Examples Paper 3B3/4 DC-AC Inverters, Resonant Converter Circuits. dc to ac converters

Transcription

1 Straightforward questions are marked! Tripos standard questions are marked * Examples Paper 3B3/4 DC-AC Inverters, Resonant Converter Circuits dc to ac converters! 1. A three-phase bridge converter using the unipolar scheme of sinusoidal pulse width modulation supplies an induction motor, as shown in Fig. 1. If the nominal dc link voltage is 562V, calculate the amplitude of the fundamental line voltage when the amplitude modulation ratio, m, is unity. Fig In State Vector Modulation of a voltage source inverter, the Direct-Direct sequence uses state 7 (111), as the zero state in sectors 1, 3 and 5, and V8, state 8 (000), as the zero state in sectors 2,4 and 6. The switching sequence remains the same during the same sector; for example in the first sector the sequence is V1, V2, V7, V1, V2, V7, and so on... The Direct-Inverse sequence, uses redundancy of the two zero states in the same vector to reduce the number of commutations per cycle. The switching sequence is reversed after passing through each zero state; for example in the first sector the sequence is V1, V2, V7, V2, V1, V8, and so on... By writing down the switching states for each leg in a table, for a few switching cycles, show that the overal switching frequency for the Direct - Inverse sequence is lower than that for the Direct - Direct sequence.

2 Resonant dc to ac inverters!3. A full bridge converter is used in square wave mode in a radio frequency heating system at a frequency of 150 khz. The load is part of a series resonant circuit to minimise the harmonic content of the load current, as shown in Fig. 3. If the load resistance is 50 Ω, find the minimum dc input voltage to the converter to obtain a load power of 1 kw. To meet regulations, the power at the third harmonic, 450 khz, must not exceed 1% of the power at the fundamental frequency. Estimate the value of L required. At the third harmonic frequency the reactance of C can be ignored. Find the value of tuning capacitance C required for 150 khz operation. Fig. 3!4. A load with resistance of 0.5 Ω and series inductance of 7.95 uh is driven in parallel resonance by a current source thyristor inverter. The frequency of operation is 10 khz and the current source is controlled to supply 100 A. Neglecting the thyristor turn-off time, chooses a value for the capacitance required in parallel with the load and its voltage rating. If the load were to vary, what measures may be taken to ensure successful commutation of the thyristors?

3 5. Consider the resonant inverter circuit of Fig. 4. Various waveforms for the circuit of Fig. 4 are shown in Fig. 5.a-c. By considering which devices are conducting, match the following descriptions to the waveforms. 1. Zero current turn on, hard switched turn off, 2. Hardswitched turn on, zero current turn off 3. Zero current turn on and turn off. For each case, state the operating frequency conditions with respect to f O. Fig. 4 (a) (c) (b) Fig. 5

4 6. For the resonant inverter circuit of Fig. 6, the capacitor Cs acts as a snubber. Consider the case when T4 is on and conducting the resonant load current. When operating at 1 MHz, with a dc supply voltage of 200 V, the current is switched at exactly 90 O with a peak current of 10 A. When T4 is turned off, the load current redirects to the capacitor Calculate the MOSFET losses for circuit operation without the capacitor Cs. Assume the MOSFET switches in 0.02 us. Comment on the MOSFET losses for circuit operation with Cs taking a value of uf. (Assume that the MOSFET current fall is instantaneous). Estimate the time taken for the switching process to be complete under these conditions. Fig. 6. (Use Power = VI 2 f for the MOSFET power losses - inductive load switching)

5 Resonant dc to dc converters *7. In the resonant step-down dc-dc converter circuit of Fig. 7, f O = 1MHz, Z O = 10Ω, Vdc = 15V, V O = 10V and the load is 10 W. Assume L f and C f are large enough to smooth the output voltage. Compare this circuit to the basic step down converter. Sketch the waveforms of V 1 and i L, starting at zero (dc load current in D). Calculate the peak switch current and resonant capacitor voltage for f << f O /2. (Hint consider the dc load current in L as a Laplace initial condition - simply a current source in parallel with L at the point in time when D recovers). Describe how the converter should be controlled to regulate the output voltage. Fig The Class D parallel loaded resonant dc-dc converter with full bridge input and rectifier is shown in Fig. 8 (see Section 20). Show that the output may be greater than the input if the current is continuous and the converter driven near resonance. Fig. 8 Dr P.R. Palmer November 2005

6 ANSWERS V RMS V, 56.2 µh, 20 nf uf, 127 V 5. Check the crib! W, 0.02 us A, 30 V