Research of Charging(Discharging) Orderly and Optimizing Load Curve for Electric Vehicles Based on Dynamic Electric Price and V2G

Firstly, using the Monte Carlo method and simulation analysis, this paper builds models for the behaviour of electric vehicles, the conventional charging model and the fast charging model. Secondly, this paper studies the impact that the number of electric vehicles which get access to power grid has on the daily load curve. Then, the paper put forwards a dynamic pricing mechanism of electricity, and studies how this dynamic pricing mechanism guides the electric vehicles to charge orderly. Last but not the least, the paper presents a V2G mechanism. Under this mechanism, electric vehicles can charge orderly and take part in the peak shaving. Research finds that massive electric vehicles’ access to the power grid will increase the peak-valley difference of daily load curve. Dynamic pricing mechanism and V2G mechanism can effectively lead the electric vehicles to take part in peak-shaving, and optimize the daily load curve.


Introduction
Compared with traditional vehicle, electric vehicle has advantages of low pollution and abundant fuel supply.According to analysis, by 2020 the number of electric vehicle ownership in china will exceed 5 million [1].Nowadays, many scholars are applying themselves to researching on the subject of large scale of electric vehicles connecting to the power grid [2][3][4][5].
This paper is organized as follows.In section , we use Monte Carlo method to model the conventional charging behaviour of electric vehicles and use analogy simulation to model the fast charging behaviour of electric vehicles.In section , we propose a kind of dynamic electricity price method which can guide electric vehicles to charge orderly.In section , we propose a kind of V2G method which can guide electric vehicles to charge(discharge) orderly.In the last section, we look back the full text and tally up textual point.

Model the Behaviour of Electric Vehicles
According to the forecast [1], by 2020 the number of electric vehicle ownership in china will exceed 5 million, of which the personal cars are more than 4.3 million, almost 86% of the total number.Electric vehicles mainly have two kinds of charging models, which are conventional charging model and fast charging model.Conventional charging facilities are generally located in residential, corporation, parking lot and so on.In general, charging power of this model is about 10kW, its charging time is longer and its charging speed is slow.Conventional charging is used to meet the needs of daily use, usually being conducted in the evening or at night.Fast charging facilities are generally located in a special charging station, mainly to meet the needs of temporary charging.Its charging speed is relatively fast and its charging power is about 40kW.When being charged half an hour in the fast charging station, electric vehicles can drive almost 100 kilometers.
We use the Monte Carlo method and analogy simulation to model the behaviors of electric vehicles.

Conventional Charging Modeling
We use DENZA charging facility in this paper which produces 10kW of power.According to related data, we can get the last trip ending and return time distribution probability density [6] and electric vehicle driving distance distribution probability density [7][8].Continuous charging time is calculated as follow: ti is the charging time of the ith datum, si is the driving distance of the ith datum.The two share the same distribution probability density.pc is the rated power of charging facility.η=0.9 is charging efficiency, k is power consumption per hundred kilometers.The k=18.6kwh refers to Qin of BYD.The result are shown in Figure 1 and Figure 2 .

Monte Carlo simulation
Monte Carlo simulation is based on Probability and Mathematical Statistics.Under this method, the problem is solved with a certain probability model, and the approximate solution of the problem is obtained by using large scale simulation [9].
The mathematical and empirical evidence show that the random variables which are influenced by plenty independent homogeneous-small effects are subject to normal distribution.That is to say, if a variable is influenced by many small independent random factors, then it can be considered to be subject to normal distribution.Charging starting time and duration of charging are related to personal preference and mutual independence.Therefore, the charging time of electric vehicle and the duration of charging can be used for the curve fitting of normal distribution [5].The results of curve fitting are as follows: a1=0.1195, b1=17.32, c1=4.721; a2=0.5283, b2=-0.3791, c2=2.113;95% confidence interval.f1(t) is the probability distribution of charging start time, f2(t) is the probability distribution of charging duration.Then daily charging expectation of single electric vehicle can be gotten by Monte Carlo simulation.The calculation is shown in Figure 3 and the result is shown in Figure 4.

