1.加了电流幅值量测公式

2.在状态估计中加了电流量测

Signed-off-by: dmy@lab <dmy@lab.lab>

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}