Optimal scheduling for vehicle-to-grid operation with stochastic connection of plug-in electric vehicles to smart grid

Applied Energy 146 (2015) 150–161

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Optimal scheduling for vehicle-to-grid operation with stochastic connection of plug-in electric vehicles to smart grid Linni Jian a,⇑, Yanchong Zheng a,b, Xinping Xiao b, C.C. Chan c,d a

Department of Electrical and Electronic Engineering, South University of Science and Technology of China, Shenzhen, China School of Science, Wuhan University of Technology, Wuhan, China c Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong d Institute for Advanced Sustainability Studies, Potsdam, Germany b

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 A novel event-triggered scheduling

scheme for vehicle-to-grid (V2G) operation is proposed.  New scheme can handle the uncertainty arising from stochastic connection of electric vehicles.  New scheme aims at minimizing the overall load variance of power grid by V2G operation.  Method to evaluate the performance of proposed scheme is elaborated and demonstrated.

a r t i c l e

i n f o

Article history: Received 10 July 2014 Received in revised form 5 January 2015 Accepted 8 February 2015

Keywords: Plug-in electric vehicle Vehicle-to-grid Optimal scheduling Load variance Smart grid

a b s t r a c t Vehicle-to-grid (V2G) operation of plug-in electric vehicles (PEVs) is attracting increasing attention since it can assist to improve the efficiency and reliability of power grid, as well as reduce the operating cost and greenhouse gas emission of electric vehicles. Within the scheme of V2G operation, PEVs are expected to serve as a novel distributed energy storage system (ESS) to help achieve the balance between supply and demand of power grid. One of the key difficulties concerning its practical implementation lies in that the availability of PEVs as ESS for grid remains highly uncertain due to their mobility as transportation tools. To address this issue, a novel event-triggered scheduling scheme for V2G operation based on the scenario of stochastic PEV connection to smart grid is proposed in this paper. Firstly, the mathematical model is formulated. Secondly, the preparation of input data for systematic evaluation is introduced and the case study is conducted. Finally, statistic analysis results demonstrate that our proposed V2G scheduling scheme can dramatically smooth out the fluctuation in power load profiles. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction

⇑ Corresponding author at: Department of Electrical and Electronic Engineering, South University of Science and Technology of China, Shenzhen, China. Tel./fax: +86 755 88018525. E-mail address: [email protected] (L. Jian). http://dx.doi.org/10.1016/j.apenergy.2015.02.030 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

Nowadays, energy crisis and global warming have become two critical issues which are threatening the sustainable development of human society. Statistics indicate that the average global temperature has increased by about 0.8 °C since 1880, and two-thirds of the warming has occurred since 1975 [1]. What is

