Lecture 10. Effect of source inductance on phase controlled AC-DC converters. 10.1 Overlap in single-phase, CT fully-controlled converter L s i 1 T 1 i L v s V max sint v i R L L s T 2 i 2 Figure 10.1 Single-phase C-T converter with source inductance The presence of source inductance means that commutation of load current from one thyristor to the next, as they are triggered with a firing angle, can not be instantaneous. This source inductance, L s, is invariably because of the inductance of the supply lines and the leakage inductance of the input transformer. For this circuit, the overlap of conduction for the duration makes the output voltage zero (which is the mean of the overlapping input voltages) during this period. Lecture 10 - Overlap in 1 F. Rahman
L s T 1 i L i 1 V max sin t v i R L v s L s T 2 i 2 Figure 10.2 Waveforms in the converter of figure 10.1, commutation overlap and commutation notches, for α = 45. Lecture 10 - Overlap in 2 F. Rahman
Figure 10.3 Waveforms in the converter of figure 10.1, commutation overlap and commutation notches, for α = 130. The part of the input voltage waveform which is missing from the output voltage is given by di (10.1) Vmax sin t Ls dt I d Vmax sintdt L s di (10.2) 0 where V max is the peak of the input AC voltage and I d is the DC level of the output (load) current. Lecture 10 - Overlap in 3 F. Rahman
Note that in each half cycle of the above waveform, the input current through the incoming thyristor rises from zero to I d in time /, starting from the instant of firing. Thus, integrating equation 10.2, Vmax cos cos L I L cos cos I s s d d V (10.3) max The commutation or overlap angle can be found from expression 10.3. It increases with load current I d at any firing angle. The output DC voltage is then given by 1 Vd Vmax sin t d t 2V max 1 L cos max s d V sin t d t I (10.4) Lecture 10 - Overlap in 4 F. Rahman
V d = 30 I d = 120 (a) Figure 10.4(a) Variation of V d with I d and firing angle α. = 30 Figure 10. 4(b) Variation of overlap angle with I d and firing angle α. I d Lecture 10 - Overlap in 5 F. Rahman
10.1.2 Overlap in single-phase, fully controlled bridge converter Without overlap, thyristors T1 & T4 or T3 & T2 conduct alternately for 180 (assuming continuous conduction). With overlap due to source inductance all four thyristors conduct during commutation of current through thyristor pairs. The part of the input voltage waveform which is missing from the output during overlap is given by di Vmax sint Ls dt (10.5) As before I d max s s d I d V sin t d t L di 2 L I 2 L cos cos I s d V (10.6) max Note that during overlap, the input current i, which flows through L s, changes by 2I d. The overlap angle can be found from the above expression. The angle increases when larger load current is commutated. The DC output voltage of the converter with overlap is given by Lecture 10 - Overlap in 6 F. Rahman
1 1 Vd Vmaxsin t d t Vmaxsin t d t 2V 2 L max s cos Id (10.7) V d = 30 = 125 = 30 Figure 10.6(a) Variation of V d and commutation angle with load current and firing angle for the converter of figure 10.5. Lecture 10 - Overlap in 7 F. Rahman I d
i s L s T 1 T 3 I d v s = V max sint v si V d Load T 2 T 4 (a) i L v si v s -v si (b) Lecture 10 - Overlap in 8 F. Rahman
v s v s -v s i L v si v s -v si =145 o (c) Figure 10.5 (a) Single-phase, F-C, bridge converter with source inductance and its waveforms; (b) for α = 45. (c) for α = 145. Lecture 10 - Overlap in 9 F. Rahman
10.1.3 Overlap in single-phase, half-controlled bridge converter In this converter, the output voltage waveform can not become negative at any time, because of the freewheeling diode D f. This diode would be forward biased when the tends to go negative by the action of the inductance of the load. The commutation of the load current through the thyristors and the diodes occur in two stages. At first, the load current commutates to the freewheeling diode (D f ) at the zero crossings of the input voltage. When an incoming thyristor is triggered, the freewheeling load current commutates from the freewheeling diode to this thyristor. The part of the input voltage waveform missing from the output is thus dropped across the source inductance due to the load current rising to I d during the commutation overlap angle when a thyristor is triggered. Consequently, the overlap angle and the DC output voltage V d for this converter with source inductance L s are given by, 1 Id max s 0 V sin td( t) L di L cos cos I V s max d (10.8) Lecture 10 - Overlap in 10 F. Rahman
The DC output voltage is given by 1 Vd Vmax sintd( t ) Vmax sintd( t ) V L V 1 cos I max d s d (10.9) Because of the removal of the lagging part of i s into D f, the fundamental component of is lags the input voltage waveform by an angle smaller than. This means that the converter with a higher input displacement factor and hence higher input power factor. This is one advantage of this converter, in addition to reduction of cost (due to fewer thyristors and gate drive circuits. However, this converter can not produce negative DC output voltage, hence, it can not regenerate into the AC source. Lecture 10 - Overlap in 11 F. Rahman
i s L s T1 T3 I d v s = V max sint v si D f V d Load D2 D4 Figure 10.6 Single-phase H-C converter v s 500-500 i L i Df v si v s -v si Figure 10.7 Waveforms in the H-C converter with source inductance; for = 45. Lecture 10 - Overlap in 12 F. Rahman
v s i L i Df v si v s -v si 0 2 3 Figure 10.8 Waveforms in the H-C converter with source inductance; for α = 145. Lecture 10 - Overlap in 13 F. Rahman