CN105528674A - Grid planning method based on stochastic dual dynamic theory - Google Patents

Grid planning method based on stochastic dual dynamic theory Download PDF

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CN105528674A
CN105528674A CN201510882815.1A CN201510882815A CN105528674A CN 105528674 A CN105528674 A CN 105528674A CN 201510882815 A CN201510882815 A CN 201510882815A CN 105528674 A CN105528674 A CN 105528674A
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曾平良
周勤勇
吴志
杨京齐
张小平
代倩
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Jiangsu Electric Power Co Ltd
University of Birmingham
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China Electric Power Research Institute Co Ltd CEPRI
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Abstract

本发明提供一种基于随机对偶动态理论的电网规划方法，包括以下步骤：建立电网规划数学模型；选取电网运行场景；求解电网规划数学模型；对电网运行场景进行校验；采用随机对偶动态理论优化电网规划数学模型。本发明计及负荷不确定性和可再生能源不确定性，考虑可再生能源利用率，使得规划方案能够满足可再生能源接入需求；考虑电网规划在不同场景下的可行性，使得规划方案具有较强鲁棒性；全面考虑N-k安全校验，使得规划方案能够满足安全运行需求；采用SDDP理论建立不确定性情形下的电网规划数学模型；采用Bender分解法求解电网规划数学模型，降低求解难度。

The invention provides a power grid planning method based on stochastic dual dynamic theory, comprising the following steps: establishing a mathematical model of power grid planning; selecting a power grid operating scene; solving the mathematical model of power grid planning; verifying the power grid operating scene; Mathematical model for grid planning. The present invention takes load uncertainty and renewable energy uncertainty into consideration, and considers the utilization rate of renewable energy, so that the planning scheme can meet the demand for renewable energy access; considering the feasibility of power grid planning in different scenarios, the planning scheme has Strong robustness; comprehensive consideration of Nk safety verification, so that the planning scheme can meet the needs of safe operation; use SDDP theory to establish the mathematical model of power grid planning under uncertainty; use Bender decomposition method to solve the mathematical model of power grid planning, reducing the difficulty of solution .

Description

一种基于随机对偶动态理论的电网规划方法A Power Grid Planning Method Based on Stochastic Dual Dynamic Theory

技术领域technical field

本发明属于电网规划技术领域，具体涉及一种基于随机对偶动态理论的电网规划方法。The invention belongs to the technical field of power grid planning, and in particular relates to a power grid planning method based on stochastic dual dynamic theory.

背景技术Background technique

由于负荷和发电容量的逐年增加，需要对电网进行加强以提高其传输容量，优化线路投资成本，并使其满足一定的运行安全约束，这就是电网规划要解决问题。伴随着可再生能源的大规模接入，需要以长距离输送的方式将远离负荷中心的可再生能源输送到负荷中心。由于可再生能源的间歇性，以及长距离输送的困难性，提高了电网规划的复杂度。Due to the increase of load and generation capacity year by year, it is necessary to strengthen the power grid to increase its transmission capacity, optimize line investment costs, and make it meet certain operational safety constraints. This is the problem to be solved by power grid planning. With the large-scale access of renewable energy, it is necessary to transport the renewable energy far away from the load center to the load center in the form of long-distance transmission. Due to the intermittent nature of renewable energy and the difficulty of long-distance transmission, the complexity of grid planning is increased.

在现有的电网规划研究中，越来越多的研究考虑电网规划中的负荷不确定性和可再生能源不确定性。多种方法被用来解决电网规划中的不确定性，其中包括随机对偶动态理论(StochasticDualDynamicProgramming，SDDP)。在文献《Generationexpansionplanningunderuncertaintywithemissionsquotas》(ElectricPowerSystemsResearch,2014,vol.114,pp.78-85)中利用SDDP研究发电规划中的不确定性；在文献《PowerSystemInvestmentPlanningusingStochasticDualDynamicProgramming》(DoctorofPhilosophy,ElectricalandComputerEngineering,UniversityofCanterbury,2008)中采用SDDP方法研究了输电-发电规划问题；在文献《Samplingstrategiesandstoppingcriteriaforstochasticdualdynamicprogramming:acasestudyinlong-termhydrothermalscheduling》(EnergySystems,2011,vol.2,pp.1-31)和文献《StochasticHydro-ThermalSchedulingUnderCO2EmissionsConstraints》(IEEETransactionsonPowerSystems,2012,vol.27pp.58-68)中采用SDDP方法研究了火电-水电调度问题。In the existing grid planning research, more and more studies consider load uncertainty and renewable energy uncertainty in grid planning. A variety of methods are used to solve the uncertainty in power grid planning, including Stochastic Dual Dynamic Programming (SDDP). In the literature "Generationexpansionplanningunderuncertaintywithmissionsquotas" (ElectricPowerSystemsResearch, 2014, vol.114, pp.78-85), SDDP is used to study the uncertainty in power generation planning;研究了输电-发电规划问题；在文献《Samplingstrategiesandstoppingcriteriaforstochasticdualdynamicprogramming:acasestudyinlong-termhydrothermalscheduling》(EnergySystems,2011,vol.2,pp.1-31)和文献《StochasticHydro-ThermalSchedulingUnderCO2EmissionsConstraints》(IEEETransactionsonPowerSystems,2012,vol.27pp.58- 68) adopts SDDP method to study thermal power-hydro power dispatching problem.

在现有电网规划研究中，对于N-k安全校验考虑不足。大多数处理方法为在规划最后阶段进行N-k校验，如果不满足N-k校验，则对相关线路进行加固。这样的处理方法可能得不到最优的规划方案。In the existing power grid planning research, insufficient consideration is given to N-k security verification. Most of the processing methods are to perform N-k verification in the final stage of planning, and if the N-k verification is not satisfied, the relevant lines will be reinforced. Such a processing method may not obtain the optimal planning scheme.

发明内容Contents of the invention

为了克服上述现有技术的不足，本发明提供一种基于随机对偶动态理论的电网规划方法，采用Benders分解法将电网规划阶段分解为电网规划主阶段和电网规划子阶段，并在电网规划主阶段和电网规划子阶段分别对电网规划数学模型进行求解，最终采用随机对偶动态理论优化电网规划数学模型。In order to overcome the deficiencies of the prior art above, the present invention provides a power grid planning method based on stochastic dual dynamic theory, which uses the Benders decomposition method to decompose the power grid planning phase into the main phase of power grid planning and the sub-phase of power grid planning, and in the main phase of power grid planning The mathematical model of power grid planning is solved separately in the sub-stages of power grid planning and power grid planning, and finally the mathematical model of power grid planning is optimized by stochastic dual dynamic theory.

为了实现上述发明目的，本发明采取如下技术方案：In order to realize the above-mentioned purpose of the invention, the present invention takes the following technical solutions:

本发明提供一种基于随机对偶动态理论的电网规划方法，所述方法包括以下步骤：The invention provides a power grid planning method based on stochastic dual dynamic theory, the method comprising the following steps:

步骤1：建立电网规划数学模型；Step 1: Establish a mathematical model for grid planning;

步骤2：选取电网运行场景；Step 2: Select the grid operation scenario;

步骤3：求解电网规划数学模型；Step 3: Solve the mathematical model of grid planning;

步骤4：对电网运行场景进行校验；Step 4: Verify the grid operation scenario;

步骤5：采用随机对偶动态理论优化电网规划数学模型。Step 5: Using stochastic dual dynamic theory to optimize the mathematical model of power grid planning.

所述步骤1中，考虑负荷和可再生能源的不确定性，以线路投资成本和期望运行成本之和最小为目标建立电网规划数学模型，目标函数F表示为：In the step 1, considering the uncertainty of load and renewable energy, the grid planning mathematical model is established with the goal of minimizing the sum of line investment cost and expected operating cost, and the objective function F is expressed as:

目标函数F相应的约束条件如下：The corresponding constraints of the objective function F are as follows:

ΣΣ gg ∈∈ GG ii ,, tt pp gg ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ee ∈∈ EE. ·· ii ff ee ,, dd tt ,, sthe s (( ξξ )) -- ΣΣ ee ∈∈ EE. ii ·· ff ee ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ww ∈∈ WW ii ,, tt pp ww ,, dd tt ,, sthe s (( ξξ )) ++ qq ii ,, dd tt ,, sthe s (( ξξ )) == DD. ii ,, dd tt (( ξξ )) ∀∀ ii ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 22 ))

-- BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ -- ff ee ,, dd tt ,, sthe s (( ξξ )) -- Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 33 ))

BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ ff ee ,, dd tt ,, sthe s (( ξξ )) ++ Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 44 ))

-- ff ‾‾ ee sthe s xx ee tt (( 11 -- hh ~~ ee sthe s )) ≤≤ ff ee ,, dd tt ,, sthe s (( ξξ )) ≤≤ ff ‾‾ ee sthe s xx ee tt (( 11 -- hh ~~ ee sthe s )) ∀∀ ee ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 55 ))

