Smart Grid and Renewable Energy, 2013, 4, 398408 http://dx.doi.org/10.4236/sgre.2013.45046 Published Online August 2013 (http://www.scirp.org/journal/sgre) Copyright © 2013 SciRes. SGRE ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Tobias Hahn1, Martin Schönfelder2, Patrick Jochem2, Vincent Heuveline3, Wolf Fichtner2 1Institute of Process Engineering in Life Sciences, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; 2Chair of Energy Economics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; 3University of Heidelberg, Interdisciplinary Center for Scientific Computing, Heidelberg, Germany. Email: tobias.hahn@kit.edu, martin.schoenfelder@kit.edu, patrick.jochem@kit.edu, vincent.heuveline@iwr.uniheidelberg.de, wolf.fichtner@kit.edu Received June 4th, 2013; revised July 4th, 2013; accepted July 11th, 2013 Copyright © 2013 Tobias Hahn et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT Managing the charging process of a large number of electric vehicles to decrease the pressure on the local electricity grid is of high interest to the utilities. Using efficient mathematical optimization techniques, the charging behavior of electric vehicles shall be optimally controlled taking into account network, vehicle, and customer requirements. We developed an efficient algorithm for calculating load shift potentials d efined as the range of all charg ing curves meeting the customer’s requirements and respecting all individual charging and discharging constraints over time. In addition, we formulated a mixed integer linear program (MIP) applying semicontinuous variables to find costoptimal load curves for every v ehicle participating in a load shift. This prob lem can be solved b y e.g. branchandb ound algorithms. Results of two scenarios of Germany in 2015 and 2030 based on mobility studies sho w that the load shifting potential of EV is significant and contribute to a necessary relaxation of the future grid. The maximum charging and discharging power and the average battery capacity are crucial to the overall load shift potential. Keywords: Electric Mobility; Load Shifting; Charging Management; Optimization 1. Introduction Tomorrow’s energy systems will exhibit a tremendous complexity reflected mainly by their dynamic behavior and heterogeneity. This will apply to Germany in par ticular because of the constantly increasing share of po wer generation from renewable energy sources (RES) as well as the ongoing decentralization of the po wer system. The regionally strongly differing potentials of RES will lead to an increasing spatial imbalance o f electricity gen eration and demand. Moreover, their fluctuating charac ter will require various measures, such as more flexible power plants, a grow ing capacity of effi cient ener gy sto r age systems, and the application of Demand Side Man agement (DSM) methods. At the same time, ongoing and extensive research and development activities regarding electric vehicles (EV) will facilitate the latters’ market penetration. A signifi cant share of EV in the passenger car fleet will lead to an increasing demand for electric energy especially during peak hours, if no controlled charging strategy is applied [1]. This could jeopardize the local power grid [2]. However, due to the normally long parking times of ve hicles used for individual mobility purposes, the degrees of freedom in charging EV are comparably high [3]. Therefore, controlled (e.g. delayed) charging of EV as one DSM approach can help to avoid load peaks. More over, controlled charging strategies could support the integration of fluctuating electricity su pply based on RES [4,5]. Even more services can be provided, if the possi bility of feeding electricity back into the grid is consid ered (e.g. auxiliary services [6]). To determine the technical potential of load shifting by EV, the complex interplay of millions of consumers and stationary and mobile energy producers has to be evalu ated with many specific restrictions and different levels of aggregation and control points. This task is highly complex in view of the heterogeneity and variety of indi vidual objects, which additionally differ in their temporal availability. Using efficient mathematical optimization techniques, the charging behavior of electric vehicles shall be opti mally controlled taking into account network, vehicle,
