UNITIV INVERTERS EE 2301 POWER ELECTRONICS SinglePhase Inverters
- Slides: 89
UNIT-IV INVERTERS EE 2301 -POWER ELECTRONICS
Single-Phase Inverters Half-Bridge Inverter One of the simplest types of inverter. Produces a square wave output. EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) Full Bridge (H-bridge) Inverter Two half-bridge inverters combined. Allows for four quadrant operation. EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) Quadrant 1: Positive step-down converter (forward motoring) Q 1 -On; Q 2 - Chopping; D 3, Q 1 freewheeling EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) Quadrant 2: Positive step-up converter (forward regeneration) Q 4 - Chopping; D 2, D 1 freewheeling EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) Quadrant 3: Negative step-down converter (reverse motoring) Q 3 -On; Q 4 - Chopping; D 1, Q 3 freewheeling EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) Quadrant 4: Negative step-up converter (reverse regeneration) Q 2 - Chopping; D 3, D 4 freewheeling EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) Phase-Shift Voltage Control - the output of the H-bridge inverter can be controlled by phase shifting the control of the component half-bridges. See waveforms on next slide. EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) The waveform of the output voltage vab is a quasisquare wave of pulse width . The Fourier series of vab is given by: The value of the fundamental, a 1= The harmonic components as a function of phase angle are shown in the next slide. EE 2301 -POWER ELECTRONICS
Single-Phase Inverters (cont’d) EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters Three-phase bridge inverters are widely used for ac motor drives. Two modes of operation - square wave and six-step. The topology is basically three half-bridge inverters, each phase-shifted by 2 /3, driving each of the phase windings. EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The three square-wave phase voltages can be expressed in terms of the dc supply voltage, Vd, by Fourier series as: EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The line voltages can then be expressed as: EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The line voltages are six-step waveforms and have characteristic harmonics of 6 n 1, where n is an integer. This type of inverter is referred to as a six-step inverter. The three-phase fundamental and harmonics are balanced with a mutual phase shift of 2 /3. EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) If the three-phase load neutral n is isolated from the center tap of the dc voltage supply (as is normally the case in an ac machine) the equivalent circuit is shown below. EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) In this case the isolated neutral-phase voltages are also six-step waveforms with the fundamental component phase-shifted by /6 from that of the respective line voltage. Also, in this case, the triplen harmonics are suppressed. EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) For a linear and balanced 3 load, the line currents are also balanced. The individual line current components can be obtained from the Fourier series of the line voltage. The total current can be obtained by addition of the individual currents. A typical line current wave with inductive load is shown below. EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The inverter can operate in the usual inverting or motoring mode. If the phase current wave, ia, is assumed to be perfectly filtered and lags the phase voltage by /3 the voltage and current waveforms are as shown below: EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters The inverter can also operate in rectification or regeneration mode in which power is pushed back to the dc side from the ac side. The waveforms corresponding to this mode of operation with phase angle = 2 /3 are shown below: EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The phase-shift voltage control principle described earlier for the single-phase inverter can be extended to control the output voltage of a three-phase inverter. EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The three waveforms va 0, vb 0, and vc 0 are of amplitude 0. 5 Vd and are mutually phaseshifted by 2 /3. The three waveforms ve 0, vf 0, and vg 0 are of similar but phase shifted by . EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The transformer’s secondary phase voltages, v. A 0, v. B 0, and vc 0 may be expressed as follows: where m is the transformer turns ratio (= Ns/Np). Note that each of these waves is a EE 2301 -POWER ELECTRONICS function of angle.
