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CN113379565B - Comprehensive energy system optimization scheduling method based on distributed robust optimization method - Google Patents

Comprehensive energy system optimization scheduling method based on distributed robust optimization method Download PDF

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CN113379565B
CN113379565B CN202110635091.6A CN202110635091A CN113379565B CN 113379565 B CN113379565 B CN 113379565B CN 202110635091 A CN202110635091 A CN 202110635091A CN 113379565 B CN113379565 B CN 113379565B
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张群
王球
陈昌铭
诸晓骏
李泽森
王鑫
李妍
王青山
王琼
吴雪妍
林振智
杨莉
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Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a comprehensive energy system optimization scheduling method based on a distributed robust optimization method, which is characterized in that comprehensive demand response and heat supply network and air supply network pipeline energy storage are cooperatively modeled into virtual energy storage, so that the scheduling flexibility of a comprehensive energy system can be improved, and the uncertainty of the distributed renewable power output in the comprehensive energy system is processed by using the distributed robust optimization method based on Wassertein distance. The comprehensive energy system distribution robust optimization scheduling scheme obtained by the method has better economy and robustness, and the economy and the robustness of the comprehensive energy system distribution robust optimization scheduling scheme can be flexibly adjusted by changing the value of the confidence level and the number of historical samples of the output prediction error of the distributed renewable power supply.

Description

一种基于分布鲁棒优化方法的综合能源系统优化调度方法An optimal scheduling method for integrated energy system based on distributed robust optimization method

技术领域：Technical field:

本发明涉及电力系统领域，具体涉及一种基于分布鲁棒优化方法的综合能源系统优化调度方法。The invention relates to the field of electric power systems, in particular to an optimal scheduling method for an integrated energy system based on a distributed robust optimization method.

背景技术：Background technique:

在能源互联网的背景下，综合能源系统(integrated energy system,IES)具有多能互补特性，可以提高能源利用效率，其优化调度已成为近年来的研究热点。In the context of the Energy Internet, the integrated energy system (IES) has the characteristics of multi-energy complementarity, which can improve the efficiency of energy utilization, and its optimal scheduling has become a research hotspot in recent years.

分布式可再生电源的出力不确定性可能会影响综合能源系统调度策略的经济性和稳定性。处理分布式可再生电源出力不确定性的常用方法是随机规划方法和鲁棒优化方法。然而，随机规划方法的求解结果过于乐观且求解时间较长，而鲁棒优化方法的求解结果过于保守。在此背景下，分布鲁棒优化方法基于随机变量的统计信息建立一个包含所有可能的概率分布的模糊集合，可以克服随机规划和鲁棒优化方法的缺点，从而有效地处理分布式可再生电源的出力不确定性。The output uncertainty of distributed renewable power sources may affect the economics and stability of integrated energy system dispatch strategies. The common methods to deal with the output uncertainty of distributed renewable power sources are stochastic programming methods and robust optimization methods. However, the solution results of the stochastic programming method are too optimistic and the solution time is long, while the solution results of the robust optimization method are too conservative. In this context, distributed robust optimization methods build a fuzzy set containing all possible probability distributions based on the statistical information of random variables, which can overcome the shortcomings of stochastic programming and robust optimization methods, and thus effectively deal with the problems of distributed renewable power generation. Output uncertainty.

在综合能源系统背景下，传统的电力需求响应拓展为综合需求响应。此外，供热网和供气网的传输延时特性可以建模为管道储能。若将综合需求响应和管道储能协同建模为虚拟储能，可以为综合能源系统的多能互补提供更大的灵活性，进而提高综合能源系统优化调度的经济性。In the context of an integrated energy system, the traditional power demand response has been extended to integrated demand response. In addition, the transmission delay characteristics of the heating network and the gas supply network can be modeled as pipeline energy storage. If the integrated demand response and pipeline energy storage are collaboratively modeled as virtual energy storage, it can provide greater flexibility for the multi-energy complementarity of the integrated energy system, thereby improving the economy of the optimal dispatch of the integrated energy system.

发明内容：Invention content:

本发明主要解决的技术问题是采用基于Wasserstein距离的分布鲁棒优化方法，提供一种基于分布鲁棒优化方法的综合能源系统优化调度方法。The technical problem that the present invention mainly solves is to adopt the distributed robust optimization method based on the Wasserstein distance to provide an integrated energy system optimal scheduling method based on the distributed robust optimization method.

本发明的技术方案如下：The technical scheme of the present invention is as follows:

一种基于分布鲁棒优化方法的综合能源系统优化调度方法，包括：An optimal scheduling method for an integrated energy system based on a distributed robust optimization method, comprising:

构建综合能源系统中的虚拟储能模型；Build a virtual energy storage model in an integrated energy system;

采用基于Wasserstein距离的分布鲁棒优化方法，构建综合能源系统中分布式可再生电源出力不确定性的模糊概率分布集合；The distributed robust optimization method based on Wasserstein distance is used to construct the fuzzy probability distribution set of the output uncertainty of distributed renewable power sources in the integrated energy system;

基于所述虚拟储能模型和所述模糊概率分布集合，构建综合能源系统分布鲁棒优化调度模型，求解出基于分布鲁棒优化方法的综合能源系统优化调度策略。Based on the virtual energy storage model and the fuzzy probability distribution set, a distributed robust optimal dispatch model of the integrated energy system is constructed, and an optimal dispatch strategy of the integrated energy system based on the distributed robust optimization method is solved.

优选地，所述综合能源系统中的虚拟储能包括综合需求响应、供热网管道储能以及供气网管道储能。Preferably, the virtual energy storage in the integrated energy system includes integrated demand response, pipeline energy storage in the heating network, and pipeline energy storage in the gas supply network.

优选地，所述构建综合能源系统中的虚拟储能模型，包括：Preferably, the construction of a virtual energy storage model in an integrated energy system includes:

首先对综合需求响应进行建模，综合需求响应包括负荷中断约束和负荷转移约束，其中，综合需求响应中的负荷中断约束表示为：Firstly, the comprehensive demand response is modeled. The comprehensive demand response includes the load interruption constraint and the load transfer constraint. The load interruption constraint in the comprehensive demand response is expressed as:

Figure GDA0003695005690000021
Figure GDA0003695005690000021

式中，上标t表示调度周期t，下同；

Figure GDA0003695005690000022
是综合需求响应中电负荷的中断功率；
Figure GDA0003695005690000023
是电负荷中断的最大比例；
Figure GDA0003695005690000024
是综合能源系统中的电负荷；In the formula, the superscript t represents the scheduling period t, the same below;
Figure GDA0003695005690000022
is the interruption power of the electrical load in the integrated demand response;
Figure GDA0003695005690000023
is the maximum proportion of electrical load interruption;
Figure GDA0003695005690000024
is the electrical load in the integrated energy system;

综合需求响应中的负荷转移约束表示为：The load transfer constraints in integrated demand response are expressed as:

Figure GDA0003695005690000025
Figure GDA0003695005690000025

Figure GDA0003695005690000026
Figure GDA0003695005690000026

Figure GDA0003695005690000027
Figure GDA0003695005690000027

Figure GDA0003695005690000028
Figure GDA0003695005690000028

式中，

Figure GDA0003695005690000029
是综合需求响应中电负荷的转移功率；
Figure GDA00036950056900000210
和
Figure GDA00036950056900000211
分别是综合需求响应中的移出电功率和移入电功率的二进制系数；
Figure GDA00036950056900000212
和
Figure GDA00036950056900000213
分别是综合需求响应中的移出电功率和移入电功率；
Figure GDA00036950056900000214
是电负荷转移的最大比例；In the formula,
Figure GDA0003695005690000029
is the transfer power of the electrical load in the comprehensive demand response;
Figure GDA00036950056900000210
and
Figure GDA00036950056900000211
are the binary coefficients of the outgoing electric power and incoming electric power in the comprehensive demand response, respectively;
Figure GDA00036950056900000212
and
Figure GDA00036950056900000213
are the outgoing electric power and incoming electric power in the comprehensive demand response, respectively;
Figure GDA00036950056900000214
is the maximum proportion of electrical load transfer;

接着对供热网管道储能进行建模，采用节点法对供热网中管道的温度准动力学和热损失进行建模，则供水管道p的出口热水温度表示为：Then, model the energy storage of the heating network pipeline, and use the node method to model the temperature quasi-dynamics and heat loss of the pipeline in the heating network. Then the outlet hot water temperature of the water supply pipeline p is expressed as:

Figure GDA00036950056900000215
Figure GDA00036950056900000215

Figure GDA00036950056900000216
Figure GDA00036950056900000216

Figure GDA00036950056900000217
Figure GDA00036950056900000217

Figure GDA00036950056900000218
Figure GDA00036950056900000218

式中，

Figure GDA00036950056900000219
和
Figure GDA00036950056900000220
分别是在t-(K-1)和t-K时刻的供水管道p入口处的热水温度；
Figure GDA00036950056900000221
是供热网的环境温度；qp和qp+1分别是供水管道p和连接到供水管道p出口的管道的质量流率；
Figure GDA0003695005690000031
和τp分别是第K-1个质块，第K个质块和供水管道p出口的质块的时间系数；kp和lp分别是温度损失系数和供水管道p的长度；In the formula,
Figure GDA00036950056900000219
and
Figure GDA00036950056900000220
are the hot water temperature at the inlet of the water supply pipe p at t-(K-1) and tK, respectively;
Figure GDA00036950056900000221
is the ambient temperature of the heating network; qp and qp +1 are the mass flow rates of the water supply pipe p and the pipe connected to the outlet of the water supply pipe p, respectively;
Figure GDA0003695005690000031
and τ p are the time coefficients of the K-1th mass, the Kth mass and the mass at the outlet of the water supply pipe p, respectively; k p and l p are the temperature loss coefficient and the length of the water supply pipe p, respectively;