00 ≤≤ pp gg ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ gg tt ∀∀ gg ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 66 ))

σσ ·&Center Dot; ΣΣ ww pp ‾‾ ww ,, dd tt (( ξξ )) ≤≤ ΣΣ ww pp ww ,, dd tt ,, sthe s (( ξξ )) ∀∀ dd ,, ∀∀ tt ,, sthe s ∈∈ SS 00 ,, ∀∀ ξξ ∈∈ ΛΛ -- -- -- (( 77 ))

00 ≤≤ pp ww ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ ww ,, dd tt (( ξξ )) ∀∀ ww ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ∈∈ SS ,, ∀∀ ξξ -- -- -- (( 77 ))

00 ≤≤ qq ii ,, dd tt ,, sthe s (( ξξ )) ≤≤ DD. ii ,, dd tt (( ξξ )) ∀∀ ii ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 99 ))

ΣΣ ii ∈∈ BB qq ii ,, dd tt ,, sthe s (( ξξ )) ≤≤ ϵϵ || sthe s || DD. dd tt (( ξξ )) ∀∀ sthe s ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ ξξ ∈∈ ΛΛ -- -- -- (( 1010 ))

xx ee tt == 11 ∀∀ ee ∈∈ EE. 00 ,, ∀∀ tt -- -- -- (( 1111 ))

xx ee tt -- 11 ≤≤ xx ee tt ,, xx ee tt ∈∈ {{ 00 ,, 11 }} ∀∀ ee ∈∈ EE. \\ EE. 00 ,, ∀∀ tt -- -- -- (( 1212 ))

其中，rt-1表示第t-1年的通胀率，t＝1,2,…,NT，NT表示规划年限；E表示所有线路集合，E0表示现有线路集合；表示第t年线路e的状态；ND表示每年划分的负荷时间段数，d＝1,2,…,ND；Δd表示每个时间段的小时数；Cg表示发电机g的发电成本，g＝1,2,…,Gt，Gt表示第t年的发电机集合；表示计算期望值，ξ表示随机变量的样本，且ξ∈Ξ，Ξ表示所有随机变量的样本集；表示发电机g在第t年第d个时段正常运行、样本ξ下的发电功率；Gi,t表示第t年节点i上的发电机集合；表示发电机g在第t年第d个时段事故s、样本ξ下的发电功率；E·i表示末端为节点i的线路集合，Ei·表示始端为节点i的线路集合；表示线路e在第t年第d个时段事故s、样本ξ下的传输功率；表示可再生能源w在第t年第d个时段事故s、样本ξ下的发电功率，w＝1,2,…,Wi,t，Wi,t表示第t年节点i上的可再生能源集合；表示在第t年第d个时段事故s、样本ξ下节点i的甩负荷量；表示第t年第d个时段、样本ξ下接在节点i上的负荷；Be表示线路e的电抗；ie和je分别表示线路e的始端节点和末端节点；表示第t年第d个时段事故s、样本ξ下的始端节点ie的相角；表示第t年第d个时段事故s、样本ξ下的末端节点je的相角；Me表示常数；表示线路e在事故s下的状态，取0表示正常运行，其取1表示退出运行；表示线路e在事故s下的最大容量；表示发电机g在第t年的发电容量；表示第t年第d个时段、样本ξ下可再生能源w的最大发电功率；σ为给定的可再生能源利用率；|s|表示事故s中发生退出运行的线路个数；ε|s|表示在事故s下允许的甩负荷比例；S表示所有事故集合；S0表示正常运行状态；Λ表示随机变量给定样本集合，ξ∈Λ；表示第t年第d个时段、样本ξ下的负荷；B表示节点集合；inve表示线路e的年投资成本，其表示为：Among them, r t-1 represents the inflation rate in year t-1, t=1,2,...,NT, NT represents the planning period; E represents the set of all lines, and E 0 represents the set of existing lines; Indicates the state of line e in year t; ND indicates the number of load time periods divided each year, d=1,2,...,ND; Δd indicates the number of hours in each time period; C g indicates the power generation cost of generator g, g= 1,2,...,G t , G t represents the set of generators in year t; Indicates to calculate the expected value, ξ indicates the sample of random variables, and ξ∈Ξ, Ξ indicates the sample set of all random variables; Indicates that generator g operates normally in the dth period of year t and generates power under sample ξ; G i,t indicates the set of generators on node i in year t; Indicates the generating power of generator g under accident s and sample ξ in the dth time period of year t; E i represents the line set whose end is node i, and E i means the line set whose start end is node i; Indicates the transmission power of the line e under the accident s and sample ξ in the dth period of the year t; Represents the power generation power of renewable energy w in the dth period of year t under the accident s and sample ξ, w=1,2,...,W i,t , W i,t represents the renewable energy on node i in year t energy collection; Indicates the load shedding of node i under the accident s and sample ξ in the dth period of the year t; Indicates the load connected to node i under the sample ξ in the dth time period of the t-th year; B e indicates the reactance of the line e; i e and j e indicate the start node and end node of the line e respectively; Indicates the phase angle of the start-end node i e under the accident s and the sample ξ in the d-th period of the t-th year; Indicates the phase angle of the end node j e under the accident s and sample ξ in the dth period of the t year; M e represents a constant; Indicates the state of line e under accident s, Take 0 to indicate normal operation, and take 1 to indicate exit operation; Indicates the maximum capacity of line e under accident s; Indicates the generating capacity of generator g in year t; Indicates the maximum power generation power of renewable energy w under the sample ξ in the dth time period of the t-th year; σ is the given renewable energy utilization rate; |s| indicates the number of lines out of operation in the accident s; ε |s | Indicates the allowable load shedding ratio under the accident s; S indicates the set of all accidents; S 0 indicates the normal operation state; Λ indicates the given sample set of random variables, ξ∈Λ; Indicates the load under the sample ξ in the dth period of the t-th year; B indicates the node set; inv e indicates the annual investment cost of the line e, which is expressed as:

inve＝Ce·r(1+r)y/((1+r)y-1)(13)inv e ＝C e ·r(1+r) y /((1+r) y -1)(13)

其中，Ce表示线路e的总投资成本，r表示通胀率，y表示线路成本回收年限。Among them, C e represents the total investment cost of line e, r represents the inflation rate, and y represents the recovery period of the line cost.

所述步骤2中，电网运行场景的选取包括以下两种情况：In the step 2, the selection of power grid operation scenarios includes the following two situations:

1)负荷大、且可再生能源发电功率小的情形下，电网能够将传统发电功率输出给负荷；1) When the load is large and the power generated by renewable energy is small, the power grid can output the traditional power to the load;

2)负荷大、且可再生能源发电功率大的情形下，电网能够将可再生能源发电功率输送给负荷。2) When the load is large and the power generated by renewable energy is large, the power grid can deliver the power generated by renewable energy to the load.

所述步骤3中，先采用Benders分解法将电网规划阶段分解为电网规划主阶段和电网规划子阶段，并在电网规划主阶段和电网规划子阶段分别对电网规划数学模型进行求解。In the step 3, the grid planning phase is decomposed into grid planning main phase and grid planning sub-phase by Benders decomposition method, and the grid planning mathematical model is solved respectively in the grid planning main phase and grid planning sub-phase.

在电网规划主阶段对电网规划数学模型进行求解，包括：Solve the grid planning mathematical model in the main stage of grid planning, including:

以电网规划主阶段中线路投资成本和期望运行成本之和最小为目标，目标函数f1表示为：Taking the minimum sum of line investment cost and expected operating cost in the main stage of grid planning as the goal, the objective function f1 is expressed as:

minmin ff 11 == ΣΣ tt == 11 NN TT rr tt -- 11 ΣΣ ee ∈∈ EE. (( xx ee tt -- xx ee tt -- 11 )) CC ee -- -- -- (( 1414 ))

其中，表示第t-1年线路e的状态；in, Indicates the state of line e in year t-1;

目标函数f1对应的约束条件为式(11)和(12)。The constraints corresponding to the objective function f 1 are formulas (11) and (12).

