Modeling and Impacts of Smart Charging PEVs in Residential Distribution Systems

Transcription

1 IEEE PES GENERAL MEETING, July 22 Modeling and Impacts of Smart Charging PEVs in Residential Distribution Systems Isha Sharma, Student Member, IEEE, Claudio A. Cañizares, Fellow, IEEE, and Kankar Bhattacharya, Senior Member, IEEE Abstract This paper presents a new modeling framework for inclusion of the charging operations of Plug-in Electric Vehicles (PEVs) within a three-phase unbalanced, residential, distribution system. Coordinated charging of the PEVs is proposed to minimize the total energy drawn from the substation, total losses in the system and the total cost of charging the PEVs. Detailed studies examine the impact of PEVs on the overall system load profile, bus load profiles, feeder currents, voltages, taps and capacitor switching. The proposed model can be used to maximize PEV charging over a 24 hour time-frame or the utilization of feeder capacity to charge the PEVs. A practical distribution test feeder is presented to demonstrate the features of the proposed model. EV EV n h l L L n n p r r n s s n t PEV loads, EV=,2,...n PEV PEV load at node n Hours, h=,2,...24 Series elements, l=,2,...,nl Loads, L=,2,...NL Loads at node n Nodes, n=,2,...n Phases, p=a,b,c Receiving-end Receiving-ends connected at node n Sending-end Sending-ends connected at node n Controllable tap changers, t=,2,...nt Index Terms Plug-in electric vehicles, Coordinated charging, three-phase unbalanced distribution system, optimal feeder operation. A. Parameters I. NOMENCLATURE ΔS Percentage voltage change for each LTC tap. θ Load power factor angle, rad. A,B,C,D Three-phase ABCD parameter matrices, p.u. C max PEV battery capacity, kwh. Io Load phase current at specified power and nominal voltage. K A constant multiplier N Total number of nodes n PEV Total number of PEV loads Nl Total number of series elements NL Total number of loads Nt Total number of controllable tap changers TOU Time-of-Use tariff W The x identity matrix X Reactance of capacitor, p.u. Z Load impedance at specified power and nominal voltage, p.u. B. Indices Controllable capacitor banks at node n C n This work is supported by Natural Sciences and Engineering Research Council (NSERC) Canada, Hydro One Networks, Inc., IBM Corporation and ABB Corporate Research USA. The authors are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L G, Canada ( i4sharma@uwaterloo.ca; ccanizar@uwaterloo.ca; kankar@uwaterloo.ca). C. Variables cap E_PEV Ip J P_PEV tap Vp n PEV A Number of capacitor blocks switched in capacitor banks Energy drawn by PEV, Wh Line current phasor, p.u. Vector of three-phase line current phasors, p.u. Objective function Power drawn by PEV, W Tap position Line voltage phasor, p.u. Vector of three-phase line voltage phasors, p.u. Total number of PEVs loads II. INTRODUCTION long with the continuously increasing penetration of renewable energy sources into power systems, plug-in electric vehicles (PEVs) have emerged as important alternatives to reduce greenhouse gas emissions and the dependence of the transport sector on imported fossil fuels. PEVs represent a step towards sustainability, using less energy and causing less pollution, noise and emissions []. A PEV is a vehicle that draws some or all of its power from the electrical power grid. Recharging the battery of a PEV can be achieved by connecting the vehicle to the grid. The majority of the PEV charging is achieved at residential garages which uses standard outlets and takes several hours to charge the battery. However, a specialized high voltage/high current electric outlet can also be used to achieve fast charging times. The charging level has a direct effect on the charging time, and using a higher level charging will bring about reduction in charging time [].