则供热网管道储能表示为：Then the energy storage of the heating network pipeline is expressed as:

Figure GDA0003695005690000032
Figure GDA0003695005690000032

式中，

Figure GDA0003695005690000033
是供热网管道储能；cw是水的比热容；Δt是两个相邻调度时间之间的时间间隔；In the formula,
Figure GDA0003695005690000033
is the heating network pipeline energy storage; c w is the specific heat capacity of water; Δt is the time interval between two adjacent dispatch times;

再对供气网管道储能进行建模，首先对供气网中管道L的管存和平均节点压力进行建模：Then model the pipeline energy storage in the gas supply network. First, model the pipe storage and the average node pressure of the pipeline L in the gas supply network:

Figure GDA0003695005690000034
Figure GDA0003695005690000034

Figure GDA0003695005690000035
Figure GDA0003695005690000035

式中，

Figure GDA0003695005690000036
和
Figure GDA0003695005690000037
分别是供气网中管道L的管存和平均节点压力；ZL是管道L的管存系数；
Figure GDA0003695005690000038
和
Figure GDA0003695005690000039
分别是供气网中管道L的气体流入量和气体流出量；
Figure GDA00036950056900000310
是供气网中的管道集合；In the formula,
Figure GDA0003695005690000036
and
Figure GDA0003695005690000037
are the storage and average node pressure of the pipeline L in the gas supply network, respectively; Z L is the storage coefficient of the pipeline L ;
Figure GDA0003695005690000038
and
Figure GDA0003695005690000039
are the gas inflow and gas outflow of the pipeline L in the gas supply network;
Figure GDA00036950056900000310
is the collection of pipes in the gas supply network;

则供气网管道储能表示为Then the energy storage of the gas supply network pipeline is expressed as

Figure GDA00036950056900000311
Figure GDA00036950056900000311

式中，

Figure GDA00036950056900000312
是供气网管道储能；In the formula,
Figure GDA00036950056900000312
It is the energy storage of the gas supply network pipeline;

最后对综合能源系统中的虚拟储能进行建模，基于上述的综合需求响应、供热网管道储能以及供气网管道储能的模型，将综合能源系统中的电力，热力和天然气的虚拟储能定义为综合需求响应、供热网管道储能以及供气网管道储能之间的协同：Finally, the virtual energy storage in the integrated energy system is modeled. Based on the above-mentioned models of integrated demand response, pipeline energy storage in the heating network and pipeline energy storage in the gas supply network, the virtual energy storage of electricity, heat and natural gas in the integrated energy system is modeled. Energy storage is defined as the synergy between integrated demand response, pipeline energy storage in the heating network, and pipeline energy storage in the gas supply network:

Figure GDA00036950056900000313
Figure GDA00036950056900000313

Figure GDA00036950056900000314
Figure GDA00036950056900000314

Figure GDA00036950056900000315
Figure GDA00036950056900000315

式中，

Figure GDA0003695005690000041
和
Figure GDA0003695005690000042
分别为电力、热力以及天然气的虚拟储能。In the formula,
Figure GDA0003695005690000041
and
Figure GDA0003695005690000042
They are virtual energy storage for electricity, heat and natural gas, respectively.

优选地，运用基于Wasserstein距离的分布鲁棒优化方法，构建综合能源系统中分布式可再生电源出力不确定性的模糊概率分布集合，包括：Preferably, a distributed robust optimization method based on Wasserstein distance is used to construct a fuzzy probability distribution set of output uncertainty of distributed renewable power sources in an integrated energy system, including:

定义综合能源系统中第i个分布式可再生电源出力的预测误差为δi，δi为随机变量，记δi的真实概率分布为

Figure GDA0003695005690000043
Define the prediction error of the output of the i-th distributed renewable power source in the integrated energy system as δ i , where δ i is a random variable, and denote the true probability distribution of δ i as
Figure GDA0003695005690000043

基于预测误差的有限历史样本

Figure GDA0003695005690000044
获取经验分布
Figure GDA0003695005690000045
其中dk表示
Figure GDA0003695005690000046
的Dirac测度；Finite historical sample based on forecast error
Figure GDA0003695005690000044
Get the experience distribution
Figure GDA0003695005690000045
where d k represents
Figure GDA0003695005690000046
Dirac measure of ;

然后通过将

Figure GDA0003695005690000047
设置为中心来构造模糊集合Φ；该模糊集合Φ中，
Figure GDA0003695005690000048
和
Figure GDA0003695005690000049
之间的距离采用Wasserstein距离测量；Then by putting
Figure GDA0003695005690000047
Set as the center to construct a fuzzy set Φ; in the fuzzy set Φ,
Figure GDA0003695005690000048
and
Figure GDA0003695005690000049
The distance between them is measured by Wasserstein distance;

对于给定的紧支撑空间Ξ和两个概率分布

Figure GDA00036950056900000410
和
Figure GDA00036950056900000411
Wasserstein距离
Figure GDA00036950056900000412
由下式表示：For a given compactly supported space Ξ and two probability distributions
Figure GDA00036950056900000410
and
Figure GDA00036950056900000411
Wasserstein distance
Figure GDA00036950056900000412
It is represented by the following formula:

Figure GDA00036950056900000413
Figure GDA00036950056900000413

式中，

Figure GDA00036950056900000414
是具有经验分布
Figure GDA00036950056900000415
的随机变量；J是以
Figure GDA00036950056900000416
和
Figure GDA00036950056900000417
为边缘分布的联合分布；
Figure GDA00036950056900000418
是两个随机变量的距离；In the formula,
Figure GDA00036950056900000414
has an empirical distribution
Figure GDA00036950056900000415
A random variable of ; J is
Figure GDA00036950056900000416
and
Figure GDA00036950056900000417
is the joint distribution of the marginal distribution;
Figure GDA00036950056900000418
is the distance between two random variables;

模糊集合

Figure GDA00036950056900000419
表示为fuzzy set
Figure GDA00036950056900000419
Expressed as

Figure GDA00036950056900000420
Figure GDA00036950056900000420

模糊集合

Figure GDA00036950056900000421
视为具有半径
Figure GDA00036950056900000422
且以经验分布
Figure GDA00036950056900000423
为中心的Wasserstein球；fuzzy set
Figure GDA00036950056900000421
considered to have a radius
Figure GDA00036950056900000422
and empirically distributed
Figure GDA00036950056900000423
a Wasserstein sphere at the center;

其中in

Figure GDA00036950056900000424
Figure GDA00036950056900000424

Figure GDA00036950056900000425
Figure GDA00036950056900000425

式中，

Figure GDA00036950056900000426
是δi的置信度；η是辅助变量；
Figure GDA00036950056900000427
是预测误差历史样本的平均值；Nsam是预测误差的历史样本数；
Figure GDA0003695005690000051
通过二分搜索法求得。In the formula,
Figure GDA00036950056900000426
is the confidence of δ i ; η is the auxiliary variable;
Figure GDA00036950056900000427
is the average value of historical samples of forecast errors; N sam is the number of historical samples of forecast errors;
Figure GDA0003695005690000051
obtained by binary search.

优选地，基于所述虚拟储能模型和所述模糊概率分布集合，构建综合能源系统分布鲁棒优化调度模型，求解出基于分布鲁棒优化方法的综合能源系统优化调度策略，包括：Preferably, based on the virtual energy storage model and the fuzzy probability distribution set, construct a distributed robust optimal scheduling model for an integrated energy system, and solve the optimal scheduling strategy for an integrated energy system based on a distributed robust optimization method, including:

将由分布式可再生电源出力预测误差引起的功率偏差分配给每个燃气轮机GT，第i个GT在t时刻的实际输出功率表示为：The power deviation caused by the output prediction error of the distributed renewable power source is allocated to each gas turbine GT, and the actual output power of the i-th GT at time t is expressed as:

Figure GDA0003695005690000052
Figure GDA0003695005690000052

式中，第i个GT的实际输出功率和计划输出功率分别为

Figure GDA0003695005690000053
和
Figure GDA0003695005690000054
Figure GDA0003695005690000055
为分布式可再生电源输出功率的预测误差；
Figure GDA0003695005690000056
是所有元素的值均为1的列向量；
Figure GDA0003695005690000057
是第i个GT的参与因子，
Figure GDA0003695005690000058
In the formula, the actual output power and planned output power of the i-th GT are respectively
Figure GDA0003695005690000053
and
Figure GDA0003695005690000054
Figure GDA0003695005690000055
is the prediction error of the output power of the distributed renewable power supply;
Figure GDA0003695005690000056
is a column vector with all elements having the value 1;
Figure GDA0003695005690000057
is the participation factor of the i-th GT,
Figure GDA0003695005690000058

综合能源系统分布鲁棒优化调度模型的目标函数是最小化综合能源系统的总运行成本，即：The objective function of the distributed robust optimal dispatch model of the integrated energy system is to minimize the total operating cost of the integrated energy system, namely:

Figure GDA0003695005690000059
Figure GDA0003695005690000059

Figure GDA00036950056900000510
Figure GDA00036950056900000510

Figure GDA00036950056900000511
Figure GDA00036950056900000511

Figure GDA00036950056900000512
Figure GDA00036950056900000512

Figure GDA00036950056900000513
Figure GDA00036950056900000513

Figure GDA00036950056900000514
Figure GDA00036950056900000514

式中，T是调度时刻数；qt＝eTδt；NGT是综合能源系统中GT的数量；

Figure GDA00036950056900000515
和
Figure GDA00036950056900000516
分别是天然气和电力的单价；
Figure GDA00036950056900000517
和
Figure GDA00036950056900000518
分别是由气源提供的天然气和由第i个GT消耗的天然气；
Figure GDA00036950056900000519
是上级电网提供的电力；
Figure GDA00036950056900000520
和
Figure GDA00036950056900000521
是第i个GT的成本系数；
Figure GDA00036950056900000522
和
Figure GDA00036950056900000523
分别是综合需求响应中负荷中断和负荷转移的单价；In the formula, T is the number of scheduling time; q t = e T δ t ; N GT is the number of GTs in the integrated energy system;
Figure GDA00036950056900000515
and
Figure GDA00036950056900000516
are the unit prices of natural gas and electricity, respectively;
Figure GDA00036950056900000517
and
Figure GDA00036950056900000518
are the natural gas provided by the gas source and the natural gas consumed by the i-th GT;
Figure GDA00036950056900000519
It is the power provided by the upper power grid;
Figure GDA00036950056900000520
and
Figure GDA00036950056900000521
is the cost coefficient of the i-th GT;
Figure GDA00036950056900000522
and
Figure GDA00036950056900000523
are the unit prices of load interruption and load transfer in comprehensive demand response, respectively;

引入辅助函数h(qt,t)线性化目标函数中的分布鲁棒部分

Figure GDA0003695005690000061
所述辅助函数如下所示：Introducing the auxiliary function h(q t ,t) to linearize the distribution robust part of the objective function
Figure GDA0003695005690000061
The helper function looks like this:

Figure GDA0003695005690000062
Figure GDA0003695005690000062

Figure GDA0003695005690000063
Figure GDA0003695005690000063

根据强对偶理论，目标函数中的分布鲁棒部分表示为According to the strong duality theory, the distributional robust part in the objective function is expressed as

Figure GDA0003695005690000064
Figure GDA0003695005690000064

Figure GDA0003695005690000065
Figure GDA0003695005690000065

式中，λt和

Figure GDA0003695005690000066
都是辅助变量；where, λ t and
Figure GDA0003695005690000066
are auxiliary variables;

运用重构线性化技术将二次约束转换为具有三个附加线性约束的一般矩阵公式，如下所示：Transform the quadratic constraints into a general matrix formulation with three additional linear constraints using the reconstructive linearization technique as follows:

Figure GDA0003695005690000067
Figure GDA0003695005690000067

式中，

Figure GDA0003695005690000068
是一个对称矩阵，其中
Figure GDA0003695005690000069
zt和ct都是辅助变量；
Figure GDA00036950056900000610
Figure GDA00036950056900000611
和
Figure GDA00036950056900000612
分别是yt的上限和下限；In the formula,
Figure GDA0003695005690000068
is a symmetric matrix, where
Figure GDA0003695005690000069
z t and c t are auxiliary variables;
Figure GDA00036950056900000610
Figure GDA00036950056900000611
and
Figure GDA00036950056900000612
are the upper and lower bounds of y t , respectively;

综合能源系统分布鲁棒优化调度模型具有如下约束条件：The distributed robust optimal dispatch model of the integrated energy system has the following constraints:

1)分布鲁棒机会约束：为了确保综合能源系统的安全运行，GT的输出功率和分布式可再生电源的功率偏差在其允许范围内的可能性应高于某个阈值；因此，本发明采用分布鲁棒机会约束，如下面两个公式所示，第一个公式表示第i个GT的输出功率在其范围内的概率至少为1-ε1,i；第二个公式确保第i个GT的输出功率的备用容量满足其限制的概率至少为1-ε2,i；1) Distributed robust chance constraint: In order to ensure the safe operation of the integrated energy system, the possibility that the output power of the GT and the power deviation of the distributed renewable power source are within its allowable range should be higher than a certain threshold; therefore, the present invention adopts Distribution robust chance constraints, as shown in the following two formulas, the first formula states that the probability that the output power of the ith GT is within its range is at least 1-ε 1,i ; the second formula ensures that the ith GT The probability that the spare capacity of the output power satisfies its limit is at least 1-ε 2,i ;

Figure GDA0003695005690000071
Figure GDA0003695005690000071

Figure GDA0003695005690000072
Figure GDA0003695005690000072

式中，ΩGT是GT的集合；

Figure GDA0003695005690000073
和
Figure GDA0003695005690000074
分别是第i个GT输出功率的上限和下限；
Figure GDA0003695005690000075
是第i个GT备用容量的上限；ε1,i和ε2,i分别是两个约束的置信系数；where Ω GT is the set of GT;
Figure GDA0003695005690000073
and
Figure GDA0003695005690000074
are the upper and lower limits of the output power of the i-th GT, respectively;
Figure GDA0003695005690000075
is the upper limit of the spare capacity of the ith GT; ε 1,i and ε 2,i are the confidence coefficients of the two constraints, respectively;

2)其他约束：包括电功率平衡约束、热功率平衡约束、天然气平衡约束、配电网潮流约束、供热网潮流约束、供气网潮流约束；2) Other constraints: including electric power balance constraints, thermal power balance constraints, natural gas balance constraints, power flow constraints in distribution networks, power flow constraints in heating networks, and power flow constraints in gas supply networks;

在Matlab平台上运用CPLEX求解器对所建立的优化调度模型进行求解即可得到综合能源系统分布鲁棒优化调度方案。Using the CPLEX solver on the Matlab platform to solve the established optimal scheduling model, the robust optimal scheduling scheme of the integrated energy system distribution can be obtained.

优选地，所述分布鲁棒机会约束的一般形式为：Preferably, the general form of the distributed robust chance constraint is:

Figure GDA0003695005690000076
Figure GDA0003695005690000076

式中，NJ是不确定约束的数量；where NJ is the number of uncertain constraints;

再采用如下的CVaR近似和松弛方法线性化分布鲁棒机会约束的一般形式；The following CVaR approximation and relaxation methods are then used to linearize the general form of the distributed robust chance constraint;

Figure GDA0003695005690000077
Figure GDA0003695005690000077

式中，ZCVaR是线性化后的分布鲁棒机会约束集合；

Figure GDA0003695005690000078
和
Figure GDA0003695005690000079
都是辅助变量。where Z CVaR is the linearized set of distributed robust chance constraints;
Figure GDA0003695005690000078
and
Figure GDA0003695005690000079
are auxiliary variables.

本发明相比现有技术具有如下有益效果：Compared with the prior art, the present invention has the following beneficial effects:

本发明方法将综合需求响应和供热网、供气网管道储能协同建模为虚拟储能，可以提高综合能源系统的调度灵活性，并利用基于Wasserstein距离的分布鲁棒优化方法来处理综合能源系统中分布式可再生电源出力的不确定性。The method of the invention models the integrated demand response and the heat supply network and the gas supply network pipeline energy storage collaboratively as virtual energy storage, which can improve the scheduling flexibility of the integrated energy system, and utilizes the distribution robust optimization method based on Wasserstein distance to deal with integrated energy storage. Uncertainty in the output of distributed renewable power sources in energy systems.

本发明方法求得的综合能源系统分布鲁棒优化调度方法具有较好的经济性和鲁棒性，且通过改变置信水平的值和分布式可再生电源出力预测误差的历史样本数量，可以灵活地调整综合能源系统分布鲁棒优化调度方案的经济性和鲁棒性；综合需求响应与供热网、供气网管道储能的协同充分发挥了综合能源系统中的多能互补特性，相比单独考虑综合需求响应或管道储能的模型而言，本发明方法求得的综合能源系统分布鲁棒优化调度方案具有更低的运行成本和更高的可再生能源消纳率。The comprehensive energy system distribution robust optimal scheduling method obtained by the method of the present invention has good economy and robustness, and by changing the value of the confidence level and the number of historical samples of the output prediction error of the distributed renewable power supply, it can be flexibly Adjusting the economy and robustness of the integrated energy system distribution robust optimization dispatch scheme; the synergy of integrated demand response and pipeline energy storage in the heating network and gas supply network gives full play to the multi-energy complementary characteristics in the integrated energy system, compared with individual energy storage. Considering the model of comprehensive demand response or pipeline energy storage, the robust optimal dispatching scheme of the comprehensive energy system distribution obtained by the method of the present invention has lower operation cost and higher renewable energy consumption rate.

附图说明:Description of drawings:

图1为本发明的整体流程示意图。(作为摘要附图)FIG. 1 is a schematic diagram of the overall flow of the present invention. (as an abstract image)

图2为综合能源系统结构图。Figure 2 is a structural diagram of an integrated energy system.

图3为电功率最优调度策略图。Fig. 3 is the optimal dispatching strategy diagram of electric power.

图4为热功率最优调度策略图。Figure 4 is a diagram of the optimal scheduling strategy for thermal power.

图5为天然气最优调度策略图。Figure 5 shows the optimal dispatch strategy for natural gas.

图6为分布鲁棒优化方法灵敏度分析图。Figure 6 is a graph showing the sensitivity analysis of the distribution robust optimization method.

图7为不同优化调度模型的弃风弃光功率图。Fig. 7 is the power diagram of curtailment of wind and light for different optimal scheduling models.

具体实施方式：Detailed ways:

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施案例对本发明进行深入地详细说明。应当理解，此处所描述的具体实施案例仅仅用以解释本发明，并不用于限定发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and implementation cases. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the invention.

