Obtain the commutation interval u and the dc-side current

Question

Single-Phase Thyristor Rectifier Bridge

Nominal values: Vs(rms) = 120 V at 60 Hz

Ls1 = 0.2 mH
Ls2 = 1.0 mH Ld = 20 mH
Rload = 5 Ω
Delay angle α = 45°

Problems

1. (a) Obtain v_s, v_d and i_d waveforms.
(b) Obtain v_s and i_s waveforms.
(c) Obtain v_m and i_s waveforms.

2. From the plots, obtain the commutation interval u and the dc-side current at the start of the commutation.

3. By means of Fourier analysis of is, calculate its harmonic components as a ratio of Is1.

4. Calculate Is, %THD in the input current, the input displacement power factor and the input power factor.

Single-Phase Full-Converter
VS 10 0 SIN (0 169.7V 60HZ)
Vg1 6 2 PULSE (0V 10V 2777.8US 1NS 1NS 100US 16666.7US)
Vg2 7 0 PULSE (0V 10V 2777.8US 1NS 1NS 100US 16666.7US)
Vg3 8 2 PULSE (0V 10V 11111.1US 1NS 1NS 100US 16666.7US)
Vg4 9 1 PULSE (0V 10V 11111.1US 1NS 1NS 100US 16666.7US)
R 11 4 10
L 4 5 20MH
VX 5 3 DC 0V; Load battery voltage
VY 10 1 DC 0V ; Voltage source to measure supply current
*Subcircuit calls for thyristor model

XT1	1	2	6	2	SCR	; Thyristor T1
XT3	0	2	8	2	SCR	; Thyristor T3
XT2	3	0	7	0	SCR	; Thyristor T2
XT4	3	1	9	1	SCR	; Thyristor T4

*Subcircuit for switched thyristor model
.SUBCKT SCR 1 2 3 2
*model anode cathode +control -control
*name voltage voltage

S1 1 5 6 2 SMOD ; Switch

RG	3	4	50
VX	4	2	DC    0V
VY	5	7	DC    0V
DT	7	2	DMOD
RT	2	6	1
CT	6	2	10UF
F1	2	6	POLY(2)  VX

; Switch diode

VY 0 50 11
.MODEL SMOD VSWITCH (RON=0.0125 ROFF=10E+5 VON=0.5V VOFF=0V)
.MODEL DMOD D(IS=2.2E-15 BV=1800V TT=0) ; Diode model parameters
.ENDS SCR ; Ends subcircuit definition
.TRAN 10US 50MS 16.67MS ; Transient analysis
.PROBE ; Graphics post-processor
.options abstol = 1.00u reltol = 1.0m vntol = 0.1 ITL5=0
.FOUR 120HZ I(VX) ; Fourier analysis
.END