Optimization Model of EV Charging and Discharging Price Considering Vehicle Owner Response and Power Grid Cost
- 551 Downloads
Abstract
The problem of load fluctuation in the distribution network and increasing power grid cost input caused by the unpredictable behavior of electric vehicle (EV) users in response to electricity price is investigated in this paper. An optimization model method for the charging and discharging price of electric vehicles is proposed, considering the vehicle owner response and power grid cost. The rule of EV user travel is first analyzed, and the travel and battery state constraints are defined. Under the constraints of user charging and discharging behavior and battery characteristics, a user transfer rate and unit energy cost function is designed to construct a multi-objective model of charging and discharging price that minimizes electricity expenditure and avoids an increase in power grid investment. Finally, an improved multi-target fish swarm algorithm is presented to solve the model optimization problem. The example analysis shows that the proposed method can reduce the peak-valley load difference of the system and cost input of the power grid, as well as provide users with regulation ability to access the power grid at different time periods.
Keywords
Electric vehicle Grid cost Demand response Multi-target immune fish algorithm1 Introduction
Promoting the use of electric power can help mitigate the fuel crisis and increasing environmental pollution by gradually reducing the consumption of gasoline, diesel, and other automotive fuels, and alleviating pollution caused by exhaust emissions. Electric vehicles (EVs) are emerging as the focus of development in the transportation industry [1, 2]. Energy for EVs is mainly sourced from the power grid, and large-scale development of such vehicles can not be separated from the support of the power system. According to forecasting by the China Automobile Engineering Association [3], the number of electric vehicles in China will reach 80 million by 2030. If the average EV power battery is equipped with 60 kW h, the equivalent storage energy will reach 48 × 10^{8} kW h, compared to the daily power consumption in China, which was only 160 × 10^{8} kW h in 2016. The energy demand is considerable, whether it absorbs electricity from the system or releases electricity into the system. Therefore, optimal management of charging and discharging behavior of EV users can provide power supply for the power grid in cases of power shortage, alleviate the balance of power supply and demand, and has great significance for improving the stability of the power grid [4].
Previous research has been conducted on the charging and discharging of electric vehicles. Literature [6] accounted for the state of charge (SOC) of EVs, and conducted modeling analysis based on time of utility (TOU) price. Literature [7] guided the orderly charging and discharging of EVs on the basis of load forecasting. In [8], the economic benefits of the power grid was analyzed, and the charging and discharging price of EVs was optimized according to the interests of the power grid. Literature [9] used Monte Carlo simulation method to extract the starting load state and charging time of EVs, and employed superposition simulation to formulate a total charging power curve of the EV after mass access to the grid. According to the division of the current regional TOU price, a method considering the two-stage effective charging strategy was proposed in literature [10]. In [11], the load and discharge curves of EVs in different periods were simulated according to the characteristics of charge and discharge batteries of different types of electric vehicles.
The remainder of this paper is organized as follows. An analysis of the charging and discharging behavior of EV users is introduced in Sect. 2. In Sect. 3, a multi-objective optimization model is constructed, which includes the minimization of additional costs and maximization of user satisfaction with charging and discharging. In Sect. 4, the simulation experiment is explained, and results are provided and discussed in Sect. 5. Finally, conclusions are presented in Sect. 6.
2 Analysis of Charging and Discharging Behavior of EV Users
- 1.
Travel constraints of EVs
- 2.
Vehicle battery load state constraints
3 Multi-objective Optimization Model for Charging and Discharging of EVs Based on User Transfer Rate
The EV user response behavior according to fluctuating electricity price is mostly reflected in changes to the load. When the stable operation of the power grid system fluctuates, the power grid company adjusts the user’s electricity structure through incentive strategies or price optimization schemes, thereby reducing the charging and discharging load within a certain period of time. Therefore, the responsiveness of users to electricity prices will be the basis for power grid companies to formulate electricity prices.
3.1 Analysis of User Transfer Rate of Different Response
- 1.
Response analysis of user demand in response to charging electricity price
- 2.
User demand response analysis in reaction to charge and discharge price
- 3.
Demand response analysis of unresponsive users
3.2 Optimization Goal
- 1.
Minimizing peak-valley difference of power grid
- 2.
Minimizing power grid cost input
- 3.
