# Dimensioning of Reactive Power Compensation in an Autonomous Island System
## 3 Needs for Reactive Power Compensation  
### Synchronous Generator Underexcited Operation in Autonomous Power Systems  
For a synchronous generator to consume reactive power, it normally needs to operate underexcited. Typically, synchronous generators are protected against extensive underexcitation by (a) the UEL that will block the reduction of the excitation current below a selected threshold to prevent loss of synchronism of the generator and (b) the LOF relay that will trip the generator in case of detecting excitation loss [12]. In large, interconnected power systems, the UELs of synchronous generators play a critical role in protecting them from rotor angle instability (loss of synchronism). Additionally, the UEL is affectively set in a way to avoid the occurrence of loss-of-field incidents during normal operation. On the other hand, the application of UELs in isolated autonomous systems should be approached with caution, given that, while there is low risk for loss of synchronism, an attempt to limit the absorption of reactive power may lead to overvoltage instability [14; 15]. The diversified behavior between isolated and interconnected power systems is demonstrated by the two capacitive networks shown in Figure 2.  
Figure 1: Rhodes 150 kV transmission network. Figure 2 shows the common configuration, where an equivalent single synchronous generator is interconnected to an infinite bus through a transmission circuits represented by a series reactance \(X\) and a concentrated shunt susceptance \(B\). With \(R<<X\) at the transmission level, the voltage difference between the two HV nodes of Figure 2a is approximately [24]:  
\[\Delta V=V_{g}-V=\frac{XQ}{V} \tag{1}\]  
\[Q=Q_{g}+BV_{g}^{2}-XI^{2} \tag{2}\]  
At light load conditions, the current and reactive power losses \(XI^{2}\) are low, there is significant local reactive power generation (\(BV_{g}^{2}\)), and the generator consumes reactive power (\(Q_{g}<0\)). However, the generator reactive power absorption is limited in order to avoid decreasing the generator excitation below a predefined threshold. This function is automatically provided by the UEL of the generator. The result is the export of reactive power surplus (\(Q>0\)) and a generator voltage rise (\(\Delta V>0\)). Figure 2b shows the case of an autonomous power system, where the equivalent generator feeds a small active power load. In this case, there is no way to export reactive power and the following constraint needs to be satisfied to obtain a feasible operating point:  
\[Q_{g}+BV_{g}^{2}=Q_{L}+XI^{2} \tag{3}\]  
Again, at light load conditions, the reactive power losses (\(XI^{2}\)) are low, as is the reactive power consumption of the load \(Q_{L}\), which results in a very low voltage difference between the two HV nodes of Figure 2b. Due to the above constraint (3), attempting to limit the generator reactive power absorption may result in overvoltage instability: increasing the field current increases the generator EMF and the system voltage, which results in further reactive power produced by the HV lines and consumed by the generator. Note that operating with constant excitation may also be unstable, as analyzed in [14; 15; 16]. It is therefore crucial to make use of the reactive power consumption capabilities of the synchronous generators and avoid inhibiting their automatic voltage regulation (e.g., by the underexcitation limiter or manual blocking of the excitation) to avoid voltage instability. Note also that, contrary to standard operator experience with conditions as shown in Figure 2a, the operational conditions of Figure 2b are not necessarily associated with high voltage levels. In addition, it is beneficial for the system to operate at a relatively low voltage, which is defined by the equivalent generator (and its step-up transformer, not shown in Figure 2), as this will result in lower reactive power generation.