Biding strategy of vehicle parking for participating in energy and spinning reserve markets

Abstract

In this paper a model for suggesting a smart parking that involves a set of electric cars is presented to auction the management ability and correct parking planning in reserve spinning market, secondary energy market and grid. Parking interest under various scenarios is analyzed and its effective results are presented by a valid model. Besides, particle swarm optimization algorithm is used for calculating maximum benefit.

Graphical abstract

Keywords

vehicle-to-grid (V2G) / spinning reserve / energy secondary market / smart parking

1 Introduction

Many papers have analyzed the effect of car technology to grid and electric cars on power grid. One can investigate these papers from two perspectives, market and profitability. Kempton and Tomic in 2005 considered electric cars as inappropriate for providing base load; in contrast, they considered them as suitable for presence in spinning reserve markets and secondary service market. In another study, they concluded that with the rise of presence of renewable resources in the future, electric cars would play a significant role in supporting these resources [1,2]. Kempton and Tomic in 2005 [1,2], organized a cumulative suggestion for car technology to grid for participating in market. In addition to the cost of changing batteries, and presenting in control market, electric cars can maximize cumulative revenue and frequency control [2]. Jang et al. in 2010, considering cumulative revenue with the aim of maximizing income, defined entrance level of electric cars in organized market [3]. In 2009, Karnama investigated the role of electric cars in filling load valleys and their effect on filling and leveling load curve in California [4], as shown in Figs. 1, 2 and 3. In 2010, Inage [5] showed that, receiving and injecting force in appropriate time, vehicle-to-grid (V2G) can reduce the difference between maximum and minimum consumption significantly.

Sortomme and EI-Sharkawi [6] demonstrated that unidirectional relationship of car technology to grid is more often considered by consumers. Applying parking lot for controlling amount of car battery charge and electric price in grid, they suggested a smart charge algorithm that is beneficial for consumer, parking lot and power grid. The mentioned technology is associated with lowest cost for maximum battery charge, maximum interest for cumulative and rise of flexibility for power, grid in presence of renewable resource. Abolfazli et al. [7] studied the condition of electric car batteries in different hours of day with a potential model and presented a model for car presence in distribution grid to provide possibility of adopting an effective decision by parking lot in addition to preventing additional load in grid. Andersson et al. [8] analyzed the effect of electric cars on regulating market. In Germany and Sweden, electric cars were suggested as load in grid for regulated reduction. Although the rise of electric car entrance into markets increases interests, it led to the saturation of regulated market and the rise of initial costs in applying cars.

Venayagamoorthy et al. [9], considering two smart parking in pre-shopping market, analyzed the effects of car technology on grid and error in profitability of electric cars and presented a model. Saber and Venayagamoorthy [10] considered two configurations for using car technology to grid in secondary service market. In the first state, parking lot controls electric cars. In second state the effect of each car is analyzed directly. Mitra and Venayagamoorthy [11], using car technology to grid, guaranteed the rise of grid consistency. Hartmann and Ozdemir [12] showed that electric cars have a positive effect on cost of power grid.

2 Suggested model

In this study a model for force exchanging between parking-grid, parking-secondary energy market, and parking-spinning reserve market is presented. Coordinating process of receiving energy and its return to the grid can show positive effects of using electric cars on power grid. In charging and discharging some of cars in parking, parking management at the time of car presence in it can plan in a way to take maximum benefit of this presence of cars in parking, in energy secondary markets and spinning reserve. Decision variables such as battery charge capacity of electric cars, time span at electric car presence in parking and number of electric cars play the greatest role in optimization process of parking interests. In the parking period of the PEVs the power willl be exchanged in the market of spinning reserve ang other ancillary services so that the parking makes the maximum profit from charging and discharging of PEVs. The framework is presented in Fig. 4.

