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TEACHING AND DEMONSTRATION OF POWER ELECTRONIC CIRCUIT ANALYSIS O.W. Andersen Norwegian Institute of Technology, Trondheim, Norway Abstract. A demo version of simulation program PECAN (Power Electronic Circuit Analysis) can be downloaded from Internet address http://www.elkraft.unit.no/~andersen/ and used freely for educational and other purposes. A student can enter component values simply by answering questions, while a circuit is displayed on the screen. He doesn’t have to learn how to make up cryptic input files. Keywords. Teaching, education, demonstration, analysis, power electronic circuits. INTRODUCTION SAMPLE CALCULATION An early version of PECAN was written in 1977 for mainframe computers, and it has since been improved and adapted for use on personal computers. The demo version is limited to 2500 time steps and 40 variables (node potentials and branch currents). This is considered to be sufficient for most educational and demonstration purposes, but the full version can handle 30000 time steps and 500 variables. It requires a 386/486 with math coprocessor or Pentium computer, with at least 4 Mb RAM. 46 input files are included in the demo. Most of them are for different power electronic circuits, but there are also some for related problems, such as regulation loops and electrical machine transients. When a circuit is examined by a student, he enters a command (under MS-DOS), such as: EXAMINE DIORECT2 where DIORECT2 is a three phase diode rectifier with current source load. A circuit diagram with explanations appears on the screen, as shown in Fig. 1. The circuit diagram is marked with node numbers, branch numbers and component numbers, with prefixes N, B and C. Fig. 1. Three phase diode rectifier with current source load. To proceed, the student simply strikes ENTER. After a few seconds, the calculations are completed. Curves are displayed in different colors for voltages between nodes and/or across components, and for branch currents, as shown in figures 2 and 3. Then, in this case, a Fourier analysis is performed automatically for a line current, and a harmonic spectrum is displayed, as shown in Fig. 4. Voltage between nodes 2 and 3 Voltage between nodes 5 and 6 For the same problem, a student can also change the component values in a very simple manner and see what it does to the voltages and currents, with the command: EXERCISE DIORECT2 In this case, he can change applied voltages, frequency, inductances and load current. The circuit is displayed on the screen, and the text above it (Fig. 1) is replaced by two lines, such as: Strike ENTER to keep old value 1 Inductances, mH? The cursor appears after the question mark, and the student can either keep the old value or change it. It is suggested to the student what he might do and what to look for. It can be observed, for example, that triple harmonic line currents are always absent in this circuit. It can also be observed how the commutation interval is affected by the load current and the series inductances. Fig. 2. Voltages. Current in branch 7 Current in branch 8 Current in branch 9 Fig. 3. Currents. Fig. 4. Harmonic spectrum. STUDENT EXERCISE LIST OF EXERCISES A total of 26 exercises of the type just described are included in the demo. They are: Basic rectifier with inductive load. Basic rectifier. Load with internal dc voltage. Basic circuit with current commutation. Single phase diode bridge rectifier with voltage source load. Three phase diode rectifier with current source load. Three phase diode rectifier with voltage source load. Basic thyristor converter, rectifier mode. Single phase thyristor controlled inductor. Single phase thyristor bridge rectifier with current source load. Three winding transformer with triac controlled inductors. Step down converter, continuous current mode. Step down converter, discontinuous current mode. Step up converter, continuous current mode. Step up converter, discontinuous current mode. Buck boost converter, step down, continuous conduction mode. Buck boost converter, step up, continuous conduction mode. Buck boost converter, step down, discontinuous conduction mode. Buck boost converter, step up, discontinuous conduction mode. Pulse width modulation. Small 0.75 kW dc motor startup. Large 75 kW dc motor startup. Armature short circuit of differentially compounded dc generator. Three stage impulse generator wavefront. Three stage impulse generator wavetail. Dc motor position control without current control loop. Dc motor speed control with internal current control loop. also possible to use shareware PRINTGL, which can be downloaded from http://ourworld.compuserve.com/homepages/ravitz/ With this, plotting can be done from an HP-GL file on practically any printer and plotter on the market. OTHER INPUT FILES Another 20 input files are included for demonstration purposes only. They are: Single phase voltage doubler rectifier. Three phase diode rectifier with dc filter. Basic thyristor converter, inverter mode. Three phase thyristor bridge rectifier with current source load. Cuk converter. Flyback converter. Single phase full bridge square wave mode inverter. Single phase full bridge inverter, voltage cancellation switching. Three phase square wave mode inverter with voltage source load. Three phase square wave mode inverter with resistive load. Three phase square wave mode inverter with inductive load. PWM with bipolar voltage switching. PWM with unipolar voltage switching. Single phase full bridge PWM inverter at open circuit. Single phase full bridge PWM inverter with voltage source load. Three phase PWM inverter with voltage source load. Programmed harmonic elimination of fifth and seventh harmonics. Basic resonant converter operating below resonant frequency. Basic resonant converter operating above resonant frequency. Transient temperatures on cables. In addition to output plotted on the screen and on paper, a numerical output file is created. It includes, if requested, calculated values at each time step, rms values, average values, etc. The file can be studied on the screen and printed. A Fourier analysis results in another numerical output file, containing values of harmonics, crest factors, form factors and harmonic distortion. METHOD OF SOLUTION A linear equation is set up for each node and each branch at each point in time, starting from t=0. The lengths of the time steps vary between limits specified in the input. For a node, the sum of the currents into the node is set equal to zero. The equation is used to find one of the currents. For a branch, the equation may involve old and new currents (for previous and present points in time) and old and new node potentials at each end. The equation is used to find one of the new potentials or the new current. An inductor has a voltage across it equal to the inductance times the difference between new and old currents, divided by the length of the time step. Mutual inductances may contribute to the voltage. This way, the number of linear equations equals the number of unknown node potentials and branch currents, and can be solved at each point in time by Gaussian elimination. PLOTTING AND PRINTING A simple command will result in the creation of an HPGL graphics language file containing plotted output or a harmonic spectrum. This can be incorporated into a Microsoft Word, WordPerfect or other word processor document and subsequently plotted on a printer. It is REFERENCE O.W. Andersen, Time Domain Circuit Analysis, IEEE Computer Applications in Power, pp. 34-38, April 1992.