# Fault Analysis and Protection Principle for the Distribution Networks Integrated with PV and BESS
## 2 Fault Characteristics of the Distribution Networks with PV and BESS
### Negative Sequence Impedance Characteristics of the Network During Asymmetric Faults  
When an asymmetric fault occurs on the line and the positive sequence voltage at the PCC of the PV and the BESS drops below 0.9 p.u., the PV and BESS need to absorb a certain amount of negative sequence reactive current to suppress the negative sequence voltage at the PCC. It should be made clear that, to absorb negative sequence reactive power for negative sequence voltage suppression, the phase of the negative sequence current vector emitted should lead the negative sequence voltage vector at the PCC by 90\({}^{\circ}\). This means that the negative sequence impedance of the PV and the BESS is purely inductive, with an impedance angle of 90\({}^{\circ}\). When the output reactive current of the PV and the BESS does not reach the limit value, the negative sequence impedance of the PV and the BESS remains constant, as Equation (3) shows:  
\[\left|Z_{bess}^{-}\right|=\frac{\left|\mathbf{U}^{-}\right|}{\left|\mathbf{I}^{-} \right|}=\frac{U_{\text{N}}}{\sqrt{3}K^{-}I_{\text{N}}}=\frac{{U_{\text{N}}}^{ 2}}{K^{-}S_{\text{N}}} \tag{3}\]  
Among them, \(Z_{bess}^{-}\) is the negative sequence impedance of the PV and the BESS; \(K^{-}\) is a constant, and its value is taken as 2 in this work; \(S_{N}\) defines the rated capacity of the PV and BESS. When the output reactive current of the PV and BESS reaches the limit value, the negative sequence reactive current output is redistributed according to Equation (2), and the negative sequence impedance exceeds the value specified in Equation (3). Next, taking the topological structure in Figure 1 as an example, the negative sequence impedance measured by PR4 is analyzed when a two-phase short-circuit fault occurs in the forward direction area or the reverse direction area of PR4. The forward protection zone is designated from Bus C to A, while the reverse protection zone is designated from Bus C to D. Figure 2 illustrates the composite sequence network associated with the two-phase short-circuit fault occurring in the system depicted in Figure 1.  
For PR4, if a fault occurs on line AB or line AC, the measured negative sequence impedance is opposite to the equivalent negative sequence impedance downstream of bus C. Since the negative sequence impedance angle of PV and BESS is 90\({}^{\circ}\), the equivalent impedance obtained by paralleling it with the line and load impedance remains resistive-inductive, and the impedance angle is within the range from 0\({}^{\circ}\) to 90\({}^{\circ}\). Therefore, when a forward fault occurs, the phase angle of the negative sequence impedance measured at PR4 is within the range from \(-\)180\({}^{\circ}\) to \(-\)90\({}^{\circ}\). When a fault occurs on line CD, the measured impedance of PR4 reflects the equivalent negative sequence impedance upstream of bus C, and its phase angle is approximately equal to the angle of the line impedance. This implies that, when a forward fault occurs, the negative sequence impedance angle measured by PR4 at this time is within the range from 0\({}^{\circ}\) to 90\({}^{\circ}\). From the above analysis, it can be seen that, in the case of asymmetric faults, it is feasible to estimate the fault direction by using the negative sequence power flow detected at PR4. When a reverse fault occurs, the change in the negative sequence measured impedance of PR4 is determined by the operation mode of the system and can be obtained from the system parameters. However, when a forward fault occurs, the specific boundaries of the amplitude and phase changes of the negative sequence measured impedance of PR4 are not clear. Therefore, it is necessary to determine the variation range of the negative sequence impedance of PV and BESS. Under the same transition resistance, the closer the fault location is to bus C, the smaller the positive sequence voltage at bus C, and the larger the negative sequence voltage.