A Pedagogical Approach for Modeling and Simulation of Switching Mode DC-DC Converters for Power Electronics Course

Transcription

1 TEKOMNIKA Indonesian Journal of Electrical Enineerin Vol., No.6, October 22, pp. 39~ A Pedaoical Approach for Modelin and Simulation of Switchin Mode DC-DC Converters for Power Electronics Course Yan Han Department of Power Electronics, School of Mechatronics Enineerin, University of Electronic Science and Technoloy of China No.26 XiYuan Road, Chendu, 673, P. R. China hanyan_facts@hotmail.com Abstract The power electronics course is a rather challenin subject for instructors and underraduate students pursuin Bachelor s Deree in Electrical Enineerin. To enhance teachin effectiveness and motivate self-learnin capabilities of the students, this paper presents a pedaoical approach for mathematical modelin and simulation of switchin mode DC-DC converters. The Buck and Boost converters are analyzed as benchmark systems to study the power converter modelin methodoloies. And a comparative analysis usin diital simulation from Matlab/Simulink and ATP/EMTP is presented. A summary of student survey is also presented, which shows a hih level of satisfaction. The presented pedaoical approach would be useful for classroom teachin for the power electronics course and similar enineerin courses. Keywords: power electronics, dc-dc converter, pedaoical approach, ATP/EMTP Copyriht 22 Universitas Ahmad Dahlan. All rihts reserved. V The input dc voltae of the dc-dc converter V(t) The output voltae of the dc-dc converter i A The input current of the dc-dc converter The series inductor R The load resistance of the converter D The duty ratio of the PWM control sinal Abbreviations Q The power electronic switch, e.. IGBT v B The diode voltae i B The diode current i The current across the inductor C The load-side capacitor T s The period of the PWM control sinal. Introduction The power converters have been widely applied for enery conversion purposes, in particular, the switchin mode power converters are increasinly used in household appliances, personal computers and when electrical enery is to be converted to mechanical enery. Power electronics tends to be a challenin discipline for students since it requires an understandin of a heteroeneous set of topics: analo electronics, circuit analysis, control theory, electromanetic field, and so on [-6, ]. The existin problems for power electronics course can be summarized as: low success rate and class attendance rate, and poor feedback for the teachin process. Hence, important modifications for pedaoical methods can be implemented to increase student motivation, improve classroom interactions and optimize the available teachin resources [7-9]. In the previous literatures, the interative underraduate photonics curriculum was developed in [], which utilizes three learnin methods: case studies, team learnin and project based learnin (PB). The presented approach was desined as introduction to optics and photonics for electrical enineerin students. In [2], a proposed new model for current-mode control retains the strenths of existin models such as ease of use and the ability to capture subharmonic oscillations, while improvin on weaknesses like dc ain accuracy. In [3], a pedaoical approach was proposed to teachin the subject of the analysis of feedback amplifiers for electrical enineerin students at the underraduate level. Special attention was Received June 24, 22; Revised September 2, 22; Accepted September 27, 22

2 32 e-issn: X iven to derivation of the input and output impedances. In order to make the procedure clear and suitable for classroom presentation an alternative proof of the Blackman's Impedance Relation was derived to stand in accord with feedback amplifier analysis methodoloy presented earlier. In [4], the problem-based learnin (PB) was presented as a motivatin, problemcentered teachin method. It was reported that, in addition to the subject matter, the PB course students learn social skills throuh interaction in small roups, how to identify and define a problem, and how to look for and filter out relevant information. In [5], the problem-based learnin (PB) was introduced and practiced in Analo Electronics. While the mode of external evaluation remains the same-that of the university holdin end-of-semester theory and practical examinations-a unique stratey has been worked out which interates PB and the traditional approach of ecture, Tutorial, and Practical (/T/P) classes. Based on the teachin experiences reported in the previous literatures, a pedaoical approach for modelin and simulation of the switchin mode dc-dc converters for power electronics course is presented. The buck and boost converters are analyzed as benchmark systems to study the converter modelin methodoloies. And a comparative analysis of the benchmark systems usin diital simulation from Matlab/Simulink and ATP/EMTP is presented. The presented pedaoical approach would be useful for classroom teachin for the power electronics course and similar enineerin courses. 2. Research Method 2. Mathematical Modelin for Buck Converters Fiure shows the circuit diaram of the buck converter. When the switch Q is turned on, the voltae across the inductor is [, 2, 4]: v = V v( t) () Fiure. Circuit Diaram of the Buck Converter. Fiure 2. Theoretical waveform of load voltae and inductor current of the Buck converter The small ripple approximation is denoted by: v V V (2) Moreover, the inductor current is derived via: di ( ) ( t) v t = (3) dt Solve for the slope, we et: di( t) v( t) V V = (4) dt which indicates that the inductor current chanes with an essentially constant slope. TEKOMNIKA IJEE Vol., No. 6, October 22 :