2 IEEE PES GENERAL MEETING, July 22 2 As PEVs begin to penetrate the market, it is important for distribution system operators to study their impact on system demand, feeder overloading conditions, power losses, power quality and feeder upgrades []. For example, if all PEV batteries are recharged simultaneously, overnight, it may result in an increase in demand during the overnight off-peak hours, thus flattening the load profile. On the other hand, with substantially high PEV penetration levels, there may occur a shifting of the peak load to overnight hours, which can be a cause for concern for generation dispatch, since base-load power plants may not be able to satisfy the peak demand at that time. In [2], a comprehensive approach is used to study a largescale distribution system planning model and the impact of different levels of PEV penetration on distribution network investments and energy losses. It is observed that uncoordinated charging can lead to an increase in investment costs for the distribution system while, with smart charging facilities, up to 6-% of the investment cost can be avoided. In [], the impact of coordinated and uncoordinated charging on a distribution system so as to minimize the power losses and maximize the grid load factor is examined. It is shown that uncoordinated charging can lead to an increase in the peak demand, decrease in distribution system efficiency, and threaten grid stability. A methodology is developed in [4] to determine the PEV charging load by using a stochastic approach. It is noted that, uncoordinated domestic and public charging can lead to significant increase in the peak demand, even for a low penetration level of 2%. Smart domestic charging incorporating real-time electricity pricing, in an optimization framework with the objective of minimizing the charging cost, results in the most effective solution for both the distribution system operator and the customer. In [], load factor and variance based objective functions for coordinated PEV charging are formulated, which results in minimizing the system losses and improves voltage regulation. This paper presents a modeling framework that incorporates the operation and charging of PEV loads within a three-phase distribution system model. The distribution optimal power flow (DOPF) model, proposed in [6], is extended to include the PEV load model. Using a variety of case studies, this paper examines the impact on the distribution system of PEV loads at the residential level. The rest of the paper structure is as follows: Section III describes the mathematical models of the three-phase distribution system components, the PEV model, and the DOPF model including the PEV constraints with different objective functions. Section IV presents and discusses the results obtained from various case studies carried out on the IEEE -node test feeder. Section V highlights the main conclusions from this research. III. THREE-PHASE DOPF MODEL WITH PEV CONSTRAINTS A. Three-phase Distribution System Model A generic distribution system consists of series and shunt components. Series components include conductors/cables, transformers, LTCs and switches. These components are modeled in the present work, using ABCD parameters which are based on relationships between the sending and receiving end voltages and currents [6]: [ ] [ ] [ ] () The ABCD parameters in conductors, cables, transformers, and switches are kept constant in the model. Switches are modeled as zero impedance models, conductors and cables are modeled as π equivalent circuits, three-phase transformer model is based on the type of connection (wye or delta connection). Voltage regulating transformers in distribution system are equipped with LTCs. ABCD parameters in LTCs cannot be considered constant as they depend on the tap positions acquired during each operation. Thus, the A and D parameters of the LTCs can be modeled using the following equations: [ ] (2) In (2) and (), tap a, tap b, and tap c are per-phase tap controls for a tap changer and considered continuous variables; these can take any value from -6 to +6 for a 2-step LTC. Thus, for three phase-phase tap changers, the following equation enables all tap operation to be identical in the three phases: (4) Shunt components consist of loads and capacitor banks and are modeled separately to represent unbalanced three phase loads. All the loads including capacitors (and excluding the PEV loads) are modeled as constant impedance loads. Capacitor banks are modeled as multiple capacitor blocks with switching options. The following equations represent wyeconnected impedance loads on a per-phase basis: () The PEV load is modeled as a constant current load on a perphase basis, as follows: ( ) (6) All the equations discussed above represent a component of the three-phase distribution system model. To model the distribution system in its totality, all these elements are combined in a network, i.e. current balance (KCL) at each node and phase: () Voltages of the components connected at each node and phase are equal to their corresponding nodal voltages: (8) B. Optimization Model A three-phase DOPF computes the optimal PEV charging schedule, taking into account the objective function, specified range of charging periods and grid constraints. Four case studies are carried out here with different objectives to identify the impact on feeder voltages/currents, tap positions of LTCs ()

3 IEEE PES GENERAL MEETING, July 22 and the capacitor switching of PEV loads. The resulting optimization model is a non-linear programming (NLP) problem with discontinuous derivatives, which is modeled in GAMS and solved using the SNOPT solver []. The following objective functions are considered here: Case : Minimize total energy drawn from the substation: () Case 2: Minimize total feeder losses: () Case : Minimize the total cost of charging PEVs: () Case 4: Maximize the PEV charging: (2) The constraints of the DOPF are as follows: the -phase distribution feeder and its components are modeled as equality constraints ()-(8). The feeder operating limits include the following limits on bus voltages, feeder currents, taps and capacitors: () (4) () (6) Additional constraints are required to represent the PEV model. Thus, the total energy drawn by the PEV battery over the charging period should not exceed the allowable battery charging capacity: () The maximum power drawn by the charger is determined by the maximum power (MaxW) of a standard electrical outlet, and on the level of charging: (8) Two