# Dynamic Load Redistribution of Power CPS Based on Comprehensive Index of Coupling Node Pairs
## 3 Power CPS Risk Propagation Considering Load Redistribution
### Subnetwork Load Reallocation
#### 3.2.2 Power Grid Load Redistribution  
After the cascade of the information side is completed, all the failed information nodes are counted and the corresponding failure nodes of the coupling power side are found, and the first round of redistribution of the power side is carried out. Considering the node heterogeneity of the power side, it can be divided into three types of nodes, namely the generator node, the load node, and the intermediate node, which constitute the power side directed topology network. It is divided into two steps to suppress the cascade fault propagation on the power side, first adjust the generator output according to the real-time operation situation for power flow adjustment, and if the power flow has not converged, the partial load is removed. (1) The first round of redistribution on the power side  
As can be seen from Figure 4, after the failure of the \(i\) node, the recovered power flow is all returned to the \(j\) node and the \(k\) node. When the system is operating normally, power conservation is met:  
\[L_{ji}+L_{ki}=\Delta L_{i}+L_{io} \tag{19}\]  
where \(L_{ji}\) and \(L_{ki}\) are the power flowing to the \(i\) node, \(\Delta L_{i}\) is the power consumed by the node \(i\), and \(L_{io}\) is the power flowing out of the \(i\) node. When node \(i\) fails, the lines directly connected around it will be cut. The power carried by nodes \(j\) and \(k\) at this time is:  
\[\left\{ \begin{array}{l}L_{j}=L_{jo}+L_{ji}+\sum L_{lloss}\\ L_{k}=L_{ko}+L_{ki}+\sum L_{kloss}\end{array} \right. \tag{20}\]  
If the parent node of the \(i\) node is not a generator node, continue to go back up to find the nearest generator. When traced back to generator nodes \(j\) and \(k\), the power flow is redistributed according to the sum of the recovered tide and the original tide according to the real-time redundancy of the node. Taking apart the \(j\) node in the above figure, it is connected to the \(i_{1}\) and \(i_{3}\) nodes and other child nodes, in addition to the \(i\) node. Figure 4: The first round of redistribution on the power side. As shown in Figure 5, at the generator node, according to the capacity redundancy allocation strategy, the power flow allocated to the \(i_{1}\) node is:  
\[\Delta L_{j_{1}}=\Delta L_{j}\frac{C_{i_{1}}-L_{i_{1}}}{\sum{(C_{jx}-L_{jx})}} \tag{21}\]  
The tide reassigned to the \(i_{3}\) node is:  
\[\Delta L_{j_{1}}=\Delta L_{j}\frac{C_{i_{3}}-L_{i_{3}}}{\sum{(C_{jx}-L_{jx})}} \tag{22}\]  
where \(j_{x}\) denotes the neighbor node of node \(j\). The other failed nodes in the first round on the power side operate as above. 1. The second round of redistribution on the power side  
The first round of cascading failure under the power flow redistribution has ended, update the adjacency matrix and node pair indicators. At this time, the generator node has begun to readjust the power flow. If the final power flow does not converge, then take the way to reduce the load to make the tide converge. The subsequent redistribution process is also carried out according to the established node-to-synthetic vulnerability indicator. As shown in Figure 6, the new loads allocated to \(i_{1}\) and \(i_{3}\) in the first round are \(\Delta L_{j1}\) and \(\Delta L_{j3}\), and the child nodes are \(a\), \(b\), \(c\), and \(d\). Similar to the information side, according to the updated comprehensive importance indicator \(I_{i}=[I_{1},I_{2},I_{3},\cdots,I_{n}\ ]\), the excess tide of the node with high importance is first redistributed. Unlike the information side, only child nodes on the power side receive the power flow.