CN113381402B - A Node-Level Decentralized Method for Obtaining Minimum-State Power Flows in AC Power Systems - Google Patents

A Node-Level Decentralized Method for Obtaining Minimum-State Power Flows in AC Power Systems Download PDF

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CN113381402B
CN113381402B CN202110599975.0A CN202110599975A CN113381402B CN 113381402 B CN113381402 B CN 113381402B CN 202110599975 A CN202110599975 A CN 202110599975A CN 113381402 B CN113381402 B CN 113381402B
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彭建春
吴鸣寰
江辉
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Abstract

A node level dispersion method for obtaining minimum state power flow of an alternating current power system belongs to the field of power engineering, and comprises the steps of firstly, establishing a linear asymptotic equation of node power balance according to the known structure and parameters of the alternating current power system; establishing a quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage; establishing a Lagrange function according to a quadratic programming model; and establishing a node level dispersion iteration formula according to a Lagrange function, and then obtaining the minimum state power flow of the alternating current power system according to the node level dispersion iteration formula. The method enables the solving result of the minimum state power flow of the alternating current power system to be unique and globally optimal, and avoids the defect that the global optimality of the solution of the state power flow in the traditional method is not guaranteed; meanwhile, the solution of the minimum state power flow of the alternating current power system is node-level dispersion and power private information of passive load is leaked.

Description

获取交流电力系统最小状态潮流的节点级分散方法A Node-Level Decentralized Method for Obtaining Minimum-State Power Flows in AC Power Systems

技术领域technical field

本申请涉及电力工程领域，尤其涉及一种获取交流电力系统最小状态潮流的节点级分散方法。The present application relates to the field of power engineering, and in particular, to a node-level decentralized method for obtaining the minimum state power flow of an AC power system.

背景技术Background technique

交流电力系统的状态潮流是确定其控制参考量的基础。目前，它要么基于人为给定的平衡节点电压值通过集中求解非线性节点功率平衡方程组获取，虽然获取可靠，但人为给定的平衡节点电压无法保障全系统运行在偏离电压额定值最小的状态，从而导致设备工作效率低的缺陷；它要么通过集中构建和求解以非线性节点功率平衡方程组为约束的优化模型获取，但约束的非线性，导致状态潮流解的全局最优性无保障的缺陷。同时，这些方法需要集中计算，从而需要收集源荷的功率私密数据，导致源荷的私密信息泄露的缺陷。The state flow of the AC power system is the basis for determining its control reference. At present, it is either obtained by centrally solving the nonlinear node power balance equations based on the artificially given voltage value of the balance node. Although the acquisition is reliable, the artificially given voltage of the balance node cannot ensure that the whole system operates in a state with the smallest deviation from the voltage rating. , which leads to the defect of low equipment work efficiency; it is either obtained by centrally building and solving an optimization model constrained by nonlinear node power balance equations, but the nonlinear constraints lead to the unguaranteed global optimality of the state power flow solution. defect. At the same time, these methods require centralized calculation, so the power privacy data of the source and load needs to be collected, which leads to the defect of leakage of the private information of the source and load.

发明内容SUMMARY OF THE INVENTION

本申请实施例提供一种获取交流电力系统最小状态潮流的节点级分散方法，能够解决传统的交流电力系统最小状态潮流的获取方法所存在的设备工作效率低、状态潮流之解的全局最优性无保障以及源荷的功率私密信息泄露的问题。The embodiment of the present application provides a node-level decentralized method for acquiring the minimum state power flow of an AC power system, which can solve the problems of low equipment work efficiency and global optimality of the state power flow solution existing in the traditional method for acquiring the minimum state power flow of an AC power system There is no guarantee and the leakage of power privacy information of the source and load.

本申请实施例的第一方面提供了一种获取交流电力系统最小状态潮流的节点级分散方法，包括：A first aspect of the embodiments of the present application provides a node-level distributed method for obtaining a minimum state power flow of an AC power system, including:

根据已知的交流电力系统的结构和参数，建立节点功率平衡的线性渐近方程；According to the known structure and parameters of the AC power system, establish the linear asymptotic equation of the node power balance;

根据所述线性渐近方程和节点电压，建立交流电力系统最小状态潮流的二次规划模型；According to the linear asymptotic equation and the node voltage, a quadratic programming model of the minimum state power flow of the AC power system is established;

根据所述二次规划模型建立拉格朗日函数；establishing a Lagrangian function according to the quadratic programming model;

根据所述拉格朗日函数建立节点级分散迭代公式，继而根据所述节点级分散迭代公式获取所述交流电力系统的最小状态潮流。A node-level decentralized iteration formula is established according to the Lagrangian function, and then the minimum state power flow of the AC power system is obtained according to the node-level decentralized iteration formula.

本申请实施例的第二方面提供了一种计算机可读存储介质，所述计算机可读存储介质存储有计算机程序，所述计算机程序被处理器执行时实现上述获取交流电力系统最小状态潮流的节点级分散方法的步骤。A second aspect of the embodiments of the present application provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, realizes the above-mentioned node for obtaining the minimum state power flow of an AC power system Steps of the Dispersion Method.