different modes of PEV charging are considered: normal (Level ) and fast (Level 2); for Level (2V/A) and Level 2 (28-24V /4 - A) charging, MaxW is 4 W and 48 W, respectively. In Case 4, the number of PEVs is treated as an integer variable, thus rendering the proposed model an MINLP problem. As the size of the distribution system increases, the number of integer and continuous variables also increase. Furthermore, the number of variables increases significantly when the proposed model is optimized over a 24-hour timeframe. A method proposed in [8], [] is adopted in this work to alleviate the use of integer variables, thus transforming the MINLP problem into an NLP problem. Hence, a quadratic term is added to the objective function with a high penalty value to the objective function at non-integer Fig.. IEEE -node Test Feeder []. solutions, thus forcing the variable n PEV close to its integer value round(n PEV ): ( ( ) ) () IV. ANALYSIS AND RESULTS A. System Description and Assumptions The developed model is validated using the IEEE -node test feeder (Figure ) []. In this work, capacitors are modeled as multiple capacitor banks with switching options; for example, the capacitor at Bus 6 is assumed to comprise five blocks of kvar capacitors in all three phases, and at Bus 6 to have blocks of kvar capacitors in phase c. The LTC and capacitors are considered to be controllable and are treated here as continuous variables. For each case study, it is assumed that the PEVs are the only controllable loads connected to the feeder. It is also assumed that PEVs are not capable of delivering power back to the grid. A load profile represents the pattern of electricity usage of the customers. In Smart Grids, loads respond to external inputs and thus cannot be considered the same at each node. For the purpose of the case studies, a load profile is generated randomly for 24 hours starting at midnight. Each load bus represents constant impedance load models; the load data provided in [] are assumed to be the peak loads. Random load scenarios are created for each hour using a normal distribution function (mean value=, standard deviation =.). The resulting load profile is then shifted in the time axis by using an integer random number in the range [-2, +2], which represents the number of hours the profile is to be shifted. The resulting system load profile is shown in Figure 2. In order to evaluate the impact of PEV charging on the distribution system, the following assumptions are made for the studies.. All the case studies are carried out considering PHEV km mid-size sedan (8.4 kwh battery capacity). PHEV km implies that 6% of the vehicle kilometers are driven on battery and the rest on gasoline.

4 Total Demand (kw) IEEE PES GENERAL MEETING, July Because of life cycle considerations, the State-of-Charge (SOC) of the PEV battery, at the start of charging, is 2% and is charged to % of its full capacity. In other words, at most % of the battery energy is assumed to be used in charge-depleting mode.. The PEV is not available for charging between AM to PM, considering that most people are at work during this period and have their cars parked at the work place. 4. Charging efficiency is 8%.. The entire load PD i at a bus on the feeder section are residential loads, and there is one PEV per residence, i.e. N EV =. 6. The average monthly electricity consumption (AV MEC ) of a residence is kwh []. The average hourly load (AV HL ) of the residence is calculated to be 2.8 kw. Using the assumptions on the feeder loads, the number of PEVs connected to a distribution feeder can be realistically estimated from the number of electricity customers on the feeder. For a PEV penetration of x in p.u., the number of PEVs is given by: a b c Fig. 2. Base system load profile. ( ( )) (2) Different penetrations of PEVs are considered from % to %, each scenario characterized by the number of PEVs expressed as a percentage of the total population of vehicles in the area. Thus, a penetration of % refers to one PEV in each residence, while % is the base case with no PEV in the system. Detailed estimates of the number of PEVs in each phase and each bus for the test feeder are presented in Table I for a % penetration. In this case, the total number of vehicles owned by residents in the area is estimated to be,4, and approximately,2 kw PEV load is added to the existing load and is distributed over the hours for charging PEVs. Time-of-Use (TOU) tariffs are used to calculate the cost of charging PEVs, which depends on the time electricity is used. These tariffs in Ontario are based on three levels of energy demand: On-peak, Mid-peak and Off-peak, referring to the period for which demand is highest, moderate and lowest, respectively. Figure shows the summer TOU tariff in Ontario, for a weekday. The simulations are carried out with the objective function and constraints discussed in Section III.B. The PEV penetration level is varied from % (no PEVs) to % (every residence has a PEV). Three parameters are compared in all the case studies: the energy drawn by the feeder, the total losses, and the total cost of charging PEVs. All the detailed analysis of system load profiles, load bus voltages, etc., in the figures presented next, are discussed for % penetration level (Table I) and Level 2 coordinated charging. B. Case The objective of this case study is to minimize the total energy drawn from the substation, given by (). Since the electrical loads in the distribution system are voltage dependent, the total energy consumption can be reduced by operating the distribution system at the lower voltage limits voltage (. p.u.). A summary of the results for energy Fig.. Summer TOU tariffs in Ontario for weekdays. TABLE I ESTIMATED NUMBER OF PEVS AT % PENETRATION Bus Phase-a Phase- b Phase- c Total Total drawn, losses, and charging costs are presented in Table II for varying degrees of PEV penetration. The results in Figure 4 show that PEV charging in phase a takes place in the early morning hours and late night hours when the demand is low. Charging in phase b is carried out at PM and PM (off-peak hours), and in phase c from PM to 6 AM and at 6 PM which are off-peak and mid-peak hours respectively. The overall system peak demand increase by 42.%,.% and.6% in phase a, b, and c, respectively, as compared to the base case. Figure illustrates the hourly variation in the Feeder 6 62 current when PEVs are charging. The feeder current reaches its peak during the early morning hours, but remains below the maximum limit.

