# Fault Analysis and Protection Principle for the Distribution Networks Integrated with PV and BESS
## 3 The Proposed Fault Direction Detection Principle
### Principle for Detecting Fault Direction Under Symmetric Faults
#### 3.2.2 Reactive Current Direction and Active Current Amplitude Direction Criterion  
As analyzed in Section 2.3, during three-phase short-circuit faults, the reactive current through PR4 is positive in its forward area and negative in its reverse area. When a three-phase short-circuit fault occurs in the reverse area of PR4, the reactive current flowing through PR4 is less than 0. Therefore, the fault direction can be judged based on the flow direction of the reactive current. However, considering the calculation error of the short circuit current, 0 cannot be used as the critical value. A critical value needs to be set.  
Figure 3: Principle for detecting fault direction during asymmetric phase-to-phase faults.  
Only when the absolute value of the detected reactive current exceeds this threshold does its positive/negative sign reliably indicate the current flow direction. Taking PR4 as an example, at this time, the fault criterion for the reverse area is shown in Equation (9):  
\[\left\{\begin{array}{l}\left|I_{p4.q}\right|>l_{q.set}\\ l_{p4.q}<0\end{array}\right. \tag{9}\]  
where \(l_{q,set}\) takes the value of 0.05 kA.  
If the detected amplitude of the reactive current exceeds the set value and its sign is positive, or the amplitude of the reactive current is less than the set value, then the active current amplitude criterion will be activated, as Equation (10) shows:  
\[\left\{\begin{array}{l}\left|I_{p4.d}\right|<\frac{1}{2}(I_{d.set1}+I_{d.set2 })\right.\text{Forwardfault}\\ \left|I_{p4.d}\right|>\frac{1}{2}(I_{d.set1}+I_{d.set2})\text{ \ \ \ Reversefault}\end{array}\right. \tag{10}\]  
where \(l_{d.set1}\) and \(l_{d.set2}\) are calculated by Equation (11) as below:  
\[\left\{\begin{array}{l}\left.I_{d.set1}=K_{\text{rel}}^{(3)}\left|I_{p4.d} \right|_{\text{max}}\\ \left.I_{d.set2}=K_{\text{rel}}^{(3)}\left|I_{p4.d}\right|_{\text{min}}\end{array}\right.\right. \tag{11}\]  
where \(K_{\text{rel}}^{(3)}\) and \(K_{\text{rel}}^{\prime(3)}\) are reliability factors, taking values of 1.05 and 0.95, respectively. The calculations of \(\left|I_{p4.d}\right|_{\text{max}}\) and \(\left|I_{p4.d}\right|_{\text{min}}\) are given in Section 2.4.  
Figure 4 illustrates the flowchart of the proposed principle.  
When the fault type is determined to be a three-phase short circuit and the positive sequence voltage at the PCC drops below 0.9 p.u., the direction criterion based on the reactive current will be activated. First, detect the amplitude of the reactive current flowing through the protection device. If the amplitude of the reactive current is less than the set value, activate the active current amplitude criterion. If the amplitude of the reactive current is greater than the setting value, then determine its positive or negative sign. If the sign is negative, it is determined to be a reverse fault; if the sign is positive, activate the  
Figure 4: Principle for detecting fault direction during symmetric faults.  
active current amplitude criterion. After entering the active current amplitude criterion, if the amplitude of the active current is greater than the set value, it is determined to be a fault in the reverse area; otherwise, it is determined to be a fault in the forward area.