实施例一：Example 1:

本发明提出了一种基于分布鲁棒优化方法的综合能源系统优化调度方法，如图1所示，其实施流程包括如下详细步骤：The present invention proposes an integrated energy system optimization scheduling method based on a distributed robust optimization method, as shown in FIG. 1 , and its implementation process includes the following detailed steps:

步骤1、构建综合能源系统中的虚拟储能模型。综合能源系统中的虚拟储能包括综合需求响应、供热网管道储能以及供气网管道储能。Step 1. Build a virtual energy storage model in an integrated energy system. Virtual energy storage in the integrated energy system includes integrated demand response, pipeline energy storage in the heating network, and pipeline energy storage in the gas supply network.

首先对综合需求响应进行建模。综合需求响应由多种能源的负荷中断和负荷转移组成，下面以电力需求为例，综合需求响应中的负荷中断约束可以表示为：The synthetic demand response is first modeled. Comprehensive demand response consists of load interruption and load transfer of multiple energy sources. Taking power demand as an example, the load interruption constraint in comprehensive demand response can be expressed as:

Figure GDA0003695005690000081
Figure GDA0003695005690000081

式中，上标t表示调度周期t，下同；

Figure GDA0003695005690000082
是综合需求响应中电负荷的中断功率；
Figure GDA0003695005690000083
是电负荷中断的最大比例；
Figure GDA0003695005690000084
是综合能源系统中的电负荷。In the formula, the superscript t represents the scheduling period t, the same below;
Figure GDA0003695005690000082
is the interruption power of the electrical load in the integrated demand response;
Figure GDA0003695005690000083
is the maximum proportion of electrical load interruption;
Figure GDA0003695005690000084
is the electrical load in the integrated energy system.

综合需求响应中的负荷转移约束可以表示为：The load transfer constraints in integrated demand response can be expressed as:

Figure GDA0003695005690000085
Figure GDA0003695005690000085

Figure GDA0003695005690000091
Figure GDA0003695005690000091

Figure GDA0003695005690000092
Figure GDA0003695005690000092

Figure GDA0003695005690000093
Figure GDA0003695005690000093

式中，

Figure GDA0003695005690000094
是综合需求响应中电负荷的转移功率；
Figure GDA0003695005690000095
和
Figure GDA0003695005690000096
分别是综合需求响应中的移出电功率和移入电功率的二进制系数；
Figure GDA0003695005690000097
和
Figure GDA0003695005690000098
分别是综合需求响应中的移出电功率和移入电功率；
Figure GDA0003695005690000099
是电负荷转移的最大比例。In the formula,
Figure GDA0003695005690000094
is the transfer power of the electrical load in the comprehensive demand response;
Figure GDA0003695005690000095
and
Figure GDA0003695005690000096
are the binary coefficients of the outgoing electric power and incoming electric power in the comprehensive demand response, respectively;
Figure GDA0003695005690000097
and
Figure GDA0003695005690000098
are the outgoing electric power and incoming electric power in the comprehensive demand response, respectively;
Figure GDA0003695005690000099
is the maximum proportion of electrical load transfer.

接着对供热网管道储能进行建模。节点法被用于对供热网中管道的温度准动力学和热损失进行建模，因为它在计算上易于处理并且具有很高的建模精度。Next, model the energy storage in the heating network pipeline. The nodal method is used to model the temperature quasi-dynamics and heat losses of pipes in a heating network because of its computational tractability and high modeling accuracy.

下面以供水管道p为例，其出口热水温度可以表示为：Taking the water supply pipe p as an example, the outlet hot water temperature can be expressed as:

Figure GDA00036950056900000910
Figure GDA00036950056900000910

Figure GDA00036950056900000911
Figure GDA00036950056900000911

Figure GDA00036950056900000912
Figure GDA00036950056900000912

Figure GDA00036950056900000913
Figure GDA00036950056900000913

式中，

Figure GDA00036950056900000914
和
Figure GDA00036950056900000915
分别是在t-(K-1)和t-K时刻的供水管道p入口处的热水温度；
Figure GDA00036950056900000916
是供热网的环境温度；qp和qp+1分别是供水管道p和连接到供水管道p出口的管道的质量流率；
Figure GDA00036950056900000917
和τp分别是第K-1个质块，第K个质块和供水管道p出口的质块的时间系数；kp和lp分别是温度损失系数和供水管道p的长度。In the formula,
Figure GDA00036950056900000914
and
Figure GDA00036950056900000915
are the hot water temperature at the inlet of the water supply pipe p at t-(K-1) and tK, respectively;
Figure GDA00036950056900000916
is the ambient temperature of the heating network; qp and qp +1 are the mass flow rates of the water supply pipe p and the pipe connected to the outlet of the water supply pipe p, respectively;
Figure GDA00036950056900000917
and τ p are the time coefficients of the K-1th mass, the Kth mass and the mass at the outlet of the water supply pipe p, respectively; k p and l p are the temperature loss coefficient and the length of the water supply pipe p, respectively.

供热网中管道的温度准动态可建模为管道储能，其定义为The temperature quasi-dynamics of pipes in a heating network can be modeled as pipe energy storage, which is defined as

Figure GDA00036950056900000918
Figure GDA00036950056900000918

式中，

Figure GDA00036950056900000919
是供热网管道储能；cw是水的比热容；Δt是两个相邻调度时间之间的时间间隔。In the formula,
Figure GDA00036950056900000919
is the heating network pipeline energy storage; c w is the specific heat capacity of water; Δt is the time interval between two adjacent dispatch times.

下面对供热网管道储能进行建模。供气网中的管存反映了气体储能特性，如下所示：Next, model the energy storage in the heating network pipeline. The tube storage in the gas supply network reflects the gas energy storage characteristics as follows:

Figure GDA0003695005690000101
Figure GDA0003695005690000101

Figure GDA0003695005690000102
Figure GDA0003695005690000102

式中，

Figure GDA0003695005690000103
和
Figure GDA0003695005690000104
分别是供气网中管道L的管存和平均节点压力；ZL是管道L的管存系数；
Figure GDA0003695005690000105
和
Figure GDA0003695005690000106
分别是供气网中管道L的气体流入量和气体流出量；
Figure GDA0003695005690000107
是供气网中的管道集合。In the formula,
Figure GDA0003695005690000103
and
Figure GDA0003695005690000104
are the storage and average node pressure of the pipeline L in the gas supply network, respectively; ZL is the storage coefficient of the pipeline L;
Figure GDA0003695005690000105
and
Figure GDA0003695005690000106
are the gas inflow and gas outflow of the pipeline L in the gas supply network;
Figure GDA0003695005690000107
It is a collection of pipes in the gas supply network.

供气网中的管道管存可以建模为管道储能，其定义为：The pipeline storage in the gas supply network can be modeled as pipeline storage, which is defined as:

Figure GDA0003695005690000108
Figure GDA0003695005690000108

式中，

Figure GDA0003695005690000109
是供气网管道储能。In the formula,
Figure GDA0003695005690000109
It is the energy storage of the gas supply network pipeline.

下面对综合能源系统中的虚拟储能进行建模。基于上述的综合需求响应、供热网管道储能以及供气网管道储能的模型，将综合能源系统中的电力，热力和天然气的虚拟储能定义为综合需求响应、供热网管道储能以及供气网管道储能之间的协同：The virtual energy storage in the integrated energy system is modeled below. Based on the above models of integrated demand response, heating network pipeline energy storage and gas supply network pipeline energy storage, the virtual energy storage of electricity, heat and natural gas in the integrated energy system is defined as integrated demand response, heating network pipeline energy storage And the synergy between the gas supply network pipeline energy storage:

Figure GDA00036950056900001010
Figure GDA00036950056900001010

Figure GDA00036950056900001011
Figure GDA00036950056900001011

Figure GDA00036950056900001012
Figure GDA00036950056900001012

式中，

Figure GDA00036950056900001013
和
Figure GDA00036950056900001014
分别为电力、热力以及天然气的虚拟储能。In the formula,
Figure GDA00036950056900001013
and
Figure GDA00036950056900001014
They are virtual energy storage for electricity, heat and natural gas, respectively.

步骤2、运用基于Wasserstein距离的分布鲁棒优化方法，构建综合能源系统中分布式可再生电源出力不确定性的模糊概率分布集合。Step 2. Use the distributed robust optimization method based on Wasserstein distance to construct a fuzzy probability distribution set of the output uncertainty of distributed renewable power sources in the integrated energy system.

综合能源系统中第i个分布式可再生电源出力的预测误差是随机变量，定义为δi。在实际中，δi的真实概率分布

Figure GDA00036950056900001015
不能被确定。但是，预测误差的有限历史样本
Figure GDA00036950056900001016
可以提供一些可靠的概率信息来得到经验分布
Figure GDA00036950056900001017
其中dk表示
Figure GDA00036950056900001018
的Dirac测度。然后，可以通过将
Figure GDA00036950056900001019
设置为中心来构造模糊集合Φ。为了构造边界清晰的模糊集合Φ，Wasserstein距离被用于精确测量
Figure GDA0003695005690000111
和
Figure GDA0003695005690000112
之间的距离。The prediction error of the output of the ith distributed renewable power source in the integrated energy system is a random variable, which is defined as δ i . In practice, the true probability distribution of δ i
Figure GDA00036950056900001015
cannot be determined. However, a limited historical sample of forecast errors
Figure GDA00036950056900001016
can provide some reliable probability information to get the empirical distribution
Figure GDA00036950056900001017
where d k represents
Figure GDA00036950056900001018
Dirac measure of . Then, by putting
Figure GDA00036950056900001019
Set as the center to construct the fuzzy set Φ. To construct a well-defined fuzzy set Φ, the Wasserstein distance is used to precisely measure
Figure GDA0003695005690000111
and
Figure GDA0003695005690000112
the distance between.