Maximizing EV user satisfaction
3.3 Multi-objective Optimization Model for Charging and Discharging Price of EV
4 Solution of Multi-target Immune Fish Model Based on Shrinking Space
To achieve the goal of minimizing peak-valley difference and peak load, user satisfaction with electricity consumption must be ensured, and added investment by grid companies should be avoided. Obviously, there are clear contradictions among the three objective functions, and the proposed multi-objective optimization will determine the optimal solution satisfying the conditions by balancing the solution values of each group. Therefore, for solving multi-objective problems, a multi-objective immune fish swarm algorithm (MOIFSA) is designed based on artificial fish swarm algorithm combined with immune algorithm and Pareto optimal solution set. Utilizing the fast convergence rate of artificial fish swarm algorithm, the multi-objective peak-valley charging and discharging price model is solved. The immune algorithm is then introduced to prevent the algorithm from prematurely converging to a local inferior solution.
4.1 Fish Swarm Optimization Method Combining Immune Antibody Fitness
- (a)
Foraging behavior
- (b)
Cluster behavior
- (c)
Tail following behavior
Taking the probability of antibody concentration as the probability of artificial fish choosing to swim to the current food source, the algorithm reduces the redundant calculation of distance to the target position when simulating the artificial fish swarm foraging solution. This ensures the uniqueness of the vector path from different points to the optimal solution, and avoids the convergence of the whole population in the optimal solution of artificial fish swarm.
4.2 Solving Steps of the Charge–Discharge Price Model by Multi-objective Optimization Algorithm
- 1.
For parameter initialization, input EV battery parameters and parameter of user transfer rate;
- 2.
Set the fish swarm size to S (simulating the number of EVs), and in the solution space, randomly initialize S antibody to generate artificial fish swarm M. The number of iterations is k;
- 3.
For determination of objective function, F_{i}(x) and U_{k}(x) are used as antigens in the multi-objective optimization model of the charge–discharge price. The hierarchical clustering method is used to stratify the population. All individual artificial fish in each layer are assigned to the initial Pareto solution bulletin board.
- 4.
For the optimization process, biological behavior of artificial fish is simulated. The artificial fish with the best behavior in the foraging process of artificial fish is selected, and the individual fish is updated.
- 5.
To evaluate the affinity between all antigens and antibodies (artificial fish), the individual fish with the highest affinity is selected and assigned to the bulletin board, and the external bulletin board of Pareto optimal solution is updated.
- 6.
Determine if the maximum number of iterations has been met. If satisfied, the optimal charge and discharge price solution set is output and the algorithm is terminated. If not, return to step 3.
5 Example Experiment and Analysis
5.1 Experiment Data and Parameter setting
- 1.
User transfer rate initialization parameters
Initial value parameter of user transfer rate
Transfer type rate | Slope K_{ab} | Dead-zone calculated value l_{ab} |
---|---|---|
Peak-flat transfer rate curve | 0.06 | 0.11 |
Peak valley transfer rate curve | 0.08 | 0.12 |
Flat valley transfer rate curve | 0.04 | 0.09 |
- 2.
Initial charge and discharge price and load data
Time sharing charging price and real-time load data
Time [h] | TOU [cent (kW h)^{−1}] | Load [MW] | Time [h] | TOU [cent (kW h)^{−1}] | Load [MW] |
---|---|---|---|---|---|
1 | 6 | 79,661 | 13 | 30 | 88,967 |
2 | 6 | 78,048 | 14 | 11 | 87,452 |
3 | 6 | 77,471 | 15 | 11 | 86,096 |
4 | 6 | 78,000 | 16 | 6 | 84,853 |
5 | 6 | 80,391 | 17 | 6 | 83,971 |
6 | 11 | 84,585 | 18 | 6 | 83,608 |
7 | 11 | 89,787 | 19 | 6 | 83,958 |
8 | 30 | 93,986 | 20 | 6 | 84,876 |
9 | 30 | 95,693 | 21 | 11 | 86,540 |
10 | 30 | 94,946 | 22 | 11 | 88,573 |
11 | 30 | 92,908 | 23 | 11 | 89,579 |
12 | 30 | 90,774 | 24 | 11 | 86,942 |
- 3.
Battery parameters for EV
EV battery parameters
Battery type | C_{B} [kW h] | p^{up} (p^{down}) [kW] | ω_{d} [cent (kW h)^{−1}] | W [(kW h) km^{−1}] |
---|---|---|---|---|
BYD | 57 | 9.5 | 4.0 | 0.215 |
NS | 24 | 4.0 | 4.0 | 0.149 |
The minimum and maximum SOC of the EV during charge and discharge were set to 15% and 95%, respectively. Electric vehicle battery charge and discharge efficiency η^{up} and η^{down} was 0.97, the power grid to charge and discharge energy conversion efficiency η was 0.85, c_{f} = 1.2 cent/(kW h), and V2G charge and discharge coefficients λ^{down} and λ^{up} were set as 0.1. According to the development of EVs [20], the number of analog electric vehicles was simulated as N = 3 × 10^{6}, and the BYD and Nissan vehicle ratio is assumed to be 1:1, that is, the variable of their battery parameters to calculate according to the average. Thus, p^{up} and p^{down} takes 6.75 kW, C_{B} takes 40.5 kW h, and W takes 0.182 kW h km^{−1}.
