CN101325336A

CN101325336A - A Method of Power Flow Matching for Multi-area Power Grid Based on State Estimation with Constraints

Info

Publication number: CN101325336A
Application number: CNA200810117176XA
Authority: CN
Inventors: 吴文传; 张伯明; 蔡斌; 孙宏斌; 吴素农; 曾兵; 万源
Original assignee: JIANGXI POWER DISPATCHING CENTER; Tsinghua University
Current assignee: JIANGXI POWER DISPATCHING CENTER; Tsinghua University
Priority date: 2008-07-25
Filing date: 2008-07-25
Publication date: 2008-12-17
Anticipated expiration: 2028-07-25
Also published as: CN101325336B

Abstract

The invention relates to a multi-area grid power flow matching method based on state estimation with constraints, and belongs to the field of power system scheduling automation. The method includes: the upper and lower power grid dispatching centers generate the internal power grid model and power flow distribution in the region according to the real-time data of the power grid, establish the corresponding external power grid equivalent model, and send the lower level power grid model and power flow data to the upper power grid dispatching center, the dispatching The center connects the upper-level and lower-level power grid models through tie lines or transformers, and merges them into a global power grid model; the model uses a constrained state estimation method to obtain the global power grid power flow distribution. This method can ensure that the power flow distribution of the upper-level power grid in the global power grid model obtained after the multi-regional power grid model is merged remains unchanged, and the boundary power flow mismatch of the upper and lower-level power grids is distributed to the lower-level power grid. The method of the invention ensures the correctness of the online safety analysis and simulation calculation results of the interconnected power grid, and is of great significance for ensuring the safe operation of the power grid.

Description

A Method of Power Flow Matching for Multi-area Power Grid Based on State Estimation with Constraints

技术领域 technical field

本发明涉及一种基于带约束状态估计的多区域电网潮流匹配方法，属于电力系统调度自动化与电网仿真技术领域。The invention relates to a multi-area power flow matching method based on state estimation with constraints, and belongs to the technical field of power system scheduling automation and power grid simulation.

背景技术 Background technique

电网是由多个区域电网互联组成的，是一个整体，事故发生后对电网的影响是全局的。在互联电网中，每个调度中心管辖的电网一般只是大电网的一个部分，调度中心的EMS系统只对管辖电网部分进行建模，对其外部电网用离线做好的等值电网代替，精度很差，也无法适应电网的发展变化，是传统EMS实用化中的难题。The power grid is composed of multiple regional power grids interconnected as a whole, and the impact on the power grid after an accident occurs is global. In the interconnected power grid, the power grid under the jurisdiction of each dispatch center is generally only a part of the large power grid. The EMS system of the dispatch center only models the part of the power grid under its jurisdiction, and replaces the external power grid with an equivalent grid prepared offline. The accuracy is very high. Poor and unable to adapt to the development and changes of the power grid, it is a difficult problem in the practical application of traditional EMS.

为了解决这一问题，通过上、下级电网纵向之间的模型交换，通过模型的合并，在线建立全局电网模型。已有方法把各个分区电网的潮流估计值作为量测，建立全局电网的状态估计模型，从而得到全局电网匹配的潮流分布。但是，这种方法把各分区电网间的潮流失配量分布到各个分区中，不能保证上级电网或需要详细分析的电网的潮流分布在模型合并前后保持不变，因此不能满足实际需求。In order to solve this problem, the global grid model is established online through the vertical model exchange between the upper and lower grids and the combination of models. Existing methods use the estimated power flow of each sub-regional power grid as a measurement to establish a state estimation model of the global power grid, thereby obtaining the matching power flow distribution of the global power grid. However, this method distributes the power flow mismatch between the sub-regional power grids to each sub-region, and cannot guarantee that the power flow distribution of the upper-level power grid or the power grid that needs to be analyzed in detail remains unchanged before and after the model is merged, so it cannot meet the actual needs.

发明内容 Contents of the invention

本发明的目的是提出一种基于带约束状态估计的多区域电网潮流匹配方法，各区域电网在各调度中心建立各自辖区内的电网模型，利用当前电网调度中心之间已经建成的高速数据通信网传送到上级调度中心，上级调度中心通过模型的合并，形成全局电网模型，使电力系统中多区域电网潮流模型在线合并，并保证合并后全局电网模型中上级电网潮流与上级电网实时状态一致，同时使上级电网潮流在合并前后保持不变。The purpose of the present invention is to propose a multi-area grid power flow matching method based on state estimation with constraints. Each regional grid establishes a grid model within its own jurisdiction in each dispatching center, and utilizes the high-speed data communication network that has been built between the current grid dispatching centers. It is transmitted to the upper-level dispatching center, and the upper-level dispatching center forms a global power grid model through the combination of models, so that the multi-regional grid power flow models in the power system can be merged online, and ensure that the upper-level grid power flow in the combined global grid model is consistent with the real-time status of the upper-level grid. Keep the power flow of the upper level grid unchanged before and after the merger.

