Power system power flow calculation (Newton-Raphson method, Gauss-Seidel method, fast decoupling method) (Matlab code implementation)

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本文目录如下：️️️

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目录

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1 概述

2 An overview of power flow calculation in power systems

2.1 The development process of power flow

2.2Newton-Raphson method for load flow calculation

 4 Matlab代码及文章讲解

4.1 高斯-赛德尔法 

4.2 牛顿-拉夫逊法 

4.3 Quick decoupling method

5 写在最后 

1 概述

最初,The power flow calculation of the power system is done manually.Later, in order to meet the growing needs of the power system,Computer networks have been formed,It provides the material basis for the power flow calculation of the power system.Power system power flow calculation is the most basic content in power system analysis and calculation,It is also an indispensable tool in the operation and design of power systems.根据系统给定的运行条件、Network wiring and component parameters,The magnitude and phase angle of each bus voltage can be determined through the power flow calculation、Power flowing through each element、power loss of the entire system, etc.

In the design of power system planning and the study of the operation mode of the existing power system,All need to use the power flow calculation to quantitatively analyze and compare the rationality of the power supply scheme or operation mode、可靠性和经济性.此外,The power flow calculation of the power system is also the basis of the dynamic and static stability of the computer system,Therefore, the power flow calculation is a very important and basic calculation to study the power system.Its development mainly revolves around these aspects：Convergence of the calculation method、可靠性;The speed of calculation speed;Requirements for computer storage capacity and convenience of calculation、灵活等.

This paper is based on the introduction of Newton-Raphson's method、Power flow calculation by Gauss-Seidel method and fast decoupling method,在MATLABin the simulation calculation.

2 An overview of power flow calculation in power systems

2.1 The development process of power flow

最初,Power system power flow calculation is done manually.Later, in order to meet the growing needs of the power system,AC computing desk is used.With the advent of electronic digital computers,1956 年 Ward et al compiled a practical computer power flow calculation program.这样,It provides an extremely powerful calculation method for the increasingly complex large-scale power system.经过几十年的发展,Power system power flow calculation has been very mature.There are two forms of power flow calculation in power system: offline calculation and online calculation.The former is mainly used for power system planning and design、Arranges how the system operates;The latter is used for real-time monitoring and real-time control of running systems.Off-line and on-line power flow calculations are the same in calculation principle,都要求满足：（1）The calculation method is reliable,收敛性好;（2）Takes up less computer memory;（3）The calculation speed is high;（4）Good for interface,方便使用.

2.2Newton-Raphson method for load flow calculation

2.2.1Node Voltage Equation

The power network equation is composed of the related parameters and variables of the network and their interrelationships,A set of mathematical equations that reflect network performance.不难想象,There are nodal voltage equations that fit this equation,Loop current equation,Cut-set voltage equation, etc.However, the cut-set voltage equation is not commonly used in power system calculations,Therefore, the node voltage equation or the loop current equation is generally used,But the parameters of the current in the system are often difficult to measure and collect,And because there are many grounding branches in the equivalent network of the power system,The nodal voltage equation has fewer equations,It is also more convenient to modify the coefficient when the network structure is changed or the transformer ratio is changed,Therefore, the node voltage equation has its obvious advantages.

2.2.2节点导纳矩阵

The nodal admittance matrix and the nodal impedance matrix are both square matrices,Its order is equal to the number of nodes in the network other than the reference noden.But the reason why we mostly use the nodal admittance matrix in the power flow calculation is that,The nodal admittance matrix is ​​a sparse matrix,The non-zero off-diagonal arity of each row is equal to the number of ungrounded branches connected to the opposite node of the row.因为节点i 、j Equal to when there is no branch directly connected between them0,This situation is very common in practical power systems,Therefore, the use of the node admittance matrix is ​​beneficial to modify the system structure.

2.2.3 Non-standard ratio transformer equivalent circuit

Equivalent circuit model for transformers,有​型等值电路、TType Equivalent Transformer Model.However, the first two do not reflect the actual voltage conversion function of the transformer,All parameters and variables in the network must be normalized to the same voltage level.但是,Equivalent transformer model can equivalently reflect the transformer voltage conversion function,It is also the transformer model used in power system analysis using computer,Although the use of this model does not exclude hand calculation.

首先,如图3-2-3（a）所示,The admittance or excitation branch of the transformer can be omitted,A two-winding transformer can be represented by a circuit with impedances in series with an ideal transformer.The ideal transformer is just one parameter,That's the ratio​.Now the transformer impedance is reduced to the low-voltage side according to the actual transformation ratio as an example,A transformer-type equivalent circuit is derived.

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Transformer impedance reduction to the low-side equivalent model equals the power flowing into and out of the ideal transformer：

For the rest of the detailed articles, see Section IV：

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 4 Matlab代码及文章讲解

The code for this article needs to click here：正在为您运送作品详情

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4.1 高斯-赛德尔法 

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4.2 牛顿-拉夫逊法 

4.3 Quick decoupling method

Equivalent circuit model for transformers,有型等值电路、TType Equivalent Transformer Model.However, the first two do not reflect the actual voltage conversion function of the transformer,All parameters and variables in the network must be normalized to the same voltage level.但是,Equivalent transformer model can equivalently reflect the transformer voltage conversion function,It is also the transformer model used in power system analysis using computer,Although the use of this model does not exclude hand calculation. 

5 写在最后 

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