Power Electroni cs Chapter 6 PWM Techniques Power E l e ct r o n i cs 2 The most widely used control technique in power electronics AC/AC DC/DC Pulse Width Modulation (PWM) (Chopping control) AC/DC DC/AC Power E l e ct r o n i cs 3 Outline 6.1 Basic principles 6.2 Some major PWM techniques in DC/AC inverters 6.3 PWM techniques with feedback control 6.4 PWM rectifiers Power E l e ct r o n i cs 4 6.1 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. Power E l e ct r o n i cs 5 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 Power E l e ct r o n i cs 6 A list of PWM techniques Triangular-wave sampling – Natural sampling – Uniform sampling Calculation – Calculation based on equal-area criterion – Selective harmonics elimination Hysteric control Space Vector Modulation (SVM, or SVPWM) Random PWM Power E l e ct r o n i cs 7 6.2 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 Power E l e ct r o n i cs 8 Triangular-wave natural sampling Uni-polar PWM in single-phase VSI Uni-polar sampling is used to realize uni-polar PWM. $POUSPM TJHOBM $BSSJFS Mudulation Carrier U d + V 1 V 2 V 3 V 4 VD 1 VD 2 VD 3 VD 4 u o R L u r u c Power E l e ct r o n i cs 9 Triangular-wave natural sampling Bi-polar PWM in single-phase VSI $POUSPM TJHOBM $BSSJFS Mudulation Carrier U d + V 1 V 2 V 3 V 4 VD 1 VD 2 VD 3 VD 4 u o R L u r u c Bi-polar sampling is used to realize bi-polar PWM. Power E l e ct r o n i cs 10 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. Power E l e ct r o n i cs 11 Triangular-wave uniform sampling Easier to realize by computer- control Modulation factor Power E l e ct r o n i cs 12 Selective harmonics elimination PWM (SHEPWM) Power E l e ct r o n i cs 13 Frequency relationship between triangular- wave carrier and control signal Asynchronous Modulation Synchronous Modulation Power E l e ct r o n i cs 14 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 w c and adjacent harmonics. w c Has the highest harmonic content. 1 0 0 2  1 23 4  0 2 +  4  0 1  3  5 +  Ma gnit ude (%) (nω c +kω r ) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 k n a=1.0 a=0.8 a=0.5 a=0 Power E l e ct r o n i cs 15 Harmonics in the PWM inverter output voltages No lower order harmonics No harmonics at ω c . The lowest frequency and highest content harmonics are ω c ±2ω r and 2ω c ±ω r . Spectrum of 3-phase bridge PWM inverter output voltage 1 0 0 2  1 23 4  0 2  4  0 1  3  5  M agn i tu d e (%) 0.2 0.4 0.6 0.8 1.0 1.2 k n a=1.0 a=0.8 a=0.5 a=0 (nω c +kω r ) Power E l e ct r o n i cs 16 Ways to improve utilization of DC input voltage and reduce switching frequency Use trapezoidal waveform as modulating signal instead of sinusoidal Power E l e ct r o n i cs 17 Ways to improve utilization of DC input voltage and reduce switching frequency Use 3k order harmonics bias in the modulating signal u c u rU1 u rV1 u rW1 u u UN' U d U d O t O u rU u rV u rW u c O t O O O O t t t t t u VN' u WN' u UV u 1 1 1 1 0.5 u P 2 U d ? 2 U d u c u r1 u O ωt u r u r1 u O ωt u r3 Power E l e ct r o n i cs 18 Connection of multiple PWM inverters Purposes – Expand output power rating – Reduce harmonics Power E l e ct r o n i cs 19 6.3 PWM techniques with feedback control Current hysteric control Voltage hysteric control Triangular-wave comparison (sampling) with feedback control Power E l e ct r o n i cs 20 Current hysteric control In Single-phase VSI Power E l e ct r o n i cs 21 Current hysteric control In 3-phase VSI Power E l e ct r o n i cs 22 Voltage hysteric control Filter +  u u * u 2 U d 2 U d Power E l e ct r o n i cs 23 Triangular-wave comparison (sampling) with feedback control Power E l e ct r o n i cs 24 6.4 PWM rectifiers Operation Principles a) Rectification mode b) Inversion mode c) Reactive power compensation mode d) Current leading by ? Power E l e ct r o n i cs 25 PWM rectifiers Three-phase circuit Power E l e ct r o n i cs 26 PWM rectifiers Indirect current control PI +  -PBE Triangular-wave sin(ωt+2kπ3) (k=0,1,2) cos(ωt+2kπ3) (k=0,1,2) u * d u d +  +   + i d u R u L X L R u A,B,C u d RL u a ,u b ,u c Power E l e ct r o n i cs 27 PWM rectifiers Direct current control PI -PBE sin(ωt+2kπ3) (k=0,1,2) u * d u d +  + i d i a,b,c u d RL u a ,u b ,u c i * a,b,c