## 1 Introduction  
The desire to reduce our dependency on fossil fuels, particularly oil and gas, and the need to lower greenhouse gas emissions have significantly increased in recent decades [1; 2; 3; 4]. This trend of attaining sustainability has had a significant impact on electrical power systems worldwide. These ambitions (reduction in fossil fuel usage) require the transformation of conventional electrical power systems into hybrid power systems, i.e., the integration of renewable energy (RE) sources into existing power networks [5; 6]. Despite the benefits provided by RE sources, integrating them into conventional power systems faces numerous problems [7], such as power system stability and reliability [8; 9; 10; 11]. Wind energy (WE) is globally the most adopted RE source used to produce electrical energy [12; 13]. However, its intermittent nature results in a variance in power generation and load demand in hybrid power systems. Such a variance in power could result in a frequency deviation (FD) [14] or a high rate of change of frequency (RoCoF) [15], which may create more complicated and uncertain conditions for hybrid power systems, or, in certain rare events, in partial or full blackouts. Some of the major blackouts in recent decades took place in (1) 2013: Italy, Scandinavia, and North America [16]; (2) 2009 and 2011: Brazil [17]; (3) 2012: India [18]; (4) 2015: San Cristobal (Ecuador) [19] and Turkey [20]; and (5) 2016: Australia [21]. Furthermore, on the islands of Flores-Azores, Portugal, wind energy penetration was limited due to low-frequency problems [22]. On the French island of Guadeloupe, power systems [23] faced critical FD problems due to the increased penetration of renewable energy (wind and solar). Therefore, after a series of FD problems in France, the French government limited renewable energy penetration to 30% in electrical power systems. Similarly, according to [24; 25; 26; 27; 28; 29], conventional power systems on various islands faced FD problems due to the penetration of renewable energy. Therefore, this study focuses on the island-based hybrid wind-diesel power system (WDPS) of San Cristobal Island, Ecuador, as a case study for primary frequency control (PFC). The diesel power plant generator, part of the hybrid WDPS examined in this paper (Section 3), has already been studied by us in our previous work [30]. Conventional power plants feature significant system inertia. In the case of contingencies or power imbalances, the available system inertia is utilized to restore the power system to its normal condition. However, in some cases, this system inertia is not enough to restore the system, particularly in hybrid isolated island power systems. In such systems, the RE penetration rate plays a vital role in power system stability. In [29; 30; 31], the impact of RE penetration on existing power systems is explained. However, in hybrid power systems, the system inertia is significantly reduced due to the intermittent nature of the RE source [32]. To overcome such problems, numerous studies have been conducted [33; 34]. Irrespective of such solutions, the WT itself is unable to release synthetic inertia [29] due to fast-acting power electronics converters [35]. However, it is possible to make WTs effective in terms of releasing hidden inertia or contribute to reducing FD by releasing synthetic inertia. Before discussing how to achieve system inertia in WTs, it is important to consider the type of WT utilized for this purpose. In recent decades, the Doubly Fed Induction Generator (DFIG)-based Variable-Speed Wind Turbine (VSWT) has become the market preference [36; 37; 38] due to its performance capabilities in a wide range of angular velocities. Therefore, numerous frequency control approaches (Figure 1) have been adopted for releasing synthetic inertia from VSWTs, as discussed in [39; 40]. Moreover, Table 1 brieflyshows various control approaches adopted in previous studies to release this inertia in WTs.