(1)P_{\mathrm{SV}}\left(i,h\right)=\mathrm{sgn}\left(s\left(i,h\right)\right)\times \left(P_{\mathrm{Bat}}\left(i\right)/{\eta }_{\mathrm{c}}\left(i\right)\right),

(2)P_{\mathrm{BV}}\left(i,h\right)=\mathrm{sgn}\left(-s\left(i,h\right)\right)\times \left(P_{\mathrm{Bat}}\left(i\right)\times {\eta }_{\mathrm{d}}\left(i\right)\right),

(3)\mathrm{sgn}\left(x\right)=\{\begin{array}{cc}\mathrm{1}\hfill & x>0,\hfill \\ \mathrm{0}\hfill & x\le 0,\hfill \end{array}

(4)S=\{\begin{array}{ll}+1\hfill & \mathrm{i}\mathrm{f}\hspace{0.17em}\mathrm{V}2\mathrm{G}\hspace{0.17em}\mathrm{i}\mathrm{s}\hspace{0.17em}\mathrm{c}\mathrm{h}\arg \mathrm{i}\mathrm{n}\mathrm{g},\hfill \\ -1\hfill & \mathrm{i}\mathrm{f}\hspace{0.17em}\mathrm{V}2\mathrm{G}\hspace{0.17em}\mathrm{i}\mathrm{s}\hspace{0.17em}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{h}\arg \mathrm{i}\mathrm{n}\mathrm{g},\hfill \\ 0\hfill & \mathrm{l}\mathrm{a}\mathrm{c}\mathrm{k}\hspace{0.17em}\mathrm{o}\mathrm{f}\hspace{0.17em}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\hspace{0.17em}\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}\hspace{0.17em}\mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}\hspace{0.17em}\mathrm{V}2\mathrm{G}\hspace{0.17em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.17em}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g},\hfill \end{array}

(5)\mathit{S}={\left[\begin{array}{lll}\hfill & \cdots \hfill & \hfill \\ ⋮\hfill & \ddots \hfill & ⋮\hfill \\ \hfill & \cdots \hfill & \hfill \end{array}\right]}_{n\times 24},

(6)P_{\mathrm{G}}\left(h\right)={\displaystyle \sum _{i=1}^n{P}_{\mathrm{BV}}\left(i,h\right)},

(7)P_{\mathrm{L}}\left(h\right)={\displaystyle \sum _{i=1}^n{P}_{\mathrm{SV}}\left(i,h\right)},

(8)P_{\mathrm{net}}\left(h\right)=P_{\mathrm{G}}\left(h\right)-P_{\mathrm{L}}\left(h\right),

(9)

(10)P_{\mathrm{net}}>0\to \mathrm{P}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g}\hspace{0.17em}\mathrm{i}\mathrm{s}\hspace{0.17em}\mathrm{a}\mathrm{s}\hspace{0.17em}\mathrm{a}\hspace{0.17em}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r},

(11)P_{\mathrm{SG}}\left(h\right)=\mathrm{sgn}\left(P_{\mathrm{net}}\left(h\right)\right)\times \left(P_{\mathrm{net}}\left(h\right)\right),

(12)P_{\mathrm{BG}}\left(h\right)=\mathrm{sgn}\left(-P_{\mathrm{net}}\left(h\right)\right)\times \left(-P_{\mathrm{net}}\left(h\right)\right),

(13)\mathrm{S}\mathrm{h}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{n}\mathrm{g}\hspace{0.17em}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\hspace{0.17em}\mathrm{o}\mathrm{f}\hspace{0.17em}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}={\displaystyle \sum _{h=1}^{24}{P}_{\mathrm{BG}}\left(h\right)\times {\lambda }_{\mathrm{BG}}\left(h\right)},

(14)\mathrm{S}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\hspace{0.17em}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\hspace{0.17em}\mathrm{o}\mathrm{f}\hspace{0.17em}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}={\displaystyle \sum _{h=1}^{24}{P}_{\mathrm{BG}}\left(h\right)\times {\lambda }_{\mathrm{BG}}\left(h\right)},