本申请实施例的第三方面提供了一种终端设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，所述处理器执行所述计算机程序时实现上述获取交流电力系统最小状态潮流的节点级分散方法的步骤。A third aspect of the embodiments of the present application provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, when the processor executes the computer program The steps of realizing the above-mentioned node-level decentralized method for obtaining the minimum state power flow of the AC power system.

本申请实施例与现有技术相比存在的有益效果是：由于获取了交流电力系统的最小状态潮流，故提高了设备工作效率；因采用线性渐近方程建立交流电力系统最小状态潮流的二次规划模型，故交流电力系统的最小状态潮流的求解结果唯一和全局最优，避免了状态潮流之解的全局最优性无保障的缺陷；同时，由于建立节点级分散迭代公式，故交流电力系统的最小状态潮流的求解既节点级分散又无源荷的功率私密信息泄露。Compared with the prior art, the embodiments of the present application have the following beneficial effects: because the minimum state power flow of the AC power system is obtained, the working efficiency of the equipment is improved; planning model, so the solution result of the minimum state power flow of the AC power system is unique and globally optimal, avoiding the defect that the global optimality of the solution of the state power flow is not guaranteed; at the same time, due to the establishment of a node-level decentralized iterative formula, the AC power system The solution of the minimum state power flow is both node-level dispersion and passive power leakage of power privacy information.

附图说明Description of drawings

为了更清楚地说明本发明实施例技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见，下面描述中的附图是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to illustrate the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the description of the embodiments. Obviously, the accompanying drawings in the following description are some embodiments of the present invention, which are common in the art. As far as technical personnel are concerned, other drawings can also be obtained based on these drawings without any creative effort.

图1是本申请实施例提供的一种获取交流电力系统最小状态潮流的节点级分散方法的实现流程图；FIG. 1 is a flow chart of the realization of a node-level decentralized method for obtaining the minimum state power flow of an AC power system provided by an embodiment of the present application;

图2是本发明实施例提供的交流电力系统通用模型的结构示意图；2 is a schematic structural diagram of a general model of an AC power system provided by an embodiment of the present invention;

图3是本发明实施例提供的一种终端设备的结构示意图。FIG. 3 is a schematic structural diagram of a terminal device according to an embodiment of the present invention.

具体实施方式Detailed ways

为了使本申请所要解决的技术问题、技术方案及有益效果更加清楚明白，以下结合附图及实施例，对本申请进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本申请，并不用于限定本申请。In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application clearer, the present application will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application.

参见图1，图1是本发明实施例提供的一种获取交流电力系统最小状态潮流的节点级分散方法的实现流程图。如图所示的获取交流电力系统最小状态潮流的节点级分散方法可包括以下步骤：Referring to FIG. 1 , FIG. 1 is a flowchart of an implementation of a node-level distributed method for obtaining a minimum state power flow of an AC power system provided by an embodiment of the present invention. The node-level decentralized method for obtaining the minimum state power flow of an AC power system as shown in the figure may include the following steps:

在步骤101中，根据已知的交流电力系统的结构和参数，建立节点功率平衡的线性渐近方程。In step 101, a linear asymptotic equation of node power balance is established according to the known structure and parameters of the AC power system.

具体实施中，步骤101可以包括步骤A1和步骤B1。In a specific implementation, step 101 may include step A1 and step B1.

在步骤A1中，根据交流电力系统的支路导纳参数、支路两端的电压幅值以及所述支路两端的电压相角，运用电功率定义式并撤分其中的耦合项，建立如下的支路传输功率的线性渐近表达式：In step A1, according to the branch admittance parameter of the AC power system, the voltage amplitude at both ends of the branch, and the voltage phase angle at both ends of the branch, the electric power definition formula is used and the coupling term is removed to establish the following branch The linear asymptotic expression of the transmission power of the channel:

Pij＝αijVi+βijVj+γijθi+δijθj P ij =α ij V i +β ij V j +γ ij θ i +δ ij θ j

Figure BDA0003092387520000031
Figure BDA0003092387520000031

其中，Pij为支路ij传输的有功功率；Qij为支路ij传输的无功功率；i和j均为交流电力系统中节点的编号，且都属于连续自然数的集合{1,2,…,n}；n为交流电力系统中节点的总个数；gij为支路ij的电导参数；bij为支路ij的电纳参数；Vi为节点i的电压幅值变量；θi为节点i的电压相角变量；Vj为节点j的电压幅值变量；θj为节点j的电压相角变量；ξij是按照ξij＝sinθij-θi+θj确定的支路ij的导纳修正系数；αij是按照αij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij/2确定的支路ij的第1修正导纳；βij是按照βij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij/2确定的支路ij的第2修正导纳；γij是按照γij＝-bijViVj/3确定的支路ij的第3修正导纳；δij是按照δij＝bijViVj/3确定的支路ij的第4修正导纳；

