Scholarly article on topic 'Online Optimal Charging Strategy for Electric Vehicles'

Online Optimal Charging Strategy for Electric Vehicles Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Chenjie Ma, Juha Rautiainen, Dirk Dahlhaus, Akhilesh Lakshman, J.-Christian Toebermann, et al.

Abstract This work investigates scheduling strategies for charging electric vehicles (EVs) in distribution grids. Our proposed scheduling strategy is realized as a moving window optimization scheme. By considering load and price forecasting and EVs’ power demand, this strategy optimizes the charging costs of an EV fleet with consideration of grid constraints. Its benefit is first demonstrated through simulation studies on workday and weekend scenarios. Furthermore, we discuss the impact of scheduling windows on the optimization result. Last, the impact of forecasting errors of energy prices on the optimization performance is quantitatively analyzed. The results show that the proposed strategy can optimally plan EV charging schedules with consideration of online information and uncertainties.

Academic research paper on topic "Online Optimal Charging Strategy for Electric Vehicles"

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Energy Procedía 73 (2015) 173- 181

9th International Renewable Energy Storage Conference, 1RES 2015

Online optimal charging strategy for Electric Vehicles

Chenjie Maa*, Juha Rautiainena, Dirk Dahlhausb, Akhilesh Lakshmana, J.-Christian Toebermanna and Martin Brauna,c

aFraunhofer Institute for Wind Energy and Energy System Technology (IWES), Kassel, Germany bCommunications Laboratory, University of Kassel, Kassel, Germany cEnergy Management and Power System Operation, University of Kassel, Kassel, Germany

Abstract

This work investigates scheduling strategies for charging electric vehicles (EVs) in distribution grids. Our proposed scheduling strategy is realized as a moving window optimization scheme. By considering load and p rice forecasting and EVs' power demand, this strategy optimizes the charging costs of an EV fleet with consideration of grid constraints. Its benefit is first demonstrated through simulation studies on workday and weekend scenarios. Furthermore, we discuss the impact of scheduling windows on the optimization result. Last, the impact of forecasting errors of energy prices on the optimization performance is quantitatively analyzed. The results show that the proposed strategy can optimally plan EV charging schedules with consideration of online information and uncertainties.

© 2015Publishedby ElsevierLtd. This isan openaccess article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy Keywords:electric vehicle, online optimization, charging, scheduling.

1. Introduction

Electric mobility has the potential to facilitate the future transportation demand with high energy efficiency and low green-house gas emissions. Potential impacts on distribution systems by charging of EVs have been investigated by recent publications. Depending on the applied charger technology, congestions may already exist in present

Corresponding author. Tel.: +49 561 7294 106; fax: +49 561 7294 200. E-mail address:chenj ie.ma@iwes.fraunhofer. de

1876-6102 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy doi: 10.1016/j.egypro.2015.07.667

distribution grids even at a low penetration rate of EVs [1]. Other problems such as the increase in voltage variations and system losses are also pointed out in [1~3].

To mitigate these risks, some studies proposed intelligent scheduling concepts for charging of EVs. As multiple stakeholders with different interests are involved, this scheduling problem expresses a highly dynamic, multi-objective complexity. EV owners naturally want to charge their EVs as fast as possible, while commercial aggregators or charging service providers have another clear objective to minimize the energy procurement cost and accordingly maximize their profit. Providing ancillary services to the grid may be a viable option, only if a proper incentive scheme or a market exists. From the perspective of a distribution system operator (DSO), the paramount task is to operate the grids efficiently and within technical limits. In such a complex context, where the interests of all stakeholders must be considered, a technical or economical optimum is difficult to achieve. In previous studies, different aspects in representing these entities as direct objectives or as limitations are discussed.

