- Email: [email protected]
Optimal charging of Electric Vehicles in residential area
Sustainable Energy, Grids and Networks 19 (2019) 100240
Contents lists available at ScienceDirect
Sustainable Energy, Grids and Networks journal homepage: www.elsevier.com/locate/segan
Optimal charging of Electric Vehicles in residential area ∗
Soumia Ayyadi , Hasnae Bilil, Mohamed Maaroufi Electrical Department, Mohammadia School of Engineers, Mohammed V University, Rabat, Morocco
article
info
Article history: Received 22 February 2019 Received in revised form 22 June 2019 Accepted 1 August 2019 Available online xxxx Keywords: Management policy of Electric Vehicles Day-ahead electricity price Electric Vehicles Initial state of charge Linear programming Monte Carlo method Residential area
a b s t r a c t Uncoordinated Electric Vehicles (EVs) charging can lead to incremental overloads, power losses and voltage fluctuations which are stressful and harmful for the distribution networks. To overcome these consequences, using EVs charging strategies is becoming of tremendous importance. We propose in this paper a new approach aiming at minimizing the EVs charging cost based on the day-ahead electricity price (DAEP) and battery degradation cost subject to the EVs state of charge (SOC) limits, the EVs maximum power charger, the EVs batteries full charging at the end of the charging period and the distribution feeder subscribed power. Besides, to deal with the EVs arrival and departure time uncertainties, Monte Carlo Simulations (MCS) have been applied based on the probability density functions of these parameters, while the EV’s initial SOC uncertainties are estimated based on their daily mileage. Finally, to show the efficiency of the proposed approach, a single phase Low Voltage (LV) distribution network in a residential area has been deployed with an EVs penetration rate of 50% and 100%. In this study, the optimization problem is solved using linear programming method. The results show that the proposed approach allows to reduce the EVs charging cost by 50% and 38% for 100% and 50% of EVs penetration rate respectively compared to uncoordinated EVs charging. © 2019 Published by Elsevier Ltd.
1. Introduction The transport sector accounts for 20% of the world carbon dioxide emissions and consumes more than 50% of the world oil consumption, according to the Organization for Economic Cooperation and Development [1]. Therefore, the electrification of the transport sector represents an attractive solution towards sustainable mobility [2], because it could reduce air pollution, greenhouse and dependence on oil, also it promotes the integration of renewable energy sources in the transport sector. However, the large-scale uncontrolled Electric Vehicles (EVs) charging could stress and harm the power system. Many studies have been devoted to evaluate the impact of the EVs charging on the distribution grid [3–7]. For instance, the authors in [6,7] reported that the uncoordinated EVs charging could double the average load. Furthermore, the studies in [1,2] showed that the EVs charging in peak hours could significantly reduce the life duration of the HV/LV transformers. The uncoordinated EVs charging could lead to voltage drops, increased losses, transformer degradation, fuse blowouts and feeders thermal limit violations reported in [8,9]. The authors in [10] demonstrated that a decreasing of transformer life duration is proportional to the EVs charging rate. Hence, the transformers with limited power can be the most ∗ Corresponding author. E-mail address: [email protected] (S. Ayyadi). https://doi.org/10.1016/j.segan.2019.100240 2352-4677/© 2019 Published by Elsevier Ltd.
affected. For every 10% of EVs charging rate, the losses increase by 3.5% [11]. To cope with the previous effects numerous studies demonstrate that the use of smart charging strategies reduce the side effects of the massive EVs charging impacting the distribution systems. The work in [12,13] showed that smart charging can reduce losses. Moreover, the authors in [14] report that a simple charging strategy could avoid the transformer loss of life duration. Based on the related literature, the coordinated EVs charging can be categorized into four main types. A charging strategy may aim at minimizing the EV charging cost, at decreasing the effect of EVs charging on the distribution system, at benefiting from the EVs batteries as a distributed generation and powered EVs by renewable energies. Several studies have been carried out in order to minimize the EVs charging cost. In [15] the authors set the EVs charging cost as an optimization problem subject to maintain acceptable distribution network voltages. Another study in [16] proposed a scheme in which the aggregator operates as a master agent and each EV is considered as a sub-agent; the master agent programs each subagent in response to the exigencies of the distribution network operator and to minimize the EVs charging costs, a penalty term has been introduced in the objective function to coordinate the performance of the sub-agents. The authors in [17] formulated a non-cooperative game model in order to minimize the EVs charging cost, they used the real-time electricity price model to encourage the EVs owners to change their charging process
2
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
from peak hours to off peak hours. New convex programming has been presented in [18] to minimize the daily operational expense of EVs. A Mixed-integer second-order cone programming model has been developed to minimize the total operational costs of electrical distribution systems by determining an optimal EVs charging strategy [19]. The study in [20] aims to minimize the EV charging cost within the electrical system constraints. A centralized approach to coordinate the EV charging has been described in [21]; the chargers and the grid constraints has been taken into account in order to minimize the EVs charging cost. The concept of removing the effect of EVs charging on the grid and its components takes a big interest in literature. An EVs optimal controlled charging policy using Artificial Immune Systems has been presented in [22] to avoid overload, higher voltage levels and to minimize power losses. Two formulations of the EVs charging problem have been proposed in [23], deterministic and stochastic; aiming to minimize power losses and voltage drops when coordinated EVs charging was the purpose of the study. The authors in [24] present a centralized smart charging algorithm to decrease the peak load of 2000 EVs, the EVs arrival and departure time have been assumed to be known. Smoothed the transformers load profile and reduced the load peak based on two stage charging strategy were the aims of [25]. Twostage stochastic optimization problem has been formulated to reduce the negative effect of EVs charging on the distribution system [26]. The authors in [27] proposed two different sub-gradient optimization methods to avoid the distribution feeders overload, one based on the primal–dual approach and the other based on the cost minimization. Decrease the power fluctuation level caused by EVs charging was the objective function of [28]; the EV owners behaviour uncertainties and the EVs charging demand have been taken into account. A comprehensive management strategy has been proposed in [29] to maximize the load factor; the results showed that the load factor has been increased by 22% versus uncoordinated method. A distributed optimal charging algorithms for EVs charging via dual splitting was studied in [30] to minimize the load variance. Online and offline algorithms have been proposed in [31], the purpose of the two algorithms is to move the EVs charging to the off-peak hours to fill the valley, the results demonstrated that the performance of offline algorithms is optimal compared to online profiles. A centralized method has been proposed in [32] to co-optimize the transformer loss-of-life with the benefits for EVs owners. Vehicle-to-Grid (V2G) and the Vehicle-to-Home (V2H) concepts have been developed to mitigate potential over-loads in the distribution grid and support the grid frequency [28,33–35]. The renewable energy sources have been deployed in many studies to power the EV charging stations. A two-stage EVs charging mechanism coupled with renewable energies was developed in [36] to reduce the system peak to average ratio. Another study defined a model to minimize the EVs charging cost connected to a charging station supplied by photovoltaic modules [37]. A stochastic scheduling model has been proposed in [38], considering the day-ahead electricity price and the renewable sources uncertainties. Based on the electricity price variation, the wind power flow and the availability of EVs, a smart charging strategy has been developed in [39] to minimize the EVs charging cost. Switching the EVs charging from night time to day time charging which would match with peak solar production can increase renewable energies penetration from 56.7% to 73% has been demonstrated in [40]. This work proposes a simple stochastic method to minimize the EVs charging cost based on the day ahead electricity price (DAEP), the battery degradation cost and the EV’s arrival, departure time uncertainties. Furthermore, this paper presents a method to calculate the initial state of charge (SOC) noticed by SOC0 of the EVs based on their daily mileage. In this case, the
