CN114285029A - A dispatch control method and system for stimulating electric vehicles to participate in vehicle-network interaction - Google Patents
A dispatch control method and system for stimulating electric vehicles to participate in vehicle-network interaction Download PDFInfo
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Abstract
本发明涉及一种激励电动汽车参与车网互动的调度控制方法及系统,所述方法包括:获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号。本发明提供的技术方案,通过在对于电动汽车参与车网互动的贡献度进行计算,采取通过完善的调度控制策略更好的调动电动汽车参与车网互动积极性,实现电网安全、稳定、经济运行。
The invention relates to a dispatching control method and system for stimulating electric vehicles to participate in vehicle-network interaction. The method includes: acquiring power information in a time period to be dispatched in an integrated energy system and a market price corresponding to the time period; The market price corresponding to the time period is input into the pre-established comprehensive energy system optimization scheduling model, and the demand data of electric vehicle charging and discharging at each time in the to-be-scheduled time period is obtained; the Nash game principle and the charging and discharging of electric vehicles at each time in the to-be-scheduled time period are used. The demand data determines the contribution of the electric vehicle to participate in the vehicle-network interaction within the to-be-scheduled period; and formulates a control signal to motivate the electric vehicle to participate in the vehicle-network interaction based on the contribution of the electric vehicle. The technical solution provided by the present invention can better mobilize the enthusiasm of electric vehicles to participate in the interaction between the vehicle and the network by calculating the contribution of the electric vehicle to participate in the interaction between the vehicle and the network, and realize the safe, stable and economical operation of the power grid.
Description
技术领域technical field
本发明涉及激励电动汽车参与车网互动的技术领域,具体涉及一种激励电动汽车参与车网互动的调度控制方法及系统。The invention relates to the technical field of stimulating electric vehicles to participate in vehicle-network interaction, and in particular relates to a scheduling control method and system for stimulating electric vehicles to participate in vehicle-network interaction.
背景技术Background technique
在我国现有的电力系统当中,通过峰谷电价制度吸引电动汽车进行有序充电。在新型高比例新能源电力系统当中,对于峰谷差过大的问题引发了许多研究,其中有效得安排电动汽车有序充电就是一个有利于电网安全稳定经济运行的良好策略。通过提前设定的峰谷电价,可以吸引用户选择在用电低谷期进行充电,避开用电高峰期,从而达到了使电动汽车有序充电,减小电网峰谷差的目的。In my country's existing power system, electric vehicles are attracted to charge in an orderly manner through the peak-valley electricity price system. In the new high-proportion new energy power system, the problem of excessive peak-to-valley difference has led to many studies. Among them, effectively arranging the orderly charging of electric vehicles is a good strategy for the safe, stable and economical operation of the power grid. The peak-valley electricity price set in advance can attract users to choose to charge during the trough period of electricity consumption and avoid the peak period of electricity consumption, thus achieving the purpose of orderly charging of electric vehicles and reducing the peak-to-valley difference in the power grid.
但是,现有技术多为峰谷电价制度,该制度十分僵化,一旦制定,就需要执行相当长的时间,甚至数年。电力系统负荷存在明显的季节性特征,并且大量新并网的分布式发电也会对电网负荷有很大的影响。如果仍然使用峰谷电价引导电动汽车充电,很多时候难以满足新型电力系统负荷快速变化的要求,甚至将会难以真实反映实际用电负荷的高峰和低谷,在某些特定时期起到反调峰的作用。其次,对于电动汽车而言,其电池属性提供了其作为等效储能的基本条件,而峰谷电价策略仅仅挖掘了其作为负荷的潜能,未能有效调动其储能能力,是对宝贵的需求侧响应资源的浪费。而且,峰谷电价制度严重低估了电动汽车有序充电为电网带来的收益,因此给与车主的奖励过少,对于车主的参与有序充电激励不够有力,导致电动汽车参与车网互动积极性较低。However, most of the existing technologies are the peak-valley electricity price system, which is very rigid. Once formulated, it needs to be implemented for a long time, even several years. The power system load has obvious seasonal characteristics, and a large number of new grid-connected distributed generation will also have a great impact on the grid load. If the peak-valley electricity price is still used to guide the charging of electric vehicles, it is often difficult to meet the requirements of rapid changes in the load of the new power system, and it will even be difficult to truly reflect the peaks and troughs of the actual electricity load. effect. Secondly, for electric vehicles, their battery properties provide the basic conditions for them to be used as equivalent energy storage, while the peak-valley electricity price strategy only taps its potential as a load and fails to effectively mobilize its energy storage capacity, which is valuable to the electric vehicle. Waste of demand-side response resources. Moreover, the peak-valley electricity price system seriously underestimates the benefits brought by the orderly charging of electric vehicles to the power grid, so the incentives given to car owners are too small, and the incentives for car owners to participate in orderly charging are not strong enough, resulting in electric vehicles participating in the vehicle-network interaction. Low.
发明内容SUMMARY OF THE INVENTION
本申请提供一种激励电动汽车参与车网互动的调度控制方法及系统,以至少解决相关技术中对于电动汽车参与车网互动积极性较低的技术问题。The present application provides a dispatching control method and system for stimulating electric vehicles to participate in vehicle-network interaction, so as to at least solve the technical problem in the related art that electric vehicles have low enthusiasm for participating in vehicle-network interaction.