Starting from the aspect of a system operator, strategies to maximize the delivered power to charge EV fleets are proposed by [4] and [5]. These authors provide solutions with pure technical considerations, where power rate of chargers, current and voltage limits of the grid and power delivery limits were clearly investigated; neither charging costs of EV nor operation costs of DSOs was a research subject. Reference [6] aimed to minimize system operation cost considering EV owners' satisfaction level. In addition, the prediction function of EVs' behavior and energy demand is formulated as an important component. In [7], charging strategies with several commonly studied objectives were compared. Based on simulation results, the strategies of different objectives were evaluated in delivered energy volume and energy costs. Besides, to maximize the usage of renewable generations by charging EVs was also investigated by [8]. This is another research subject especially in the context of micro-grids. Other strategies from an aggregator's point of view often share a common objective, which is to minimize the energy procurement costs for charging EVs. As proposed in [9—11], the goal was to achieve minimum charging cost by optimally arranging EVs' charging power and time. Providing the ancillary service to distribution systems, e.g. congestion management, was considered as a system constraint.

Scheduling algorithms for EVs can optimize charging decisions for the next time step solely based on present information on the distribution system and EVs. This scheme is only suitable for objectives without the factor of time, e.g. the grid capacity or charging demand of EVs [4, 5]. On the other hand, implementations with a global scale over long periods are demonstrated by [7] and [10]. They emphasized that the system optimality can be achieved under the assumption of a complete knowledge in the studied period. However, this assumption is not realistic and therefore only possible in offline analysis. To overcome this limitation and to guarantee the online applicability of a strategy, moving window scheduling algorithms are introduced by [6], [8],[9] and [11]. These strategies had in common that they required forecast over a fixed time horizon. Charging decisions over the next short period were made based on the forecasting data. During the execution of the algorithm, information and solutions were updated in a moving window pattern.

In this study, we implement and improve the moving window optimization method for scheduling EV charging. A binary linear optimization strategy is implemented in a centralized scheme, where distribution grid limits and EV's charging demand are both taken as constraints. The focus of this work is to evaluate the effect of the selection of the optimization window, which is carried out by numerical simulations. We analyzed this effect in terms of costs and technical variables. Lastly, impacts of the forecasting error on the optimization result are also quantitatively analyzed.

This paper is outlined as follows. Section 2 describes the proposed charging scheduling algorithm. In Section 3, the system model and simulation parameters are presented. Evaluations on scheduling strategies are performed based on simulations on specific scenarios. Finally, a short conclusion and discussion is given in Section 5.

2. Problem formulation

Considering forecasting data of electricity price and driving information of EVs, we proposed a centralized strategy with the objective to minimize the charging cost of an EV fleet consisting of multiple vehicles. In this section, the objective function and the associated boundary conditions are first discussed. The optimization scheme and the work flow of the scheduling algorithm are presented subsequently.

2.1. Objective function

The EV scheduling algorithm optimizes the charging set-points of an EV fleet in a discrete manner. As input data, the proposed algorithm requires a prediction of total load in the system under investigation, a prediction of electricity price over a fixed horizon as well as the energy demand of EVs and desired departure time estimated by users. The main objective of the algorithm is to minimize the total charging costs of all EVs based on online energy price forecast. We consider grid operation limits, limits of charging time window determined by EV users and energy demand of individual EVs as constraints. The optimization problem is formulated as a binary linear programming problem and solved using the OPTimization Interface (OPTI) Toolbox [12]. The overall objective function can be expressed as follows:

min f • PEVn • Sdn ^) (1)

deDneN

D set of all time steps within the optimization window;

N set of all EVs in the fleet;

cd forecast electricity price at time step d;

PEVn rated charging power of the nth EV, assumed as constant quantities;

Sdn charging schedule of the nth EV at time step d (0 for not charging, 1 for charging);

At length of a time step.

For technical constraints, we first consider the grid operation limit, which is defined in this work as the annual maximum load (Piim) without EV. As described by Eq. (2), the sum of total charging power and the total demand of loads at each time step must remain lower than the permissible power limit. Here, L is the set of all loads in the grid; P loadl stands for the power demand of the lth load.

Z(PEV,n * Sdn )+Z(^oad,l )d ^ Pm d * D (2)

neN leL

The availability condition of charging an EV is formulated as Eq. (3). A schedule is valid, only if the EV is connected to the grid at the corresponding time step.

f0, when EV is not connected to the grid

Sdn <■] , d e D & n e N (3)

[1, when EV is connected to the grid

Finally, Eq. (4) describes the constraints of energy demandof the EV battery. At the end of a scheduling interval, all EVs should be fully charged. EEVndenotes the energy demand of an EV defined by initial SOC level at the beginning of a scheduling window.

