## 1 Introduction
### FRT Capability and DRES Reaction During Grid Faults
#### 3.5.2 Measurement and Quantification  
The following measurement and quantification methods are suggested in order to transform the contribution to fault clearing and the associated FRT capability as an AS: A fault condition can be detected by the sudden reduction of the 20 ms RMS values of any of the DRES phase-voltages below a limit which is adjustable by the DSO [11; 12]. Next, the DRES switches to current control mode and starts injecting currents in the faulty phases like the one shown in Figure 11, emulating the operation of a SG under short circuit. The current resembles the fault current of a conventional SG with a subtransient, \(t_{\text{subtr}}\) and transient \(t_{\text{tr}}\) period. The respective RMS value of the current is \(l^{\prime\prime}\) and \(l^{\prime}\). The subtransient period starts immediately after the detection of the fault, while the transient period ends as soon as the voltage recovers to steady-state values. All of these parameters can be configured by the DSO starting from zero up to a maximum value determined by the thermal limit of the converter switches in the case of the converter-interfaced DRES. In the case of DRES that are directly coupled with SGs, the aforementioned parameters are not configurable, but are determined by the SG construction. However, in both cases the contribution to fault clearing can be measured and quantified based on the energy quantity \(l^{2}\cdot t\) as follows:  
\[ \begin{array}{l}E_{fault\_claring}=E_{Subtransient}+E_{Transient}\text{ where}\\ E_{Subtransient}=\int{(l^{\prime\prime})^{2}dt}=(l^{\prime\prime})^{2}\cdot t_{ subtr}\\ E_{Transient}=\int{(l)^{2}dt}=(l^{\prime})^{2}\cdot t_{tr}\end{array}  \tag{17}\]  
It is known that the grid codes among the various countries differ with respect to the requested FRT capability of the DRES [105; 106]. However, the implementation of an FSS system enables each  
Figure 11: DRES fault current [105]. DSO to configure its own FRT curve on each individual DRES. Such a generic FRT curve is shown in Figure 12 determined by eight points. The required storage capacity of the FSS, \(C_{\text{FSS}}\), is estimated by the case where, during the fault, the primary source is providing the nominal DRES power, \(P_{\text{NOM}}\), while for the time period \(t_{4}-t_{0}\) the electrical power injected is zero, i.e., the DRES injects either zero or only reactive current. The required \(C_{\text{FSS}}\) is given by Equation (18):  
\[ \begin{array}{l}E_{\text{FRT}}=P_{\text{NOM}}\cdot(t_{4}-t_{0})\\ C_{\text{FSS}}=\frac{2E_{\text{FRT}}}{V_{\text{FSS,rated}}^{2}}\end{array}  \tag{18}\]  
In case the DRES is required or allowed to inject active current, then only a portion of \(C_{\text{FSS}}\) calculated by (18) is required. In this case, the DRES will inject the maximum allowable current which is equal to the nominal current. Therefore, the active power will be directly proportional to the terminal  
Figure 12: Energy estimation (**bottom**) for supercapacitor sizing based on the generic FRT curve (**top**), [105]. voltage. This portion, \(C^{\prime}_{\text{FSS}}\) is calculated by (19) where \(P_{1}\) is the active power injected under voltage \(V_{1}\), etc. \[ \begin{split} E^{\prime}_{\text{FRT}}&=P_{\text{NOM} }\cdot\left[\begin{array}{l}(1-V_{1})\cdot(t_{1}-t_{0})+(1-V_{2})\cdot\ (t_{2}-t_{1})+\\ +\frac{1}{2}(V_{3}-V_{2})\cdot(t_{3}-t_{2})\ +\\ +(1-V_{3})\cdot(t_{3}-t_{2})+(1-V_{3})\cdot(t_{4}-t_{3})\end{array}\right]\\ C^{\prime}_{\text{FRT}}&=\frac{2E^{\prime}_{\text{FRT}}}{V^{2}_{\text{FSS, rated}}}\end{split}  \tag{19}\]  
\(V_{\text{FSS\_rated}}\) is the rated voltage of the FSS in Volts (V), while all the rest voltages \(V_{1},\ V_{2},\ V_{3},\ V_{4}\) are expressed in pu. It is noted that (18) or (19) give the size of the ultracapacitor that should remain discharged in order to absorb the power mismatch. Another case that should be considered is the following: the DRES should contribute with active fault currents when the primary source is not available, e.g., during the night for a PV system.