本发明提出的基于带约束状态估计的多区域电网潮流匹配方法，包括以下步骤：The multi-area power flow matching method based on state estimation with constraints proposed by the present invention includes the following steps:

(1-1)上级电网调度中心根据所管辖电网的实时数据，自动生成本区域内部电网模型和潮流分布，同时建立与该内部电网模型相连接的外部电网等值模型，内部电网模型、外部电网等值模型通过联络线或变压器相互连接形成上级电网模型；(1-1) The upper-level power grid dispatching center automatically generates the internal power grid model and power flow distribution in the region according to the real-time data of the power grid under its jurisdiction, and at the same time establishes an equivalent model of the external power grid connected to the internal power grid model. Equivalent models are connected to each other through tie lines or transformers to form a superior grid model;

(1-2)下级各分区电网调度中心根据所管辖电网的实时数据，自动生成本区域内部电网模型和潮流分布，同时建立与该内部电网模型相连接的外部电网等值模型，内部电网模型、外部电网等值模型通过联络线或变压器相互连接形成下级电网模型，并通过广域网将该下级电网模型和下级电网的潮流数据发送给上级电网调度中心；(1-2) According to the real-time data of the power grid under its jurisdiction, the power grid dispatching center of each lower level automatically generates the internal power grid model and power flow distribution in the region, and at the same time establishes the equivalent model of the external power grid connected to the internal power grid model, the internal power grid model, The equivalent model of the external power grid is connected to each other through tie lines or transformers to form a lower-level power grid model, and the lower-level power grid model and the power flow data of the lower-level power grid are sent to the upper-level power grid dispatching center through the wide area network;

(1-3)上级电网调度中心将上级电网模型和接收到的各下级电网模型通过联络线或变压器相互连接，连接时删除上级电网模型和各下级电网模型中的外部电网等值模型，合并成全局电网模型；(1-3) The upper-level grid dispatching center connects the upper-level grid model and the received lower-level grid models to each other through tie lines or transformers. When connecting, delete the upper-level grid model and the external grid equivalent models in each lower-level grid model, and merge them into Global grid model;

(1-4)利用带约束状态估计方法，估计出上述全局电网模型的潮流。(1-4) Estimate the power flow of the above global power grid model by using the state estimation method with constraints.

上述方法中，利用带约束状态估计方法，估计出上述全局电网模型的潮流的过程，具体包括以下步骤：In the above method, the process of estimating the power flow of the above global power grid model by using the constrained state estimation method specifically includes the following steps:

(2-1)为全局电网构造一个包含潮流等式约束和节点注入不等式约束的加权二乘法状态估计模型：(2-1) Construct a weighted square method state estimation model including power flow equality constraints and node injection inequality constraints for the global power grid:

$min min J J ((V V,, θ θ)) = = \frac{11}{22} {Σ Σ}_{i i = = 11}^{m m} {w w}_{i i} {(({Z Z}_{i i} - - {h h}_{i i} ((V V,, θ θ))))}^{22}$

满足以下约束条件：The following constraints are met:

$P_{ij} = P_{ij}^{0},$ i∈A，j∈A $P_{ij} = P_{ij}^{0},$ i ∈ A, j ∈ A

$Q_{ij} = Q_{ij}^{0},$ i∈A，j∈A $Q_{ij} = Q_{ij}^{0},$ i ∈ A, j ∈ A

P _j＜P_j＜P_j，j∈A P _j ＜ P _j ＜ P _j , j∈A

Q _j＜Q_j＜Q_j，j∈A Q _j ＜ Q _j ＜ Q _j , j∈A

其中，Z_i是上、下级电网模型合并前的状态估计值，包括电网线路或变压器的有功功率P_ij和无功功率Q_ij，母线的电压幅值V_i以及母线的有功注入功率P_i和无功注入功率Q_i，h_i(V，θ)是量测方程，w_i为加权二乘法状态估计中的加权系数，A是上级电网的节点集，A是所有下级电网的节点集，P_ij、P_ij ⁰分别是上、下级电网之间的联络线在上级电网侧的合并后有功功率和合并前有功功率，Q_ij、Q_ij ⁰是上、下级电网之间的联络线在上级电网侧的合并后无功功率和合并前无功功率，P_j、P _j、P_j分别是下级电网节点j的注入有功功率、有功功率下限和有功功率上限，Q_j、Q _j、Q_j分别是下级电网节点j的注入无功功率、无功功率下限和无功功率上限，V和θ分别是电网所有节点的电压幅值和相角；Among them, Z _i is the state estimation value before the combination of the upper and lower power grid models, including the active power P _ij and reactive power Q _ij of the grid lines or transformers, the voltage amplitude V _i of the bus, and the active injected power P _i and Reactive injected power Q _i , h _i (V, θ) is the measurement equation, w _i is the weighting coefficient in the state estimation of the weighted square method, A is the node set of the upper-level power grid, A is the node set of all lower-level power grids, P _ij , P _ij ⁰ are the combined active power and active power before combination of the connection line between the upper and lower power grids on the upper power grid side, and Q _ij , Q _ij ⁰ are the connection lines between the upper and lower power grids in the upper power grid P _j , P _j , and P _j are the injected active power, the lower limit of active power, and the upper limit of active power of the lower-level power grid node j respectively, and Q _j , Q _j , and Q _j are respectively is the injected reactive power, the lower limit of reactive power and the upper limit of reactive power of node j of the lower-level power grid, and V and θ are the voltage amplitude and phase angle of all nodes in the power grid, respectively;

上述量测方程h_i(V，θ)的定义为：The above measurement equation h _i (V, θ) is defined as:

线路或变压器的量测方程为：The measurement equation for a line or transformer is:

$\{\begin{matrix} {P P}_{ij ij} = = {V V}_{i i}^{22} {g g}_{ij ij} - - {V V}_{i i} {V V}_{j j} (({g g}_{ij ij} cos cos {θ θ}_{ij ij} - - {b b}_{ij ij} sin sin {θ θ}_{ij ij})) \\ {Q Q}_{ij ij} = = - - {V V}_{i i}^{22} (({b b}_{ij ij} + + {y the y}_{c c})) - - {V V}_{i i} {V V}_{j j} (({g g}_{ij ij} sin sin {θ θ}_{ij ij} - - {b b}_{ij ij} cos cos {θ θ}_{ij ij})) \end{matrix}$

上式中，P_ij是线路或变压器的有功功率，Q_ij是线路或变压器的无功功率；In the above formula, P _ij is the active power of the line or transformer, and Q _ij is the reactive power of the line or transformer;