L. Jian et al. / Applied Energy 146 (2015) 150–161

more, the exploitable reserves of fossil fuels may be exhausted in the near future due to the rapid growth of global energy consumption. Most recently, transport electrification has been deemed as a promising solution to address these challenges: Firstly, the transport sector accounts for the largest share of the total growth in world consumption of liquid fuels [2]. Secondly, the greenhouse gases (GHGs) emission produced by internal combustion engines has become one of the major contributors to the global warming. The latest IPCC climate change report indicates that the transport sector produced 13% of global GHGs emission [3]. In China, the transport sector produced 709.2 million tones of CO2 in 2012, which accounts for 8.6% of the total 8250.1 million tones of CO2 emission in the same year [4]. Apparently, the popularization of electric vehicles (EVs) will greatly enhance the energy security by integrating renewable energies as well as improving the energy conversion efficiencies. Consequently, the emission of GHGs will be remarkably reduced. In addition, the worries on public health risks arising from the air pollutants including fine particulate matters (PM 2.5) become a powerful incentive to promote EVs in many countries most recently. Plug-in electric vehicle (PEV) is an important subcategory of EVs. Relatively large-capacity batteries are often equipped in PEVs. In addition, these batteries are rechargeable through plugging into the power grid. Hence, PEVs are a novel kind of electric load for power grid, and on the other hand, they may also play the potential role as distributed energy storage devices for power grid. In this regard, PEVs are able to deposit extra electricity at valley-load hours and then feed back electricity to grid at peak-load hours. The bi-directional power flow between PEVs and power grid is known as vehicle-to-grid (V2G) [5,6]. Previous research has demonstrated that V2G operation of PEVs can bring in lots of benefits, such as, providing frequency regulation services [7], flattening power load variation [8], reducing overall operating cost [9–11], promoting the integration of renewable energy sources [12–15], and reducing the greenhouse gases emissions [16–19]. The key to the effective implementation of V2G operation is to what extent informatics can be effectively integrated into electrical energy conversion, transmission and distribution. Otherwise, the deep penetration of PEVs may trigger extreme surges in demand at rush hours, and fatally harm the stability and security of the existing power grid. Therefore, V2G should be carried out within the framework of smart grid [20–24], so that the status information of power grid can be perceived. Another prerequisite is the massive data processing capability, such as cloud computing [25], since there are so much information should be taken into account, for example, the traffic condition, the weather condition, the operation condition of power grid, vehicles and charging facilities, and the demand of PEV owners. The demand of PEV owners should take the top priority among various types of information, and this means that the fundamental function of PEVs as transportation tools has to be guaranteed all the time. Another issue which deserves special attention is the possible degradation of onboard batteries caused by V2G operation [26,27]. An important theoretical challenge concerning V2G operation is on the optimal charging/discharging strategy of PEVs which aims at maximizing the potential benefits arising from V2G [28]. There are several different targets, such as minimizing the power losses [29,30], minimizing the peak load [31], controlling the trading risks [32,33], maximizing the operation profits [34–39], avoiding the frequency droop [7,40], minimizing the power load variance [41], and maximizing the integration of renewable energies [42,43]. The PEV owner’s degree of satisfaction has also been taken into consideration most recently [44]. The equivalence of different optimization targets has been investigated. It indicates that for practical systems, minimizing load variances will minimize power losses

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approximately, and maximizing load factor is almost equivalent to minimizing the load variance [45]. Essentially speaking, the optimal scheduling for V2G operation is a dynamic programming problem with various constraints ought to be taken into account. Firstly, we should guarantee that there is enough electricity deposited in the onboard battery of PEV for its next itinerary. Secondly, we should make sure that the charging/discharging rate of PEVs will never exceed the capability of its battery and the charging facility. Thirdly, the charging/discharging profiles of PEVs should match the conventional load profile of the power grid, so that the aforementioned benefits of V2G operation can be maximized. It is easy to understand that the optimal scheduling for V2G should be conducted by power grid operators but not the PEVs owners, considering that PEV owners lack sufficient input information and powerful computing resource. Nevertheless, there are also some proposals for V2G implementation in which PEV owners are involved in the scheduling by engaging incentive mechanisms, such as floating electricity prices and bidding strategies [46–48]. This could be an effective way to promote V2G since it has the potential to reduce the uncertainty and complexity of the scheduling problem by wielding influence on people’s lifestyles. However, in our opinion, it is difficult to achieve optimal scheduling such as minimizing the load variance of power grid. Also, it takes the risk of threatening the security of power grid under a failed biding. In [49], the risks arising from various uncertainties are taken into account when designing bidding strategies. The purpose of this paper is to propose a novel optimal scheduling strategy for V2G operation based on the scenario of stochastic PEV connection to smart grid. In practical applications, it is quite difficult to acquire the information on the availability of PEVs, viz., when and where the PEVs will be connected to or disconnected from the power grid. To address this issue, the problem formulation regarding minimizing the power load variance with stochastic PEV connection to grid will be elaborated in Section 2. After that, the method to prepare for the input data for systematic evaluation will be introduction in Section 3. Section 4 will be devoted to case study and results analysis. Finally, conclusions will be drawn in Section 5. 2. Problem formulation with stochastic PEV connection to smart grid 2.1. General description Within the scheme of V2G operation, PEVs are expected to serve as a novel distributed energy storage system (ESS) to help achieve the balance between supply and demand of power grid, so as to smooth out the fluctuation of the power load profiles. For most power grids which adopt centralized supervisory control schemes, the grid operators are always eager to find effective measures to keep the total power load curves as flat as possible. Engaging energy storages can greatly suppress the fluctuation of load curves, and it can remarkably relieve the burden of grid operators in generation scheduling, load dispatching, frequency regulation, and so on. However, unlike the conventional ESS, the availability of PEVs as ESS remains highly uncertain due to their mobility as transportation tools. This definitely causes headache problems to the optimal scheduling for charging/discharging of PEVs. In the most previous studies, this issue is artfully avoided by using either statistics or assumptions. In order to promote the practical implementation of V2G technology, a scheme named ‘‘Event-Triggered Scheduling’’ is proposed to address this problem. Fig. 1 depicts the general scheme of the proposed event-triggered scheduling for V2G operation. The scheduling center takes charge of acquiring and processing the key signals, and