本申请第一方面实施例提出一种激励电动汽车参与车网互动的调度控制方法,所述方法包括:The embodiment of the first aspect of the present application proposes a scheduling control method for stimulating electric vehicles to participate in vehicle-network interaction, and the method includes:
获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;Obtain the power information in the to-be-dispatched period of the integrated energy system and the market price corresponding to the period;
将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;Inputting the power information and the market price corresponding to the time period into the pre-established integrated energy system optimization scheduling model, and obtaining the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period;
利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;Using the Nash game principle and the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period to determine the contribution of the electric vehicle to the vehicle-network interaction in the to-be-scheduled time period;
基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,并基于所述控制信号进行电动汽车参与车网互动的调度控制。Based on the contribution degree of the electric vehicle, a control signal to motivate the electric vehicle to participate in the vehicle-network interaction is formulated, and based on the control signal, scheduling control of the electric vehicle's participation in the vehicle-network interaction is performed.
本申请第二方面实施例提出一种激励电动汽车参与车网互动的调度控制系统,所述系统包括:The embodiment of the second aspect of the present application proposes a dispatching control system for motivating electric vehicles to participate in vehicle-network interaction. The system includes:
第一获取模块,用于获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;a first acquisition module, configured to acquire power information within the to-be-scheduled period of the integrated energy system and the market price corresponding to the period;
第二获取模块,用于将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;The second acquisition module is configured to input the power information and the market price corresponding to the time period into the pre-established integrated energy system optimization scheduling model, and obtain the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period;
确定模块,用于利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;A determination module, configured to determine the contribution of electric vehicles participating in the vehicle-network interaction within the to-be-scheduled time period by using the Nash game principle and the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period;
控制模块,用于基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,并基于所述控制信号进行电动汽车参与车网互动的调度控制。The control module is configured to formulate a control signal to motivate the electric vehicle to participate in the vehicle-network interaction based on the contribution of the electric vehicle, and to perform scheduling control of the electric vehicle's participation in the vehicle-network interaction based on the control signal.
本申请第三方面实施例提出一种计算机设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,处理器执行计算机程序时,实现如本申请第一方面的预测方法。An embodiment of the third aspect of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the prediction of the first aspect of the present application is achieved. method.
本申请的实施例提供的技术方案至少带来以下有益效果:The technical solutions provided by the embodiments of the present application bring at least the following beneficial effects:
本发明提供了一种激励电动汽车参与车网互动的调度控制方法及系统,其中,所述方法包括:获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,并基于所述控制信号进行电动汽车参与车网互动的调度控制。本发明提供的技术方案,通过在对于电动汽车参与车网互动的贡献度进行计算,采取通过完善的调度控制策略更好的调动电动汽车参与车网互动积极性,实现电网安全、稳定、经济运行。The present invention provides a dispatching control method and system for stimulating electric vehicles to participate in vehicle-network interaction, wherein the method includes: acquiring power information in an integrated energy system to be dispatched in a time period to be dispatched and a market price corresponding to the time period; The power information and the market price corresponding to the time period are input into the pre-established optimal scheduling model of the integrated energy system to obtain the charging and discharging demand data of electric vehicles at each moment in the to-be-dispatched period; using the Nash game principle and the electric vehicle at each moment in the to-be-dispatched period The vehicle charging and discharging demand data determines the contribution of electric vehicles to participate in the vehicle-network interaction within the to-be-scheduled period; formulate a control signal to motivate the electric vehicle to participate in the vehicle-network interaction based on the contribution of the electric vehicle, and conduct electric vehicle participation based on the control signal Dispatch control of vehicle-network interaction. The technical scheme provided by the present invention can better mobilize the enthusiasm of electric vehicles to participate in the interaction between the vehicle and the network by calculating the contribution of the electric vehicle to participate in the interaction of the vehicle and the network, and realize the safe, stable and economical operation of the power grid.
本申请附加的方面以及优点将在下面的描述中部分给出,部分将从下面的描述中变得明显,或通过本申请的实践了解到。Additional aspects and advantages of the present application will be set forth, in part, from the following description, and in part will become apparent from the following description, or may be learned by practice of the present application.
附图说明Description of drawings
本申请上述的和/或附加的方面以及优点从下面结合附图对实施例的描述中将变得明显和容易理解,其中:The above and/or additional aspects and advantages of the present application will become apparent and readily understood from the following description of embodiments taken in conjunction with the accompanying drawings, wherein:
图1是根据本申请一个实施例提供的一种激励电动汽车参与车网互动的调度控制方法的流程图;1 is a flowchart of a scheduling control method for stimulating electric vehicles to participate in vehicle-network interaction provided according to an embodiment of the present application;
图2是根据本申请一个实施例提供的一种激励电动汽车参与车网互动的调度控制系统的结构图;2 is a structural diagram of a dispatching control system for stimulating electric vehicles to participate in vehicle-network interaction provided according to an embodiment of the present application;
图3是根据本申请一个实施例提供的一种激励电动汽车参与车网互动的调度控制系统中控制模块的结构图。FIG. 3 is a structural diagram of a control module in a dispatch control system for incentivizing electric vehicles to participate in vehicle-network interaction provided according to an embodiment of the present application.
具体实施方式Detailed ways
下面详细描述本申请的实施例,所述实施例的示例在附图中示出,其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的,旨在用于解释本申请,而不能理解为对本申请的限制。The following describes in detail the embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to be used to explain the present application, but should not be construed as a limitation to the present application.
本申请提出的一种激励电动汽车参与车网互动的调度控制方法及系统,所述方法包括:获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,并基于所述控制信号进行电动汽车参与车网互动的调度控制。本发明提供的技术方案,通过在对于电动汽车参与车网互动的贡献度进行计算,采取通过完善的调度控制策略更好的调动电动汽车参与车网互动积极性,实现电网安全、稳定、经济运行。A dispatching control method and system for stimulating electric vehicles to participate in vehicle-network interaction proposed in the present application, the method includes: acquiring power information in a time period to be dispatched in an integrated energy system and a market price corresponding to the time period; The market price corresponding to the time period is input into the pre-established integrated energy system optimization scheduling model, and the demand data of electric vehicle charging and discharging at each time in the to-be-scheduled time period is obtained; the Nash game principle and the electric vehicle charging and discharging requirements at each time in the to-be-scheduled time period are used. The discharge demand data determines the contribution of the electric vehicle to participate in the vehicle network interaction during the to-be-scheduled period; formulate a control signal to motivate the electric vehicle to participate in the vehicle network interaction based on the contribution degree of the electric vehicle, and based on the control signal, the electric vehicle participates in the vehicle network interaction. Interactive scheduling control. The technical scheme provided by the present invention can better mobilize the enthusiasm of electric vehicles to participate in the interaction between the vehicle and the network by calculating the contribution of the electric vehicle to participate in the interaction of the vehicle and the network, and realize the safe, stable and economical operation of the power grid.