对于给定的紧支撑空间Ξ和两个概率分布

Figure GDA0003695005690000113
和
Figure GDA0003695005690000114
Wasserstein距离
Figure GDA0003695005690000115
由下式表示：For a given compactly supported space Ξ and two probability distributions
Figure GDA0003695005690000113
and
Figure GDA0003695005690000114
Wasserstein distance
Figure GDA0003695005690000115
It is represented by the following formula:

Figure GDA0003695005690000116
Figure GDA0003695005690000116

式中，

Figure GDA0003695005690000117
是具有经验分布
Figure GDA0003695005690000118
的随机变量；J是以
Figure GDA0003695005690000119
和
Figure GDA00036950056900001110
为边缘分布的联合分布；
Figure GDA00036950056900001111
是两个随机变量的距离，使用1-范数||·||1是因为它在DRO问题中具有出色的数值可扩展性。In the formula,
Figure GDA0003695005690000117
has an empirical distribution
Figure GDA0003695005690000118
A random variable of ; J is
Figure GDA0003695005690000119
and
Figure GDA00036950056900001110
is the joint distribution of the marginal distribution;
Figure GDA00036950056900001111
is the distance of two random variables, the 1-norm || || 1 is used because of its excellent numerical scalability in DRO problems.

根据上面的定义，模糊集合

Figure GDA00036950056900001112
可以表示为According to the above definition, fuzzy sets
Figure GDA00036950056900001112
It can be expressed as

Figure GDA00036950056900001113
Figure GDA00036950056900001113

需要注意的是，可以将

Figure GDA00036950056900001114
其视为具有半径
Figure GDA00036950056900001115
且以经验分布
Figure GDA00036950056900001116
为中心的Wasserstein球。It should be noted that the
Figure GDA00036950056900001114
It is considered to have a radius
Figure GDA00036950056900001115
and empirically distributed
Figure GDA00036950056900001116
Centered Wasserstein Sphere.

Figure GDA00036950056900001117
对于基于Wasserstein距离的分布鲁棒优化调度方法的性能非常重要，它可以控制调度策略的保守性。构建
Figure GDA00036950056900001118
需要基于预测误差的可用历史样本，如下所示：
Figure GDA00036950056900001117
It is very important for the performance of the distributed robust optimization scheduling method based on Wasserstein distance, which can control the conservativeness of the scheduling policy. Construct
Figure GDA00036950056900001118
An available historical sample based on forecast error is required, as follows:

Figure GDA00036950056900001119
Figure GDA00036950056900001119

Figure GDA00036950056900001120
Figure GDA00036950056900001120

式中，

Figure GDA00036950056900001121
是δi的置信度；η是辅助变量；
Figure GDA00036950056900001122
是预测误差历史样本的平均值；Nsam是预测误差的历史样本数。
Figure GDA00036950056900001123
可以通过二分搜索法求得。In the formula,
Figure GDA00036950056900001121
is the confidence of δ i ; η is the auxiliary variable;
Figure GDA00036950056900001122
is the average of the historical samples of forecast errors; Nsam is the number of historical samples of forecast errors.
Figure GDA00036950056900001123
It can be obtained by binary search method.

步骤3、基于上述虚拟储能模型和模糊概率分布集合，构建综合能源系统分布鲁棒优化调度模型，求解出基于分布鲁棒优化方法的综合能源系统优化调度策略。Step 3. Based on the above-mentioned virtual energy storage model and the fuzzy probability distribution set, construct a distributed robust optimal scheduling model of the comprehensive energy system, and solve the optimal scheduling strategy of the comprehensive energy system based on the distributed robust optimization method.

将由分布式可再生电源出力预测误差引起的功率偏差分配给每个燃气轮机(gasturbine,GT)，第i个GT在t时刻的实际输出功率可以表示为：The power deviation caused by the output prediction error of the distributed renewable power source is allocated to each gas turbine (GT), and the actual output power of the i-th GT at time t can be expressed as:

Figure GDA0003695005690000121
Figure GDA0003695005690000121

式中，第i个GT的实际输出功率和计划输出功率分别为

Figure GDA0003695005690000122
和
Figure GDA0003695005690000123
Figure GDA0003695005690000124
为分布式可再生电源输出功率的预测误差；
Figure GDA0003695005690000125
是所有元素的值均为1的列向量；
Figure GDA0003695005690000126
是第i个GT的参与因子，
Figure GDA0003695005690000127
In the formula, the actual output power and planned output power of the i-th GT are respectively
Figure GDA0003695005690000122
and
Figure GDA0003695005690000123
Figure GDA0003695005690000124
is the prediction error of the output power of the distributed renewable power supply;
Figure GDA0003695005690000125
is a column vector with all elements having the value 1;
Figure GDA0003695005690000126
is the participation factor of the i-th GT,
Figure GDA0003695005690000127

基于分布鲁棒优化方法的综合能源系统分布鲁棒优化调度模型的目标函数是最小化综合能源系统的总运行成本，即：The objective function of the distributed robust optimization scheduling model of the integrated energy system based on the distributed robust optimization method is to minimize the total operating cost of the integrated energy system, namely:

Figure GDA0003695005690000128
Figure GDA0003695005690000128

Figure GDA0003695005690000129
Figure GDA0003695005690000129

Figure GDA00036950056900001210
Figure GDA00036950056900001210

Figure GDA00036950056900001211
Figure GDA00036950056900001211

Figure GDA00036950056900001212
Figure GDA00036950056900001212

Figure GDA00036950056900001213
Figure GDA00036950056900001213

式中，T是调度时刻数；qt＝eTδt；NGT是综合能源系统中GT的数量；

Figure GDA00036950056900001214
和
Figure GDA00036950056900001215
分别是天然气和电力的单价；
Figure GDA00036950056900001216
和
Figure GDA00036950056900001217
分别是由气源提供的天然气和由第i个GT消耗的天然气；
Figure GDA00036950056900001218
是上级电网提供的电力；
Figure GDA00036950056900001219
和
Figure GDA00036950056900001220
是第i个GT的成本系数；
Figure GDA00036950056900001221
和
Figure GDA00036950056900001222
分别是综合需求响应中负荷中断和负荷转移的单价。In the formula, T is the number of scheduling time; q t = e T δ t ; N GT is the number of GTs in the integrated energy system;
Figure GDA00036950056900001214
and
Figure GDA00036950056900001215
are the unit prices of natural gas and electricity, respectively;
Figure GDA00036950056900001216
and
Figure GDA00036950056900001217
are the natural gas provided by the gas source and the natural gas consumed by the i-th GT;
Figure GDA00036950056900001218
It is the electricity provided by the upper power grid;
Figure GDA00036950056900001219
and
Figure GDA00036950056900001220
is the cost coefficient of the i-th GT;
Figure GDA00036950056900001221
and
Figure GDA00036950056900001222
are the unit prices of load interruption and load transfer in integrated demand response, respectively.

基于分布鲁棒优化方法的综合能源系统分布鲁棒优化调度模型的目标函数是一个“min-max”问题，很难直接求解。The objective function of the distributed robust optimal scheduling model of the integrated energy system based on the distributed robust optimization method is a "min-max" problem, which is difficult to solve directly.

为了线性化目标函数中的分布鲁棒部分，即

Figure GDA00036950056900001223
引入辅助函数h(qt,t)，其定义为To linearize the distribution-robust part in the objective function, i.e.
Figure GDA00036950056900001223
A helper function h(q t ,t) is introduced, which is defined as

Figure GDA00036950056900001224
Figure GDA00036950056900001224

Figure GDA0003695005690000131
Figure GDA0003695005690000131

根据强对偶理论，目标函数中的分布鲁棒部分可以表示为According to the strong duality theory, the distributional robust part of the objective function can be expressed as

Figure GDA0003695005690000132
Figure GDA0003695005690000132

Figure GDA0003695005690000133
Figure GDA0003695005690000133

式中，λt和

Figure GDA0003695005690000134
都是辅助变量。where, λ t and
Figure GDA0003695005690000134
are auxiliary variables.

因此，目标函数的分布鲁棒部分已通过强对偶理论转化为线性公式，可以容易地被商业求解器求解。但是，新引入的二次约束仍需要进行处理。重构线性化技术在解决二次约束方面是有效的，因此，本发明运用重构线性化技术将二次约束转换为具有三个附加线性约束的一般矩阵公式，如下所示：Therefore, the distributionally robust part of the objective function has been transformed into a linear formulation by strong duality theory, which can be easily solved by commercial solvers. However, the newly introduced quadratic constraints still need to be handled. Reconstruction linearization techniques are effective in solving quadratic constraints, therefore, the present invention employs reconstruction linearization techniques to convert quadratic constraints into a general matrix formulation with three additional linear constraints, as follows:

Figure GDA0003695005690000135
Figure GDA0003695005690000135

式中，

Figure GDA0003695005690000136
是一个对称矩阵，其中
Figure GDA0003695005690000137
zt和ct都是辅助变量；
Figure GDA0003695005690000138
Figure GDA0003695005690000139
和
Figure GDA00036950056900001310
分别是yt的上限和下限。In the formula,
Figure GDA0003695005690000136
is a symmetric matrix, where
Figure GDA0003695005690000137
z t and c t are auxiliary variables;
Figure GDA0003695005690000138
Figure GDA0003695005690000139
and
Figure GDA00036950056900001310
are the upper and lower bounds of y t , respectively.