在电网规划子阶段，根据事故数量的不同，有|s|＝0,1,2,…,k，k表示需要考虑的N-k安全校验的等级，将电网规划子阶段划分为k+1类；具体分为以下两种情况：In the power grid planning sub-stage, according to the number of accidents, there are |s|=0,1,2,...,k, k represents the level of N-k safety verification that needs to be considered, and the power grid planning sub-stage is divided into k+1 categories ; Specifically divided into the following two situations:

1)电网正常运行状态下，|s|＝0，记为SP-0，需要校验在给定场景下，甩负荷和可再生能源利用率能够达到要求；将SP-0划分为SP-0(t，d,ξ)，以甩负荷量和可再生能源利用量之和最小为目标，目标函数f2表示为：1) In the normal operation state of the power grid, |s|=0, which is recorded as SP-0. It needs to be verified that in a given scenario, the load shedding and the utilization rate of renewable energy can meet the requirements; divide SP-0 into SP-0 (t, d, ξ), with the goal of minimizing the sum of load shedding and renewable energy utilization, the objective function f2 is expressed as:

Mm ii nno ff 22 == ΣΣ ii ∈∈ BB qq ii ,, dd tt ,, 00 (( ξξ )) ++ jj dd tt (( ξξ )) -- -- -- (( 1515 ))

目标函数f2对应的约束条件如下： The constraints corresponding to the objective function f2 are as follows:

ΣΣ gg ∈∈ GG ii ,, tt pp gg ,, dd tt ,, 00 (( ξξ )) ++ ΣΣ ee ∈∈ EE. ·· ii ff ee ,, dd tt ,, 00 (( ξξ )) -- ΣΣ ee ∈∈ EE. ii ·· ff ee ,, dd tt ,, 00 (( ξξ )) ++ ΣΣ ww ∈∈ WW ii ,, tt pp ww ,, dd tt ,, 00 (( ξξ )) ++ qq ii ,, dd tt ,, 00 (( ξξ )) == DD. ii ,, dd tt (( ξξ )) ∀∀ ii -- -- -- (( 1616 ))

-- BB ee (( θθ ii ee ,, dd tt ,, 00 (( ξξ )) -- θθ jj ee ,, dd tt ,, 00 (( ξξ )) )) ≤≤ -- ff ee ,, dd tt ,, 00 (( ξξ )) -- Mm ee (( 11 -- xx ~~ ee tt )) ∀∀ ee -- -- -- (( 1717 ))

BB ee (( θθ ii ee ,, dd tt ,, 00 (( ξξ )) -- θθ jj ee ,, dd tt ,, 00 (( ξξ )) )) ≤≤ ff ee ,, dd tt ,, 00 (( ξξ )) ++ Mm ee (( 11 -- xx ~~ ee tt )) ∀∀ ee -- -- -- (( 1818 ))

ff ee ,, dd tt ,, 00 (( ξξ )) ≤≤ ff ‾‾ ee 00 xx ~~ ee tt ∀∀ ee -- -- -- (( 1919 ))

-- ff ee ,, dd tt ,, 00 (( ξξ )) ≤≤ ff ‾‾ ee 00 xx ~~ ee tt ∀∀ ee -- -- -- (( 2020 ))

00 ≤≤ pp gg ,, dd tt ,, 00 (( ξξ )) ≤≤ pp ‾‾ gg tt ∀∀ gg -- -- -- (( 21twenty one ))

σσ ·&Center Dot; ΣΣ ww pp ‾‾ ww ,, dd tt ,, 00 (( ξξ )) ≤≤ ΣΣ ww pp ww ,, dd tt ,, 00 (( ξξ )) ++ jj dd tt (( ξξ )) -- -- -- (( 22twenty two ))

其中，表示在第t年第d个时段正常运行、样本ξ下节点i的甩负荷量；表示第t年第d个时段正常运行、样本ξ下可再生能源w的利用量；表示线路e在第t年第d个时段正常运行、样本ξ下的传输功率；表示可再生能源w在第t年第d个时段正常运行、样本ξ下的发电功率；表示第t年第d个时段正常运行、样本ξ下的始端节点ie的相角；表示第t年第d个时段正常运行、样本ξ下的末端节点je的相角；表示电网规划中第t年线路e的状态；表示线路e正常运行的最大容量；表示第t年第d个时段、样本ξ下可再生能源w正常运行的最大发电功率；in, Indicates the load shedding of node i under sample ξ during normal operation in the dth period of year t; Indicates the utilization of renewable energy w under the sample ξ during normal operation in the dth period of the t-th year; Indicates the transmission power of the line e under the normal operation of the d-th period of the year t under the sample ξ; Indicates the normal operation of renewable energy w in the dth period of year t, and the power generation under the sample ξ; Indicates the phase angle of the start-end node i e under the sample ξ under normal operation in the d-th period of the t-th year; Indicates the phase angle of the terminal node j e under the sample ξ under normal operation in the dth period of the t-th year; Indicates the state of the line e in the t-th year in the power grid planning; Indicates the maximum capacity of line e in normal operation; Indicates the maximum power generation power of the renewable energy w under the normal operation of the sample ξ in the d-th period of the t-th year;

2)电网处于事故状态下，|s|＝k，记为SP-k，将SP-k划分为以甩负荷量最小为目标，目标函数f3表示为：2) When the power grid is in an accident state, |s|=k, denoted as SP-k, and SP-k is divided into Taking the minimum load shedding as the goal, the objective function f3 is expressed as:

Mm ii nno ff 33 == ΣΣ ii ∈∈ BB qq ii ,, dd tt ,, sthe s (( ξξ )) -- -- -- (( 23twenty three ))

目标函数f3对应的约束条件如下：The constraints corresponding to the objective function f3 are as follows:

ΣΣ gg ∈∈ GG ii ,, tt pp gg ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ee ∈∈ EE. ·· ii ff ee ,, dd tt ,, sthe s (( ξξ )) -- ΣΣ ee ∈∈ EE. ii ·&Center Dot; ff ee ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ww ∈∈ WW ii ,, tt pp ww ,, dd tt ,, sthe s (( ξξ )) ++ qq ii ,, dd tt ,, sthe s (( ξξ )) == DD. ii ,, dd tt (( ξξ )) ∀∀ ii -- -- -- (( 24twenty four ))

-- BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ -- ff ee ,, dd tt ,, sthe s (( ξξ )) -- Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2525 ))

BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ ff ee ,, dd tt ,, sthe s (( ξξ )) ++ Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2626 ))

ff ee ,, dd tt ,, sthe s (( ξξ )) ≤≤ ff ‾‾ ee sthe s xx ee ee (( 11 -- hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2727 ))

-- ff ee ,, dd tt ,, sthe s (( ξξ )) ≤≤ ff ‾‾ ee sthe s xx ee tt (( 11 -- hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2828 ))

00 ≤≤ pp gg ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ gg tt ∀∀ gg -- -- -- (( 2929 ))

00 ≤≤ pp ww ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ ww ,, dd tt ∀∀ ww -- -- -- (( 3030 ))

00 ≤≤ qq ii ,, dd tt ,, sthe s (( ξξ )) ≤≤ DD. ii ,, dd tt ∀∀ ii -- -- -- (( 3131 ))

其中，表示第t年第d个时段、可再生能源w的最大发电功率；表示第t年第d个时段、接在节点i上的负荷。in, Indicates the maximum power generation power of renewable energy w in the d-th period of the t-th year; Indicates the load connected to node i in the d-th period of the t-th year.

所述步骤4具体包括以下步骤：Described step 4 specifically comprises the following steps:

步骤4-1：进行甩负荷和可再生能源利用率校验；具体有：Step 4-1: Carry out load shedding and renewable energy utilization rate verification; details include:

电网正常运行状态下，有SP-0(t，d,ξ)，如果电网正常运行状态下甩负荷量和可再生能源利用量之和大于0，则表明存在甩负荷和可再生能源利用量未达到相应比例，即甩负荷和可再生能源利用率未通过校验；In the normal operation state of the power grid, there is SP-0(t, d, ξ). If the sum of the load shedding and the utilization of renewable energy is greater than 0 in the normal operation of the power grid, it indicates that there is load shedding and the utilization of renewable energy is not sufficient. The corresponding ratio is reached, that is, the load shedding and the utilization rate of renewable energy have not passed the verification;

步骤4-2：进行N-k安全校验；具体有：Step 4-2: Carry out N-k security verification; specifically:

电网处于事故状态下，有如果电网处于事故状态下最小负荷量大于允许的甩负荷量，则表明N-k安全校验未通过。When the power grid is in an emergency state, there are If the grid is in an accident state, the minimum load is greater than the allowable load shedding, indicating that the Nk safety check has failed.