5.2 Experimental Comparison and Analysis of MOIFSA
Convergence index data of Pareto solutions
Convergence | Best | Worst | Mean | Std |
---|---|---|---|---|
MOAFSA | 0.0002 | 0.0030 | 0.0017 | 0.0013 |
MOIFSA | 0.0003 | 0.0029 | 0.0015 | 0.0014 |
Diversity index data of Pareto Solution
Diversity | Best | Worst | Mean | Std |
---|---|---|---|---|
MOAFSA | 9.2e−04 | 0.0203 | 0.0078 | 0.0044 |
MOIFSA | 7.13e−05 | 0.0181 | 0.0061 | 0.0031 |
Error ratio index data of Pareto solution
Error | Best | Worst | Mean | Std |
---|---|---|---|---|
MOAFSA | 0.0015 | 0.0921 | 0.0517 | 0.0289 |
MOIFSA | 0.0010 | 0.0811 | 0.0425 | 0.0259 |
As can be seen from Table 4, MOIFSA does not demonstrate much improvement to convergence performance compared with MOAFSA.
As illustrated in Table 5, the uniformity index value of MOIFSA algorithm increased by approximately 18%.
Table 6 shows that the average error of MOIFSA algorithm is 11.9% less than that of MOAFSA algorithm.
5.3 Example Analysis of Optimization Model
To solve issues with the model, MOIFSA is proposed in this paper. The relevant parameters are used as follows: population size S is 100, maximum number of iterations k = 100, Visual = 0.5, and δ = 0.25.
After random access of the EV, the peak load of the system increased from 95,693 to 97,042.76 MW, and the peak-valley difference increased from 18,222 to 19,397.7 MW. For the common purpose of minimizing peak load and peak-valley load difference, the optimization of the charging and discharging price of EVs can be divided into three situations as discussed below:
- 1.
Minimizing power grid cost input as the target
According to the proposed model, to avoid the maximization of investment into the power grid, only the minimum input of the power grid is considered, and the load curve of the EV can be obtained after optimization.
- 2.
Maximizing EV user satisfaction as the target
- 3.
Multi-objective optimization model
The daily load curve before and after optimization is shown in Fig. 8. It can be seen that the peak load has been reduced by 1057.91 MW, and the peak and valley difference has decreased by 29,020.41 MW.
As shown in Fig. 7, the load of the peak period is reduced, the charge and discharge load begin to shift to peak time and valley period, and the system load changes smoothly. The response mode of the user begins to change compared to before the optimization, in which the user of the response discharge price begins to discharge to the power grid in the peak period of the system load. This relieves the demand for charging load after EV access, and users responding to the charging price change their charging time in the low valley peak period, reducing the rush hour charging pressure of electricity.
Optimization results under different targets
Optimization period | Before optimization | Users satisfaction max. | Avoiding max. grid investment | Multi-objective model |
---|---|---|---|---|
Charging price [cent (kW h)^{−1}] | ||||
Peak time | 30 | 37.21 | 39.53 | 38.49 |
Normal time | 11 | 9.51 | 9.74 | 9.52 |
Valley time | 6 | 4.02 | 4.21 | 4.41 |
Discharging price [cent (kW h)^{−1}] | ||||
Peak time | 37.08 | 41.18 | 43.65 | 40.12 |
Normal time | 16.89 | 11.72 | 11.96 | 15.32 |
Valley time | 11.58 | 5.87 | 6.07 | 9.89 |
Avoiding cost invested [10^{6} dollars] | – | 423.28 | 440.07 | 428.41 |
Total satisfaction | 1 | 0.89 | 0.42 | 0.79 |
According to the results in Fig. 7 and Table 7, the multi-objective model is superior to other models for load regulation and power grid input reduction, and has good user satisfaction. If only one objective is optimized, only one objective can be achieved, and other objectives will be affected.
6 Conclusion
The unpredictable behavior of EV users in response to electricity price was investigated in this paper, considering the fluctuation of the power grid load, the new cost input of operators, and the satisfaction of users in responding to electricity price. An optimization model was constructed for the charging and discharging price of EVs, considering vehicle owner response and power grid cost. An improved immune fish swarm algorithm was then proposed to optimize the multi-objective model of charging and discharging price. Experimental analysis illustrated that the multi-objective electricity price optimization method can reduce the peak-valley load difference of the system and the cost input of operators. Using this method, the ability of users to respond to electricity prices was maximized, along with the regulation ability for users to access the power grid during different time periods.