(15)h_{\mathrm{c}}\left(i\right)={\displaystyle \frac{\left|{\mathrm{Soc}}_{\mathrm{o}}\left(i\right)-{\mathrm{Soc}}_{\mathrm{i}}\left(i\right)\right|}{P_{\mathrm{Bat}}\left(i\right)E_{\mathrm{t}}\left(i\right)}},

(16){\lambda }_{\mathrm{SV}}^{\mathrm{as}}\left(i,h\right)=\mathrm{sort}\left({\lambda }_{\mathrm{SV}}{\left(h\right)}_{h=h_i\left(i\right)}^{h_{\mathrm{o}}\left(i\right)}\right),

(17)\mathrm{S}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\hspace{0.17em}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\hspace{0.17em}\mathrm{t}\mathrm{o}\hspace{0.17em}\mathrm{c}\mathrm{a}\mathrm{r}=\mathrm{sgn}\left({\mathrm{Soc}}_{\mathrm{o}}\left(i\right)-{\mathrm{Soc}}_{\mathrm{i}}\left(i\right)\right)\times {\displaystyle \frac{P_{\mathrm{Bat}\left(i\right)}}{{\eta }_{\mathrm{c}}\left(i\right)}}\times {\displaystyle \sum _{h=1}^{h_{\mathrm{c}}\left(i\right)}{\lambda }_{\mathrm{SV}}^{\mathrm{as}}\left(i,h\right)},

(18){\lambda }_{\mathrm{SV}}^{\mathrm{ds}}\left(i,h\right)=\mathrm{sort}\left(P_{\mathrm{rBV}}{\left(h\right)}_{h=h_i\left(i\right)}^{h=h_{\mathrm{o}}\left(i\right)}\right),

where, P_Bat(i): amount of power that ith car can receive or deliver;

{\eta }_{\mathrm{c}}: random A car charge;

S(i,h): situation of power exchange of all cars during day and night;

P_G(h): all the power delivered to V2Gs during day-night by parking;

P_BG: amount of power that parking buys from grid in time h during 24 h;

P_SG: amount of power that parking sells to grid during 24 h;

P_SR: amount of power that is sold in spinning reserve market during 24 h;

P_SE: amount of power that is sold in energy secondary market during 24 h;

P_BV: amount of power that parking owner buys from ith cars during 24 h;

P_SV: amount of power that parking owner sells to ith car during 24 h.

Soc_i (i): V2G ith charge percent when entrance to parking;

Soc_o(i): V2G ith charge percent when exist from parking;

E_t(i): all the amount of energy that V2G ith battery can save in itself;

{\eta }_{\mathrm{d}}\left(i\right): discharge car random of V2G ith;

S: V2G power exchange situation matrix.

For calculating maximum parking profit, in addition to the amount of power needed in energy secondary market, spinning reserve, grid and delivery power of each cars, the curve of day night price in each market should be available. Besides, it is necessary to calculate the cost that is paid to grid for buying power in order to act according to the suggested Eq. (19).

(19)\mathrm{Profit}\hspace{0.17em}\mathrm{parking}={\displaystyle \sum _{i=1}^{24}{P}_{\mathrm{SR}}{\lambda }_{\mathrm{SR}}}+{\displaystyle \sum _{i=1}^{24}{P}_{\mathrm{SE}}{\lambda }_{\mathrm{SE}}}+{\displaystyle \sum _{i=1}^{24}{P}_{\mathrm{SG}}{\lambda }_{\mathrm{SG}}}+{\displaystyle \sum _{i=1}^{24}{P}_{\mathrm{SV}}{\lambda }_{\mathrm{SV}}}-{\displaystyle \sum _{i=1}^{24}{P}_{\mathrm{BG}}{\lambda }_{\mathrm{BG}}},

where, \lambda: shopping rate of electricity from grid;

$$\begin{gathered} \\ {\lambda }_{\mathrm{SG}} \end{gathered}$$: selling rate of electricity to grid;

