# Optimal Management of High-Voltage Line Congestions Using Power Source Redispatching
## 4 Calculation Results and Discussion
### Computational Case  
The selected operating state of the test network from Figure 3 was considered. The emergency state was analyzed as a shutdown of the 400 kV transmission line connecting nodes 8-30. As a result of the emergency shutdown of this line, five 110 kV lines were overloaded. These are the lines connecting nodes 100-103 (line overload of 35%), 17-113 (line overload of 26%), 23-24 (line overload of 10%), 94-95 (line overload of 7%), and 16-17 (line overload of 3%). These are typical values of current overloads that occur in real networks when performing computational analyses. Sometimes, overloads are observed on lines located far from the source connection point. This state is illustrated in Figure 3.  
For the emergency case of network operation, shown in Figure 3, the matrix \(\mathbf{A_{u}}\), the individual expressions of which are determined from relation (5), and the matrix inverse to it \(\mathbf{A_{u}^{-1}}\) are illustrated in Figure 4. Figure 4a,c shows the filling density of both matrices. Figure 4b,d additionally illustrates the values of the individual terms of both distribution matrices. In such a situation, the network operator should take appropriate steps to eliminate the threat. One of the remedial actions is the proposed methodology described in point 3. According to this methodology, in the first step, all sources responsible for the load of the previously indicated 110 kV lines were designated. For this purpose, the active power flow tracking method was used, which resulted in determining the values of the \(u_{ijk}\) coefficients using Equation (4). Additionally, the power values flowing through individual lines from the selected RESs were calculated. These results are presented in Tables 1-5. Each of these tables contains separate results for each overloaded line. In each table, the RESs (conventional sources that participate in maintaining the power balance and therefore cannot be considered as decision variables in the optimization process) that have the greatest impact on the load of the 110 kV line are marked in blue. These sources are the decision variables in the optimization process. Debates on whether all RESs should be used to limit power (even those with a very low participation factor) or only those that have the greatest impact on overloading a given line were conducted in article [14] from the literature list. In the case of power reduction in sources with a small contribution to line overload, they have no measurable significance for its effective load relief. Taking into account only the sources with the greatest share in the power flow on a given line allows for minimising the number of RESs covered by power reduction. This reduces the size of thetask due to the smaller number of decision variables, which allows for a shorter calculation time and allows us to limit the number of signals necessary to be sent to the sources during the power redispatching process. This increases the effectiveness and efficiency of the entire process. The optimization is carried out in the next part. The effectiveness of the proposed methodology is also proven.