## 1 Introduction
### Power Reserve Control (PRC)
In this sense, it becomes crucial to develop an algorithm able to adapt the control strategy to the boundary conditions of the problem (i.e., meteorological conditions, level of power reserve demanded by the system operator) [17]. This is why the present work adopts the approach proposed in [17], to be able to work on both sides of the power-voltage curve, exploiting the advantages of the operation on the two sides as a function of the situation. Together with the photovoltaic technology, wind turbines are certainly the most exploited solution to drive the energy sector through the decarbonization. For photovoltaic systems, the algorithms to control the active power output through the power reserve control are relatively similar to each other in the logical sequence, but for wind turbines this does not happen. Indeed, there are different techniques to provide inertial control and, in particular, primary frequency control. The large variety of solutions is well described in [20]. Primary frequency control with wind turbines is an autonomous response to a change in system frequency that emulates the governor control of synchronous generators. More precisely, when a change in frequency is detected, the wind turbine modulates its power output to respond to this change and help to balance the system. Figure 3 summarizes different categories of methods for inertial control and primary frequency control in wind power plants. First of all, it is important to offer an overview of the different types of wind turbines present in the market. In general, there are fixed speed wind turbines, semi-fixed speed wind turbines, and variable speed wind turbines (VSWT) [20]. Fixed and semi-fixed speed turbines have an inertia constant but are smaller with respect to the conventional synchronous generator ones, due to the lower coupling of induction generators with the grid frequency. This makes their inertial response lower and slower compared to the conventional generation [20]. On the other hand, as already mentioned, variable speed wind turbines (which are dominant in the market due to their higher efficiency) are decoupled from grid frequency due to the presence of the power electronics converter, so their contribution to the system inertia is null. However, it is possible to achieve a short-term inertial response from VSWTs by introducing an additional control loop in their control system. This control modifies the operation, allowing the turbine to exploit the kinetic energy of its rotating mass to modulate the electrical power output of the system and so to contribute to participation in the inertial control. The functioning principle is simple: if the control detects a frequency variation, a signal is sent to the turbine speed governor or torque governor, temporarily modifying the power setup according to the magnitude of the frequency variation and enabling the possibility to exploit an amount of the kinetic energy of the rotor. For example, if an increase in power output is required to balance a frequency decay, the kinetic energy stored in the rotor is temporarily released. In this case, an unbalance between the electrical power injected into the grid and the mechanical power extracted from the wind is created, causing a deceleration of the rotor (i.e., a decrease in kinetic energy). This slowing down reduces the lift, discharging aerodynamically the blades, and increasing the stall risk at the bottom sections of the blade. To avoid stalling, the overproduction period has to be followed by an underproduction period in which the rotational speed of the rotor is increased [20]. There are different models for the inertial control described in the literature, but they can be conceptually divided into two main categories: a \"simple\" inertial control, which takes into account just the absolute value of the frequency deviation \(\Delta f\) or the frequency derivative \(df/dt\), or an inertial-droop control, which takes into account both. The first category is presented for example in [21; 22], while the second is adopted in [23; 24].