全局电网任意母线i的电压量测方程：The voltage measurement equation of any bus i in the global grid:

V_i＝V_i V _i =V _i

全局电网任意母线i的注入量测方程：The injection measurement equation of any bus i in the global grid:

$\{\begin{matrix} {P P}_{i i} = = {V V}_{i i}^{22} {G G}_{ii i} + + {Σ Σ}_{j j &Element; &Element; i i}^{j j &NotEqual; &NotEqual; i i} {V V}_{i i} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) \\ {Q Q}_{i i} = = - - {V V}_{i i}^{22} {B B}_{ii i} + + {Σ Σ}_{j j &Element; &Element; i i}^{j j &NotEqual; &NotEqual; i i} {V V}_{i i} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) \end{matrix}$

上式中，P_i、Q_i是全局电网中任意发电机或负荷i的有功注入功率和无功注入功率；In the above formula, P _i and Q _i are the active and reactive injection power of any generator or load i in the global grid;

(2-2)采用内点法求解上述加权二乘法状态估计模型；(2-2) adopt interior point method to solve above-mentioned weighted square method state estimation model;

(2-3)根据上述求解的全局电网所有节点的电压幅值V和相角θ，得到全局电网的潮流分布。(2-3) According to the voltage amplitude V and phase angle θ of all nodes of the global power grid obtained above, the power flow distribution of the global power grid is obtained.

本发明提出的基于带约束状态估计的多区域电网潮流匹配方法，其特点是：上级电网调度中心和下级各分区电网调度中心分别建立和维护本级别、本区域电网的潮流模型，以符合分级、分区调度的现有管理模式。下级电网调度中心需要将本辖区电网实时潮流模型发送给上级调度中心，上级调度中心收集到下级各分区电网的潮流模型后，将各下级各分区电网模型和上级电网模型合并，形成全局电网模型。放开部分量测的约束，对合并成计算用的全局电网模型进行状态估计，得到上、下级电网匹配的潮流分布。整个过程自动完成，适合大规模互联电网的在线安全分析、调度决策和模拟仿真。因此本发明方法具有以下优点：The multi-area power flow matching method based on state estimation with constraints proposed by the present invention is characterized in that: the upper-level power grid dispatching center and the lower-level power grid dispatching centers of each sub-area respectively establish and maintain the power flow models of this level and the regional power grid, so as to conform to the classification, Existing management mode for partition scheduling. The lower-level power grid dispatching center needs to send the real-time power flow model of the power grid in its jurisdiction to the upper-level dispatching center. After the upper-level dispatching center collects the power flow models of the lower-level sub-regional power grids, it merges the lower-level sub-regional power grid models with the upper-level power grid model to form a global power grid model. Let go of the constraints of partial measurement, and estimate the state of the global power grid model combined into calculations to obtain the matching power flow distribution of the upper and lower power grids. The whole process is completed automatically, which is suitable for online security analysis, scheduling decision-making and simulation of large-scale interconnected power grids. Therefore the inventive method has the following advantages:

1、各级电网调度中心只需维护各自电网潮流模型，不增加维护工作量；1. Power grid dispatching centers at all levels only need to maintain their respective power grid power flow models, without increasing the maintenance workload;

2、通过各分区电网模型的汇总和状态估计，自动实现多区域电网潮流模型的在线合并，形成全局匹配的潮流分布；2. Through the summarization and state estimation of the power grid models in each area, the online merging of the power flow models of the multi-regional power grid is automatically realized to form a globally matching power flow distribution;

3、合并后全局电网潮流模型中上级电网部分和实际情况一致，保证了互联电网安全分析、控制决策和模拟仿真精度，从而确保电网的安全运行。3. After the merger, the part of the upper-level grid in the global grid power flow model is consistent with the actual situation, which ensures the safety analysis, control decision-making and simulation accuracy of the interconnected grid, thereby ensuring the safe operation of the grid.

4、合并后全局电网潮流模型中下级电网的重要发电机和负荷在合并后不会出现大的变化，同时使所有发电机的出力保持在限额范围。4. After the merger, the important generators and loads of the lower-level power grid in the power flow model of the global power grid will not change greatly after the merger, and at the same time, the output of all generators will be kept within the limit range.

附图说明 Description of drawings

图1为本发明的电网潮流模型的在线合并方法示意图；Fig. 1 is the schematic diagram of the online merging method of power grid power flow model of the present invention;

其中，图1(a)是下级电网潮流模型，图1(b)是上级电网潮流模型，图1(c)是合并后的全局电网潮流模型。Among them, Figure 1(a) is the power flow model of the lower-level power grid, Figure 1(b) is the power flow model of the upper-level power grid, and Figure 1(c) is the combined power flow model of the global power grid.

图2为利用本发明方法合并后的全局电网潮流模型示意图。Fig. 2 is a schematic diagram of the global power grid power flow model merged by the method of the present invention.

图1和图2中，1是下级电网调度中心自动生成的本区域内部电网模型，2是连接内部电网模型、外部电网等值模型的联络线或变压器，3是与该内部电网模型相连接的外部电网等值模型，4是与该内部电网模型相连接的外部电网等值模型，5是连接内部电网模型、外部电网等值模型的联络线或变压器，6是上级电网调度中心自动生成的本区域内部电网模型，7是上级电网模型，8是联络线或联络变压器上级电网侧的潮流量测，9是联络变压器，10是联络线路，11是下级电网，12是联络线或联络变压器下级电网侧的潮流量测，13是下级电网中母线的注入潮流量测。In Figure 1 and Figure 2, 1 is the internal grid model of the region automatically generated by the lower-level grid dispatching center, 2 is the tie line or transformer connecting the internal grid model and the equivalent model of the external grid, and 3 is connected to the internal grid model External grid equivalent model, 4 is the external grid equivalent model connected with the internal grid model, 5 is the tie line or transformer connecting the internal grid model and the external grid equivalent model, and 6 is the local grid automatically generated by the superior grid dispatching center Regional internal grid model, 7 is the upper grid model, 8 is the power flow measurement of the tie line or the upper grid side of the tie transformer, 9 is the tie transformer, 10 is the tie line, 11 is the lower power grid, and 12 is the tie line or the lower power grid of the tie transformer side power flow measurement, 13 is the injection power flow measurement of the bus in the lower power grid.

