## 1 Introduction
### Power Reserve Control (PRC)
A non-linear least-squares fitting is also used in [17], proposing further and deeper observations about the possibility to follow the actual characteristics of the PV modules when temperature and irradiance change, and demonstrating that the non-linear least squares fitting works well also in changing ambient conditions if measurements close to the MPP or on its right are used. Since the current-voltage curves of PV modules are almost superposed for different temperatures on the left side, it is not possible to estimate the correct one if measurements are taken on that side. However, since the temperature dynamics are slower than the irradiance one, it is possible to operate with measurements on the left side, at least for short periods. A different method is used in [16]: the MPP is found using a polynomial function of the irradiance and the temperature, which in this case, differently from the previous ones, are measured. The coefficients for the polynomial relation are found by calculating the value of the module current (with Equation (7)) for all the expected irradiance, temperature, and voltage values, then numerically finding the power maximums and interpolating them with a linear regression. It is also worth stating that, in photovoltaic systems, another possibility to find the MPP are the Perturb  
Figure 2: Single-stage grid-connected PV system. and Observe methods [19], representing the traditional methods of estimation, which in this case are not useful since the knowledge of the entire power-voltage curve is necessary. Once the MPP is known for the actual operating condition (so for an irradiance/ temperature pair) the required operating point to deliver the curtailed active power output desired has to be calculated. The most used control variable is the PV voltage: the voltage level corresponding to the desired output power is calculated and then it is compared with the actual voltage applied to the PV system to produce a duty cycle signal by means of a proportional-integral (PI) controller. This approach is used in [14; 16; 17]. The same reasoning is adapted with the power as a reference variable in [13; 15], where the desired value of power is compared with the actual value to produce a duty cycle signal for the boost converter. It is also important to notice that, for a certain level of curtailed power desired, there are two options in terms of voltage, respectively, on the left and on the right side of the maximum power point in the power-voltage curve. The scientific literature does not agree on which is the best side of the power curve of the PV module to operate the power curtailment. All the existing algorithms work only on one side. Since the operating condition throughout the year can be very different, this can be limiting. In fact, operating on the right side allows a bigger variation range of the power, but at the same time modest reductions in irradiance can lead to a drop in the power output. This behavior can be easily explained looking at the characteristic power-voltage curve shape: reasoning at fixed irradiance, a request of power reduction from the system operator can be easily satisfied with small variations of the operational voltage. This is intrinsic to the high slope of the right part of the power-voltage curve. On the contrary, in a context in which the irradiance variates a lot, if a reduction in irradiance occurs at constant voltage the power output would immediately reduce, and even become null. Instead, on the left part of the curve the pros and the cons are shifted due to the lower slope of the curve: there is a moderate insensitivity to the irradiance, but at the same time the range of variation of power is very restricted. From these observations, it can be immediately pointed out how the choice of a single side of the power-voltage curve for power curtailment can influence the actual capability of the plant to participate in frequency control.