PSPICE Simulation of Three-phase Inverters by Means of Swiching Functions (Salazar; Joós)

35IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 9, NO. 1 JANUARY 1994 PSPICE Simulation of Three-phase Inverters by Means of Switching Functions L. Salazar, Member, IEEE, and G. J o ~ s , Member, IEEE Abstract-Static power converters can be analyzed by means of widely available circuit simulation software packages such as PSPICE. However, they are usually modeled as a set of real switches, which results in long execution times and possible convergence problems in the case of complex circuits. This paper proposes macromodels to simulate three-phase power converters on such packages. The proposed macromodels are based on converter switching functions rather than actual circuit configuration, and they are suited for steady state and large signal transient analysis at system level. In this approach, voltage source inverters (VSI), current source inverters (CSI), and controlled rectifiers (CR) are simulated as multiport networks avoiding the physical nonlinear micromodels of the power switches. Computer memory and the run-times required for the simulation are thereby minimized. Complete examples of VSI, CSI and CR, with different PWM techniques, are given with specific reference to the PSPICE software to illustrate the effectiveness of the proposed models. I. INTRODUCTION sources are two or three-level switching functions defined by the PWM technique and the converter mode of operation (i.e., inverter or rectifier). The main objective of this paper is to illustrate how the functional definition of a switching converter can be used to model any three-phase voltage source inverter (VSI), current source inverter (CSI) or PWM controlled rectifier (CR) with its respective control circuit on PSPICE, allowing higher levels of analysis and simulation in a low-cost computer environment. Furthermore, a new classification of the CR is introduced. This family includes two members: the voltage-controlled rectifier (VCR), also known as a PWM ac/dc rectifier, and the current-controlled rectifier (CCR), also described as a PWM boost rectifier [6]. Detailed examples of VSI, CSI, VCR, and CCR operation with different PWM schemes are given to illustrate the effectiveness of the proposed models and simulation methods. T HE SPICE circuit simulation program has become an 11. LEVELSOF SIMULATION IN POWER ELECTRONICS industry standard. The major advantage of using SPICE in A . Simulation at the Switch and Converter Circuit Levels power electronics is that, with the same software, a particular PSPICE micromodels are in common use for simulation circuit can be designed and analyzed at different system and subsystem levels, i.e., at the levels of the power switch (de- analysis at the level of the switch circuit, i.e., power switch, vice), the converter circuit, and converter systems, including driver or snubber circuit, allowing for example to study feedback control. However, for higher levels of simulation, switching losses. Models to simulate a variety of semiconsimplified models for the switch and the converter must be ductor devices on PSPICE have been proposed [7] and they implemented, in order to minimize convergence problems and can be adapted, through parameter adjustments, to power applications. These are physical intrinsic micromodels of the reduce the run times. Recent research work in switching power converters has appropriate semiconductor technology, usually available from demonstrated that the transfer or switching function concept a library of parts provided by various companies. However, [ 1, 2, 31 is a powerful tool in understanding and optimizing these micromodels are not practical at the converter circuit the performance of converters such as the voltage source and system levels of simulation for the following reasons: inverter (VSI), current source inverter (CSI) and controlled Diodes, bipolar transistors, and switches in general are PWM rectifier (CR). Furthermore, general functional models described as non-linear controlled source by means of for three-phase PWM inverter/rectifier converters have also functions that contain exponential terms, resulting in been proposed [3,4]. A functional model produces a