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UNIT-IV INVERTERS 4/16/2017 Copyright by

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**Single-Phase Inverters**

Half-Bridge Inverter One of the simplest types of inverter. Produces a square wave output. 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

Full Bridge (H-bridge) Inverter Two half-bridge inverters combined. Allows for four quadrant operation. 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

Quadrant 1: Positive step-down converter (forward motoring) Q1-On; Q2 - Chopping; D3,Q1 freewheeling 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

Quadrant 2: Positive step-up converter (forward regeneration) Q4 - Chopping; D2,D1 freewheeling 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

Quadrant 3: Negative step-down converter (reverse motoring) Q3-On; Q4 - Chopping; D1,Q3 freewheeling 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

Quadrant 4: Negative step-up converter (reverse regeneration) Q2 - Chopping; D3,D4 freewheeling 4/16/2017 Copyright by

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**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. 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

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**Single-Phase Inverters (cont’d)**

The waveform of the output voltage vab is a quasi-square wave of pulse width . The Fourier series of vab is given by: The value of the fundamental, a1= The harmonic components as a function of phase angle are shown in the next slide. 4/16/2017 Copyright by

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**Single-Phase Inverters (cont’d)**

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**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. 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

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**Three-Phase Bridge Inverters (cont’d)**

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**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: 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

The line voltages can then be expressed as: 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

The line voltages are six-step waveforms and have characteristic harmonics of 6n1, 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. 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

If the three-phase load neutral n is isolated from the the center tap of the dc voltage supply (as is normally the case in an ac machine) the equivalent circuit is shown below. 4/16/2017 Copyright by

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**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. 4/16/2017 Copyright by

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**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. 4/16/2017 Copyright by

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**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: 4/16/2017 Copyright by

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**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: 4/16/2017 Copyright by

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**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. 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

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**Three-Phase Bridge Inverters (cont’d)**

The three waveforms va0,vb0, and vc0 are of amplitude 0.5Vd and are mutually phase-shifted by 2/3. The three waveforms ve0,vf0, and vg0 are of similar but phase shifted by . 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

The transformer’s secondary phase voltages, vA0, vB0, and vc0 may be expressed as follows: where m is the transformer turns ratio (= Ns/Np). Note that each of these waves is a function of angle. Copyright by 4/16/2017

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**Three-Phase Bridge Inverters (cont’d)**

The output line voltages are given by: While the component voltage waves va0, vd0, vA0 … 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 = 6n1 at a phase angle . 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

The Fourier series for vA0 and vB0 are given by: 4/16/2017 Copyright by

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**Three-Phase Bridge Inverters (cont’d)**

The Fourier series for vAB is given by: Note that the triplen harmonics are removed in vAB although they are present in vA0 and vB0. 4/16/2017 Copyright by

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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. 4/16/2017 Copyright by

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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 v1 has max. amplitude = 4Vd/ for a square wave output but by creating notches, the amplitude of v1 is reduced (see next slide). 4/16/2017 Copyright by

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**PWM Principle (cont’d)**

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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 4/16/2017 Copyright by

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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. 4/16/2017 Copyright by

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**Sinusoidal PWM (cont’d)**

Single-Phase (Half-Bridge) Inverter Implementation 4/16/2017 Copyright by

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**Sinusoidal PWM (cont’d)**

when va0> vT T+ on; T- off; va0 = ½Vd va0 < vT T- on; T+ off; va0 = -½Vd 4/16/2017 Copyright by

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**Sinusoidal PWM (cont’d)**

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**Sinusoidal PWM (cont’d)**

Definition of terms: Triangle waveform switching freq. = fc (also called carrier freq.) Control signal freq. = f (also called modulation freq.) Amplitude modulation ratio, m = Vp VT Frequency modulation ratio, mf (P)= fc / f Peak amplitude of control signal Peak amplitude of triangle wave 4/16/2017 Copyright by

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**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 4/16/2017 Copyright by

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**Generate the gating signal**

2 Reference Signals, vr, -vr 4/16/2017 Copyright by

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**Comparing the carrier and reference signals**

Generate g1 signal by comparison with vr Generate g4 signal by comparison with -vr 4/16/2017 Copyright by

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**Comparing the carrier and reference signals**

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**Potential problem if Q1 and Q4 try to turn ON at the same time!**

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**If we prevent the problem**

Output voltage is low when g1 and g4 are both high 4/16/2017 Copyright by

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**This composite signal is difficult to generate**

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**Generate the same gate pulses with one sine wave**

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Alternate scheme 4/16/2017 Copyright by

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rms output voltage Depends on the modulation index, M Where δm is the width of the mth pulse 4/16/2017 Copyright by