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 399 and customer requirements. For individual vehicles con nected to a charging station and given electricity price levels, a cost minimizing charge function is determined with the customer requirements being taken into consid eration. The local load shifting potential is defin ed as the range of alternative charging functions that meet the customer requirements. However, not all of these charg ing functions may be economically optimal for the cus tomer. The electricity supplier therefore needs to pay for the customer’s permission to choose a different load curve that better fulfills the global conditions (e.g. plan ed generating capacity, network utilization, etc.). In this way, system efficiency can be increased considerably by appropriate Demand Side Management. This paper presents a model to compute the range of actual load shift potentials under the constraints of indi vidual preferences, technical restrictions, and the elec tricity demand of EV. The model will be used as a basis for further investigations, e.g. to optimize the network utilization under macroeconomic and energyeconomic criteria by adjusting the charging functions of each in volved EV with respect to individual technical restric tions. Recently, numerous works were published in the research field addressed by this paper. Especially the op timization of EV charging subject to network constraints is addressed with several models seeking to determine gridcompatible charging strategies [710] or simulating the grid effects of different charging strategies [1,11,12]. Other works focus on methods to influence consumer behavior to achieve gridoptimal EV charging [13,14]. Some MultiAgent Systems (MAS) have also been pro posed [1517] to achieve a decentralized optimal behav ior. In contrast to the works mentioned, our focus is on the online determination of load shift potentials for the next hours. This is the relevant information for the local distribution system operator (DSO). Furthermore, our mo del allows for the use of actual load shifts within the si mulated potentials (e.g. by a central instance). The soft ware updates the aggregated potentials of the fu ture with out neglecting the underlying constraints. This is achieved by constantly reoptimizing the distributed charging stra tegies subject to updated constraints. The paper is divided into seven sections. Section 2 in troduces the mathematical model to calculate the aggre gated load shift potential. Besides the formal definition of load curves, the mathematical description of the indi vidual as well as of the aggregated load shift potential is given. In the third section the optimization problem for the generation of optimal load curves is presented. Fur thermore, the optimization problem is adapted to deter mine the upper and lower limits of the charging functions used to compute th e load shift potential o f all vehicles. In Section 4, DSM operation and processing of load shifts are described. Section 5 covers the application of the model to two realistic scenarios while Section 6 gives an outloo k b efore coming to t he co nc lusions in Section 7. 2. Mathematical Model This section describes all quantities and mathematical definitions involved in the optimization problem to be sol v e d i n Section 3. The load curve of a vehicle can be any function in time, which fulfills the customer requirements and follows the technical restrictions. The main customer requirement is a full battery at the end. The technical restric tions include upp er and lower limits for th e charge and feed power. The upper limits are usually imposed by the b attery or charging station, while the lower limits are due to a cer tain threshold which ensures a flow of energy. Furthermore, the available amount of energy shall not drop below the minimum reserve and the battery’s ca pacity must not be exceeded. For the grid, the quantities of interest are the amounts of energy required and avail able ra ther than the indi vidual states of charge or reser ve levels. The constraints are formulated with the help of these quantities in the sections below. 2.1. Load Curve For a vehicle V that is to be charged with a certain amount of energy 0 V E in a time interval V T ,, be tt the load curve V Lt to reach the desired amount of energy during charging time is required, i.e. d, VVV TLttE (1) where we assume, that this is technically feasible. In case the charging time is not sufficient to fill the battery, the desired amount of energy shall be set to the amount that can be reached. The maximum capacity constraint can be expressed by staying below the required amount of energy at any point of the charging process, d<. b t VVe tLttE tt (2) The same applies to the amount of available regenera tive energy 0 V E, d<. b t VVe tLttE tt (3) The technical restrictions include upper and lower lim its for th e charge and feed power. ,min ,max 0<: >0, VV PtLtPttLt (4) ,min ,max 0>: <0. VV PtLtPttLt (5) Figure 1 shows an example of a load curve within the admissible ranges. The limits as well as the load curve may be discontinuous. In this case, the load curve is piecewise constant.