dramatic slow execution times, large amounts of generated data simplification of the total converter circuit. This approach has (small time steps are required in the numerical integrabeen shown to be a very useful technique for harmonic analysis tion process), and occasional convergence problems. and system simulation of different converter topologies on Accurate modeling of complex converter circuits may personal computers (PC) with limited memory and speed [4, lead to a very large number of devices and components 5, 81. Moreover, it allows a converter to be modeled as a and the simulation becomes very time consuming. The multiport circuit that contains only voltage-controlled voltage same applies when increasing the switching frequency sources, and current-controlled current sources connected at and the simulation time interval. The probability of the input and output ports. The signals controlling these encountering convergence problems also increases with the number of comDonents. Manuscript received January 2, 1991; revised September 29, 1993. The default parameters a i d the device models in the PSPICE The authors are with Department of Electrical and Computer Engineering, program can be adjusted to reduce the above difficulties. RecConcordia University, Montreal, P.Q., H3G 1M8 Canada. IEEE Log Number 9214829. ommended values and guidelines to simulate power converter 0885-8993/94$04.00 0 1994 IEEE Two switch macromodel with voltage controlled source for a three-phase converter leg. The Mosfet switch execute faster than the bipolar switch and presents less convergence problems. Simulation at the system level is concerned with the design verification and performance analysis of the converter as a module. 9. JANUARY 1994 36 TABLE I TYPICAL PARAMETERS A N D GUIDELINES TO SIMULATE POWERCONVERTER CIRCUITS ON PSPICE (10 kW 100 kW) . The simulation results are shown in Fig.SCH). further simplifications of the converter model are required to reduce the design cycle. constitute the main objectives of the analysis. Instead. simulation of multiconverter systems. Simulation at the System Level The examples presented in the previous section show that simplified switch models in PSPICE can be used to fully simulate three-phase rectifier-inverter structures with reasonable run times on a low cost computer.OOI CBS=O. and its interaction with the respective input source. Use small resistors in series with voltage sources. Use of controlled source to replace the non-linear active device and integrated analog circuit.IEEE TRANSACTIONS ON POWER ELECTRONICS. The transfer function of this multiport network can be easily simulated on PSPICE by using controlled sources in the Analog Behavioral Modeling option (ABM). the threephase inverter driven by (1 KHz triangular waveform carrier) shown in Fig. ac. Therefore. a simple model for a two-switch converter with controlled voltage sources and diodes. CONVERTER MODELS A . 3. 5. 9. 2 has been simulated using a sinusoidal PWM switching pattern with PSPICE running on a 386. Transfer Functions Analytical models for the VSI. has been used successfully by the authors [ 101 for simulation at the converter circuit level. Fig.OOl CJ O=O. 8. simplified device models using controlled sources have been proposed to speed up the simulation [8. Floating nodes are eliminated by using a large resistor to ground (node 0). CVR and CCR are derived by using the transfer function concept for a generalized converter [ 3 ] .01 to 0.05 values ~ between o 1 @ A~ to 1 mA values between 1 p V to 1 mV : ITL5=O Notes: 1. Large resistors must be used in parallel with current sources and inductors. results in large computation times.001 UF) NMOS (VTO=3 KP=20 CBD=O. + SPICE VSll SCH OFTIONS RELTOL=On5 ABSTOL=IGUAms=n LIB C WELUB CR TRAN IMVS zom n m SOUP mc $"'+. 111. R-C circuits are useful to minimize ringing oscillation and convergence problems. DM 3 I XJDP IDP ZSWDV X3DN 1DN 5' 1 I 15 Fig. wherein the time solution of the currents and voltages.I CJE=0. subcircuit 2SWDV. Voltage and current controlled switches run slower than mosfet switches and present convergence problems. VOL. shown in Fig. 7. For example. and control.The converter as a non-linear multiport network has three ports: dc. 2. NO. Table I1 presents a comparison of the simulation run-times using this model and the PSPICE transistor micromodels. 