Figure BDA0003092387520000041
是按照
Figure BDA0003092387520000042
Figure BDA0003092387520000043
确定的支路ij的第5修正导纳；φij是按照φij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi/3确定的支路ij的第6修正导纳；χij是按照χij＝-gijViVj/3确定的支路ij的第7修正导纳；ψij是按照ψij＝gijViVj/3确定的支路ij的第8修正导纳；Vi和Vj均为标幺值电压。gij和bij为已知的电力系统参数。Among them, P ij is the active power transmitted by the branch ij; Q ij is the reactive power transmitted by the branch ij; i and j are the numbers of the nodes in the AC power system, and both belong to the set of continuous natural numbers {1, 2, ...,n}; n is the total number of nodes in the AC power system; g ij is the conductance parameter of branch ij; b ij is the susceptance parameter of branch ij; V i is the voltage amplitude variable of node i; θ i is the voltage phase angle variable of node i ; V j is the voltage amplitude variable of node j ; θ j is the voltage phase angle variable of node j ; Admittance correction coefficient of path ij ; _ _ _ _ _ _ _ The first modified admittance of the branch ij determined by j ξ ij / 2 ; 3+b ij V i ξ ij /2 determines the second modified admittance of branch ij; γ ij is the third modified admittance of branch ij determined according to γ ij =-b ij V i V j /3; δ ij is the fourth modified admittance of branch ij determined according to δ ij =b ij V i V j /3;
Figure BDA0003092387520000041
is according to
Figure BDA0003092387520000042
Figure BDA0003092387520000043
The 5th modified admittance of the determined branch ij ; φ ij is according to The 6th modified admittance of the branch ij determined by Vi /3; χ ij is the 7th modified admittance of the branch ij determined according to χ ij =-g ij Vi V j /3; ψ ij is according to ψ ij =g ij V i V j /3 determines the 8th modified admittance of branch ij; both V i and V j are per-unit voltages. g ij and b ij are known power system parameters.

通过将非线性的电功率的定义式变换为线性渐近表达式，避免了以非线性方程为约束的优化规划模型难以求解的问题。By transforming the definition of nonlinear electric power into a linear asymptotic expression, the problem that the optimization programming model constrained by nonlinear equations is difficult to solve is avoided.

在步骤B1中，根据线性渐近表达式和交流电力系统的支路连接结构，按Kirchhoff电流定律建立如下的节点i的功率平衡的线性渐近方程：In step B1, according to the linear asymptotic expression and the branch connection structure of the AC power system, the following linear asymptotic equation of the power balance of node i is established according to Kirchhoff's current law:

Figure BDA0003092387520000044
Figure BDA0003092387520000044

Figure BDA0003092387520000045
Figure BDA0003092387520000045

其中，PGi为接于节点i的电源的有功功率参数；QGi为接于节点i的电源的无功功率参数；PDi为接于节点i的负荷的有功功率参数；QDi为接于节点i的负荷的无功功率参数。QGi、QDi、PGi和PDi都为已知的电力系统参数。Among them, P Gi is the active power parameter of the power supply connected to node i; Q Gi is the reactive power parameter of the power supply connected to node i; P Di is the active power parameter of the load connected to node i; Q Di is the active power parameter of the load connected to node i The reactive power parameter of the load at node i. Q Gi , Q Di , P Gi and P Di are all known power system parameters.

上述节点功率平衡的线性渐近方程是关于节点电压幅值和相角的线性方程，且节点功率平衡的线性渐近方程随节点电压幅值和相角逼近真值而逼近按照电功率定义和Kirchhoff电流定律得到的精确的节点功率平衡方程。这正是称上述线性渐近方程为节点功率平衡的线性渐近方程的缘故。The linear asymptotic equation of the node power balance above is a linear equation about the node voltage amplitude and phase angle, and the linear asymptotic equation of the node power balance approaches the true value as the node voltage amplitude and phase angle approach the true value according to the definition of electric power and the Kirchhoff current. The exact nodal power balance equation obtained by the law. This is the reason why the above-mentioned linear asymptotic equation is called the linear asymptotic equation of node power balance.

在步骤102中，根据线性渐近方程和节点电压，建立交流电力系统最小状态潮流的二次规划模型。In step 102, a quadratic programming model of the minimum state power flow of the AC power system is established according to the linear asymptotic equation and the node voltage.

步骤102包括：以线性渐近方程为约束、以节点电压幅值相对1的偏移量的平方和与节点电压相角的平方和之和最小为目标函数，建立如下的交流电力系统最小状态潮流的二次规划模型：Step 102 includes: taking the linear asymptotic equation as a constraint, and taking the minimum sum of the square sum of the offset of the node voltage amplitude relative to 1 and the sum of the square sum of the node voltage phase angle as the objective function, establish the following minimum state power flow of the AC power system: The quadratic programming model of :

Figure BDA0003092387520000051
Figure BDA0003092387520000051

Figure BDA0003092387520000052
Figure BDA0003092387520000052

Figure BDA0003092387520000053
Figure BDA0003092387520000053

其中，编号为n的节点是交流电力系统功率平衡节点。i和j均为交流电力系统中节点的编号，且都属于连续自然数的集合{1,2,…,n}；n为交流电力系统中节点的总个数；gij为支路ij的电导参数；bij为支路ij的电纳参数；Vi为节点i的电压幅值变量；θi为节点i的电压相角变量；Vj为节点j的电压幅值变量；θj为节点j的电压相角变量；ξij是按照ξij＝sinθij-θi+θj确定的支路ij的导纳修正系数；αij是按照αij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij/2确定的支路ij的第1修正导纳；βij是按照βij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij/2确定的支路ij的第2修正导纳；γij是按照γij＝-bijViVj/3确定的支路ij的第3修正导纳；δij是按照δij＝bijViVj/3确定的支路ij的第4修正导纳；