所述步骤5具体包括以下步骤：Described step 5 specifically comprises the following steps:

步骤5-1：设置迭代次数ll为0，并设置电网规划子阶段中第ll次迭代时运行成本估算值为0；Step 5-1: Set the number of iterations ll to 0, and set the operating cost estimate at the llth iteration in the grid planning sub-stage is 0;

步骤5-2：选取N个随机变量的样本ξ1,ξ2,...,ξN；Step 5-2: Select N random variable samples ξ 1 , ξ 2 ,...,ξ N ;

步骤5-3：增加迭代次数ll＝ll+1，并计算建设成本与期望运行成本之和的最小值z，有：Step 5-3: Increase the number of iterations ll=ll+1, and calculate the minimum value z of the sum of the construction cost and the expected operating cost, which is:

其中，表示电网规划子阶段中第ll-1次迭代时运行成本估算值，c表示线路建设成本，cT表示c的转置，x表示变量；中间量 表示n1阶段的线路状态集合，A表示矩阵，b表示向量；in, Indicates the estimated operating cost of the ll-1 iteration in the grid planning sub-stage, c represents the line construction cost, c T represents the transposition of c, x represents the variable; the intermediate quantity Represents the line state set of n 1 stage, A represents a matrix, and b represents a vector;

之后更新线路状态xll，设置z的下限zl；Then update the line state x ll and set the lower limit z l of z;

步骤5-4：从ξ1,ξ2,...,ξN中选取M个随机变量的样本ξ1,ξ2,...,ξM，对于当前解xll∈χ，计算电网规划子阶段中的函数其对应的约束条件为Tx+Wy＝h，其中q,h均为向量，qT表示q的转置，W、T为矩阵，y为变量，且y≥0；Step 5-4: Select samples ξ 1 , ξ 2 ,..., ξ M of M random variables from ξ 1 , ξ 2 ,..., ξ N , and calculate the grid planning for the current solution x ll ∈ χ functions in subphases The corresponding constraints are Tx+Wy=h, where q and h are both vectors, q T represents the transposition of q, W and T are matrices, y is a variable, and y≥0;

记电网规划子阶段中函数在不同随机变量的样本下的最优解为θj，且yj表示第j个变量，j＝1,2,…,M，表示qj的转置，qj表示第j个向量；Remember the function in the grid planning sub-stage The optimal solution under samples of different random variables is θ j , and y j represents the jth variable, j=1,2,...,M, Represents the transpose of q j , q j represents the jth vector;

计算z的上限zu和标准方差σu，有：To calculate the upper limit z u and the standard deviation σ u of z, there are:

zz uu == cc TT xx ++ 11 Mm ΣΣ jj == 11 Mm θθ jj -- -- -- (( 3333 ))

σσ uu == 11 Mm ΣΣ jj == 11 Mm (( cc TT xx ++ θθ jj )) 22 -- zz uu 22 -- -- -- (( 3434 ))

如果成立则停止向前推算，其中γα/2为标准正态分布的(1-α)的分位数；if If it is established, stop the forward calculation, where γ α/2 is the (1-α) quantile of the standard normal distribution;

步骤5-5：向后推算，包括：Step 5-5: Extrapolate backwards, including:

对于当前解xll∈χ，以及任意ξ＝ξjj＝1,...,N，计算电网规划子阶段中函数以及函数的对偶函数 对应的约束条件为Tx+Wy＝h，对应的约束条件为WTπ≤q，π、h、q表示向量，πT为π的转置，W、T表示矩阵，WT为W的转置，y为变量，且y≥0；For the current solution x ll ∈ χ, and any ξ=ξ j j=1,...,N, calculate the function in the grid planning sub-stage and the function the dual function of The corresponding constraint condition is Tx+Wy=h, The corresponding constraints are W T π≤q, π, h, and q represent vectors, π T represents the transpose of π, W and T represent matrices, W T represents the transpose of W, y is a variable, and y≥0;

记电网规划子阶段中和的解分别为和 表示Tj的转置，Tj表示第j个向量，πj表示第j个向量；In the grid planning sub-stage and The solutions are and Represents the transpose of T j , T j represents the jth vector, π j represents the jth vector;

令中间量中间量 ρ l l ( x - x l l ) = - 1 N Σ j = 1 N T j T π j , 计算有：Make the middle amount Intermediate amount ρ l l ( x - x l l ) = - 1 N Σ j = 1 N T j T π j , calculate Have:

返回步骤5-3。Return to step 5-3.

与现有技术相比，本发明的有益效果在于：Compared with prior art, the beneficial effect of the present invention is:

1)本发明计及负荷不确定性和可再生能源不确定性，考虑可再生能源利用率，使得规划方案能够满足可再生能源接入需求；1) The present invention takes load uncertainty and renewable energy uncertainty into consideration, and considers the utilization rate of renewable energy, so that the planning scheme can meet the demand for renewable energy access;

2)本发明考虑电网规划在不同场景下的可行性，使得规划方案具有较强鲁棒性；2) The present invention considers the feasibility of power grid planning in different scenarios, so that the planning scheme has strong robustness;

3)本发明全面考虑N-k安全校验，使得规划方案能够满足安全运行需求；3) The present invention fully considers the N-k safety verification, so that the planning scheme can meet the safe operation requirements;

4)本发明采用SDDP理论建立不确定性情形下的电网规划数学模型；4) The present invention adopts SDDP theory to establish the grid planning mathematical model under the uncertainty situation;

5)本发明采用Bender分解法求解电网规划数学模型，降低求解难度。5) The present invention uses the Bender decomposition method to solve the grid planning mathematical model, reducing the difficulty of solving.

附图说明Description of drawings

图1是本发明实施例中采用随机对偶动态理论优化电网规划数学模型流程图。Fig. 1 is a flow chart of optimizing a mathematical model of power grid planning using stochastic dual dynamic theory in an embodiment of the present invention.

具体实施方式detailed description

下面结合附图对本发明作进一步详细说明。The present invention will be described in further detail below in conjunction with the accompanying drawings.

本发明提供一种基于随机对偶动态理论的电网规划方法，所述方法包括以下步骤：The invention provides a power grid planning method based on stochastic dual dynamic theory, the method comprising the following steps:

步骤1：建立电网规划数学模型；Step 1: Establish a mathematical model for grid planning;

步骤2：选取电网运行场景；Step 2: Select the grid operation scenario;

步骤3：求解电网规划数学模型；Step 3: Solve the mathematical model of grid planning;

步骤4：对电网运行场景进行校验；Step 4: Verify the grid operation scenario;

步骤5：采用随机对偶动态理论优化电网规划数学模型。Step 5: Using stochastic dual dynamic theory to optimize the mathematical model of power grid planning.

所述步骤1中，考虑负荷和可再生能源的不确定性，以线路投资成本和期望运行成本之和最小为目标建立电网规划数学模型，目标函数F表示为：In the step 1, considering the uncertainty of load and renewable energy, the mathematical model of power grid planning is established with the goal of minimizing the sum of line investment cost and expected operating cost, and the objective function F is expressed as:

目标函数F相应的约束条件如下：The corresponding constraints of the objective function F are as follows:

ΣΣ gg ∈∈ GG ii ,, tt pp gg ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ee ∈∈ EE. ·· ii ff ee ,, dd tt ,, sthe s (( ξξ )) -- ΣΣ ee ∈∈ EE. ii ·· ff ee ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ww ∈∈ WW ii ,, tt pp ww ,, dd tt ,, sthe s (( ξξ )) ++ qq ii ,, dd tt ,, sthe s (( ξξ )) == DD. ii ,, dd tt (( ξξ )) ∀∀ ii ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 22 ))

-- BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ -- ff ee ,, dd tt ,, sthe s (( ξξ )) -- Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 33 ))

BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ ff ee ,, dd tt ,, sthe s (( ξξ )) ++ Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 44 ))

-- ff ‾‾ ee sthe s xx ee tt (( 11 -- hh ~~ ee sthe s )) ≤≤ ff ee ,, dd tt ,, sthe s (( ξξ )) ≤≤ ff ‾‾ ee sthe s xx ee tt (( 11 -- hh ~~ ee sthe s )) ∀∀ ee ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 55 ))

00 ≤≤ pp gg ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ gg tt ∀∀ gg ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 66 ))

σσ ·&Center Dot; ΣΣ ww pp ‾‾ ww ,, dd tt (( ξξ )) ≤≤ ΣΣ ww pp ww ,, dd tt ,, sthe s (( ξξ )) ∀∀ dd ,, ∀∀ tt ,, sthe s ∈∈ SS 00 ,, ∀∀ ξξ ∈∈ ΛΛ -- -- -- (( 77 ))

00 ≤≤ pp ww ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ ww ,, dd tt (( ξξ )) ∀∀ ww ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ∈∈ SS ,, ∀∀ ξξ -- -- -- (( 88 ))

00 ≤≤ qq ii ,, dd tt ,, sthe s (( ξξ )) ≤≤ DD. ii ,, dd tt (( ξξ )) ∀∀ ii ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ sthe s ,, ∀∀ ξξ -- -- -- (( 99 ))

ΣΣ ii ∈∈ BB qq ii ,, dd tt ,, sthe s (( ξξ )) ≤≤ ϵϵ || sthe s || DD. dd tt (( ξξ )) ∀∀ sthe s ,, ∀∀ dd ,, ∀∀ tt ,, ∀∀ ξξ ∈∈ ΛΛ -- -- -- (( 1010 ))

xx ee tt == 11 ∀∀ ee ∈∈ EE. 00 ,, ∀∀ tt -- -- -- (( 1111 ))

xx ee tt -- 11 ≤≤ xx ee tt ,, xx ee tt ∈∈ {{ 00 ,, 11 }} ∀∀ ee ∈∈ EE. \\ EE. 00 ,, ∀∀ tt -- -- -- (( 1212 ))