5 Feeder Current (A) Demand (kw) Voltage (p.u.) IEEE PES GENERAL MEETING, July 22 TABLE II CASE RESULTS FOR DIFFERENT PEV PENETRATION LEVELS Penetration Energy Drawn (MWh) Loss (MW) Cost ($/day) % % % % % % % % %.. 2. % % Fig. 6. Feeder 62-6 current Fig. 4. System load profile with % penetration and without PEV Fig.. Feeder 6-62 current. a w/o PEV b w/o PEV c w/o PEV a with PEV b with PEV c with PEV Figure 6 shows that the hourly variation of Feeder 62-6 current reaches its maximum value in the early morning hours in phase a, while current in phase b and phase c is below the maximum limit. This is attributed to the PEV charging schedule at Bus 6. The same conclusions cannot be made for all feeders, because loading in each phase and bus is different. As the objective in this case is to minimize the total energy, the bus voltages are maintained near the lower voltage limits (. p.u.) by switching LTCs and capacitors. Figure shows the phase voltages for buses with the lowest voltage magnitude at peak load Fig.. Bus voltages. C. Case 2 64-a 646-b 6-c TABLE III CASE 2 RESULTS FOR DIFFERENT PEV PENETRATION LEVELS Penetration Energy Drawn (MWh) Loss (MW) Cost ($/day) % 6.6. % % % % % % % % %.2.6. % The objective of this case study is to minimize the total feeder losses, given by (). Simulations are carried out by varying the PEV penetration level and the results are presented in Table III. In this case study, the system load is more evenly distributed over hours as compared to Case, and system peak demand increases in phase a, phase b, phase c by.8%,.% and.%, respectively (Figure 8). Charging takes place during the mid-peak interval and off-peak hours. Maximum charging is carried out in the early morning hours. All the feeder currents are much below the maximum feeder current limits. Magnitudes of the system feeder currents do not fluctuate much (Figure ), unlike Case.

6 Demand (kw) Demand (kw) IEEE PES GENERAL MEETING, July a w/o PEV b w/o PEV c w/o PEV a with PEV b with PEV c with PEV Fig. 8. System load profile with % penetration and without PEV. TABLE IV CASE RESULTS FOR DIFFERENT PEV PENETRATION LEVELS Penetration Energy (MWh) Loss (MW) Cost ($/day) % % % % % % % % % % a w/o PEV b w/o PEV c w/o PEV a with PEV b with PEV c with PEV Fig.. Feeder 6-62 current. 2 2 Fig.. Feeder 62-6 current. At Bus 6, the load is distributed evenly in the late night hours and early morning hours and thus less fluctuation is observed in the demand curve as compared to Case. Since the loading is more uniform, current in phase a is below its maximum limit (Figure ), unlike Case. All the feeder currents and bus voltages are within the specified limits. Fig.. System load profile with % penetration and without PEV. D. Case The objective of this case study is to minimize the total cost of PEV charging, given by (). The idea is to manage the charging of multiple PEVs and to leverage the flexibility in the time of charge to lower the total cost of charging. Simulations are carried out by varying the penetration level of PEVs in the system, and the results are presented in Table IV. In this case study, charging of PEVs is achieved strictly at off-peak hours because the cost of energy, the TOU tariffs are lowest at that time. Peaks are observed in the early morning hours and late night hours strictly because of the charging of PEVs. System peak demand in phase a, phase b and phase c increases by 6.%,.%, and 4.%, respectively (Figure ). Loading in phase b and phase c increases by a significant amount as compared to Case. Because of these peaks, feeder current magnitudes fluctuate and reach maximum limits in phase a. Currents in phase b and phase c are below the maximum feeder current; however, peaks are observed when charging takes place (Figure 2). Figure demonstrates the effect of PEV load on Bus 6. Since maximum charging is done when electricity prices are low, peaks are obtained for both demand and feeder current during that time interval. Feeder currents in phase a and phase c reach their maximum limit, and feeder current in phase b is below the maximum limit. Tap and capacitors operations ensure that voltages are maintained within limits. The voltages are greater than. p.u., which results in increase energy demand. Due to large fluctuations in demand and currents, losses also increase as compared to Case and Case 2.