utility would not need to collect the SOC0 of the vehicles from the owners and the EVs consumption will be forecasted, which could help the distribution system operator to predict the EVs energy demand. The proposed optimal charging approach implemented in this work has satisfied the lower and upper bound of the battery, the EVs maximum power charger, the SOC requirements and the subscribed power. Monte Carlo Simulations have been applied in order to handle the arrival and departure times as well as the initial state of charge uncertainties. The remainder of the paper is structured as follows. In Section 2, the problem formulation and the proposed algorithm are described. The distribution network and the optimization parameters value are presented in Section 3. Results and discussions have been performed in Section 4 to assess the effectiveness of the proposed algorithm. Finally, Section 5 provides the conclusion. 2. Problem formulation We consider the case of a neighbourhood including buildings and houses where users own N EVs and they can charge their batteries in the parking lot. It is assumed in this approach that a central controller (CC) is able to communicate with the EVs. The CC receives the EVs batteries characteristics mainly the maximum i capacity (Cmax ) of the battery and the maximum power of each i EV charger (Pmax ). Then, it executes the proposed control strategy and Finally it sends the set-point of the charging rate (xit ) to the corresponding EV. Fig. 1 provides an illustrative scheme of the proposed approach. Moreover, The CC estimates the SOC0 using the statistical data of the EVs daily driving mileage. The objective function of this charging strategy is to minimize the EVs energy consumption cost, while constraints on the state of charge, the maximum power of the charger and the subscribed power are fulfilled. This optimization problem can be formulated given in Eq. (1) subject to (2)–(5) min
T N ∑ ∑
(Prt + ηCbat )xit ∆t
(1)
t =1 i=1
subject to i 0 ≤ xit ≤ Pmax
SOCmin ≤
(2)
SOCti
≤ SOCmax ∑T i t =1 (η xt )∆t i i SOCT = SOC0 + = SOCmax i Cmax
(3) (4)
∑N
i i=1 xt + Dt ) ≤ S ∀t = 1, 2, 3, . . . , T ∀i = 1, 2, 3, . . . , N
(
(5)
where Prt represents the DAEP at each time step t, Cbat is the battery degradation cost rate in e/kWh, η is the charging efficiency, xit represents the EV charging rate for the i th connected EV at the t th time index, ∆t is the time step (in hour), T is the charging period of the EVs, and N is the number of connected EVs. The constraints that the objective function (1) is subject to are listed i in (2) to (5), where Pmax in (2) indicates the maximum EV charger power labelled i, this parameter takes discrete values in this paper. To avoid impacting the batteries states of health, the partial states of charge (SOCti ) must be limited between boundaries as in (3), where SOCmin and SOCmax are the minimum and maximum state of charge. In order to ensure the main goal of the EVs which is the transport of the individuals; all EVs are supposed to be connected to the electrical grid with an initial state of charge (SOC0 ). Eq. (4) has been assumed to be equal to SOCmax to guarantee that the battery of the EV labelled i, is fully charged at the end of time step T . The constraint presented in (5) aims to avoid exceeding the subscribed power (S), with Dt is the base demand.
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
3
Fig. 1. Illustrative schematic of the proposed approach.
2.1. Implementation of the optimization The objective function and the constraints are presented by linear equations. For this reason, the Linear Programming has been chosen to solve the optimization problem. The total electricity cost for each time step t = 1, 2, 3, . . . , T is expressed by (6). The process of the optimization proposed in this work is undertaken in two steps as listed below. These steps have been explained in the optimal charging algorithm. Ptot (t) = Prt + ηCbat
(6)
2.1.1. Calculation of the initial state of charge of the vehicle Forecasting the SOC0 of the EVs is the advantage of this work, this parameter can allow the utility to predict the EVs optimal charging. The most factor that the SOC0 depends on is the daily i driving mileage [41], it can be calculated by (7) and (8), with Cmax i is the maximum capacity of each vehicle (kWh), Carr is the arrival capacity of EV labelled i (kWh), ξ i represents the consumption of each vehicle in (kWh/km), and d is the daily driving mileage of the EVs in (km). SOC0i =
i Carr i Cmax
i i Carr = Cmax − ξi ∗ d
(7)
Fig. 2. Single-phase distribution network. Table 1 Parameters of the optimization model. Parameters
Value
Total number of EVs (N) Charging efficiency (η) Battery degradation cost (Cbat ) i The maximum power of charger (Pmax ) SOCmin SOCmax Subscribed power (S) The number of Monte Carlo iterations (K)
100 0.9 0.032 e/kWh 2.3 kW, 3.3 kW 20% 80% 82.5 kW 5000
(8)
2.1.2. Solving the problem with MATLAB Optimization Toolbox After determining the SOC0 in the first step, MATLAB Optimization Toolbox which includes a function called linprog, is applied to minimize the problem presented in this work. Monte Carlo Simulations are adopted in order to handle the arrival time, the departure time and the initial state of charge uncertainties. 3. Distribution network case study 3.1. System test The objective of this paper is to implement an EV charging strategy to minimize the charging cost based on predictable SOC0 , EVs arrival and departure time. To evaluate the performance of the proposed algorithm, a single-phase distribution network has been used as illustrated in Fig. 2. This network comprises 50 houses, it has been assumed that each house has two EVs which makes a fleet of 100 EVs. In order, to take into account the EVs diversity, three kinds of EVs have been adopted in this work:
• Electric Vehicle with a maximum capacity of 16 kWh, consumption of 0.19 kWh/km and maximum power charger of 3.3 kW. • Electric Vehicle with a maximum capacity of 20 kWh, consumption of 0.18 kWh/km and maximum power charger of 3.3 kW. • Electric Vehicle with a maximum capacity of 24 kWh, consumption of 0.18 kWh/km and maximum power charger of 2.3 kW. The parameters values deployed in the optimization are listed in Table 1. It has been set that the state of charge is between 20% and 80%, in order to satisfy the condition presented by (3) and to improve the battery life. The battery degradation price is 0.032e/kWh which has been taken from the measurementsbased prediction laboratory [42]. the maximum powers of the chargers are equal to 2.3kW and 3.3kW.
4
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
3.2. Electricity price and base demand The simulated period in this work is 24h with a resolution of 1 hour. The base demand (from 01h to 00h) for individual households is generated using the CREST model [43], which is an open source tool that generates daily household electricity demand. A January weekday for domestic loads is chosen in this study which usually has a power factor of 0.9. The UK DAEP for a January weekday from [44] is illustrated in Fig. 3 with the base demand curve. The total electricity cost for scheduling EVs charging Ptot (t), can be calculated for each time step t = 1, 2, 3, . . . , T using (6). Fig. 3. The base demand of 50 households and UK day-ahead electricity price.
Algorithm: The optimal charging algorithm 1:
2: 3: 4: 5: 6: 7:
INPUT: The utility knows the EVs arrival time (tarr ), the EVs i departure time (tdep ), the maximal capacity (Cmax ) of each EV, the number of Monte Carlo Simulations iteration K , the total electricity cost (Ptot (t)) at each time step t = 1, 2, 3, ..., T , the number of EVs (N), the maximum power of the charger i of each EV (Pmax ), the subscribed power (S), the base load profile (Dt ) at each time step t = 1, 2, 3, ..., T , the energy consumption of each EV (ξ i ) and the daily driving mileage (d). OUTPUT: At each time step t = 1, 2, 3, ..., T output the charging profile x = (x1 , x2 ,...,xT ) PROCEDURE: for i = 1 to N do Pick tarr and tdep for j = 1 to K do i i Carrj = Cmax − ξ i ∗ dj i Carrj
8:
i SOC0j ←−
9:
Optimize ∑T min t =1 (Prt + ηCbat )xit ∆t
10:
11:
13: 14: 15: 16: 17:
(
g(x|µ, σ , ν ) =
∑T
⎪ SOCTi = SOC0i + ⎪ ⎪ ⎪ ⎪ = SOCmax ⎪ ⎪ ⎪ ⎪ ⎩ ∀t = 1, 2, 3, ..., T
i t =1 (ηxt )∆t Cmax
end for xit =
12:
3.3.1. The driving mileage The driving mileage of each trip follows Birnbaum–Saunders distribution presented by (10). Where g(.) is the PDF of the Birnbaum–Saunders distribution. β is the scale parameter and γ is shape parameter. Based on MLE, β = 10.15 and γ = 0.95. The real data curve and the Birnbaum–Saunders fitting curve are illustrated in Fig. 4.
i Cmax
⎧ i 0 ≤ xit ≤ Pmax ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ SOCmin ≤ SOCti ≤ SOCmax ⎪ ⎪ ⎨
s.t .