4. Accurate models for the converter switch are not required at this level of simulation.OPTIONS DIODE BIPOLAR MOSFET RELTOL: ~ ~ D (IS=O. The models for simulation at the system level using this approach are presented in the next section. 2. A three-phase VSI system with a sinusoidal PWM pattem simulated in PSPICE by using the switch macromodel shown in Fig.OOl) values between 0. 3 (run time was 12. 1. Moreover. in the input and output terminal.OOl) NPN (BF=1000 RB=O. l). circuits on PSPICE [7. 81 are given in Table I.7 minutes with a step size = 10 ps).MODEL .OOI UF RS=O. load or other converter if any. 1. The switching signal (PULSE) should he defined with a rise and fall time different from zero. 1 (schematic file VSI I .20 MHz P C . CSI. Moreover. in the complete system. B . The dc and ac ports can . to evaluate the simulation run-times with a larger number of such switches (Fig. However. each converter can be simulated as a multiport network. even with the use of the simplified switch model. 6. I . 101. 5 os I I IomS 5m9 I5ms 2oms I I I os I loms 5ms Isms 2oms b) Fig.5 Vfc) 0 0 IV *) v v v v v v v v v vv. and i. &?(t) (1) (2) where G o ( t ) = [ v a ( t )u b ( t ) vc(t)lT is a vector that contains the instantaneous three-phase output voltages. Current Source Inverter (CSI) Model The CSI transfer functions can be obtained from (1) and (2) by applying the duality principle. 3. B. . the output becomes . ( k ) are the instantaneous input voltage and current respectively (dc quantities). A two-level SF ( s 2 ) is used to generate the ac output leg voltage in a VSI. Simulation results for the VSI system shown in Fig. cycle = 50% (*) A dead time of 2 c i s is required in vectorial form: Output (ac) : ij. ( t ) = 60(t)T. (a) Sinusoidal PWM generation. The transfer function is the instantaneous relation between the dc input/output and the ac input/output variables. (s%. r .89 d) -400 VkY) os 5na IOma l5mS zoms Fig.MODEL Operating Conditions: = ohm. these two types of SF can be considered dual.37 SALAZAR AND JO6S: PSPlCE SIMULATION OF THREE-PHASE INVERTERS 1. Voltage Controlled Rectifrer (VCR) Model The transfer functions are derived from (3) and (4) by applying the inversion principle. or the dc output voltage in a VCR. the output voltage is generated by reflecting simultaneously the instantaneous input voltage to the output. i 3 ( t ) v . Similarly. By using the concept of switching functions. v.( .oo 1. E .TIME 2 p s 100 p s 0 2 p s values given in Table I .5 0. as shown in the next sections.01 ITL5 = 0 . The control port consists only of inputs. Output (ac) : Input (dc) : .(t) = [ i a ( t )ib(t) ic(t)lT is a vector that contains the three instantaneous output line currents. Thus. SMYtching Functions The signals applied to the control input port are two-level or three-level switching functions (SFs). both defined by the same switching function applied to the control port. = v Frequency = 2o k ~ z D~~~ .ter (VU) Model In a VSI. & ( t ) Input (dc) : i i ( t ) = & ( t ) T.OPTIONS RELTOL = 0. 4. the functional representation of various types of converters is derived.39 1. Hence. or the dc output current in a CCR. 2.. Also.(t) = w i ( t ) . Examples for both are shown in Fig.02 sec 17. (b) two-level switching function I .24 sec SPEED FACTOR 1. (c) DC-link capacitor voltage ( I . (b) three-level SF (5'3). . Typical switching function (SF). and with the assumptions of no losses and no parasitic reactive elements in the converter. and the instantaneous output line current to the input during intervals defined by the switching function. and & ( t ) = [ s a ( t )sb(t) sc(t)lT is a vector that contains the two-level switching functions for each leg of the converter. Lbltage Source 1inw.(t) and i . ( t ) . 4.(r ) ) .(t) = i .v v v v v VI -0.( / .+3(t) (3) (4) where i 3 ( t ) is a vector that contains the three-level switching function for each line of the converter. TABLE II TIMEOF A HALFBRIDGE DC-DC CONVERTER USINGDIFFERENT SWITCHES PSPICE SIMULATION SWITCH Bipolar (*) Mosfet (8) Controlled Source 0 TIME 25.90 sec 13. These two processes can be formulated in analytical form by the following equations.I ( C i ) ) . (a) two-level SF (S2).1 1 ) ) and VSI input current ( J ( L / / ). Thus. a three-level SF ( s 3 ) is used to generate the ac output line current in a CSI. L = 200 L l ~ vin . A general converter has a current and a voltage transfer function. C. D .