3 TEKOMNIKA IJEE e-issn: X 32 When the switch Q is turned off, the voltae across the inductor is: v = v( t) (5) The small ripple approximation: v = V (6) The inductor current can be derived via: di ( ) ( t) v t = (7) dt Solve for the slope, we et: di( t) V =. (8) dt From the above analysis, the theoretical waveform of the load voltae and inductor current of buck converter is derived, as shown in Fiure 2. Therefore, the chane in the inductor current can be derived as: V V 2 i = DTs (9) Hence the inductor parameter is derived as: V V = DT 2 i s () Fiure 3. Dynamic response of the inductor current Fiure 3 shows the transient response of the inductor current. The trianular waveform can be observed due to dynamic charin and discharin process of the inductor. When the converter operates in equilibrium, we et: i (( n + ) T ) = i ( nt ) () s s 2.2. Mathematical Modelin for Boost Converters Fiure 4 shows the circuit diaram of the boost converter. When the switch Q is turned on, the voltae across the inductor is [, 4, 5]: v = V, i = v / R (2) C The small ripple approximation can be derived as: v = V, i = V / R (3) C When the switch Q is turned off, the voltae across the inductor is: v = V v, i = i v / R (4) C A Pedaoical Approach for Modelin and Simulation of Switchin Mode DC- (Yan Han)

4 322 e-issn: X Small ripple approximation of Eq.(4) is derive as: v = V V, i = I V / R (5) C Fiure 4. Circuit diaram of the Boost Converter Fiure 5. Theoretical waveform of load voltae and inductor current of the Boost converter From Eq.(2)-Eq.(5), the theoretical waveform of load voltae and inductor current of boost converter is derived, as shown in Fiure 5. Hence, the net volt-seconds applied to inductor over one switchin period: T s v ( t ) dt = V DT s + ( V V ) D ' T s (6) Equate to zero and collect terms, we et: V = V / D' (7) The voltae conversion ratio is therefore: M ( D) = V / V = / D ' = / ( D) (8) Capacitor chare balance equation: T s i C ( t ) dt = ( V / R ) DT s + ( I V / R ) D ' T s (9) Collect terms and equate to zero, the dc component of inductor current is derived as: 2 I = V / ( D ' R) (2) The inductor current slope when Q is turned on: di( t) v( t) V = = (2) dt Thus the chane in inductor current is denoted as: V 2 i( t) = DTs (22) Solve for peak ripple, we et: V i( t) = DTs (23) 2 Fiure 6 shows the waveform of load voltae and inductor current of the Buck converter. Notably, the parameter can be chosen such that desired ripple manitude is obtained. Similarly, the voltae ripple across the capacitor can be calculated as: TEKOMNIKA IJEE Vol., No. 6, October 22 :

