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Switch-Mode DC-AC Converters EE 442/642 8-1 Some Applications: AC Motor Drives & PV Inverters 8-2 Switch-Mode DC-AC Inverter Four quadrants of operation. 8-3 Half-Bridge Inverter: 1. Capacitors provide the mid-point. 2. The transistors TA+ and TA- are switched using pulse-width-modulation (PWM). 8-4 Synthesis of a Sinusoidal Output by PWM Amplitude and frequency modulation ratios: ma Vcontrol f , mf s , Vtri f1 For small values of mf ( e.g., ≤ 21), the two signals must be synchronized to avoid sub-harmonics. Peak value of fundamental voltage: 1 ˆ (VAo )1 maVd , 2 for ma 1 The harmonics in the inverter output appear as sidebands around mf, 2mf, 3mf, …,kmf,… Only odd harmonics are present in the output voltage waveform →mf should be an odd integer value. 8-5 Harmonics in the DC-AC Inverter Output Voltage 1. The fundamental voltage is proportional to the amplitude modulation index. 2. Some harmonics can be larger than the fundamental component. 8-6 Fundamental Voltage as a Function of ma 1. Note the linear and the over-modulation regions; with squarewave operation in the limit. 1 2 ˆ Vd (VAo )1 Vd , 2 for ma 1 8-7 Harmonics in the Over-Modulation Region The side bands start to spread out to a point where all the integer harmonics appear in the frequency spectrum (including the low-order harmonics which are hard to filter). 8-8 Square-Wave Mode of Operation Fundamental and harmonic voltages: 2 ˆ (VAo )1 Vd , 2 ˆ (VAo ) h Vd , h 3,5,7... h 8-9 Single-Phase Full-Bridge DC-AC Inverter 1. No need for capacitor mid-point. 2. The output voltage now switches between +Vd and -Vd. 8-10 PWM to Synthesize Sinusoidal Output: Bipolar Switching Peak value of fundamental voltage: Vˆo1 maVd , for 4 ˆ Vd Vo1 Vd , ma 1 for ma 1 8-11 Analysis with Ideal Filters vo (t ) 2Vo sin(1t ), io (t ) 2 I o sin(1t ) Vd id* (t ) vo (t )io (t ), id* (t ) ... I d 2 I d 2 cos(21t ) where VI VI I d o o cos( ), I d 2 o o VD 2Vd 8-12 PWM Unipolar Voltage Switching Legs A and B are controlled separately: Vˆo1 maVd , for 4 ˆ Vd Vo1 Vd , ma 1 for ma 1 The harmonics in the inverter output appear as sidebands around 2mf, 4mf, 6mf, … Note the harmonics at and around mf, 3mf, 5mf, … are absent → lower harmonic content. Note also only odd harmonics are present. 8-13 DC-Side Current with PWM Unipolar Switching The ripple content is significantly less than when using bipolar switching. 8-14 Sinusoidal Synthesis by Voltage Shift (Modified Square Wave) 4 ˆ (Vo ) h Vd sin(h ), h 1,3,5,7... h 8-15 Fundamental and Ripple in Inverter Output δ Vo1Eo V01Eo cos( ) Eo2 sin( ), Q Active and Reactive Power: P 1L 1L 8-16 Square-Wave versus PWM Operation PWM results in much smaller ripple current. 8-17 Push-Pull Inverter (requires transformer with center tap) Vˆo1 maVd / n, Vd ˆ 4 Vd Vo1 , n n for for ma 1 ma 1 1. vo switches between Vd/n and –Vd/n where n is the transformer turn ratio. 2. Advantage: no more than one switch conducts at any time → less voltage drop. Also the control drives have the same ground. 3. Difficulty: strong magnetic coupling between the two half windings is required to reduce the energy associated with the leakage inductance. 8-18 Three-Phase Inverter 1. Three inverter legs; 2. No mid-capacitor point is required. 8-19 Three-Phase PWM Waveforms Legs A, B and C are controlled separately: VˆLL1 3 maVd 0.612maVd , 2 2 3 6 ˆ Vd VLL1 Vd , 2 2 for for ma 1 ma 1 The frequency modulation index, mf, should be an odd number that is a multiple of 3 to cancel out the most dominant harmonics See harmonic content of line voltage during linear modulation in the next slide. 8-20 Three-Phase Inverter Harmonics 8-21 Three-Phase Inverter Output 8-22 DC-Side Current in a Three-Phase Inverter The current consists of a dc component and the switching-frequency related harmonics. 8-23 Three-Phase Inverter: Fundamental Frequency Vd id* (t ) v An (t )i A (t ) vBn (t )iB (t ) vCn (t )iC (t ), 3Vo I o i (t ) ... I d cos( ), Vd * d (DC quantity only) 8-24 Three-Phase Inverter: Square-Wave Mode 8-25 Square-Wave Operation 8-26 Square-Wave and PWM Operation PWM results in much smaller ripple current 8-27 PWM Operation: Short-Circuit States 8-28 Blanking Time: Non-Ideal switches Instantaneous switching from ON to OFF and vice versa. In practice, the turn-on and turn-off times are finite (non-zero). Blanking Time is chosen to avoid crossconduction through the leg. Impact on output voltage: 8-29 Effect of Blanking Time on Voltage (during current zero crossing) 8-30 Programmed Harmonic Elimination The notch angles are based on the desired output. 8-31 Current Control: Tolerance-Band Current Control Variable switching frequency which depends on the load inductance, motor back emf, and DC voltage. 8-32 Fixed-Frequency Operation 8-33 Transition from Inverter to Rectifier Mode 8-34