基于主从博弈及分时电价引导的电动汽车充放电控制策略研究Study on Charge and Discharge Control Strategies of Electric Vehicles Based on Stackelberg Game and Time-of-Use Price Guidance

DOI: 10.12677/SG.2018.84034, PDF, HTML, XML, 下载: 573  浏览: 1,370

Abstract: With the increase in the number of electric vehicles entering the grid, how to maximize the inter-ests of both the grid and vehicle owners on the basis of meeting the stability of the electric power system is an urgent problem to be solved. Based on the Stackelberg game theory and the time-of-use price incentive mechanism, this paper establishes a time-average tariff that takes into account the load fluctuation rate of the grid and the owner's revenue, as well as the charging and discharging power optimization model of the electric vehicle. And under the comprehensive con-straints of grid load balancing, system static stability, and the capacity of electric vehicles that can be networked, the charging and discharging strategies and time-shared price of electric vehicles satisfying the maximization of the interests of both parties are determined. The results show that when the available capacity of electric vehicles accounts for 2.33% of the maximum load capacity, the Stackelberg game and the time-shared price guide strategy can reduce the peak load-to-valley load ratio of the power grid by 12.15% and the standard deviation of the voltage stability margin by 24.7%. The average daily income of vehicles reached 10.8 RMB, and good control effects were achieved.

1. 引言

2. 静态电压稳定性

2.1. 充放电负荷

$f\left(x\right)=\frac{1}{x\sigma \sqrt{2\text{π}}}\mathrm{exp}\left[-\frac{{\left(\mathrm{ln}x-\mu \right)}^{2}}{2{\sigma }^{2}}\right]$ (1)

$\text{SOC}=\left({\text{SOC}}_{0}-\frac{d}{{d}_{m}}\right)\ast 100%$ (2)

Figure 1. The stopping rate of electric vehicles at each time

2.2. 电压稳定裕度

${V}_{\text{margin}}=\frac{{\lambda }_{\mathrm{max}}-1}{{\lambda }_{\mathrm{max}}}$ (3)

3. 主从博弈模型

3.1. 博弈模型及目标函数

Figure 2. Simulation network system one-line diagram

Figure 3. Flowchart of Stackelberg game process

${J}_{1}=\underset{t=1}{\overset{24}{\sum }}{\left({P}_{D,t}+{P}_{EV,t}-{P}_{avr}\right)}^{2}$ (4)

${P}_{avr}=\underset{t=1}{\overset{24}{\sum }}\left({P}_{D,t}+{P}_{EV,t}\right)/24$ (5)

${J}_{2}=\underset{t=1}{\overset{24}{\sum }}\text{ }{P}_{EV,t}{C}_{t}+{C}_{loss}$ (6)

${C}_{loss}=\underset{t=1}{\overset{24}{\sum }}\text{ }\mathrm{min}\left({P}_{EV,t},0\right){C}_{b}$ (7)

3.2. 约束条件

${C}_{ope}=\underset{t=1}{\overset{24}{\sum }}\left({P}_{D,t}+{P}_{EV,t}\right){C}_{t}$ (8)

${C}_{f}=\left({C}_{p}+{C}_{v}\right)/2$ (9)

$\underset{t=1}{\overset{24}{\sum }}\text{ }{P}_{EV,t}^{d}\le {P}_{total}^{d}$ (10)

$\underset{t=1}{\overset{24}{\sum }}\text{ }{P}_{EV,t}^{c}={P}_{total}^{c}$ (11)

$-{N}_{EV,t}^{\mathrm{max}}\ast {P}_{d}^{\mathrm{max}}\le {P}_{EV,t}\le {N}_{EV,t}^{\mathrm{max}}\ast {P}_{c}^{\mathrm{max}}$ (12)

3.3. 求解算法

${J}_{2}\left({\gamma }_{1},{\gamma }_{2}\right)\ge {J}_{2\mathrm{max}}-\epsilon$ (13)

${J}_{1}^{*}=\underset{{\gamma }_{1}\in {\Gamma }_{1}}{\mathrm{min}}\underset{{\gamma }_{2}\in {\Gamma }_{2}\left({\gamma }_{1}\right)}{\mathrm{max}}{J}_{1}\left({\gamma }_{1},{\gamma }_{2}\right)$ (14)

${J}_{1}\left({\gamma }_{1}^{*},{\gamma }_{2}^{*}\right)=\underset{{\gamma }_{2}\in {\Gamma }_{2}\left({\gamma }_{1}^{*}\right)}{\mathrm{min}}{J}_{1}\left({\gamma }_{1}^{*},{\gamma }_{2}\right)$ (15)

4. 算例

V2G模式下，不同规模及响应率电动汽车入网，负荷曲线变化情况如图4所示。

Figure 4. Load curves of power grid under different V2G modes

Figure 5. Voltage stability margin of power grid under different V2G modes

Table 1. Comparison of load characteristics of electric vehicles

Table 2. Comparison of voltage stability of electric vehicle

Table 3. Time-of-use price before and after the game

Table 4. Car owner’s income under different V2G modes

5. 结语

1) 电动汽车响应V2G策略入网有利于负荷平抑与电压稳定性的提高。在可用电池容量低于3%最大负荷容量的情况下，电动汽车的有序充放电可使负荷峰谷差率降低12.15%，电压稳定裕度的标准差提高24.7%。

2) 主从博弈模型适用于电动汽车参与V2G的分时电价决策问题。执行电网与电动汽车车主充分博弈后的分时电价，能够实现在电网售电收益不变的前提下，显著提升电动车主的综合收益。

3) 随着电动汽车规模以及电池响应率的增加，谷段电价的降低以及峰段、平段电价的提高，更有利于电网负荷曲线的平抑、电压稳定裕度的提高以及车主收益的增加。

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