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Fig. 1. Scheme of proposed event-triggered scheduling for V2G operation with stochastic PEV connection to smart grid.

based on that, generating optimal charging instructions to guide the interchange of electric power between PEVs and grid which is bridged by the charging facilities. When PEVs are connected into grid, their owners are requested to set the time slot when they will be disconnected from grid, and what the demanded amount of electricity will be for their next itineraries. These inputs will be sent to the scheduling center via designated communication network under specific protocols. If a PEV is disconnected from grid before the original time slot set by its owner, it called unexpected disconnection. Herein, the triggering events include: (1) PEV connected into grid, and (2) PEV unexpectedly disconnected from grid. Once triggering event occurs, the scheduling center will communicate with the PEV involved, and acquire the necessary information, such as, the time of the trigger point, the state of charge (Soc) and the departure time of the newly-connected PEV, and so on. After that, the mathematical model will be updated as per the changes of the inputs, and the re-scheduling with updated model will be conducted in the scheduling center. Finally, the updated scheduling instructions will be sent to the charging facilities to coordinate the energy interchange between PEVs and power grid. The procedures will keep going until the next triggering event happens. However, it will not trigger the rescheduling procedure if a PEV is disconnected at or after the expected time set by its owner. 2.2. Basic period and time slot As illustrated in Fig. 2, the length of the basic period is set to be 24 h which is in accordance with the one-day cycle. The starting time ts is chosen as 06:00 AM of the current day and the ending

time te is chosen as 06:00 AM of the next day. We use M to denote the series number of the basic periods, for example, M = 0 for the current period, M = 1 for the first period next to the current period, and M = 1 for the first period previous to the current period. The basic period is equivalently divided into several time slots. The scheduling program will determine the charging/discharging power for every PEVs being involved in the V2G operation. The scheduled charging power is remain unchanged during each time slot. Herein, the length of the time slot Dt is set as 15 min, thus there are 96 time slots in the 24-h period. Actually, a tradeoff should be made when setting the length of the time slot. If the time slot is too long, a coarse optimization cannot ensure satisfactory results, while, if the time slot is too short, the number of variables involved will become incredible large and the complexity of the problem will become unacceptably high. We use N to denote the series number of the time slots, for example, N = 1 for the first time slot and N = 96 for the last time slot. 2.3. Mathematical modeling Each PEV is arranged to be involved into V2G operation at the beginning of the time slot right after its connection into the grid. Before the N-th time slot begins, the scheduling center collects all the necessary information to build up the N-th optimization model denoted by Model (N), where N = 1, 2, 3, . . . , 96, as illustrated in Fig. 2. Firstly, define the set SN to indicate the collection of all the PEVs that could be involved in V2G operation for the Model (N). It contains three subsets, namely:

Fig. 2. Basic period and time slot.

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L. Jian et al. / Applied Energy 146 (2015) 150–161 ðM¼0Þ

ðM¼1Þ

S N ¼ SN

[ SN

ðMP2Þ

[ SN

ð1Þ

where

ðM¼0Þ

SN

ðM¼1Þ

SN

ðMP2Þ SN

indicates the collection of all the PEVs which are set to be disconnected from the grid in the current period, indicates the collection of all the PEVs which are set to be disconnected from the grid in the first period next to the current period, and indicates the collection of all the PEVs which are set to be disconnected from the grid after the first period next to the current period.