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**Fourier coefficients of the output voltage**

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Harmonic Profile 4/16/2017 Copyright by

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**Compare with multiple-pulse case for p=5**

Distortion Factor is considerably less 4/16/2017 Copyright by

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**Series-Resonant Inverter**

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Operation T1 fired, resonant pulse of current flows through the load. The current falls to zero at t = t1m and T1 is “self – commutated”. T2 fired, reverse resonant current flows through the load and T2 is also “self-commutated”. The series resonant circuit must be underdamped, R2 < (4L/C) 4/16/2017 Copyright by

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**Operation in Mode 1 – Fire T1**

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To find the time when the current is maximum, set the first derivative = 0 4/16/2017 Copyright by

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To find the capacitor voltage, integrate the current The current i1 becomes = t=t1m 4/16/2017 Copyright by

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**Operation in Mode 2 – T1, T2 Both OFF**

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t2m 4/16/2017 Copyright by

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**Operation in Mode 3 – Fire T2**

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**Space Vector Modulation**

Space Vector Diagram Active vectors: to (stationary, not rotating) Zero vector: Six sectors: I to VI 4/16/2017 Copyright by

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**Space Vector Modulation**

Space Vectors Three-phase voltages (1) Two-phase voltages (2) Space vector representation (3) (2) (3) (4) where 4/16/2017 Copyright by

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**Space Vector Modulation**

Space Vectors (Example) Switching state [POO] S1, S6 and S2 ON and (5) (5) (4) (6) Similarly, (7) 4/16/2017 Copyright by

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**Space Vector Modulation**

Active and Zero Vectors Active Vector: 6 Zero Vector: 1 Redundant switching states: [PPP] and [OOO] 4/16/2017 Copyright by

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**Space Vector Modulation**

Reference Vector Vref Definition Rotating in space at ω (8) Angular displacement (9) 4/16/2017 Copyright by

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**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 4/16/2017 Copyright by

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**Space Vector Modulation**

Dwell Time Calculation Volt-Second Balancing (10) Ta, Tb and T0 – dwell times for and Ts – sampling period Space vectors , and (11) (11) (10) (12) 4/16/2017 Copyright by

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**Space Vector Modulation**

Dwell Times Solve (12) (13) 4/16/2017 Copyright by

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**Space Vector Modulation**

Vref Location versus Dwell Times 4/16/2017 Copyright by

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**Space Vector Modulation**

Modulation Index (15) (16) 4/16/2017 Copyright by

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**Space Vector Modulation**

Modulation Range Vref,max (17) (17) (16) ma,max = Modulation range: 0 ma 1 (18) 4/16/2017 Copyright by

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**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. 4/16/2017 Copyright by

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**Space Vector Modulation**

Seven-segment Switching Sequence Selected vectors: V0, V1 and V2 Dwell times: Ts = T0 + Ta + Tb Total number of switchings: 6 4/16/2017 Copyright by

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**Space Vector Modulation**

Undesirable Switching Sequence Vectors V1 and V2 swapped Total number of switchings: 10 4/16/2017 Copyright by

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**Space Vector Modulation**

Switching Sequence Summary (7–segments) Note: The switching sequences for the odd and ever sectors are different. 4/16/2017 Copyright by

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**Space Vector Modulation**

Simulated Waveforms f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms 4/16/2017 Copyright by

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**Space Vector Modulation**

Waveforms and FFT 4/16/2017 Copyright by

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**Space Vector Modulation**

Waveforms and FFT (Measured) 4/16/2017 Copyright by

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**Space Vector Modulation**

Waveforms and FFT (Measured) ( and ) 4/16/2017 Copyright by

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**(starts and ends with [OOO]) (starts and ends with [PPP])**

Space Vector Modulation Even-Order Harmonic Elimination Type-A sequence (starts and ends with [OOO]) Type-B sequence (starts and ends with [PPP]) 4/16/2017 Copyright by

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**Space Vector Modulation**

Even-Order Harmonic Elimination Space vector Diagram 4/16/2017 Copyright by

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**Space Vector Modulation**

Even-Order Harmonic Elimination Measured waveforms and FFT 4/16/2017 Copyright by

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**Space Vector Modulation**

Even-Order Harmonic Elimination ( and ) 4/16/2017 Copyright by

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**Space Vector Modulation**

Five-segment SVM 4/16/2017 Copyright by

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**Space Vector Modulation**

Switching Sequence ( 5-segment) 4/16/2017 Copyright by

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**Space Vector Modulation**

Simulated Waveforms ( 5-segment) f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms No switching for a 120° period per cycle. Low switching frequency but high harmonic distortion 4/16/2017 Copyright by

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