5 TEKOMNIKA IJEE e-issn: X 323 V v = DTs (24) 2RC Therefore, the parameter C can be chosen such that the desired voltae ripple manitude is obtained. In practice, the capacitor equivalent series resistance (ESR) leads to increased voltae ripple. Fiure 6. Theoretical waveform of load voltae and inductor current of the Buck converter Fiure 7. A eneralized control block of the dc-dc converters Fiure 7 shows the control block diaram of the switchin mode dc-dc converters. The objective of the controller is to maintain the output voltae v(t) constant in spite of the disturbance in source voltae v (t) and load current i load (t). The typical variation in v (t) is Hz or 2Hz ripple, produced by the rectifier circuit. On the other hand, a step-chane in load current may occur for the practical circuit. Normally, the circuit elements are constructed to some specified tolerance. Hence we cannot expect to set the duty cycle to a sinle value and obtain a constant output voltae under all conditions. Thus, a feedback control law must be applied to adjust the duty cycle in real-time to et the specified output voltae with a hih accuracy, reard-less of disturbances or components tolerance [3, 4, 6]. As shown in Fiure 7, a feedback control is applied and the compensator is adopted to derive the modulation sinal, which is utilized to synthesize the time-varyin duty cycle. The mathematical model of the dc-dc converters in the frequency domain can be referred to [2-4]. Therefore, the typical PI controller can be devised usin the siso-tool in the Matlab/Simulink environment. The parameters are adjusted to meet the stability constraint and the dynamic performance specifications [5, 6]. 3. Results and Analysis In this section, the simulation results obtained from Matlab/Simulink and ATP-EMTP are presented. Besides, the students feedback on the teachin approach is also reported. 3.. Simulation Results Obtained from Matlab/Simulink Fiures 8 and 9 show simulation results of Buck and Boost converter obtained from Matlab/Simulink. In Fiure 8, the parameters of Buck converter are: V =2V, =5mH, R= Ohm, load-side back electromanetic force (EMF) V EM =8V, T p =ms, Duty cycle=.6. It shows that the source and diode current cover the risin and fallin portion of the load current. And trianular waveforms are obtained in the load current and voltae. In Fiure 9, the parameters of the Boost converter are: V =5V, =2mH, R=.2Ohm, C dc =2uF, R dc =Ohm, T p =ms, Duty cycle=.6. It shows that the switch current and load current cover the risin and fallin A Pedaoical Approach for Modelin and Simulation of Switchin Mode DC- (Yan Han)

6 324 e-issn: X portion of the source current. And trianular waveforms are obtained in the source current and load voltae. Fiure 8. Simulation results of the Buck converter obtained from Matlab/Simulink with a constant duty cycle (d=.6) Fiure 9. Simulation results of the Boost converter obtained from Matlab/Simulink with a constant duty cycle (d=.6) 3.2. Simulation Results Obtained from ATP-EMTP To further illustrate the principle of switchin mode dc-dc converters, the simulation usin the Electromanetic Transient Proram - Alternative Transient Proram (EMTP-APF) is also performed [9]. The Transient Analysis of Control System (TACS) and the MODES lanuae in the EMTP software are adopted to implement the control alorithm. Fiures and show simulation results of Buck and Boost converter obtained from ATP/EMTP. The circuit parameters are same as those adopted in Matlab. It shows that the simulation results obtained from ATP/EMTP are consistent with those obtained from Matlab/Simulink [ms] 3 (file Buck_CCM.pl4; x-var t) t: IS t: IOAD t: IDIODE t: V t: VOAD factors: offsets: Fiure. Simulation results of the Buck converter obtained from ATP/EMTP with a constant duty cycle (d=.6) [ms] 2 (file Boost_CCM_Control_RC.pl4; x-var t) t: IS t: IOAD t: ISW t: VOAD factors: offsets: Fiure. Simulation results of the Boost converter obtained from Matlab/Simulink with a constant duty cycle (d=.6) Fiure 2 shows the transient response of Buck converter usin constant current control scheme, and the parameters are the same as those in Fiure. The reference is set to be 3A initially and a step chane of reference to 35A is applied at t=ms. It shows that the TEKOMNIKA IJEE Vol., No. 6, October 22 :