Fast charging modeling
Because it is hard to estimate the fast charging behaviour, we get the load curve of fast charging through modeling the business of fast charging station.The vehicle flow of charging station is not the same in different time [10].The power of charging facility is 40kW, which is referred to BYD's charging facility.The modeling of fast charging behaviour is shown in Table 1.We choose the daily load of a northern city in China as the basic load.When the number of electric vehicles is 100,000, 200,000 and 500,000 respectively, the daily load curves are shown in Figure 6.

Table 1. Model of fast charging behavior
In the formulations above, γg and γf are peak superposition and valley superposition respectively.p'min is valley load which contains both basic load and electric vehicle load; p'max is peak load which contains both basic load and electric vehicle load.pmin is basic valley load and pmax is basic peak load.The result of calculation about load curve that electric vehicles connect to the grid is shown in Table 2.  .2, the load characteristics of electric vehicles are similar to the city's electricity load characteristics.The reason is that most users tend to charge electric vehicles after stopping work and arriving at home in the evening in the meanwhile the charging period is also the peak period.This characteristic makes the difference between peak load and valley load bigger.In addition, it can be inferred from Figure .1 and Figure .2that the electric vehicle is usually used as a tool replacing the foot, so the driving distance is not so long.This characteristic makes it unavailable to fill the valley by charging in the midnight.The characteristics discussed above may waste the power, increase the power loss and increase the burden of power grid.From what has been discussed above, we may safely arrive at the conclusion that due attention has to be paid to guide the charging behaviors of electric vehicles.
In formulation (7), ε is price elasticity index; △Dt and △Ct are demand changes and price changes respectively in tth moment; Dt and △Ct are demand and price in tth moment.
In this paper, one day is separated into 24 electric price ranges.Each range starts at the beginning of this hour and the price continues one hour.The electric price of each range is related to the total load of this range and the mean load of the whole day.The models are as follows: D't is the load adjusted by dynamic electric price, D is the mean demand of the day, T is the time range, ε=-0.3 [11], the number of electric vehicles connecting to power grid is 500,000.Comparison of load curves before and after being adjusted by dynamic electric price are shown in Figure 7 and Table 3.It can be seen from Figure .7 and Table .3that load curve condition is improved by dynamic electric price.Under this dynamic electric price, although γg has a little decrease, γf has a significant reduction.γf decreases from 15.030% to 11.381%, having 3.649% fall.In addition δ decreases from 45.74% to 43.97%, having 1.77% fall.So it can be concluded that it is useful for this dynamic electric price to guide the charging behaviors of electric vehicles and smooth the load curve.

V2G Regulation
Vehicle to Grid is called V2G for short [12].V2G describes a system where plug-in electric vehicles communicate with the electric power grid to sell demand response [13].Hence, V2G application is transformational and revolutionary in that it precipitates the confluence of transportation and electric power system, thereby introducing electricity as a meaningful automotive fuel [14].Under V2G regulation, electric vehicles require charging and discharging batteries.Its model is as followed: -The electric vehicle can obtain power from power grid when it need to charge; -The electric vehicle can release power energy to power grid when it need to discharge.It can be inferred from Figure .1 and Figure .2that most users drive their electric vehicles not so far.So their charging time is not so long.Charging time is less than 4 hours in a day for most users.It means that when the battery is full, there will be a long time without any activities for electric vehicles.The free time can be used to fill the valley of load curve in order to reduce the burden of power grid and conserve the energy.Under V2G regulation, electric vehicles are discharged in peak period and charged in valley period.
Based on Figure .1, Figure .7 and the experience, the users who get home from 16:00pm to 23:00pm can be regarded as main force to participate in V2G program.Referring to the step electric price mechanism of Beijing [15], we set the peak load period from 18:00pm to 23:00pm and the valley load period from 23:00pm to 7:00am.Under the prerequisite of fully charging in electric vehicles, the cars participating in V2G program discharge in peak load period and charge in valley load period.The main mission of V2G program set by us in this paper is to clip the peak load and fill the valley load.The car that begins to discharge in i o'clock.The model is as follows: tfi is the maximum discharging time of electric vehicles that begin to discharge in i o'clock, tci is the charging time of electric vehicles which begin to discharge in i o'clock.After calculation, the maximum discharging time of electric vehicles that begin to discharge in i o'clock is shown in Table 5.In Table 4, the first row represents duration and the first column represents starting time.Definition: aij is the discharging element exiting in Table .5. i is the beginning time of discharging, j is the duration of charging.The total number of electric vehicle accessing the grid is A=500,000, pi is the probability of charging in i o'clock, qj is the probability of that electric vehicle charge for j hour(s), Di is the power that is injected to the grid by electric vehicles in i o'clock.Search the aij above the Table.5 one by one and calculate the total contribution every aij makes to Di. Sum of Di is the power injection.The calculation and results are shown in Figure .8and Table 5    In Table 5, the first row represents the time period of discharging and the first column represents the start time of discharging.
After getting tfi and tci, we can calculate t'ci, the value of charging time in valley load period.
' ci fi ci t t t (15) We separate the valley load period into 8 time periods.Each aij select one period that has the minimum load.Generally speaking, from 23:00-7:00, the later time is, the lower the loads are.So the charging rule we propose is that charging in later time period is prior than charging in the early time period.If aij can charges only 1.3h, for example, it charges 1h in the time period of 6:00-7:00 and charges 0.3h in the time period of 5:00-6:00.In other words, it charges from 6:00 to 7:00 at rated power and charges from 5:00 to 6:00 at 30% rated power.The calculation of charging is shown in Figure .9and Table 6.