Figure BDA0003092387520000054
是按照
Figure BDA0003092387520000055
Figure BDA0003092387520000056
确定的支路ij的第5修正导纳；φij是按照φij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi/3确定的支路ij的第6修正导纳；χij是按照χij＝-gijViVj/3确定的支路ij的第7修正导纳；ψij是按照ψij＝gijViVj/3确定的支路ij的第8修正导纳；Vi和Vj均为标幺值电压。PGi为接于节点i的电源的有功功率参数；QGi为接于节点i的电源的无功功率参数；PDi为接于节点i的负荷的有功功率参数；QDi为接于节点i的负荷的无功功率参数。gij、bij、QGi、QDi、PGi和PDi都为已知的电力系统参数。Among them, the node numbered n is the power balance node of the AC power system. i and j are the numbers of nodes in the AC power system, and both belong to the set of continuous natural numbers {1,2,…,n}; n is the total number of nodes in the AC power system; g ij is the conductance of the branch ij parameter; b ij is the susceptance parameter of branch ij; V i is the voltage amplitude variable of node i; θ i is the voltage phase angle variable of node i; V j is the voltage amplitude variable of node j ; The voltage phase angle variable of j; ξ ij is the admittance correction coefficient of branch ij determined according to ξ ij = sinθ ij -θ i +θ j ; α ij is according to α ij =g ij V i -g ij cosθ ij V j /2-b ij V j θ i /3+b ij V j θ j /3-b ij V j ξ ij /2 determines the first modified admittance of branch ij; β ij is based on β ij =- b ij V i θ i /3-V i g ij cosθ ij /2-b ij V i θ j /3+b ij V i ξ ij /2 determines the second modified admittance of branch ij; γ ij is The third modified admittance of branch ij determined according to γ ij =-b ij V i V j /3; δ ij is the fourth modified derivation of branch ij determined according to δ ij =b ij V i V j /3 accept;
Figure BDA0003092387520000054
is according to
Figure BDA0003092387520000055
Figure BDA0003092387520000056
The 5th modified admittance of the determined branch ij ; φ ij is according to The 6th modified admittance of the branch ij determined by Vi /3; χ ij is the 7th modified admittance of the branch ij determined according to χ ij =-g ij Vi V j /3; ψ ij is according to ψ ij =g ij V i V j /3 determines the 8th modified admittance of branch ij; both V i and V j are per-unit voltages. P Gi is the active power parameter of the power supply connected to node i; Q Gi is the reactive power parameter of the power supply connected to node i; P Di is the active power parameter of the load connected to node i; Q Di is the active power parameter of the load connected to node i The reactive power parameters of the load. g ij , b ij , Q Gi , Q Di , P Gi and P Di are all known power system parameters.

通过上述二次规划模型，在满足节点功率平衡的线性渐近方程约束下，既实现节点电压幅值变化平稳，又使节点电压相角最小。Through the above quadratic programming model, under the constraints of the linear asymptotic equation satisfying the node power balance, the node voltage amplitude changes smoothly and the node voltage phase angle is minimized.

上述二次规划模型中目标函数的二次项系数都大于零，故是凸函数，约束条件是线性等式，因此是凸二次规划。按最优化理论，它的局部最优解唯一且是全局最优解。因此，二次规划模型的拉格朗日函数的驻点就是唯一的全局最优解。The quadratic coefficients of the objective function in the above quadratic programming model are all greater than zero, so it is a convex function, and the constraint condition is a linear equation, so it is a convex quadratic programming. According to optimization theory, its local optimal solution is unique and global optimal solution. Therefore, the stationary point of the Lagrangian function of the quadratic programming model is the only global optimal solution.

在步骤103中，根据二次规划模型建立拉格朗日函数。In step 103, a Lagrangian function is established according to the quadratic programming model.

步骤103包括：根据二次规划模型，按拉格朗日函数的定义建立如下的拉格朗日函数。Step 103 includes: establishing the following Lagrangian function according to the definition of the Lagrangian function according to the quadratic programming model.

