Power Electronics,Chapter 7 PWM Techniques,The most widely used control technique in power electronics,Pulse Width Modulation (PWM) (Chopping control),DC/DC,AC/AC,DC/AC,AC/DC,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,No lower order harmonics The lowest frequency harmonics is wc and adjacent harmonics. wc has the highest harmonic content.,Spectrum of 1-phase bridge PWM inverter output voltage,Harmonics in the PWM inverter output voltages,No lower order harmonics No harmonics at wc. The lowest frequency and highest content harmonics are wc2wr and 2wcwr.,Spectrum of 3-phase bridge PWM inverter output voltage,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),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,Vector Space of 3-phase Line-to-Line Variables,Line-to-Line Voltage Space Vector,where,ab ,bc,ca,v,v,Space vector,If Vm is the amplitude of balanced, symmetrical, three-phase line-to-line voltages, then,Switching States for 3-phase Voltage Source Inverter,Switching State Vector pnn,ab, ,bc,ca,v,v,Switching State Vector ppn,ab, ,bc,ca,v,Switching State Vector ppp,ab, ,bc,ca,Switching State Vectors,Reference Voltage Vector, Vref,Vref (),V1(),V2(),T1,T2,T0,TS,t,Total area of,= Area of,For example,v,Definition of High Frequency Synthesis,Synthesis of Vref using Switching State Vectors,From HF synthesis definition,Assume is constant in TS ,where,Duty Ratio of Switching State Vectors in SVPWM,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,PWM rectifiers,Three-phase circuit,PWM rectifiers,Indirect current control,PWM rectifiers,Direct current control,