李强(1981), 男, 博士, 研究员级高级工程师, 从事电力系统分析与控制、电力市场、博弈论等相关工作(E-mail:
朱丹丹(1991), 女, 博士, 高级工程师, 从事电力系统分析与控制、电力市场、博弈论等相关工作
黄地(1989), 男, 博士, 高级工程师, 从事综合能源系统及仿真相关工作
虚拟电厂(VPP)是管理分布式能源的重要手段,合理制定VPP运营商与电动汽车(EV)用户的定价策略,可引导EV充分消纳风、光等可再生能源,实现VPP运营商与EV用户的双赢。在此背景下,文中首先提出VPP作为售电运营商参与EV有序充电管理的主从博弈模型,其中运营商通过主从博弈制定合理的售电价格引导EV有序充电,并协调各类分布式资源参与电力市场。然后,计及风电出力的波动性和常规负荷的不确定性,在建模中引入条件风险价值(CVaR)理论,并通过Karush-Kuhn-Tucker(KKT)条件和对偶理论将模型转化为混合整数线性规划问题进行求解。最后,基于算例给出VPP运营商的最优定价策略及出力计划,并分析不同EV比例、储能最大容量、风险偏好系数对最优解的影响,为提高VPP运营收益提供优化思路。
Virtual power plant (VPP) is an important means of managing distributed energy. Reasonably formulating pricing strategies for VPP operators and electric vehicle (EV) users can guide EVs to fully consume renewable energy such as wind and solar, thus achieving a win-win situation for VPP operators and EV users. A stackelberg game model is firstly proposed in which a VPP with EVs is used as the electricity sales operator to participate in the orderly charging management of EVs. Operators formulate reasonable electricity selling prices through stackelberg game to guide the orderly charging of EVs, and coordinate various distributed resources to participate in the electricity market. Then, taking into account the volatility of wind power output and the uncertainty of conventional loads, the conditional value at risk (CVaR) theory is introduced into the modeling, and the model is transformed into a mixed integer linear programming problem solved by Karush-Kuhn-Tucker (KKT) conditions and dual theory. Finally, based on an example, the optimal pricing strategy and output plan of VPP operators are given. The influence of different EV proportions, maximum energy storage capacity, and risk preference coefficient on the optimal solution is analyzed, which provides optimization ideas for VPP operators to improve revenue.
近年来,电动汽车(electric vehicle, EV)以其低碳、节能的优势被大范围推广应用[
目前,国内已有针对EV有序充电管理、VPP运营商与EV博弈的相关研究。文献[
目前,为处理风电出力和常规负荷波动给VPP运行带来的风险[
基于上述文献提到的EV有序充电管理方法、博弈论及CVaR理论,文中提出以VPP作为售电运营商,协调燃气轮机组、风电机组、储能、常规负荷和需求响应负荷,参与EV有序充电管理的主从博弈模型。模型中,VPP通过整合内部资源并制定合理的定价策略引导EV有序充电,这不仅解决了VPP运营商与EV用户间的利益分配问题,且完成了内部资源的整合优化。进一步地,考虑风电出力的波动性及常规负荷的不确定性对VPP运营收益的影响,文中将CVaR理论引入VPP运营商与EV用户的主从博弈定价模型中,用于衡量运营商风险收益,为VPP运营商依据自身风险偏好制定运营策略提供了参考。
文中VPP结构由燃气轮机组、风电机组、储能、常规负荷、需求响应负荷和EV组成[
(1) 当日能量市场交易结束前,EV用户向运营商提交次日的充电时段和充电需求电量。VPP运营商则基于EV用户需要,整合协调内部各类可控负荷后,确定次日各时段电量需求,拟定次日的购售电计划。
(2) VPP运营商在日前市场同电网签订购售电合同后,及时向EV用户发布次日各时段电价信息,并安排内部其余可控资源的出力计划。另外,文中规定VPP运营商的零售电价不得高于其在日前市场中的购电价格,且设置电价上限及均值,避免VPP恶意定价,尽可能保证EV用户利益。
(3) EV用户在入网后由智能终端自动控制EV充电,并即时支付充电费用,对未按照约定时段及电量充电的EV用户,予以履约考核。
基于上述运营模式,VPP运营商工作的重点是制定次日各时段的充电电价,与传统的定价优化问题不同,运营商的收入取决于EV的充电策略及各类可控资源的运行安排,但EV的充电行为并不受运营商的直接控制,而是受电价的影响。根据电价约定,日均充电价格不变,如果VPP运营商刻意抬升某时段电价,势必有其他时段的电价低于平均值,此时智能终端会自动选择电价较低的时段为EV自动充电。综上,EV用户、VPP运营商与电网的互动架构如
EV用户、VPP运营商与电网的互动架构
Interactive architecture between EV users, VPP operators and power grid
主从博弈模型的上层问题为VPP日运营收益最大,其目标函数为式(1),需要满足的约束条件为式(7)—式(23)。
式中:
式中:
式中:
式中:
式中:
充电价格的相关约束为:
式中:
可控分布式电源的相关约束为:
式中:
储能设备的相关约束为:
式中:
需求响应负荷的相关约束为:
式中:
另外,由于式(4)转化为式(5)的过程中引入了辅助变量,应增加相应约束条件:
VPP与电网交互的相关约束为:
式中:
功率平衡约束为:
式中:
CVaR相关约束为[
式(22)、式(23)表示
主从博弈模型下层描述的是EV用户充电策略的优化问题,其优化目标为:
约束条件为:
式中:
目标函数式(24)表示EV用户在VPP运营商给出的电价下,最小化充电成本。约束条件中,式(25)表示EV在并网时充电至离网需求电量;式(26)为EV充电功率约束;式(27)表示EV在离网后的充电功率为0。
综上,VPP运营商定价策略与EV用户充电策略形成了主从博弈关系。式(1)—式(27)中,VPP运营商应考虑EV用户对充电价格的反应,故
对于主从博弈模型中的下层问题,因EV用户在决策时,其收到的充电价格由VPP运营商制定,故首先通过KKT条件[
式(30)和式(31)为原约束与其对偶变量的互补松弛性条件,因其是非线性的,故进行线性化后才能求解,进而对互补松弛条件进行线性化处理。参考文献[
式中:
进一步,对目标函数式(1)进行线性化。因式(1)中的
综上所述,VPP运营商与EV用户的主从博弈模型可转化为混合整数线性规划问题。
混合整数线性规划式(40)可通过商业求解器Gurobi 9.1.1进行求解。
文中算例将等值聚合后的EV分为3组,即EV1为100辆、EV2为60辆、EV3为40辆,用(100, 60, 40)表示。每组EV的充电时段见
EV充电时段
Charging period of EV
|
EV1 | EV2 | EV3 |
|
EV1 | EV2 | EV3 | |
1 | 1 | 1 | 0 | 13 | 0 | 0 | 1 | |
2 | 1 | 1 | 0 | 14 | 0 | 0 | 1 | |
3 | 1 | 1 | 0 | 15 | 0 | 0 | 1 | |
4 | 1 | 1 | 0 | 16 | 0 | 0 | 1 | |
5 | 1 | 1 | 0 | 17 | 0 | 0 | 1 | |
6 | 0 | 1 | 0 | 18 | 0 | 1 | 1 | |
7 | 0 | 1 | 0 | 19 | 0 | 1 | 1 | |
8 | 0 | 1 | 0 | 20 | 0 | 1 | 0 | |
9 | 0 | 0 | 1 | 21 | 0 | 1 | 0 | |
10 | 0 | 0 | 1 | 22 | 1 | 1 | 0 | |
11 | 0 | 0 | 1 | 23 | 1 | 1 | 0 | |
12 | 0 | 0 | 1 | 24 | 1 | 1 | 0 |
EV基本参数
Basic parameters of EV
基本参数 | EV1 | EV2 | EV3 |
63.30 | 63.30 | 63.30 | |
19.99 | 37.98 | 31.65 | |
|
0.95 | 0.85 | 0.90 |
7 | 7 | 7 |
分时电价
Time-of-use tariff
时段 | 电价/[元·(kW·h)-1] | |
谷 | 00:00—08:00 | 0.348 1 |
平 | 12:00—17:00, 21:00—24:00 | 0.562 9 |
峰 | 08:00—12:00, 17:00—21:00 | 0.777 7 |
VPP运行参数
Operating parameters of VPP
元件 | 参数 | 数值 |
燃气轮机组 | 1 200 | |
200 | ||
0.35 | ||
0 | ||
储能设备 | 1 000 | |
10 000 | ||
500 | ||
0.30 | ||
|
0.92 | |
|
0.90 | |
需求响应负荷 | 0.3 | |
4 000 | ||
300 | ||
75 |
基于4.1节的参数设置,取
VPP运营商的最优售电定价
Optimal electricity sales pricing for VPP operators
EV用户的最优充电方案
Optimal charging solution for EV users
VPP运营商的购售电功率
Electric power purchased and sold by VPP operators
需求响应负荷的实际与期望功率
The actual and expected power of demand response load
燃气轮机组的输出功率
The output power of the gas turbine unit
储能设备的充放电功率
The charging and discharging power of the energy storage equipment
EV1数量明显多于另外2组,由
由
在EV总数不变的前提下,设EV数量分别为(100, 60, 40),(60, 60, 80),(200, 0, 0),(0, 200, 0),(0, 0, 200),得到不同EV比例下VPP运营商的最优定价策略,如
不同EV比例下VPP运营商的定价策略
Pricing strategies of VPP operators under different EV ratios
不同EV比例下VPP运营商收益与EV充电成本对比
Comparison of VPP operator revenue and EV user charging costs under different EV ratios
由
由
进一步地,当3种类型的EV数量较为均匀时,VPP运营收益会降低。这是因为当VPP中EV充电类型过于单一时,运营商会将该类型EV充电时段的电价调高,不充电时段的电价调低,最大程度获得盈利。而当3类EV的数量较为均衡时,VPP运营商为满足多种充电时段需求,各个时段的充电价格不能设置太高,从而导致总收益减少。
设
不同
VPP operating income under different
由
不同
不同
VPP operating income under different
|
VPP运营收益/元 |
|
VPP运营收益/元 | |
0 | 1 154.8 | 0.60 | 1 104.6 | |
0.20 | 1 138.1 | 0.80 | 1 087.8 | |
0.40 | 1 121.3 | 0.99 | 1 071.9 |
文中提出了基于主从博弈的VPP运营商与EV用户之间的主从博弈模型,在协调各类可控资源时,既考虑了EV充电策略对VPP售电价格的影响,也考虑了VPP定价策略受EV充电行为的影响,实现了VPP运营商与EV用户的双赢。
文中通过KKT条件和对偶理论,将非线性的主从博弈模型转化成可求解的混合整数线性规划问题进行求解。算例证明了求解方法的有效性,得出在一定范围内增加储能最大容量是VPP运营商提高运营收益的重要途径。VPP运营商在获得高收益的同时也面临着高风险,在低风险时获得的收益也很低,故VPP运营商应根据自身风险偏好程度及VPP内可控资源的出力特点,灵活衡量风险与收益之间的关系。
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