(d) Line-to-line output voltage ( I . be inputs or outputs depending on the mode of operation. y ) ) and line output current ( I ( L 1 ) ) . representing the output of a differential amplifier with a clamped output. CSI's. The PSPICE input file for each of these is presented in Appendix 11. The ORCAD program generates the input netlist for PSPICE from the schematic circuit diagram files. VCR's. The mathematical expression can contain the variable TIME and any mixture of voltages and current. low cost and complete . IV. Also. The symbols are stored in a schematic dedicated library file (SCH. PSPICE Implementation Using the ABM option in PSPICE. or the inversion principle to (1) and (2). i 3 ( t ) 1 (5) (6) where . I .03. 9. Current Controlled Rectifier (CCR) Model The transfer functions for a CCR can be obtained by applying the duality principle to ( 5 ) and (6). SIMULATION ENVIRONMENT The PSPICE software. and clamped to (-10. E and G. Input (ac) : ~ ~ = ( 6. 20 MHz PC. The PSPICE post-processor PROBE is used as a calculator. The symbols are listed in Appendix I. The sinusoidal and hysteresis control methods require a comparator circuit to generate the switching function. The standard SPICE polynomial function operator (POLY) can also be employed. The schematic capture program ORCAD. 5. the implementation of the converter macromodels shown in Fig. 10) when the range of the table is exceeded.(t)' t ) Output (dc) : io(t) = . The amplitude (modulation index) and the frequency of this sinusoidal reference are modified externally with two dc sources (or regulator error signals). The macromodel for a comparator (subcircuit CPNF) is implemented by means of a voltage source E. 5 (see Appendix 11) can be done directly. This non-linear amplifier is defined as a lookup table (TABLE) as follows: I el(t) = va(t)*S3a(t) eZ(t) = vb(t)*S3b(t) e3(1) = vc(t)*S3c(t) ea@)= vi(t)*SZa(t) eqt) = vi(t)*S2b(t) ec(1) = vi(t)*S2C(l) ia(t) = ii(t)*S3a(t) ib(t) = ii(t)*S3b(t) ic(t) = ii(t)*S3c(t) CSI VSl E034 TABLE{G*(V(l) .V ( 2 ) ) )= (-1. E2. version 4. The macromodels for the converter and PWM switching function generators are implemented as subcircuit modules and stored in a separate library (CIR. with the ABM option. VOL.22 [ 1 11 is employed as an effective frontend to PSPICE. It allows modification of all parameters and components values directly on the circuit schematic. The output is interpolated for inputs between -1 and 1. XCP2. However. CPH for the hysteresis control method. Input (ac) : Output (dc) : i z ( t )= i o ( t ). 10) The ideal amplifier has a high gain G(G > 10 K) and the input to the table is the difference between V(1) and V(2). The subcircuit 3PWM uses three comparators (subcircuits XCP1. and the input becomes an output. Symbols for each subcircuit have been implemented by using ORCAD. The overall system is a very flexible. XCP3) and a three-phase sinusoidal reference ( E l .&(t) (7) (8) The respective circuit macromodels derived from (1) to (8) for the three-phase VSI's.IEEE TRANSACTIONS ON POWER ELECTRONICS. can be defined as a mathematical expression in standard notation using the keyword VALUE. has been used to validate the proposed macro-models. Proposed macromodels of three-phase converters RVH 5010 XCPN 16260 CPNF an input. G.0)*0. Switching Function Implementation il(t) = ia(t)*SZa(t) iZ(1) = ib(t)*SZb(t) i3(t) = ic(l)*SZc(I) The PWM subcircuits control modules designed to generate the switching functions are: 3PWM for the sinusoidal PWM method. Hence. NO. S . F . and CCR's in terms of the controlled voltage and current sources are shown in Fig.001 UF CCR VCR VH 50{ VHYST} Fig. In this option the controlling function of the controlled Fource. many other transfer functions are not well represented by polynomials. i 3 ( t ) v o ( t ) C.LIB). running on a 386.0)*V(6.05} The hysteresis band is defined by the voltage source VH and it can be modified with the keyword PARAMS: VHYST = (value). i&t) . The programs are linked by means of a batch