## 1 Introduction
### Frequency Containment Reserves (FCR)
#### 3.3.2 Measurement and Quantification  
In order for this response to be treated as AS, its provision should be similar to the conventional PPs, i.e., the DRES should be able to provide the balancing power both upwards and downwards. To achieve the latter without adding any storage device, a variable-output DRES should operate below its MPP, \(P_{MPP}(t)\), with a headroom specified by the aggregator/DSO. Since the MPP varies with time, it is reasonable to define the headroom as a constant portion of the available \(P_{MPP}(t)\), which means that the DRES output power at time instant \(t\), will be:  
\[P(t)=P_{MPPT}(t)\cdot(1-p_{head}) \tag{10}\]  
where, \(p_{head}\), is the headroom expressed in pu with respect to \(P_{MPP}(t)\). This operating mode will be followed as long as \(f_{0}-\frac{\Delta f}{2}\leq f(t)\leq f_{0}+\frac{\Delta f}{2}\). In case the frequency is outside the set deadband, the power of the DRES will be determined by the frequency measured at its PCC and the slopes of the droops. From Figure 10 it can be deduced that  
\[P(t)=P_{MPP}(t)+s_{du}[f(t)-f_{\min}]\text{ for }f(t)<f_{0}-\frac{\Delta f}{2} \tag{11}\]  
and:  
\[P(t)=P_{\min}(t)+s_{do}[f(t)-f_{\max}]\text{ for }f(t)>f_{0}+\frac{\Delta f}{2} \tag{12}\]  
It is noted that \(f_{\min},\ f_{\max}\), \(\Delta f\), \(p_{head}\), \(S_{du}\), \(S_{do}\) are interrelated and fully configurable by the DSO/aggregator. The aggregator/DSO may enable/disable the operation of a particular DRES as FCR according to agreements made with the TSO. The contribution of a DRES to the PFR over a period \(T\), can be evaluated by:  
\[E_{PFR}^{T}=\int\limits_{t=t_{\text{enable}}}^{t_{\text{disable}}}P_{MPPT}(t) \cdot dt-\int\limits_{t=t_{\text{enable}}}^{t_{\text{disable}}}P(t)\cdot dt \tag{13}\]  
where \(T=t_{\text{disable}}-t_{\text{enable}}\) and \(t_{\text{enable}}\) is the time instant when the DSO sends to the DRES the enable signal to start operating as FCR, while \(t_{\text{disable}}\) is the time when the DSO sends to the DRES the disable signal, to finish the AS. It is noted that, while \(P(t)\) is the measured active power at the PCC of the DRES during the period \(T\), the power \(P_{MPP}(t)\) can only be calculated because it was not actually delivered. It can be calculated by the measured MPPT power (actually the available \"mechanical\" power, \(P_{m-MPPT}(t)\)) at the output of the DRES primary source (PV, wind generator, etc) and the efficiency of the DRES converter(s). Analytical tools for estimating the efficiency \(\eta_{DRES}(P_{m-MPPT})\) as a function of \(P_{m-MPPT}(t)\) have been developed in [21,22]. Thus, \(P_{MPP}(t)\) can be calculated as:  
\[P_{MPPT}(t)=P_{m-MPPT}(t)\cdot\eta_{DRES}(P_{m-MPPT}) \tag{14}\]It is evident that Equation (13) represents the lost opportunity cost (i.e., the energy that would be otherwise injected into the grid) in order for the DRES to act as a FCR entity. Therefore, this expression is suggested as a method for the quantification of the contribution of a DRES to PFR. It is noted that \(P_{m-MPPT}(t)\) is internally calculated and registered by each variable-output DRES because they use it as control objective. However, in order to practically implement (13), the value of \(P_{m-MPPT}(t)\) should be retrieved from the internal registers of the DRES in synchronization with the measured \(P(t)\). Regarding the accuracy of the various measurements, the specifications set in the IEEE 1547-2018 standard [10] are suggested considering that PFR is a quasi-steady state condition: frequency should be measured with 10 mHz accuracy over a window of 50 cycles (1 s). The active powers in (13) are suggested to be averaged over the same period (1 s) with an accuracy equal to 1% of the nominal DRES power. This suggestion is stricter than the respective specifications in [11; 12], where the accuracy in the measurement of the power should be 10% of the nominal power and should be averaged over 1 min.