K 1 ∑
K
j
xt
(9)
j=1
end ∑for N i if i=1 xt + Dt ≤ S then
∑N
x ←− else x ←− 0 end if
i=1
A survey has been conducted in Beijing city in China on private vehicle owners driving behaviour [45]. The data recorded by the global positioning system (GPS) installed on 112 private cars from June 2012 to March 2013 has been used in this work. According to the survey, the distributed percentages revealed that the mileage for each trip is significantly concentrated in 3 to 30 km range, this paper assumed that the EVs make two trips each day (from home to workplace and from the workplace to home). The travelling periods of the EVs during weekdays are concentrated between 6:00–09:00 (At the morning) and 16:00–19:00 (At the evening). To improve the Monte Carlo simulation credibility. The statistics of EVs travelling behaviour has been fitted by different probability distribution functions (PDFs) to determine the best PDF that fits well the data, the maximum likelihood estimates (MLE) is used to get the selected PDF parameters.
xit
3.3. Electric vehicles owners behaviour The uncoordinated and coordinated EVs energy consumption can be predicted based on the EV owners behaviour. However, EV owners behaviour is a random factor. Hence, the study of this factor gives more reliability to the forecasted EVs energy consumption.
( ν+1 )
Γ √ 2 ( ) σ νπ Γ ν2
[
ν+
( x−µ )2 ] ν
1 − ν+ 2
)
σ
(10)
3.3.2. The EVs departure time The departure time of the EVs follows the t location-scale distribution presented by (11). where g(.) is the PDF of the t location-scale distribution. Γ (.) is the gamma function, µ is the location parameter, σ is the scale parameter, and ν is the shape parameter. Based on MLE, µ =8.30, σ =1 and ν = 2.12. The real data curve and the location-scale distribution fitting curve are illustrated in Fig. 5. (
g(x|µ, σ , ν ) =
( ν+1 )
Γ √ 2 ( ) σ νπ Γ ν2
[
ν+
( x−µ )2 ] ν
σ
1 − ν+ 2
)
(11)
3.3.3. The EVs arrival time The arrival time of the EVs follows the lognormal distribution presented by (12), where g(.) is the PDF of the lognormal distribution. µ and σ are the mean and the standard deviation value respectively. Based on MLE, µ = 18.30, σ = 2.79. The real data curve and the lognormal distribution fitting curve are illustrated in Fig. 5. g(x|µ, σ ) =
1
xσ
√
2π
e
−(ln(x)−µ)2 2σ
(12)
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
5
Fig. 7. Uncoordinated charging of 50 EVs. Fig. 4. Daily driving mileage per trip (km).
Fig. 8. Coordinated charging of 100 EVs (Estimated results). Fig. 5. Departure time and the arrival time of EVs for each trip.
Fig. 6. Uncoordinated charging of 100 EVs.
4. Results and discussions To show the efficiency of the proposed algorithm, three scenarios have been considered. Including uncoordinated charging, coordinated charging and base demand (without EVs). In these scenarios, the EVs arrival, departure time and the daily driving mileage follow the PDFs which have been described in Section 3.3. Two different EVs penetration levels have been treated in this paper 50% and 100%. Figs. 6 and 7 illustrate the total power demand of distribution network, the uncoordinated EVs charging of both penetration levels. This scenario assumes that the EV users are aware about the high electricity price in the early evening and they have intention to minimize their EVs charging cost. Hence, they connect their EVs to the electrical network after midnight. In this case, all EVs owners can charge their vehicles during the low peak which
creates a high peak demand after midnight. As results, the peak demand of the distribution network increases to 128 kW and 99 kW which are 55% and 20% higher to the subscribed power for 100% and 50% of EVs penetration rate respectively at 01h. The associated total EVs charging cost for this scenario is 32.65e and 14.6e for 100% and 50% EVs penetration rate respectively. It can be observed from the results that the uncoordinated EVs charging is going to harm the distribution network. To avoid this consequence the electricity system operator should make a smart charging strategy, which is the purpose of this paper. The results of the proposed algorithm based on Monte Carlo simulations have been shown in Figs. 8 and 9. We notice that the total power over the charging period is less to the subscribed power. The optimized EVs total charging cost during the simulation period for this distribution network is 16.23e and 9e for 100% and 50% of the EVs penetration rate respectively; which represents 50% and 38% of cost saving for 100% and 50% EVs penetration rate respectively compared to the uncoordinated charging. In order to give more credibility to the proposed method. The actual and the estimated results have been assessed to determine the error generated by the use of Monte Carlo Simulations. The fitted data has been used in the estimated results, although the actual results have been based on the statistical data (real EV owners behaviour). Figs. 10 and 11 showed the obtained results based on the real EV owners behaviour. The average energy error between the actual results and the estimated results is 2% and 7.44% for 100% and 50% penetration rate respectively. Table 2 illustrated the EVs charging cost of different methods used in this work. The charging cost based on the Monte Carlo simulations is 2.82% and 8.43% higher than the charging cost using the real EV owners behaviour data for 100% and 50% penetration rate respectively.
6
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
optimization problem have been respected. The estimated results showed that the coordinated charging could reduce EVs charging cost by 50% and 38% for 100% and 50% of the EVs penetration rate respectively compared to an uncoordinated charging. The actual and the estimated results have been compared, the charging cost error and the average energy error results are small enough to use the proposed method to predict the EVs optimal charging. This work has great importance because the utility could forecast the EVs consumption, which would help the distribution system operator to manage its production sources. Declaration of competing interest
Fig. 9. Coordinated charging of 50 EVs (Estimated results).
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References
Fig. 10. Coordinated charging of 100 EVs (Actual results).
