inverter[1]

Chapter 4DC to AC Conversion(INVERTER)•General concept•Single-phase inverter•Harmonics•Modulation•Three-phase inverterPower Electronics and 1DC to AC Converter (Inverter)•DEFINITION: Converts DC to AC power by switching the DC input voltage (or current)in apre-determined sequence so as to generate ACvoltage (or current) output.•General block diagram•TYPICAL APPLICATIONS:–Un-interruptible power supply (UPS), Industrial(induction motor) drives, Traction, HVDCPower Electronics and 2Simple square-wave inverter (1)•To illustrate the concept of AC waveform generationS3S2Power Electronics and 3Power Electronics and 4AC Waveform GenerationVV S3V v tS1,S2 ON; S3,S4 OFFfor t 1 < t < t 2-V tS3,S4 ON ; S1,S2 OFFfor t 2 < t < t 3S2Power Electronics and 5AC WaveformsFUNDAMENTAL COMPONENT3RD HARMONIC5RDHARMONICV-V dcV 131V 51VPower Electronics and 6Harmonics Filtering•Output of the inverter is “chopped AC voltage with zero DC component”. It contain harmonics.•An LC section low-pass filter is normally fitted at the inverter output to reduce the high frequency harmonics.•In some applications such as UPS, “high purity ” sine wave output is required. Good filtering is a must.•In some applications such as AC motor drive, filtering is not required.v O 1v O 2BEFORE FILTERING AFTER FILTERING INVERTERLOADDC SUPPLYVariable Voltage VariableFrequency Capabilityt•Output voltage frequency can be varied by “period”of the square-wave pulse.•Output voltage amplitude can be varied by varying the “magnitude” of the DC input voltage.•Very useful: e.g. variable speed induction motor drivePower Electronics and 7Output voltage harmonics/distortion•Harmonics cause distortion on the output voltage.•Lower order harmonics (3rd, 5th etc) are very difficult to filter, due to the filter size and high filter order. They can cause serious voltage distortion.•Why need to consider harmonics?–Sinusoidal waveform quality must match TNBsupply.–“Power Quality” issue.–Harmonics may cause degradation ofequipment. Equipment need to be “de-rated”.•Total Harmonic Distortion (THD) is a measure to determine the “quality” of a given waveform.Power Electronics and 8Power Electronics and 9Total Harmonics Distortion (THD)()()()()frequency.harmonic at impedance the is :THD Current known,is vaveform for the voltage rms the If .... voltage,harmonic th the is If :THD Voltage ,122,,122,12,12,22,32,2,122,n nn n RMS n RMS n RMSn RMS RMS RMSRMS RMS RMS RMS n RMS n n Z Z V I I I THDi V V V THDv V V V V V V THDv n V ==−=+++== ∞=∞=∞=Power Electronics and 10Fourier Series•Study of harmonics requires understanding of wave shapes. Fourier Series is a tool to analyse wave shapes.()()()tn b n a a v f d n v f b d n v f a d v f a n n n o n n o ωθθθθθπθθπθππππ=++==== ∞= where sin cos 21)(FourierInverse term) sin"(" sin )(1term) cos"(" cos )(1term) DC"(" )(1Series Fourier 1202020Power Electronics and11Harmonics of square-wave (1)()()()()−== −== −+= πππππππππθθθθπθθθθπθθπ202020sin sin 0cos cos 01d n d n V b d n d n V a d V d V a dc n dcn dc dco V dc-V dcθ ωPower Electronics and 12Harmonics of square wave (2)()()[][][][]ππππππππππππθθππππn V b n b n n n n V n n n V n n n n V n n n V b dc n n dcdcdcdc n 41cos odd, is n When exist)not do harmonics even i.e.(01cos even, is When )cos 1(2)cos 1()cos 1()cos 2(cos )cos 0(cos cos cos Solving,20==−==−=−+−=−+−=+−=Spectra of square waven•Spectra (harmonics) characteristics:–Harmonic decreases with a factor of (1/n).