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 400 2.2. Individual Load Shift Potential Usually, there is a large number of load curves i V L which satisfy the conditions in 2.1 . The range of all these load curves then defines the load shift potential St: . i V i StL t (6) This means that for every point in S, we can find at least one load curve passing this point and thus allowing for shifting this point in time. As the load shift potential is a subset of the technically admissible range of load curves, S is a union of three disjoint sets: ,max,min,min,max :,0 ,. VV VV St StSt StSt (7) The colored areas in Figure 1 show the subsets. If the EV arrives with a low battery level, it cannot discharge in the beginning, which is depicted by the growing lower area. In order to fulfill constraint (1), the EV cannot dis charge in the en d, which is why the lower area is shrink ing again. 2.3. Accumulated Load Shift Potential of Vehicles For the DSM, it is reasonable to divide the load shift po tentials into three subpotentials for the producible, un avoidable, and compensable load: Negative load shift potential (load generation): The area between maximum load generation and the cur rent load curve ,max :, VV V RtSt Lt (8) Positive load shift p o ten tia l (load reduction): The area between the current load curve and the minimum load generation ,min :max0, , VV V RtLtSt (9) Superpositive load shift potential (power genera tion): The area between 0 (or the current load curve, if power is currently generated) and the maximum power genera tion ,max min 0,. VV V RtLtSt (10) Figure 2 shows the load shift potential for a vehicle, which is unable to discharge in the b eginning. This is the result of a common requirement: The battery is first charged to a specified minimum with full power in order to be able to reach important places, e.g. a hospital. In the end, the upper level might be reduced due to reservation of power for preconditioning of the vehicle, see Section 4.1. Figure 1. Example load curve and range of values. Figure 2. Exemplary load shift potentials for one vehicle. Dividing the load shift potential into three subpoten tials allows to draw them separately versus the non manageable grid load, as shown in Figure 3. The lower edge of R+ may provide additional information on the unavoidable load when it deviates from the grid load. The impact of vehicletogrid functionality can be di rectly read from R*, as only participating vehicles add t o it. 3. Optimization Problem DSM starts with offering a timeflexible tariff taking into account all expected fluctuations in electricity generation and demand which is supposed to make the customer schedule highly energyconsuming activities accordingly. Other cost functions are also possible, e.g. based on the CO2 emissions. In reality, however, the reaction to dy namic tariffs depends on the customer’s acceptance [18], which is why we assume only reasonably behaving cus tomers. Furthermore, there should be a tariff for feeding energy from the battery into the grid, which should not correspond to the charging tariff in the same interval.
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 401 Figure 3. Accumulated load shift potential for all vehicles shown with nonmanageable (static) load. Otherwise, a costoptimal load cu rve might be oscillatin g instead of just staying at zero. 3.1. Generation of Optimal Load Curves Finding a costoptimal load curve for a complex tariff with case differentiation or a direct algorithm will be difficult in the future when taking into account more complex constraints like battery wear and other physical effects. Even now, the absolute tariffs are not the only decisive factor. Their ratios have to be considered as well. It is thus reasonable to calculate the solution by formu lating an optimization problem. Nonlinearities are to be avoided in order to apply faster linear programming tech niques. An optimal load curve ,V opt L is defined as an admis sible load curve that minimizes the cost for a given tar iff/weigh t functi on Wt: ,d. min V optV T Lt V Lt LtWtt (11) As there are two intervals enclosing zero, where charg ing or discharging is not allowed, the domain becomes nonconvex. Without simplification, solution of the op timization problem will require a large expenditure [19]. Hence, we discretize the problem and construct con straints in order to select values from the admissible range only. We can expect the cost function to be piecewise con stant in the future, as all other forms of tariff will most probably overstrain the customer. Without loss of gen erality, we expect the intervals where the tariff/weight function Wt is constant to be of constant length (e.g. one hour), such that we can use a vector form i Ww. As we are only interested in nonoscillating load curves which are constant over the time intervals, we use the same vectorized form to define load curve representa tions L. We now consider different tariffs for charging and feeding , ,, for 0. for <0 iVi iViiVi wl wl wl (12) To avoid case differentiation, V L is decomposed into charging and discharging curves, as shown in Fi gur e 4, . VVV LZZ (13) The objective is then reformulated to , . min VV ZZ VV WZ WZ (14) It has to be ensured that both curves lie within the al lowed ranges and charging and discharging do not hap pen at the same time. The admissible ranges are ,,,min,,max, 0,, ViViViVi zzPP (15) ,,,max,,min, 0,. ViViViVi zzPP (16) Many modern mixed integer programming (MIP) solvers directly support this kind of semicontinuous variables, such that no additional integers have to be manually introduced to fulfill the eitheror condition above. On the other hand, without adding further variables, the constraint that only one of the functions V and V can be nonzero at a time, can only be written in a bilinear form, 0, VV ZZ (17) which is not allowed in most conventional MIP solvers. Specialized algorithms exist [20], but usually take more computing time. We hence introduce binary indicator functions , 0,1n VV CF (18) as also shown in Figure 4. The additional constraints ,,max, , , Vi ViVi cP zi (19) ,,max, , , Vi ViVi Pzi (20) ensure the correct setting of V C and V . For example, ,>0 Vi z implies ,1 Vi c . Figure 4. Decomposition into charging and discharging curves and introduction of binary indicator s.
