# Research on Interference Mechanism of 25 Hz Phase Sensitive Track Equipment from Unbalanced Current
## 2 Cause Analysis of Abnormal Red Ribbon
### Influence of Unbalanced Current Intrusion on Relay  
#### 2.4.1 Interference Analysis of Unbalanced Impulse Current on Relay Wing Plate  
In order to simplify the research on the problem of misoperation caused by the unbalanced impulse current to relay interference, the linear inductance in the transformer is regarded as a fixed value.  
For a 25 Hz track circuit, the interference frequency is 50 Hz in its two working cycles. The torque generated on the relay wing plate when the unbalanced impulse current invades can be obtained, as shown in Equation (7):  
\[M=\frac{KI_{G}I_{I}}{0.08}\int_{0}^{0.08}\left[2\omega\sin(2\omega t+\theta- \beta+\pi/2)+p\sin(\theta-\beta)e^{-pt}\right]\cdot\sin(\omega t)dt \tag{7}\]  
where the angular velocity is set to \(2\omega\); the angular velocity of the local coil side current is set to \(\omega\); \(I_{G}\) is the peak current flowing through the relay track coil side; \(I_{I}\) is the peak current flowing through the local coil side; the time constant \(p\) is \(R/L\); \(K\) is the structural coefficient of the binary two-bit relay.  
When \(\theta-\beta=\pi/2\), the relay wing plate torque is Equation (8):  
\[M=\frac{KI_{G}I_{I}}{0.08}\int_{0}^{0.08}\left[-2\omega\sin(2\omega t)+pe^{- pt}\right]\cdot\sin(\omega t)dt \tag{8}\]  
The excitation impedance angle of the transformer is set to 75\({}^{\circ}\). The frequency of the unbalanced traction current is the power frequency. The time constant is the value obtained by Equation (9).  
\[p=R/L=100\pi/tg75^{\circ}\approx 84 \tag{9}\]  
Therefore, it can be calculated that \(M\approx 2.7766 KI_{G}I_{I}\).  
The current frequency of the coil side of the relay is 25 Hz, and the peak current is \(I_{G}\). It is assumed that the relay is in the optimal pull-in state, that is, the phase lag of the track current is 90\({}^{\circ}\), and the excitation inductance of the transformer is considered to be linear  
Figure 5: DC bias of choke transformer. (**a**) The change of magnetic flux curve when the impulse current flows into the transformer; (**b**) The working characteristic curve of the transformer under normal working condition; (**c**) The change of excitation waveform when the impulse current flows into the transformer.  
inductance. According to the peak value of the AC component, the torque value in two working cycles can be calculated as Equation (10).  
\[M=\frac{50\pi KI_{G}I_{J}}{0.08}\int_{0}^{0.08}\sin^{2}(50\pi t)dt\approx 78.5 KI_{G}I_{J} \tag{10}\]  
In practice, the maximum impulse current of the circuit is 6-8 times of the steady-state value, so the torque generated by the track coil side of the relay is about (16.7-22.2) \(KI_{G}I_{J}\). The current parameter of the track coil side of the binary two-bit relay in the 25 Hz track circuit is 0.038 A. Therefore, when the impulse current invading the track coil side reaches 0.14 A, the torque will be disturbed, thus causing the relay to misoperate.  
When \(\theta-\beta=3\pi/2\), the initial value of the DC component was \(I_{M}\sin(\theta-\beta)=-I_{M}\). Therefore, the actual value of the torque generated on the relay wing when the unbalanced impulse current invades is \(\pm 2.7755 KI_{G}I_{J}\). It can be seen that the interference of the unbalanced impulse current to the relay is uncertain, which may cause the relay wing to misoperate.