## 1 Introduction
### Power Reserve Control (PRC)  
This control logic can be seen as a particular case of the PLC algorithm. In fact, instead of imposing a certain constant power output level, in the PRC algorithm the PV output is regulated as a percentage of the maximum available power in each time instant. This dynamically changing fraction of the MPP is called Power Reserve (\(\Delta P\)). The output power is then obtained as:  
\[P_{res}=P_{MPP}-\Delta P \tag{3}\]  
Additionally, in this case, the challenge is to estimate the MPP, since it is one of the inputs necessary for the controller. The detailed explanation of this algorithm as well as of the determination of the power-voltage curve (and so of the MPP) is provided in Section 2, where the complete implementation of a model to control the active power output of photovoltaic modules in order to enable their capability to participate in the primary frequency control is described. This work is focused on the third solution. To better organize the literature review regarding PRC, the differences between approaches are outlined under some key aspects: PV plant model, estimation output, controlled variable, MPP tracking method, and operational side of the power-voltage curve. The summary of reviewed articles is presented in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{N}^{\circ}\) & **Authors** & **Reference** \\ \hline
1 & [PERSON] et al. & [13] \\
2 & [PERSON] et al. & [14] \\
3 & [PERSON] et al. & [15] \\
4 & [PERSON] et al. & [16] \\
5 & [PERSON] et al. & [17] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of reviewed articles about Power Reserve Control of PV systems. The starting point of each work about the power reserve control of a photovoltaic grid-connected system is the model adopted for the plant itself. There are two main approaches: the most complete one is the two-stage model [18], which comprehends all the conversion stages between the modules and the grid. It includes the boost converter to step up the voltage to the DC-link value, the inverter, and an LCL filter. However, since the actual power output control is operated on the DC-DC converter, the single-stage model is the most commonly used in the literature, as represented in Figure 2, where the duty cycle command is obtained using a control module. The main differences between all the reviewed methods are found in this control module. The logical process of the control block is a sequence of some key operations. First of all, the maximum power point is estimated in real-time. This calculation can be performed through a variety of techniques. The approach proposed in [13] is probably the most widespread: the power-voltage curve is estimated from past measurements of power and voltage, in the current window close to the operating point, through the equation for the power-voltage curve shown in Section 2. The measurements are referred to the last temperature value recorded and fitted through a least-squares curve fitting method, whose output are the five characteristic parameters of the module, as presented in Section 2. Qualitatively, without entering in the detail of the mathematical formulation, which is not the focus of this paper, the least squares fitting consist in finding the power-voltage curve that best approximates the measurements, i.e., gives the lowest difference between the measurements and the estimated values. A similar approach is used in [14], but with a combination of a linear and a quadratic approximation. The interesting aspect of [14] is that, focusing on multi-string PV plants, one string called \"master string\" is operated at the MPP, but using the estimation of the MPP of the master as reference, while the others are in the curtailed mode.