ECEN5807, Spring 2005ECEN5807Modeling and Control of Power Electronic Systems• Instructor: Dragan Maksimovic• Office: EE1B71, phone: 303-492-4863, fax: 303-492-2758• E-mail: [email protected]• Office hours: Monday, Tuesday, Friday 9:30-10:30am • Course web site:• http://ece.colorado.edu/~ecen5807• Announcements, course materials, assignments, solutions• Textbook:• Erickson and Maksimovic, Fundamentals of Power Electronics, 2ndedition, Kluwer 2001• On-line course lectures (Tegrity system):• Accessible through the CAETE site: http://caeteport.colorado.eduECEN5807, Spring 2005Assignments• Weekly homeworks (11-12 total), 35% of the grade• Midterm exam (open book/notes, take-home), 25% of the grade• Final exam (comprehensive, open book/notes, take-home), 40% of the grade• All assignments, due dates, and solutions will be posted on the course web site• For homework assignments, the due date for off-campus students is (postmarked) one week after the due date published for on-campus students• Homework assignments and the final exam may require use of a Spice simulator (free student version of PSpice is sufficient)ECEN5807, Spring 2005Power Electronics Program at CU BoulderECEN5797Introduction to Power ElectronicsECEN5807Modeling and Control of PE SystemsECEN5817Resonant and Soft-Switching Techniques in PEECEN5017Power Electronics LabFall semestersSpring semestersAlternate Spring semesters (2006)Alternate Spring semesters (2005)Professional Certificate in Power ElectronicsPower Electronics 2: Introduction3Topics1. Averaged switch modeling and simulation (3 weeks)CCM, DCM, and other examples. Computer simulation2. Techniques of design-oriented analysis, with switching converterapplications (4 weeks)Middlebrook’s feedback and extra element theoremsInput filter designWriting complicated transfer functions by inspection3. Current programmed control of PWM converters (3 weeks)4. Modern rectifiers, power system harmonics, and low harmonicrectifiers (3 weeks)Power Electronics 2: Introduction41. Averaged switch modeling and simulationl Section 7.4, Chapter 11, and Appendix Bl This approach has recently become quite popularl Can be applied to a wide variety of convertersWe will use it to model CCM, DCM, and current programmedconvertersAlso useful for incorporating switching loss into ac model of CCMconvertersl Computer simulation of small-signal transfer functionsObjectives of simulationPSPICE examplesAveraged switch modeling+–Switching converter circuitSwitchingnetwork+–+–Large-signal averaged circuit modelAveragedswitchmodeld+–+–DC and small-signal averaged circuit modelD+d^2)/(/)/1(1/1)(ooscocwswsQwsGsG++−=1D2S3K4A5dutyccm-dcm1+-DC, AC and Transient simulationModel implementation for simulationsimulationmodellinearizationAnalytical results:steady-state characteristicsand small-signal dynamicsaveragingPower Electronics 2: IntroductionCircuit / switch averaging+–Time-invariant networkcontaining converter reactive elementsCL+ vC(t) –iL(t)R+v(t)–vg(t)Power inputLoadSwitch networkport 1port 2d(t)Controlinput+v1(t)–+v2(t)–i1(t) i2(t)+–Averaged time-invariant networkcontaining converter reactive elementsCL+ 〈vC(t)〉Ts –〈iL(t)〉TsR+〈v(t)〉Ts–〈vg(t)〉TsPower inputLoadAveragedswitch networkport 1port 2d(t)Controlinput+〈v2(t)〉Ts–〈i1(t)〉Ts〈i2(t)〉Ts+〈v1(t)〉Ts–Separate switch network fromremainder of converter:Average switch waveforms:Power Electronics 2: Introduction7Discontinuous conduction mode:Equivalent circuit and Small-signal ModelingDCCCMDCM+–1 : M(D)VgR+V–+–VgR+V–+–+–1 : M(D)LeCR+–v(s)e(s) d(s)j(s) d(s)AC+–Rvg(s)+–v(s)vg(s)??• Chapter 11Power Electronics 2: Introduction8Averaged switch modeling: CCM vs. DCM+–1 : d(t)i1(t)Tsi2(t)Ts+–v2(t)Tsv1(t)TsAveraged switch modelSwitch networkCCM+v2(t)–+v1(t)–i1(t) i2(t)i2(t)Ts+–v2(t)Tsv1(t)Tsi1(t)TsRe(d1)+–DCM+v2(t)–+v1(t)–i1(t) i2(t)p(t)TsPower Electronics 2: Introduction9The dependent power sourcep(t)+v(t)–i(t)v(t)i(t) = p(t)v(t)i(t)Power Electronics 2: Introduction10Example: DCM buck-boost converterAveraged switch modeli2(t)Tsv2(t)Tsv1(t)Tsi1(t)TsRe(d)+–LCR+–+––+v(t)Tsvg(t)Tsp(t)TsPower Electronics 2: Introduction11Small-signal ac modelingBuck converter example+–+–v1r1j1dg1v2i1g2v1j2dr2i2v2+–LCRDCM buck switch network small-signal ac model+–vgviLPower Electronics 2: Introduction122. Techniques of Design-Oriented AnalysisChapter 10, Appendix C, and supplementary notes on webNull double injection methods for analysis of complex analog systemsl Converter applicationsInput filter designExact analysis of a fifth-order converter systeml Middlebrook’s extra element theoremHow to easily determine the effect of an extra element on a circuit transferfunction, without starting the analysis all over againl The n extra element theoremHow to write complicated transfer functions by inspection, in rational forml Middlebrook’s feedback theoremHow to easily construct the loop gain and closed-loop transfer functions of acomplex feedback circuitPower Electronics 2: Introduction13Input filter design• Filter can seriously degrade converter control system behavior• Use extra element theorem to derive conditions which ensure that converterdynamics are not affected by input filter• Must design input filter having adequate damping• Input EMI filter is required to meet regulationsconcerning electromagnetic emissions• A well-knownand classicproblem withinthe powerelectronics field+–InputfilterConverterT(s)ControllervgZo(s) Zi(s)H(s)dvPower Electronics 2: Introduction14Effect of input filter on Gvd(s)f|| Gvd ||∠ Gvd0˚– 360˚– 540˚0 dB– 10 dB20 dB30 dB100 Hz40 dB1 kHz 10 kHz– 180˚10 dB|| Gvd ||∠ GvdBuck converterexampleDashed lines: noinput filter. 2 poles.Solid lines: with LCinput filter. 4 polesand 2 RHP zeroes.Power Electronics 2, Spring 2003Use Extra-Element Theorem(Appendix C)Simple methods to find ZNand ZDHow to design the input filter so that it does not change anything:DoNoZvdvdZZZZGsGo++==11)(0 ,DoNoZZZZ<<<<Power Electronics 2: Introduction16Design of damped input filters that donÕtdegrade converter transfer functions-20 dBΩ-10 dBΩ0 dBΩ10 dBΩ20 dBΩ1 kHz 10 kHz 100 kHzSection 1aloneCascadedsections 1 and 230 dBΩ|| ZN |||| ZD ||fo+–vgL1n1L1R1C1L2n2L2R2C26.9 µF31.2 µH15.6 µH1.9 Ω0.65 Ω 2.9 µH5.8 µH11.7 µFDesign criteria derived via ExtraElement