7 Demand (kw) IEEE PES GENERAL MEETING, July 22 a w/o PEV b w/o PEV c w/opev Fig. 2. Feeder 6-62 current a with PEV b with PEV c with PEV Fig. 4. System load profile with % penetration and without PEV Fig.. Feeder 62-6 current. E. Case 4 The objective of this case study is to maximize the PEV charging (2), to use the feeder system to its full capacity to charge PEVs without violating voltage or feeder current limits. Note that, in this case study, there is no limit on the number of PEVs that residential customers can charge. The results show that a total of MW of PEV load could be added to this system and is distributed over hours. System peak load increases by 4.%, 64.% and 6.% in phase a, phase b and phase c, respectively, as compared to the base case (Figure 4). The base demand in phase b is less as compared to demand in phase a and phase c; therefore, in this case there is a big increase in the loading in phase b. As expected, feeder current for the system is at its maximum or very close to maximum limit when PEVs are charged during mid-peak and off-peak hours (Figure ). Bus 6 is chosen to illustrate the effect of loading at a particular bus. In the base case, Bus 6 has a balanced load and by adding PEVs to this bus, it becomes an unbalanced load. Loading in phase b increases more than three times when compared to the base case. Voltages and feeder currents magnitudes are maintained within the limits due to capacitors and tap operation. Fig.. Feeder 6-62 current. No PEV Case Case 2 Case Case 4 F. Comparison TABLE V SUMMARY FOR % PENETRATION Total energy Drawn (kwh) 62,66.6 (Min energy),26.2 (6.%),22.6 (6.4%),.6 (22.4%),4.6 (6.8%) Total Losses (kw),2.4 (Min losses) 2,4.6 (4.%),62. (2.%) 2,44.8 (.4%),66. (8.46%) Total Cost for charging PEVs ($/day). (.6%). (.6%) 8. (%) 2,. (24.44%) For the base case, the total energy and losses are obtained by minimizing energy and losses as the objective function, respectively. When compared with Case, Case 2 and Case for % penetration, and Case 4, it is observed that energy, losses and cost increase because of the presence of PEV loads. Comparing Case, Case 2 and Case, one notes that the minimum energy drawn at the substation is obtained in Case, minimum losses in Case 2, and minimum cost in Case, as expected (Table V). Case 4 results in significant increase in energy demand, losses and costs as compared to other case studies because of the MW PEV load added to the system (Figure 6).