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 402 The substitution of 0 VV ZZ is given by ,, 1. Vi Vi cf i (21) Finally, the constraints formulated in (1)(3) can be rewritten for a charging time of n intervals of length t : Full charging ,, 1 , n Vi ViV i tz zE (22) Upper capacity limit ,, < 1 < k ViViVk n i tz zE (23) Lower capacity limit ,, < 1 <. k ViViVk n i tz zE (24) This final formulation is completely linear, it consists of the objective (14), constraints (19)(24), and admissi ble ranges (15), (16) and (18). The problem can be solved with established methods like branch andbound [21 ] or branch andcut, which ex tends the former algorithm by cutting planes. The im plementation chosen here is lp_solve [22], a free branch andbound solv er supporting semicontinuous variables. In case semicontinuous variables are not available, two additional constraints are needed: ,,min, , , Vi ViVi cP zi (25) ,,min, , . Vi ViVi Pzi (26) In this way, the problem can be solved with conven tional MIP routines as offered by computing environ ments like Maple. As the integer variables are binary, it is possible to consider all configurations and solve a set of linear problems only. This is no practical method, but punctuates the global optimality of the solution. From the variety of heuristic methods, simulated an nealing would be suited well for mixed integer problems. However, as the computation times with lp_solve are in the range of a few seconds ev en for large lo ad shifts on a standard dualcore office PC, they were not considered. The degrees of freedom of the optimization problem can also be reduced by joining intervals with equal cost val ues. 3.2. Load Shift Potential The method described above can also be used to compute the load shift potential by changing the objective func tion to finding the charge curve reaching a maximum or minimum value at a certain point in time. Four optimiza tion problems would have to be solved for every vehicle and point in time, which would be associated with too high a computational expenditure. As the objective func tions are simpler in this case, a direct algorithm can be formulated for determining the four boundaries: ,minV S The algorithm has to deliver the requested amount of energy without exceeding the upper and lower limits of the battery capacity. The maximum amount of energy within the charging window is given by ,max,Vj j tP . Subtracting V E results in the amount of energy which is not needed for charging. The lower power limit of each interval can be found by shifting this area within the charging window, such that we can calculate ,minVi S as the minimum power level necessary by ,min, 1 ,min, ,max,,max, min ,. Vi ViViV jV t j S PPP E (27) ,maxV S To find the upper limit, the amount of energy not needed for charging has to be shifted more spe cifically: When discharging at a high state of charge, the amount of chargeable energy increases. This means that charging should start with full power from interval i until the end or until V E is reached. If we do not have ,max, ,max,ViVi SP yet, we try discharging from interval 1 to 1i, such that we can increase the power level at i in a stepwise manner. ,maxV S The discharging power limit can be computed similarly: The higher the state of charge, the more energy can be discharged. This means that charg ing starts with full power, leaving out the interval i and bearing the upper limit V E in mind. When the battery capacity is reached, ,max,Vi S is low ered in steps to ,max,Vi P as long as there are inter vals left for charging. ,minV S This boundary is equal to ,minV S, if ,max,Vi S ,min,Vi P, otherwise it is set to zero. 4. DSM Operation The accumulated load shift potential is highly timede pendent, as vehicles are constantly arriving and departing. At the same time, the set of alternative load curves for each connected EV is constantly reduced when values are fixed over time. The operation of the DSM, including this update of potentials, is given in Listing 1. In a time step, arrival events have to be processed first (Line 2), then all re maining vehicles are updated with the amount of energy they received during the last interval. Departing vehicles are automatically removed in this step. At this point, all information items have been updated to compute the load shift potential (Line 3) and process
