ) ∀k ∈ K

 PF(tk ) =

1.1 PAPV (tk ) < PSPV (tk ) ∀k ∈ K 0.9 PAPV (tk ) > PSPV (tk ) ∀k ∈ K

 PF(tk ) =

1.25 PAPV (tk ) < PSPV (tk ) ∀k ∈ K 0.75 PAPV (tk ) > PSPV (tk ) ∀k ∈ K

(24a)

(24b)

(24c)

Most EVs are parked on an average of 95% of the time when they can potentially participate in V2G services [26]. Driving patterns of such EVs represent the distance driven during each hour of the daily driving [27]. This determines the battery capacity required for driving and the potential V2G capacity. EVs with similar driving patterns are clustered into fleets using FCM [28]. The elbow method is used to determine the sufficient number of clusters which provides the desired modeling accuracy with an acceptable computational load [29]. FCM, in combination with the elbow method, categorizes the EVs into 6 fleets of similar 24-h driving patterns.

(20)

Lc is the battery lifetime in cycles which is calculated based on the depth-of-discharge of the battery (DoD). The total capital cost for V2G service (Cc ) is uniformly distributed over the life time to calculate the annualized capital cost (Cac ) as: Cac =

PF(tk ) =

2.4. Driving patterns for EV

The roundtrip efficiency () is:  = c · d

137

−1

· Cc

(21)

2.3.2. Economic model for PV The proposed collaborative strategy reduces the forecast uncertainties and increases the utilization of PV power. This provides some revenues for the PV producer in the form of renewable electricity production tax credits (PTC). The revenue for the PV supplier is given by [22]:

∀k ∈ K

(25)

MCS uses the ARMA model of PV generation and driving pat(j) terns of the EV fleets to generate a sample (xn,t ) for each input

random variable (x(j) ). The output for each sample is calculated by h(x(j) ). Each sample is compared with previous ones to avoid redundancy. MCS is repeated for a specified number of simulations (N) that ensures convergence. The system behavior is simulated using the sample outputs.

(22) 2.6. PSO

A production tax credit of 0.5 ¢/kWh is considered for our study [23]. The Federal Energy Regulatory Commission (FERC) considers three imbalance deviation bands to charge for generation imbalances in the Bonneville Power Administration (BPA) balancing authority. Band 1 corresponds to deviations within ±1.5% of the scheduled power or ±2 MW. These deviations are subject to charges which are settled at BPA’s incremental costs. Band 2 corresponds to deviations which are greater than the ones for Band 1 and within ±7.5% of the schedule or ±10 MW. 110% or 90% of BPA’s incremental costs are used to charge the generation which is less or greater than the schedule for this band. Band 3 is for deviations that are greater than the ones for band 2. A 25% penalty factor (PF) is used to charge for the imbalance between the scheduled and actual renewable generation. The deviations of intermittent generation are penalized based on real-time market clearing prices (MCPs) as [24]:

  Cpen (tk ) = PSPV (tk ) − PAPV (tk ) · PF(tk ) · MCP(tk ) ∀k ∈ K

The uncertainties of the PV power and stochastic nature of driving patterns are characterized by MCS. This technique simulates the system states and repeats the simulation process for many trials to obtain distributions for the output random variables [30]. The output and input random vectors are related by the function h as: Y = h(x)

Table 2 provides the cost parameters for the EV.

RPV (tk ) = Pw (tk ) · tk · PTC

2.5. MCS

(23)

This paper uses a PSO technique to optimally charge and discharge the V2G capacity of the EV fleets for minimizing the penalty costs for PV power imbalances. The classical optimization methods cannot be used because of the non-convexity and non-linearity of the problem due to the conditional equations of (11) and (24). In addition, the optimization problem is a stochastic program where the traditional derivative-based optimization methods cannot handle the random calculations. The probabilistic transition rules used in PSO make it an appropriate solution for the stochastic problem of the EVs charging/discharging. PSO searches an a-dimensional space to adapt a velocity and retain a memory of the best position attained for each particle. The velocity and position for the ith particle are updated by [31]: Vib+1 = wVib + ˛1 1 (Pbestib − Uib ) − ˛2 2 (Gbestib − Uib )