Figure BDA0003092387520000061
Figure BDA0003092387520000061

其中，

Figure BDA0003092387520000062
是拉格朗日函数；λi为对应节点i的有功功率平衡方程的拉格朗日乘子；ξi为对应节点i的无功功率平衡方程的拉格朗日乘子；编号为n的节点是交流电力系统功率平衡节点。i和j均为交流电力系统中节点的编号，且都属于连续自然数的集合{1,2,…,n}；n为交流电力系统中节点的总个数；gij为支路ij的电导参数；bij为支路ij的电纳参数；Vi为节点i的电压幅值变量；θi为节点i的电压相角变量；Vj为节点j的电压幅值变量；θj为节点j的电压相角变量；ξij是按照ξij＝sinθij-θi+θj确定的支路ij的导纳修正系数；αij是按照αij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij/2确定的支路ij的第1修正导纳；βij是按照βij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij/2确定的支路ij的第2修正导纳；γij是按照γij＝-bijViVj/3确定的支路ij的第3修正导纳；δij是按照δij＝bijViVj/3确定的支路ij的第4修正导纳；
Figure BDA0003092387520000063
是按照
Figure BDA0003092387520000064
Figure BDA0003092387520000065
确定的支路ij的第5修正导纳；φij是按照φij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi/3确定的支路ij的第6修正导纳；χij是按照χij＝-gijViVj/3确定的支路ij的第7修正导纳；ψij是按照ψij＝gijViVj/3确定的支路ij的第8修正导纳；Vi和Vj均为标幺值电压。Pti为接于节点i的电源的有功功率参数；QGi为接于节点i的电源的无功功率参数；PDi为接于节点i的负荷的有功功率参数；QDi为接于节点i的负荷的无功功率参数。gij、bij、QGi、QDi、PGi和PDi都为已知的电力系统参数。in,
Figure BDA0003092387520000062
is the Lagrangian function; λ i is the Lagrangian multiplier of the active power balance equation corresponding to node i; ξ i is the Lagrangian multiplier of the reactive power balance equation corresponding to node i; A node is an AC power system power balancing node. i and j are the numbers of nodes in the AC power system, and both belong to the set of continuous natural numbers {1,2,…,n}; n is the total number of nodes in the AC power system; g ij is the conductance of the branch ij parameter; b ij is the susceptance parameter of branch ij; V i is the voltage amplitude variable of node i; θ i is the voltage phase angle variable of node i; V j is the voltage amplitude variable of node j ; The voltage phase angle variable of j; ξ ij is the admittance correction coefficient of branch ij determined according to ξ ij = sinθ ij -θ i +θ j ; α ij is according to α ij =g ij V i -g ij cosθ ij V j /2-b ij V j θ i /3+b ij V j θ j /3-b ij V j ξ ij /2 determines the first modified admittance of branch ij; β ij is based on β ij =- b ij V i θ i /3-V i g ij cosθ ij /2-b ij V i θ j /3+b ij V i ξ ij /2 determines the second modified admittance of branch ij; γ ij is The third modified admittance of branch ij determined according to γ ij =-b ij V i V j /3; δ ij is the fourth modified derivation of branch ij determined according to δ ij =b ij V i V j /3 accept;
Figure BDA0003092387520000063
is according to
Figure BDA0003092387520000064
Figure BDA0003092387520000065
The 5th modified admittance of the determined branch ij ; φ ij is according to The 6th modified admittance of the branch ij determined by Vi /3; χ ij is the 7th modified admittance of the branch ij determined according to χ ij =-g ij Vi V j /3; ψ ij is according to ψ ij =g ij V i V j /3 determines the 8th modified admittance of branch ij; both V i and V j are per-unit voltages. P ti is the active power parameter of the power supply connected to node i; Q Gi is the reactive power parameter of the power supply connected to node i; P Di is the active power parameter of the load connected to node i; Q Di is the active power parameter of the load connected to node i The reactive power parameters of the load. g ij , b ij , Q Gi , Q Di , P Gi and P Di are all known power system parameters.

在步骤104中，根据拉格朗日函数建立节点级分散迭代公式，继而根据节点级分散迭代公式获取交流电力系统的最小状态潮流。In step 104, a node-level decentralized iteration formula is established according to the Lagrangian function, and then the minimum state power flow of the AC power system is obtained according to the node-level decentralized iteration formula.

具体实施中，步骤104可以包括步骤A2和步骤B2。In a specific implementation, step 104 may include step A2 and step B2.

在步骤A2中，根据拉格朗日函数，按驻点的定义建立如下的驻点方程组：In step A2, according to the Lagrangian function, the following stationary point equations are established according to the definition of stationary point:

Figure BDA0003092387520000071
Figure BDA0003092387520000071

其中，

Figure BDA0003092387520000072
是拉格朗日函数；λi为对应节点i的有功功率平衡方程的拉格朗日乘子；ξi为对应节点i的无功功率平衡方程的拉格朗日乘子；编号为n的节点是交流电力系统功率平衡节点。i和j均为交流电力系统中节点的编号，且都属于连续自然数的集合{1,2,…,n}；n为交流电力系统中节点的总个数；gij为支路ij的电导参数；bij为支路ij的电纳参数；Vi为节点i的电压幅值变量；θi为节点i的电压相角变量；Vj为节点j的电压幅值变量；θj为节点j的电压相角变量；ξij是按照ξij＝sinθij-θi+θj确定的支路ij的导纳修正系数；αij是按照αij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij/2确定的支路ij的第1修正导纳；βij是按照βij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij/2确定的支路ij的第2修正导纳；γij是按照γij＝-bijViVf/3确定的支路ij的第3修正导纳；δij是按照δij＝bijViVj/3确定的支路ij的第4修正导纳；
Figure BDA0003092387520000073
是按照
Figure BDA0003092387520000074
Figure BDA0003092387520000081
确定的支路ij的第5修正导纳；φij是按照φij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi/3确定的支路ij的第6修正导纳；χij是按照χij＝-gijViVj/3确定的支路ij的第7修正导纳；ψij是按照ψij＝gijViVj/3确定的支路ij的第8修正导纳；Vi和Vj均为标幺值电压。PGi为接于节点i的电源的有功功率参数；QGi为接于节点i的电源的无功功率参数；PDi为接于节点i的负荷的有功功率参数；QDi为接于节点i的负荷的无功功率参数；gij、bij、QGi、QDi、PGi和PDi都为已知的电力系统参数。in,
Figure BDA0003092387520000072
is the Lagrangian function; λ i is the Lagrangian multiplier of the active power balance equation corresponding to node i; ξ i is the Lagrangian multiplier of the reactive power balance equation corresponding to node i; A node is an AC power system power balancing node. i and j are the numbers of nodes in the AC power system, and both belong to the set of continuous natural numbers {1,2,…,n}; n is the total number of nodes in the AC power system; g ij is the conductance of the branch ij parameter; b ij is the susceptance parameter of branch ij; V i is the voltage amplitude variable of node i; θ i is the voltage phase angle variable of node i; V j is the voltage amplitude variable of node j ; The voltage phase angle variable of j; ξ ij is the admittance correction coefficient of branch ij determined according to ξ ij = sinθ ij -θ i +θ j ; α ij is according to α ij =g ij V i -g ij cosθ ij V j /2-b ij V j θ i /3+b ij V j θ j /3-b ij V j ξ ij /2 determines the first modified admittance of branch ij; β ij is based on β ij =- b ij V i θ i /3-V i g ij cosθ ij /2-b ij V i θ j /3+b ij V i ξ ij /2 determines the second modified admittance of branch ij; γ ij is The third modified admittance of branch ij determined according to γ ij =-b ij V i V f /3; δ ij is the fourth modified derivation of branch ij determined according to δ ij =b ij V i V j /3 accept;
Figure BDA0003092387520000073
is according to
Figure BDA0003092387520000074
Figure BDA0003092387520000081
The 5th modified admittance of the determined branch ij ; φ ij is according to The 6th modified admittance of the branch ij determined by Vi /3; χ ij is the 7th modified admittance of the branch ij determined according to χ ij =-g ij Vi V j /3; ψ ij is according to ψ ij =g ij V i V j /3 determines the 8th modified admittance of branch ij; both V i and V j are per-unit voltages. P Gi is the active power parameter of the power supply connected to node i; Q Gi is the reactive power parameter of the power supply connected to node i; P Di is the active power parameter of the load connected to node i; Q Di is the active power parameter of the load connected to node i The reactive power parameters of the load; g ij , b ij , Q Gi , Q Di , P Gi and P Di are all known power system parameters.

通过求驻点方程组的解，从而获取到目标函数取极小值时各个变量的值。By finding the solution of the stationary point equations, the value of each variable when the objective function takes the minimum value can be obtained.

在步骤B2中，基于驻点方程组，建立如下的节点级分散迭代公式，继而根据节点级分散迭代公式获取交流电力系统的最小状态潮流：In step B2, based on the stationary point equations, the following node-level decentralized iterative formula is established, and then the minimum state power flow of the AC power system is obtained according to the node-level decentralized iterative formula:

Figure BDA0003092387520000082
Figure BDA0003092387520000082

其中，(t+1)表示第t+1步的迭代结果；(t)表示第t步的迭代结果；σ为大于0小于1的惯性参数；Ωi是编号为i的节点的所有邻居节点之编号集合；Ωn是编号为n的节点的所有邻居节点之编号集合。Among them, (t+1) represents the iterative result of the t+1th step; (t) represents the iterative result of the t-th step; σ is the inertia parameter greater than 0 but less than 1; Ω i is all the neighbor nodes of the node numbered i The numbered set of Ω n is the numbered set of all neighbor nodes of the node numbered n.

按上述节点级分散迭代公式迭代计算，直至收敛，所得交流电力系统的各节点电压最终解所构成的向量，就是表示交流电力系统的最小状态潮流的向量。从而实现交流电力系统最小状态潮流的节点级分散获取。Iteratively calculate according to the above node-level decentralized iterative formula until convergence, and the vector formed by the final solution of the voltage at each node of the AC power system is the vector representing the minimum state power flow of the AC power system. In this way, the node-level decentralized acquisition of the minimum state power flow of the AC power system is realized.

步骤B2按照控制理论，将连续方程组(驻点方程组)转化为离散迭代表达式(节点级分散迭代公式)。按上述节点级分散迭代公式计算编号为i的节点的θi、Vi、λi和ξi时，只需要编号属于集合Ωi的节点(也就是只需要邻居节点)的电压幅值和相角及拉格朗日乘子，不需要邻居节点的源荷功率私密数据。计算θn和Vn时的情况也一样。因此，上述节点级分散迭代公式是节点级分散的，且邻居节点的源荷功率私密信息无泄露。这正是称本发明给出的方法为获取交流电力系统最小状态潮流的节点级分散方法的缘故。In step B2, according to the control theory, the continuous equation system (stationary point equation system) is converted into a discrete iterative expression (node-level decentralized iterative formula). When calculating θ i , V i , λ i and ξ i of the node numbered i according to the above node-level decentralized iteration formula, only the voltage amplitude and phase of the node numbered belonging to the set Ω i (that is, only the neighbor nodes) are needed. angle and Lagrangian multipliers, and do not need the source-load power private data of neighbor nodes. The same is true when calculating θ n and V n . Therefore, the above node-level decentralized iterative formula is node-level decentralized, and the source-load power private information of neighbor nodes is not leaked. This is the reason why the method provided by the present invention is called a node-level decentralized method for obtaining the minimum state power flow of the AC power system.