实施例1Example 1
图1为本公开实施例提供的一种激励电动汽车参与车网互动的调度控制方法的流程图,如图1所示,所述一种激励电动汽车参与车网互动的调度控制方法,包括:FIG. 1 is a flowchart of a scheduling control method for incentivizing electric vehicles to participate in vehicle-network interaction provided by an embodiment of the present disclosure. As shown in FIG. 1 , the scheduling control method for incentivizing electric vehicles to participate in vehicle-network interaction includes:
步骤1:获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;Step 1: Acquire the power information in the to-be-dispatched period of the integrated energy system and the market price corresponding to the period;
在本公开实施例中,所述综合能源系统待调度时段内的功率信息包括:综合能源系统中的微型燃气轮机、分布式光伏、电动汽车充电站及负荷的日前功率、实时功率。In the embodiment of the present disclosure, the power information in the to-be-scheduled period of the integrated energy system includes: day-ahead power and real-time power of micro-turbines, distributed photovoltaics, electric vehicle charging stations and loads in the integrated energy system.
步骤2:将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;Step 2: Inputting the power information and the market price corresponding to the time period into the pre-established integrated energy system optimization scheduling model, and obtaining the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period;
所述预先建立的综合能源系统优化调度模型的建立过程包括:The establishment process of the pre-established integrated energy system optimal dispatch model includes:
基于综合能源系统中的微型燃气轮机、分布式光伏、电动汽车充电站及负荷的日前功率、实时功率,构建所述综合能源系统优化调度模型的目标函数,其中,以综合能源系统最大收益为目标建立综合能源系统最大收益目标函数;Based on the day-ahead power and real-time power of the micro gas turbine, distributed photovoltaic, electric vehicle charging station and load in the integrated energy system, the objective function of the integrated energy system optimal dispatch model is constructed. The objective function of the maximum benefit of the integrated energy system;
为所述模型的目标函数构建约束条件:分布式光伏的发电功率约束、综合能源系统负荷功率柔性负荷约束、微型燃气轮机的功率约束、电动汽车充电站中电动汽车的充放电功率约束和电动汽车充电站的充放电上下限约束。Constraints are constructed for the objective function of the model: power generation constraints for distributed photovoltaics, flexible load constraints for integrated energy system load power, power constraints for micro-turbines, power constraints for charging and discharging electric vehicles in electric vehicle charging stations, and electric vehicle charging The upper and lower limits of charging and discharging of the station.
需要说明的是,所述综合能源系统最大收益目标函数的计算式如下所示:It should be noted that the calculation formula of the maximum benefit objective function of the comprehensive energy system is as follows:
式中,μ为综合能源系统的收益,γs为第s种电动汽车参数下对应的权重, 为第s种电动汽车参数下t时刻对应的日前收益与实时收益之和,为第s种电动汽车参数下t时刻对应的日前收益,为第s种电动汽车参数下t时刻对应的实时收益,ai为第i台型燃气轮机的发电价格,ΦS为电动汽车参数种类的总数,ΦT为待调度时段内时刻总数, 为t时刻对应的日前市场售电价格,Pt DA为t时刻对应的日前功率, 为t时刻对应的实时市场售电价格,为第s种电动汽车参数下t时刻对应的实时功率,为第s种电动汽车参数下t时刻第i台微型燃气轮机的实时功率, 为t时刻第i台微型燃气轮机的日前功率,ΦMT为微型燃气轮机的总数,为t时刻第α台分布式光伏的日前功率,ΦPV为分布式光伏的总数,Pt CSD,DA为t时刻电动汽车充电站的日前放电功率,Pt CSC,DA为t时刻电动汽车充电站的日前充电功率,Pt L,DA为t时刻系统日前负荷, 为第s种电动汽车参数下t时刻第α台分布式光伏的实时功率,为第s种电动汽车参数下t时刻电动汽车充电站的实时放电功率,为第s种电动汽车参数下t时刻电动汽车充电站的实时充电功率,为第s种电动汽车参数下t时刻系统实时负荷。In the formula, μ is the income of the integrated energy system, γ s is the corresponding weight under the s-th electric vehicle parameter, is the sum of the day-ahead income and real-time income corresponding to time t under the s-th electric vehicle parameter, is the day-ahead income corresponding to time t under the s-th electric vehicle parameter, is the real-time income corresponding to time t under the s-th electric vehicle parameter, a i is the power generation price of the ith-type gas turbine, Φ S is the total number of electric vehicle parameter types, Φ T is the total number of moments in the to-be-scheduled period, is the day-ahead market electricity sales price corresponding to time t, P t DA is the day-ahead power corresponding to time t, is the real-time market electricity sales price corresponding to time t, is the real-time power corresponding to time t under the s-th electric vehicle parameter, is the real-time power of the i-th micro-turbine at time t under the s-th electric vehicle parameters, is the day-ahead power of the i-th micro-turbine at time t, Φ MT is the total number of micro-turbines, is the day-ahead power of the αth distributed photovoltaic at time t, Φ PV is the total number of distributed photovoltaics, P t CSD,DA is the day-ahead discharge power of the electric vehicle charging station at time t, P t CSC,DA is the charging of electric vehicles at time t The day-ahead charging power of the station, P t L,DA is the system's day-ahead load at time t, is the real-time power of the α-th distributed photovoltaic at time t under the s-th electric vehicle parameters, is the real-time discharge power of the electric vehicle charging station at time t under the s-th electric vehicle parameter, is the real-time charging power of the electric vehicle charging station at time t under the s-th electric vehicle parameter, is the real-time system load at time t under the s-th electric vehicle parameter.