具体实施方式 Detailed ways

以下结合附图和本发明的一个实施例，详细介绍基于带约束状态估计的多区域电网潮流匹配方法。The method for power flow matching of multi-area power grids based on state estimation with constraints will be described in detail below with reference to the accompanying drawings and an embodiment of the present invention.

本发明的具体实现方法如图1所示，包括以下步骤：Concrete implementation method of the present invention as shown in Figure 1, comprises the following steps:

步骤一、如图1(b)所示，上级电网调度中心根据所管辖电网实时数据，利用公知的电网状态估计方法，自动生成本区域内部电网模型6和潮流分布，电网模型6和潮流分布包括电网拓扑结构，电网发电机的有功功率、无功功率或机端母线电压，电网负荷的有功功率和无功功率，电网母线电压和线路的有功功率和无功功率，以及变压器的有功功率、无功功率，变压器分接头档位等；同时建立与该内部电网相连接的外部电网等值模型4，所述内、外部模型通过两者之间实际存在的联络线5相连形成上级电网模型；Step 1. As shown in Figure 1(b), the upper-level power grid dispatching center automatically generates the internal power grid model 6 and power flow distribution in the region according to the real-time data of the power grid under its jurisdiction, and the power flow distribution includes Grid topology, grid generator active power, reactive power or terminal bus voltage, grid load active power and reactive power, grid bus voltage and line active power and reactive power, and transformer active power, reactive power Work power, transformer tap position, etc.; establish the external grid equivalent model 4 connected with the internal grid at the same time, and the internal and external models are connected to form a superior grid model through the connection line 5 that actually exists between the two;

步骤二、如图1(a)所示，下级各分区电网调度中心根据所管辖电网实时数据，利用公知的状态估计方法自动生成本区域内部电网模型1和潮流分布，电网模型1和潮流分布包括电网拓扑结构，电网发电机的有功功率、无功功率或机端母线电压，电网负荷的有功功率和无功功率，电网母线电压和线路的有功功率和无功功率，以及变压器的有功功率、无功功率，变压器分接头档位等，同时建立与该内部电网相连接的外部电网等值模型3，所述内、外部模型通过两者之间实际存在的联络线2相连形成下级电网模型，并通过广域网将所述下级电网模型和潮流数据发送给上级电网调度中心；Step 2. As shown in Figure 1(a), the power grid dispatching center of each sub-district at the lower level uses the known state estimation method to automatically generate the internal power grid model 1 and power flow distribution in the region according to the real-time data of the power grid under its jurisdiction. The power grid model 1 and power flow distribution include Grid topology, grid generator active power, reactive power or terminal bus voltage, grid load active power and reactive power, grid bus voltage and line active power and reactive power, and transformer active power, reactive power Work power, transformer tap position, etc., and establish an external grid equivalent model 3 connected to the internal grid, the internal and external models are connected to form a lower-level grid model through the actual connection line 2 between the two, and Send the lower-level power grid model and power flow data to the upper-level power grid dispatching center through the wide area network;

步骤三、上级电网调度中心接收上述各分区电网调度中心发来的下级电网模型和潮流数据，首先剔除各自电网模型中的外网等值模型(虚线)部分，然后，将所述上级电网模型和各下级电网模型通过它们之间的联络线5对接(联络线2、5表示同一组联络线，这里采用上级电网侧的5)，就可以将上、下级电网模型合并成计算用的全局电网模型，如图1(c)所示，可以看出这个全局电网模型是将图1(a)和图1(b)中模型分别去掉虚线部分区域后通过联络线对接在一起而得到的。Step 3: The upper-level power grid dispatching center receives the lower-level power grid models and power flow data sent by the above-mentioned sub-regional power grid dispatching centers, first removes the external network equivalent model (dotted line) part of the respective power grid models, and then combines the upper-level power grid models and The lower-level power grid models are connected through the tie lines 5 between them (the tie lines 2 and 5 represent the same group of tie lines, and 5 on the upper-level power grid side is used here), and the upper-level and lower-level power grid models can be combined into a global power grid model for calculation , as shown in Figure 1(c), it can be seen that the global power grid model is obtained by removing the dotted line parts of the models in Figure 1(a) and Figure 1(b), respectively, and connecting them together through tie lines.

步骤四、把上、下级电网的各自估计结果作为设备量测，并通过带约束状态估计方法进行全网估计。这种带约束的状态估计方法可以估计得到新的上、下级电网匹配的全网潮流分布，并且可以保证上级电网状态在估计前后保持不变。具体步骤如下：Step 4: Use the respective estimated results of the upper and lower power grids as equipment measurements, and perform network-wide estimation through a constrained state estimation method. This constrained state estimation method can estimate the power flow distribution of the new matching upper and lower power grids, and can ensure that the state of the upper power grid remains unchanged before and after estimation. Specific steps are as follows:

(1)首先构造一个含上、下级电网间的联络线和联络变压器器潮流等式约束和节点注入不等式约束的加权二乘法状态估计模型，也就是求出一组电网状态变量(包括电网所有节点的电压幅值V和相角θ)在满足约束条件下的优化模型：(1) First construct a weighted square method state estimation model including the tie line between the upper and lower power grids and the tie transformer power flow equation constraints and node injection inequality constraints, that is, to find a set of grid state variables (including all nodes of the grid The optimization model of the voltage amplitude V and phase angle θ) satisfying the constraints:

满足以下约束：Satisfy the following constraints:

$P_{ij} = P_{ij}^{0},$ i∈A，j∈A $P_{ij} = P_{ij}^{0},$ i ∈ A, j ∈ A

$Q_{ij} = Q_{ij}^{0},$ i∈A，j∈A(1) $Q_{ij} = Q_{ij}^{0},$ i∈A,j∈A(1)

P _j＜P_j＜P_j，j∈A P _j ＜ P _j ＜ P _j , j∈A

Q _j＜Q_j＜Q_j，j∈A Q _j ＜ Q _j ＜ Q _j , j∈A

量测方程h_i(V，θ)的定义如下：The measurement equation h _i (V, θ) is defined as follows:

线路或变压器的量测方程：Measurement equations for lines or transformers:

$\{\begin{matrix} {P P}_{ij ij} = = {V V}_{i i}^{22} {g g}_{ij ij} - - {V V}_{i i} {V V}_{j j} (({g g}_{ij ij} cos cos {θ θ}_{ij ij} - - {b b}_{ij ij} sin sin {θ θ}_{ij ij})) \\ {Q Q}_{ij ij} = = - - {V V}_{i i}^{22} (({b b}_{ij ij} + + {y the y}_{c c})) - - {V V}_{i i} {V V}_{j j} (({g g}_{ij ij} sin sin {θ θ}_{ij ij} - - {b b}_{ij ij} cos cos {θ θ}_{ij ij})) \end{matrix} - - - - - - ((22))$

V_i＝V_i (3)V _i =V _i (3)

$\{\begin{matrix} {P P}_{i i} = = {V V}_{i i}^{22} {G G}_{ii i} + + {Σ Σ}_{j j &Element; &Element; i i}^{j j &NotEqual; &NotEqual; i i} {V V}_{i i} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) \\ {Q Q}_{i i} = = - - {V V}_{i i}^{22} {B B}_{ii i} + + {Σ Σ}_{j j &Element; &Element; i i}^{j j &NotEqual; &NotEqual; i i} {V V}_{i i} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) \end{matrix} - - - - - - ((44))$

(2)采用内点法求解式(1)代表的带约束的状态估计问题(2) Using the interior point method to solve the constrained state estimation problem represented by formula (1)

对于式(1)可以写成如下非线性规划标准型：For formula (1), it can be written as the following non-linear programming standard form:

minimize f(x)minimize f(x)

subject to h(x)＝0 (5)subject to h(x)＝0 (5)

g≤g(x)≤g g ≤ g(x) ≤ g

其中：x∈R⁽ⁿ⁾，h(x)≡[h₁(x)，…，h_m(x)]^T，g(x)≡[g₁(x)，…，g_r(x)]^T。where: x∈R ⁽ⁿ⁾ , h(x)≡[h ₁ (x),…,h _m (x)] ^T , g(x)≡[g ₁ (x),…,g _r (x) ] ^T.

引入松弛变量(l，u)∈R^(r)，将(5)式变换成带等式约束和简单变量约束的非线性规划形式如下：Introduce the slack variable (l, u)∈R ^(r) , and transform (5) into a nonlinear programming form with equality constraints and simple variable constraints as follows:

minimize f(x)minimize f(x)

subjectto h(x)＝0subjectto h(x)＝0

g(x)-l-g＝0 (6)g(x)-l- g = 0 (6)

g(x)+u-g＝0g(x)+u-g=0

(l，u)≥0(l,u)≥0

定义(6)式的拉格朗日函数为：Define the Lagrangian function of formula (6) as:

$L L ((x x,, l l,, u u;; y the y,, z z,, w w;; \overset{~ ~}{z z},, \overset{~ ~}{w w})) &equiv; &equiv; f f ((x x)) {- - y the y}^{T T} h h ((x x)) - - {z z}^{T T} ((g g ((x x)) - - l l - - \underset{&OverBar; &OverBar;}{g g}))$

$- - {w w}^{T T} ((g g ((x x)) + + u u - - \overset{&OverBar; &OverBar;}{g g})) - - {\overset{~ ~}{z z}}^{T T} l l - - {\overset{~ ~}{w w}}^{T T} u u - - - - - - ((77))$

这里，y∈R^(m)和 $(z, w, \tilde{z}, \tilde{w}) &Element; R^{(r)}$ 是拉格朗日乘子。Here, y∈R ^(m) and $(z, w, \tilde{z}, \tilde{w}) &Element; R^{(r)}$ is the Lagrangian multiplier.

根据Karush-Kuhn-Tucker定理，最优解必须满足如下KKT系统：According to the Karush-Kuhn-Tucker theorem, the optimal solution must satisfy the following KKT system:

${&dtri; &dtri;}_{x x} L L &equiv; &equiv; {&dtri; &dtri;}_{x x} f f ((x x)) - - {&dtri; &dtri;}_{x x} h h ((x x)) y the y - - {&dtri; &dtri;}_{x x} g g ((x x)) ((z z + + w w)) = = 00 - - - - - - ((88))$

${&dtri; &dtri;}_{y the y} L L &equiv; &equiv; h h ((x x)) = = 00 - - - - - - ((99))$

${&dtri; &dtri;}_{z z} L L &equiv; &equiv; g g ((x x)) - - l l - - \underset{&OverBar; &OverBar;}{g g} = = 00 - - - - - - ((1010))$

${&dtri; &dtri;}_{w w} L L &equiv; &equiv; g g ((x x)) + + u u - - \overset{&OverBar; &OverBar;}{g g} = = 00 - - - - - - ((1111))$