Z(PEv,n • Sd,n "At )> EEv,n, n e N (4)

2.2. Optimization scheme

In order to account for uncertainties of user behavior as well as system load and market prices, our charging scheduling strategy is implemented as a moving window optimization scheme. In Fig. 1, the temporal behavior of this scheme is demonstrated. Here, the optimizer requires the aforementioned forecast information of the future over a fixed horizon, which can span over several time steps. Based on the online prediction data, the algorithm optimizes charging set-points of EVs for this scheduling window. As the time advances, the algorithm updates the predicted

information and determines charging schedules for the next window. Although schedules are made over several time steps, only charging decisions are carried out in the present time step, which is marked in blue in the figure. This forward looking character takes future uncertainty into consideration by making decision for the current step; its constantly window-moving scheme reduces the demand of forecasting information. In opposite, global optimization schemes from literature review assumed a complete knowledge about the future. Their determined schedule would be valid for the complete time span.

t = t1

t = t2

' ' Time t = tn I-1-1_I_I_I-1-1-1-1-^

t1 t2 t3 tn

Fig. 1.Scheme of moving window optimization

3. System modeling

In this work, we investigate a synthetic low voltage system with 50 % penetration of EVs. Applied data source and models are presented in this section.

3.1. EV charging model

EV charging models are derived from our previous work [3], where detailed physical models of EV charger and Li-Ion battery packs are established and validated. In this work, EV models are also parameterized based on the specifications of Mitsubishi i-MiEV[13]. It is powered by a 16 kWh Li-ion battery pack. For charging device, a standard power rate of 3.7 kW is assumed.

3.2. EV behavior model

The user behavior of EVs in this work is based on a surveyed dataset, which is collected by the project "Mobility in Germany 2008" [14]. This survey covered driving behavior of thousands of households over one year. Exact trips on workdays and weekends and the energy consumption are recorded in this database. In the simulation, trips are randomly selected from the database and assigned as driving behavior for individual EVs.

3.3. Power consumption and energy price

A winter week (third week of 2013) is selected as the study period. A set of household load profiles is generated based on German statistics [15]. These profiles describe the electric power consumption of 146households of different types with time resolution of 1 minute. We use the 1 h average value of intraday price profile from the

Scheduling window

1 " 1 Time ■ ■_I_I_I_I_I_I_I_I_►

t1 t2 t3 '—■—'

Time step

' 1 Time i_' '_i_i_i_i_i_i_i_^

t1 t2 t3

EEX spot market [16]. The price profiles in a 24 h period of a workday and a weekend (Saturday) scenario are shown in Fig. 2.

a) Workday b) Weekend

Fig. 2. Energy profile in a 24 h period

4. Results of the fleet optimization

The proposed scheduling algorithm is tested on the generic grid model with a high EV penetration ratio of 50 %. Typical workday and weekend scenarios are simulated with different optimization parameters. In this section, impacts of schedule window size and forecasting error on charging costs are discussed.

4.1. Coordinated and uncoordinated charging

Figure 3 illustrates the charging behavior of EVs and total power demand in a 24 hour period of a typical workday and a weekend day scenario. On the workday, the uncoordinated charging scheme indicates charging of EVs immediately after they are connected to the grid. This yields severe peaks of total power demand between 6 and 8 pm. The coordinated charging strategy schedules the charging of EVs during midnight as it is sensitive to the energy prices. On the weekend, EVs stay plugged in longer and more often during daytime than in a workday. This provides a higher flexibility for the scheduling algorithm. Accordingly, the achieved solution avoids charging EVs during peak hours of high demand and shifts the charging to hours of low energy prices (between 11 am and 9 pm).

4.2. Impact of forecasting error on moving window optimization results

A sensitivity analysis of the optimization results on imperfect price forecasts is performed in this part. It is assumed that the forecasting error subjects to a normal distribution with increasing standard deviation as a function of time. We exemplarily study hourly increments of 0.5 % and 1 % on forecasting error for the price profile. This corresponds to error bands of 12 % and 24 % for a forecast in the coming 24th hour. The optimal charging costs calculated for 50 simulations are presented in Fig. 4. In the workday scenario, we observe that the lowest charging costs are reached at a larger scheduling window if the price forecast contains errors, as opposed to simulations with a perfect forecast. The error adds more uncertainty at a larger window size, so that the obtained optimal charging costs increase if the window size further increases. However, this effect is, although still visible, less significant on the weekend day. In addition, the global optimization scheme is more sensitive to error, as it achieves much higher costs for both of the scenarios. The difference between two error bands is marginal.