  Soccon EV kN N   PNj EV kN CardðSN Þ   EV kN Socdis N

  Socmin EV kN N Secondly, define the series number of the time slot at the end of which the specific PEV considered will end its V2G operation for the current period as:



Cend EV kN N



8   < Cdis EV k ; if : EV k 2 SðM¼0Þ N N N N ¼ : ðM¼1Þ ðMP2Þ k 96; if : EV N 2 SN [ SN

  Pmax EV kN N 

g EV kN ð2Þ



  BatCap EV kN N

the (N  1)-th time slot, otherwise, if EV kN is   newly-connected, Socstart EV kN is equal to N   EV kN , and, Soccon N indicates the Soc of the specific PEV when it is connected to grid, indicates the scheduled charging power of the specific PEV during the j-th time slot, indicates the number of elements of the set SN, indicates the demanded Soc when the specific PEV disconnected from the grid, and it is set by the PEV owner for the next itinerary when it is connected into grid, indicates the allowed minimum Soc of the specific PEV, indicates the allowed maximum charging power of the specific PEV, indicates the charging efficiency of the specific PEV, and indicates the capacity of the onboard battery equipped on the specific PEV.

where

EV kN k Cdis N ðEV N Þ

indicates the specific PEV considered, and it is an element of SN, viz., SN = {EV 1N ; EV 2N , . . . , EV kN , . . .}, indicates the series number of the time slot at the end of which the specific PEV considered will be disconnected from the grid, and it is set by the PEV owner when it is connected into grid. Moreover, it lies between 1 and 96, even if the disconnection does not happen in the current period.

  Thirdly, Socend EV kN denotes the demanded Soc value of the specific N PEV considered when ending its V2G operation for the current period. It can be determined by (3) and should satisfy (4),

   3 2 end ðEV kN Þ Dt  P j EV k  g EV k     CN X N N N 4 5; N   Socend EV kN ¼ Socstart EV kN þ N N EV kN Bat Cap j¼N N ¼ 1; 2;    ; 96; k ¼ 1; 2; . . . ; CardðSN Þ; j P N

ð3Þ

Eq. (4) defines the limitations on the Soc value of the specific PEV considered when ending its V2G operation for the current period. Firstly, if the PEV will be disconnected from the grid in the current period (M = 0), this value should be equal to that set by its owner for the next itinerary when it was connected into grid. Secondly, if the PEV will be disconnected from the grid in the first period next to the current period (M = 1), this value should be larger than the allowed minimum Soc of the PEV, moreover, this value should guarantee that the requested amount of electricity by its owner for the next itinerary could be fulfilled when it is disconnected from the grid in the next period. In this regard, we can deduce the minimum Soc value by assuming that the PEV will be charged with the maximum charging power from the beginning of the next period to the time slot when it will be disconnected. Finally, if the PEV will be disconnected from the grid after the first period next to the current period (M P 2) this value should be larger than the allowed minimum Soc of the PEV, and with no other limitations. Fourthly, for each PEV, the scheduled charging/discharging power should satisfy:

      Pmax EV kN 6 PNj EV kN 6 Pmax EV kN N N

    8 ðM¼0Þ > Socend EV kN ¼ Socdis EV kN ; if : EV kN 2 SN > N N > > >     < ðMP2Þ if : EV kN 2 SN Socend EV kN P Socmin EV kN ; N N >   >       DtPmax EV k Cdis EV k g EV k > > ð NÞ N ð NÞ ð NÞ ðM¼1Þ > : Socend ; if : EV kN 2 SN EV kN P max Socmin EV kN ; Socdis EV kN  N Cap N N N BatN ðEV kN Þ

in which,   Socstart EV kN N

ð5Þ

ð4Þ

Moreover, at any time, the Soc value of the onboard battery should be lower than the allowed maximum value and higher than the allowed minimum value, viz.: indicates the Soc of the specific PEV at the EV kN

beginning of the N-th time slot. If is already involved in the previous models,   Socstart EV kN equals its Soc value at the end of N