(26)

Uib+1 = Uib + Vib+1

(27)

138

M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142

where Uib , Vib , Pbestib and Gbestib are the a-dimensional vectors of position and velocity, best position and global best position for the ith particle at the bth iteration. b b b Uib = (Ui,1 , Ui,2 , . . ., Ui,a )

(28)

b b b Vib = (Vi,1 , Vi,2 , . . ., Vi,a )

(29)

b b b Pbestib = (Pbesti,1 , Pbesti,2 , . . ., Pbesti,a )

(30)

Gbest b = (Gbest1b , Gbest2b , . . ., Gbestab )

(31)

Input data (historical clearness index and transportation behavior) Generate an ARMA model for PV and a driving pattern for each EV fleet Initialize PSO with random velocities and positions

n=1

2.7. PSO-based MCS k=1

Fig. 1 shows the flowchart for the proposed PSO-based MCS. The vectors of input and output random variables are: (32)

Y = [S, Pc , Pd ]

(33)

Historical clearness index and transportation data are used to generate the ARMA model of PV and driving patterns of EV fleets. A set of positions and velocities is randomly selected from the feasible solution space and used to initiate PSO. MCS is then used to simulate the system states by producing samples for the N scenarios. Each scenario includes 7 sets of 24-hour samples for the scheduled PV power and driving patterns of six EV fleets. For each hour, the driving pattern samples are utilized to determine the availability of the EV fleets for charging/discharging. An EV fleet is available for the hours when the driving pattern has 0 driving distance, i.e. the EV is parked. The sample of the scheduled PV power is then compared with the actual PV power and the charging/discharging status is determined accordingly. The available EV fleets are charged/discharged to minimize the penalty cost for PV power over-/under-production. The PV power in excess of the scheduled output is used to optimally charge the available V2G capacities. The V2G capacity for each fleet is the residual battery capacity of the fleet after deducting the capacity required for driving. The V2G capacity for each hour is updated based on the driven distance which releases the associated capacity for V2G usage. The available V2G capacity is optimally discharged to reduce power imbalances during PV power under-production periods. The PSO updates the velocities and changes the positions accordingly to optimize the solution. The solution minimizes the penalty cost for the mismatch between the scheduled and actual PV power where the objective function is: Obj.Function = Min CPen. = Min

K 

CPen. (tk )

(j) Produce a sample (x n, t ) using the PV ARMA model and EV driving patterns

Is any EV fleet parked?

k=k+1

Yes

Yes Charge V2G using (9.a)

k≤N No

Yes

n=n+1

n≤N No

Evaluate the objective function and constraints

Update velocity and position using (21) and (22)

No

Termination criterion?

Yes

(34)

End

For each sample, the violated constraints are assigned a large penalty coefficient () and combined with the objective function f to assign a higher cost to an infeasible solution [32]. 2

PAPV > PSPV

Discharge V2G using (9.b)

k=1

¯ = f (¯x, u) ¯ + v[h(¯x, u)] ¯ f  (¯x, u)

No

Yes No

b=b+1

X = [clearness index, transportation behavior]

(35)

¯ h(¯x, u), ¯ x¯ and u¯ are the objective function, constraints, where f (¯x, u), dependent and decision variables, respectively. The charging and discharging power of EVs are the decision variables for the optimization. The PSO halts upon reaching the sufficient number of iterations that ensure convergence to the global best position. A one-year simulation period is considered for this study to account for seasonal variations and different types of days. This provides a more accurate representation of the system’s behavior as compared to deterministic models where the simulation is performed for typical days.

Fig. 1. Flowchart for the proposed smart scheduling of EVs.

3. Case studies The proposed method is used to provide a collaborative strategy between the EV owners and PV producers to minimize the imbalance cost of 12 MW capacity of PV generation. 424 EVs are considered for this study with the fast charging capabilities of 50 kW or more in 15–30 min [18]. The collaboration requires the available EVs to purchase the PV power in excess of the scheduled output. This reduces the penalty cost for PV power over-production. The available V2G capacity is then discharged to minimize the penalty cost for PV power under-production. The V2G trade is settled at real-time MCPs. The collaboration increases the revenues and incentives for both PV participants and EV owners.