500 '400

£ 100

500 '400

CO £ CD

-o 200

70 60 50

-o 40 ¡5 30 20 10

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

a) Workday, uncoordinated

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

b) Workday, coordinated

500 400 300

-o 200

500 400 300

-o 200

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

70 60 50

-o 40 > 30 20

mii. :: i i •

__J_ 70

Charging schedule Available for charging 60

* 11 : i i i •

•IBB* : ii • ■

: i: i

-o 40 > 30 20 10

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

c) Weekend, uncoordinated

10 12 14 16 18 20 22 24 2 4 6 8 10 Time [h]

d) Weekend, coordinated

Fig. 3.Uncoordinated and coordinated charging on workday and weekend scenarios

'ra CD -C

o "(D o

O) C CT

"rö o

42 41 -40 39 38

49 48 47 46 45

I Error increment: 0.5%/h I Error increment: 1%/h

ii *» *t

' 'MiiwHiifimnMt

9 11 13 15 17 19 21 23 . Global Optimization window, [h] °ptimizati°n

b) Weekend

-J I_Error increment: 0.5%/h 1 Error increment: 1%/h

ill 25-75th Un fljl nn ^percentile U U[j Median u rfV III 1 »1 ifl Hf|iMH|'r J 1 1 1 III

Optimization window, [h] a) Workday

Fig. 4.Optimal charging costs with imperfect forecasting data

optimization

4.3. Impact of scheduling window size

In order to analyze the impact of selecting the moving window, simulations on different window size from 1 to 24 hours are carried out with perfect forecasting data. Comparisons of scheduling window sizes against the global optima are presented in Fig. 5(the global optimum is the optimum solution obtained by a global optimization scheme mentioned in Section 2.2.) As the window size increases, the optimal charging costs obtained by the moving window scheme approach to the global optima obtained by the global optimization scheme on both workday and weekend scenarios. Although different convergence characteristics are observed, the moving window scheme is able to provide solutions as good as the global optimization scheme. On the specific test scenarios, optimal solutions are achieved by a window size of 12 h and 19 h, respectively. In practice, EVs availability range and the shape of price profiles should be considered by optimal selection of the window size.

■a 45

ra (Ô

35 30.

ÎÔHHHHHf

Uncoordinated charging ["

Global optimum

MW KHK

"I l-t H

"7 9 11 13 15 17 19 21 Optimization window, [h]

a) Workday

CT (Ô

Uncoordinated charging

Global optimum

X X X It M H X It K

7 9 11 13 15 17 19 21 Optimization window, [h]

b) Weekend

Fig. 5.Comparison of optimal charging costs of one day at different scheduling windows (The solver is incapable to obtain viable solutions with a window size fewer than 7 h.)

5. Conclusion

This work proposed an implementation of scheduling strategy based on moving window optimization scheme. This strategy shows generally a fast convergence characteristic and is more robust against the global optimization scheme. These advantages enable a reliable determination of optimum charging schedules in low costs. Also, moving window optimization scheme is suitable for online applications due to continuously information update pattern and a fixed forecasting horizon. For a real application, a window size between 12 and 19 h can be recommended from test results. If forecasting data contain errors, the selection of optimal window size requires more detailed studies. Based on the exemplary test cases, a window size of 17 h shows lowest charging costs in both workday and weekend scenarios. To consolidate the implemented algorithms, more simulation tests on real scenarios with longer duration will be studied in the next steps. Technical impacts on distribution grids will also studied using detailed system simulation models. Finally, the real time performance of the strategy requires more attention.

Acknowledgements

The presented paper is based on research performed in the project 'Systemintegration von Elektromobilität (SIEM)' (FKZ 0325402). The authors thank the German Federal Ministry for Economic Affairs and Energy (BMWi) and the Projektträger Jülich (PTJ) for supporting this project and take full and sole responsibility for the content of this paper.

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