基于分布鲁棒优化方法的综合能源系统分布鲁棒优化调度模型具有如下约束条件：The distributed robust optimal scheduling model of the integrated energy system based on the distributed robust optimization method has the following constraints:

1)分布鲁棒机会约束：为了确保综合能源系统的安全运行，GT的输出功率和分布式可再生电源的功率偏差在其允许范围内的可能性应高于某个阈值。因此，本发明采用分布鲁棒机会约束，如下面两个公式所示。第一个公式表示第i个GT的输出功率在其范围内的概率至少为1-ε1,i；第二个公式确保第i个GT的输出功率的备用容量满足其限制的概率至少为1-ε2,i。1) Distributed Robust Chance Constraint: In order to ensure the safe operation of the integrated energy system, the possibility that the output power of GT and the power deviation of distributed renewable power sources are within their allowable ranges should be higher than a certain threshold. Therefore, the present invention adopts a distributed robust chance constraint, as shown in the following two formulas. The first formula states that the probability that the output power of the ith GT is within its limits is at least 1-ε 1,i ; the second formula ensures that the spare capacity of the output power of the ith GT meets its limit with a probability of at least 1 -ε 2,i .

Figure GDA0003695005690000141
Figure GDA0003695005690000141

Figure GDA0003695005690000142
Figure GDA0003695005690000142

式中，ΩGT是GT的集合；

Figure GDA0003695005690000143
和
Figure GDA0003695005690000144
分别是第i个GT输出功率的上限和下限；
Figure GDA0003695005690000145
是第i个GT备用容量的上限；ε1,i和ε2,i分别是两个约束的置信系数。where Ω GT is the set of GT;
Figure GDA0003695005690000143
and
Figure GDA0003695005690000144
are the upper and lower limits of the output power of the i-th GT, respectively;
Figure GDA0003695005690000145
is the upper limit of the spare capacity of the ith GT; ε 1,i and ε 2,i are the confidence coefficients of the two constraints, respectively.

上面两个分布鲁棒机会约束是非凸约束，这导致本发明所提模型不容易被商业求解器求解。CVaR近似和松弛方法被证明可以有效地线性化机会约束，因此本发明运用该方法对上面两个分布鲁棒机会约束进行线性化。为了便于描述，首先给出分布鲁棒机会约束的一般形式：The above two distribution-robust chance constraints are non-convex constraints, which makes the model proposed in the present invention not easy to be solved by commercial solvers. The CVaR approximation and relaxation methods are proved to be able to effectively linearize the chance constraints, so the present invention uses this method to linearize the above two distributed robust chance constraints. For ease of description, the general form of the distributional robust chance constraint is first given:

Figure GDA0003695005690000146
Figure GDA0003695005690000146

式中，NJ是不确定约束的数量。where NJ is the number of uncertain constraints.

然后，通过如下的CVaR近似和松弛方法来线性化分布鲁棒机会约束的一般形式：Then, the general form of the distribution robust chance constraint is linearized by the CVaR approximation and relaxation method as follows:

Figure GDA0003695005690000147
Figure GDA0003695005690000147

式中，ZCVaR是线性化后的分布鲁棒机会约束集合；

Figure GDA0003695005690000148
和
Figure GDA0003695005690000149
都是辅助变量。where Z CVaR is the linearized set of distributed robust chance constraints;
Figure GDA0003695005690000148
and
Figure GDA0003695005690000149
are auxiliary variables.

2)其他约束：包括电功率平衡约束、热功率平衡约束、天然气平衡约束、配电网潮流约束、供热网潮流约束、供气网潮流约束。2) Other constraints: including electric power balance constraints, thermal power balance constraints, natural gas balance constraints, power flow constraints in distribution networks, power flow constraints in heating networks, and power flow constraints in gas supply networks.

至此，基于分布鲁棒优化方法的综合能源系统分布鲁棒优化调度模型已建立。在Matlab平台上运用CPLEX求解器对模型进行求解即可得到综合能源系统分布鲁棒优化调度方案。So far, the distributed robust optimal scheduling model of the integrated energy system based on the distributed robust optimization method has been established. Using the CPLEX solver on the Matlab platform to solve the model, the robust optimal scheduling scheme of the integrated energy system distribution can be obtained.

应用实施例一：Application Example 1:

为了进一步理解本发明，以下以由IEEE-33节点配电网，44节点供热网和20节点供气网组成的综合能源系统为例，来解释本发明的实际应用。In order to further understand the present invention, the practical application of the present invention is explained below by taking an integrated energy system composed of an IEEE-33 node power distribution network, a 44 node heating network and a 20 node gas supply network as an example.

由IEEE-33节点配电网，44节点供热网和20节点供气网组成的综合能源系统结构图如图2所示，配电网、供热网和天然气网这三种能源网络通过能源集线器中的燃气轮机GT、电转气装置P2G、电锅炉EB和热电联产机组CHP进行耦合。The structure diagram of the comprehensive energy system composed of IEEE-33 node distribution network, 44-node heating network and 20-node gas supply network is shown in Figure 2. The three energy networks of distribution network, heating network and natural gas network pass the energy The gas turbine GT, the power-to-gas device P2G, the electric boiler EB and the cogeneration unit CHP in the hub are coupled.

IES中电力、热力和天然气的最优调度策略如图3～图5所示。由图3可知，在整个调度期间，IES中的DG出力是足够的，因此IES不需要从上级电网购买电力，甚至在RES出力较大的晚上或中午时间段需要削减RES的输出功率。由于13:00时光伏(photovoltaic,PV)的输出功率大且13:00的电价低，因此在13:00时，1.6MW的PV功率存储在VES中并在16:00-21:00的高电价时期放电，这样可以降低IES的运行成本，又可以减少弃光。由图4可知，EB在整个调度周期内都处于全功率运行，以提高可再生能源消纳率。由于CHP在“以热定电”模式下运行，并且夜间的热负荷大于白天的负荷，因此晚上CHP的热功率和电功率较大。由图2可知，风电(wind turbine,WT)在夜间的输出功率较大，而电负荷较低，因此CHP在夜间的较大的电功率可能会导致较多的弃风。因此，VES在1:00-11:00以及23:00-24:00释放热能，以降低CHP的热功率，从而减少WT的输出功率。由图5可知，在整个调度期间，P2G、气源和虚拟储能一起供应天然气负荷以及CHP和GT的天然气需求。The optimal dispatching strategies for electricity, heat and natural gas in IES are shown in Figures 3 to 5. It can be seen from Figure 3 that the DG output in the IES is sufficient during the entire dispatching period, so the IES does not need to purchase power from the upper-level power grid, and even the output power of the RES needs to be reduced at night or noon when the RES output is large. Since the output power of photovoltaic (PV) is large at 13:00 and the electricity price at 13:00 is low, so at 13:00, 1.6MW of PV power is stored in the VES and at the high of 16:00-21:00 Discharge during the electricity price period, which can reduce the operating cost of the IES and reduce the abandonment of light. It can be seen from Figure 4 that EB is running at full power throughout the dispatch cycle to improve the renewable energy consumption rate. Since the CHP operates in the mode of "heating and electricity", and the thermal load at night is greater than that during the day, the thermal power and electrical power of the CHP are larger at night. It can be seen from Fig. 2 that the output power of wind turbine (WT) is larger at night, and the electrical load is lower, so the larger electric power of CHP at night may lead to more wind curtailment. Therefore, the VES releases thermal energy at 1:00-11:00 and 23:00-24:00 to reduce the thermal power of the CHP, thereby reducing the output power of the WT. It can be seen from Figure 5 that during the whole dispatch period, P2G, gas source and virtual energy storage together supply the natural gas load and the natural gas demand of CHP and GT.

表1展示了基于分布鲁棒优化方法

Figure GDA0003695005690000151
随机规划方法和鲁棒优化方法综合能源系统优化调度模型之间的综合能源系统运行成本的比较。从表1可以看出，分布鲁棒优化方法的运行成本低于鲁棒优化方法的运行成本，而高于随机规划方法的运行成本，这是因为鲁棒优化方法完全忽略了概率信息，而随机规划方法假定了综合能源系统中不确定性的精确概率分布。换句话说，鲁棒优化方法和随机规划方法分别给出了综合能源系统的过度优化和过度保守的调度策略，而分布鲁棒优化方法基于综合能源系统中随机变量的历史样本建立了一个包含所有可能概率分布的模糊集合，与随机规划方法相比，它的乐观度较低，而保守度比鲁棒优化方法低。从表1还可以看出，分布鲁棒优化方法的运行成本随着预测误差的历史样本量的增加而降低，即当历史样本量较小时，分布鲁棒优化方法采取像鲁棒优化方法的保守调度策略；相反地，当预测误差的历史样本量较大时，分布鲁棒优化方法会使用类似于随机规划方法的乐观调度策略。这是因为当历史样本量较小时，可以提取的概率分布有限，因此Wasserstein球的边界更宽，综合能源系统的调度策略更加保守；随着历史样本量的增加，Wasserstein球的半径减小，模糊集合更小，综合能源系统的调度策略的保守性也降低了。Table 1 shows the distribution-based robust optimization methods
Figure GDA0003695005690000151
Comparison of Integrated Energy System Operating Costs between Stochastic Programming Methods and Robust Optimization Methods Integrated Energy System Optimal Scheduling Models. It can be seen from Table 1 that the operating cost of the distribution robust optimization method is lower than that of the robust optimization method, but higher than that of the stochastic programming method, because the robust optimization method completely ignores the probability information, while the random programming method completely ignores the probability information. The planning method assumes precise probability distributions of uncertainties in the integrated energy system. In other words, robust optimization methods and stochastic programming methods give over-optimized and over-conservative scheduling strategies for integrated energy systems, respectively, while distributed robust optimization methods build a A fuzzy set of possible probability distributions, which is less optimistic than stochastic programming methods and less conservative than robust optimization methods. It can also be seen from Table 1 that the operating cost of the distribution robust optimization method decreases with the increase of the historical sample size of the prediction error, that is, when the historical sample size is small, the distribution robust optimization method adopts the conservative method like the robust optimization method. Scheduling strategy; Conversely, when the historical sample size of prediction errors is large, the distribution robust optimization method uses an optimistic scheduling strategy similar to the stochastic programming method. This is because when the historical sample size is small, the probability distribution that can be extracted is limited, so the boundary of the Wasserstein sphere is wider, and the scheduling strategy of the integrated energy system is more conservative; as the historical sample size increases, the radius of the Wasserstein sphere decreases, blurring The set is smaller and the conservatism of the dispatch strategy of the integrated energy system is also reduced.