进一步的,所述分布式光伏发电功率约束的计算式如下所示:Further, the calculation formula of the distributed photovoltaic power generation power constraint is as follows:
式中,为t时刻第α台分布式光伏的功率,PPV,max为分布式光伏的最大功率;In the formula, is the power of the αth distributed photovoltaic at time t, and P PV,max is the maximum power of the distributed photovoltaic;
所述综合能源系统负荷功率柔性负荷约束的计算式如下所示:The calculation formula of the flexible load constraint of the integrated energy system load power is as follows:
式中,PL,min为综合能源系统负荷功率柔性负荷的最小值,Pt L为t时刻综合能源系统负荷功率,PL,max为综合能源系统负荷功率柔性负荷的最大值;In the formula, PL,min is the minimum value of the flexible load of the integrated energy system load power, PtL is the load power of the integrated energy system at time t , and PL ,max is the maximum value of the flexible load of the integrated energy system load power;
所述微型燃气轮机的功率约束的计算式如下所示:The calculation formula of the power constraint of the micro gas turbine is as follows:
式中,为第i台微型燃气轮机的最大爬坡率,为第i台微型燃气轮机的最大功率;In the formula, is the maximum ramp rate of the i-th micro-turbine, is the maximum power of the i-th micro-turbine;
所述电动汽车充电站中电动汽车的充放电功率约束的计算式如下所示:The calculation formula of the charging and discharging power constraint of the electric vehicle in the electric vehicle charging station is as follows:
式中,为t时刻第q台电动汽车的最大充电功率,为第q台电动汽车的最大充电功率,为t时刻第q台电动汽车的电池电量,为第q台电动汽车在恒流充电模式下电池荷电状态阈值,当荷电量达到了这个阈值之后转换为恒压充电模式,可以描述为部分代表电动汽车恒压模式下的充电过程,表示电动汽车充电时状态为恒流充电或者恒压充电,为t时刻第q台电动汽车的最大放电功率,为第q台电动汽车的最大放电功率,为第q台电动汽车从恒流充电模式转换为恒压充电模式的阈值;其中, 为t-1时刻第q台电动汽车的电池电量,为第q台电动汽车电池的额定容量,为第q台电动汽车在充放电过程中法圣的损耗,为t-1时刻第q台电动汽车的充电功率,为t-1时刻第q台电动汽车的放电功率;In the formula, is the maximum charging power of the qth electric vehicle at time t, is the maximum charging power for the qth electric vehicle, is the battery power of the qth electric vehicle at time t, It is the battery state-of-charge threshold of the qth electric vehicle in the constant current charging mode. When the charge reaches this threshold, it switches to the constant voltage charging mode, which can be described as Part represents the charging process of an electric vehicle in constant voltage mode, Indicates that the charging state of the electric vehicle is constant current charging or constant voltage charging, is the maximum discharge power of the qth electric vehicle at time t, is the maximum discharge power of the qth electric vehicle, is the threshold for switching from constant current charging mode to constant voltage charging mode for the qth electric vehicle; where, is the battery power of the qth electric vehicle at time t-1, is the rated capacity of the qth electric vehicle battery, is the loss of Fasheng during the charging and discharging process of the qth electric vehicle, is the charging power of the qth electric vehicle at time t-1, is the discharge power of the qth electric vehicle at time t-1;
所述电动汽车充电站的充放电上下限约束的计算式如下所示:The calculation formula of the upper and lower limit constraints of charging and discharging of the electric vehicle charging station is as follows:
式中,为第q台电动汽车到达电动汽车充电站的时间对应的电池电量,为第q台电动汽车开始充电时的电量,为第q台电动汽车离开电动汽车充电站的时间对应的电池电量,为设定的第q台电动汽车结束充电时需要达到的电量。In the formula, Time for the qth EV to arrive at the EV charging station the corresponding battery power, The amount of electricity when the qth electric car starts to charge, Time to leave the EV charging station for the qth EV the corresponding battery power, The amount of electricity that needs to be reached when the set qth electric vehicle is finished charging.
需要说明的是,所述电动汽车参数的确定过程包括:It should be noted that the process of determining the parameters of the electric vehicle includes:
利用正态分布分别确定电动汽车到达时间、离开时间和初始电量的平均值和方差;Use normal distribution to determine the mean and variance of electric vehicle arrival time, departure time and initial charge, respectively;
基于所述电动汽车到达时间、离开时间和初始电量的平均值和方差获得各个电动汽车参数。The respective electric vehicle parameters are obtained based on the average value and variance of the electric vehicle arrival time, departure time and initial charge.
需要说明的是,研究表明EV到达时间,离开时间和初始电量的不确定性遵从正态分布,用概率密度函数表示为:It should be noted that the research shows that the uncertainty of EV arrival time, departure time and initial charge follow a normal distribution, which is expressed by the probability density function as:
式中,μ代表平均值,σ代表标准差,x可以分别表示代表EV到达时间,离开时间和初始电量实际取值,f(x)代表取得该值的概率。In the formula, μ represents the average value, σ represents the standard deviation, x can represent the EV arrival time, departure time and the actual value of the initial power, respectively, and f(x) represents the probability of obtaining the value.
