## 3 Current Differential Protection Based on Adaptive Angle Compensation Coefficient  
### Action Characteristics of Traditional Current Differential Protection  
According to the fault characteristics of the active distribution network, the CDP based on the PSCFC can better solve the protection challenges of the active distribution network, which has the following advantages:  
* Using the PSCFC to construct protection can effectively eliminate the influence of load currents, reflect all fault types, and solve the weak-infeed problem of active distribution network protection;
* Data transmission is significantly reduced compared to the traditional split-phase CDP. In the distribution network, three-phase recclosing is mainly used, and it is not necessary to judge the fault type. Therefore, the advantage of using a positive-sequence component to construct protection is more prominent.  
The traditional current differential protection (TCDP) criterion based on PSCFC [16] can be expressed as  
\[\left|\Delta\dot{I}_{m}+\Delta\dot{I}_{n}\right|>K\left|\Delta\dot{I}_{m}- \Delta\dot{I}_{n}\right| \tag{4}\]  
where \(\mid\Delta\dot{I}_{m}+\Delta\dot{I}_{n}\mid\) is the differential current; \(\mid\Delta\dot{I}_{m}-\Delta\dot{I}_{n}\mid\) is the restraint current; \(K\) is the restraint coefficient, which is usually adjusted according to the CT saturation current and takes a value between 0 and 1. Assuming \(K=0.5\), the action characteristics of the TCDP are represented by the amplitude and phase diagram, as shown in Figure 5.  
In any operating conditions and fault scenarios, the amplitude ratio and phase difference relationship of the PSCFCs on both sides of the protected feeder can be expressed as a point in the unit circle. The distance from the point to the origin is the amplitude ratio \(\lambda\) of the PSCFCs on the DG side and the GRID side of the feeder, whose value can be expressed as  
\[\lambda=\frac{1}{\varepsilon}=\frac{\Delta\dot{I}_{n}}{\Delta\dot{I}_{m}} \tag{5}\]  
According to the analysis in Section 2, it is known that the TCDP based on the positive-sequence current fault component has the following action characteristics in the active distribution network:  
Figure 5: Action characteristics of the TCDP in active distribute networks.  
* The downstream feeder of the fault point contains SBDG. When a fault occurs inside the protected feeder, the phase difference of the PSCFCs on both sides is slight, and the TCDP can trip correctly;
* The downstream feeder of the fault point contains IBDG. When a fault occurs inside the protected feeder, the phase difference of the PSCFCs on both sides has an extensive range, and the maximum value can reach nearly 180\({}^{\circ}\). In the limit case, the amplitude ratio \(\varepsilon\) on both sides of the feeder is 1.6, and the corresponding \(\lambda\) is 0.63. In the process of the fault approaching the limit state, the sensitivity of the TCDP gradually decreases, and finally, it cannot trip correctly. If a specific fault scenario falls within the light red zone in Figure 5, the TCDP will refuse to trip. By reducing the restraint coefficient \(K\), the sensitivity of the TCDP action in case of an in-zone fault can be improved, and the tripping area of the TCDP is expanded simultaneously. However, if the value of \(K\) is too small, it may lead to the misjudging of TCDP in cases of external faults, and the reliability is reduced.