Chapter 7 PWM Techniques Power Electronics Chapter 7 PWM Techniques

The most widely used control technique in power electronics AC/AC DC/DC Pulse Width Modulation (PWM) (Chopping control) AC/DC DC/AC

Outline 7.1 Basic principles 7.2 Some major PWM techniques in DC/AC inverters 7.3 PWM techniques with feedback control 7.4 PWM rectifiers

7.1 Basic principles of PWM Similar response to different shape of impulse input The equal-area theorem: Responses tend to be identical when input signals have same area and time durations of input impulses become very small.

Basic principles of PWM Application of the equal-area theorem This is sinusoidal PWM (SPWM) The equal-area theorem can be applied to realize any shape of waveforms

A list of PWM techniques Triangular-wave sampling Natural sampling Uniform sampling Calculation Calculation based on equal-area criterion Selective harmonics elimination Hysteretic control Space Vector Modulation (SVM, or SVPWM) Random PWM

7.2 Some major PWM techniques Natural sampling Uniform sampling Selective harmonics elimination Some practical issues Synchronous modulation and asynchronous modulation Harmonics in the PWM inverter output voltages Ways to improve DC input voltage utilization and reduce switching frequency Connection of multiple PWM inverters

Triangular-wave natural sampling Uni-polar PWM in single-phase VSI Uni-polar sampling is used to realize uni-polar PWM.

Triangular-wave natural sampling Bi-polar PWM in single-phase VSI Bi-polar sampling is used to realize bi-polar PWM.

Triangular-wave natural sampling In 3-phase VSI Three-phase bridge inverter can only realize bi-bolar PWM therefore should be controlled by bipolar sampling.

Triangular-wave uniform sampling Easier to realize by computer-control Modulation factor

Selective harmonics elimination PWM (SHEPWM)

Frequency relationship between triangular-wave carrier and control signal Asynchronous Modulation Synchronous Modulation

Harmonics in the PWM inverter output voltages Spectrum of 1-phase bridge PWM inverter output voltage No lower order harmonics The lowest frequency harmonics is wc and adjacent harmonics. wc has the highest harmonic content.

Harmonics in the PWM inverter output voltages Spectrum of 3-phase bridge PWM inverter output voltage No lower order harmonics No harmonics at wc. The lowest frequency and highest content harmonics are wc2wr and 2wcwr.

Ways to improve utilization of DC input voltage and reduce switching frequency Use trapezoidal waveform as modulating signal instead of sinusoidal

Ways to improve utilization of DC input voltage and reduce switching frequency Use 3k order harmonics bias in the modulating signal

Connection of multiple PWM inverters Purposes Expand output power rating Reduce harmonics

Space Vector PWM (SVPWM or SVM) Vector Space of 3-phase Line-to-Line Variables Phase variables (a, b and c) produce line-to-line variables (ab, bc and ca) in plane- Line-to-line variables (ab, bc and ca) do not have -component in -coordinate system a c b ab bc ca   [1 1 1]T 

Line-to-Line Voltage Space Vector where Space vector  bc v   ab  v If Vm is the amplitude of balanced, symmetrical, three-phase line-to-line voltages, then ca

Switching States for 3-phase Voltage Source Inverter ia ib ic va vc vb sa sb sc p n Vdc idc idc vab Vdc sa sc sb 1 ic ib ib+ic ia ia+ic ia+ib ia+ib+ic Switching state pnn ppn npn npp nnp pnp ppp nnn vca vbc -Vdc

Switching State Vector [pnn]  bc v   ab,  v ca

Switching State Vector [ppn]  bc v   ab,  ca

Switching State Vector [ppp]  bc ab,  ca

Switching State Vectors Sector I IV III II V VI at center point ab,  bc ca  30 150 90 -90 -150 -30   (°)

Reference Voltage Vector, Vref ab,  bc ca   v v where In general,  Assume  at center point ref V r

Definition of High Frequency Synthesis  For example v V1() V2() Vref () t T1 T2 T0 TS Total area of = Area of

Synthesis of Vref using Switching State Vectors ab,  bc ca   v v  ref V r ia ib ic va vc vb sa sb sc p n Vdc idc a b c 1 I IV III II VI 

Duty Ratio of Switching State Vectors in SVPWM From HF synthesis definition, Assume is constant in TS , where ref V r  

7.3 PWM techniques with feedback control Current hysteretic control Voltage hysteretic control Triangular-wave comparison (sampling) with feedback control

Current hysteretic control In Single-phase VSI

Current hysteretic control In 3-phase VSI

Voltage hysteretic control

Triangular-wave comparison (sampling) with feedback control

7.4 PWM rectifiers Operation Principles a) Rectification mode b) Inversion mode c) Reactive power compensation mode d) Current leading by

PWM rectifiers Three-phase circuit

PWM rectifiers Indirect current control

PWM rectifiers Direct current control