# Dimensioning of Reactive Power Compensation in an Autonomous Island System
## 1 Introduction
The implementation of the right capacity of reactive power compensation facilities, as needed to minimize negative effects of increased reactive power absorption requirements from online generators for the autonomous power system of Rhodes, is the topic addressed in this paper. Both an investment-oriented and an operational approach are evaluated to derive the optimal size of shunt reactors needed for alleviating the reactive power equilibrium-based distortions introduced in the power system of Rhodes after reinforcement of its HV network. To determine an acceptable commitment status of thermal units adhering to the reactive power absorption specificities of the Rhodes system, a suitable UC-ED model for islands is implemented [17; 18] that has been amended to include simplified reactive power constraints. System operation is investigated under several reactive compensation levels, ranging from full to no compensation. System operation is simulated for an entire year, through consecutive execution of the daily UC-ED process. The impact of reactive power constraints on key system performance indices, such as the annual RES penetration levels, system generation cost, and operation of thermal units, is evaluated to determine the preferable size of shunt reactors from an operating cost and efficiency viewpoint. To assess the feasibility of the obtained results in terms of operational security of the system, a frequency stability analysis is performed, examining system operation at lowest annual demand and thus minimum inertia conditions. Frequency stability is assessed for two major system disturbances and three different reactive power compensation levels. In brief, the main contribution of this study lies in the development and application of a coherent method to determine the optimum size of reactive compensators for a real-world study case island. The method quantifies the tangible system benefits deriving from the introduction of shunt reactors to a system facing VAr excess by utilizing a detailed UC-ED methodology. The proposed UC-ED model builds upon the classical MILP mathematical formulation [19; 20; 21], and further incorporates the reactive power absorption capabilities of thermal units so that they deal with the excess of reactive power generated by the HV network of the island during low load periods. The mathematical formulation incorporates reactive power equilibria during normal operating conditions, as well as events impacting the reactive power absorption capability, such as the loss of online generating units. The model employed in the paper incorporates the low-loading operation of thermal units, which has been presented in detail in a previous work of ours [22], and contributes to the feasibility of the UC solution for this specific case study. Additionally, the proposed UC-ED model complements the network analysis tools typically used for this purpose to justify a reasonable level for reactive compensation. Overall, the objective and contribution of this work is to optimally size reactive compensation in real-world island systems by concurrently evaluating several indices, including RES curtailment levels, system economics, constraints of thermal units, and operating security criteria. The remainder of the paper is organized as follows. Section 2 describes the specificities of the Rhodes power system. Section 3 addresses how limitations in the reactive power absorption capability of synchronous generators may cause voltage instability in autonomous power systems and defines the reactive power consumption requirements of the system. Section 4 describes the mathematical formulation of the UC-ED optimization and performs the cost-benefit analysis regarding the feasibility of introducing new reactive power compensator. Section 5 presents the dynamic security assessment of the results of the cost-benefit analysis and Section 6 discusses the main conclusions.