Fig. 11. Coordinated charging of 50 EVs (Actual results). Table 2 Charging cost comparison for all methods proposed in this paper. Method
Charging cost of 100 EVs (e)
Charging cost of 50 EVs (e)
Uncoordinated charging
32,65
14.6
Coordinated charging (Monte Carlo simulations)
16.23
9
Coordinated charging (Real EV owners behaviour data)
15.77
8.27
5. Conclusion A new intelligent approach for charging coordination of multiple EVs in a residential area has been presented in this paper. Where the EVs optimal charging can be predictable based on the EV owners behaviour data, the DAEP and the battery cost degradation. This approach ensures that all constraints in the
[1] Q. Gong, S. Midlam-Mohler, V. Marano, G. Rizzoni, Study of PEV charging on residential distribution transformer life, IEEE Trans. Smart Grid 3 (1) (2012) 404–412. [2] A. Maitra, J. Taylor, D. Brooks, M. Alexander, M. Duvall, Integrating plug-inelectric vehicles with the distribution system, in: International Conference and Exhibition on Electricity Distribution, CIRED, June, 2009. [3] S. Sachan, N. Kishor, Charging of electric vehicles under contingent conditions in smart distribution grids, in: IEEE International Conference on Power Electronics, Drives and Energy Systems, PEDES, Dec. 2016. [4] M. Amini, M.P. Moghaddam, O. Karabasoglu, Simultaneous allocation of electric vehicles parking lots and distributed renewable resources in smart power distribution networks, Sustainable Cities Soc. 28 (2017) 332–342. [5] A. Dubey, S. Santoso, Electric vehicle charging on residential distribution systems: impacts and mitigations, IEEE Access 3 (2015) 1871–1893. [6] I. Rahman, P.M. Vasant, B.S.M. Singh, Review of recent trends in optimization techniques for plug-in hybrid, and electric vehicle charging infrastructures, Renew. Sustain. Energy Rev. 58 (2016) 1039–1047. [7] Y. Li, C. Davis, Z. Lukszo, Electric vehicle charging in China power system: energy, economic and environmental trade-offs and policy implications, Appl. Energy 173 (2016) 535–554. [8] D.T. Hoang, P. Wang, D. Niyato, E. Hossain, Charging and discharging of plug-in electric vehicles (PEVs) in vehicle-to-grid (V2G) systems: a cyber insurance-based model, IEEE Access 5 (2017) 732–754. [9] L. Pieltain Fernandez, T. Gomez San Roman, R. Cossent, C. Mateo Domingo, P. Frias, Assessment of the impact of plug-in electric vehicles on distribution networks, IEEE Trans. Power Syst 26 (1) (2011) 206–213. [10] H. Turker, S. Bacha, D. Chatroux, A. Hably, Low-voltage transformer loss-oflife assessments for a high penetration of plug-in hybrid electric vehicles (PHEVs), IEEE Trans. Power Deliv. 27 (3) (2012) 1323–1331. [11] M.S. EL Nozahy, M.M.A. Salama, A comprehensive study of the impacts of PHEVs on residential distribution networks, IEEE Trans. Sustain. Energy 5 (1) (2014) 332–342. [12] P. Papadopoulos, S. Skarvelis-Kazakos, I. Grau, L.M. Cipcigan, N. Jenkins, Predicting electric vehicle impacts on residential distribution networks with distributed generation, in: IEEE Vehicle Power and Propulsion Conference, VPPC, Sept 2010. [13] E. Sortomme, M.M. Hindi, S.D.J. MacPherson, S.S. Venkata, Coordinated charging of plug-in hybrid electric vehicles to minimize distribution system losses, IEEE Trans. Smart Grid 2 (1) (2011) 198–205. [14] M.J. Rutherford, V. Yousefzadeh, The impact of Electric Vehicle battery charging on distribution transformers, in: IEEE Applied Power Electronics Conference and Exposition, APEC, March 2011. [15] Y. Wang, D. Infield, S. Gill, Smart charging for electric vehicles to minimise charging cost, J. Power Energy 231 (1) (2017) 526–534. [16] S. Ruggeri, F. Pilo, N. Natale, S. Mocci, Multi-agent control system to coordinate optimal electric vehicles charging and demand response actions in active distribution networks, in: Renewable Power Generation Conference, RPG, Sept. 2014. [17] H. Liu, Y. Wang, Y. Wang, Z. Li, Strategic scheduling of PEV charging load: a non-cooperative game model, in: 36th Chinese Control Conference, Jul 2017. [18] E. Sortomme, M.M. Hindi, S.D.J. MacPherson, S.S. Venkata, Charging, power management, and battery degradation mitigation in plug-in hybrid electric vehicles: a unified cost-optimal approach, Mech. Syst. Signal Process. 87 (2017) 14–16. [19] J. Lopez, D.C. Moreno, Optimal plug-in electric vehicles charging coordination in electrical distribution networks, in: IEEE Third Ecuador Technical Chapters Meeting, ETCM, Oct 2018.
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240 [20] M.A.S. Masoum, S.M.H. Nabavi, Hybrid optimal online-overnight charging coordination of plug-in electric vehicles in smart grid, J. Power Sources 330 (2016) 7–17. [21] A. Ovalle, A. Hably, S. Bacha, Grid Optimal Integration of Electric Vehicles, Springer International Publishing, 2018, p. 137, (Chapter 2). [22] D.Q. Oliveira, A.C. Zambroni de Souza, L.F.N. Delboni, Optimal plug-in hybrid electric vehicles recharge in distribution power systems, Electr. Power Syst. Res. 98 (2013) 77–85. [23] K. Clement-Nyns, E. Haesen, J. Driesen, The impact of charging plug-in hybrid electric vehicles on a residential distribution grid, IEEE Trans. Power Syst. 25 (1) (2010) 371–380. [24] E.C. Kara, J.S. Macdonald, D. Black, M. Berges, G. Hug, S. Kiliccote, Estimating the benefits of electric vehicle smart charging at non-residential locations: a data-driven approach, Appl. Energy 155 (2015) 515–525. [25] M.F. Bandpey, K.G. Firouzjah, Two-stage charging strategy of plug-in electric vehicles based on fuzzy control, Comput. Oper. Res. 96 (2018) 236–243. [26] F. Wu, R. Sioshansi, A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints, Transp. Res. B 102 (2017) 55–82. [27] A. Ghavami, K. Kar, A. Gupta, Decentralized charging of plug-in electric vehicles with distribution feeder overload control, IEEE Trans. Automat. Control 61 (2016) 3527–3532. [28] C. Liu, K.K. Chai, E.T. Lau, Y. Wang, Y. Chen, Optimised electric vehicles charging scheme with uncertain user-behaviours in smart grids, in: 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications, PIMRC, Oct 2017. [29] M. Honarmand, N.S. Gilani, H. Modaghegh, Comprehensive management strategy for plug-in hybrid electric vehicles using national smart metering program in Iran, Called FAHAM, in: 5th International Conference on Smart Cities and Green ICT Systems, SMARTGREENS, April 2016. [30] C. Floch, F. Belletti, S. Moura, Optimal charging of electric vehicles for load shaping: a dual splitting framework with explicit convergence bounds, IEEE Trans. Transport. Electrific. 27 (1) (2012) 268–279. [31] N. Chen, C.W. Tan, T.Q.S. Quek, Electric vehicle charging in smart grid: optimality and valley-filling algorithms, IEEE J. Sel. Topics Signal Process 8 (6) (2014) 1073–1083.
7
[32] P. Richardson, D. Flynn, A. Keane, Optimal charging of electric vehicles in low-voltage distribution systems, IEEE Trans. Power Syst. 27 (1) (2012) 268–279. [33] S. Gao, K.T. Chau, C. Liu, D. Wu, C.C. Chan, Integrated energy management of plug-in electric vehicles in power grid with renewables, IEEE Trans. Veh. Technol. 63 (7) (2014) 3019–3027. [34] J.J. Escudero-Garzas, A. Garcia-Armada, G. Seco-Granados, Fair design of plug-in electric vehicles aggregator for V2G regulation, IEEE Trans. Veh. Technol. 61 (8) (2012) 3406–3419. [35] H. Turker, S. Bacha, Optimal minimization of plug-in electric vehicle charging cost with vehicle-to-home and vehicle-to-grid concepts, IEEE Trans. Veh. Technol. 67 (8) (2018) 10281–10292. [36] R. Wang, P. Wang, G. Xiao, Two-stage mechanism for massive electric vehicle charging involving renewable energy, IEEE Trans. Veh. Technol. 65 (8) (2016) 4159–4171. [37] V. Nguyen, T. Tran-Quoc, S. Bacha, N. Luu, Charging strategies to minimize the energy cost for an electric vehicle fleet, in: IEEE PES Innovative Smart Grid Technologies, Europe, PES, Oct 2014. [38] S. Sachan, N. Kishor, Charging of electric vehicles under contingent conditions in smart distribution grids, in: 2016 IEEE International Conference on Power Electronics, Drives and Energy Systems, PEDES, Dec. 2016. [39] S. Sachan, Integration of electric vehicles with optimum sized storage for grid connected photovoltaic system, AIMS Energy 5 (6) (2017) 997–1012. [40] K.E. Forrest, B. Tarroja, L. Zhang, B. Shaffer, S. Samuelsen, Charging a renewable future: the impact of electric vehicle charging intelligence on energy storage requirements to meet renewable portfolio standards, J. Power Sources 336 (2016) 63–74. [41] S.M. Arif, T. Lie, B.C. Seet, A novel simulation model for analyzing the state of charge of electric vehicle, in: IEEE Innovative Smart Grid Technologies - Asia, ISGT Asia, May, 2018. [42] S.B. Peterson, J.F. Whitacre, J. Apt, The economics of using plug-in hybrid electric vehicle battery packs for grid storage, J. Power Sources 195 (8) (2010) 2377–2384. [43] E. McKenna, M. Thomson, High-resolution stochastic integrated thermalelectrical domestic demand model, Appl. Energy 165 (2016) 445–461. [44] View hourly UK prices. (Online) Available: http://www.nordpoolspot.com/ Market-data1/GB/Auction-prices/UK/Hourly/. (Accessed 12 Nov 2018). [45] H. Wang, X. Zhang, L. Wu, C. Hou, H. Gong, Q. Zhang, M. Ouyang, Beijing passenger car travel survey: implications for alternative fuel vehicle deployment, Mitig. Adapt. Strat. Global Change 20 (5) (2015) 817–835.