${&dtri; &dtri;}_{l l} L L &equiv; &equiv; z z - - \overset{~ ~}{z z} = = 00 - - - - - - ((1212))$

${&dtri; &dtri;}_{u u} L L &equiv; &equiv; w w + + \overset{~ ~}{w w} = = 00 - - - - - - ((1313))$

$L L \overset{~ ~}{Z Z} e e = = 00 - - - - - - ((1414))$

$U u \overset{~ ~}{W W} e e = = 00 - - - - - - ((1515))$

$((l l,, u u)) &GreaterEqual; &Greater Equal; 00,, ((\overset{~ ~}{z z},, \overset{~ ~}{w w})) &GreaterEqual; &Greater Equal; 00,, y the y &NotEqual; &NotEqual; 00 - - - - - - ((1616))$

其中，(L，U，Z，W)∈R^(r×r)依据数学规划中的惯例，表示元素为l，u，z，w的对角线矩阵，e≡[1，…，1]^T∈R^(r)。Among them, (L, U, Z, W)∈R ^(r×r) represents a diagonal matrix whose elements are l, u, z, w according to the convention in mathematical programming, e≡[1,…,1] ^T ∈ R ^(r) .

将(12)(13)式和互补条件(14)(15)式合并，再根据扰动KKT理论，引入扰动参数μ＞0，松弛合并后的互补条件，将(12)-(15)替换为：Combine formulas (12)(13) and complementary conditions (14)(15), and then according to the disturbance KKT theory, introduce a disturbance parameter μ>0, relax the combined complementary conditions, and replace (12)-(15) with :

${&dtri; &dtri;}_{l l}^{μ μ} L L &equiv; &equiv; LZe LZ - - μe μe = = 00 - - - - - - ((1717))$

${&dtri; &dtri;}_{u u}^{μ μ} L L &equiv; &equiv; UWe UW + + μe μe = = 00 - - - - - - ((1818))$

直接应用牛顿法求解上述扰动KKT系统(8)-(11)，(17)-(18)，得到如下修正系统：The above perturbed KKT system (8)-(11), (17)-(18) is solved directly by Newton's method, and the following modified system is obtained:

$(({&dtri; &dtri;}_{x x}^{22} f f ((x x)) - - {&dtri; &dtri;}_{x x}^{22} h h ((x x)) y the y - - {&dtri; &dtri;}_{x x}^{22} g g ((x x)) ((z z + + w w)))) Δx Δx - - - - - - ((1919))$

$- - {&dtri; &dtri;}_{x x} h h ((x x)) Δy Δy - - {&dtri; &dtri;}_{x x} g g ((x x)) ((Δz Δz + + Δw Δw)) = = - - {&dtri; &dtri;}_{x x} {L L}_{00}$

${&dtri; &dtri;}_{x x} h h {((x x))}^{T T} Δx Δx = = - - {&dtri; &dtri;}_{y the y} {L L}_{00} - - - - - - ((2020))$

${&dtri; &dtri;}_{x x} g g {((x x))}^{T T} Δx Δx - - Δl Δl = = - - {&dtri; &dtri;}_{z z} {L L}_{00} - - - - - - ((21 twenty one))$

${&dtri; &dtri;}_{x x} g g {((x x))}^{T T} Δx Δx + + Δu Δu = = - - {&dtri; &dtri;}_{w w} {L L}_{00} - - - - - - ((22 twenty two))$

$ZΔl ZΔl + + LΔz LΔz = = - - {&dtri; &dtri;}_{l l}^{μ μ} {L L}_{00} - - - - - - ((23 twenty three))$

$WΔu WΔu + + UΔw UΔw = = - - {&dtri; &dtri;}_{u u}^{μ μ} {L L}_{00} - - - - - - ((24 twenty four))$

其中， $({&dtri;}_{x} L_{0}, {&dtri;}_{y} L_{0}, {&dtri;}_{z} L_{0}, {&dtri;}_{w} L_{0}, {&dtri;}_{l}^{μ} L_{0}, {&dtri;}_{u}^{μ} L_{0})$ 是扰动KKT系统的残差。

和

是f(x)，h(x)和g(x)的海森矩阵。in,

({&dtri;}_{x} L_{0}, {&dtri;}_{the y} L_{0}, {&dtri;}_{z} L_{0}, {&dtri;}_{w} L_{0}, {&dtri;}_{l}^{μ} L_{0}, {&dtri;}_{u}^{μ} L_{0})

is the residual of the perturbed KKT system.

and

is the Hessian matrix of f(x), h(x) and g(x).

化简(19-24)，消去Δl，Δu，Δz，Δw，得到最终的简约KKT系统如下：Simplify (19-24), eliminate Δl, Δu, Δz, Δw, and get the final reduced KKT system as follows:

其中：in:

$((- - {&dtri; &dtri;}_{x x}^{22} f f ((x x)) + + {&dtri; &dtri;}_{x x}^{22} h h ((x x)) y the y + + {&dtri; &dtri;}_{x x}^{22} g g ((x x)) ((z z + + w w)))) = = {H h}_{g g} + + {H h}_{h h} - - - - - - ((2626))$

$J J ((x x)) &equiv; &equiv; {&dtri; &dtri;}_{x x} h h {((x x))}^{T T} - - - - - - ((2727))$

$- - {&dtri; &dtri;}_{x x} g g ((x x)) (((({U u}^{- - 11} - - {L L}^{- - 11})) μe μe - - - - - - ((2828))$

$+ + {L L}^{- - 11} Z Z ((g g ((x x)) - - l l - - \underset{&OverBar; &OverBar;}{g g})) - - {U u}^{- - 11} W W ((g g ((x x)) + + u u - - \overset{&OverBar; &OverBar;}{g g}))))$

及消去后，Δl，Δu，Δz，Δw的表达式：And after elimination, the expression of Δl, Δu, Δz, Δw:

$Δl Δl = = {&dtri; &dtri;}_{x x} {g g ((x x))}^{T T} Δx Δx + + ((g g ((x x)) - - l l - - \underset{&OverBar; &OverBar;}{g g})) - - - - - - ((2929))$

$Δu Δu = = - - {&dtri; &dtri;}_{x x} g g {((x x))}^{T T} Δx Δx - - ((g g ((x x)) + + u u - - \overset{&OverBar; &OverBar;}{g g})) - - - - - - ((3030))$

$Δz Δz = = - - {L L}^{- - 11} Z Z {&dtri; &dtri;}_{x x} g g {((x x))}^{T T} Δx Δx - - {L L}^{- - 11} ((((LZe LZ - - μe μe)) + + Z Z ((g g ((x x)) - - l l - - \underset{&OverBar; &OverBar;}{g g})))) - - - - - - ((3131))$

$Δw Δw = = {U u}^{- - 11} W W {&dtri; &dtri;}_{x x} {g g ((x x))}^{T T} Δx Δx - - {U u}^{- - 11} ((((UWe UW + + μe μe)) - - W W ((g g ((x x)) + + u u - - \overset{&OverBar; &OverBar;}{g g})))) - - - - - - ((3232))$

(26)式中，H(□)由两部分组成：H_h是f(x)，h(x)和g(x)海森矩阵的线性组合；H_g称作障碍矩阵(Barrier Matrix)。H_g项防止不等式约束g(x)违反它们的双边极限。In formula (26), H(□) consists of two parts: H _h is the linear combination of f(x), h(x) and g(x) Hessian matrices; H _g is called the barrier matrix (Barrier Matrix). The H _g term prevents inequality constraints g(x) from violating their two-sided limits.

由此产生的路径跟踪法内点迭代格式如下：The resulting interior point iteration format of the path tracing method is as follows:

(0)初始化。置k＝0，K_max，中心参数(centering parameter)σ∈(0，1]，收敛精度ε＝10^-6。选择[l，u]^T＞0，[z＞0，w＜0，y＝0]^T，这里，k，K_max分别是迭代计数和最大允许迭代次数；(0) initialization. Set k=0, K _max , centering parameter (centering parameter) σ∈(0, 1], convergence precision ε=10 ^-6 . Choose [l, u] ^T > 0, [z > 0, w < 0, y =0] ^T , here, k, K _max are the iteration count and the maximum allowable iteration number respectively;

(1)如果k＜K_max，继续；否则，打印不收敛；(1) If k<K _max , continue; otherwise, printing does not converge;

(2)计算互补间隙(complementary gap)C_Gap：(2) Calculate the complementary gap (complementary gap) C _Gap :

${C C}_{Gap Gap} &equiv; &equiv; {Σ Σ}_{i i = = 11}^{r r} (({l l}_{i i} {z z}_{i i} - - {u u}_{i i} {w w}_{i i})) - - - - - - ((3333))$

如果C_Gap＜ε，停止，输出最优解；If C _Gap <ε, stop and output the optimal solution;

(3)求解修正系统(25)-(32)，获取修正量[Δx，Δy]，[Δl，Δu]和[Δz，Δw]；(3) Solve the correction system (25)-(32), and obtain the correction amount [Δx, Δy], [Δl, Δu] and [Δz, Δw];

(4)比值检验，确定原始和对偶空间中的最大步长：(4) Ratio test to determine the maximum step size in the original and dual spaces:

${step step}_{P P} = = 0.9995 0.9995 min min {{\underset{i i}{min min} ((\frac{- - {l l}_{i i}}{Δ Δ {l l}_{i i}} : : Δ Δ {l l}_{i i} < < 00;; \frac{- - {u u}_{i i}}{Δ Δ {u u}_{i i}} : : Δ Δ {u u}_{i i} < < 00)),, 11}} - - - - - - ((3434))$

${step step}_{D D.} = = 0.9995 0.9995 min min {{\underset{i i}{min min} ((\frac{- - {z z}_{i i}}{Δ Δ {z z}_{i i}} : : Δ Δ {z z}_{i i} < < 00;; \frac{- - {w w}_{i i}}{Δ Δ {w w}_{i i}} : : Δ Δ {w w}_{i i} > > 00)),, 11}} - - - - - - ((3535))$

i＝1，2，…，ri=1,2,...,r

(5)更新原始和对偶变量：(5) Update the original and dual variables:

$[\begin{matrix} x x \\ l l \\ u u \end{matrix}] = = [\begin{matrix} x x \\ l l \\ u u \end{matrix}] + + {step step}_{P P} [\begin{matrix} Δx Δx \\ Δl Δl \\ Δu Δu \end{matrix}] - - - - - - ((3636))$

$[\begin{matrix} y the y \\ z z \\ w w \end{matrix}] = = [\begin{matrix} y the y \\ z z \\ w w \end{matrix}] + + {step step}_{D D.} [\begin{matrix} Δy Δy \\ Δz Δz \\ Δw Δw \end{matrix}] - - - - - - ((3737))$

(6)k＝k+1，回(1)；(6) k=k+1, back to (1);

(3)通过上一步求出系统的状态变量(包括电网所有节点的电压幅值V和相角θ)，就可以求出全网的潮流分布。由于式(1)中包含了上级电网与下级电网间所有的联络线和联络变压器的有功和无功保持不变的等式约束，同时上级电网的潮流分布在合并前就是收敛的，因此合并后上级电网的潮流分布可以保持不变。另外，下级电网按加权最小二乘的原则把与上级电网的偏差量在本级电网中分布，同时利用式(1)中节点注入的不等式约束适得下级电网重要的发电机和负荷在合并后不会出现大的变化，同时使所有发电机的出力保持在限额范围。(3) By obtaining the state variables of the system (including the voltage amplitude V and phase angle θ of all nodes of the power grid) in the previous step, the power flow distribution of the whole network can be obtained. Since formula (1) contains the equality constraint that the active power and reactive power of all tie lines and tie transformers between the upper-level power grid and the lower-level power grid remain unchanged, and the power flow distribution of the upper-level power grid is convergent before the merger, so after the merger The power flow distribution of the superordinate grid can remain unchanged. In addition, the lower-level power grid distributes the deviation with the upper-level power grid in the current-level power grid according to the principle of weighted least squares, and at the same time uses the inequality constraints of node injection in formula (1) to ensure that the important generators and loads of the lower-level power grid are combined. There will be no major changes, while keeping all generators within limits.