表1基于分布鲁棒优化方法、随机规划方法和鲁棒优化方法综合能源系统优化调度模型之间的综合能源系统运行成本的比较Table 1 Comparison of integrated energy system operating costs among integrated energy system optimal dispatch models based on distributed robust optimization method, stochastic programming method and robust optimization method

Figure GDA0003695005690000161
Figure GDA0003695005690000161

为了分析本发明所提模型对置信度和样本数量的灵敏性，在不同置信度和样本数量下综合能源系统的运行成本和可再生能源消纳率(renewable energy consumptionlevel,RECL)的比较如图6所示。从图6可以看出，随着置信度的提高，综合能源系统的运行成本增加，综合能源系统的RECL减小，这是因为随着置信度β的增加，综合能源系统的调度策略趋于更加保守。此外，随着历史样本量的增加，综合能源系统的运行成本降低，而综合能源系统的RECL增加，这是因为随着历史样本量的增加，模糊集合缩小，因此综合能源系统调度策略的保守性会降低。因此，该模型可以根据置信度和历史样本数来调整综合能源系统调度策略的经济性和鲁棒性。In order to analyze the sensitivity of the proposed model to the confidence level and the number of samples, the comparison of the operating cost and the renewable energy consumption level (RECL) of the integrated energy system under different confidence levels and sample numbers is shown in Figure 6 shown. As can be seen from Figure 6, as the confidence increases, the operating cost of the integrated energy system increases, and the RECL of the integrated energy system decreases, because with the increase of the confidence β, the dispatching strategy of the integrated energy system tends to be more keep. In addition, with the increase of the historical sample size, the operating cost of the integrated energy system decreases, while the RECL of the integrated energy system increases, this is because the fuzzy set shrinks with the increase of the historical sample size, so the conservativeness of the integrated energy system scheduling strategy will decrease. Therefore, the model can adjust the economy and robustness of the integrated energy system dispatch strategy according to the confidence and the number of historical samples.

为了验证本发明所提模型的有效性，将不考虑综合需求响应和管道储能的综合能源系统最优调度模型(M-WIP)、考虑管道储能(M-PESs)的综合能源系统最优调度模型、考虑综合需求响应的综合能源系统最优调度模型(M-IDR)与考虑虚拟储能的本发明所提模型(M-VES)进行比较。表2给出了M-WIP、M-PESs、M-IDR和本发明所提M-VESs在综合能源系统运行成本和RECL方面的比较，这四种模型均使用基于Wasserstein距离的分布鲁棒优化方法处理分布式可再生电源的出力不确定性。从表2可以看出，M-VES的运行成本分别比M-WIP、M-PES和M-IDR低2.8％、0.8％和1.4％。此外，M-VESs的RECL分别比M-WIP、M-PES和M-IDR高5.8％、1.4％和3.4％。这是因为虚拟储能(即IDR与管道储能之间的协作)可以充分利用多种能量互补特性来增强综合能源系统的调度灵活性，从而可以降低综合能源系统的运行成本并提高RECL。M-PES和M-IDR的比较表明，综合需求响应和管道储能都可以降低综合能源系统的运营成本并提高REC的RECL，并且管道储能的性能优于综合需求响应。In order to verify the validity of the model proposed in the present invention, the integrated energy system optimal dispatch model (M-WIP) that does not consider integrated demand response and pipeline energy storage, and the integrated energy system optimal scheduling model considering pipeline energy storage (M-PESs) will be The dispatch model, the optimal dispatch model of the integrated energy system (M-IDR) considering integrated demand response, and the proposed model of the present invention (M-VES) considering virtual energy storage are compared. Table 2 shows the comparison of M-WIP, M-PESs, M-IDR and M-VESs proposed in the present invention in terms of operating cost and RECL of the integrated energy system. These four models all use distributed robust optimization based on Wasserstein distance. The method deals with the output uncertainty of distributed renewable power generation. It can be seen from Table 2 that the operating cost of M-VES is 2.8%, 0.8% and 1.4% lower than that of M-WIP, M-PES and M-IDR, respectively. Furthermore, the RECL of M-VESs was 5.8%, 1.4% and 3.4% higher than that of M-WIP, M-PES and M-IDR, respectively. This is because virtual energy storage (that is, the collaboration between IDR and pipeline energy storage) can make full use of multiple energy complementary characteristics to enhance the dispatch flexibility of the integrated energy system, which can reduce the operating cost of the integrated energy system and improve RECL. The comparison of M-PES and M-IDR shows that both integrated demand response and pipeline energy storage can reduce the operating costs of integrated energy systems and improve the RECL of RECs, and that pipeline energy storage outperforms integrated demand response.

表2M-WIP、M-PESs、M-IDR和本发明所提M-VESs在综合能源系统运行成本和RECL方面的比较Table 2 Comparison of M-WIP, M-PESs, M-IDR and M-VESs proposed in the present invention in terms of operating cost and RECL of integrated energy systems

Figure GDA0003695005690000171
Figure GDA0003695005690000171

图7显示了M-WIP，M-PES，M-IDR和本发明所提M-VESs在减少弃风弃光方面的比较。从图7可以看出，分布式可再生电源的弃风弃光发生在1:00-14:00和23:00-24：00，因为在这些时段中分布式可再生电源出力很大而电负荷很低。由于缺少综合需求响应和管道储能，M-WIP无法利用综合能源系统的多能互补来促进可再生能源消纳，因此在整个调度周期内削减了16.2MW的风光出力。管道储能和综合需求响应分别在M-PES和M-IDR中使用，因此M-PES和M-IDR的RECL有所提高。本发明所提的M-VESs中考虑了管道储能和综合需求响应之间的协同作用，以充分利用综合能源系统的多能互补特性，因此M-VESs的弃风弃光在四个模型中最低。Figure 7 shows the comparison of M-WIP, M-PES, M-IDR and the M-VESs proposed in the present invention in reducing wind and light abandonment. It can be seen from Figure 7 that the curtailment of wind and light from distributed renewable power sources occurs at 1:00-14:00 and 23:00-24:00, because the distributed renewable power sources have a large output during these periods and the electricity Load is low. Due to the lack of integrated demand response and pipeline energy storage, M-WIP could not utilize the multi-energy complementarity of the integrated energy system to promote renewable energy consumption, thus cutting 16.2MW of wind and solar output during the entire dispatch cycle. Pipeline energy storage and integrated demand response are used in M-PES and M-IDR, respectively, so the RECL of M-PES and M-IDR has increased. The synergy between pipeline energy storage and integrated demand response is considered in the M-VESs proposed in the present invention to make full use of the multi-energy complementary characteristics of the integrated energy system. Therefore, the curtailment of wind and solar energy in M-VESs is in the four models. lowest.

Claims (3)