Contents lists available at ScienceDirect
Sustainable Energy, Grids and Networks journal homepage: www.elsevier.com/locate/segan
Optimal charging of Electric Vehicles in residential area ∗
Soumia Ayyadi , Hasnae Bilil, Mohamed Maaroufi Electrical Department, Mohammadia School of Engineers, Mohammed V University, Rabat, Morocco
article
info
Article history: Received 22 February 2019 Received in revised form 22 June 2019 Accepted 1 August 2019 Available online xxxx Keywords: Management policy of Electric Vehicles Day-ahead electricity price Electric Vehicles Initial state of charge Linear programming Monte Carlo method Residential area
a b s t r a c t Uncoordinated Electric Vehicles (EVs) charging can lead to incremental overloads, power losses and voltage fluctuations which are stressful and harmful for the distribution networks. To overcome these consequences, using EVs charging strategies is becoming of tremendous importance. We propose in this paper a new approach aiming at minimizing the EVs charging cost based on the day-ahead electricity price (DAEP) and battery degradation cost subject to the EVs state of charge (SOC) limits, the EVs maximum power charger, the EVs batteries full charging at the end of the charging period and the distribution feeder subscribed power. Besides, to deal with the EVs arrival and departure time uncertainties, Monte Carlo Simulations (MCS) have been applied based on the probability density functions of these parameters, while the EV’s initial SOC uncertainties are estimated based on their daily mileage. Finally, to show the efficiency of the proposed approach, a single phase Low Voltage (LV) distribution network in a residential area has been deployed with an EVs penetration rate of 50% and 100%. In this study, the optimization problem is solved using linear programming method. The results show that the proposed approach allows to reduce the EVs charging cost by 50% and 38% for 100% and 50% of EVs penetration rate respectively compared to uncoordinated EVs charging. © 2019 Published by Elsevier Ltd.
1. Introduction The transport sector accounts for 20% of the world carbon dioxide emissions and consumes more than 50% of the world oil consumption, according to the Organization for Economic Cooperation and Development [1]. Therefore, the electrification of the transport sector represents an attractive solution towards sustainable mobility [2], because it could reduce air pollution, greenhouse and dependence on oil, also it promotes the integration of renewable energy sources in the transport sector. However, the large-scale uncontrolled Electric Vehicles (EVs) charging could stress and harm the power system. Many studies have been devoted to evaluate the impact of the EVs charging on the distribution grid [3–7]. For instance, the authors in [6,7] reported that the uncoordinated EVs charging could double the average load. Furthermore, the studies in [1,2] showed that the EVs charging in peak hours could significantly reduce the life duration of the HV/LV transformers. The uncoordinated EVs charging could lead to voltage drops, increased losses, transformer degradation, fuse blowouts and feeders thermal limit violations reported in [8,9]. The authors in [10] demonstrated that a decreasing of transformer life duration is proportional to the EVs charging rate. Hence, the transformers with limited power can be the most ∗ Corresponding author. E-mail address: [email protected] (S. Ayyadi). https://doi.org/10.1016/j.segan.2019.100240 2352-4677/© 2019 Published by Elsevier Ltd.
affected. For every 10% of EVs charging rate, the losses increase by 3.5% [11]. To cope with the previous effects numerous studies demonstrate that the use of smart charging strategies reduce the side effects of the massive EVs charging impacting the distribution systems. The work in [12,13] showed that smart charging can reduce losses. Moreover, the authors in [14] report that a simple charging strategy could avoid the transformer loss of life duration. Based on the related literature, the coordinated EVs charging can be categorized into four main types. A charging strategy may aim at minimizing the EV charging cost, at decreasing the effect of EVs charging on the distribution system, at benefiting from the EVs batteries as a distributed generation and powered EVs by renewable energies. Several studies have been carried out in order to minimize the EVs charging cost. In [15] the authors set the EVs charging cost as an optimization problem subject to maintain acceptable distribution network voltages. Another study in [16] proposed a scheme in which the aggregator operates as a master agent and each EV is considered as a sub-agent; the master agent programs each subagent in response to the exigencies of the distribution network operator and to minimize the EVs charging costs, a penalty term has been introduced in the objective function to coordinate the performance of the sub-agents. The authors in [17] formulated a non-cooperative game model in order to minimize the EVs charging cost, they used the real-time electricity price model to encourage the EVs owners to change their charging process
2
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
from peak hours to off peak hours. New convex programming has been presented in [18] to minimize the daily operational expense of EVs. A Mixed-integer second-order cone programming model has been developed to minimize the total operational costs of electrical distribution systems by determining an optimal EVs charging strategy [19]. The study in [20] aims to minimize the EV charging cost within the electrical system constraints. A centralized approach to coordinate the EV charging has been described in [21]; the chargers and the grid constraints has been taken into account in order to minimize the EVs charging cost. The concept of removing the effect of EVs charging on the grid and its components takes a big interest in literature. An EVs optimal controlled charging policy using Artificial Immune Systems has been presented in [22] to avoid overload, higher voltage levels and to minimize power losses. Two formulations of the EVs charging problem have been proposed in [23], deterministic and stochastic; aiming to minimize power losses and voltage drops when coordinated EVs charging was the purpose of the study. The authors in [24] present a centralized smart charging algorithm to decrease the peak load of 2000 EVs, the EVs arrival and departure time have been assumed to be known. Smoothed the transformers load profile and reduced the load peak based on two stage charging strategy were the aims of [25]. Twostage stochastic optimization problem has been formulated to reduce the negative effect of EVs charging on the distribution system [26]. The authors in [27] proposed two different sub-gradient optimization methods to avoid the distribution feeders overload, one based on the primal–dual approach and the other based on the cost minimization. Decrease the power fluctuation level caused by EVs charging was the objective function of [28]; the EV owners behaviour uncertainties and the EVs charging demand have been taken into account. A comprehensive management strategy has been proposed in [29] to maximize the load factor; the results showed that the load factor has been increased by 22% versus uncoordinated method. A distributed optimal charging algorithms for EVs charging via dual splitting was studied in [30] to minimize the load variance. Online and offline algorithms have been proposed in [31], the purpose of the two algorithms is to move the EVs charging to the off-peak hours to fill the valley, the results demonstrated that the performance of offline algorithms is optimal compared to online profiles. A centralized method has been proposed in [32] to co-optimize the transformer loss-of-life with the benefits for EVs owners. Vehicle-to-Grid (V2G) and the Vehicle-to-Home (V2H) concepts have been developed to mitigate potential over-loads in the distribution grid and support the grid frequency [28,33–35]. The renewable energy sources have been deployed in many studies to power the EV charging stations. A two-stage EVs charging mechanism coupled with renewable energies was developed in [36] to reduce the system peak to average ratio. Another study defined a model to minimize the EVs charging cost connected to a charging station supplied by photovoltaic modules [37]. A stochastic scheduling model has been proposed in [38], considering the day-ahead electricity price and the renewable sources uncertainties. Based on the electricity price variation, the wind power flow and the availability of EVs, a smart charging strategy has been developed in [39] to minimize the EVs charging cost. Switching the EVs charging from night time to day time charging which would match with peak solar production can increase renewable energies penetration from 56.7% to 73% has been demonstrated in [40]. This work proposes a simple stochastic method to minimize the EVs charging cost based on the day ahead electricity price (DAEP), the battery degradation cost and the EV’s arrival, departure time uncertainties. Furthermore, this paper presents a method to calculate the initial state of charge (SOC) noticed by SOC0 of the EVs based on their daily mileage. In this case, the
