# Dimensioning of Reactive Power Compensation in an Autonomous Island System
## 4 UC-ED-Oriented Cost-Benefit Analysis
### Reactive Compensation Requirements and Feasibility Analysis  
From the analysis performed so far, it has become clear that in order to secure system operation with respect to the reactive power absorption requirements, an unreasonable unit commitment and load dispatch schedule must be applied, with an excessive number of units in operation, including peaking OCGTs during base load periods, and prolonged operation below the TML levels of the units. Figure 4: System operation during the lowest demand day of the year (**a**) with full and (**b**) without any reactive compensation scheme. Figure 5: Fulfillment of system reactive power requirements by online thermal units at G and G-1 conditions, for the operating conditions of Figure 4.  
To address these issues, the operation of the Rhodes power system is investigated in this section assuming seven different levels of reactive power compensation, evaluating the  
Figure 6: Loading levels of thermal units committed to meet demand requirements for the cases of Figure 4.  
Figure 7: Hourly variable generation cost of the system in the lowest demand day, with reactive power constraints and in their absence. positive effects on generation cost and RES curtailments, which provide the basis for the cost-benefit analysis of investments in reactive compensation. The business-as-usual/no-compensation scenario is characterized by a 27 MVAr reactive power consumption from online thermal units during low demand periods (\(Q^{req}=-27\) MVAr). Compensating reactors are then introduced in steps of 4 MVAr capacity, as shown in Table 1.  
Renewable curtailments and the annual duration of thermal units' operation below their technical minimum loading are presented in Figure 8 as a function of the installed reactor capacity. The introduction of appropriately sized inductive compensation can reduce both curtailments and TML violations. It appears that a reactor capacity of 12 MVAr brings about the entire anticipated benefit, reducing annual RES curtailments by 5%, from 13% to 8%, and the hours of TML violations by almost 93% (from 2400 h/y to less than 180 h/y cumulatively for all thermal units). The introduction of additional reactor capacity is pointless with regard to these performance indicators. The achieved reduction in the annual generation cost of the Rhodes system through the installation of compensating reactors is shown in Figure 9. This is primarily due to two factors. First, easing reactive power constraints (21)-(27) UC-ED leads to the commitment of fewer units in low demand periods, with a lower cumulative TML and therefore more room available to accommodate renewable production. The reduction in RES curtailments shown in Figure 8 is translated into a lower system variable cost, due to the substitution of more expensive thermal generation. In addition, the commitment of expensive OCGT units during low demand periods (see Figure 6) is now avoided, resulting in further savings. Overall, significant variable cost reductions are observed for inductive compensation up to around 8 MVAr. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multicolumn{2}{c}{**Reactive Compensation Level**} & \multirow{2}{*}{\(Q^{req}\) **at Minimum Load**} \\  & **(MVAr, Inductive)** & \\ \hline
1 & 0 & \(-27\) \\
2 & 4 & \(-23\) \\
3 & 8 & \(-19\) \\
4 & 12 & \(-15\) \\
5 & 16 & \(-11\) \\
6 & 20 & \(-7\) \\
7 & 24 & \(-3\) \\
8 & 27 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examined reactive compensation levels. Figure 8: (**a**) RES curtailments and (**b**) annual hours of thermal unit TML violations, as a function of reactor capacity in the power system of Rhodes. The system benefit due to the presence of inductive compensation is calculated as the cost difference between the business-as-usual scenario without reactive compensation and the scenario that includes the examined size of inductive compensator.