diff --git a/run.m b/run.m index c3be1c0..7e1265d 100644 --- a/run.m +++ b/run.m @@ -1,5 +1,6 @@ clear clc +close all % yalmip('clear') addpath('.\Powerflow') [~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('E:\\feeder33\feeder33ieee.txt', '0'); @@ -9,7 +10,7 @@ sigma=0.03;% loop=1; VoltAAE=0; VAngleAAE=0; -LineIndex=[1:16]; +LineIndex=[1]; while 1 %% ѹ %ѹֵ diff --git a/公式/公式.tex b/公式/公式.tex index b088d4f..34b4475 100644 --- a/公式/公式.tex +++ b/公式/公式.tex @@ -203,6 +203,119 @@ Q_{ij}&=-\frac{V_1^2}{k^2}B_{ij}-\frac{V_1}{k} V_2[sin(\theta_1 - \theta_2)G_{ij \end{aligned} \end{equation} + +推导电流量测的公式 +之前已经有 +\begin{equation} + \begin{aligned} + \dot{I}_{12}&=(V_1e^{j \theta_1} - V_2e^{j \theta_2}) + (G_{ij}+jB_{ij}) + \end{aligned} +\end{equation} +将其写成完全极坐标形式 + \begin{equation} + \begin{aligned} + \dot{I}_{12}=(V_1e^{j \theta_1} - V_2e^{j \theta_2}) + Y_{12}e^{j \alpha} + \end{aligned} + \end{equation} + + \begin{equation} + \begin{aligned} + \dot{I}_{12}=V_1e^{j \theta_1}Y_{12}e^{j \alpha} - V_2e^{j \theta_2}Y_{12}e^{j \alpha} + \end{aligned} + \end{equation} + + \begin{equation} + \begin{aligned} + \dot{I}_{12}=V_1Y_{12}e^{j \theta_1 + \alpha} - V_2eY_{12}^{j \theta_2+\alpha} + \end{aligned} + \end{equation} + +\begin{equation} +\begin{aligned} +\dot{I}_{12}=V_1Y_{12}[cos(\theta_1 + \alpha) +1jsin(\theta_1 + \alpha)] +-V_2Y_{12}[cos(\theta_2 + \alpha) +1jsin(\theta_2 + \alpha)] +\end{aligned} +\end{equation} + + 电流实部为 + +\begin{equation} +\begin{aligned} +I_{r12}=V_1Y_{12}cos(\theta_1 + \alpha) +-V_2Y_{12}cos(\theta_2 + \alpha) +\end{aligned} +\end{equation} + +电流虚部为 + +\begin{equation} +\begin{aligned} +I_{i12}=V_1Y_{12}sin(\theta_1 + \alpha) +-V_2Y_{12}sin(\theta_2 + \alpha) +\end{aligned} +\end{equation} + +对电流实部求导 + +\begin{equation} +\frac{\partial I_{r12}}{\partial V_1}= +Y_{12}cos(\theta_1 +\alpha) +\end{equation} + +\begin{equation} +\frac{\partial I_{r12}}{\partial V_2}= +-Y_{12}cos(\theta_2 +\alpha) +\end{equation} + +\begin{equation} +\frac{\partial I_{r12}}{\partial \theta_1}= +-V_1Y_{12}sin(\theta_1 +\alpha) +\end{equation} + +\begin{equation} +\frac{\partial I_{r12}}{\partial \theta_2}= +V_2Y_{12}sin(\theta_2 +\alpha) +\end{equation} + +对电流虚部求导 + +\begin{equation} +\frac{\partial I_{i12}}{\partial V_1}= +Y_{12}sin(\theta_1 +\alpha) +\end{equation} + +\begin{equation} +\frac{\partial I_{i12}}{\partial V_2}= +-Y_{12}sin(\theta_2 +\alpha) +\end{equation} + +\begin{equation} +\frac{\partial I_{i12}}{\partial \theta_1}= +V_1Y_{12}cos(\theta_1 +\alpha) +\end{equation} + +\begin{equation} +\frac{\partial I_{i12}}{\partial \theta_2}= +-V_2Y_{12}cos(\theta_2 +\alpha) +\end{equation} + +状态估计中用得更多的是电流幅值的平方,即 + +\begin{equation} +I^2_{12}=I_{r12}^2+I_{i12}^2 +\end{equation} +对其求导 + +\begin{equation} +\frac{\partial I^2_{12}}{\partial V_1}= +2\frac{\partial I_{r12}}{\partial V_1} ++ +2\frac{\partial I_{i12}}{\partial V_1} +\end{equation} + + 为了推潮流公式,先从简单的开始推起。 \begin{equation}