{\lambda }_{\mathrm{SR}}: selling rate to spinning reserve market;

{\mathit{\lambda }}_{\mathrm{SE}}: selling rate to energy secondary market;

{\lambda }_{\mathrm{SV}}: rate of selling power to V2G;

A conceptual framework of the proposed algorithm is presented in Fig. 5. Finding the charging and discharging schedule of the power electric vehicles (PEVs) is a nonlinear programming problem. A conceptual flowchart of the particle swarm optimization (PSO) algorithm applied to solve the problem is provided in Fig. 6.

In the suggested model, it is assumed that smart parking has enough space for acceptance of referenced cars and owner with a pre-determined contract gives information about car number, amount of battery charge and discharge, entrance time to the parking in a telecommunicative way. Having the arrival-departure time table and charging and discharging management, the parking can participate in spinning reserve and ancillary energy markets. So, the PSO algorithm is used for optimizing parking profit in energy secondary market and turning reserve one. For satisfying car owners, parking management in an interval of 4 h of cars presence in parking sells energy with the lowest price. In this paper, alternative exit and pollution index is not considered. Figure 7 shows the information needed of smart parking for participating in markets.

3 Numerical study

According to Table 1, assuming having price of energy exchange in secondary market, grid, spinning reserve market, entrance and exit program of all V2Gs to parking in their 4 h presence (2 h charge and 2 h discharge), and the initial and final battery charges of the PEVs are considered to be 0 and 100%, respectively, the parking profit changes increase with the rise of car numbers and battery capacity of cars. Figure 8 shows the entrance and exit curve of 10 electric vehicle cars to parking during 24 h. Figure 9 is the power selling price curve to energy secondary market, turning reserve market, grid and selling price to V2G.

In this step, parking profit is calculated using the PSO algorithm for 5 cars. Figure 10 depicts the parking profit, from which it can be seen that the maximum parking profit has reached 12 $/kWh. From this step there has been no change, and this point is the optimized point of the PSO algorithm and maximum parking profit for this number of cars.

Figure 11 shows the power exchanged in different hours between the parking and different markets. Using Fig. 11 the parking manager can assess the value of the power exchanged between the parking and ancillary energy, spinning reserve and grid markets in different hours. Having this information in hand, the parking owners can participate in tomorrow’s market and gain more profit via a proper planning. Parking owner can achieve more profits with the right planning.

Figure 12 shows the entrance and exit time to parking for the status of charge and discharge of each car, the power delivered to parking at the time of car presence in parking, and the amount of car SOC charge to parking management and car owner.

Figure 13 illustrates the benefit increase with battery capacity. At first battery capacity is made constant at 10 kW. Then the parking profit is calculated. The battery capacity of cars increased to 20 kW, 30 kW, 40 kW, and 50 kW. Each step shows the results of the simulation, and rise of the parking profit. The rise of battery capacity of cars give this possibility to parking to save more amount of energy at times when the price is low.

At this stage, at first the time length of each car charging was assumed as Z hours and calculated the parking profit. Figure 4 shows the reduction of parking profit. So increasing charging length time can lead to a reduction in parking profit while reducing charging length time increases the profit. It can be said with 4 h presence of cars in parking and reduction of charging time, the parking owner can have the opportunity to make maximum utility of car presence in parking.

As can be seen from Fig. 15 that increasing the number of vehicles has the same effect as increasing the battery capacity. The parking profit has been calculated for 5, 10 and 15 PEVs and the results of simulations show that increasing the number of PEVs increases the parking profit. The reason for this is that increasing the number of PEVs increases the energy storing capability of the parking as well as the ability of delivering electrical energy in peak load periods.