通过上述正态分布公式,只要确定EV到达时间,离开时间和初始电量的μ平均值与σ标准差参数,就可以用电脑随机生成不同电动汽车的参数。Through the above normal distribution formula, as long as the arrival time of EV, departure time and initial electric quantity of μ mean and σ standard deviation parameters are determined, the parameters of different electric vehicles can be randomly generated by computer.
步骤3:利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;Step 3: Use the Nash game principle and the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period to determine the contribution of the electric vehicle to the vehicle-network interaction in the to-be-scheduled time period;
在本公开实施例中,所述利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度,包括:In the embodiment of the present disclosure, the use of the Nash game principle and the electric vehicle charging and discharging demand data at each moment in the to-be-scheduled time period to determine the contribution of the electric vehicle to the vehicle-network interaction in the to-be-scheduled time period includes:
基于为所述合能源系统优化调度模型的目标函数构建的约束条件和利用正态分布确定的电动汽车在到达电动汽车充电站的时间至离开时间之间的电动汽车充放电功率建立电充汽车不参与车网互动的对比模型,对比得到电动汽车车网互动对于区域能源系统的贡献度。Based on the constraints constructed for the objective function of the optimal dispatch model for the integrated energy system and the electric vehicle charging and discharging power of the electric vehicle between the arrival time of the electric vehicle charging station and the departure time determined using the normal distribution, the electric vehicle charging and discharging power is established. Participate in the comparison model of vehicle-network interaction, and compare the contribution of electric vehicle vehicle-network interaction to the regional energy system.
具体的,利用上述得到的电动汽车在到达时间到离开时间之间的电动汽车充放电功率以及系统约束条件的基础上,利用该数据制定电动汽车对照模型,包括:为了更好的确定电动汽车车网互动的贡献,以合理制定控制策略以及利润返还,文中运用了纳什博弈原理。根据纳什博弈原理需要建立一个对比模型,对比得到电动汽车车网互动对于区域能源系统的贡献。其主要区别为,不互动模型中,电动汽车采用即插即用模式,开始充电后就以功率约束允许的最大功率充电直至充电结束。而在车网互动模型当中,电动汽车的充电功率可以通过区域能源系统调控在允许的最大充电功率和最大放电功率之间切换。Specifically, on the basis of the above-obtained electric vehicle charging and discharging power and system constraints between the arrival time and the departure time of the electric vehicle, use the data to formulate an electric vehicle comparison model, including: in order to better determine the electric vehicle vehicle The contribution of network interaction, in order to reasonably formulate control strategies and return profits, the Nash game principle is used in this paper. According to the principle of Nash game, a comparative model needs to be established, and the contribution of the interaction between the electric vehicle and the network to the regional energy system is obtained by comparison. The main difference is that in the non-interactive model, the electric vehicle uses a plug-and-play mode, which starts charging at the maximum power allowed by the power constraints until the end of charging. In the vehicle-network interaction model, the charging power of electric vehicles can be switched between the maximum allowable charging power and the maximum discharging power through the regulation of the district energy system.
通过收集综合能源系统中的电力负荷数据与分布式发电数据和充电站的电动汽车到达时间、离开时间和所需电量等数据,生成最优的电动汽车调度控制信号。同时根据对照模型,明确计算放置于我方充电桩的电动汽车所获得的收益,通过电动汽车实际根据电网要求进行的充电策略调整量大小作为依据,判断电动汽车对于车网互动的贡献度,从而作为其获取收益多少的依据,其公式表达为:式中,SCRq为第q台电动汽车在待调度时段内参与车网互动的贡献度,为第s种电动汽车参数下第q台电动汽车在待调度时段内电动汽车不互动模型和互动模型对比的充电策略改变量,为第s种电动汽车参数下第q台电动汽车在待调度时段内电动汽车不互动模型和互动模型对比的放电策略改变量。By collecting the power load data and distributed generation data in the integrated energy system and data such as the arrival time, departure time and required power of electric vehicles at the charging station, the optimal electric vehicle dispatching control signal is generated. At the same time, according to the comparison model, the income obtained by the electric vehicles placed on our charging piles is clearly calculated, and the electric vehicle’s contribution to the vehicle-network interaction is judged based on the actual charging strategy adjustment of the electric vehicle according to the requirements of the power grid. As the basis for how much income it obtains, its formula is expressed as: In the formula, SCR q is the contribution of the qth electric vehicle participating in the vehicle-network interaction during the period to be dispatched, is the change in the charging strategy of the qth electric vehicle during the to-be-scheduled period under the sth type of electric vehicle parameters compared with the non-interaction model and the interactive model, is the discharge strategy change of the qth electric vehicle during the to-be-scheduled period under the sth electric vehicle parameters compared with the non-interaction model and the interactive model.
步骤4:基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,并基于所述控制信号进行电动汽车参与车网互动的调度控制。Step 4: Formulate a control signal to motivate the electric vehicle to participate in the vehicle-network interaction based on the contribution of the electric vehicle, and perform scheduling control for the electric vehicle to participate in the vehicle-network interaction based on the control signal.
在本公开实施例中,所述基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,包括:In the embodiment of the present disclosure, the formulating a control signal to motivate the electric vehicle to participate in the vehicle-network interaction based on the contribution of the electric vehicle includes:
利用所述电动汽车的贡献度确定电动汽车用户预计获得的奖励;Determine the reward expected to be obtained by the electric vehicle user by using the contribution of the electric vehicle;
基于所述奖励制定激励电动汽车参与车网互动的控制信号。Based on the reward, a control signal that motivates the electric vehicle to participate in the vehicle-network interaction is formulated.