M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142

Fleet 1

25

Driving Patterns (miles)

Fleet 2

Table 3 Simulation results for the total imbalances, penalty cost and utilization of PV power.

Fleet 3

20

Fleet 4 Fleet 5

15

Fleet 6

139

Total PV power imbalances Total penalty cost for PV power imbalances Total PV power utilization

No V2G service

Proposed V2G service

3646 (MWh) 262.395 (k$)

336 (MWh) 17.268 (k$)

71.6%

97.34%

10 Table 4 Simulation results for the revenue and cost of V2G service for the one-year simulation period.

5 0

5

10

15 T ime (ho urs)

20

Fleet

1

2

3

4

5

6

CV2G (k$) RV2G (k$)

106.025 53.490

81.350 46.214

83.286 40.614

107.974 57.742

103.540 55.765

89.067 47.069

Fig. 2. Driving patterns for fleets 1–6.

The clearness index and MCP data are from the Mesonet and California ISO [33,34]. Two cases are studied: Case I, where the PV power is scheduled based on the forecast with no scheme to reduce the power imbalances; and Case II, where the EVs are optimally charged/discharged to minimize the forecast uncertainty and enhance the dispatchability of PV power. Efficiency of the proposed collaborative strategy is evaluated for different forecast errors. Root mean square error (RMSE) is used as an index to calculate the accuracy of the forecast by:



N

1 2 RMSE =  (Pˆ PV (i) − PAPV (i)) N

(36)

i=1

where N is the total number of hours, Pˆ PV (i) and PAPV (i) are the forecast and actual values of the PV power at hour i. Figs. 2–6 and Tables 3 and 4 provide the simulation results for Cases I and II with the forecast error of 283.90 MW. 100%

80%

70%

Fig. 2 shows the driving patterns of the EV fleets with 95, 40, 73, 80, 71 and 65 EVs for fleets 1–6. Fig. 3 shows the daily distributions of the actual PV power as well as the forecast for the one-year simulation period. It provides the percentage of days with a certain range of PV power for the scenarios generated by MCS. Different percentages of the generated samples are captured within the different power ranges. These percentages provide the probabilities of PV power coverage for all scenarios. For example, the probability of sample coverage for the first power range is 30%. The probability increases to 100% with all the generated samples captured within the last power range. The PV power imbalance between the scheduled output and actual power is 0 MW for hours 1–5 and 20–24 as solar energy is only available during daylight hours. Fig. 4 shows the daily SOC distributions of the EV fleets for the one-year simulation period. The distributions provide the percentage of EVs within a certain SOC interval for the scenarios generated by MCS. For example, 30% of EVs of Fleet 1 have SOC values less than 0.02 MW for hour 14. This value increases to 0.33, 0.92, 1.46, 60%

50%

40%

30%

Actual PV Power (MW)

10 8 6 4 2 0

2

4

6

8

10

12 14 T ime (h )

16

18

20

22

24

2

4

6

8

10

12 14 T ime (h )

16

18

20

22

24

Predicted PV Power (MW)

12 10 8 6 4 2 0

Fig. 3. Daily distributions of the actual and predicted PV power for the one-year simulation period.

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M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142

100%

80 %

70 %

60 %

2

1

0

5

10

15

20

1

0

5

10

SOC for Fleet4 (MWh)

SOC for Fleet3 (MWh)

20

15

20

15

20

3

2

1

5

10

15

20

2

1

0

5

10

T ime (h)

T ime (h) 3 SOC for Fleet6 (MWh)

3 SOC for Fleet5 (MWh)

15 T ime (h)

3

2

1

0

30 %

2

T ime (h)

0

40 %

3 SOC for Fleet2 (MWh)

SOC for Fleet1 (MWh)

3

50 %

5

10

15

20

2

1

0

5

10

T ime (h)

T ime (h)

Fig. 4. Daily SOC distribution of EV fleets for the one-year simulation period.