Notes
Acknowledgements
Key projects of the National Natural Science Foundation of China (51437003). Jilin Province Science and Technology Development Plan Project, China (20160623004TC, 20180201092GX). Jilin Science and Technology Innovation Development Plan Project, China (201830817).
References
- 1.Bae SH, Park JW et al (2018) A study on optimal operation strategy for mild hybrid electric vehicle based on hybrid energy storage system. J Electr Eng Technol 13(2):631–636Google Scholar
- 2.Leemput N, Van Roy J et al (2012) Comparative analysis of coordination strategies for electric vehicles. In: IEEE PES international conference and exhibition on innovative smart grid technologies. IEEE, pp 1–8Google Scholar
- 3.Liao Q, Zhao Z (2012) Economic analysis on China’s industry development policy of new energy. In: World automation congress IEEE, pp 1–4Google Scholar
- 4.Hu Z, Song Y, Xu Z et al (2012) Impacts and utilization of electric vehicles integration into power systems. Proc CSEE 32(4):1–10Google Scholar
- 5.Al-Awami AT, Sortomme E (2012) Coordinating vehicle-to-grid services with energy trading. IEEE Trans Smart Grid 3(1):453–462CrossRefGoogle Scholar
- 6.Cao Y, Tang S, Li C et al (2012) An optimized EV charging model considering TOU price and SOC curve. IEEE Trans Smart Grid 3(1):388–393CrossRefGoogle Scholar
- 7.Liu L, Lu X, Jiang C et al (2014) Decision-making of determining the start time of charging/discharging of electrical vehicle based on prospect theory. J Electr Eng Technol 9(3):803–811CrossRefGoogle Scholar
- 8.Ahmadian A, Sedghi M et al (2017) Cost-benefit analysis of V2G implementation in distribution networks considering PEVs battery degradation. IEEE Trans Sustain Energy 9(2):961–970CrossRefGoogle Scholar
- 9.Luo Z, Hu C, Song Y et al (2011) Research on charging calculation of electric vehicle. Autom Electr Power Syst 35(14):36–42Google Scholar
- 10.Liang W, Ai X, Cui S et al (2014) Study on coordinated charging strategy of PEV with price stimulation. In: IEEE transportation electrification Asia-Pacific, pp 1–5Google Scholar
- 11.Chekired DAE, Dhaou S et al (2017) Dynamic pricing model for EV charging-discharging service based on cloud computing scheduling. In: Wireless communications and mobile computing conference IEEE, pp 1010–1015Google Scholar
- 12.Changhui Y, Meng C et al (2018) Residential electricity pricing in China: the context of price-based demand response. Renew Sustain Energy Rev 81(2):2870–2878Google Scholar
- 13.Zhou G, Li Y et al (2018) Artificial fish swarm based power allocation algorithm for MIMO-OFDM relay underwater acoustic communication. IET Commun 12(9):1079–1085CrossRefGoogle Scholar
- 14.El-Naggar MFM et al (2018) Multi-objective optimal predictive energy management control of grid-connected residential wind-PV-FC-battery powered charging station for plug-in electric vehicle. J Electr Eng Technol 13(2):742–751Google Scholar
- 15.PJM ISO (2014) Markets & operations, energy markets. Day-ahead energy market. http://www.pjm.com/markets-and-operations/energy/real-ti-me/hourly-prelim-loads.aspx
- 16.Zhang L, Brown T, Samuelsen S (2013) Evaluation of charging infrastructure requirements and operating costs for plug-in electric vehicles. J Power Sources 240(31):515–524CrossRefGoogle Scholar
- 17.Xiang D, Song Y, Hu Z et al (2013) Research on optimal time of use price for electric vehicle participating V2G. Proc CSEE 33(31):15–25Google Scholar
- 18.Lu L, Han X, Li J et al (2013) A review on the key issues for lithium-ion battery management in electric vehicles. J Power Sources 226(3):272–288CrossRefGoogle Scholar
- 19.Geng Y, Ma Z, Xue B et al (2013) Co-benefit evaluation for urban public transportation sector a case of Shenyang, China. J Clean Prod 58(7):82–91CrossRefGoogle Scholar
- 20.Yining W, Wang L (2014) China’s new energy vehicles industry development status quo of the research. In: International conference on information management, innovation management and industrial engineering IEEE, vol 1, pp 189–192Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.