# Optimal Management of High-Voltage Line Congestions Using Power Source Redispatching
## 3 Description of the Research Methodology
In each iteration, the power flow problem is solved. As mentioned earlier, during the optimization process, the power in RES is reduced in order to eliminate the resulting line overloads. The resulting loss of generated power \(\Delta P_{\text{G}}\) in the system should be supplemented by an increase in generation in conventional sources (their number is \(L\)). This is conducted by dividing the power deficit \(\Delta P_{\text{G}}\) into conventional sources. These sources are assigned appropriate \(p_{\text{fi}}\) (participationfactor) coefficients. For each source \(k\) that takes part in covering the power imbalance, the participation coefficient \(w_{k}\) is determined according to the following equation:  
\[w_{k}=\frac{p_{\text{f}k}}{\sum\limits_{i=1}^{L}p_{\text{f}i}} \tag{12}\]  
Taking into account the power loss \(\Delta P_{\text{G}}\) and the \(w_{k}\) coefficients, the changes in power in the sources responsible for the balance are determined according to the following equation:  
\[\Delta P_{\text{G}k}=w_{k}\cdot\Delta P_{\text{G}} \tag{13}\]  
Different methods of determining the \(p_{\text{f}i}\) coefficients can be considered. This article uses the following five methods to distribute the power imbalance:  
* Case 1 (C1)-the power deficit is covered only by the source connected in the balancing node theoretical case;
* Case 2 (C2)-the distribution of the power deficit is determined in relation to the maximum power of the sources responsible for maintaining the balance;
* Case 3 (C3)-the distribution of the power deficit is determined in relation to the difference between the maximum and current power of the sources responsible for maintaining the balance;
* Case 4 (C4)-the distribution of the power deficit is determined using the same coefficients for each source responsible for maintaining the balance;
* Case 5 (C5)-power deficit distribution is determined by different coefficients for each source responsible for maintaining the balance, which is determined arbitrarily. Figure 2: AIG algorithm block diagram. Maintaining the power balance in the power system in practice is usually covered by conventional power plants. This can be performed in different ways, as described by cases C2, C3, C4, and C5. Of the methods mentioned, cases C2 and C3 are the most realistic. Therefore, case C1 is only a theoretical case that has been added for comparison with other methods. The proposed methodology can be used by network operators. The time to obtain the result in not very extensive networks is several minutes. In extensive networks (large in size), the number of decision variables and constraints can be significantly greater. Therefore, the computation time can be longer. The speed of the computational process also depends on the power and efficiency of the computing unit. In dispatch centers, computing units are much more efficient and faster than standard computers used for research at universities. The costs of implementing such a solution should not be high. The proposed methodology can be easily implemented through integration with the existing power grid management system.