utility would not need to collect the SOC0 of the vehicles from the owners and the EVs consumption will be forecasted, which could help the distribution system operator to predict the EVs energy demand. The proposed optimal charging approach implemented in this work has satisfied the lower and upper bound of the battery, the EVs maximum power charger, the SOC requirements and the subscribed power. Monte Carlo Simulations have been applied in order to handle the arrival and departure times as well as the initial state of charge uncertainties. The remainder of the paper is structured as follows. In Section 2, the problem formulation and the proposed algorithm are described. The distribution network and the optimization parameters value are presented in Section 3. Results and discussions have been performed in Section 4 to assess the effectiveness of the proposed algorithm. Finally, Section 5 provides the conclusion. 2. Problem formulation We consider the case of a neighbourhood including buildings and houses where users own N EVs and they can charge their batteries in the parking lot. It is assumed in this approach that a central controller (CC) is able to communicate with the EVs. The CC receives the EVs batteries characteristics mainly the maximum i capacity (Cmax ) of the battery and the maximum power of each i EV charger (Pmax ). Then, it executes the proposed control strategy and Finally it sends the set-point of the charging rate (xit ) to the corresponding EV. Fig. 1 provides an illustrative scheme of the proposed approach. Moreover, The CC estimates the SOC0 using the statistical data of the EVs daily driving mileage. The objective function of this charging strategy is to minimize the EVs energy consumption cost, while constraints on the state of charge, the maximum power of the charger and the subscribed power are fulfilled. This optimization problem can be formulated given in Eq. (1) subject to (2)–(5) min
T N ∑ ∑
(Prt + ηCbat )xit ∆t
(1)
t =1 i=1
subject to i 0 ≤ xit ≤ Pmax
SOCmin ≤
(2)
SOCti
≤ SOCmax ∑T i t =1 (η xt )∆t i i SOCT = SOC0 + = SOCmax i Cmax
(3) (4)
∑N
i i=1 xt + Dt ) ≤ S ∀t = 1, 2, 3, . . . , T ∀i = 1, 2, 3, . . . , N
(
(5)
where Prt represents the DAEP at each time step t, Cbat is the battery degradation cost rate in e/kWh, η is the charging efficiency, xit represents the EV charging rate for the i th connected EV at the t th time index, ∆t is the time step (in hour), T is the charging period of the EVs, and N is the number of connected EVs. The constraints that the objective function (1) is subject to are listed i in (2) to (5), where Pmax in (2) indicates the maximum EV charger power labelled i, this parameter takes discrete values in this paper. To avoid impacting the batteries states of health, the partial states of charge (SOCti ) must be limited between boundaries as in (3), where SOCmin and SOCmax are the minimum and maximum state of charge. In order to ensure the main goal of the EVs which is the transport of the individuals; all EVs are supposed to be connected to the electrical grid with an initial state of charge (SOC0 ). Eq. (4) has been assumed to be equal to SOCmax to guarantee that the battery of the EV labelled i, is fully charged at the end of time step T . The constraint presented in (5) aims to avoid exceeding the subscribed power (S), with Dt is the base demand.
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
3
Fig. 1. Illustrative schematic of the proposed approach.
2.1. Implementation of the optimization The objective function and the constraints are presented by linear equations. For this reason, the Linear Programming has been chosen to solve the optimization problem. The total electricity cost for each time step t = 1, 2, 3, . . . , T is expressed by (6). The process of the optimization proposed in this work is undertaken in two steps as listed below. These steps have been explained in the optimal charging algorithm. Ptot (t) = Prt + ηCbat
(6)
2.1.1. Calculation of the initial state of charge of the vehicle Forecasting the SOC0 of the EVs is the advantage of this work, this parameter can allow the utility to predict the EVs optimal charging. The most factor that the SOC0 depends on is the daily i driving mileage [41], it can be calculated by (7) and (8), with Cmax i is the maximum capacity of each vehicle (kWh), Carr is the arrival capacity of EV labelled i (kWh), ξ i represents the consumption of each vehicle in (kWh/km), and d is the daily driving mileage of the EVs in (km). SOC0i =
i Carr i Cmax
i i Carr = Cmax − ξi ∗ d
(7)
Fig. 2. Single-phase distribution network. Table 1 Parameters of the optimization model. Parameters
Value
Total number of EVs (N) Charging efficiency (η) Battery degradation cost (Cbat ) i The maximum power of charger (Pmax ) SOCmin SOCmax Subscribed power (S) The number of Monte Carlo iterations (K)
100 0.9 0.032 e/kWh 2.3 kW, 3.3 kW 20% 80% 82.5 kW 5000
(8)
2.1.2. Solving the problem with MATLAB Optimization Toolbox After determining the SOC0 in the first step, MATLAB Optimization Toolbox which includes a function called linprog, is applied to minimize the problem presented in this work. Monte Carlo Simulations are adopted in order to handle the arrival time, the departure time and the initial state of charge uncertainties. 3. Distribution network case study 3.1. System test The objective of this paper is to implement an EV charging strategy to minimize the charging cost based on predictable SOC0 , EVs arrival and departure time. To evaluate the performance of the proposed algorithm, a single-phase distribution network has been used as illustrated in Fig. 2. This network comprises 50 houses, it has been assumed that each house has two EVs which makes a fleet of 100 EVs. In order, to take into account the EVs diversity, three kinds of EVs have been adopted in this work:
• Electric Vehicle with a maximum capacity of 16 kWh, consumption of 0.19 kWh/km and maximum power charger of 3.3 kW. • Electric Vehicle with a maximum capacity of 20 kWh, consumption of 0.18 kWh/km and maximum power charger of 3.3 kW. • Electric Vehicle with a maximum capacity of 24 kWh, consumption of 0.18 kWh/km and maximum power charger of 2.3 kW. The parameters values deployed in the optimization are listed in Table 1. It has been set that the state of charge is between 20% and 80%, in order to satisfy the condition presented by (3) and to improve the battery life. The battery degradation price is 0.032e/kWh which has been taken from the measurementsbased prediction laboratory [42]. the maximum powers of the chargers are equal to 2.3kW and 3.3kW.
4
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
3.2. Electricity price and base demand The simulated period in this work is 24h with a resolution of 1 hour. The base demand (from 01h to 00h) for individual households is generated using the CREST model [43], which is an open source tool that generates daily household electricity demand. A January weekday for domestic loads is chosen in this study which usually has a power factor of 0.9. The UK DAEP for a January weekday from [44] is illustrated in Fig. 3 with the base demand curve. The total electricity cost for scheduling EVs charging Ptot (t), can be calculated for each time step t = 1, 2, 3, . . . , T using (6). Fig. 3. The base demand of 50 households and UK day-ahead electricity price.
Algorithm: The optimal charging algorithm 1:
2: 3: 4: 5: 6: 7:
INPUT: The utility knows the EVs arrival time (tarr ), the EVs i departure time (tdep ), the maximal capacity (Cmax ) of each EV, the number of Monte Carlo Simulations iteration K , the total electricity cost (Ptot (t)) at each time step t = 1, 2, 3, ..., T , the number of EVs (N), the maximum power of the charger i of each EV (Pmax ), the subscribed power (S), the base load profile (Dt ) at each time step t = 1, 2, 3, ..., T , the energy consumption of each EV (ξ i ) and the daily driving mileage (d). OUTPUT: At each time step t = 1, 2, 3, ..., T output the charging profile x = (x1 , x2 ,...,xT ) PROCEDURE: for i = 1 to N do Pick tarr and tdep for j = 1 to K do i i Carrj = Cmax − ξ i ∗ dj i Carrj
8:
i SOC0j ←−
9:
Optimize ∑T min t =1 (Prt + ηCbat )xit ∆t
10:
11:
13: 14: 15: 16: 17:
(
g(x|µ, σ , ν ) =
∑T
⎪ SOCTi = SOC0i + ⎪ ⎪ ⎪ ⎪ = SOCmax ⎪ ⎪ ⎪ ⎪ ⎩ ∀t = 1, 2, 3, ..., T
i t =1 (ηxt )∆t Cmax
end for xit =
12:
3.3.1. The driving mileage The driving mileage of each trip follows Birnbaum–Saunders distribution presented by (10). Where g(.) is the PDF of the Birnbaum–Saunders distribution. β is the scale parameter and γ is shape parameter. Based on MLE, β = 10.15 and γ = 0.95. The real data curve and the Birnbaum–Saunders fitting curve are illustrated in Fig. 4.
i Cmax
⎧ i 0 ≤ xit ≤ Pmax ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ SOCmin ≤ SOCti ≤ SOCmax ⎪ ⎪ ⎨
s.t .