1.58, 2.16 and 2.46 MW for 40, 50, 60, 70, 80 and 100% of EVs of Fleet 1, respectively. The daily absolute values of the average PV power difference between the predicted and actual output are calculated for the oneyear simulation period and provided in Fig. 5. The proposed V2G

service significantly reduces PV power imbalances when compared to the case with no V2G service. This shows the efficiency of the proposed method to enhance the predictability of PV power. The penalty cost is calculated as the daily average of the cost of PV power imbalances for the generated scenarios. Fig. 6 shows the

1.4 Average Value of PV Power Imbalances (MW)

No V2G Service Prop osed V2G Service

1.2

1

0.8

0.6

0.4

0.2

0 4

6

8

10

12 T ime (h )

14

16

Fig. 5. Average PV power imbalances for the scenarios generated by MCS.

18

20

M. Ghofrani et al. / Electric Power Systems Research 117 (2014) 134–142

141

90 No V2G Serv ice 80

Proposed V2G Service

70

Penalty Cost ($)

60 50 40 30 20 10 0 4

6

8

10

12 T ime (h )

14

16

18

20

Fig. 6. Average daily penalty cost of PV power imbalances for the scenarios generated by MCS.

Table 5 Simulation results for different forecast accuracies for the one-year simulation period. Performance measure (RMSE) Total penalty – No V2G service Total penalty – proposed V2G service

173.48 (MW)

283.90 (MW)

389.38 (MW)

163.464 (k$)

262.394 (k$)

363.252 (k$)

2.690 (k$)

17.268 (k$)

42.655 (K$)

penalty cost of Cases I and II for the one-year simulation period. In Case II, the PV power producer incurs significantly less energy imbalance charges with the proposed smart scheduling of V2G services. The sum of the PV power imbalances is calculated for the oneyear simulation period and provided in Table 3 along with the associated penalty cost. The percentage of PV power utilization is also calculated for the proposed collaborative strategy as well as the case with no V2G service. The PV power utilization increases from 71.6% for the base case to 97.34% for the V2G service. This demonstrates a better utilization of renewable generation as a result of the collaboration between PV participants and EV owners. Table 4 provides the simulation results for cost–benefit analysis of the V2G service. The results show that the V2G revenues alone cannot justify the cost of V2G services for the proposed application. However, the cost may be justified by including some other services or credits such as fast-response capacity reserve, regulating power, and renewables capacity firming. Technological advances and cost reduction of automotive battery technologies may justify the V2G cost and provide the EV owners with economic incentives to trade their V2G power for the proposed service. The Department of Energy (DOE) estimates that the cost of lithium-ion batteries will drop to $125/kWh by 2022 [20]. Based on the DOE estimates for the battery cost and an inflation rate of 2%, our cost–benefit analysis results in V2G cost of $64.931k, $45.239k, $50.779k, $63.792k, $60.377k and $52.483k for fleets 1–6. The 2022 projected revenues are $62.548k, $54.094k, $47.490k, $67.548k, $65.244k and $55.064 for fleets 1–6 which economically justify the estimated costs of fleets 2, 4, 5, and 6. Table 5 shows the efficiency of the proposed V2G service for different forecast accuracies. Three cases are considered for low, average and high forecast errors with RMSEs of 173.48, 283.90 and