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 403 1 for step=1 to noSteps 2 —Process mobility events 3 Computeshiftpotentials// acc .to3.2. 4 for request=1to noShiftRequests 5 —Save targetloads (request) 6 for interval=1 to duration(request) 7 —Sort vehicles 8 —Determine participating vehicles 9 for vehicle=1to noInvolvedVehicles 10 —Shiftloadcurve// acc .to3.1. 11 —Fixthisintervalin load curve 12 —Updateshiftpotential(vehicle ) — Listing 1. Overview of the DSM cycle. possible load shift requests (Line 4). Load shift requests are issued by the supplier in reaction to unforeseen de viations from the planned load curve or because of eco nomic considerations. The direct algorithm for computa tion of potentials is cheap and can be parallelized. Proc essing of load shift requests can be distributed as well, but requires more communication to exactly achieve the requested shift. Load shifts over several intervals are processed in steps in temporal order (Line 6). The average goal values are saved, as the cumulative load changes while shifting (Line 5). A request is first compared to the potentials, thereafter the satisfiable part of it is assigned to the par ticipating vehicles. Normally, the vehicles with the long est remaining charging time offer the highest flexibility and load shift potential. Hence, they are sorted in de scending order according to their departure times (Line 7). The partial shifts are performed with a greedy algo rithm. For one vehicle after another (Line 9), the maxi mum possible shift is performed by generating a new curve (Line 10) which attains a minimum or maximum. When processing the next partial load shift, the previ ously treated intervals are fixed (Line 11), such that the achieved shift cannot be reverted accidentally. Temporal resolution influences the runtime and accu racy of the simulation. On the one hand, it seems rea sonable to choose a small time step for more precise load curves, as vehicles are constantly arriving and departing. On the other hand, a longer interval gives more reliable information on the shift potential. When processing shifts over several intervals, the potential changes after the first step, such that the request might not be fulfilled in the second. In this sense, a load shift is understood to be an averaged shift referred to the medium load value in the interval and longer time steps of 5 to 10 minutes are pre ferred. Figure 5 shows the load curve and potentials of one vehicle in a demonstrator application. 4.1. Preconditioning Preconditioning demonstrates exemplary the integration of further constraints into the model. Constant energy Figure 5. Exemplary vehicle with load curve (black), upper and lower power limits (red/green) and shift potentials (areal). For a sample tariff, discharging between 17:45 and 18:45 as well as between 20:30 and 21:30 is beneficial and full charging postponed accordingly . supply during parking and the strictly limited amount of energy while moving make it reasonable to start air con ditioning before leaving. Depending on the difference to the preferred temperature, preconditioning is started 10 to 20 minutes before departure. The necessary amount of energy for heating or cooling is calculated from the ther mal energy . heat Ec mT (28) The outside temperature curve is specified in the XML data and the vehicle is assumed to arrive with the goal temperature. The product of mass and heat capacity is set to a typi cal value of 100 kJ/kg and thermal transfer through the vehicle body to 75 W/K [23]. To calculate the amount of energy for preconditioning, we first determine the interior temperature at the begin ning of preconditioning via 100 kJ11. 75 W inout in TttT tTt (29) 0. in goal TT (30) We now assume that the target temperature is ap proached linearly and, hence, compute thermal transfer during preconditioning as 1 75 . 2 transgoal in W PTT (31) The heating or cooling power is then /1 100 . a cgoalin rec kJ PTT Kt (32) In order to obtain the final value, which is subtracted from the upper power limit ,maxV P, we assume a typical coefficient of performance of 1.52 and a ventilation con sumption of 5 00W [23]. / .500 1.52 a ctrans prec PP PW (33)
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 404 5. Exemplary Application To quantify the potentials, two scenarios are constructed as outlined in Table 1. The results given in the following sections have to be interpreted as an upper limit for the load shift potential, since it is assumed that all vehicles are connected to the grid during parking time. Scenario 1 (year 2015) is based on the goals of the German Federal Government, which were developed in the socalled National Electric Mobility Platform (NPE) and published in its second report [24]. Scenario 2 (year 2030) is based on a forward projection of these goals, as shown in Figure 6. The data on the behavior of the vehicles are required from a representative German mobility study which is based on realistic driving profiles for more than 32,000 distinct routes [25]. Due to the limited size of the data set, only some of the EV assumed to exist in total are explic itly represented in the simulation. As a simple scaling of the data set would not have increased the significance, each scenario is limited to 10,000 vehicles and approx. 