file.LIB). version 3. The hysteresis comparator (subcircuit CPH) is designed by adding positive feedback to the comparator CPNF with another controlled source (EVH) applied through a capacitor: il(t) = ia(t)*SZa(t) 12(t) = Ib(t)*SZb(t) a ( t ) = lC(t)*S2C(t) e2(t) = vb(I)*S3b(t) e3(t) = vc(t)*S3c(t) ea@) = vi(t)*SZa(t) eqt) = vl(t)*S2b(t) =(I) = VI(t)*S2C(t) ia(t) = io(l)*S3a(t) ib(t) = io(t)*S3b(t) ic(t) = io(t)*S3c(t) CERR 1620. ( t ) and G l ( t ) are vectors that contain the three-phase instantaneous input current and voltage respectively. harmonic analyzer and for waveform display. -10)(1. EVH 31 VALUE = {V(5. E3). and SHES7 for a PWM switching pattern method that eliminates harmonics 5 and 7. Hence.(t)' . and the respective subcircuits list are presented in Appendix 11. JANUARY 1994 38 ii(t) H . the syntax for specifying the polynomial is quite difficult to use. 7 . 6. Example 1 . 6. Resistances are incorporated in the circuits to account for the losses. This source is defined as subcircuit REC in Appendix 11. Example 4. The schematic input file is shown in Fig. Table I11 compares the run times ABS(V(3) where V(1).39 + Fig. Fig. Example 5. SPICE vsw SCH OPnoNS RELTOL-0 05 lTL5=0 ABSTot=IuA LIB c \pEL\LIB CIR ?RAN lous Zomsoms IOurulC PROBE 4 - 2mh ic. CSI.14 C 3 M ( M k = 190.8 Fig.SCH simulated laboratory for analysis and design of three-phase power converters. The same applies to VCR and CCR for discontinuous current analysis in the dc output terminal. input file VSIH2. 7. input file CSI2. 6. The modulation index and the frequency are varied by changing the values of the voltage sources Vm (magnitude) and Vf (frequency). the performance of standard three-phase converter systems (VSI.26 2mh ic -115.28 c 1 m K-48.34. as a first approximation.SCH Fig. as they would appear on the screen of a PC computer with the ORCAD software.4 U5OM ic = -125.cIR APPLICATION EXAMPLES AND SIMULATION RESULTS In order to establish the effectiveness of the proposed models and simulation methods. input file VSIZSCH. Moreover. V ( 3 )are the phase voltages. a 1 kHz sinusoidal PWM modulator (SUBCIRCUIT 3PWM) is employed to generate a three-phase. . Example 3. The respective input schematic diagrams for PSPICE are shown in Figs.9 2mh ic= 81. 8.LIBC\PEL\LIB. input file VCR2. 9. Example 1: Rectifier-VSI with Sinusoidal PWM + ABS(V(2) - V(3)) + - V(1))IPl In this example. One diode is still used to account for the unidirectional current in the dc bus. input file CCR2. the threephase rectifier in the example 2 and 3 has been replaced with one equivalent voltage source E defined as follows c I l l MSIR 3HYs PARMI: Fig. The three-phase rectifier could also have been replaced by ideal voltage and current sources. and 10. two-level switching function. V(2). Notice that the only non-linear physical elements used in the simulation are the diodes in the front-end three-phase rectifier of the VSI and CSI systems. I . VCR.SCH. 9. 8. 10. CCR) operating with different PWM control methods is evaluated.respectively.SCH. Example 2. v. by using a functional definition for a rectifier in terms of absolute value. E 46 VALUE = { [ ABS(V(1) - V(2)) A . TIME Statement 100 ps 20 ms 100 p s 1 p s 20 ms 10 ps 761. The schematic input file for PSPICE is illustrated in Fig. 13. TABLE I11 SIMULATION TIMEOF A THREEPHASE VsI BY ON PSPICE USING THE PROPOSED MODELS Model Controlled Source Fig. Simulation results for Example 1 (see Fig. 12. 7). 14.. Simulation results for Example 4 (see Fig. 1. 1 I . Fig. the three-phase rectifier lomS l5ms 2oms (b) Fig. 12 shows the results obtained with the proposed methods. the control module SHE57 is used to control a CSI.. 2omS 15ms I 400 0 I I os 5mS l5ms (b) (b) Fig. Notice that an important reduction in the run time is achieved by using the converter macromodels. Fig. VSI). 8). Simulation results for Example 3 (see Fig. Esample 2 : Rectifier-VSI with Hysteresis The schematic input file for this example is shown in Fig. The first result is for the simulation of the VSI with the simplified switch model shown in Fig. The range of the hysteresis band is modified by using the statement “PARAMS:” on the schematic diagram. NO.IEEE TRANSACTIONS ON POWER ELECTRONICS. 2 Converter Model Fig. 5 (a). 