本申请实施例首先根据已知的交流电力系统的结构和参数，建立节点功率平衡的线性渐近方程；根据线性渐近方程和节点电压，建立交流电力系统最小状态潮流的二次规划模型；根据二次规划模型建立拉格朗日函数；根据拉格朗日函数建立节点级分散迭代公式，继而根据节点级分散迭代公式获取交流电力系统的最小状态潮流。由于获取了交流电力系统的最小状态潮流，故提高了设备工作效率；因采用线性渐近方程建立交流电力系统最小状态潮流的二次规划模型，故交流电力系统的最小状态潮流的求解结果唯一和全局最优，避免了状态潮流之解的全局最优性无保障的缺陷；同时，由于建立节点级分散迭代公式，故交流电力系统的最小状态潮流的求解既节点级分散又无源荷的功率私密信息泄露。The embodiment of the present application first establishes a linear asymptotic equation of node power balance according to the known structure and parameters of the AC power system; according to the linear asymptotic equation and node voltage, establishes a quadratic programming model of the minimum state power flow of the AC power system; according to The quadratic programming model establishes the Lagrangian function; according to the Lagrangian function, the node-level decentralized iteration formula is established, and then the minimum state power flow of the AC power system is obtained according to the node-level decentralized iteration formula. Because the minimum state power flow of the AC power system is obtained, the working efficiency of the equipment is improved; because the linear asymptotic equation is used to establish the quadratic programming model of the minimum state power flow of the AC power system, the solution results of the minimum state power flow of the AC power system are unique and sum. The global optimality avoids the defect that the global optimality of the solution of the state power flow is not guaranteed; at the same time, due to the establishment of a node-level decentralized iterative formula, the solution of the minimum state power flow of the AC power system is both node-level decentralized and passive load power. Disclosure of private information.

本申请实施例第二方面提供的是一种计算机可读存储介质，所述计算机可读存储介质存储有计算机程序，所述计算机程序被处理器执行时实现上述获取交流电力系统最小状态潮流的节点级分散方法的步骤。A second aspect of the embodiments of the present application provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, realizes the above-mentioned node for obtaining the minimum state power flow of an AC power system Steps of the Dispersion Method.

图3是本申请实施例第三方面提供的终端设备的示意图。该实施例的终端设备3包括：处理器30、存储器31以及存储在所述存储器31中并可在所述处理器30上运行的计算机程序32，所述处理器30执行所述计算机程序32时实现上述获取交流电力系统最小状态潮流的节点级分散方法实施例中的各个步骤，例如图1所示的步骤101至104。本领域技术人员应当理解，图3仅仅是终端设备3的示例，并不构成对终端设备3的限定。所述终端设备3包括但不限于处理器30、存储器31以及存储在所述存储器31中并可在所述处理器30上运行的计算机程序32，例如所述终端设备是本身存储器上或外接可移动存储器上存储有所述计算机程序32的服务器、计算机、掌上电脑及其与输入输出设备和网络接入设备的组合。FIG. 3 is a schematic diagram of a terminal device provided by a third aspect of an embodiment of the present application. The terminal device 3 in this embodiment includes: a processor 30 , a memory 31 , and a computer program 32 stored in the memory 31 and executable on the processor 30 , when the processor 30 executes the computer program 32 Each step in the above embodiment of the node-level distributed method for obtaining the minimum state power flow of an AC power system is implemented, for example, steps 101 to 104 shown in FIG. 1 . Those skilled in the art should understand that FIG. 3 is only an example of the terminal device 3 , and does not constitute a limitation on the terminal device 3 . The terminal device 3 includes, but is not limited to, a processor 30, a memory 31, and a computer program 32 stored in the memory 31 and running on the processor 30. The server, computer, palmtop computer and its combination with input and output devices and network access devices that store the computer program 32 on the mobile memory.

以上所述实施例仅用以说明本申请的技术方案，而非对其限制；尽管参照前述实施例对本申请进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本申请实施例技术方案的精神和范围，均应包含在本申请的保护范围之内。The above-mentioned embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that the foregoing embodiments can still be used for The recorded technical solutions are modified, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions in the embodiments of the present application, and should be included in the present application. within the scope of protection.