Socstart EV kN N and,



   3 2 J   Dt  P Nj EV kN  g EV kN X 4 5 6 Socmax EV k   þ N N EV kN Bat Cap j¼N N

ð6Þ

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   3 2 J   Dt  P Nj EV kN  g EV kN X k 4 5 P Socmin EV k   Socstart N N ðEV N Þ þ N EV kN BatCap j¼N N

ð7Þ

  where J ¼ N; N þ 1; N þ 2; . . . ; Cend EV kN . N Finally, in order to minimize the power load variance in the current period, the objective function of the optimization scheduling problem can be given by:

8 92 96 < X j  k = 1 X j j min P  P Av g þ PN EV N ; 97  N j¼N : Con k

ð8Þ

EV N 2SN

where P Aj v g is determined by:

PAj v g

2 3 96 X j k 1 X j 4P þ ¼ PN EV N 5 97  N j¼N Con k

ð9Þ

EV N 2SN

j and PCon indicates the power of the conventional loads (excluding the PEV loads) during the j-th time slot. With the development of smart grid technology, it is believed to be possible to conduct 24-h-ahead conventional power load forecasting with acceptably high accuracy in the future based on meteorological information and historic data [50–52]. Up till now, the Model (N) has been successfully built up. Based on this model, the scheduling center determines the optimal charging profile for every PEV involved. If there is no triggering event occurs, the calculation model will not be updated. However, once there is any PEV being newly-added to V2G operation, or there is some PEV being unexpectedly disconnected from grid, the calculation model will be changed as per these updated inputs. After that, the rescheduling will be conducted in the scheduling center.

between 12 kW h and 20 kW h. The capacity of the onboard batteries has significant impact on the driving range of PEVs. For small and mid-size cars, 20 kW h battery pack is able to ensure 130 km range [55]. We investigated the driving patterns of passenger cars in China by using GPS tracking devices. The statistics show that on weekdays, the average driving range of 112 sample cars is 35.4 km, while, on weekends and holidays, this figure goes to 41.7 km. We believe that it would be better to be very cautious to choose the capacities of PEVs’ onboard battery pack before significant breakthroughs of battery technology have been made. Large volume batteries definitely add the vehicle’s net weight, and therefore, decrease the overall energy efficiency. Moreover, the self-discharge problem of batteries [56] also indicates that it is not reasonable to deposit too much electricity in PEVs. Secondly, the number of PEVs involved in the V2G operation for the current period is denoted by X. Moreover, 5% of them are selected out and assumed to be connected into grid before the current period by using Bernoulli distribution. For these selected PEVs, some assumptions are also made: their detention time (in Hours) follows a uniform distribution between 2 h and 14 h, their Soc at the start time follows a uniform distribution between 0.2 and 0.8, and their demanded Soc when disconnected from the grid follows a uniform distribution between 0.4 and 0.7. Next, for the remaining 95% PEVs which are connected into grid during the current period, their arriving time (for example, arriving at parking lots and ready for connection into grid) is assumed to follow Chi-square distribution with its probability density function given by:

f ðxÞ ¼

1 2n=2 Cðn=2Þ

xn=21 ex=2 ; x P 0

ð10Þ

where

CðaÞ ¼

Z

1

xa1 ex dx for a > 0

ð11Þ

0

3. Preparation of input data for systematic evaluation In order to evaluate the effectiveness of the proposed scheduling scheme, the input data should be generated to simulate the real situations in a reasonable and indiscriminative way. Nevertheless, some assumptions have to be engaged for simplicity. Firstly, for all the PEVs involved, some parameters are assumed to be identical: the allowed maximum charging power is set as 4 kW, the allowed minimum and maximum Soc values are set to be 0.2 and 0.8, respectively, and the charging efficiency is set as 0.9. Generally, the charging of PEVs can be classified into slow charging, fast charging and ultrafast charging (also named ‘rapid charging’), depending on the charging power [53,54]. Slow charging is conducted via the onboard charger of PEVs, and the charging power is around 3.3 kW. PEVs can be directly connected to the utility grid through single-phase ac cable. Therefore, slow charging does not involve extra investments on equipping off-board charging equipments and upgrading the facilities of regional power grid. The power levels of fast charging and ultrafast charging range from 10 kW to 50 kW. External dc charger has to be equipped due to the charger’ bulky size and cooling requirements of the electronics integrated. Moreover, the prerequisite for equipping high power external charger is to increase the capacities of the regional grid’s facilities, such as transformers, switches, cables and so forth. Therefore, fast charging and ultrafast charging are usually used in specific charging stations operated by power grid companies. As aforementioned, the essence of V2G is to exploit the potential of PEVs’ onboard batteries to help increase the stability and operating efficiency of power grid, thus slow charging is preferable in the scheme of V2G operation. In addition, the capacity of the onboard batteries (in kW h) is assumed to follow uniform distribution

