[b]0 Introduction[/b] In high-voltage power grids, with the development of power systems, considering the economic benefits of equipment investment and the difficulties of land acquisition, multi-terminal transmission lines with three or more terminals may emerge. The emergence of multi-terminal transmission lines brings many adverse effects to the design and operation of relay protection. This paper conducts digital simulation and calculations on a 110 kV line of a certain power system. The results show that directional relays involving zero-sequence components may make incorrect judgments in T-connections, causing the protection to fail to operate. In actual T-connection line protection, whether each directional relay is suitable for the protected system requires careful and detailed simulation calculations of different faults at different locations under various operating modes to correctly determine the protection scheme. [b]1 System Parameters and Calculation Methods[/b] 1.1 System Parameters The simulation system structure is shown in Figure 1. The transmission line structure and parameters are similar to those of a 110 kV line in a certain power grid in my country. The equivalent system parameters are also approximately equal to those of the actual line system. Line I and Line II are parallel double-circuit lines. There is a T-connection line at the midpoint of Line I, with a length half that of Line I. The unit length parameters are exactly the same as those of Line I. The parallel line parameters are: positive sequence impedance ZL1 = 0.792 Ω, zero sequence impedance ZL0 = 2.772 Ω, zero sequence mutual impedance ZLP = 0.9504 Ω, positive sequence impedance angle L1 = 75°, zero sequence impedance angle L0 = 65°, zero sequence mutual impedance angle LP = 65°. All negative sequence parameters are consistent with the positive sequence parameters. The equivalent impedance of the M-side is: ZM1 = ZM2 = 0.6051 + j6.9168 (Ω), ZM0 = 0.5453 + j3.0928 (Ω). The equivalent impedance of the N-side system is: ZN1 = ZN2 = 3.8565 + j44.08 (Ω), ZN0 = 4.3553 + j24.7 (Ω). The leakage reactance of the T-side transformer is: ZT = 1.3225 + j13.225 (Ω), its transformation ratio is: nT = 110 kV/35 kV, and its connection method is: Y/△-11. Figure 1. Simulation Calculation System Structure Diagram 1.2 Simulation Calculation Method This paper uses the general electromagnetic transient calculation program (EMTP) for simulation calculation. The simulation model is shown in Figure 2. Parallel double-circuit lines I and II adopt the six-phase transmission line model in EMTP and are divided into 8 equal segments, i.e., 9 fault points are set on each line. The T-connection line adopts the three-phase transmission model and is divided into 4 equal segments, i.e., 4 additional fault points are added. Since it is a 110 kV line, the influence of line distributed capacitance is ignored. The power supply on the M and N sides adopts the 14-type power supply in EMTP (i.e., a three-phase symmetrical sinusoidal power supply), and the system impedance is also simulated using an equivalent line model. The T side is simulated using the transformer model in EMTP, and the saturation effect is not considered. Because the zero-sequence potential on the delta side of a Y/Δ connected transformer with no load at the end in EMTP is floating, a symmetrical large impedance ZLoad = 1000 + j500 (Ω) is connected to the low-voltage side of the transformer in the simulation to simulate its load (this is one of the recommended methods in EMTP; other methods are to ground one corner of the transformer delta side or add a symmetrical small capacitor on the delta side). Figure 2 Simulation calculation system model [b]2 Simulation Calculation Results[/b] Table 1 shows the calculated phase differences of the sequence voltages and currents in the relays on the three sides of the T-connection line when a single-phase ground fault (referring to phase A ground fault) occurs inside the line. As can be seen from the table, the phase differences of both the positive and negative sequence voltages and currents accurately reflect the direction of the internal fault. Since the positive and negative sequence parameters in the simulation system are consistent, the calculated results of the phase differences of the positive and negative sequence voltages and currents are also completely consistent. On the T side, because the load impedance ZLoad = 1000 + j500 (Ω) was added in the simulation calculation, there are also small power frequency changes in the positive and negative sequence currents during the fault, so the phase difference can also be calculated. However, in practical applications, this cannot be used to determine the direction of the fault because such a small current will be approximately zero after considering the influence of interference and measurement errors, making it impossible to accurately measure its phase difference. The phase difference between zero-sequence voltage and current cannot completely and accurately reflect the direction of the internal fault (see the data marked with * in column 4 of the table). When a fault occurs at the M-side bus outlet, the phase difference between the zero-sequence voltage and current on the N-side incorrectly determines the direction of the internal fault. The reason for this incorrect judgment can be further analyzed. The incorrect judgment of the N-side zero-sequence directional protection occurs when a fault occurs at or near the M-side outlet. Let's assume the fault occurs at the outlet; then the equivalent circuit diagram of the zero-sequence network shown in Figure 3 can be easily obtained. Clearly, the direction of the N-side zero-sequence current depends on the relative levels of the T-contact and the N-side zero-sequence voltage (ignoring the differences in zero-sequence impedance angles). The magnitude of the N-side zero-sequence voltage is mainly determined by the relative magnitudes of impedances ZL0 and Zsn0, while the magnitude of the T-contact zero-sequence voltage is mainly determined by the relative magnitudes of ZT0 and the zero-sequence impedance ZL0/2 between the M-side and the T-contact. Under certain parameter conditions, it is entirely possible for the N-side zero-sequence voltage to be higher than the T-contact zero-sequence voltage, thus causing the N-side zero-sequence directional relay to incorrectly determine the direction of the internal fault. The zero-sequence directional protection on the M side may also exhibit this situation. Extending this further, could the positive-sequence and negative-sequence directional relays also exhibit this situation? The answer is yes. This situation could occur in the simulation system presented in this paper, but the parameters do not meet the conditions for its occurrence: the difference between the equivalent positive-sequence and negative-sequence impedances of the two power supply sides is not significant, and there is a line connection between the T side and the