具体的,通过计算电动汽车参与车网互动时对比电动汽车不参与车网互动的总收益,确定车网互动的总价值,在扣除综合能源系统提供车网互动条件的软件、硬件的支持所应得的收益后,通过电动汽车车网互动贡献度SCRq决定其具体收益;Specifically, the total value of the vehicle-network interaction is determined by calculating the total revenue of the electric vehicle participating in the vehicle-network interaction compared with that of the electric vehicle not participating in the vehicle-network interaction. After the income obtained, the specific income is determined by the interactive contribution SCR q of the electric vehicle network;
其中,fq=(1-ε)SCRqfR,fR=fR,1-fR,0,其中,fR,1和fR,0分别表示车网互动条件下的电动汽车收益,通过计算得到电动汽车参与电网调度的合作剩余。描述了具体电动汽车用户可以得到的收益金额,ε代表提供车网互动服务的平台应该收取的回报,fR通过车网互动合作得到的合作剩余,fq表示第q台电动汽车用户可以得到了奖励。Among them, f q =(1-ε)SCR q f R , f R =f R,1 -f R,0 , where f R,1 and f R,0 represent the electric vehicle revenue under the condition of vehicle-network interaction, respectively , the cooperative surplus of electric vehicles participating in grid scheduling is obtained through calculation. Describes the amount of revenue that specific electric vehicle users can get, ε represents the return that should be charged by the platform that provides car-network interactive services, f R is the cooperation surplus obtained through car-network interaction and cooperation, and f q represents the qth electric car user can get award.
进一步的,在计算得到奖励后可,通过信息平台进行信息互联实时通知充电站通知该电动汽车获得了应得的奖励,并将收益信息传导到响应的充电桩,减免充电产生的费用,若所获得收益大于充电费所需,则额外的金额可以用于下一次充电中。Further, after the reward is calculated, the information interconnection through the information platform can be used to notify the charging station in real time to notify the electric vehicle that the electric vehicle has obtained the reward it deserves, and transmit the income information to the corresponding charging pile to reduce or exempt the cost of charging. If the benefit is greater than the charging fee, the extra amount can be used for the next charging.
综上所述,本公开实施例提供的一种激励电动汽车参与车网互动的调度控制方法,通过在对于电动汽车参与车网互动的贡献度进行计算,采取通过完善的调度控制策略更好的调动电动汽车参与车网互动积极性,实现电网安全、稳定、经济运行。To sum up, the embodiments of the present disclosure provide a scheduling control method for stimulating electric vehicles to participate in vehicle-network interaction. Mobilize the enthusiasm of electric vehicles to participate in the interaction of the vehicle network and realize the safe, stable and economic operation of the power grid.
实施例2Example 2
图2为本公开实施例提供的一种激励电动汽车参与车网互动的调度控制系统的结构图,如图2所示,所述一种激励电动汽车参与车网互动的调度控制系统,包括:FIG. 2 is a structural diagram of a dispatching control system for stimulating electric vehicles to participate in vehicle-network interaction provided by an embodiment of the present disclosure. As shown in FIG. 2 , the dispatching control system for stimulating electric vehicles to participate in vehicle-network interaction includes:
第一获取模块100,用于获取综合能源系统待调度时段内的功率信息和所述时段对应的市场价格;The first obtaining
第二获取模块200,用于将所述功率信息和所述时段对应的市场价格输入预先建立的综合能源系统优化调度模型中,获得待调度时段内各时刻电动汽车充放电需求数据;The second obtaining
确定模块300,用于利用纳什博弈原理和所述待调度时段内各时刻电动汽车充放电需求数据确定待调度时段内电动汽车参与车网互动的贡献度;The determining
控制模块400,用于基于所述电动汽车的贡献度制定激励电动汽车参与车网互动的控制信号,并基于所述控制信号进行电动汽车参与车网互动的调度控制。The
在本公开实施例中,所述预先建立的综合能源系统优化调度模型的建立过程包括:In the embodiment of the present disclosure, the establishment process of the pre-established integrated energy system optimal dispatch model includes:
基于综合能源系统中的微型燃气轮机、分布式光伏、电动汽车充电站及负荷的日前功率、实时功率,构建所述综合能源系统优化调度模型的目标函数,其中,以综合能源系统最大收益为目标建立综合能源系统最大收益目标函数;Based on the day-ahead power and real-time power of the micro gas turbine, distributed photovoltaic, electric vehicle charging station and load in the integrated energy system, the objective function of the integrated energy system optimal dispatch model is constructed. The objective function of the maximum benefit of the integrated energy system;
为所述模型的目标函数构建约束条件:分布式光伏的发电功率约束、综合能源系统负荷功率柔性负荷约束、微型燃气轮机的功率约束、电动汽车充电站中电动汽车的充放电功率约束和电动汽车充电站的充放电上下限约束。Constraints are constructed for the objective function of the model: power generation constraints for distributed photovoltaics, flexible load constraints for integrated energy system load power, power constraints for micro-turbines, power constraints for charging and discharging electric vehicles in electric vehicle charging stations, and electric vehicle charging The upper and lower limits of charging and discharging of the station.
