## 3 Solution Approach
### Method of the Control Center under Unbalanced Power  
If an ECPS suffers a splitting incident, based on Algorithm 3, the remaining buses in the main area will lead to an unbalanced power distribution. The control center will collect the electrical information of the buses in the main area, calculate the unbalanced power, and adjust the outputs of each of the generators. The method proposed in this paper can be applied in three situations:  
**Situation I**: If the splitting incident only causes the separation of generators, the remaining generators in this area must increase their outputs to keep the balance between supply and demand. The total amount of the increased power should be \(\Delta P=\sum P_{gen}^{*}\), where \(\sum P_{gen}^{*}\) is the sum of the lost generator outputs.  
**Situation II**: If the splitting incident only causes the separation of loads, the remaining generators in this area must decrease their outputs to keep the balance between supply and demand. The total amount of the reduced power should be \(-\Delta P=\sum P_{load}^{*}\), where \(\sum P_{load}^{*}\) is the sum of the lost loads.  
**Situation III**: If the splitting incident causes both the separation of generators and loads, the control center should first calculate the unbalanced power by \(\Delta P=\sum P_{gen}^{*}+\sum P_{load}^{*}\). If \(\Delta P>0\), take the same strategy in Situation I; if \(\Delta P<0\), take the same strategy in Situation II; and \(\Delta P=0\), take no adjustment strategy.  
**Remark 3**: _In the above generator power adjustment method, the distribution of the total unbalanced power to each generator should be decided in weighted terms. The specific distribution methods will be introduced in Algorithm 4._  
Algorithm 4 is used to calculate the weighted adjustment of each generator in the main area after the splitting incident. Generators near the tripped buses may be distributed with higher weighted terms. Let \(V_{G}^{\prime}\subset V^{\prime}\) be the set of generators in the main area \(G^{\prime}=(V^{\prime},E^{\prime})\) after the splitting incident.  
```
1: Input \(G^{\prime}\), \(\Delta P\) and the tripped branch \((i,j)\) with node \(m\) (generator or load bus)
2: Let \(l=w=[0,0,\dots,0]\), \(S=0\)
3: For \(k=1:|V_{G}^{\prime}|\)
4: Reconnect branch \((i,j)\) to \(G^{\prime}\), and calculate \(L_{km},l(k)=L_{km}\), \(S=S+1/l(k)\)
5: End
6: For \(k=1:|V_{G}^{\prime}|\)
7: Calculate the weight \(w(k)=l(k)/S\) and the adjustment \(P_{k}^{w}=\Delta P\cdot w(k)\)
8: End
```  
**Algorithm 4** Calculate the weighted adjustment  
**Remark 4**: _If the adjusted output of a generator is beyond the output limit, then modify the output of this generator to the nearby limit. The rest of the total power adjustment value should be \(\Delta P^{\prime}=(\Delta P-\sum P_{i}^{w})+\sum\left(P_{i}^{w}-\Delta P_{i}^{ \mathrm{limit}}\right)=\Delta P-\sum\Delta P_{i}^{\mathrm{limit}}\), where \(P_{i}^{w}\) is the weighted adjustment output of generator \(i\) and \(\Delta P_{i}^{\mathrm{limit}}\) is the actually adjustable output of generator \(i\)._  
**Remark 5**.: _If there are \(n\) generators and loads tripped at a splitting incident, Algorithm 4 should be used for dealing with each tripped bus, respectively._