16,000 distinct routes. This number of vehicles corre sponds to the size of the original data set and the as sumptions regarding the participation in DSM measures. However, the calculated load shift potentials are scaled up to the total number of EV in each scenario. Table 1. Basic information on applied scenarios. Parameter Scenario 1 Scenario 2 Year 2015 2030 Duration (starting at 12 noon) 24 hours 24 hours Total number of EV o n the road 200,000 6,000,000 Vehicles participating in DSM 50% 90% Maximum power at home 3.68 kW 10 kW Maximum power at public places 10 kW 22 kW Number of selec t ed vehicles 10,000 10,000 Approx. number of distinct routes 16,000 16,000 Scaleup factor 20 600 Share of hybrid EV 60% 40% Average battery capacity 9635 Wh 18,239 Wh Vehicles participating in V2G 30% 50% Figure 6. Predicted number of EV in Germany. The simulation uses a predefined static load curve which is independent of the power demand of the EV. This exogenous load cu rve correlates with the p redefined tariffs shown in Figure 7 and illustrates a realistic load situation. Preconditioning was not considered in these examples to produce more general results without any dependencies on a given whether situation. 5.1. Scenario 1 (Year 2015) The NPE goals [24] include one million EV on German roads in the year 2020. A nonlinear extrapolation using the current number of vehicles and the NPE schedule leads to an approximate number of 200,000 vehicles in the year 2015 as shown in Figure 6. In this scenario, the average battery capacity is 9635 Wh because of the comparably high share of hybrid EV which generally have a significantly lower battery capacity than pure EV. Furthermore the share of vehicles which participate in V2G is only 30% due to an assumed lack of acceptance. After initialization, the DSM computes the aggregated load shift potential of the currently connected vehicles. Perfect foresight is assumed regarding the departure of connected vehicles, but not for new arrivals. This leads to a realistic representation of the degrees of freedom for the simulated DSM to respond to load shift requests in each individual time step. Running the simulation with out any load shift requests leads to a bare visualization of the varying potentials over the corresponding time hori zon. Table 2 shows selected results, the notations refer to the definitions given in Section 2.3. The results show that this setup already leads to sig nificant load shift potentials. Especially the constantly high negative potential is remarkable. However, if the execution of a load shift is requested, the corresponding potentials in future time slots will decrease significantly. Figures 8 and 9 show the aggregated load shift potential over the considered time horizon, without taking the pos sible realization of load shifts into account. As the load shift potential changes in each time step i t it is in fact twodimensional. The curves in Figures 8 and 9 show the specific load shift potential available at i t when the point in time i tt is reached. Figure 7. Predefined grid load curve and tariffs for the simulation.
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 405 Figure 8. Resulting limits of load shift potentials (10,000 EV) in Scenario 1 (Year 2015). Figure 9. Resulting limits of load shift potentials (10,000 EV) in Scenario 2 (Year 2030). 5.2. Scenario 2 (Year 2030) Again based on the NPE goals [24] and the German mo bility study [25], a nonlinear extrapolation leads to an estimated number of 6 million EV in Germany in the year 2030 (Figure 6). Due to the assumed increasing number of pure EV and the decreasing share of hybrid EV as well as the expected development of battery tech nology, the average battery capacity is significantly high er than in the year 2015 (cf. Table 1). Furthermore, ris ing acceptance for V2G measures is expected, which is why the share of participating vehicles is set to 50%. The results given in Table 3 differ significantly from those of Scenario 1. Due to the increased average battery capacity, the aggregated load shift potential increases at almost all points of the simulation. Consequently, the DSM has higher degrees of freedom in utilizing load shifting potentials. Especially the rise in the superpo sitive load shift potential is remarkable. This may be ex plained by the higher share of vehicles participating in V2G measures. To assess the results, a short example will be given below. The released positive secondary power reserve in Germany from October 24 to 30, 2011 reached a peak of approx. 2 GW. This means that the providers have to decrease their loads or to feed electricity into the grid. This form of power reserve can only be provided by ve hicles which take part in V2G measures. In our nomen clature, the sum of positive and superpositive load shift potential serves to fulfill requests of positive reserve power. The results in Table 3 show that the peak demand in the week considered could have been met by EV at every time in the time horizon of the simulation. How ever, the duration of the request and the profitability for the customer [26] have a significant influence on its fea sibility.