7 TEKOMNIKA IJEE e-issn: X 325 load current tracks the reference quite well in the steady state and durin transient process. Fiure3 shows the steady-state waveforms of the Buck converter with RC load for C dc =uf, R=.5 Ohm. The capacitor current is multiplied by 5 times to ive a clearer illustration. It can be observed that the charin and discharin process of the capacitor corresponds to the risin and fallin edes of the load current, which is exactly synchronized with turn-on process of Q in Fiure. The comparative analysis of the benchmark systems is helpful for motivatin underraduate students to enhance self-learnin capabilities and improve overall performance [ms] 6 (file Buck_CCM_Control.pl4; x-var t) t: IREF t: IOAD Fiure 2. Transient response of the constant current control mode for the Buck Converter obtained from ATP/EMTP [ms] 8. (file Buck_CCM_Control_RC.pl4; x-var t) t: IOAD t: IR t: IC factors: offsets: 5 Fiure 3. Steady state waveforms of load current, resistance and capacitor currents of the Buck converter with RC load. Fiure 4. Results of student survey. The radin scale spans from -poor to 6-excellent Summary of the Classroom Survey In order to evaluate the effectiveness of pedaoical approach for the power electronics course, a survey was conducted at the end of the concludin week of the semester. Some of the survey questions were listed as followin: () Is the course interestin? (2) Is the course material clear? (3) Have you acquired sufficient insint into the subject? (4) Can you build your own power electronic circuit usin Matlab/Simulink? (5) Can you build your own power electronic circuit usin ATP/EMTP? (6) Do you understand the similarities and differences between the two softwares? (7) How about the difficulty of this course? (8) What about your level of satisfaction obout this course? A Pedaoical Approach for Modelin and Simulation of Switchin Mode DC- (Yan Han)

8 326 e-issn: X The results of a recent student survey are shown in Fiure 5, which shows a very hih level of satisfaction. The survey indicates that the pedaoical approach is indeed helpful to ensure effective classroom teachin. 4. Conclusion The Bachelor s deree in Electrical enineerin and Its Automation at University of Electronic Science and Technoloy requires a minimum of four years of study. Power Electronics is a mandatory course for these under-raduate students, tauht durin the third year. The factors led to the poor understandin of the subject include the inherent complexity with inadequate knowlede of the students due to curriculum time constraints. This paper reports the pedaoical methodoloies for modellin and simulation of switchin mode dc-dc converters, the effectiveness of the presented approach is confirmed by the students survey, which show a hih level of satisfaction. The reported approach can be useful for underraduate classroom teachin and can also be applied to similar enineerin courses. Acknowledement This project is supported by the Fundamental Research Funds for the Central Universities of China (ZYGX2J93). References [] Dewan S. B., Strauhen A., Power Semiconductor Circuits, John Wiley and Sons, New York, 975. [2] Hart D.W., Introduction to Power Electronics, Prentice-Hall, 994. [3] Mohan N., Power Electronics, 3rd Edition, Wiley, 23. [4] Robert W. E., Draan M., Fundamentals of Power Electronics, Second Edition, Spriner, ISBN [5] Sen P.C., Power Electronics, McGraw-Hill, 5th reprint, 992. [6] Shepherd W., et al., Power Electronics and motor control, Cambride University Press, 2nd Edition 995. [7] Kantonidou M. M., Enineerin Education and Enineerin Practice: A Student Teacher Perspective // Electronics and Electrical Enineerin. 2. No. 6. P [8] Badanavicius N., Andriukaitis D., et al., Possibilities of Electronics Enineerin Studies in University and Collee // Electronics and Electrical Enineerin. 2. No. 7. P [9] Prikler., Høidalen H. K., ATPDraw Users Manual, SINTEF Enery Research, 22 [] P. D. Tan and R. D. Middlebrook, A unified model for current-prorammed converters, IEEE Trans. Power Electron., vol., no. 4, pp , Jul [] R. A Cheville, A. McGovern, and K. S Bull, The liht applications in science and enineerin research collaborative underraduate laboratory for teachin (ASER CUT)-relevant experiential learnin in photonics, IEEE Trans. Educ., vol. 48, no. 2, pp , May 25. [2] R. Holloway and G. Eirea, Model current-mode control with ease and accuracy, Power Electron. Technol., pp , Nov. 28. [3] A. Abramovitz, A practical approach for analysis of input and output impedances of feedback amplifiers, IEEE Trans. Educ., vol. 52, no., pp , Feb. 29. [4]. R. J. Costa, M. Honkala, and A. ehtovuori, Applyin the problembased learnin approach to teach elementary circuit analysis, IEEE Trans. Educ., vol. 5, no., pp. 4 48, Feb. 27. [5] A. Mantri, S. Dutt, J. P. Gupta, and M. Chitkara, Desin and evaluation of a PB-based course in analo electronics, IEEE Trans. Educ., vol. 5, no. 4, pp , Nov. 28. TEKOMNIKA IJEE Vol., No. 6, October 22 :