9). l b 300 I I 0 I I u l u u u u u u u u l \ U U I 400 (I(Li)-l(Ci))*2 I 4 200 200 0 -100 I os I 5ms l h I5ms 2oms 0 os Sms (b) Fig. B . VOL. The amplitude of the reference and the frequency are modified on the schematic diagram by changing the value of the voltage sources VA and VF. and Fig.38 s 240. and the second corresponds to the proposed converter macromodel of Fig. 8. Simulation results for Example 2 (see Fig. 7. Example 3: Rectifier-CSI with Selective Harmonic Elimination Technique In this example. In the input file. A current feedback loop and hysteresis control with a sinusoidal reference (SUBCIRCUIT 3HYS) is used in this example to generate sinusoidal currents at the output terminal of the inverter.JANUARY 1994 40 350 - 200 7 600. Fig. 2 and 6.79 s 59. Fig. 5ms loznS r I . and confirms that the converter macromodel gives the same results as those shown in Fig. 11 displays input and output waveforms. . 6). 3. three-level PWM switching function that eliminates the 5th and 7th harmonics in the output current of the inverter. I. . 6 . os 400. 5(a).10 s 436. 9. . 13 shows the simulation results. Moreover. I . C . This module generates a three-phase.54 s and the VSI are now incorporated as subcircuits (REC. Fig. The time step can also be increased to speed up the simulation. I 0 . for the VSI systems shown in Figs. Close agreement was found. 15. I These models are also valid when simulating the behavior of converter systems with feedback control loops. VI.LIB) I U XPWM 3PWM 0 (b) Fig. These values were checked against the results obtained with exact modeling of the converter system and with experimental set-ups. distortion factor and power factor. the harmonic contents. Simulation results for Example 5 (see Fig. confirming the validity of the macromodels proposed in this paper. These parameters include the average. E-vaniple 5: CCR Mith Hystesesis Control This example simulates the performance of a CCR that provides near unity input power factor. CONCLUSION In order to optimize the run times and the amount of memory required. 9.41 SALAZAR AND JObS: PSPICE SIMULATION OF THREE-PHASE INVERTERS 200. The simulation results are shown in Fig. F . Perforniaizce Analysis Different circuit parameters have been computed for the previous examples from the data generated in the simulation by using the post-processor (PROBE). and to reduce convergence problems in computer simulations of three-phase converter circuits using SPICE. E. and the converter macromodel at the system level. IO).CIR) . D . The simulation results are shown in Fig. SUBCIRCUITS APPENDIX I1 LIBRARY USED IN PSPICE (LIB. The schematic input file for this example is shown in Fig. VCRs and CCR's at the system level have been proposed and evaluated for use on the PSPICE simulation package. 0 APPENDIX I SCHEMATIC LIBRARY FILEUSEDIN ORCAD 450 . rms and peak values. 14. These models greatly reduce the computational times without affecting the accuracy of the results obtained for converter input and output variables. X3H 3HYS E . In this paper macromodels which simulate standard three-phase VSI's. the switch macromodel at the single converter level. (PEL.\-aniple 4 : VCR MVth Selective Husmonic Eliniiriatiori Technique The modulation technique (SUBCIRCUIT SHE57) of Example 3 is utilized here to minimize harmonics in the input line current of a VCR system. and almost sinusoidal input line currents by using the same hysteresis control module (3HYS) as in Example 2. The schematic input file is shown in Fig. appropriate modeling must be used. This includes the physical micromodel at the switch level. 15. CSI's. IO. May/June 1983. Ind. Montreal.Eng. V Patel. . I .. 1985 [5] D Vincenti. 3 4 4 4 . Concepci6n. Stefanovic. 78-84. 1986.” Conf. vol 14. 1234-1240. Ziogas dnd R. CA: MicroSim Corp. Salmon. vol IA-21. Rec./Oct. Epler. Montredl. pp. Ziogas and D.D. P D. “Generalized functional model for three phase PWM inverter/rectifier converters. where he is involved in teaching and research in the areas of power converters and electrical drives. vol IA-19. degrees from Mc Gill University. ORCAD/SDT 111 Addendum.” IEEE Trans Itid A p p ( .D. R. 1988. in 1974 and 1987. Vincenti. 1987. 