Claims (3)

1. A node-level dispersion method for obtaining the minimum state power flow of an alternating current power system is characterized by comprising the following steps:
according to the known structure and parameters of the alternating current power system, a linear asymptotic equation of node power balance is established;
establishing a quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage;
establishing a Lagrange function according to the quadratic programming model;
establishing a node level dispersion iteration formula according to the Lagrangian function, and then obtaining the minimum state power flow of the alternating current power system according to the node level dispersion iteration formula;
the linear asymptotic equation for establishing the node power balance according to the known structure and parameters of the alternating current power system comprises:
according to the branch admittance parameters of the alternating current power system, the voltage amplitudes at two ends of the branch and the voltage phase angles at two ends of the branch, an electric power definition formula is applied, and coupling terms in the electric power definition formula are removed, so that the following linear asymptotic expression of the branch transmission power is established:
Pij＝αijVi+βijVj+γijθi+δijθj
Figure FDA0003534875240000011
wherein, PijActive power transmitted for branch ij; qijThe reactive power transmitted for the branch ij; i and j are serial numbers of nodes in the alternating current power system, and both belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; bijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj3 determining the 4 th modified admittance of said branch ij;
Figure FDA0003534875240000021
is according to
Figure FDA0003534875240000022
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of said branch ij determined; chi shapeijIs according to chiij＝-gijViVj(ii)/3 determining a 7 th modified admittance of said branch ij; psiijIs in accordance with psiij＝gijViVj(iv) the 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value;
according to the linear asymptotic expression and a branch connection structure of the alternating current power system, establishing a linear asymptotic equation of the power balance of the node i according to a Kirchhoff current law as follows:
Figure FDA0003534875240000023
Figure FDA0003534875240000024
wherein, PGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
the establishing of the quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage comprises the following steps:
establishing a quadratic programming model of the minimum state power flow of the alternating current power system by taking the linear asymptotic equation as a constraint and taking the minimum sum of squares of the offset of the node voltage amplitude relative to 1 and the square sum of the phase angle of the node voltage as an objective function, wherein the quadratic programming model comprises the following components:
Figure FDA0003534875240000025
Figure FDA0003534875240000026
Figure FDA0003534875240000027
the node numbered n is a power balance node of the alternating current power system; i and j are numbers of nodes in the alternating current power system, and belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; bijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha (alpha) ("alpha")ijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj(ii)/3 determining a 4 th modified admittance of said branch ij;
Figure FDA0003534875240000031
is according to
Figure FDA0003534875240000032
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi3 the 6 th modified admittance of said branch ij; chi shapeijIs according to chiij＝-gijViVj(ii)/3 determining a 7 th modified admittance of said branch ij; psiijIs according to psiij＝gijViVj(iii) an 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value; pGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
the establishing of the Lagrangian function according to the quadratic programming model comprises the following steps:
according to the quadratic programming model, establishing a Lagrangian function according to the definition of the Lagrangian function;
Figure FDA0003534875240000033
wherein,
Figure FDA0003534875240000034
is a pullA Grenarian function; lambda [ alpha ]iA Lagrange multiplier of an active power balance equation corresponding to the node i; xiiA lagrange multiplier of a reactive power balance equation corresponding to the node i; the node with the number n is an alternating current power system power balance node; i and j are serial numbers of nodes in the alternating current power system, and both belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; bijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj(ii)/3 determining a 4 th modified admittance of said branch ij;
Figure FDA0003534875240000041
is according to
Figure FDA0003534875240000042
Figure FDA0003534875240000043
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of said branch ij determined; chi shapeijIs according to xij＝-gijViVj3 determining the 7 th modified admittance of said branch ij; psiijIs according to psiij＝gijViVj(iii) an 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value; pGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
the establishing a node-level decentralized iterative formula according to the Lagrangian function, and then obtaining the minimum state power flow of the alternating current power system according to the node-level decentralized iterative formula comprises the following steps:
according to the Lagrange function, establishing the following stagnation point equation set according to the definition of stagnation points:
Figure FDA0003534875240000051
wherein,
Figure FDA0003534875240000052
is the lagrange function; lambda [ alpha ]iA Lagrange multiplier of an active power balance equation corresponding to the node i; xiiA lagrange multiplier of a reactive power balance equation corresponding to the node i; the node with the number n is an alternating current power system power balance node; i and j are serial numbers of nodes in the alternating current power system and belong to continuous natural numbersSet of {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; b is a mixture ofijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj3 determining the 4 th modified admittance of said branch ij;
Figure FDA0003534875240000053
is according to
Figure FDA0003534875240000054
Figure FDA0003534875240000055
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of said branch ij determined; chi shapeijIs according to chiij＝-gijViVj(ii)/3 determining a 7 th modified admittance of said branch ij; psiijIs according to psiij＝gijViVj(iii) an 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value; pGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
based on the stagnation point equation set, the following node level dispersion iterative formula is established, and then the minimum state power flow of the alternating current power system is obtained according to the node level dispersion iterative formula:
Figure FDA0003534875240000061
wherein, (t +1) represents the iteration result of the t +1 step; (t) representing the iteration result of the t step; sigma is an inertia parameter which is more than 0 and less than 1; omegaiIs the number set of all the neighbor nodes of the node with the number i; omeganIs the number set of all neighbor nodes of the node numbered n.
2. A computer-readable storage medium, storing a computer program, which, when being executed by a processor, carries out the steps of the node-level decentralized method of obtaining a minimum state power flow of an ac power system according to claim 1.
3. A terminal device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized in that said processor when executing said computer program implements the steps of the node-level decentralized method of obtaining a minimum state power flow of an ac power system according to claim 1.
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