# Dimensioning of Reactive Power Compensation in an Autonomous Island System
## 4 UC-ED-Oriented Cost-Benefit Analysis
### System Operation with and without Reactive Power Constraints  
The operation of the Rhodes power system during the lowest demand day of the year is presented in Figure 4 for two cases. Figure 4 presents system operation ignoring reactive power constraints; this case effectively represents operation with a full reactive compensation scheme in place. Figure 4 refers to system operation when all reactive power constraints are introduced, without implementing any reactive compensation measures; in this case, the reactive power absorption capability of online units during the lowest demand period should exceed 27 MVAr at G-1 conditions. Figure 5 illustrates the fulfillment of system reactive power requirements by online thermal units at G and G-1 conditions for both cases described above, while Figure 6 shows the corresponding loading levels of thermal units committed to meet demand requirements.  
Apparently, during the low demand intervals of the examined day (hours 00:00-08:00), where maximum reactive power absorption requirements apply, the secure operation of the system cannot be guaranteed at G-1 conditions in the absence of reactive power constraints integrated in the UC-ED (yellow solid line of Figure 5). Note that without the introduction of reactive constraints, the operation of the system could be compromised even at G conditions, given that the four online units committed by the optimization algorithm at low demand hours (Steam#1 & ICE#7-#9) marginally fulfill the reactive power absorption requirements (red dashed line in Figure 5). Obviously, such a UC-ED outcome would be optimal for a power system that does not face reactive power challenges, yet it cannot be acceptable for the examined case study.  
This is circumvented by introducing constraints (21)-(27), ensuring that the committed thermal units provide the necessary level of reactive power absorption capabilities at G and G-1 conditions, as can be seen in Figure 5b. However, to achieve this, at least six generators are required to be online during the low demand hours of the examined day (Steam#1, OCGT#4, ICE#1-#2 & ICE#6-#7).  
The fulfilment of system reactive power constraints comes at a cost in terms of achievable RES penetration levels, system economics, and the management of thermal units. Comparing Figure 4a,b it is apparent that RES curtailments are increased when reactive power constraints apply, due to the increased number of thermal units required to be online, which present a higher total minimum loading level (solid red line/TML of Figure 4), limiting the RES hosting capacity. This is only partially alleviated through the low load operation of thermal units during low demand periods (gray line/rML of Figure 4).  
It is worth observing that the only feasible solution that concurrently fulfills the active and reactive power constraints of the problem involves the commitment of an expensive OCGT unit during the low demand hours, since the OCGT presents at the same time increased reactive power absorption capability (see Appendix A) and a very low TML, below 20% of its rated power. However, this leads to a substantial escalation in the production cost of the system, as demonstrated in Figure 7.