N side, or between the T side and the M side. This situation is even more likely to occur in three-terminal power supply systems. These conclusions are easily confirmed through the analysis of the equivalent circuit diagram, and will not be elaborated upon here. Figure 3. Equivalent circuit diagram of zero-sequence network when the busbar outlet on the M side is faulty. Note: Zsm0 and Zsn0 are the equivalent zero-sequence impedances of the M and N side systems, ZL0 is the zero-sequence impedance of line II, and ZL0/2 is the zero-sequence impedance of line I on the M and N sides (assuming that the impedances on both sides are equal). It should be noted that the zero-sequence mutual inductance between line I and line II is not considered in the zero-sequence equivalent circuit of Figure 3. If it is considered, some impedance parameters in the figure need to be modified appropriately. ZT0 is the sum of the zero-sequence impedance on the T side of the T-connected line and the equivalent zero-sequence impedance on the load side. U0 is the zero-sequence voltage value at the fault port. Table 2 shows the calculation results of the phase difference of each sequence voltage and current in the relays on the three sides of the T-connected line when a two-phase ground fault occurs inside the T-connected line (here referring to the AB two-phase ground fault). As can be seen from the table, similar to Table 1, the phase differences of positive-sequence voltage and current, as well as the phase differences of negative-sequence voltage and current, can correctly reflect the direction of the internal fault. However, the phase difference of zero-sequence voltage and current cannot completely and correctly reflect the direction of the internal fault (see the data marked with * in column 4 of the table). That is, when a fault occurs at the M-side bus outlet, the phase difference of zero-sequence voltage and current on the N-side incorrectly determines the direction of the internal fault. The reason for this incorrect judgment is exactly the same as the previous analysis, because the previous analysis did not assume what type of fault it was. Unlike Table 1, the calculated results of the phase differences of positive-sequence voltage and current and negative-sequence voltage and current are inconsistent. This is because the equivalent sequence network diagram for calculating the two-phase ground fault current is different from that for single-phase ground fault. In the case of a two-phase ground fault, the relative relationship between positive-sequence current and negative-sequence current is also affected by the zero-sequence current. Therefore, although the positive-sequence parameters and negative-sequence parameters in the simulation system are consistent, the phase differences of positive-sequence voltage and current are still inconsistent. Furthermore, the positive and negative sequence voltage and current directions on the T side exhibit the same issues as those faced with single-phase grounding faults. Table 3 shows the calculated phase differences of zero-sequence voltage and current in the relays on the three sides of the T-connection line when a single-phase grounding fault (referring to phase A grounding fault) occurs within the T-connection line, under different grounding transition resistances. As can be seen from the table, the phase difference of zero-sequence voltage and current also cannot completely and accurately reflect the direction of the internal fault (see the data marked with * in columns 2, 5, and 8 of the table). For different grounding transition resistances, the difference in the phase difference of zero-sequence voltage and current is not significant. Therefore, the transition resistance has little impact on the determination of the fault direction; that is, the directional relay is not sensitive to the transition resistance. Note: The fault points in Tables 1, 2, and 3 refer to the locations where the fault occurs. ILINE1 to ILINE9 refer to the points where LINEI is divided into 8 equal segments and arranged sequentially from the M side to the N side. TLINE1 to TLINE4 refer to the points where the T-connection line is divided into 4 equal segments and arranged sequentially from the T-connection point to the T side. P_M0, P_M1, P_M2, P_N0, P_N1, P_N2, P_T0, P_T1, and P_T2 represent the phase differences between the zero-sequence, positive-sequence, and negative-sequence voltages and currents on the M, N, and T sides, respectively. Each voltage and current represents the power frequency variation during a fault. R_f is the transition resistance value during a ground fault. In summary, under the parameter conditions of the simulated system calculated in this paper, the positive-sequence and negative-sequence fault component directional relays can correctly reflect the direction of the internal fault under various conditions, while the zero-sequence fault component directional relay may make incorrect judgments. Through analysis, it was found that this situation is possible and reasonable in T-connected lines, and if the system parameters of the T-connected line meet certain conditions, the positive-sequence and negative-sequence fault component directional relays may also make incorrect judgments. Therefore, directional relays should be used with caution in T-connected circuits. If their use is unavoidable, a detailed simulation calculation should be performed on the performance of the directional relays based on the actual parameters of the T-connected circuit and the various operating modes of the system. This is to ensure that all directional relays operate correctly or to indicate under which specific operating modes the directional relays cannot be put into operation. Furthermore, the grounding transition resistance has little effect on the sequence component directional relays and its influence can be disregarded. 3 Conclusions Through simulation calculations and data analysis, the following conclusions can be drawn: (1) Whether the directional relay for power frequency variation in a T-connected line can correctly determine the direction of an internal fault depends on the connection status and parameters of the system in which the T-connected line is located. A more detailed simulation calculation is required to fully and correctly determine the performance of the directional relay; (2) Protection systems with good performance in ordinary lines are not necessarily suitable for T-connected lines. The special characteristics of T-connected lines must be fully considered when designing the protection system; (3) Similar to ordinary lines, when a ground fault occurs in a T-connected line, the transition resistance has little effect on the directional relay, and its effect can even be disregarded. **References** 1. Dommel HW, Theory of Electromagnetic Transient Calculation in Power Systems, translated by Li Yongzhuang et al., Beijing: China Water Resources and Electric Power Press, 1990. Editor: He Shiping