–Even harmonics are absent–Nearest harmonics is the 3rd. If fundamental is50Hz, then nearest harmonic is 150Hz.–Due to the small separation between thefundamental an harmonics, output low-passfilter design can be very difficult.Power Electronics and 13Power Electronics and 14Quasi-square wave (QSW)()[]()()[]()()()[]()[]παπαπαπαπαπαπαπαπαπαπθπθθπαπααπαn n n V n n n n V b n n n n n n n n n n n n V n n V d n V b a dc dcn dcdc dc n n cos 1cos 2cos cos cos 2cos cos sin sin cos cos cos cos :Expanding cos cos 2cos 2sin 12symmetry) wave -half to (due .0 that Note −=−= =+=−=−−−=−= ==−−V dc-V dcPower Electronics and 15Harmonics control()()nn b b Note V b n n V b b odcdcn n o31190:if eliminated be will harmonic general,In waveform. the from eliminated is harmonic third or the ,0then ,30 if example For :n Eliminatio Harmonics , adjusting by controlled be also can Harmonics by varying controlled is ,, l fundamenta The :cos 4:is l fundamenta the of amplitude ,particular In cos 4 odd, is n If ,0 even, is n If ===== = ααααπαπPower Electronics and 16Exampledegrees30with case wave square -quasi for (c) and (b)Repeat harmonicszero -non e first thre the using by THDi the c)harmonics zero -non e first thre the using by THDv the b)formula.exact"" the using THDv the a):Calculate series.in 10mH L and 10R R is load The 100V. is ge link volta DC The signals. wave square by fed is inverter phase single bridge -full A ===αPower Electronics and 17Half-bridge inverter (1)V 2Vdc 2Vdc −S1 ON S2 OFFS1 OFF S2 ONt•Also known as the “inverter leg”.•Basic building block for full bridge, three phase and higher order inverters.•G is the “centre point”.•Both capacitors have the same value. Thus the DC link is equally “spilt” into two.•The top and bottom switch has to be“complementary”, i.e. If the top switch is closed (on), the bottom must be off, and vice-versa.Power Electronics and 18Shoot through fault and“Dead-time”•In practical, a dead time as shown below is required to avoid “shoot-through” faults, i.e. short circuit across the DC rail.•Dead time creates “low frequency envelope”. Low frequency harmonics emerged.•This is the main source of distortion for high-qualitysine wave inverter.t dt d"Dead time' = t dS 1signal (gate)S 2signal (gate)+−V dc"Shoot through fault" .I short is very largePower Electronics and 19Single-phase, full-bridge (1)•Full bridge (single phase) is built from two half-bridge leg.•The switching in the second leg is “delayed by 180 degrees” from the first leg.S2dcV V −tttV G R o V V V RG '−=groumd"virtual " is G LEG R LEG R'dcV +-Three-phase inverter•Each leg (Red, Yellow, Blue) is delayed by 120 degrees.• A three-phase inverter with star connected load is shown belowBBPower Electronics and 20Power Electronics and 21132,423,54354,641,56512,661,32Inverter PhaseVoltage (or pole switchingwaveform)V RGIntervalPositive device(s) on Negative device(s) on2V DC V DC -V DC /3-2V DC V -V V DC /2-V DC/2Quasi-square wave operation voltage waveformsV DC /2V DC /2-V DC -V DC /2V YGV BGlIne-to -ine Voltage V RYSix-step Waveform V RNPulse Width Modulation (PWM)•Triangulation method (Natural sampling)–Amplitudes of the triangular wave (carrier) andsine wave (modulating) are compared to obtainPWM waveform. Simple analogue comparatorcan be used.–Basically an analogue method. Its digitalversion, known as REGULAR sampling iswidely used in industry.Power Electronics and 22PWM types •Natural (sinusoidal) sampling (as shown on previous slide)–Problems with analogue circuitry, e.g. Drift,sensitivity etc.