INVERTERS (DC-AC Converters)

INVERTERS for SEE 4433 Square wave inverters (1-phase) Amplitude and harmonic control (quasi square wave) Total Harmonic Distortion INVERTERS for SEE 4433 Pulse Width Modulation (PWM) (1-phase) Bipolar and unipolar Harmonics 3-phase inverters Square wave (six-step) PWM

INVERTERS In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge A. Full-bridge inverter Vdc Q1 Q2 Q3 Q4 + vo − D1 D3 D2 D4 io Upper and lower switches cannot be ON simultaneously Depending on the switches positions, there can be 3 possible output voltage: (Vdc), (-Vdc) and 0

INVERTERS In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge B. half-bridge inverter The capacitors equally devide the voltage Vdc Depending on the switches positions, the output voltage can be either (Vdc/2) or (−Vdc/2) Q1 D1 C1 + Vdc/2 − Vdc + vo − C2 + Vdc/2 − D2 Q2

INVERTERS Square-wave inverter (with full-bridge) It can be shown that: Can also be implemented using half-bridge inverters

INVERTERS Square-wave inverter (with full-bridge) Current path for inductive load: Vdc Q1 Q2 Q3 Q4 + vo − D1 D3 D2 D4 io SEE EXAMPLE 8-2

INVERTERS TOTAL HARMONIC DISTORTION THD is used to measure the quality of the AC voltage or current The closer the waveform to sinusoidal, the smaller is the THD Can be applied to voltage or current SEE EXAMPLE 8-3

INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Duration of ZERO output voltage is introduced and it can be shown that: Amplitude of the fundamental component can be controlled (by controlling α) Certain harmonic contents can be eliminated (also by controlling α !) Amplitude and harmonics cannot be controlled independently Cannot be implemented using the half-bridge inverter.

INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Fourier series of the output voltage is given by: where

INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Amplitude control Amplitude of fundamental component:  By changing α the amplitude of the fundamental will change Harmonic control The nth harmanic can be eliminated if its amplitude made zero For example, the amplitude of the third harmonic (n=3) is zero when α = 30o

INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Simultaneous control of amplitude and harmonic In order to be able to control amplitude and harmonic simultaneously, variable Vdc has to be added Controlled via DC link Fixed DC voltage Variable DC Load Inverter DC-DC converter

INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Switching signals (full-bridge inverter)        2  2 S1 S1 S2 S2 S3 S3 S4 S4

INVERTERS Pulse Width Modulation Is a method used to control the output voltage (amplitude and frequency) of an inverter by modulating the width of the pulses of the output waveform Main advantages of PWM control: Filter requirement is reduced Amplitude and frequency can be control independently Significant reduction in THD of load current (inductive load) Disadvantages of PWM control: More complex control circuit Higher switching losses In SEE4433, two switching scheme for single-phase inverter will be discussed: Bipolar switching scheme Unipolar switching scheme

INVERTERS Pulse Width Modulation Bipolar switching scheme (vsine > vtri) : Q1 and Q2 ON; vo=Vdc (vsine < vtri) : Q3 and Q4 ON; vo=-Vdc

INVERTERS Pulse Width Modulation Bipolar switching scheme fsine Frequency modulation index ftri Vm,tri Vm,sine Amplitude modulation index The amplitude of the fundamental component of vo is proportional to ma: V1=maVdc

INVERTERS Harmonics in PWM single-phase inverter

INVERTERS Harmonics in PWM single-phase inverter : Bipolar switching scheme If mf is chosen as odd integer with the triangular wave synchronize with the modulating signal, then the PWM output is an odd quarter-wave symmetry. an = 0 and bn exist only for odd  Graphically, this can be represented using frequency spectrum diagram : OR using a normalized Fourier coefficients table:

INVERTERS Pulse Width Modulation Unipolar switching scheme (vsine > vtri) : Q1 ON, Q4 OFF; va= Vdc (vsine < vtri) : Q1 OFF, Q4 ON; va= 0 (-vsine > vtri) : Q3 ON, Q2 OFF; vb= Vdc (-vsine < vtri) : Q3 OFF, Q2 ON; vb= 0 Vab = va - vb

INVERTERS Harmonics in PWM single-phase inverter : Unipolar switching scheme The frequency of the output voltage is doubled. If mf is chosen as even integer then the first cluster of harmonics appear around 2mf (the harmonic at 2mf itself is zero) Graphically, this can be represented using frequency spectrum diagram : Or using a normalized Fourier coefficients table:

INVERTERS Harmonics in PWM single-phase inverter : Comparison between square wave and PWM SQUARE-WAVE Contains harmonics at relatively low frequency: 3rd, 5th, 7th, 9th, etc. In order to improve the THDV , a low pass filter can be employed  filter will be bulky since cutoff frequency is low  difficult to remove harmonics since at the same time must ensure fundamental component is not attenuated. PWM Harmonics appear around mf which is further away from fundamental. To improve THDV, filter with higher cutoff can be used  smaller in size  easier to filter out harmonics. Square wave PWM mf = 21 1 3 5 7 9 11 13 n 1 3 5 7 9 11 13 15 17 19 21 23 25

INVERTERS Three-phase inverters Six-step inverter Vdc S4 S5 S6 C B n S3 S1 o S1 S2 S3 S4 S5 S6 vAo Vdc THDV of line-line and line-n are both 31% THDI of line current depends on load, however it will be smaller than the single phase vBo vCo vAB vAn

INVERTERS Three-phase inverters PWM inverter mf is chosen to be multiple of 3 so that the harmonic at multiple of 3, including mf (and its multiple) are suppressed (or canceled out) in the line-line voltage