其中，rt-1表示第t-1年的通胀率，t＝1,2,…,NT，NT表示规划年限；E表示所有线路集合，E0表示现有线路集合；表示第t年线路e的状态；ND表示每年划分的负荷时间段数，d＝1,2,…,ND；Δd表示每个时间段的小时数；Cg表示发电机g的发电成本，g＝1,2,…,Gt，Gt表示第t年的发电机集合；表示计算期望值，ξ表示随机变量的样本，且ξ∈Ξ，Ξ表示所有随机变量的样本集；表示发电机g在第t年第d个时段正常运行、样本ξ下的发电功率；Gi,t表示第t年节点i上的发电机集合；表示发电机g在第t年第d个时段事故s、样本ξ下的发电功率；E·i表示末端为节点i的线路集合，Ei·表示始端为节点i的线路集合；表示线路e在第t年第d个时段事故s、样本ξ下的传输功率；表示可再生能源w在第t年第d个时段事故s、样本ξ下的发电功率，w＝1,2,…,Wi,t，Wi,t表示第t年节点i上的可再生能源集合；表示在第t年第d个时段事故s、样本ξ下节点i的甩负荷量；表示第t年第d个时段、样本ξ下接在节点i上的负荷；Be表示线路e的电抗；ie和je分别表示线路e的始端节点和末端节点；表示第t年第d个时段事故s、样本ξ下的始端节点ie的相角；表示第t年第d个时段事故s、样本ξ下的末端节点je的相角；Me表示常数；表示线路e在事故s下的状态，取0表示正常运行，其取1表示退出运行；表示线路e在事故s下的最大容量；表示发电机g在第t年的发电容量；表示第t年第d个时段、样本ξ下可再生能源w的最大发电功率；σ为给定的可再生能源利用率；|s|表示事故s中发生退出运行的线路个数；ε|s|表示在事故s下允许的甩负荷比例；S表示所有事故集合；S0表示正常运行状态；Λ表示随机变量给定样本集合，ξ∈Λ；表示第t年第d个时段、样本ξ下的负荷；B表示节点集合；inve表示线路e的年投资成本，其表示为：Among them, r t-1 represents the inflation rate in year t-1, t=1,2,...,NT, NT represents the planning period; E represents the set of all lines, and E 0 represents the set of existing lines; Indicates the state of line e in year t; ND indicates the number of load time periods divided each year, d=1,2,...,ND; Δd indicates the number of hours in each time period; C g indicates the power generation cost of generator g, g= 1,2,...,G t , G t represents the set of generators in year t; Indicates to calculate the expected value, ξ indicates the sample of random variables, and ξ∈Ξ, Ξ indicates the sample set of all random variables; Indicates that generator g operates normally in the dth period of year t and generates power under sample ξ; G i,t indicates the set of generators on node i in year t; Indicates the generating power of generator g under accident s and sample ξ in the dth time period of year t; E i represents the line set whose end is node i, and E i means the line set whose start end is node i; Indicates the transmission power of the line e under the accident s and sample ξ in the dth period of the year t; Represents the power generation power of renewable energy w in the dth period of year t under the accident s and sample ξ, w=1,2,...,W i,t , W i,t represents the renewable energy on node i in year t energy collection; Indicates the load shedding of node i under the accident s and sample ξ in the dth period of the year t; Indicates the load connected to node i under the sample ξ in the dth time period of the t-th year; B e indicates the reactance of the line e; i e and j e indicate the start node and end node of the line e respectively; Indicates the phase angle of the start-end node i e under the accident s and the sample ξ in the d-th period of the t-th year; Indicates the phase angle of the end node j e under the accident s and sample ξ in the dth period of the t year; M e represents a constant; Indicates the state of line e under accident s, Take 0 to indicate normal operation, and take 1 to indicate exit operation; Indicates the maximum capacity of line e under accident s; Indicates the generating capacity of generator g in year t; Indicates the maximum power generation power of renewable energy w under the sample ξ in the dth time period of the t-th year; σ is the given renewable energy utilization rate; |s| indicates the number of lines out of operation in the accident s; ε |s | Indicates the allowable load shedding ratio under the accident s; S indicates the set of all accidents; S 0 indicates the normal operation state; Λ indicates the given sample set of random variables, ξ∈Λ; Indicates the load under the sample ξ in the dth period of the t-th year; B indicates the node set; inv e indicates the annual investment cost of the line e, which is expressed as:

inve＝Ce·r(1+r)y/((1+r)y-1)(13)inv e ＝C e ·r(1+r) y /((1+r) y -1)(13)

其中，Ce表示线路e的总投资成本，r表示通胀率，y表示线路成本回收年限。Among them, C e represents the total investment cost of line e, r represents the inflation rate, and y represents the recovery period of the line cost.

所述步骤2中，电网运行场景的选取包括以下两种情况：In the step 2, the selection of power grid operation scenarios includes the following two situations:

1)负荷大、且可再生能源发电功率小的情形下，电网能够将传统发电功率输出给负荷；1) When the load is large and the power generated by renewable energy is small, the power grid can output the traditional power to the load;

2)负荷大、且可再生能源发电功率大的情形下，电网能够将可再生能源发电功率输送给负荷。2) When the load is large and the power generated by renewable energy is large, the power grid can deliver the power generated by renewable energy to the load.

所述步骤3中，先采用Benders分解法将电网规划阶段分解为电网规划主阶段和电网规划子阶段，并在电网规划主阶段和电网规划子阶段分别对电网规划数学模型进行求解。In the step 3, the grid planning phase is decomposed into grid planning main phase and grid planning sub-phase by Benders decomposition method, and the grid planning mathematical model is solved respectively in the grid planning main phase and grid planning sub-phase.

在电网规划主阶段对电网规划数学模型进行求解，包括：Solve the grid planning mathematical model in the main stage of grid planning, including:

以电网规划主阶段中线路投资成本和期望运行成本之和最小为目标，目标函数f1表示为：Taking the minimum sum of line investment cost and expected operating cost in the main stage of grid planning as the goal, the objective function f1 is expressed as:

minmin ff 11 == ΣΣ tt == 11 NN TT rr tt -- 11 ΣΣ ee ∈∈ EE. (( xx ee tt -- xx ee tt -- 11 )) CC ee -- -- -- (( 1414 ))

其中，表示第t-1年线路e的状态；in, Indicates the state of line e in year t-1;

目标函数f1对应的约束条件为式(11)和(12)。The constraints corresponding to the objective function f 1 are formulas (11) and (12).

在电网规划子阶段，根据事故数量的不同，有|s|＝0,1,2,…,k，k表示需要考虑的N-k安全校验的等级，将电网规划子阶段划分为k+1类；具体分为以下两种情况：In the power grid planning sub-stage, according to the number of accidents, there are |s|=0,1,2,...,k, k represents the level of N-k safety verification that needs to be considered, and the power grid planning sub-stage is divided into k+1 categories ; Specifically divided into the following two situations:

1)电网正常运行状态下，|s|＝0，记为SP-0，需要校验在给定场景下，甩负荷和可再生能源利用率能够达到要求；将SP-0划分为SP-0(t，d,ξ)，以甩负荷量和可再生能源利用量之和最小为目标，目标函数f2表示为：1) In the normal operation state of the power grid, |s|=0, which is recorded as SP-0. It needs to be verified that in a given scenario, the load shedding and the utilization rate of renewable energy can meet the requirements; divide SP-0 into SP-0 (t, d, ξ), with the goal of minimizing the sum of load shedding and renewable energy utilization, the objective function f2 is expressed as:

Mm ii nno ff 22 == ΣΣ ii ∈∈ BB qq ii ,, dd tt ,, 00 (( ξξ )) ++ jj dd tt (( ξξ )) -- -- -- (( 1515 ))

目标函数f2对应的约束条件如下： The constraints corresponding to the objective function f2 are as follows:

ΣΣ gg ∈∈ GG ii ,, tt pp gg ,, dd tt ,, 00 (( ξξ )) ++ ΣΣ ee ∈∈ EE. ·&Center Dot; ii ff ee ,, dd tt ,, 00 (( ξξ )) -- ΣΣ ee ∈∈ EE. ii ·· ff ee ,, dd tt ,, 00 (( ξξ )) ++ ΣΣ ww ∈∈ WW ii ,, tt pp ww ,, dd tt ,, 00 (( ξξ )) ++ qq ii ,, dd tt ,, 00 (( ξξ )) == DD. ii ,, dd tt (( ξξ )) ∀∀ ii -- -- -- (( 1616 ))

-- BB ee (( θθ ii ee ,, dd tt ,, 00 (( ξξ )) -- θθ jj ee ,, dd tt ,, 00 (( ξξ )) )) ≤≤ -- ff ee ,, dd tt ,, 00 (( ξξ )) -- Mm ee (( 11 -- xx ~~ ee tt )) ∀∀ ee -- -- -- (( 1717 ))