Claims

1. A multi-area grid power flow matching method based on band constraint state estimation, characterized in that the method comprises the following steps:

(1-1) The upper-level power grid dispatching center automatically generates the internal power grid model and power flow distribution in the region according to the real-time data of the power grid under its jurisdiction, and at the same time establishes an equivalent model of the external power grid connected to the internal power grid model. Equivalent models are connected to each other through tie lines or transformers to form a superior grid model;

(1-2) According to the real-time data of the power grid under its jurisdiction, the power grid dispatching center of each lower level automatically generates the internal power grid model and power flow distribution in the region, and at the same time establishes the equivalent model of the external power grid connected to the internal power grid model, the internal power grid model, The equivalent model of the external power grid is connected to each other through tie lines or transformers to form a lower-level power grid model, and the lower-level power grid model and the power flow data of the lower-level power grid are sent to the upper-level power grid dispatching center through the wide area network;

(1-3) The upper-level grid dispatching center connects the upper-level grid model and the received lower-level grid models to each other through tie lines or transformers. When connecting, delete the upper-level grid model and the external grid equivalent models in each lower-level grid model, and merge them into Global grid model;

(1-4) Estimate the power flow of the above global power grid model by using the state estimation method with constraints.

2. The method according to claim 1, characterized in that, the process of estimating the power flow of the above-mentioned global power network model by using a constrained state estimation method in the step (1-4) specifically includes the following steps:

(2-1) Construct a weighted square method state estimation model including power flow equality constraints and node injection inequality constraints for the global power grid:

min min J J ((V V,, θ θ)) = = \frac{11}{22} {Σ Σ}_{i i = = 11}^{m m} {w w}_{i i} {(({Z Z}_{i i} - - {h h}_{i i} ((V V,, θ θ))))}^{22}

The following constraints are met:

P_{ij} = P_{ij}^{0},

i ∈ A, j ∈ A

Q_{ij} = Q_{ij}^{0},

i ∈ A, j ∈ A

P _j ＜ P _j ＜ P _j , j∈A

Q _j ＜ Q _j ＜ Q _j , j∈A

Among them, Z _i is the state estimation value before the combination of the upper and lower power grid models, including the active power P _ij and reactive power Q _ij of the grid lines or transformers, the voltage amplitude V _i of the bus, and the active injected power P _i and Reactive injected power Q _i , h _i (V, θ) is the measurement equation, w _i is the weighting coefficient in the state estimation of the weighted square method, A is the node set of the upper-level power grid, A is the node set of all lower-level power grids, P _ij , P _ij ⁰ are the combined active power and active power before the combination of the tie line between the upper and lower power grids on the upper power grid side, respectively, Q _ij , Q _ij ⁰ are the tie lines between the upper and lower power grids at the upper level The combined reactive power and reactive power before the grid side, P _j , P _j , P _j are the injected active power, the lower limit of active power and the upper limit of active power of the lower-level grid node j respectively, Q _j , Q _j , Q _j are the injected reactive power, the lower limit of reactive power and the upper limit of reactive power of node j of the lower-level power grid, and V and θ are the voltage amplitude and phase angle of all nodes in the power grid, respectively;

The above measurement equation h _i (V, θ) is defined as follows:

Measurement equations for lines or transformers:

\{\begin{matrix} {P P}_{ij ij} {= = V V}_{i i}^{22} {g g}_{ij ij} - - {V V}_{i i} {V V}_{j j} (({g g}_{ij ij} cos cos {θ θ}_{ij ij} - - {b b}_{ij ij} sin sin {θ θ}_{ij ij})) \\ {Q Q}_{ij ij} = = - - {V V}_{i i}^{22} (({b b}_{ij ij} + + {y the y}_{c c})) - - {V V}_{i i} {V V}_{j j} (({g g}_{ij ij} sin sin {θ θ}_{ij ij} - - {b b}_{ij ij} cos cos {θ θ}_{ij ij})) \end{matrix}

In the above formula, P _ij is the active power of the line or transformer, Q _ij is the reactive power of the line or transformer; the voltage measurement equation of any bus i in the global grid:

V _i =V _i

The injection measurement equation of any bus i in the global grid:

\{\begin{matrix} {P P}_{i i} = = {V V}_{i i}^{22} {G G}_{ii i} + + {Σ Σ}_{j j &Element; &Element; i i}^{j j &NotEqual; &NotEqual; i i} {V V}_{i i} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) \\ {Q Q}_{i i} = = - - {V V}_{i i}^{22} {B B}_{ii i} + + {Σ Σ}_{j j &Element; &Element; i i}^{j j &NotEqual; &NotEqual; i i} {V V}_{i i} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) \end{matrix}

In the above formula, P _i and Q _i are the active and reactive injection power of any generator or load i in the global grid;

(2-2) adopt interior point method to solve above-mentioned weighted square method state estimation model;

(2-3) According to the voltage amplitude V and phase angle θ of all nodes of the global power grid obtained above, the power flow distribution of the global power grid is obtained.