9. V. a professor at the Ecole de Technologie Supbrieure. he has been with the Department of Electrical and Computer Engineering of Concordia University. New York Van Nomand-Reinhold. IA-23. “A novel simulation progrdm for power electronics equipment. in 1980. Canada. Dixon and A. simulation and control method during the Ph. Montreal. 1987. “A threephase controlled current PWM converter with leading power factor. 1989. pp. Odi: J. “Computer-modelling the pulse with modulated (PWM) inverter. and from 1978 to 1988. Cdndda G. Salazar. Salazar (S’86-M’91) received the B S degree in electrical engineering from Concepcidn University. P. Chile. OR: ORCAD Systems Corp. Quebec. and Ph. D. 1063-1068.” Cotif Rec IEEE /AS’ 86. Sept. NO. program in Concordia UniverWy. He specialized in switch-mode power supply design. R.”/EEE Tiatis I d Appl .. JANUARY 1994 REFERENCES [ I ] P Wood. “A computer aided analysis and design approach for static voltage \ource inverters. PSPICE Manual. Appl.” IEEE Circ. D Ziogas and V. P Wiechmann. 89-97.rDevices Mag. 198l [Z] P D Ziogas. pp. pp. C. Jan. Hillsboro. Sept. vol. /AS’ 88.” Can J Elecr Comp Eng . M Boost. 401408. he was a design engineer with Brown Boveri Canada. B. respectively. Mar. L. 24-27. Kulkami. VOL. B. ‘‘Spice2 application notes for dependent sources. in Montreal. pp. 1980. “Simple models for spice assist power electronics circuit simulation on PC’s. P. Stefanovic. D. Since 1988. From 1975 to 1978. Lautaro D. [3] E. Wiechman and V. 141 P. Quebec. J.rtit. D Ziogas.” IEEE Trans. T. Joos (M’79-SM’89) received the M. Theot? of Suijching Power Converter. 9 8 4 9 9 3 . “Synthesis of optimum gain functions for static power converters. DD.I IEEE TRANSACTIONS ON POWER ELECTRONICS./Feb. B. Bello.“ Pou<ercon7. W. E P. pp. Documents Similar To PSPICE Simulation of Three-phase Inverters by Means of Swiching Functions (Salazar; Joós)Skip carouselcarousel previouscarousel nextPower Electronics Ppts_0Power Electronics 26.Multiconverter Unified PowerMy ProjectAssignment1_CTPE+2011V EX (SY)290911035844A Common-Mode Voltage Reduction Strategy for AFPETBoseappd.pdfHigh-performance Decoupled ControlT__Power Ele_28-07_16_EE_LS2-sol_1243Single Phase MatrixReport87. A Novel Three-Phase Three-Leg AC-AC Converter.pdfInverter GeneratorPspice TutorialDrivesWall-Mounted Power DatasheetPEPSPICE Tutorial 2ijrte02061361382010 BOOKSmart Module(Tigo).Pdf11.28UPEC2006 Atif RevisedResearchpaper Z Source Inverter Fed Induction Motor.prob_intGrainger Brandon ETD Thesis Final April 2011Optimized Hybrid Phase Disposition PWM Control Method for Multilevel Inverter68684773-acs800-104-0400-5-inverter-r8i-500v-400kvadu-dt-acs800-104-0400-5e205v991 (1)More From luism_falconiSkip carouselcarousel previouscarousel next01-ITF-Practica Supervisada-Proteccion Contra Descargas Atmosfericas y Puesta a Tierra de ProteccionSintenax_valio.pdfNormas-Iram-2010-Parte-3-Simbolos-Graficos-Electrotecnicos.pdfestuido de cortocircuito.pdfAPUNTES DE CABLES 2007.pdfmanual_instalador Electricista_catIII.pdfAEA Reglamentacion Lineas aereas de baja tension.pdfSintenax_valio.pdfCatalogo_BT_Prysmian_2013_2.pdfindice_90364_64 - Ot - Tiemposguia-instalaciones-electricas-2008-s.e.pdf3- Ot - AlcanceWEG-guia-de-especificacion-50039910-manual-espanol.pdfIndiceVector Approximation Method With Parameter AdaptationGuia de Problemas I Parcial AControl VoltajeGuia de Problemas I Parcial cIII Parcial de AspiII PARCIAL DE ANALISIS DE SIST DE POT III 2012.pdfII PARCIAL DE ANALISIS DE SIST DE POT III 2012.pdfGuia de Problemas I Parcial bCapítulo 6.pdfGuia de ProblemasFallas Asimetricasguia-instalaciones-electricas-2008-s.e.pdfFall Ass i Metric Asmanual_instalador Electricista_catIII.pdfTwo Reaction Theory of Synchronous Machines Generalized Method of Analysis - Part I (R. H. PARK)Footer MenuBack To TopAboutAbout ScribdPressOur blogJoin our team!Contact UsJoin todayInvite FriendsGiftsLegalTermsPrivacyCopyrightSupportHelp / FAQAccessibilityPurchase helpAdChoicesPublishersSocial MediaCopyright © 2018 Scribd Inc. .Browse Books.Site Directory.Site Language: English中文EspañolالعربيةPortuguês日本語DeutschFrançaisTurkceРусский языкTiếng việtJęzyk polskiBahasa indonesiaSign up to vote on this titleUsefulNot usefulYou're Reading a Free PreviewDownloadClose DialogAre you sure?This action might not be possible to undo. Are you sure you want to continue?CANCELOK