## 4 Influence of Unmeasurable Load Branches on Protection and Countermeasures
### Principle of the Auxiliary Criterion  
This section focuses on solving the problem of misjudging non-faulted feeder _MN_ protection caused by the ULB when a fault occurs at point \(f_{2}\). The proposed auxiliary criterion is mainly for the protection of feeder sections containing the ULB, while the protection of other feeder sections is not equipped with an auxiliary criterion. Usually, voltage transformers are installed at grid-connected points of DGs, and voltage and current can be measured at grid-connected points. According to the action equation of amplitude-comparison directional impedance relay, the action impedance \(Z_{\rm act}\) can be expressed as  
\[Z_{\rm act}=\left|\frac{1}{2}Z_{\rm set}\right|-\left|Z_{\rm mea}-\frac{1}{2}Z _{\rm set}\right| \tag{17}\]  
where \(Z_{\rm mea}\) indicates measuring impedance; \(Z_{\rm set}\) indicates setting impedance, which is the line impedance between the DG grid-connected point and the GRID side of the feeder section with the ULB; when the fault occurs within the protection range of the impedance relay, \(Z_{\rm act}>0\) and a logic signal of \"1\" is sent; when the fault occurs outside the protection range, \(Z_{\rm act}<0\) and a logic signal of \"0\" is sent. The general idea of the auxiliary criterion configuration is shown in Figure 11.  
Figure 11: Configuration process of the auxiliary criterion. The following is an analysis of the protection configuration of the feeder section \(M\)N in Figure 12.  
In Figure 12, the feeder section \(M\)N contains the ULB, and the auxiliary criteria need to be configured for its ACDP. Firstly, finding the DG1 grid-connected point downstream of the feeder \(M\)N and the upstream protective device 7 connected to it obtains the local voltage and current information; then the amplitude-comparison action criterion is established, as shown in Equation (18), and its protection range is \(BM\). If the fault occurs in \(BM\), \(Z_{\text{act}}>0\), protective device 7 sends \"1\" to the ACDP of feeder \(M\)N and \"0\", and vice versa. \[\left\{ \begin{array}{l}Z_{\text{act}}=\left|\frac{1}{2}Z_{\text{set}}\right|- \left|Z_{\text{mea}}-\frac{1}{2}Z_{\text{set}}\right|\\ Z_{\text{set}}=K_{\text{rel}}Z_{\text{BM}}\end{array} \right. \tag{18}\]  
where \(Z_{\text{BM}}\) is the line impedance value between protective devices 7 and 4; \(K_{\text{rel}}\) is the reliability coefficient determined by transformer error, relay error, and other factors. To make the measured impedance proportional to the distance from the DG grid-connected point to the fault point and not affected by the type of DG, penetration rate, fault type, and other factors, three sets of phase-to-phase voltages and corresponding phase-to-phase currents are used to calculate the three measured impedance values, respectively. As long as any one of \(Z_{\text{mea}}\) makes \(Z_{\text{act}}\) greater than 0, it indicates that the fault occurs in the corresponding protection area of \(Z_{\text{set}}\). It should be noted that when there is a load branch in the protection range, the existence of the load branch will not affect the discrimination of the action impedance polarity since the equivalent impedance of the load branch is much larger than the line impedance. At the same time, considering that the fault resistance value of the fault point increases rapidly after the fault occurs during 0.1-0.15 s [32], the action impedance measurement is completed instantly after the fault, so the influence of the fault resistance on the polarity discrimination of the action impedance can be ignored. The overall implementation process of the CDP based on the adaptive phase angle compensation coefficient is shown in Figure 13. After the protection relay is started, the real-time current signal detected by the CT before and after the fault is recorded by the intelligent electronic device, and then the full-cycle subtraction method [33] is used to calculate the current fault component.