BB ee (( θθ ii ee ,, dd tt ,, 00 (( ξξ )) -- θθ jj ee ,, dd tt ,, 00 (( ξξ )) )) ≤≤ ff ee ,, dd tt ,, 00 (( ξξ )) ++ Mm ee (( 11 -- xx ~~ ee tt )) ∀∀ ee -- -- -- (( 1818 ))

ff ee ,, dd tt ,, 00 (( ξξ )) ≤≤ ff ‾‾ ee 00 xx ~~ ee tt ∀∀ ee -- -- -- (( 1919 ))

-- ff ee ,, dd tt ,, 00 (( ξξ )) ≤≤ ff ‾‾ ee 00 xx ~~ ee tt ∀∀ ee -- -- -- (( 2020 ))

00 ≤≤ pp gg ,, dd tt ,, 00 (( ξξ )) ≤≤ pp ‾‾ gg tt ∀∀ gg -- -- -- (( 21twenty one ))

σσ ·· ΣΣ ww pp ‾‾ ww ,, dd tt ,, 00 (( ξξ )) ≤≤ ΣΣ ww pp ww ,, dd tt ,, 00 (( ξξ )) ++ jj dd tt (( ξξ )) -- -- -- (( 22twenty two ))

其中，表示在第t年第d个时段正常运行、样本ξ下节点i的甩负荷量；表示第t年第d个时段正常运行、样本ξ下可再生能源w的利用量；表示线路e在第t年第d个时段正常运行、样本ξ下的传输功率；表示可再生能源w在第t年第d个时段正常运行、样本ξ下的发电功率；表示第t年第d个时段正常运行、样本ξ下的始端节点ie的相角；表示第t年第d个时段正常运行、样本ξ下的末端节点je的相角；表示电网规划中第t年线路e的状态；表示线路e正常运行的最大容量；表示第t年第d个时段、样本ξ下可再生能源w正常运行的最大发电功率；in, Indicates the load shedding of node i under sample ξ during normal operation in the dth period of year t; Indicates the utilization of renewable energy w under the sample ξ during normal operation in the dth period of the t-th year; Indicates the transmission power of the line e under the normal operation of the d-th period of the year t under the sample ξ; Indicates the normal operation of renewable energy w in the dth period of year t, and the power generation under the sample ξ; Indicates the phase angle of the start-end node i e under the sample ξ under normal operation in the d-th period of the t-th year; Indicates the phase angle of the terminal node j e under the sample ξ under normal operation in the dth period of the t-th year; Indicates the state of the line e in the t-th year in the power grid planning; Indicates the maximum capacity of line e in normal operation; Indicates the maximum power generation power of the renewable energy w under the normal operation of the sample ξ in the d-th period of the t-th year;

2)电网处于事故状态下，|s|＝k，记为SP-k，将SP-k划分为以甩负荷量最小为目标，目标函数f3表示为：2) When the power grid is in an accident state, |s|=k, denoted as SP-k, and SP-k is divided into Taking the minimum load shedding as the goal, the objective function f3 is expressed as:

Mm ii nno ff 33 == ΣΣ ii ∈∈ BB qq ii ,, dd tt ,, sthe s (( ξξ )) -- -- -- (( 23twenty three ))

目标函数f3对应的约束条件如下：The constraints corresponding to the objective function f3 are as follows:

ΣΣ gg ∈∈ GG ii ,, tt pp gg ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ee ∈∈ EE. ·· ii ff ee ,, dd tt ,, sthe s (( ξξ )) -- ΣΣ ee ∈∈ EE. ii ·· ff ee ,, dd tt ,, sthe s (( ξξ )) ++ ΣΣ ww ∈∈ WW ii ,, tt pp ww ,, dd tt ,, sthe s (( ξξ )) ++ qq ii ,, dd tt ,, sthe s (( ξξ )) == DD. ii ,, dd tt (( ξξ )) ∀∀ ii -- -- -- (( 24twenty four ))

-- BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ -- ff ee ,, dd tt ,, sthe s (( ξξ )) -- Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2525 ))

BB ee (( θθ ii ee ,, dd tt ,, sthe s (( ξξ )) -- θθ jj ee ,, dd tt ,, sthe s (( ξξ )) )) ≤≤ ff ee ,, dd tt ,, sthe s (( ξξ )) ++ Mm ee (( 11 -- xx ee tt ++ hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2626 ))

ff ee ,, dd tt ,, sthe s (( ξξ )) ≤≤ ff ‾‾ ee sthe s xx ee ee (( 11 -- hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2727 ))

-- ff ee ,, dd tt ,, sthe s (( ξξ )) ≤≤ ff ‾‾ ee sthe s xx ee tt (( 11 -- hh ~~ ee sthe s )) ∀∀ ee -- -- -- (( 2828 ))

00 ≤≤ pp gg ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ gg tt ∀∀ gg -- -- -- (( 2929 ))

00 ≤≤ pp ww ,, dd tt ,, sthe s (( ξξ )) ≤≤ pp ‾‾ ww ,, dd tt ∀∀ ww -- -- -- (( 3030 ))

00 ≤≤ qq ii ,, dd tt ,, sthe s (( ξξ )) ≤≤ DD. ii ,, dd tt ∀∀ ii -- -- -- (( 3131 ))

其中，表示第t年第d个时段、可再生能源w的最大发电功率；表示第t年第d个时段、接在节点i上的负荷。in, Indicates the maximum power generation power of renewable energy w in the d-th period of the t-th year; Indicates the load connected to node i in the d-th period of the t-th year.

所述步骤4具体包括以下步骤：Described step 4 specifically comprises the following steps:

步骤4-1：进行甩负荷和可再生能源利用率校验；具体有：Step 4-1: Carry out load shedding and renewable energy utilization rate verification; details include:

电网正常运行状态下，有SP-0(t，d,ξ)，如果电网正常运行状态下甩负荷量和可再生能源利用量之和大于0，则表明存在甩负荷和可再生能源利用量未达到相应比例，即甩负荷和可再生能源利用率未通过校验；In the normal operation state of the power grid, there is SP-0(t, d, ξ). If the sum of the load shedding and the utilization of renewable energy is greater than 0 in the normal operation of the power grid, it indicates that there is load shedding and the utilization of renewable energy is not sufficient. The corresponding ratio is reached, that is, the load shedding and the utilization rate of renewable energy have not passed the verification;

步骤4-2：进行N-k安全校验；具体有：Step 4-2: Carry out N-k security verification; specifically:

电网处于事故状态下，有如果电网处于事故状态下最小负荷量大于允许的甩负荷量，则表明N-k安全校验未通过。When the power grid is in an emergency state, there are If the grid is in an accident state, the minimum load is greater than the allowable load shedding, indicating that the Nk safety check has failed.

如图1，所述步骤5具体包括以下步骤：As shown in Figure 1, the step 5 specifically includes the following steps:

步骤5-1：设置迭代次数ll为0，并设置电网规划子阶段中第ll次迭代时运行成本估算值为0；Step 5-1: Set the number of iterations ll to 0, and set the operating cost estimate at the llth iteration in the grid planning sub-stage is 0;

步骤5-2：选取N个随机变量的样本ξ1,ξ2,...,ξN；Step 5-2: Select N random variable samples ξ 1 , ξ 2 ,...,ξ N ;

步骤5-3：增加迭代次数ll＝ll+1，并计算建设成本与期望运行成本之和的最小值z，有：Step 5-3: Increase the number of iterations ll=ll+1, and calculate the minimum value z of the sum of the construction cost and the expected operating cost, which is:

其中，表示电网规划子阶段中第ll-1次迭代时运行成本估算值，c表示线路建设成本，cT表示c的转置，x表示变量；中间量 表示n1阶段的线路状态集合，A表示矩阵，b表示向量；in, Indicates the estimated operating cost of the ll-1 iteration in the grid planning sub-stage, c represents the line construction cost, c T represents the transposition of c, x represents the variable; the intermediate quantity Represents the line state set of n 1 stage, A represents a matrix, and b represents a vector;

之后更新线路状态xll，设置z的下限zl；Then update the line state x ll and set the lower limit z l of z;

步骤5-4：向前推算，包括：Steps 5-4: Extrapolate forward, including:

从ξ1,ξ2,...,ξN中选取M个随机变量的样本ξ1,ξ2,...,ξM，对于当前解xll∈χ，计算电网规划子阶段中的函数其对应的约束条件为Tx+Wy＝h，其中q,h均为向量，qT表示q的转置，W、T为矩阵，y为变量，且y≥0；Select M samples of random variables ξ 1 , ξ 2 ,..., ξ M from ξ 1 , ξ 2 ,..., ξ N , and for the current solution x ll ∈ χ, calculate the function in the grid planning sub-stage The corresponding constraints are Tx+Wy=h, where q and h are both vectors, q T represents the transposition of q, W and T are matrices, y is a variable, and y≥0;

记电网规划子阶段中函数在不同随机变量的样本下的最优解为θj，且yj表示第j个变量，j＝1,2,…,M，表示qj的转置，qj表示第j个向量；Remember the function in the grid planning sub-stage The optimal solution under samples of different random variables is θ j , and y j represents the jth variable, j=1,2,...,M, Represents the transpose of q j , q j represents the jth vector;