Herein, the degrees of freedom n is set as 5, and the obtained profile of PEV with different arriving time is shown in Fig. 3, when the total PEV number X = 200. It can be observed that most PEVs arrive at parking lots in the morning, and this is in accordance with the scenario of week days when people drive to work in the morning and then park their vehicles in the parking lots in the vicinity of their workplaces. Then, the detention time of the PEVs connected into grid during the current period is assumed to follow normal distribution with its mean equal to 10 h and its variance equal to 9 h. In most cases,

Fig. 3. Number of PEVs with different arriving time (X = 200).

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4. Case study and results analysis

Fig. 4. Number of PEVs with different detention time (X = 200).

people arrive at workplaces at round 8:00 AM, and leave for home at around 6:00 PM. Therefore, the detention time of their PEVs is about 10 h. Fig. 4 gives the number of PEVs with different detention time, when the total PEV number X = 200. In addition, for the PEVs which are connected into grid during the current period, their Soc at the start time is assumed to follows a uniform distribution between 0.3 and 0.6, and their demanded Soc when disconnected from the grid follows a uniform distribution between 0.4 and 0.7. After that, we use Bernoulli distribution once again to select 1% of all the PEVs, and assume that these selected PEVs will unexpectedly disconnected from grid, namely, their detention time will be shorter than that set by the owners when connected into grid. Then, we use uniform distribution to determine when these triggering events occur. Finally, Fig. 5 illustrates the conventional power load profile of the regional grid considered during the current period. These data are supplied by the local power company, and it represents the power consuming in a typical weekday. The peak hours occur at around 11: 00 AM and 18:00 PM. The difference between the highest power and the lowest power is about 27 kW, and the mean and the variance of the curve are 92.37 kW and 108.98 kW2, respectively. The load fluctuation in one-day period is quite fierce, and this definitely results in huge energy losses.

Fig. 5. Conventional power load profile in one-day cycle.

In order to show how the proposed event-triggered scheduling method works, we depict the whole process step by step in Figs. 6– 8. In this case, the number of PEVs involved X is 200 and the preparation of the input data was elaborated in Section 3. As we can see, there are some models not shown herein due to that there is no triggering events happen. For example, there is not any triggering events happening in the second time slot, so the Model (2) is not shown since the rescheduling is not conducted and the planned PEV charging profile does not change based on that scheduled in Model (1). It can also be observed that there is not obverse difference among the scheduling results obtained in some adjacent models, such as Model (1) – Model (5), Model (18) – Model (22), and Model (41) – Model (47). That is because although PEVs are newly connected into grid or unexpected disconnected from grid during these time slots, the variation on the capacity of storage offered by the aggregation of PEVs is tiny, and these small changes will not lead to significant impact on the scheduling results. Nevertheless, remarkable differences can also be observed between Model (6) and Model (5), Model (23) and Model (22), Model (50) and Model (47), and so forth. Model (74) is the last one shown for this case since after that there is no triggering events occur for the current period. The scheduling results for the V2G operation obtained in Model (74) will be carried out until the end of this period. In other words, Model (74) exhibits the final performance of the V2G operation in this case with our proposed scheduling method. With the PEVs serving as energy storage systems, the total load power curve become very smooth. Its variation value equals 2.53, which is significantly smaller than the variance of the conventional power load curve equal to 108.98 kW2. Moreover, we can tell the prominent difference between the scheduled charging profiles obtained in Model (1) and Model (74). The incremental changes in every step can lead to profound impacts on the final results. That is why we should take into account the contribution of every single PEV being connecting into or disconnecting from the grid. It is easy to understand that the number of PEVs involved should affect the performance of V2G operation. For figure this out, we regenerated the input data with different number of PEVs X according to the procedures presented in Section 3. Consequently, the scheduling results of these new cases obtained by using the proposed event-triggered scheduling method are illustrated in Fig. 9. For X = 100, the last model in the selected case shown in Fig. 9(a) is Model (66), and the variance value of the total power load curve is 14.52 kW2. For X = 150, 250 and 300, the last models in the selected cases shown in Fig. 9(b)–(d) are Model (71), Model (64) and Model (63), and the corresponding variances are 7.71 kW2, 2.32 kW2 and 1.94 kW2, respectively. The larger number of PEVs is involved, the smaller load variance can be resulted in. As we all know, the reduction of load variance can greatly improve the operation efficiency and security of the power grid. That is why V2G is becoming a very hot issue as far as the future smart grid is concerned. In order to evaluate the effectiveness of the proposed scheduling method, the algorithm has been operated for 1000 times with different scales of PEVs involved. The input data were generated stochastically according to the method stated in Section 3. Fig. 10 shows the distribution of the resulted variance of load power curves. When X = 100, the resulted 1000 variance values spans from 7.84 kW2 to 21.72 kW2, the median equals 14.06 kW2, and the middle 50% lie between 12.72 kW2 and 15.56 kW2. When X = 300, the resulted 1000 variance values spans from 0.09 kW2 to 7.67 kW2, the median equals 2.15 kW2, and middle 50% lie between 1.47 kW2 and 3.10 kW2. Again, compared with the