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 406 Table 2. Selected scaledup simulation results of Scenario 1 (2015). Load shift potential [kW] EV load Negative Positive Superp. Number of EV 1:00 pm 30,529 70,724 26,422 21,363 33,729 6:00 pm 26,614 90,552 21,739 50,603 63,870 3:00 am 1903 61,127 1718 57,434 76,281 8:00 am 22,019 109,945 15,758 66,233 79,145 Max. 36,951 115,365 29,497 82,894 90,994 Min. 1112 59,445 987 12,907 26,075 Table 3. Selected scaledup simulation results of Scenario 2 (2030). Load shift potential [MW] EV load Negative Positive Superp. Number of EV 1:00 pm 2067 14,122 1665 6555 1.824 M 6:00 pm 2241 20,078 1749 14,713 3. 445 M 3:00 am 150 17,675 143 17,055 4.098 M 8:00 am 1414 23,183 821 19,730 4.257 M Max. 2347 25,596 1795 23,538 4.873 M Min. 94 12,376 86 4330 1.408 M 5.3. Load Shifting As explained in 4, the simulation result highly depends on the temporal resolution. Choosing a larger time step gives information on the attainable load shift over a longer time period. Figure 10 shows the remaining av erage potential in percent in comparison to the 5minute time step used for the examples above. The difference between 2015 and 2030 results from the higher participa tion in DSM measures, allowing higher shortterm shifts. Figure 11 shows the result of a load shift of +1500 kW from 23:00 to 0:00 (approx. 25% of the 5 min. potential at 23:00) for the 2015 scenario. Depending on the given tariff, the effects of a shift might be visible for several hours: The vehicles are forced to charge during 23:00 and 0:00, reduce their power or even discharge from 0:00 to 5:00, and fill up the battery between 5:00 and 6:00 because of a slightly cheaper tariff level (Figure 7). Meanwhile, the negative potential is reduced to 2000 kW during the shift and considerably decreased after wards. This information could be used for drafting risk based DSM algorithms using load shift potentials as a measure of remaining flexibility. 6. Outlook The knowledge and software developed in the course of this analysis is highly relevant for DSO and will be the basis for various further developments, from grid devel opment planning to drafting business models. Figure 10. Remaining negative shift potential in percent for larger time steps. Figure 11. Resulting absolute change in load and potentials when performing a shift of 1500 kW from 23:00 to 0:00. Real battery data or advanced battery models should be used in further studies to assess the real wear of the vehicle batteries. More reliable data for the future distri bution of EV and their corresponding user patterns would also improve the results. Stochastic influences should be included as well to simulate customer reactions to unforeseen ev ents and the partly unreliable communication between the agents. Not only flexible and robust algorithms, but also communica tion protocols are needed for more realistic simulations. Currently, no gridimposed constraints are included. Due to fast charging stations at home, a shortage in the local grid might occur especially in the evening hours. Besides the lowestvoltage grid, also the low and me diumvoltage grid might be affected in some regions [26]. Furthermore, the time of charging has an impact on the specific CO2 emissions (and other emissions) during EV usage due to the timedependent energy mix [27]. Both issues could be incorporated in future studies. In addition, simulations of the actual power flow will have to be applied to include grid topology. This will be achieved by coupling the algorithms for optimal power flow computations presented in [28] with the existing software. An adaptive algorithm for optimal control of the distributed local grid as a function of the flexible de mand of other users or even flexible or fluctuating elec tricity supply by combined heat and power units or photovoltaic systems might be an interesting extension of this project. The variety of proposed DSM algorithms (P2P, heuristic, deterministic) can be evaluated for dif
ModelBased Quantification of Load Shift Potentials and Optimized Charging of Electric Vehicles Copyright © 2013 SciRes. SGRE 407 ferent scenarios in the future, with CO2 minimizing stra tegies being taken into account. 7. Conclusions A bottomup simulation algorithm is presented, which allows for determining the cumulative load curve and load shifting potentials of EV in the charging process in a generic energy grid. A direct algorithm was developed for this purpose that can be efficiently applied to all ve hicles in parallel. For a manual change of the grid load by requesting load shifts, a costoptimal shift is performed by altering the original charging curve of some participating vehicles within their individual constraints, e.g. departure with desired state of charge of the battery. A mixedinteger linear program (MIP) has been developed that can be solved more efficiently than the ori ginal nonconvex for mulation. Results of two scenarios based on mobility studies show that the load shifting potential of EV is significant and contribute to a necessary relaxation of the future grid. The maximum charging and discharging power and the average battery capacity are crucial to the overall load shift potential. However, the individual willingness to participate will depend on the profitability for the cus tomer, which is why future projects should pay particular attention to this issue. 8. Acknowledgements This work was supported by the Energy Solution Center (EnSoC), an association of major industrial corporations and research institutions in Germany. EnSoC focuses on projects using highperformance computing technology in applicationoriented energy research. The authors would like to thank EnSoC for the continuous support and the professional project management. We acknowledge support by Deutsche Forschungsge meinschaft and Open Access Publishing Fund of Karl sruhe Institute of Technology. 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