•Regular sampling–simplified version of natural sampling thatresults in simple digital implementation •Optimised PWM–PWM waveform are constructed based oncertain performance criteria, e.g. THD.•Harmonic elimination/minimisation PWM –PWM waveforms are constructed to eliminatesome undesirable harmonics from the outputwaveform spectra.–Highly mathematical in nature•Space-vector modulation (SVM)– A simple technique based on volt-second that isnormally used with three-phase inverter motor-drivePower Electronics and 23Power Electronics and 24waveformmodulating the of Frequency veformcarrier wa the of Frequency M )(M Ratio) (Frequency Ratio Modulation veform carrier wa the of Amplitude waveform modulating the of Amplitude M :M Depth)n (Modulatio Index Modulation R R I I ======p pPower Electronics and 25()(1,2,3...)integer an is and signal modulating the of frequency the is where M :at located normally are harmonics The spectra.in the harmonics of (location)incident the determines ratio dulation M ly.respective voltage,(DC)input and voltage output the of l fundamenta are , where M 1, M 0 If component l fundamenta voltage output the s deterrmine Index Modulation R 1I 1I k f f k f o V V V V m m in in=−−−−−−−−−−−−−−−−−−−−−−−−−−−−=<<Power Electronics and 26Regular samplingRegular sampling PWMttvAsymmetric and symmetricregular sampling−Generating of PWM waveform regular samplingPower Electronics and 27Power Electronics and 28Power Electronics and 29Unipolar switching schemeABCarrier waveform (a)(b)(c)(d)1S 3S pwmVBipolar PWM switching: Pulse-width characterizationPower Electronics and 30The k th PulseThekthPWMpulsePower Electronics and 31Power Electronics and 32Determination of switching anglesfor kth PWM pulse (1)2211second,- volt the Equating p s p s A A A A ==Power Electronics and 33PWM Switching angles (2)()()()()()()()()[])sin(2Similarly,)sin(sin 2 cos )2cos(sin sinusoid, by the supplied second - volt The 222half, second for the Similarly 222:as given is pulse PWM the of cycle half first the during second -Volt The 22122221111o k m o s o k o m k o k m m s o k dc k o dc k dc p o k dc k o dc k dc p V A V V d V A V V V A V V V A kok δαδδαδαδαθθδδδδδδδδδδαδα+=−=−−==−=− − =−=− − = −Power Electronics and 34Switching angles (3)()()()()[])sin(1:by given is waveform PWM the of cycle half first for the width pulse the Thus,modulation as known is 2Ratio, Modulation the ,definition By sin(2)sin(2pulse,PWM of cycle half first the for the Hence, ;strategy, modulation the derive To )sin(2)sin(2,sin angle small For 111221121o k I o k dc mI o k o dc mo k o k m o o k dc s p s p o k m o s o k m o s o o oM )(V V M V V V V A A A A V A V A δαδδδαδδδδαδδδδαδδαδδδδ−+= =−=− −=−==−= −= →Power Electronics and 35PWM switching angles (4)[][]k I o k kk o k I o k kk M M αδδδδδδδδαδαδδδαsin 1 Hence,Modulation Symmetric For different. are and i.e ,Modulation Asymmetric for valid is equation above The : angle edge trailing the And )sin(1: waveform PWM of cycle half second the of width pulse method,similar Using :is pulse kth the of angle switching edge leading the Thus k2k 1k 2k 1k 221+= ==+++=−Power Electronics and 36Example•For the PWM shown below, calculate the switching angles pulses no. 2.5.12πPower Electronics and37−+ + −== +++−−−o k k k k k k k k k o k d n V d n V d n V d n v f b dc dc dc T nk δαδαδαδαδαδαθθπθθπθθπθθπ2202211sin 22sin 22sin 22sin )(12:as computed be can pulse PWM (kth) each of content harmonic symmetry, wave half is waveform PWM the AssumingPower Electronics