4. Equivalent circuit and total decay time during faults
It is important to establish the mathematical relation between the circuit parameters and fault related parameters. In this work, two fault related parameters are defined: fault clearance time tf and total decay time td. The fault clearance (isolation) time tfcorresponds to the time between fault occurrence and shutdown of converter (by adjusting duty cycle D to zero with the help of proposed control scheme). Even the converter is isolated from the fault by the proposed control scheme, the inductor currentiL becomes zero after a specific time depending upon the converter and transmission line parameters. The time between turn-off of dc circuit breaker (D = 0) and zero inductor current value is defined as the total decay time td. The fault clearance time tf is related with the control parameters and circuit parameters. For the given values of circuit parameters, the fault clearance time is decided by the PI control parameters: Kpv, Kiv, Kpi, and Kii. The Kpv and Kiv are PI controller proportional and integral gain of the output voltage vo adjustment. The Kpi and Kii are PI controller proportional and integral gain of the inductor current iL adjustment.
The circuit parameters Ldc and Co, and transmission line parameters RT and LT influence the total decay time td. To derive a mathematical relation between decay time and converter/transmission line parameters, an equivalent circuit is derived during faulty condition and presented in Fig. 9. The equivalent circuit corresponds to the turn-off period of dc circuit breaker (refer to Fig. 5 and Fig. 6), and short circuited (across the dc circuit breaker) transmission line. The energy in the output filter capacitor Co and dc inductor Ldc is dissipated by the transmission line impedance. According to the Kirchhoff's current theorem, the node current equation is:
equation(6)