## 2 Short-Circuit Current Calculation in Distribution Network with Renewable DGs
### Equivalent Model of Renewable DGs for Short-Circuit Calculation  
In the short-circuit calculation of the AC power grid with renewable DGs, the equivalent model of DGs is usually analyzed according to the voltage drop of the PCC point, whether for the distributed access of a single DG to the AC power grid or the centralized access of large-scale DGs to the AC power grid. Common DGs in distribution networks can be generally divided into two categories according to the type of grid connection control strategy, including a doubly fed induction generator (DFIG) belonging to the part-power inverter-based power sources and photovoltaic sources and a permanent-magnet direct-drive wind turbine belonging to full-power inverter-based distributed generators (IIDGs). Since the control strategies of a DFIG and IIDG are different, the equivalent models need to be discussed separately. When the voltage drop value at the grid point of a DFIG is big, about 0.2-0.4 p.u. of the rated voltage, the crowbar protection is put into operation to avoid the rotor inrush current. And then, the DFIG is equivalent to the induction motor after the crowbar resistance is strung; the short-circuit current and the voltage at the grid point are linearly correlated. When the voltage drop value is limited, about 0.4-0.9 p.u., the crowbar resistance is not put into use, and the reactive output current would be adaptively regulated via the control system according to the voltage drop value at the terminal of DGs. The above output characteristics of a DFIG are summarized as a mathematical expression in the form of a segmented function, which can be equated to mode 1 and mode 2 by analyzing the results of various research scholars, as shown in Equations (10) and (11), respectively. The difference between Equations (10) and (11) is in the treatment of the intermediate nonlinearization intervals when the voltage of the PCC is in the range of [0.2 0.9] p.u. Different from Equation (10), the saturation current of the inverter, which is limited by the current carrying capacity of the power electronic devices, is specially considered in Equation (11). In the meantime, the normal output active current, \(I_{N}\), is also considered in Equation (11), while only the reactive current is considered in Equation (10). According to refs. [28; 29], the equivalent modes of a DFIG for output current calculation can be expressed with Equations (10) and (11), while the equivalent mode of an IIDG is expressed with Equation (12). \[I_{\text{DFIG}}\,=\, \begin{cases}0&0<U_{\text{DFIG}}\,<0.2\text{ p.u.}\\ k_{\text{s}-1}U_{\text{DFIG}}&0.2\text{ p.u.}\,\leq U_{\text{DFIG}}\,<0.4\text{ p.u.}\\ k_{\text{s}-2}(0.9-U_{\text{DFIG}})&0.4\text{ p.u.}\,\leq U_{\text{DFIG}}\,<0.9\text{ p.u.}\\ P_{0}/U_{\text{DFGG}(0)}&0.9\text{ p.u.}\,\leq U_{\text{DFIG}}\,\leq 1.0\text{ p.u.}\end{cases}  \tag{10}\]  
where \(I_{\text{DFIG}}\) represents the ratio of output current to the rated current for a DFIG; \(U_{\text{DFIG}}\) and \(U_{\text{DFIG}(0)}\) represent the DFIG terminal voltage before and after the fault occurred, respectively; \(P_{0}\) represents the output power before the fault occurred; \(k_{\text{s}\,-\,1}\) and \(k_{\text{s}\,-\,2}\) represent the coefficients in the LVRT strategies, which are determined by the structure and capacity of the DFIG. \[I_{\text{DFIG}}\,=\, \begin{cases}0&0<U_{\text{DFIG}}\,<0.2\text{ p.u.}\\ k_{\text{s}-1}U_{\text{DFIG}}&0.2\text{ p.u.}\,\leq U_{\text{DFIG}}\,<U_{\text{ p1}}\\ l_{\text{s}max}&U_{\text{p1}}<U_{\text{DFIG}}\,\leq U_{\text{p2}}\\ \sqrt{I_{N}^{2}+k_{\text{s}-2}(0.9-U_{\text{DFIG}})}&U_{\text{p2}}<U_{\text{DFIG }}\,<0.9\text{ p.u.}\\ P_{0}/U_{\text{DFGG}(0)}&0.9\text{ p.u.}\,\leq U_{\text{DFIG}}\,\leq 1.0\text{ p.u.}\end{cases}