and 38{}[]equation. this of n computatio the shows slide Next :i.e. period, one over pulses for the of sum isthe waveform PWM for the coefficent Fourier ly.The productivesimplified be cannot equation This 2cos cos 2 )2(cos )(cos 2Yeilding,)2(cos )(cos )(cos )(cos )(cos )2(cos :to reduced be can Which 1112121 ==+−−−=+−++−−++−−−−=pk nkn nk o k k k k k dcnk o k k k k k k k k k o k dcnk b b p b n n n n n V b n n n n n n n V b δααδαπδαδαδαδαδαδαπPower Electronics and 39PWM Spectra2.0=I M Fundamental.0.0.0.0.1NORMALISED HARMONIC AMPLITUDES FOR SINUSOIDAL PULSE-WITDH MODULATIONPWM spectra observations•The harmonics appear in “clusters” at multiple of the carrier frequencies .•Main harmonics located at :f = kp(f m);k=1,2,3....where f m is the frequency of the modulation (sine)waveform.•There also exist “side-bands” around the main harmonic frequencies.•Amplitude of the fundamental is proportional to the modulation index.The relation ship is given as:V1= M I V in•The amplitude of the harmonic changes with M I.Its incidence (location on spectra) is not.•When p>10, or so, the harmonics can benormalised. For lower values of p, the side-bandsclusters overlap-normalised results no longer apply.Power Electronics and 40Tabulated Bipolar PWM HarmonicsPower Electronics and 41Three-phase harmonics•For three-phase inverters, there is significant advantage if M R is chosen to be:–Odd: All even harmonic will be eliminatedfrom the pole-switching waveform.–triplens(multiple of three (e.g. 3,9,15,21, 27..):All triplens harmonics will be eliminated fromthe line-to-line output voltage.•By observing the waveform, it can be seen that with odd M R, the line-to-line voltage shape looks more“sinusoidal”.•As can be noted from the spectra, the phase voltage amplitude is 0.8 (normalised). This is because themodulation index is 0.8. The line voltage amplitude is square root three of phase voltage due to thethree-phase relationshipPower Electronics and 42Power Electronics and 43Effect of odd and “triplens”2dc V 2dcV −2dc V 2dcV −2dcV −2dcV −2dc V 2dcV dcV dcV dcV −dc V −ππ2RGV RGV RYV RYV YGV YGV 6.0,8==M p 6.0,9==M p ILLUSTRATION OF BENEFITS OF USING A FREQUENCY RATIO THAT IS A MULTIPLE OF THREE IN A THREE PHASE INVERTERPower Electronics and 44Spectra: effect of “triplens”.0.0.0.0.1.1.1.1.1COMPARISON OF INVERTER PHASE VOLTAGE (A) & INVERTER LINE VOLTAGE (B) HARMONIC (P=21, M=0.8)BComments on PWM schemeas large as possible.•It is desirable to have MR•This will push the harmonic at higher frequencies on the spectrum. Thus filtering requirement isreduced.•Although the voltage THD improvement is not significant, but the current THD will improvegreatly because the load normally has some current filtering effect.has side effects:•However, higher MR–Higher switching frequency: More losses.–Pulse width may be too small to be constructed.“Pulse dropping” may be required.Power Electronics and 45Power Electronics and 46Example Harmonicnumber Amplitude (pole switching waveform)Amplitude (line-to line voltage)11190.3210.8230.3370.1390.2410.25430.25450.2470.1570.05590.1610.15630.2650.15670.1690.05The amplitudes of the pole switching waveform harmonics of the red phase of a three-phase inverter is shown in Table below. The inverter uses a symmetric regular sampling PWM scheme. The carrier frequency is 1050Hz and the modulating frequency is 50Hz. The modulation index is 0.8. Calculate the harmonic amplitudes of the line-to-voltage (i.e. red to blue phase) and complete the table.。