计算z的上限zu和标准方差σu，有：To calculate the upper limit z u and the standard deviation σ u of z, we have:

zz uu == cc TT xx ++ 11 Mm ΣΣ jj == 11 Mm θθ jj -- -- -- (( 3333 ))

σσ uu == 11 Mm ΣΣ jj == 11 Mm (( cc TT xx ++ θθ jj )) 22 -- zz uu 22 -- -- -- (( 3434 ))

如果成立则停止向前推算，其中γα/2为标准正态分布的(1-α)的分位数；if If it is established, stop the forward calculation, where γ α/2 is the (1-α) quantile of the standard normal distribution;

步骤5-5：向后推算，包括：Step 5-5: Extrapolate backwards, including:

对于当前解xll∈χ，以及任意ξ＝ξjj＝1,...,N，计算电网规划子阶段中函数以及函数的对偶函数 对应的约束条件为Tx+Wy＝h，对应的约束条件为WTπ≤q，π、h、q表示向量，πT为π的转置，W、T表示矩阵，WT为W的转置，y为变量，且y≥0；For the current solution x ll ∈ χ, and any ξ=ξ j j=1,...,N, calculate the function in the grid planning sub-stage and the function the dual function of The corresponding constraint condition is Tx+Wy=h, The corresponding constraints are W T π≤q, π, h, and q represent vectors, π T represents the transpose of π, W and T represent matrices, W T represents the transpose of W, y is a variable, and y≥0;

记电网规划子阶段中和的解分别为和 表示Tj的转置，Tj表示第j个向量，πj表示第j个向量；In the grid planning sub-stage and The solutions are and Represents the transpose of T j , T j represents the jth vector, π j represents the jth vector;

令中间量中间量 ρ l l ( x - x l l ) = - 1 N Σ j = 1 N T j T π j , 计算有：Make the middle amount Intermediate amount ρ l l ( x - x l l ) = - 1 N Σ j = 1 N T j T π j , calculate Have:

返回步骤5-3。Return to step 5-3.

最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，所属领域的普通技术人员参照上述实施例依然可以对本发明的具体实施方式进行修改或者等同替换，这些未脱离本发明精神和范围的任何修改或者等同替换，均在申请待批的本发明的权利要求保护范围之内。Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Those of ordinary skill in the art can still modify or equivalently replace the specific implementation methods of the present invention with reference to the above embodiments. Any modification or equivalent replacement departing from the spirit and scope of the present invention is within the protection scope of the claims of the present invention pending application.

Claims (8)

