# A Multi-Period Optimal Reactive Power Dispatch Approach Considering Multiple Operative Goals
## 3 Tests and Results
### Results
#### 3.3.2 IEEE 118-Bus Test System  
One of the objectives within the MP-ORPD is to maintain adequate voltage profiles for the set of pilot nodes. In this paper, four settings of voltage values were defined for an operation day, namely minimum, low, medium, and high voltages, which ware characterized by the demand behavior and user requirements. Figure 7 shows the reference voltage profiles and the voltage after optimization for a sample of pilot nodes (5, 63, 46, and 8). Additionally, as a particular case, bus 5 was set to have a higher voltage profile in the peak periods (0.058 p.u with respect to its minimum reference and a 138 kV voltage base). The results show that even with an \"aggressive\" voltage profile, it is possible to follow the voltage reference value.  
Figure 4: Voltage profiles of pilot nodes (48, 29, 36, and 31) for IEEE 57-bus system.  
Figure 5: Absolute reactive power output of generators for each period for the IEEE 57-bus system.  
The maximum error between the reference and the optimized voltage is less than 0.95 kV, as shown in Figure 8, where the indicated period is not the same in each node, although it is the period with the greatest difference. In Figure 8, pilot node 49 in period 11 has an error of \(-0.94\) kV; this difference is not constant in the other periods, which have lower absolute values.  
The sum of the reactive power in terms of the absolute value of the set of generators at each period is a way of representing the use of the dynamic reactive power reserve, which in a power system is necessary to manage uncertainty and contingencies [49]. Figure 9 presents the dynamic reserve of the reactive power in the base case (orange) and its subsequent optimization (blue). In this case, reactive power reserves after optimization represent only 31.3% of the base case. This is important, since it allows the system operator to better react in cases of disturbance and uncertainty, while maintaining sufficient reactive reserves in the most quick and effective VAR sources, which is an intrinsic requirement for proper corrective control actions.  
In this case, compared to the 57-bus system, there are about three times as many elements that can control the reactive dispatch, so the system is able to follow the voltage profile of the pilot nodes.  
Figure 6: Tap position settings over one operation day (values expressed in p.u) for the IEEE 57-bus test system.  
Figure 7: Voltage profiles of pilot nodes (5, 63, 46, and 8) for the IEEE 118-bus test system.  
Figure 10 presents the reactive power output for each generator, representing a sample set of generators in a random period (in this case: generators 4, 10, 59, 69, 77, and 90; period 11). A significant reduction in reactive power can be observed in the optimized case (blue) versus the base case (orange).  
Figure 8: Maximum error between reference and optimized voltage in pilot nodes (kV) for the IEEE 118-bus test system.  
Figure 10: Reactive power outputs of generators (4, 10, 59, 69, 77, and 90) during period 11 for the IEEE 118-bus test system.  
Figure 9: Absolute reactive power output of generators for each period for the IEEE 118-bus test system.  
Figure 11 shows the variations in tap positions (expressed in terms of a ratio) for each transformer throughout a day of operation. It can be observed that the numbers of maneuvers on the tap are greater during periods with high demand and with high-voltage profiles; nonetheless, the maximum number of maneuvers is kept the same, as indicated in Equation (21).  
These results show the relationship between the number of transformer operations and the availability of additional elements for reactive power control. When there are other elements that can be used for reactive power control in a given area in addition to the transformers, the number of maneuvers in these elements is reduced. This is the case for transformers T81-80 and T8-5, which are located in small control areas with other elements that provide reactive power control, resulting in lower numbers of transformer maneuvers.