# A Multi-Period Optimal Reactive Power Dispatch Approach Considering Multiple Operative Goals
## 3 Tests and Results
### Sensibility of Objective Function Components  
Table 3 shows a sensitivity analysis of the results for the IEEE 57-bus test system. The first row shows the total number of taps operations. The second row corresponds to the total number of operations on shunt elements, while the third and fourth rows indicate the reactive deviation of the generators and the voltage deviation with respect to the pilot nodes. When evaluating a single objective, the proposed approach manages to reduce the objective function considerably. For the reactive deviation, the formulation that only considers the TQG is the lowest of all cases analyzed, while the lowest number of maneuvers is achieved with the TQD formulation, with a total number of 51 maneuvers; similarly, it can be observed that the lowest voltage deviation, with a value of 0.18, is obtained with the TVD formulation. It was already mentioned that this test system requires a higher reactive power support. This fact can be seen when comparing the maximum and minimum values of the reactive power deviations in generators and the voltage deviations of the pilot nodes. The last column in Table 3 (TQG + TVD + TQD) indicates the best trade-off in the use of elements for reactive power control; the results are shown in Figures 4-6.  
Table 4 presents a comparison of each component of the objective function and their combinations in order to evaluate the individual and joint sensitivity of the objective function. The number of maneuvers carried out on the transformer taps, the number of maneuvers carried out on the shunt elements, the absolute value of the reactive power used by the generators, and the voltage deviation in the pilot nodes with respect to the reference value were evaluated; all information corresponds to an operation period of 24 h.  
Figure 11: Tap position settings over one operation day (values expressed in p.u) for the IEEE 118-bus test system.  
For this system, there is a large reactive power reserve, which is evident when comparing the maximum and minimum values of the formulations illustrated in Table 4. For this case, the compared values have a greater range of variation with respect to the IEEE 57-bus test system. The last column in Table 4 (TQG + TVD + TQD) indicates the best trade-off in the use of elements for reactive power control; these results are shown in Figures 7-11. In this case, the simulation time was 121 s. Note that the use of dynamic reactive power reserves was reduced to more than one-third of the base case; in addition, the results followed the voltage profiles successfully.  
The simulation times obtained with the objective function given by Equation (1) for the IEEE 57-bus and IEEE 118-bus test systems were 17.5 s and 100 s, respectively. Additionally, an experiment was performed in which the whole set of nodes was included in the optimization problem. In this case, the objective voltage profiles of the nodes correspond to the values previously defined in each control area and are represented by the pilot nodes. The computation times in this experiment were 128 s and 239 s for the IEEE 57-bus and IEEE 118-bus, respectively. This shows that selecting a reduced set of nodes (pilot nodes) improves the computational time of the algorithm.