ECEN 5807 Modeling and Control of Power Electronic Systems Instructor: Prof. Bob Erickson Office telephone: (303) 492-7003 Fax: (303) 492-2758 Email: rwe@colorado.edu Course web page http://ece.colorado.edu/~ecen5807 Textbook Erickson and Maksimovic, Fundamentals of Power Electronics, second edition. Springer ScienceBusiness, 2001. ISBN: 0-7923-7270-0 http://ece.colorado.edu/~pwrelect/book/seced.html Online course lectures http://engineeringonline.colorado.edu/tegrityutils/ getcourserss.asp?courseid=ecen5807091 1
Power Electronics Program at CU Boulder ECEN5807 Modeling and Control of PE Systems ECEN5797 Introduction to Power Electronics Fall semesters Alternate Spring semesters (2007) ECEN5817 Resonant and Soft-Switching Techniques in PE Alternate Spring semesters (2008) Professional Certificate in Power Electronics ECEN5517 Power Electronics Lab Spring semesters ECEN5807, Spring 2007
Grading Homework: Midterm exam: Final exam: 50% 17% 33% 2
Required Software Available to local students in ECE teaching labs (power electronics lab, circuits lab) Spice simulator Free version of Pspice or LTspice is sufficient MATLAB/Simulink Student version is sufficient Can be purchased online or through CU Bookstore 3
Topics 1. Averaged switch modeling and simulation CCM, DCM, and other examples. Computer simulation 2. Techniques of design-oriented analysis, with switching converter applications Middlebrook s feedback and extra element theorems Input filter design Writing complicated transfer functions by inspection 3. 4. Current programmed control of PWM converters Introduction to digital control of PWM converters 5. Rectifiers Rectifier harmonics in power systems Low harmonic PWM rectifiers and power factor correctors 4
1. Averaged switch modeling and simulation Section 7.4, Chapter 11, and Appendix B This approach has recently become quite popular Can be applied to a wide variety of converters We will use it to model CCM, DCM, and current programmed converters Also useful for incorporating switching loss into ac model of CCM converters Computer simulation of small-signal transfer functions Objectives of simulation PSPICE examples 5
ECEN5807, Spring 2007
2. Techniques of Design-Oriented Analysis Chapter 10, Appendix C, and supplementary notes on web Null double injection methods for analysis of complex analog systems Converter applications Input filter design Exact analysis of a fifth-order converter system Middlebrook s extra element theorem How to easily determine the effect of an extra element on a circuit transfer function, without starting the analysis all over again The n extra element theorem How to write complicated transfer functions by inspection, in rational form Middlebrook s feedback theorem How to easily construct the loop gain and closed-loop transfer functions of a complex feedback circuit 6
Middlebrook s Extra Element Theorem Appendix C How a given transfer function is modified by addition of an element: v out (s) v in (s) = G(s) Z(s) 1 Z N(s) Z(s) 1 Z D(s) Z(s) Simple methods to find Z N (s) and Z D (s) How to design circuit so that new element doesn t change anything: Z(j ) > Z N (j ) Z(j ) > Z D (j ) Design oriented result: construct Bode plots of above impedances 7
Input filter design H(s) G vd 40 db 30 db G vd G vd Input filter Z o (s) Z i (s) v g Converter v 20 db 10 db 0 db G vd 0 d T(s) 10 db 180 Controller 360 Filter can seriously degrade converter control system behavior Use extra element theorem to derive conditions which ensure that converter dynamics are not affected by input filter 100 Hz Must design input filter having adequate damping 540 1 khz 10 khz f 8
Design of damped input filters that don t degrade converter transfer functions Design criteria derived via Extra Element theorem: Two-section damped input filter design: 30 db 20 db Z D Z N R 2 n 2 L 2 0.65 2.9 H R 1 1.9 n 1 L 1 15.6 H 10 db f o Cascaded sections 1 and 2 Section 1 alone v g L 2 5.8 H C 2 11.7 F L 1 31.2 H C 1 6.9 F 0 db -10 db -20 db 1 khz 10 khz 100 khz Z(j ) > Z N (j ) Z(j ) > Z D (j ) 9
Write the line-to-output transfer function by inspection Example: buck-boost with input filter L f (V L g V)d 1 : D D' : 1 v g R f C f Id Id C R C b Solution: use n extra element theorem 10
3. Current Programmed Control Buck converter i s L i L Chapter 12 v g Q 1 D 1 C v R A very popular method for controlling PWM converters Measure switch current R f i s Clock Transistor turns off when its current i s is equal to the control input i c i s R f i c R f Analog comparator 0 T s S Q R Latch Simpler dynamics, more robust compensator Control signal i c Control input Current-programmed controller m 1 Switch current i s Compensator v v ref Transistor status: 0 dt s T s on off t Conventional output voltage controller Clock turns transistor on Comparator turns transistor off 11
Effect of current programming on transfer functions Buck converter example Comparison of control-to-output transfer functions Averaged switch model used in PSPICE simulations G 40 db 20 db 0 db G vc G vd G V g 12 V 1 2 L 3 i L R L 4 5 1 2 CCM-DCM1 35 H X switch f s = 200 khz L = 35 0.05 C 100 F i LOAD R 10 v 20 db 4 3 40 db 60 db G vc G vd 0 90 d d CPM control current 1 2 X cpm R f = 1 f s = 200 khz L = 35 V a = 0.6 V 180 10 Hz 100 Hz 1 khz 10 khz 100 khz f v c R f i L v(1)v(3) v(3) E i E 1 E 2 12
CoPEC Digitally Controlled Buck Converter Simulink Model Digital PWM A/D converter The buck converter block is the same as in the continuoustime system Note the parts of the system that model the digital controller including: A/D converter Discrete-time compensator, and Digital PWM Discrete-time compensator ECEN5807 5
4. Modern rectifiers, power system harmonics, and low harmonic rectifiers Harmonic amplitude, percent of fundamental 100% 80% 60% 40% 20% 0% 100% 91% 73% 52% THD = 136% Distortion factor = 59% 32% 19% 15% 15% 13% 9% 1 3 5 7 9 11 13 15 17 19 Harmonic number 13
The Ideal Rectifier Modeling the basic functions of ideal converters Dc-dc converter: dc transformer Ac-dc rectifier: loss-free resistor 1 : M(D) i ac Ideal rectifier (LFR) p = v ac 2 / R e i V g R V v ac R e (v control ) v ac input dc output v control 14
Controlling a dc-dc converter to behave as an ideal rectifier dc-dc converter i g i ac 1 : M(d) i v ac v g v C R d i g controller v g Controller varies d as necessary, to cause i g to be proportional to v g 15
Next lecture Begin with circuit averaging and averaged switch modeling Assignment: Read Sections 7.4 and 7.5 16