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Fig. 6. Scheduling results of Model (1) – Model (17) with proposed event-triggered scheduling method (X = 200).

L. Jian et al. / Applied Energy 146 (2015) 150–161

Fig. 7. Scheduling results of Model (18) – Model (33) with proposed event-triggered scheduling method (X = 200).

157

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Fig. 8. Scheduling results of Model (35) – Model (74) with proposed event-triggered scheduling method (X = 200).

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Fig. 9. Scheduling results with different numbers of PEVs involved: (a) X = 100; (b) X = 150; (c) X = 250; (d) X = 300.

Table 1 Specification of cases studied. Number of PEVs involved

X = 100 X = 150 X = 200 X = 250 X = 300

Fig. 10. Distributions of resulted variance of load power curves.

variance of the conventional power load curve which is equal to 108.98 kW2, the resulted load curves have been dramatically smoothen out by the proposed V2G operation scheme.

Number of variables in 1000-times experiments

Computing time consumed for single model (ms)

Maximum value

Minimum value

Maximum value

Minimum value

4896 7888 10764 13467 15912

384 402 736 1440 1632

382 1021 1896 2948 4575

2 2 3 84 196

Table 1 lists the specification of all the cases studied. For different scales of PEVs involved, the number of variables and the computing time consumed for single model in all 1000-time experiments are recorded. All the models are run on the same workstation (CPU 3.20 GHz, RAM 6 GB) in our lab. It can be seen that the time spent on solving one single model is less than 5 s for the cases with X = 300, and this is definitely acceptable considering the length of each time-slot is 15 min.

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5. Conclusions In this paper, a novel optimal scheduling scheme for V2G operation is proposed. One of the key difficulties in the practical implementation of V2G operation lies in that the availability of PEVs as a kind of distributed energy storage system is uncertain due to their mobility as transportation tools. The proposed event-triggered scheduling scheme can solve this problem by updating the optimization model and conducting rescheduling as long as triggering events including PEV connected into grid and PEV unexpectedly disconnected from grid occur. The problem formulation aiming at minimizing the overall load variance is built up. The method to generate the input data for systematic evaluation is introduced. It is able to reasonably and objectively simulate the real situations. In case study, the operating process of the proposed optimal scheduling is depicted step by step, and it demonstrates that the incremental changes in every step can lead to profound impacts on the final results. The effectiveness of the proposed scheduling method is verified by a large number of simulation tests. The statistic analysis results demonstrate that it can dramatically reduce the variance of total load power curves, and therefore help improve the operation efficiency and security of the power grid.

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