1. A power grid planning method based on a random dual dynamic theory is characterized in that: the method comprises the following steps:
step 1: establishing a power grid planning mathematical model;
step 2: selecting a power grid operation scene;
and step 3: solving a power grid planning mathematical model;
and 4, step 4: checking a power grid operation scene;
and 5: and optimizing a power grid planning mathematical model by adopting a random dual dynamic theory.
2. The power grid planning method based on the stochastic dual dynamics theory according to claim 1, wherein: in the step 1, the uncertainty of the load and the renewable energy is considered, a power grid planning mathematical model is established by taking the sum of the line investment cost and the expected operation cost as a target, and an objective function F is expressed as:
the corresponding constraints of the objective function F are as follows:
Σ g ∈ G i , t p g , d t , s ( ξ ) + Σ e ∈ E · i f e , d t , s ( ξ ) - Σ e ∈ E i · f e , d t , s ( ξ ) + Σ w ∈ W i , t p w , d t , s ( ξ ) + q i , d t , s ( ξ ) = D i , d t ( ξ ) ∀ i , ∀ d , ∀ t , ∀ s , ∀ ξ - - - ( 2 )
- B e ( θ i e , d t , s ( ξ ) - θ j e , d t , s ( ξ ) ) ≤ - f e , d t , s ( ξ ) - M e ( 1 - x e t + h ~ e s ) ∀ e , ∀ d , ∀ t , ∀ s , ∀ ξ - - - ( 3 )
B e ( θ i e , d t , s ( ξ ) - θ j e , d t , s ( ξ ) ) ≤ f e , d t , s ( ξ ) + M e ( 1 - x e t + h ~ e s ) ∀ e , ∀ d , ∀ t , ∀ s , ∀ ξ - - - ( 4 )
- f ‾ e s x e t ( 1 - h ~ e s ) ≤ f e , d t , s ( ξ ) ≤ f ‾ e s x e t ( 1 - h ~ e s ) ∀ e , ∀ d , ∀ t , ∀ s , ∀ ξ - - - ( 5 )
0 ≤ p g , d t , s ( ξ ) ≤ p ‾ g t ∀ g , ∀ d , ∀ t , ∀ s , ∀ ξ - - - ( 6 )
σ · Σ w p ‾ w , d t ( ξ ) ≤ Σ w p w , d t , s ( ξ ) ∀ d , ∀ t , s ∈ S 0 , ∀ ξ ∈ Λ - - - ( 7 )
0 ≤ p w , d t , s ( ξ ) ≤ p ‾ w , d t ( ξ ) ∀ w , ∀ d , ∀ t , ∀ s ∈ S , ∀ ξ - - - ( 8 )
0 ≤ q i , d t , s ( ξ ) ≤ D i , d t ( ξ ) ∀ i , ∀ d , ∀ t , ∀ s , ∀ ξ - - - ( 9 )
Σ i ∈ B q i , d t , s ( ξ ) ≤ ϵ | s | D d t ( ξ ) ∀ s , ∀ d , ∀ t , ∀ ξ ∈ Λ - - - ( 10 )
x e t = 1 ∀ e ∈ E 0 , ∀ t - - - ( 11 )
x e t - 1 ≤ x e t , x e t ∈ { 0 , 1 } ∀ e ∈ E \ E 0 , ∀ t - - - ( 12 )
wherein r ist-1The swelling rate in the t-1 year is shown, t is 1,2, …, NT and NT show the planned years; e denotes the set of all lines, E0Representing an existing set of lines;indicating the state of the line e in the t year; ND represents the number of load time segments divided per year, d is 1,2, …, ND; Δ d represents the number of hours per time period; cgRepresents the power generation cost of the generator G, G is 1,2, … and Gt，GtRepresents the generator set of the t year;denotes a calculated expected value, ξ denotes samples of random variables, and ξ∈ xi, xi denote a set of samples of all random variables;representing the generated power of the generator G under a sample ξ when the generator G normally operates in the tth period of the yeari,tRepresenting a set of generators at node i of the t year;representing the power generation power of the generator g under the accident s and the sample ξ in the tth period of the t year·iRepresenting a set of lines ending in node i, Ei·Representing a line set with a starting end as a node i;represents the transmission power of line e at the d-th time period of the year, incident s, sample ξ;represents the generated power of renewable energy source W under the d-th time period accident s and the sample ξ in the t year, wherein W is 1,2, … and Wi,t，Wi,tRepresenting a set of renewable energy sources on node i in the t year;representing the load shedding amount of node i at the tth period accident s, sample ξ in the t year;representing the load on node i at the d-th time period of year t, sample ξ, BeRepresents the reactance of line e; i.e. ieAnd jeRespectively representing a starting node and a tail end node of a line e;represents the initial node i under the d period accident s and the sample ξ in the t yeareThe phase angle of (d);represents the end node j under the d period accident s, sample ξ of the t yeareThe phase angle of (d); meRepresents a constant;indicating the state of the line e under the accident s,taking 0 for normal operation and 1 for quitting operation;represents the maximum capacity of line e under accident s;representing the power generation capacity of the generator g in the t year;the method comprises the steps of obtaining a total power of renewable energy sources w under a sample ξ in the ith time period of the t year, wherein the total power is the maximum power generation power of the renewable energy sources w under the sample ξ;|s|indicating the allowable load shedding proportion under the accident s; s represents all accident sets; s0Λ denotes a given sample set of random variables, ξ∈Λ;representing the load under the sample ξ at the d-th period of the year t, B representing the set of nodes, inveRepresents the annual investment cost of line e, expressed as:
inve＝Ce·r(1+r)y/((1+r)y-1)(13)
wherein, CeRepresents the total investment cost of the line e, r represents the percent swelling, and y represents the line cost recovery years.
3. The power grid planning method based on the stochastic dual dynamics theory according to claim 2, wherein: in the step 2, the selection of the power grid operation scene comprises the following two conditions:
1) under the conditions of large load and small power generation power of renewable energy sources, the power grid can output the traditional power generation power to the load;
2) when the load is large and the power generated by the renewable energy source is large, the power grid can transmit the power generated by the renewable energy source to the load.
4. The power grid planning method based on the stochastic dual dynamics theory according to claim 3, wherein: in the step 3, the power grid planning stage is firstly decomposed into a power grid planning main stage and a power grid planning sub-stage by adopting a Benders decomposition method, and the power grid planning mathematical model is solved in the power grid planning main stage and the power grid planning sub-stage respectively.
5. The power grid planning method based on the stochastic dual dynamics theory according to claim 4, wherein: solving the power grid planning mathematical model in the main power grid planning stage, wherein the solving comprises the following steps:
the objective function f is used for minimizing the sum of the line investment cost and the expected operation cost in the main stage of power grid planning1Expressed as:
min f 1 = Σ t = 1 N T r t - 1 Σ e ∈ E ( x e t - x e t - 1 ) C e - - - ( 14 )
wherein,representing the state of the line e in the t-1 year;
objective function f1The corresponding constraints are equations (11) and (12).
6. The power grid planning method based on the stochastic dual dynamics theory according to claim 5, wherein: in a power grid planning sub-stage, according to different accident quantities, the sub-stage of power grid planning is divided into k +1 classes, wherein s is 0,1,2, …, k and k represent the level of N-k safety check to be considered; the following two cases are specifically distinguished:
1) dividing SP-0 into SP-0(t, d, ξ), and taking the minimum sum of load shedding amount and renewable energy utilization amount as the target function f2Expressed as:
M i n f 2 = Σ i ∈ B q i , d t , 0 ( ξ ) + j d t ( ξ ) - - - ( 15 )
objective function f2The corresponding constraints are as follows:
Σ g ∈ G i , t p g , d t , 0 ( ξ ) + Σ e ∈ E · i f e , d t , 0 ( ξ ) - Σ e ∈ E i · f e , d t , 0 ( ξ ) + Σ w ∈ W i , t p w , d t , 0 ( ξ ) + q i , d t , 0 ( ξ ) = D i , d t ( ξ ) ∀ i - - - ( 16 )
- B e ( θ i e , d t , 0 ( ξ ) - θ j e , d t , 0 ( ξ ) ) ≤ - f e , d t , 0 ( ξ ) - M e ( 1 - x ~ e t ) ∀ e - - - ( 17 )
B e ( θ i e , d t , 0 ( ξ ) - θ j e , d t , 0 ( ξ ) ) ≤ f e , d t , 0 ( ξ ) + M e ( 1 - x ~ e t ) ∀ e - - - ( 18 )
f e , d t , 0 ( ξ ) ≤ f ‾ e 0 x ~ e t ∀ e - - - ( 19 )
- f e , d t , 0 ( ξ ) ≤ f ‾ e 0 x ~ e t ∀ e - - - ( 20 )
0 ≤ p g , d t , 0 ( ξ ) ≤ p ‾ g t ∀ g - - - ( 21 )
σ · Σ w p ‾ w , d t , 0 ( ξ ) ≤ Σ w p w , d t , 0 ( ξ ) + j d t ( ξ ) - - - ( 22 )
wherein,represents the load shedding amount of node i under sample ξ for the normal operation at the tth period in the t year;representing the amount of renewable energy w utilization at sample ξ for normal operation at the tth period of time in year t;represents the transmission power at sample ξ for line e operating normally during the tth period of the year;represents the generated power of renewable energy source w under sample ξ in the normal operation of the tth time period of the t year;represents the starting node i under the sample ξ for the d period of normal operation in the t yeareThe phase angle of (d);represents the end node j under sample ξ for the d-th period of the t-th year in normal operationeThe phase angle of (d);representing the state of a circuit e in the t year in power grid planning;represents the maximum capacity of line e for normal operation;represents the maximum generated power of the renewable energy source w under the sample ξ in the ith time period of the t year;
2) when the power grid is in an accident state, | s | ═ k, recorded as SP-k, and dividing SP-k intoTarget function f with minimum load shedding amount as target3Expressed as:
M i n f 3 = Σ i ∈ B q i , d t , s ( ξ ) - - - ( 23 )
objective function f3The corresponding constraints are as follows:
Σ g ∈ G i , t p g , d t , s ( ξ ) + Σ e ∈ E · i f e , d t , s ( ξ ) - Σ e ∈ E i · f e , d t , s ( ξ ) + Σ w ∈ W i , t p w , d t , s ( ξ ) + q i , d t , s ( ξ ) = D i , d t ( ξ ) ∀ i - - - ( 24 )
- B e ( θ i e , d t , s ( ξ ) - θ j e , d t , s ( ξ ) ) ≤ - f e , d t , s ( ξ ) - M e ( 1 - x e t + h ~ e s ) ∀ e - - - ( 25 )
B e ( θ i e , d t , s ( ξ ) - θ j e , d t , s ( ξ ) ) ≤ f e , d t , s ( ξ ) + M e ( 1 - x e t + h ~ e s ) ∀ e - - - ( 26 )
f e , d t , s ( ξ ) ≤ f ‾ e s x e t ( 1 - h ~ e s ) ∀ e - - - ( 27 )
- f e , d t , s ( ξ ) ≤ f ‾ e s x e t ( 1 - h ~ e s ) ∀ e - - - ( 28 )
0 ≤ p g , d t , s ( ξ ) ≤ p ‾ g t ∀ g - - - ( 29 )
0 ≤ p w , d t , s ( ξ ) ≤ p ‾ w , d t ∀ w - - - ( 30 )
0 ≤ q i , d t , s ( ξ ) ≤ D i , d t ∀ i - - - ( 31 )
wherein,represents the maximum generated power of the renewable energy source w in the d-th time period of the t year;representing the load on node i at the d-th time period of year t.
7. The power grid planning method based on the stochastic dual dynamics theory according to claim 6, wherein: the step 4 specifically comprises the following steps:
step 4-1: load shedding and renewable energy utilization rate verification are carried out; the method specifically comprises the following steps:
the method comprises the following steps that SP-0(t, d, xi) exists in a normal operation state of a power grid, if the sum of load shedding amount and renewable energy utilization amount is larger than 0 in the normal operation state of the power grid, it is indicated that the load shedding amount and the renewable energy utilization amount do not reach a corresponding proportion, namely the load shedding amount and the renewable energy utilization rate do not pass verification;
step 4-2: carrying out N-k security check; the method specifically comprises the following steps:
in the event of an accident in the power grid, there areAnd if the minimum load capacity of the power grid in the accident state is larger than the allowed load shedding capacity, the N-k safety check is not passed.
8. The power grid planning method based on the stochastic dual dynamics theory according to claim 1, wherein: the step 5 specifically comprises the following steps:
step 5-1: setting the iteration number ll to be 0, and setting the estimated value of the running cost in the ll iteration in the sub-stage of the power grid planningIs 0;
step 5-2, selecting samples ξ of N random variables1,ξ2,...,ξN；
Step 5-3: increasing the iteration number ll +1, and calculating the minimum value z of the sum of the construction cost and the expected operation cost, wherein the minimum value z comprises the following steps:
wherein,representing the estimated value of the operation cost in the ll-1 iteration in the sub-stage of the power grid planning, c representing the line construction cost, cTDenotes the transpose of c, x denotes the variable; intermediate volume Represents n1A line state set of stages, wherein A represents a matrix and b represents a vector;
then updating the line state xllSetting a lower limit z of zl；
Step 5-4: forward estimation, including:
from ξ1,ξ2,...,ξNIn which samples ξ of M random variables are selected1,ξ2,...,ξMFor the current solution xll∈% for calculating the function in the network planning sub-stageThe corresponding constraint condition is Tx + Wy ═ h, wherein q and h are vectors, and q isTRepresenting the transposition of q, wherein W, T is a matrix, y is a variable and is more than or equal to 0;
recording function in power grid planning sub-phaseThe optimal solution under the samples of different random variables is thetajAnd isyjDenotes the j-th variable, j-1, 2, …,M，denotes qjTranspose of (q)jRepresents the jth vector;
calculating the upper limit z of zuAnd standard deviation σuThe method comprises the following steps:
z u = c T x + 1 M Σ j = 1 m θ j - - - ( 33 )
σ u = 1 M Σ j = 1 M ( c T x + θ j ) 2 - z u 2 - - - ( 34 )
if it is notIf true, stopping forward estimation, wherein gammaα/2Quantile of (1- α) for a standard normal distribution;
step 5-5: backward estimation, including:
for the current solution xll∈ χ, and optionally ξ ═ ξjj 1.. N, calculating a function in a network planning sub-stageAnd a functionDual function of (2) The corresponding constraint is Tx + Wy-h,corresponding constraint is WTPi is less than or equal to q, pi, h and q represent vectors, piTIs a transposition of π, W, T denotes the matrix, WTIs the transposition of W, y is variable and is more than or equal to 0;
in the sub-stage of power grid planningAndare respectively solved asAnd represents TjTranspose of (1), TjDenotes the jth vector, πjRepresents the jth vector;
make an intermediate amountIntermediate volume ρ l l ( x - x l l ) = - 1 N Σ j = 1 N T j T π j , ComputingComprises the following steps:
and returning to the step 5-3.
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