进一步的,所述综合能源系统最大收益目标函数的计算式如下所示:Further, the calculation formula of the maximum benefit objective function of the integrated energy system is as follows:
式中,μ为综合能源系统的收益,γs为第s种电动汽车参数下对应的权重, 为第s种电动汽车参数下t时刻对应的日前收益与实时收益之和,为第s种电动汽车参数下t时刻对应的日前收益,为第s种电动汽车参数下t时刻对应的实时收益,ai为第i台型燃气轮机的发电价格,ΦS为电动汽车参数种类的总数,ΦT为待调度时段内时刻总数, 为t时刻对应的日前市场售电价格,Pt DA为t时刻对应的日前功率, 为t时刻对应的实时市场售电价格,为第s种电动汽车参数下t时刻对应的实时功率,为第s种电动汽车参数下t时刻第i台微型燃气轮机的实时功率, 为t时刻第i台微型燃气轮机的日前功率,ΦMT为微型燃气轮机的总数,为t时刻第α台分布式光伏的日前功率,ΦPV为分布式光伏的总数,Pt CSD,DA为t时刻电动汽车充电站的日前放电功率,Pt CSC,DA为t时刻电动汽车充电站的日前充电功率,Pt L,DA为t时刻系统日前负荷, 为第s种电动汽车参数下t时刻第α台分布式光伏的实时功率,为第s种电动汽车参数下t时刻电动汽车充电站的实时放电功率,为第s种电动汽车参数下t时刻电动汽车充电站的实时充电功率,为第s种电动汽车参数下t时刻系统实时负荷。In the formula, μ is the income of the integrated energy system, γ s is the corresponding weight under the s-th electric vehicle parameter, is the sum of the day-ahead income and real-time income corresponding to time t under the s-th electric vehicle parameter, is the day-ahead income corresponding to time t under the s-th electric vehicle parameter, is the real-time income corresponding to time t under the s-th electric vehicle parameter, a i is the power generation price of the ith-type gas turbine, Φ S is the total number of electric vehicle parameter types, Φ T is the total number of moments in the to-be-scheduled period, is the day-ahead market electricity sales price corresponding to time t, P t DA is the day-ahead power corresponding to time t, is the real-time market electricity sales price corresponding to time t, is the real-time power corresponding to time t under the s-th electric vehicle parameter, is the real-time power of the i-th micro-turbine at time t under the s-th electric vehicle parameters, is the day-ahead power of the ith micro-turbine at time t, Φ MT is the total number of micro-turbines, is the day-ahead power of the αth distributed photovoltaic at time t, Φ PV is the total number of distributed photovoltaics, P t CSD,DA is the day-ahead discharge power of the electric vehicle charging station at time t, and P t CSC,DA is the charging of electric vehicles at time t The day-ahead charging power of the station, P t L,DA is the system's day-ahead load at time t, is the real-time power of the α-th distributed photovoltaic at time t under the s-th electric vehicle parameters, is the real-time discharge power of the electric vehicle charging station at time t under the s-th electric vehicle parameter, is the real-time charging power of the electric vehicle charging station at time t under the s-th electric vehicle parameter, is the real-time system load at time t under the s-th electric vehicle parameter.
其中,所述分布式光伏发电功率约束的计算式如下所示:Wherein, the calculation formula of the distributed photovoltaic power generation power constraint is as follows:
式中,为t时刻第α台分布式光伏的功率,PPV,max为分布式光伏的最大功率;In the formula, is the power of the αth distributed photovoltaic at time t, and P PV,max is the maximum power of the distributed photovoltaic;
所述综合能源系统负荷功率柔性负荷约束的计算式如下所示:The calculation formula of the flexible load constraint of the integrated energy system load power is as follows:
式中,PL,min为综合能源系统负荷功率柔性负荷的最小值,Pt L为t时刻综合能源系统负荷功率,PL,max为综合能源系统负荷功率柔性负荷的最大值;In the formula, PL,min is the minimum value of the flexible load of the integrated energy system load power, PtL is the load power of the integrated energy system at time t , and PL ,max is the maximum value of the flexible load of the integrated energy system load power;
所述微型燃气轮机的功率约束的计算式如下所示:The calculation formula of the power constraint of the micro gas turbine is as follows:
式中,为第i台微型燃气轮机的最大爬坡率,为第i台微型燃气轮机的最大功率;In the formula, is the maximum ramp rate of the i-th micro-turbine, is the maximum power of the i-th micro-turbine;
所述电动汽车充电站中电动汽车的充放电功率约束的计算式如下所示:The calculation formula of the charging and discharging power constraint of the electric vehicle in the electric vehicle charging station is as follows:
式中,为t时刻第q台电动汽车的最大充电功率,为第q台电动汽车的最大充电功率,为t时刻第q台电动汽车的电池电量,为第q台电动汽车在恒流充电模式下电池荷电状态阈值,当荷电量达到了这个阈值之后转换为恒压充电模式,可以描述为部分代表电动汽车恒压模式下的充电过程,表示电动汽车充电时状态为恒流充电或者恒压充电,为t时刻第q台电动汽车的最大放电功率,为第q台电动汽车的最大放电功率,为第q台电动汽车从恒流充电模式转换为恒压充电模式的阈值;其中, 为t-1时刻第q台电动汽车的电池电量,为第q台电动汽车电池的额定容量,为第q台电动汽车在充放电过程中法圣的损耗,为t-1时刻第q台电动汽车的充电功率,为t-1时刻第q台电动汽车的放电功率;In the formula, is the maximum charging power of the qth electric vehicle at time t, is the maximum charging power for the qth electric vehicle, is the battery power of the qth electric vehicle at time t, It is the battery state-of-charge threshold of the qth electric vehicle in the constant current charging mode. When the charge reaches this threshold, it switches to the constant voltage charging mode, which can be described as Part represents the charging process of an electric vehicle in constant voltage mode, Indicates that the charging state of the electric vehicle is constant current charging or constant voltage charging, is the maximum discharge power of the qth electric vehicle at time t, is the maximum discharge power of the qth electric vehicle, is the threshold value for the qth electric vehicle to convert from constant current charging mode to constant voltage charging mode; where, is the battery power of the qth electric vehicle at time t-1, is the rated capacity of the qth electric vehicle battery, is the loss of Fasheng during the charging and discharging process of the qth electric vehicle, is the charging power of the qth electric vehicle at time t-1, is the discharge power of the qth electric vehicle at time t-1;
所述电动汽车充电站的充放电上下限约束的计算式如下所示:The calculation formula of the upper and lower limit constraints of charging and discharging of the electric vehicle charging station is as follows:
式中,为第q台电动汽车到达电动汽车充电站的时间对应的电池电量,为第q台电动汽车开始充电时的电量,为第q台电动汽车离开电动汽车充电站的时间对应的电池电量,为设定的第q台电动汽车结束充电时需要达到的电量。In the formula, Time for the qth EV to arrive at the EV charging station the corresponding battery power, The amount of electricity when the qth electric car starts to charge, Time to leave the EV charging station for the qth EV the corresponding battery power, The amount of electricity that needs to be reached when the set qth electric vehicle is finished charging.
