**1. Introduction**

The different services carried out by the transmission system operators (TSO) for a reliable and secure power system are known as ancillary services [1]. Among them, load-frequency control focuses on mitigating the effects of unpredictable changes both in the demand and in the generation units that can address frequency deviations [2]. In fact, power imbalances between generation and consumption cause frequency variations [3]. In Europe, frequency control has a hierarchical structure, usually organized in up to five layers (from fast to slow timescales): (i) frequency containment (also known as primary frequency control); (ii) imbalance netting; (iii) automatic and/or manual frequency restoration (also known as secondary frequency control), and (iv) replacement [4]. If the different reserves of such frequency control layers are consumed or unable to keep frequency within an acceptable range, a variety of strategies called special protection systems are then used. Load shedding is included in those special protection systems. Moreover, it is considered as the last option to prevent frequency instability [5]. Despite load shedding being an effective solution to prevent a power system collapse after a major imbalance, it is considered as an undesirable situation and it is important to reduce it as much as possible [6–8].

Traditionally, power systems have been based on conventional power plants with synchronous generators directly connected to the grid, automatically providing their stored kinetic energy after a generation-load mismatch [9]. However, in recent decades, power systems have been suffering a slow change from conventional synchronous power plants to inverter-interfaced renewable energy sources (II-RES), i.e., wind power plants based on variable speed wind turbines (VSWTs) and/or solar photovoltaic (PV) [10]. Among them, VSWTs are considered as the most efficient, developed, and installed renewable resource, and currently they account for more than 650 GW of installed capacity around the world [11,12]. This remarkable integration of wind power plants requires an important reformulation of their contribution to ancillary services [13]. Moreover, as they are connected to the grid through power inverters, the synchronous inertia of the power system decreases when such renewable source replaces conventional power plants [14]. Indeed, faster rate of change of frequency (RoCoF) and larger frequency deviations are related to low synchronous system inertia values [15]. These effects are even more critical in isolated power systems [16,17]. As a result, Toulabi et al. consider that, due to the massive integration of VSWTs, their participation into frequency control is necessary [18]. With this aim, different frequency control approaches can be found in the specific literature to effectively replace conventional power plants by VSWTs and maintain a reliable power system operation [19]. These strategies are summarized in Figure 1 according to the different approaches [20,21].

**Figure 1.** General classification for Variable Speed Wind Turbines (VSWTs) frequency control techniques.

VSWTs are designed to work in their maximum power point (MPP) according to the available wind speed *sw*: *pMPP*(*sw*) [22]. As a consequence, the first approach (deloading technique) consists of operating the VSWTs in a suboptimal power point *pdel*, below *pMPP*(*sw*). Therefore, a certain amount of power Δ*pd* can be supplied in case of a power imbalance [23,24]. Two different possibilities are identified [25]: (i) the pitch-angle control and (ii) over-speed control. In the first one, the pitch angle is increased from *β*0 to *β*1 for a constant *sw*. Subsequently, the generated power *pdel* is below the maximum power *pMPP* [26–29]. When the additional power Δ*pd* is supplied, the pitch angle reduces to *β*0. The over-speed control increases the rotational speed of the rotor, shifting the supplied power *pdel* towards the right of the maximum power *pMPP* [30–32]. When the additional power Δ*pd* is supplied, the rotor speed has to be reduced to *ωMPP*, releasing kinetic energy [33]. However, despite the fact that this technique can improve the long term frequency regulation, it is not an economically viable solution for wind power plants' operators due to loss of profits [34].

Due to the power inverter, VSWTs cannot naturally provide the kinetic energy stored in their rotor and generator. To overcome this, one or more additional control loops must be included in the power inverter. Three different possibilities can be found in the specific literature: (i) the droop control, (ii) the hidden inertia emulation control, and (iii) the fast power reserve approach. The droop control provides an additional active power Δ*p* proportional to the frequency deviation Δ *f* , following Δ*p* = − Δ*f RWT* , where *RWT* is the droop control setting of the VSWT [35–39]. This definition of Δ*p* gives an adaptive response depending on the frequency excursion severity and thus emulating primary frequency control of conventional generation units [40]. The hidden inertia emulation control usually includes two different loops: one considering the RoCoF and the other considering the frequency excursion ( Δ*p* ∝ RoCoF & Δ *f*) [41–43]. However, there are also proposals to use only one additional loop, being Δ*p* ∝ RoCoF [44–46]. Even though these methods improved the nadir frequency (minimum value), a little frequency dip was observed in later stages. This was due to a small reduction in the generated power compared to the prefault active power (thus, not operating in the MPP) [47]. The fast power reserve approach defines the overproduction power Δ*p* as a constant value independent of the power system configuration and frequency deviation [48–51] or as a variable value depending on the frequency deviation or minimum rotor speed limits [52–54]. With these three techniques, as the additional power Δ*p* is provided, the rotor and generator rotational speeds decrease (subsequently, modifying their torques). Rotor speed variations cause large amplitude edgewise vibrations for the blades [55], affecting the productivity and reducing the efficiency [56]. Large torque increases can address severe mechanical loads on the turbine, even causing critical situations under high mechanical stress conditions [57]. Moreover, consecutive torque increments is related to random load cycles, with important influences on fatigue loads [58].

In this work, a new fast power reserve controller for frequency regulation is proposed for isolated power systems including conventional generation (thermal units) and wind power plants (VSWTs). The proposed adaptive frequency controller is based on a linear regression from different power system parameters (i.e., RoCoF, active power supplied by each synchronous group, and synchronous inertia) to estimate the additional power provided by the wind power plants by maintaining certain frequency thresholds. This way mechanical stress is reduced without excessively prejudicing power system. Subsequently, VSWTs do not always participate in the frequency control but only when they are required according to both the monitored variables. VSWTs frequency control contributions are thus optimized, improving the grid frequency response and providing similar or lower load shedding actions in line with previous frequency control strategies. This proposed VSWT controller approach is tested in the Gran Canaria Island (Canarian archipelago, Spain), an isolated power system where the wind power capacity has doubled since 2017 (from 90 to 180 MW) [59]. Moreover, from 2005 to 2010, more than 200 trips of generators were registered per year in the Canarian archipelago, hence activating the corresponding load shedding programs [60].

The rest of the paper is organized as follows: Section 2 describes the mathematical model used to simulate the power system under consideration; the new frequency control approach proposed in this work is explained in Section 3; cases of study and simulation results are provided in Section 4; Finally, Section 5 gives the conclusions.