Three-Phase Bridge Inverters (cont’d) The output line voltages are given by: While the component voltage waves va 0, vd 0, v. A 0 … etc. all contain triplen harmonics, they are eliminated from the line voltages because they are co-phasal. Thus the line voltages are six-step waveforms with order of harmonics = 6 n 1 at a phase angle . EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The Fourier series for v. A 0 and v. B 0 are given by: EE 2301 -POWER ELECTRONICS
Three-Phase Bridge Inverters (cont’d) The Fourier series for v. AB is given by: Note that the triplen harmonics are removed in v. AB although they are present in v. A 0 and v. B 0. EE 2301 -POWER ELECTRONICS
PWM Technique While the 3 6 -step inverter offers simple control and low switching loss, lower order harmonics are relatively high leading to high distortion of the current wave (unless significant filtering is performed). PWM inverter offers better harmonic control of the output than 6 -step inverter. EE 2301 -POWER ELECTRONICS
PWM Principle The dc input to the inverter is “chopped” by switching devices in the inverter. The amplitude and harmonic content of the ac waveform is controlled by the duty cycle of the switches. The fundamental voltage v 1 has max. amplitude = 4 Vd/ for a square wave output by creating notches, the amplitude of v 1 is reduced (see next slide). EE 2301 -POWER ELECTRONICS
PWM Principle (cont’d) EE 2301 -POWER ELECTRONICS
PWM Techniques Various PWM techniques, include: • Sinusoidal PWM (most common) • Selected Harmonic Elimination (SHE) PWM • Space-Vector PWM • Instantaneous current control PWM • Hysteresis band current control PWM • Sigma-delta modulation EE 2301 -POWER ELECTRONICS
Sinusoidal PWM The most common PWM approach is sinusoidal PWM. In this method a triangular wave is compared to a sinusoidal wave of the desired frequency and the relative levels of the two waves is used to control the switching of devices in each phase leg of the inverter. EE 2301 -POWER ELECTRONICS
Sinusoidal PWM (cont’d) Single-Phase (Half-Bridge) Inverter Implementation EE 2301 -POWER ELECTRONICS
Sinusoidal PWM (cont’d) when va 0> v. T T+ on; T- off; va 0 = ½Vd EE 2301 -POWER ELECTRONICS va 0 < v. T T- on; T+ off; va 0 = -½Vd
Sinusoidal PWM (cont’d) EE 2301 -POWER ELECTRONICS
Sinusoidal PWM (cont’d) Definition of terms: Triangle waveform switching freq. = fc (also called carrier freq. ) Control signal freq. = f (also called modulation Peak amplitude freq. ) of control signal Amplitude modulation ratio, m = Vp VT Peak amplitude of triangle wave Frequency modulation ratio, EE 2301 -POWER mf (P)= fc / f ELECTRONICS
Multiple Pulse-Width Modulation • In multiple-pulse modulation, all pulses are the same width • Vary the pulse width according to the amplitude of a sine wave evaluated at the center of the same pulse EE 2301 -POWER ELECTRONICS
Generate the gating signal 2 Reference Signals, vr, -vr EE 2301 -POWER ELECTRONICS
Comparing the carrier and reference signals • Generate g 1 signal by comparison with vr • Generate g 4 signal by comparison with -vr EE 2301 -POWER ELECTRONICS
Comparing the carrier and reference signals EE 2301 -POWER ELECTRONICS
Potential problem if Q 1 and Q 4 try to turn ON at the same time! EE 2301 -POWER ELECTRONICS
If we prevent the problem Output voltage is low when g 1 and g 4 are both high EE 2301 -POWER ELECTRONICS
This composite signal is difficult to generate EE 2301 -POWER ELECTRONICS
Generate the same gate pulses with one sine wave EE 2301 -POWER ELECTRONICS
Alternate scheme EE 2301 -POWER ELECTRONICS
rms output voltage • Depends on the modulation index, M Where δm is the width of the mth pulse EE 2301 -POWER ELECTRONICS
Fourier coefficients of the output voltage EE 2301 -POWER ELECTRONICS
Harmonic Profile EE 2301 -POWER ELECTRONICS
Compare with multiple-pulse case for p=5 Distortion Factor is considerably less EE 2301 -POWER ELECTRONICS
Series-Resonant Inverter EE 2301 -POWER ELECTRONICS
Operation T 1 fired, resonant pulse of current flows through the load. The current falls to zero at t = t 1 m and T 1 is “self – commutated”. T 2 fired, reverse resonant current flows through the load and T 2 is also “self-commutated”. The series resonant circuit must be underdamped, R 2 < (4 L/C) EE 2301 -POWER ELECTRONICS