4 Conclusions

The positive effects of PEVs have been discussed in this paper based on the results of proposed model for coordination of delivering and receiving of the electrical energy.

The parking managers can maximize their profit via proper scheduling of the charging and discharging PEVs (4 h including 2 h charging period and 2 h discharging period). It has been shown that they can make more money participating in ancillary energy markets and spinning reserve market. Based on the results of case studies, the effects of changing the parameters with higher effects on the parking profit are discussed here.

Decision variables which play significant role in optimizing parking profit are

1) Battery charging capacity of electric cars: parking profits for 10 kW, 20 kW, 30 kW, 40 kW and 50 kW capacities were analyzed. The simulation results show a direct relation between battery capacity and parking profit.

2) Time length of charging electric cars in parking: car charging time in parking was analyzed at 2 h, 3 h and 4 h. The simulation results show that parking profit at 2 h of charging is maximum while at 3 h it is reduced significantly. So the parking profit increases with the increase of the time of charging.

3) Number of electric cars: the effect of increasing electric cars on parking profit for 5, 10, 15 cars was analyzed. The results of simulations show that increasing the number of PEVs will increase the parking profit.

4) Other parameters including state of charging and discharging of 10 cars and energy exchange in market, turning reserve, energy secondary market, gird and electric car at each hour was analyzed.

In the suggested model it is assumed that the acceptance capacity of each car in parking is limited so that each parking owner can have a number of parked cars during day-night according to its situation in city and public transportation. Therefore, the curve of the number of parked case in parking during a day is also available and 10% of energy in turning reserve market and 90% in energy secondary market sells to grid.

References

[1] Kempton W, Tomic J. Vehicle-to-grid power fundamentals: Calculating capacity and net revenue. Journal of Power Sources, 2005, 144(1): 268–279

[2] Kempton W, Tomic J. Vehicle-to-grid power implementation: From stabilizing the grid to supporting Large-scale renewable energy. Journal of Power Sources, 2005, 144(1): 280–294

[3] Jang S, Han S, Han S H, Sezaki K. Optimal decision on contract size for V2G aggregator regarding frequency regulation, In: Proceedings of the 12th International Conference on Optimization of Electrical and Electronic Equipment . Brasov, Romania, 2010, 54–62

[4] Karnama A. Analysis of intergration of plug-in hybrid electric vehicles in the distribution grid. Dissertation for the Master's Degree. Stockholm, Sweden: Royal Institute of Technology, 2009

[5] Inage S. Modelling Load Shifting Using Electric Vehicles in a Smart Grid Environment, 2013–10

[6] Sortomme E, El-Sharkawi M A. Optimal charging strategies for unidirectional vehicle-to-grid. IEEE Transactions on Smart Grid, 2011, 2(1): 131–138

[7] Abolfazli M, Bahmani M H, Afsharnia S, Ghazizadeh M S. A probabilistic method to model PHEV for participation in electricity market. 2013–10

[8] Andersson S L, Elofsson A K, Galus M D, Göransson L, Karlsson S, Johnsson F, Andersson G. Plug-in hybrid electric vehicles as regulating power providers: Case studies of Sweden and Germany. Energy Policy, 2010, 38(6): 2751–2762

[9] Venayagamoorthy G K, Mitra P, Corzine K, Huston C. Real time modeling of distributed plug-in vehicles for V2G transactions. 2013–10

[10] Saber A Y, Venayagamoorthy G K. Efficient utilization or renewable energy sources by gridable vehicles in cyber-physical energy systems. IEEE Systems Journal, 2010, 4(3): 285–294

[11] Mitra P, Venayagamoorthy G K. Wide area control for improving stability of a power system with plug in electric vehicles. IET Generation, Transmission & Distribution, 2010, 4(10): 1151–1163

[12] Hartmann N, Ozdemir E D. Impact of different utilization scenarios of electric vehicles on the German grid in 2030. Journal of Power Sources, 2011, 196(4): 2311–2318

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