Table 6. Power of charging
23:00-0:00 0:00-1:00 1:00-2:00 2:00-3:00 3:00-4:00 4:00-5:00 5:00-6:00 Based on Figure 8, Figure 9, Table 5 and Table 6, we can get the daily load curve adjusted by dynamic electric price and V2G.The comparison between load curve and load curve adjusted by dynamic electric price and V2G is shown in Figure .10and Table 7.The number of electric vehicles connecting the grid is 500,000.It can be known from Figure .10,and Table .7 that the method of V2G is valuable for improvement of power load characteristics.But it should be noticed that the valley time has been changed after V2G method adopted.If the number of electric vehicles remain elevated, V2G maybe be not enough.The problems will be more complicated.If we just make use of V2G simply when the number of electric vehicles is large enough, the new valley load period may appear.

Conclusion
When the number of electric vehicles connecting to power grid is small, the influence to the grid is limited.When the number of electric vehicles connecting power grid is big, the influence to the grid is tremendous.Dynamic electric price is available to optimize the daily load curve.It can guide electric vehicle users to charge their cars orderly.V2G is more useful to optimize the daily load curve.It allows users of electric vehicles to participate in peak/valley load regulating of power system.But it should be noticed that the valley time has been changed after V2G method being adopted.If the number of electric vehicles remain elevated, V2G will be not enough.If we just make use of V2G simply when the number of electric vehicles is large enough, the new valley load period may appear.Many problems still need to be further studied, such as charging/discharging period segmentation, the subsidy rule to V2G users, coordination between renewable energy and electric vehicles and so on.

Figure 1 .Figure 2 .
Figure 1.Last trip ending and return time distribution probability density

Figure 3 .
Figure 3. Calculation of Monte Carlo simulation

Figure 4 .
Figure 4. Daily load curve of single electric vehicle According to calculation, the daily load curve of fast charging is obtained as Figure.5.

Figure 5 .
Figure 5. Daily load curve of fast charging 2.4 Fast charging modeling

Figure 6 .
Figure 6.Daily load curve after electric vehicles connecting to the grid Definite peak valley ratio: Different power prices in different time can guide charging behaviors of electric vehicles.When the price is high, users tend to charge at other times.Conversely, when the price is low, users tend to charge in this time.The price elasticity function can explain this phenomenon:

Figure 7 .
Figure 7.The effect of dynamic electric price 1

Figure 10 .
Figure 10.The effects of V2G and dynamic electric price 1

Table 2 .
The calculation about the electric vehicles connecting to the grid

Table 3 .
The effect of dynamic electric price 2

Table 4 .
Maximum discharging time respectively.

Table 5 .
Power of discharging

Table 7 .
The effects of V2G and dynamic electric price 2