8 Energy (kwh) IEEE PES GENERAL MEETING, July Base Case Case Case 2 Case Case 4 Fig. 6. Comparison of total energy drawn at the substation. V. CONCLUSIONS The paper presented the modeling of PEVs within a threephase unbalanced distribution optimal power flow framework. Smart charging of the PEVs was achieved considering various objective functions, both from the perspective of the utility system and the customer. Application case studies on a realistic test system demonstrate that the desired objectives of minimizing the energy drawn from the substation, total losses and total cost of charging PEVs, and maximizing PEV charging can be achieved within voltage, feeder current, taps and capacitor limits. It was observed from the studies that PEV charging at home during mid-peak and off-peak hours with low cost of electricity and without any major electrical upgrades to the home was successfully achieved with % PEV penetration level, for the battery size considered. With increase in the penetration level of PEVs, the peak demand was shifted to early morning hours. This model can be further improved by incorporating capacitors and taps as integer variables. There is always a trade-off between mathematical precision and computational effort. Since this problem is a NLP problem, the optimal solution obtained may be a local or global optimum. Other computational methods such as those based on genetic algorithm or simulated annealing can be used to obtain a global optimal solution to the problem using integer variables; however, the computational costs increase significantly. VI. ACKNOWLEDGEMENT The authors acknowledge the support provided by Sumit Paudyal, PhD. student at the University of Waterloo, in modeling the distribution system. [4] K. Quin, C. Zhou, M. Allan and Y. Yuan, "Modelling of Load Demand Due to EV Battery Charging in Distribution Systems," IEEE Trans. Power Syst., vol. 26, no., pp. 82-8, May 2. [] E. Sortmme, M. M. Hindi, S. D. James and S. S. Venkata, "Coordinated charging of Plug-in Hybrid Electric Vehicles to Minimize Dsitribution System Losses," IEEE Trans. Smart Grid., vol. 2, no., pp. 8-2, Mar. 2. [6] S. Paudyal, C. A. Canizares and K. Bhattacharya, "Optimal Operation of Distribution Feeders in Smart Grids," IEEE Trans. Ind. Electron., vol. 8, no., pp. 44-4, Oct. 2. [] GAMS Release 2.2, A User Guide, Washington, DC: GAMS Develop. Corp., 8. [8] M. B. Liu, C. A. Canizares and W. Huang, "Reactive Power and voltage control in distribution systems with limited switching operations," IEEE Trans. Power Syst., vol. 24, no. 2, pp. 88-8, May 2. [] M. Liu, S. K. Tso and Y. Cheng, "An extended nonlinear primal-dual interior-point algorithm for reactive power optimization of large-scale power systems with discrete control variables," IEEE Trans. Power Syst., vol., no. 4, pp. 82-, Nov. 22. [] W. H. Kersting, "Radial distribution test feeders," Proc. IEEE PES Winter Meeting, vol. 2, pp. 8-2, 2. [] C. Rao, A. P. Meliopoulos, J. Meisel and T. Overbye, "Power system level impacts of plug-in hybrid electric vehicles using simulation data," in Proc. IEEE Energy, Atlanta, GA, Nov. -8, 28. Isha Sharma (S ) received the bachelor s degree in Electrical and Computer Engineering from the University of Windsor, Windsor, Ontario, Canada in 2. She is currently working toward the Ph.D. degree in Electrical Engineering at the University of Waterloo, Waterloo, ON, Canada. Claudio A. Cañizares (S 8, M, SM, F ) received in April 84 the Electrical Engineer Diploma from the Escuela Polit ecnica Nacional (EPN), Quito-Ecuador, where he held different teaching and administrative positions from 8 to. His MS (88) and PhD () degrees in Electrical Engineering are from the University of Wisconsin-Madison. Dr. Cañizares has held various academic and administrative positions at the E&CE Department of the University of Waterloo since, where he is currently a full Professor, the Hydro One Endowed Chair and the Associate Director of the Waterloo Institute for Sustainable Energy (WISE). His research activities concentrate on the study of modeling, simulation, control, stability, computational and dispatch issues in sustainable power and energy systems in the context of competitive markets and Smart Grids. Kankar Bhattacharya (M, SM ) received the Ph.D. degree in Electrical Engineering from the Indian Institute of Technology, New Delhi, India in. He was in the faculty of Indira Gandhi Institute of Development Research, Mumbai, India, during -8, and then the Department of Electric Power Engineering, Chalmers University of Technology, Gothenburg, Sweden, during He joined the E&CE Department of the University of Waterloo, Canada, in where he is currently a full Professor. His research interests are in power system economics and operational aspects. REFERENCES [] Waterloo Institute of Sustainable Energy Report Submitted to Ontario Centres for Excellence, "Towards on Ontario Action Plan for Plug-In- Electric Vehicles (PEVs)," University of Waterloo, Waterloo, ON, 2. [2] L. P. Fernandez, T. G. S. Roman, R. Cossent and C. M. Domingo, "Assessment of the Impact of Plug-in Electric Vehicles on Distribution Networks," IEEE Trans. Power Syst., vol. 26, no., pp. 26-2, Feb. 2. [] K. Nyns, E. Haesen and J. Driesen, "The impact of Charging Plug-in Hybrid Electric Vehicles on a Resedential Distribution Grid," IEEE Trans. on Power Syst., vol. 2, no., pp. -8, Feb. 2.