K 1 ∑
K
j
xt
(9)
j=1
end ∑for N i if i=1 xt + Dt ≤ S then
∑N
x ←− else x ←− 0 end if
i=1
A survey has been conducted in Beijing city in China on private vehicle owners driving behaviour [45]. The data recorded by the global positioning system (GPS) installed on 112 private cars from June 2012 to March 2013 has been used in this work. According to the survey, the distributed percentages revealed that the mileage for each trip is significantly concentrated in 3 to 30 km range, this paper assumed that the EVs make two trips each day (from home to workplace and from the workplace to home). The travelling periods of the EVs during weekdays are concentrated between 6:00–09:00 (At the morning) and 16:00–19:00 (At the evening). To improve the Monte Carlo simulation credibility. The statistics of EVs travelling behaviour has been fitted by different probability distribution functions (PDFs) to determine the best PDF that fits well the data, the maximum likelihood estimates (MLE) is used to get the selected PDF parameters.
xit
3.3. Electric vehicles owners behaviour The uncoordinated and coordinated EVs energy consumption can be predicted based on the EV owners behaviour. However, EV owners behaviour is a random factor. Hence, the study of this factor gives more reliability to the forecasted EVs energy consumption.
( ν+1 )
Γ √ 2 ( ) σ νπ Γ ν2
[
ν+
( x−µ )2 ] ν
1 − ν+ 2
)
σ
(10)
3.3.2. The EVs departure time The departure time of the EVs follows the t location-scale distribution presented by (11). where g(.) is the PDF of the t location-scale distribution. Γ (.) is the gamma function, µ is the location parameter, σ is the scale parameter, and ν is the shape parameter. Based on MLE, µ =8.30, σ =1 and ν = 2.12. The real data curve and the location-scale distribution fitting curve are illustrated in Fig. 5. (
g(x|µ, σ , ν ) =
( ν+1 )
Γ √ 2 ( ) σ νπ Γ ν2
[
ν+
( x−µ )2 ] ν
σ
1 − ν+ 2
)
(11)
3.3.3. The EVs arrival time The arrival time of the EVs follows the lognormal distribution presented by (12), where g(.) is the PDF of the lognormal distribution. µ and σ are the mean and the standard deviation value respectively. Based on MLE, µ = 18.30, σ = 2.79. The real data curve and the lognormal distribution fitting curve are illustrated in Fig. 5. g(x|µ, σ ) =
1
xσ
√
2π
e
−(ln(x)−µ)2 2σ
(12)
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
5
Fig. 7. Uncoordinated charging of 50 EVs. Fig. 4. Daily driving mileage per trip (km).
Fig. 8. Coordinated charging of 100 EVs (Estimated results). Fig. 5. Departure time and the arrival time of EVs for each trip.
Fig. 6. Uncoordinated charging of 100 EVs.
4. Results and discussions To show the efficiency of the proposed algorithm, three scenarios have been considered. Including uncoordinated charging, coordinated charging and base demand (without EVs). In these scenarios, the EVs arrival, departure time and the daily driving mileage follow the PDFs which have been described in Section 3.3. Two different EVs penetration levels have been treated in this paper 50% and 100%. Figs. 6 and 7 illustrate the total power demand of distribution network, the uncoordinated EVs charging of both penetration levels. This scenario assumes that the EV users are aware about the high electricity price in the early evening and they have intention to minimize their EVs charging cost. Hence, they connect their EVs to the electrical network after midnight. In this case, all EVs owners can charge their vehicles during the low peak which
creates a high peak demand after midnight. As results, the peak demand of the distribution network increases to 128 kW and 99 kW which are 55% and 20% higher to the subscribed power for 100% and 50% of EVs penetration rate respectively at 01h. The associated total EVs charging cost for this scenario is 32.65e and 14.6e for 100% and 50% EVs penetration rate respectively. It can be observed from the results that the uncoordinated EVs charging is going to harm the distribution network. To avoid this consequence the electricity system operator should make a smart charging strategy, which is the purpose of this paper. The results of the proposed algorithm based on Monte Carlo simulations have been shown in Figs. 8 and 9. We notice that the total power over the charging period is less to the subscribed power. The optimized EVs total charging cost during the simulation period for this distribution network is 16.23e and 9e for 100% and 50% of the EVs penetration rate respectively; which represents 50% and 38% of cost saving for 100% and 50% EVs penetration rate respectively compared to the uncoordinated charging. In order to give more credibility to the proposed method. The actual and the estimated results have been assessed to determine the error generated by the use of Monte Carlo Simulations. The fitted data has been used in the estimated results, although the actual results have been based on the statistical data (real EV owners behaviour). Figs. 10 and 11 showed the obtained results based on the real EV owners behaviour. The average energy error between the actual results and the estimated results is 2% and 7.44% for 100% and 50% penetration rate respectively. Table 2 illustrated the EVs charging cost of different methods used in this work. The charging cost based on the Monte Carlo simulations is 2.82% and 8.43% higher than the charging cost using the real EV owners behaviour data for 100% and 50% penetration rate respectively.
6
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240
optimization problem have been respected. The estimated results showed that the coordinated charging could reduce EVs charging cost by 50% and 38% for 100% and 50% of the EVs penetration rate respectively compared to an uncoordinated charging. The actual and the estimated results have been compared, the charging cost error and the average energy error results are small enough to use the proposed method to predict the EVs optimal charging. This work has great importance because the utility could forecast the EVs consumption, which would help the distribution system operator to manage its production sources. Declaration of competing interest
Fig. 9. Coordinated charging of 50 EVs (Estimated results).
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References
Fig. 10. Coordinated charging of 100 EVs (Actual results).
Fig. 11. Coordinated charging of 50 EVs (Actual results). Table 2 Charging cost comparison for all methods proposed in this paper. Method
Charging cost of 100 EVs (e)
Charging cost of 50 EVs (e)
Uncoordinated charging
32,65
14.6
Coordinated charging (Monte Carlo simulations)
16.23
9
Coordinated charging (Real EV owners behaviour data)
15.77
8.27
5. Conclusion A new intelligent approach for charging coordination of multiple EVs in a residential area has been presented in this paper. Where the EVs optimal charging can be predictable based on the EV owners behaviour data, the DAEP and the battery cost degradation. This approach ensures that all constraints in the
[1] Q. Gong, S. Midlam-Mohler, V. Marano, G. Rizzoni, Study of PEV charging on residential distribution transformer life, IEEE Trans. Smart Grid 3 (1) (2012) 404–412. [2] A. Maitra, J. Taylor, D. Brooks, M. Alexander, M. Duvall, Integrating plug-inelectric vehicles with the distribution system, in: International Conference and Exhibition on Electricity Distribution, CIRED, June, 2009. [3] S. Sachan, N. Kishor, Charging of electric vehicles under contingent conditions in smart distribution grids, in: IEEE International Conference on Power Electronics, Drives and Energy Systems, PEDES, Dec. 2016. [4] M. Amini, M.P. Moghaddam, O. Karabasoglu, Simultaneous allocation of electric vehicles parking lots and distributed renewable resources in smart power distribution networks, Sustainable Cities Soc. 28 (2017) 332–342. [5] A. Dubey, S. Santoso, Electric vehicle charging on residential distribution systems: impacts and mitigations, IEEE Access 3 (2015) 1871–1893. [6] I. Rahman, P.M. Vasant, B.S.M. Singh, Review of recent trends in optimization techniques for plug-in hybrid, and electric vehicle charging infrastructures, Renew. Sustain. Energy Rev. 58 (2016) 1039–1047. [7] Y. Li, C. Davis, Z. Lukszo, Electric vehicle charging in China power system: energy, economic and environmental trade-offs and policy implications, Appl. Energy 173 (2016) 535–554. [8] D.T. Hoang, P. Wang, D. Niyato, E. Hossain, Charging and discharging of plug-in electric vehicles (PEVs) in vehicle-to-grid (V2G) systems: a cyber insurance-based model, IEEE Access 5 (2017) 732–754. [9] L. Pieltain Fernandez, T. Gomez San Roman, R. Cossent, C. Mateo Domingo, P. Frias, Assessment of the impact of plug-in electric vehicles on distribution networks, IEEE Trans. Power Syst 26 (1) (2011) 206–213. [10] H. Turker, S. Bacha, D. Chatroux, A. Hably, Low-voltage transformer loss-oflife assessments for a high penetration of plug-in hybrid electric vehicles (PHEVs), IEEE Trans. Power Deliv. 27 (3) (2012) 1323–1331. [11] M.S. EL Nozahy, M.M.A. Salama, A comprehensive study of the impacts of PHEVs on residential distribution networks, IEEE Trans. Sustain. Energy 5 (1) (2014) 332–342. [12] P. Papadopoulos, S. Skarvelis-Kazakos, I. Grau, L.M. Cipcigan, N. Jenkins, Predicting electric vehicle impacts on residential distribution networks with distributed generation, in: IEEE Vehicle Power and Propulsion Conference, VPPC, Sept 2010. [13] E. Sortomme, M.M. Hindi, S.D.J. MacPherson, S.S. Venkata, Coordinated charging of plug-in hybrid electric vehicles to minimize distribution system losses, IEEE Trans. Smart Grid 2 (1) (2011) 198–205. [14] M.J. Rutherford, V. Yousefzadeh, The impact of Electric Vehicle battery charging on distribution transformers, in: IEEE Applied Power Electronics Conference and Exposition, APEC, March 2011. [15] Y. Wang, D. Infield, S. Gill, Smart charging for electric vehicles to minimise charging cost, J. Power Energy 231 (1) (2017) 526–534. [16] S. Ruggeri, F. Pilo, N. Natale, S. Mocci, Multi-agent control system to coordinate optimal electric vehicles charging and demand response actions in active distribution networks, in: Renewable Power Generation Conference, RPG, Sept. 2014. [17] H. Liu, Y. Wang, Y. Wang, Z. Li, Strategic scheduling of PEV charging load: a non-cooperative game model, in: 36th Chinese Control Conference, Jul 2017. [18] E. Sortomme, M.M. Hindi, S.D.J. MacPherson, S.S. Venkata, Charging, power management, and battery degradation mitigation in plug-in hybrid electric vehicles: a unified cost-optimal approach, Mech. Syst. Signal Process. 87 (2017) 14–16. [19] J. Lopez, D.C. Moreno, Optimal plug-in electric vehicles charging coordination in electrical distribution networks, in: IEEE Third Ecuador Technical Chapters Meeting, ETCM, Oct 2018.