Operation in Mode 1 – Fire T 1 EE 2301 -POWER ELECTRONICS
EE 2301 -POWER ELECTRONICS
To find the time when the current is maximum, set the first derivative = 0 EE 2301 -POWER ELECTRONICS
To find the capacitor voltage, integrate the current The current i 1 becomes = 0 @ t=t 1 m EE 2301 -POWER ELECTRONICS
EE 2301 -POWER ELECTRONICS
Operation in Mode 2 – T 1, T 2 Both OFF EE 2301 -POWER ELECTRONICS
t 2 m EE 2301 -POWER ELECTRONICS
Operation in Mode 3 – Fire T 2 EE 2301 -POWER ELECTRONICS
EE 2301 -POWER ELECTRONICS
EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Space Vector Diagram • Active vectors: to (stationary, not rotating) • Zero vector: • Six sectors: I to VI EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Space Vectors • Three-phase voltages (1) • Two-phase voltages (2) • Space vector representation (3) (2) (3) (4) where EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Space Vectors (Example) Switching state [POO] S 1, S 6 and S 2 ON and (5) (4) (6) Similarly, (7) EE 2301 -POWER ELECTRONICS (5)
Space Vector Modulation • Active and Zero Vectors • Active Vector: 6 • Zero Vector: 1 • Redundant switching states: [PPP] and [OOO] EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Reference Vector Vref • Definition • Rotating in space at ω (8) • Angular displacement (9) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Relationship Between Vref and VAB • Vref is approximated by two active and a zero vectors • Vref rotates one revolution, VAB completes one cycle • Length of Vref corresponds to magnitude of VAB EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Dwell Time Calculation • Volt-Second Balancing (10) • Ta, Tb and T 0 – dwell times for and • Ts – sampling period • Space vectors , and (11) (10) (12) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Dwell Times Solve (12) (13) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Vref Location versus Dwell Times EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Modulation Index (15) (16) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Modulation Range • Vref, max (17) (16) • ma, max = 1 • Modulation range: 0 ma 1 EE 2301 -POWER ELECTRONICS (18)
Space Vector Modulation • Switching Sequence Design • Basic Requirement: Minimize the number of switchings per sampling period Ts • Implementation: Transition from one switching state to the next involves only two switches in the same inverter leg. EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Seven-segment Switching Sequence • Selected vectors: V 0, V 1 and V 2 • Dwell times: Ts = T 0 + Ta + Tb • Total number of switchings: 6 EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Undesirable Switching Sequence • Vectors V 1 and V 2 swapped • Total number of switchings: 10 EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Switching Sequence Summary (7–segments) Note: The switching sequences for the odd and ever sectors are different. EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Simulated Waveforms f 1 = 60 Hz, fsw = 900 Hz, ma = 0. 696, Ts = 1. 1 ms EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Waveforms and FFT EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Waveforms and FFT (Measured) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Waveforms and FFT (Measured) ( and EE 2301 -POWER ELECTRONICS )
Space Vector Modulation • Even-Order Harmonic Elimination Type-A sequence (starts and ends with [OOO]) Type-B sequence (starts and ends with [PPP]) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Even-Order Harmonic Elimination Space vector Diagram EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Even-Order Harmonic Elimination • Measured waveforms and FFT EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Even-Order Harmonic Elimination ( and EE 2301 -POWER ELECTRONICS )
Space Vector Modulation • Five-segment SVM EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Switching Sequence ( 5 -segment) EE 2301 -POWER ELECTRONICS
Space Vector Modulation • Simulated Waveforms ( 5 -segment) • f 1 = 60 Hz, fsw = 600 Hz, ma = 0. 696, Ts = 1. 1 ms • No switching for a 120° period per cycle. • Low switching frequency but high harmonic distortion EE 2301 -POWER ELECTRONICS
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