进一步的,所述电动汽车参数的确定过程包括:Further, the determination process of the electric vehicle parameters includes:
利用正态分布分别确定电动汽车到达时间、离开时间和初始电量的平均值和方差;Use normal distribution to determine the mean and variance of electric vehicle arrival time, departure time and initial charge, respectively;
基于所述电动汽车到达时间、离开时间和初始电量的平均值和方差获得各个电动汽车参数。The respective electric vehicle parameters are obtained based on the average value and variance of the electric vehicle arrival time, departure time and initial charge.
在本公开实施例中,所述确定模块300具体用于:In this embodiment of the present disclosure, the determining
基于为所述合能源系统优化调度模型的目标函数构建的约束条件和利用正态分布确定的电动汽车在到达电动汽车充电站的时间至离开时间之间的电动汽车充放电功率建立电充汽车不参与车网互动的对比模型,对比得到电动汽车车网互动对于区域能源系统的贡献度。Based on the constraints constructed for the objective function of the optimal dispatch model for the integrated energy system and the electric vehicle charging and discharging power of the electric vehicle between the arrival time of the electric vehicle charging station and the departure time determined using the normal distribution, the electric vehicle charging and discharging power is established. Participate in the comparison model of vehicle-network interaction, and compare the contribution of electric vehicle vehicle-network interaction to the regional energy system.
需要说明的是,所述电动汽车车网互动对于区域能源系统的贡献度的计算式如下所示:It should be noted that the calculation formula of the contribution of the electric vehicle network interaction to the regional energy system is as follows:
式中,SCRq为第q台电动汽车在待调度时段内参与车网互动的贡献度,为第s种电动汽车参数下第q台电动汽车在待调度时段内电动汽车不互动模型和互动模型对比的充电策略改变量,为第s种电动汽车参数下第q台电动汽车在待调度时段内电动汽车不互动模型和互动模型对比的放电策略改变量。In the formula, SCR q is the contribution of the qth electric vehicle participating in the vehicle-network interaction during the period to be dispatched, is the change in the charging strategy of the qth electric vehicle during the to-be-scheduled period under the sth type of electric vehicle parameters compared with the non-interaction model and the interactive model, is the discharge strategy change of the qth electric vehicle during the to-be-scheduled period under the sth electric vehicle parameters compared with the non-interaction model and the interactive model.
在本公开实施例中,所述控制模块400,如图3所示,包括:In this embodiment of the present disclosure, the
确定单元401,用于利用所述电动汽车的贡献度确定电动汽车用户预计获得的奖励;A
制定单元402,用于基于所述奖励制定激励电动汽车参与车网互动的控制信号;A formulating
控制单元403,用于基于所述控制信号进行电动汽车参与车网互动的调度控制。The
综上所述,本公开实施例提供的一种激励电动汽车参与车网互动的调度控制系统,通过在对于电动汽车参与车网互动的贡献度进行计算,采取通过完善的调度控制策略更好的调动电动汽车参与车网互动积极性,实现电网安全、稳定、经济运行。To sum up, a dispatching control system for stimulating electric vehicles to participate in vehicle-network interaction provided by the embodiments of the present disclosure, by calculating the contribution of electric vehicles to participating in vehicle-network interaction, and adopting a better dispatching control strategy. Mobilize the enthusiasm of electric vehicles to participate in the interaction of the vehicle network and realize the safe, stable and economic operation of the power grid.
实施例3Example 3
为了实现上述实施例,本公开还提出一种计算机设备。In order to realize the above embodiments, the present disclosure also proposes a computer device.
本实施例提供的计算机设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,处理器执行计算机程序时,实现实施例1中的方法。The computer device provided in this embodiment includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the method in Embodiment 1 is implemented.
在本说明书的描述中,参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本申请的至少一个实施例或示例中。在本说明书中,对上述术语的示意性表述不必须针对的是相同的实施例或示例。而且,描述的具体特征、结构、材料或者特点可以在任一个或多个实施例或示例中以合适的方式结合。此外,在不相互矛盾的情况下,本领域的技术人员可以将本说明书中描述的不同实施例或示例以及不同实施例或示例的特征进行结合和组合。In the description of this specification, description with reference to the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples", etc., mean specific features described in connection with the embodiment or example , structure, material or feature is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, those skilled in the art may combine and combine the different embodiments or examples described in this specification, as well as the features of the different embodiments or examples, without conflicting each other.
流程图中或在此以其他方式描述的任何过程或方法描述可以被理解为,表示包括一个或更多个用于实现定制逻辑功能或过程的步骤的可执行指令的代码的模块、片段或部分,并且本申请的优选实施方式的范围包括另外的实现,其中可以不按所示出或讨论的顺序,包括根据所涉及的功能按基本同时的方式或按相反的顺序,来执行功能,这应被本申请的实施例所属技术领域的技术人员所理解。Any process or method description in the flowcharts or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing custom logical functions or steps of the process , and the scope of the preferred embodiments of the present application includes alternative implementations in which the functions may be performed out of the order shown or discussed, including performing the functions substantially concurrently or in the reverse order depending upon the functions involved, which should It is understood by those skilled in the art to which the embodiments of the present application belong.
尽管上面已经示出和描述了本申请的实施例,可以理解的是,上述实施例是示例性的,不能理解为对本申请的限制,本领域的普通技术人员在本申请的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limitations to the present application. Embodiments are subject to variations, modifications, substitutions and variations.
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