# A Multi-Period Optimal Reactive Power Dispatch Approach Considering Multiple Operative Goals
## 3 Tests and Results
### Results
#### 3.3.1 IEEE 57-Bus Test System  
Figure 4 depicts the voltage profile curves of four pilot nodes. Note that the voltage control implemented in this system fits the reference curve proposed for each pilot node. The shape of the voltage profiles of the pilot nodes is in accordance with the operational strategy, which increases the reference values of these nodes at peak demand in order to guarantee the voltage stability of the system.  
The proposed system has a high reactive power demand and must meet the voltage profiles required in the pilot nodes, as shown in Figure 4. In addition, of the 26 control elements, only 10 have the capacity to provide reactive power, and of these, 7 are generation units. This shows that the IEEE 57-bus test system is quite limited for an adequate reactive power dispatch. Figure 5 shows the reactive power outputs of all generators of the system for each period. In periods of low demand, in order to obtain the desired voltage in the pilot nodes, it is necessary to increase the amount of reactive power injected, while for periods of medium and high demand, a smaller increase in reactive power injection is observed. This behavior is an indicator of the depletion of reactive power reserves and provides signals for the expansion of reactive power sources.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pilot Node** & **Lower Voltage Limit (p.u)** & **Shunt** & **MVAr** \\ \hline V\({}_{\text{np69}}\) & 0.935 & Q\({}_{\text{L5}}\) & \(-40\) \\ V\({}_{\text{np5}}\) & 0.9481 & Q\({}_{\text{C34}}\) & \(14\) \\ V\({}_{\text{np37}}\) & 0.9276 & Q\({}_{\text{L37}}\) & \(-25\) \\ V\({}_{\text{np56}}\) & 0.9427 & Q\({}_{\text{C44}}\) & \(10\) \\ V\({}_{\text{np77}}\) & 0.9349 & Q\({}_{\text{C45}}\) & \(10\) \\ V\({}_{\text{np66}}\) & 0.90 & Q\({}_{\text{C46}}\) & \(10\) \\ V\({}_{\text{np46}}\) & 0.9341 & Q\({}_{\text{C48}}\) & \(15\) \\ V\({}_{\text{np23}}\) & 0.90 & Q\({}_{\text{C74}}\) & \(12\) \\ V\({}_{\text{np12}}\) & 0.932 & Q\({}_{\text{C79}}\) & \(20\) \\ V\({}_{\text{np270}}\) & 0.9434 & Q\({}_{\text{C82}}\) & \(20\) \\ V\({}_{\text{np17}}\) & 0.90 & Q\({}_{\text{C83}}\) & \(10\) \\ V\({}_{\text{np63}}\) & 0.90 & Q\({}_{\text{C105}}\) & \(20\) \\ V\({}_{\text{np80}}\) & 0.954 & Q\({}_{\text{C107}}\) & \(6\) \\ V\({}_{\text{np8}}\) & 0.9655 & Q\({}_{\text{C110}}\) & \(6\) \\ V\({}_{\text{np49}}\) & 0.9542 & & \\ V\({}_{\text{np32}}\) & 0.90 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Lower voltage limits of pilot nodes and MVAr parameters of shunt elements (IEEE 118-bus test system).  
Figure 6 shows the operation of the taps for four randomly selected transformers. They behave according to the demand of the control area of each pilot node and the availability of shunt elements and generators. Transformer T10-51 is the only control element in the area it controls; therefore, its behavior features a greater number of maneuvers, while transformers T24-26 and T7-29 have internal or nearby control elements, such as shunt compensation, shunt generation, and the transformers themselves, which is why the numbers of maneuvers for these elements are lower.