Question 13.10: FINDING THE CLOSED-LOOP RESPONSE OF THE OUTPUT VOLTAGE FOR T...
FINDING THE CLOSED-LOOP RESPONSE OF THE OUTPUT VOLTAGE FOR THE DIODE RECTIFIER–BOOST CONVERTER
A diode rectifier followed by a boost converter is shown in Figure 13.36. The input voltage is v_{s} = 170 sin(120πt). The circuit is operated closed loop, so that the output voltage is V_{o} = 220 ± 0.2 V, and the input current is sinusoidal with an error of ±0.2 A. Use PSpice to plot the transient response of output voltage v_{o} and the input current i_{s}.
The model parameters for the IGBT are:
TAU=287.56E9 KP=50.034 AREA=37.500E-6 AGD=18.750E6
VT=4.1822 KF=.36047 CGS=31.942E9 COXD=53.188E9
VTD=2.6570
The model parameters for the BJT are:
IS=2.33E−27 and BF=13
and those for the diode are:
IS=2.2E−15, BV=1200V, CJO=1PF, and TT=0.
The peak input voltage is V_{m} = 170 V. Assuming a diode drop of 1 V, the peak rectified voltage becomes 170 − 2 = 168 V. The input frequency is f = 60 Hz. The block diagram for closed-loop control is shown in Figure 13.37(a). The error of the output voltage after passing through a controller generates the reference current for the current controller, whose output is the carrier signal for the PWM generator. Equating rectified output power to the load power, we get
V_{in(DC)} I_{in(DC)}=\frac{V^{2}_{o} }{R} (13.8)
Because for a rectified sine wave V_{(average)} = 2V_{(peak)} /π, Equation 13.8 becomes
\frac{2V_{m} }{\pi }\frac{2I_{m}}{\pi } =\frac{V^{2}_{o} }{R}
which gives the multiplication constant δ as
\delta =\frac{I_{m}}{V_{m}} =\frac{\pi ^{2}V^{2}_{o} }{4RV^{2}_{m} } (13.9)
=\frac{\pi ^{2}\times 220^{2} }{4\times 400\times 168^{2} } =0.01
A value of δ higher than 0.01 would increase the sensitivity and give better transient response. But the PWM generator will be operated in the overmodulation region if it is too high. Let us assume δ = 0.05.
We use a proportional controller with an error band of ±1. The circuit for PSpice simulation of the current controller is shown in Figure 13.37(b). The multiplication is implemented with VALUE. The voltage and current controllers are implemented
by TABLE.
The listing of the subcircuit CONTR for Figure 13.37(b) is as follows:
| * Subcircuit definition for CONTR current controller: .SUBCKT CONTR 2 3 4 5 6 * model desired output rec. input input current carrier * name voltage voltage voltage signal (voltage) signal E1 8 0 TABLE{V(2,3)} = ; Voltage controller + (−0.2, 2) (0, 1) (0.2, 0) E2 5 7 VALUE = {0.05*V(4)*V(8)} ; Reference current E3 6 0 TABLE{V(7)} = ; Current controller + (−0.2, 0) (0, 5) (0.2, 10) .ENDS CONTR |
The PWM subcircuit is implemented with an ABM, ABM2 with two inputs. The
listing of the subcircuit PWM is as follows:
| * Sub circuit definition PWM: .SUBCKT PWM 1 2 3 * model reference carrier output * name voltage signal voltage E_ABM21 3 0 VALUE {IF(V(2)-V(1)>0, 10, 0)} .ENDS PWM |
Using 20 pulses per half cycle of the input voltage, the switching frequency of the PWM generator is f_{s} = 40 × 60 = 2.4 kHZ, and the switching period is T_{s} = 416.67 μsec.
The PSpice schematic is shown in Figure 13.38 for a unity power factor diode with a boost converter.
The listing of the circuit file for Figure 13.38 is as follows:
Example 13.10 Diode rectifier with PWM current control
| .PARAM Vo_ref=220V Freq=2.0kHz Vr 8 0 PULSE (0 10 0 {1/({2*{Freq}})-1ns} 1ns 1ns {1/{2*{Freq}}} ) ; Reference Signal Vo_ref 16 0 DC {Vo_ref}SOURCE VS 4 11 SIN (0V 170V 60HZ) CIRCUIT VZ 4 12 DC 0V ; Measures supply current D1 12 1 DMOD ; Rectifier diodes ANALYSIS .TRAN 1US 35MS ; Transient analysis .PROBE ; Graphics post-processor .END |
The plots of the output voltage V(5) and input current I(VZ) are shown in Figure 13.39(a).The expanded waveforms are shown in Figure 13.39(b). The current controller forces the input current to be in phase with the input supply voltage and to follow a sinusoidal reference current. This improves the input power factor. A small filter can remove the high-frequency components of the input current. The upper bound of the output voltage is limited by the proportional controller. It should be noted that the load voltage has not yet reached the steady-state condition. The lowerlimit depends on the time constant of the load circuit. It requires careful design to determine the values of L and C, the controller parameters, and the switching frequency. A proportional–integral (PI) controller, coupled with a large value for the load filter capacitor, should give faster response of the output voltage.
The Fourier components of the input current are as follows:
DC COMPONENT = 3.606477E–02
| Harmonic
No |
Frequency (Hz) |
Fourier Component |
Normalized Component |
Phase (Deg) |
Normalized Phase (Deg) |
| 1 | 6.000E+01 | 8.195E+00 | 1.000E+00 | 2.291E+00 | 0.000E+00 |
| 2 | 1.200E+02 | 6.478E–02 | 7.905E–03 | 5.133E+01 | 5.591E+01 |
| 3 | 1.800E+02 | 2.039E+00 | 2.488E–01 | 1.678E+02 | 1.747E+02 |
| 4 | 2.400E+02 | 5.545E–02 | 6.766E–03 | 1.601E+02 | 1.509E+02 |
| 5 | 3.000E+02 | 7.729E–01 | 9.432E–02 | 3.090E+01 | 1.944E+01 |
| 6 | 3.600E+02 | 4.388E–02 | 5.354E–03 | 3.395E+01 | 2.020E+01 |
| 7 | 4.200E+02 | 2.740E–01 | 3.344E–02 | 1.189E+02 | 1.350E+02 |
| 8 | 4.800E+02 | 6.214E–02 | 7.582E–03 | 1.638E+02 | 1.455E+02 |
| 9 | 5.400E+02 | 8.967E–02 | 1.094E–02 | 1.693E+02 | 1.899E+02 |
| 10 | 6.000E+02 | 8.997E–02 | 1.098E–02 | 2.126E+01 | 4.417E+01 |
| TOTAL HARMONIC DISTORTION = 2.689696E+01 PERCENT | |||||
For THD = 26.89% and φ_{1} = −2.291°, Equation 7.3
PF_{i} =\frac{I_{1(rms)} }{I_{s} } \cos \phi _{1} =\frac{1}{\sqrt{1+(\frac{\%THD}{100} )^{2} } } \cos \phi _{1} (7.3)
gives the input power factor of the rectifier as
PF_{i}=\frac{1}{\sqrt{1+\left\lgroup \frac{\%THD}{100} \right\rgroup ^{2} } }\cos \phi _{1} =\frac{1}{\sqrt{1+\left\lgroup\frac{26.89}{100} \right\rgroup ^{2} } } \cos (-2.291^{\circ } )=0.965 (lagging)