S. Ayyadi, H. Bilil and M. Maaroufi / Sustainable Energy, Grids and Networks 19 (2019) 100240 [20] M.A.S. Masoum, S.M.H. Nabavi, Hybrid optimal online-overnight charging coordination of plug-in electric vehicles in smart grid, J. Power Sources 330 (2016) 7–17. [21] A. Ovalle, A. Hably, S. Bacha, Grid Optimal Integration of Electric Vehicles, Springer International Publishing, 2018, p. 137, (Chapter 2). [22] D.Q. Oliveira, A.C. Zambroni de Souza, L.F.N. Delboni, Optimal plug-in hybrid electric vehicles recharge in distribution power systems, Electr. Power Syst. Res. 98 (2013) 77–85. [23] K. Clement-Nyns, E. Haesen, J. Driesen, The impact of charging plug-in hybrid electric vehicles on a residential distribution grid, IEEE Trans. Power Syst. 25 (1) (2010) 371–380. [24] E.C. Kara, J.S. Macdonald, D. Black, M. Berges, G. Hug, S. Kiliccote, Estimating the benefits of electric vehicle smart charging at non-residential locations: a data-driven approach, Appl. Energy 155 (2015) 515–525. [25] M.F. Bandpey, K.G. Firouzjah, Two-stage charging strategy of plug-in electric vehicles based on fuzzy control, Comput. Oper. Res. 96 (2018) 236–243. [26] F. Wu, R. Sioshansi, A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints, Transp. Res. B 102 (2017) 55–82. [27] A. Ghavami, K. Kar, A. Gupta, Decentralized charging of plug-in electric vehicles with distribution feeder overload control, IEEE Trans. Automat. Control 61 (2016) 3527–3532. [28] C. Liu, K.K. Chai, E.T. Lau, Y. Wang, Y. Chen, Optimised electric vehicles charging scheme with uncertain user-behaviours in smart grids, in: 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications, PIMRC, Oct 2017. [29] M. Honarmand, N.S. Gilani, H. Modaghegh, Comprehensive management strategy for plug-in hybrid electric vehicles using national smart metering program in Iran, Called FAHAM, in: 5th International Conference on Smart Cities and Green ICT Systems, SMARTGREENS, April 2016. [30] C. Floch, F. Belletti, S. Moura, Optimal charging of electric vehicles for load shaping: a dual splitting framework with explicit convergence bounds, IEEE Trans. Transport. Electrific. 27 (1) (2012) 268–279. [31] N. Chen, C.W. Tan, T.Q.S. Quek, Electric vehicle charging in smart grid: optimality and valley-filling algorithms, IEEE J. Sel. Topics Signal Process 8 (6) (2014) 1073–1083.
7
[32] P. Richardson, D. Flynn, A. Keane, Optimal charging of electric vehicles in low-voltage distribution systems, IEEE Trans. Power Syst. 27 (1) (2012) 268–279. [33] S. Gao, K.T. Chau, C. Liu, D. Wu, C.C. Chan, Integrated energy management of plug-in electric vehicles in power grid with renewables, IEEE Trans. Veh. Technol. 63 (7) (2014) 3019–3027. [34] J.J. Escudero-Garzas, A. Garcia-Armada, G. Seco-Granados, Fair design of plug-in electric vehicles aggregator for V2G regulation, IEEE Trans. Veh. Technol. 61 (8) (2012) 3406–3419. [35] H. Turker, S. Bacha, Optimal minimization of plug-in electric vehicle charging cost with vehicle-to-home and vehicle-to-grid concepts, IEEE Trans. Veh. Technol. 67 (8) (2018) 10281–10292. [36] R. Wang, P. Wang, G. Xiao, Two-stage mechanism for massive electric vehicle charging involving renewable energy, IEEE Trans. Veh. Technol. 65 (8) (2016) 4159–4171. [37] V. Nguyen, T. Tran-Quoc, S. Bacha, N. Luu, Charging strategies to minimize the energy cost for an electric vehicle fleet, in: IEEE PES Innovative Smart Grid Technologies, Europe, PES, Oct 2014. [38] S. Sachan, N. Kishor, Charging of electric vehicles under contingent conditions in smart distribution grids, in: 2016 IEEE International Conference on Power Electronics, Drives and Energy Systems, PEDES, Dec. 2016. [39] S. Sachan, Integration of electric vehicles with optimum sized storage for grid connected photovoltaic system, AIMS Energy 5 (6) (2017) 997–1012. [40] K.E. Forrest, B. Tarroja, L. Zhang, B. Shaffer, S. Samuelsen, Charging a renewable future: the impact of electric vehicle charging intelligence on energy storage requirements to meet renewable portfolio standards, J. Power Sources 336 (2016) 63–74. [41] S.M. Arif, T. Lie, B.C. Seet, A novel simulation model for analyzing the state of charge of electric vehicle, in: IEEE Innovative Smart Grid Technologies - Asia, ISGT Asia, May, 2018. [42] S.B. Peterson, J.F. Whitacre, J. Apt, The economics of using plug-in hybrid electric vehicle battery packs for grid storage, J. Power Sources 195 (8) (2010) 2377–2384. [43] E. McKenna, M. Thomson, High-resolution stochastic integrated thermalelectrical domestic demand model, Appl. Energy 165 (2016) 445–461. [44] View hourly UK prices. (Online) Available: http://www.nordpoolspot.com/ Market-data1/GB/Auction-prices/UK/Hourly/. (Accessed 12 Nov 2018). [45] H. Wang, X. Zhang, L. Wu, C. Hou, H. Gong, Q. Zhang, M. Ouyang, Beijing passenger car travel survey: implications for alternative fuel vehicle deployment, Mitig. Adapt. Strat. Global Change 20 (5) (2015) 817–835.