1. A comprehensive energy system optimization scheduling method based on a distributed robust optimization method is characterized by comprising the following steps: the method comprises the following steps:
the method for constructing the virtual energy storage model in the comprehensive energy system comprises the following steps:
Firstly, modeling a comprehensive demand response, wherein the comprehensive demand response comprises a load interruption constraint and a load transfer constraint, and the load interruption constraint in the comprehensive demand response is expressed as follows:
Figure FDA0003695005680000011
in the formula, the superscript t represents the scheduling period t, and the same applies below;
Figure FDA0003695005680000012
is the interrupt power of the electrical load in the integrated demand response;
Figure FDA0003695005680000013
is the maximum proportion of electrical load interruptions;
Figure FDA0003695005680000014
is the electrical load in the integrated energy system;
the load shifting constraint in the integrated demand response is expressed as:
Figure FDA0003695005680000015
Figure FDA0003695005680000016
Figure FDA0003695005680000017
Figure FDA0003695005680000018
in the formula (I), the compound is shown in the specification,
Figure FDA0003695005680000019
is the transferred power of the electrical load in the integrated demand response;
Figure FDA00036950056800000110
and
Figure FDA00036950056800000111
binary coefficients for the shifted-out electric power and the shifted-in electric power, respectively, in the integrated demand response;
Figure FDA00036950056800000112
and
Figure FDA00036950056800000113
respectively, the removed electric power and the moved electric power in the integrated demand response;
Figure FDA00036950056800000114
is the maximum proportion of electrical load transfer;
and then modeling the energy storage of the pipeline of the heat supply network, and modeling the temperature quasi-dynamics and the heat loss of the pipeline in the heat supply network by adopting a node method, wherein the temperature of the outlet hot water of the water supply pipeline p is expressed as follows:
Figure FDA00036950056800000115
Figure FDA00036950056800000116
Figure FDA00036950056800000117
Figure FDA00036950056800000118
in the formula (I), the compound is shown in the specification,
Figure FDA00036950056800000119
and
Figure FDA00036950056800000120
the hot water temperatures at the inlet of the water supply pipe p at times t- (K-1) and t-K, respectively;
Figure FDA00036950056800000121
is the ambient temperature of the heating network; q. q.s p And q is p+1 The mass flow rates of the water supply pipe p and the pipe connected to the outlet of the water supply pipe p, respectively;
Figure FDA0003695005680000021
And τ p Respectively is the K-1 mass block, the K mass block and a water supply pipeline pTime coefficient of mass of mouth; k is a radical of p And l p The temperature loss coefficient and the length of the water supply pipe p, respectively;
the heating network pipeline energy storage is expressed as:
Figure FDA0003695005680000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003695005680000023
the heat supply network pipeline stores energy; c. C w Is the specific heat capacity of water; Δ t is the time interval between two adjacent scheduling times;
modeling the energy storage of the gas supply network pipeline, namely modeling the pipe storage and the average node pressure of the pipeline L in the gas supply network:
Figure FDA0003695005680000024
Figure FDA0003695005680000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003695005680000026
and
Figure FDA0003695005680000027
respectively, the inventory and average node pressure of the pipeline L in the gas supply network; z L Is a pipeline L (ii) a inventory factor of;
Figure FDA0003695005680000028
and
Figure FDA0003695005680000029
the inflow of gas and the gas of the line L in the gas supply network, respectivelyVolume of body outflow;
Figure FDA00036950056800000210
is a collection of pipes in an air supply network;
the gas supply network pipeline energy storage is expressed as
Figure FDA00036950056800000211
In the formula (I), the compound is shown in the specification,
Figure FDA00036950056800000212
the gas supply network pipeline stores energy;
and finally, modeling virtual energy storage in the comprehensive energy system, and defining the virtual energy storage of the electric power, the heating power and the natural gas in the comprehensive energy system as the cooperation among the comprehensive demand response, the heat supply network pipeline energy storage and the air supply network pipeline energy storage based on the model of the comprehensive demand response, the heat supply network pipeline energy storage and the air supply network pipeline energy storage:
Figure FDA00036950056800000213
Figure FDA00036950056800000214
Figure FDA00036950056800000215
In the formula (I), the compound is shown in the specification,
Figure FDA0003695005680000031
and
Figure FDA0003695005680000032
virtual energy storage of electricity, heat and natural gas respectively；
Constructing a fuzzy probability distribution set of the output uncertainty of the distributed renewable power supply in the comprehensive energy system by adopting a Wasserstein distance-based distribution robust optimization method;
constructing a comprehensive energy system distribution robust optimization scheduling model based on the virtual energy storage model and the fuzzy probability distribution set, and solving a comprehensive energy system optimization scheduling strategy based on a distribution robust optimization method, wherein the comprehensive energy system optimization scheduling strategy comprises the following steps:
the power deviation caused by the distributed renewable power source contribution prediction error is distributed to each gas turbine GT, and the actual output power of the ith GT at time t is expressed as:
Figure FDA0003695005680000033
wherein the actual output power and the planned output power of the ith GT are respectively
Figure FDA0003695005680000034
And
Figure FDA0003695005680000035
Figure FDA0003695005680000036
a prediction error for the distributed renewable power source output power;
Figure FDA0003695005680000037
is a column vector with all elements having a value of 1;
Figure FDA0003695005680000038
is a factor in the participation of the ith GT,
Figure FDA0003695005680000039
the objective function of the distributed robust optimization scheduling model of the integrated energy system is to minimize the total operating cost of the integrated energy system, namely:
Figure FDA00036950056800000310
Figure FDA00036950056800000311
Figure FDA00036950056800000312
Figure FDA00036950056800000313
Figure FDA00036950056800000314
Figure FDA00036950056800000315
wherein T is the number of scheduling moments; q. q.s t ＝e T δ t ；N GT Is the number of GT's in the integrated energy system;
Figure FDA00036950056800000316
and
Figure FDA00036950056800000317
the unit price of natural gas and electricity, respectively;
Figure FDA00036950056800000318
And
Figure FDA00036950056800000319
natural gas provided by a gas source and natural gas consumed by the ith GT, respectively;
Figure FDA00036950056800000320
is the power provided by the superior power grid;
Figure FDA00036950056800000321
and
Figure FDA00036950056800000322
is the cost coefficient of the ith GT;
Figure FDA0003695005680000041
and
Figure FDA0003695005680000042
unit prices of load interruption and load transfer in the comprehensive demand response are respectively;
introducing an auxiliary function h (q) t T) linearizing the distributed robust part of the objective function
Figure FDA0003695005680000043
The helper function is as follows:
Figure FDA0003695005680000044
Figure FDA0003695005680000045
according to the strong dual theory, the distribution robust part in the objective function is expressed as
Figure FDA0003695005680000046
Figure FDA0003695005680000047
In the formula, λ t And
Figure FDA0003695005680000048
are all auxiliary variables;
the quadratic constraint is converted into a matrix formula with three additional linear constraints using reconstruction linearization techniques, as follows:
Figure FDA0003695005680000049
in the formula (I), the compound is shown in the specification,
Figure FDA00036950056800000410
is a symmetric matrix in which
Figure FDA00036950056800000411
z t And c t Are all auxiliary variables;
Figure FDA00036950056800000412
Figure FDA00036950056800000413
and
Figure FDA00036950056800000414
are each y t The upper and lower limits of (d);
the comprehensive energy system distribution robust optimization scheduling model has the following constraint conditions:
1) distribution robust opportunity constraint: two equations for the distributed robust opportunity constraint are as follows, the first equation representing the probability that the output power of the ith GT is within its range of at least 1- ε 1,i (ii) a The second formula ensures that the probability that the reserve capacity of the output power of the ith GT satisfies its limit is at least 1-epsilon 2,i ；
Figure FDA0003695005680000051
Figure FDA0003695005680000052
In the formula, omega GT Is a set of GT;
Figure FDA0003695005680000053
and
Figure FDA0003695005680000054
upper and lower limits, respectively, of the ith GT output power;
Figure FDA0003695005680000055
Is the upper limit of the ith GT reserve capacity; epsilon 1,i And ε 2,i Confidence coefficients for the two constraints, respectively;
2) other constraints are: the method comprises the following steps of electric power balance constraint, thermal power balance constraint, natural gas balance constraint, power distribution network power flow constraint, heat supply network power flow constraint and air supply network power flow constraint;
solving the established optimized scheduling model by using a CPLEX solver on a Matlab platform to obtain a comprehensive energy system distribution robust optimized scheduling scheme;
the distributed robust opportunity constraint is of the form:
Figure FDA0003695005680000056
in the formula, N J Is the number of uncertainty constraints;
then, the following CVaR approximation and relaxation method is adopted to linearize the form of distribution robust opportunity constraint;
Figure FDA0003695005680000057
in the formula, Z CVaR Is a linearized distribution robust opportunity constraint set;
Figure FDA0003695005680000058
and
Figure FDA0003695005680000059
are all auxiliary variables.
2. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 1, wherein: the virtual energy storage in the integrated energy system comprises integrated demand response, heat supply network pipeline energy storage and air supply network pipeline energy storage.
3. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 1, wherein:
A distributed robust optimization method based on Wasserstein distance is applied to construct a fuzzy probability distribution set of the output uncertainty of a distributed renewable power supply in a comprehensive energy system, and the fuzzy probability distribution set comprises the following steps:
defining the prediction error of the output of the ith distributed renewable power source in the integrated energy system as delta i ，δ i For random variables, note delta i Has a true probability distribution of
Figure FDA0003695005680000061
Limited historical samples based on prediction error
Figure FDA0003695005680000062
Obtaining an empirical distribution
Figure FDA0003695005680000063
Wherein d is k To represent
Figure FDA0003695005680000064
The Dirac measure of (a);
then by mixing
Figure FDA0003695005680000065
Setting the fuzzy set phi as a center to construct a fuzzy set phi; in the fuzzy set of values phi,
Figure FDA0003695005680000066
and
Figure FDA0003695005680000067
the distance between the two is measured by Wasserstein distance;
for a given tight support space xi and two probability distributions
Figure FDA0003695005680000068
And
Figure FDA0003695005680000069
wasserstein distance
Figure FDA00036950056800000610
Represented by the formula:
Figure FDA00036950056800000611
in the formula (I), the compound is shown in the specification,
Figure FDA00036950056800000612
is to have an empirical distribution
Figure FDA00036950056800000613
A random variable of (a); j is at
Figure FDA00036950056800000614
And
Figure FDA00036950056800000615
a joint distribution which is an edge distribution;
Figure FDA00036950056800000616
is the distance of two random variables;
fuzzy sets
Figure FDA00036950056800000617
Is shown as
Figure FDA00036950056800000618
Fuzzy sets
Figure FDA00036950056800000619
Is regarded as having a radius
Figure FDA00036950056800000620
And are distributed empirically
Figure FDA00036950056800000621
A central Wasserstein ball; wherein
Figure FDA00036950056800000622
Figure FDA00036950056800000623
In the formula (I), the compound is shown in the specification,
Figure FDA00036950056800000624
is delta i The confidence of (2); η is an auxiliary variable;
Figure FDA00036950056800000625
is the average of historical samples of prediction error; n is a radical of sam Is the number of historical samples of prediction error;
Figure FDA00036950056800000626
the result is obtained by a binary search method.
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