389.38 MW. As shown, our proposed method reduces the penalty cost more when the forecast error increases. 4. Conclusions This paper proposes a stochastic framework to optimally utilize the V2G capacities of EVs and reduce the uncertainty of PV power. A PSO-based MCS is developed to minimize the penalty cost for PV power imbalances between the scheduled output and actual power. The proposed method provides a collaborative strategy between the PV producers and EV owners to increase the revenues and incentives for both participants. An economic model is developed that includes the V2G costs and revenues to evaluate the feasibility of the proposed V2G service. Simulation results demonstrate the efficiency of the proposed algorithm to enhance the utilization and predictability of PV power. The penalty cost is significantly reduced for the coordinated charging/discharging scenario when compared to the case with no V2G service. Simulation results of the cost–benefit analysis show that V2G revenues alone cannot justify the cost of V2G services for the proposed application. However, the cost may be justified by including some other services or credits such as fast-response capacity reserve, regulating power, renewables capacity firming and production tax credits. Our cost–benefit analysis justifies V2G service as a means of hedging against PV power imbalances in a near future. This is mainly due to industrial advances of automotive battery technologies which significantly reduce the cost of lithium-ion batteries for EVs. References [1] Solar Photovoltaic (PV) Integration Cost Study. A Black & Veatch (B&V) Report Prepared for Arizona Public Service Company, 2012. [2] P. Denholm, E. Ela, B. Kirby, M. Milligan, The Role of Energy Storage With Renewable Electricity Generation. Technical Report, NREL/TP-6A2-47187, 2010. [3] C.A. Hill, M.C. Such, D. Chen, J. Gonzalez, W.M. Grady, Battery energy storage for enabling integration of distributed solar power generation, IEEE Trans. Smart Grid 3 (2) (2012) 850–857. [4] M. Datta, T. Senjyu, A. Yona, T. Funabashi, C. Kim, Photovoltaic output power fluctuations smoothing methods for single and multiple PV generators, Curr. Appl. Phys. 10 (2010) 265–270. [5] J.K. Kaldellis, D. Zafirakis, E. Kondili, Optimum sizing of photovoltaic-energy storage systems for autonomous small islands, Int. J. Electr. Power Energy Syst. 32 (2010) 24–36. [6] H. Rezk, A.M. El. Sayed, Sizing of a stand-alone concentrated photovoltaic system in Egyptian site, Int. J. Electr. Power Energy Syst. 45 (2013) 325–330.

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[24] F. Kreikebaum, R. Moghe, A. Prasai, D. Divan, Evaluating the application of energy storage and day-ahead solar forecasting to firm the output of a photovoltaic plant, in: IEEE Energy Conversion Congress and Exposition (ECCE), Phoenix, AZ, 2011. [25] Bonneville Power Administration, 2010 Initial Transmission Proposal: Study and Documentation for 2010 Ancillary Services and Control Area Services. TR10-E-BPA-03, 2009. [26] M. Ehsani, M. Falahi, S. Lotfifard, Vehicle to grid services: potential and applications, Energies 5 (2012) 4076–4090. [27] M. Pantos, Exploitation of electric-drive vehicles in electricity markets, IEEE Trans. Power Syst. 27 (2) (2012) 682–694. [28] J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981. [29] D.J. Ketchen, C.L. Shook, The application of cluster analysis in strategic management research: an analysis and critique, Strateg. Manage. J. 17 (1996) 441–458. [30] R.Y. Rubinstein, Simulation and the Monte Carlo Method, Wiley, New York, 1981. [31] M.A. Hassan, M.A. Abido, Optimal design of microgrids in autonomous and gridconnected modes using particle swarm optimization, IEEE Trans. Power Electr. 26 (3) (2011) 755–769. [32] T. Weise, Global Optimization Algorithms – Theory and Application, 2nd ed., 2009, June, Available at: http://www.it-weise.de/projects/book.pdf [33] http://mesonet.agron.iastate.edu/agclimate/info.phtml [34] http://www.caiso.com/about/Pages/default.aspx Mahmoud Ghofrani received his B.Sc. degree in electrical engineering from AmirKabir University of Technology, Tehran, Iran in 2005, the M.Sc. degree from University of Tehran, Tehran, Iran, in 2008, and the Ph.D. degree from University of Nevada, Reno, in 2014. Since September 2013, he has been with the School of Science, Technology, Engineering and Mathematics, University of Washington, Bothell, where he is currently an Assistant Professor. His research interests include power systems operation and planning, renewable energy systems, smart grids, electric vehicles and electricity market. Amirsaman Arabali received his B.Sc. degree in electrical engineering from Semnan University, Semnan, Iran, and the M.Sc. degree from Sharif University of Technology, Tehran, Iran, in 2005 and 2010, respectively. He received the Ph.D. degree from University of Nevada, Reno (UNR) in 2014. His research interests include power systems operation and planning, power market, energy management, electric vehicles and renewable energy systems. Mohadesseh Ghayekhloo received her B.Sc. degree in computer engineering from Mazandaran University of Science and Technology, Babol, Iran, and the M.Sc. degree from Science and Research Branch, Islamic Azad University, Qazvin, Iran in 2011 and 2014, respectively. Her research interests include optimization algorithms, artificial neural networks, computational intelligence and their applications in power systems.