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Abstract: Circuit modeling is an essential tool in the design of power electronic applications. Both the on-state forward voltage drop and transient thermal impedance of high power SCR’s and Diodes are complex functions requiring, in the past, tedious, copious, inefficient, semi-mechanical calculations to evaluate one or two specific conditions for a given power electronic application. Today, with the availability of personal computers, greater efficiency and accuracy can be realized using mathematical models of these basic characteristics. The widespread use of these models, depends upon; the understanding of how to use these models, the trade-off of the accuracy and simplicity of the models and the availability of parametric data for devices. This main objective of this paper is how to use the modeling equations to evaluate a given Power Electronic Application. Previous papers by the authors1,2,3 and others6,8 have addressed this subject. As has been described, the forward on-state forward voltage drop can be modeled by both the classical ABCD and the new MNOP… parameters. The transient thermal impedance has been shown to be well represented via four or five exponential terms representing the significant transient thermal time constants of the device. The methodology to quickly and accurately calculate the forward voltage drop and transient thermal impedance modeling parameters has been discussed and described in detail1,2,3. This paper will describe the techniques for using the basic device modeling equations to evaluate a given power electronic application. Both the digital (hard code) simulation and "analog" PSPICE simulation techniques will be described. Also, a new tool, called STARSim, will be described. STARSim permits comparison of the older superposition method and new modeling method by performing the calculations using both approaches. A simple SCR model for PSPICE incorporating the on-state forward voltage drop and transient thermal impedance models is also described and evaluated. This information is considered to be important in providing the tools required for power electronic design engineers to quickly evaluate a given device in proposed or existing power electronic application.
Vtm, TRANSIENT THERMAL IMPEDANCE MODELS The output of the STARS Visual System for the Powerex TBK7 (600V, 3000A) SCR is illustrated in Figure 1. This is the standard five points per decade table evaluated in Reference [5] where the validity of linear interpolation was carefully investigated. Note the wide range of the independent variables (On-State Current and time) required to permit surge and overload ratings to be evaluated and a reasonable range of applications simulated. This forward voltage drop and transient thermal impedance are represented in STARS by Data Tables as illustrated in Figure 1. For a given instantaneous anode current the corresponding On-State Forward Voltage Drop is looked up and linearly interpolated. For a given point in time the Transient Thermal Impedance is looked up and also linearly interpolated. The calculation of junction temperature in STARS and in the past has been accomplished with superposition[6]. Here one evaluation point on the power waveform is chosen and the waveform prior to this point is divided into a number of time slices. The power dissipation for each segment is calculated and the temperature rise for that section is calculated by looking up the transient thermal impedance from the evaluation point to the leading edge (heating) and falling edge (cooling). All of the sections are then summed to get the junction temperature rise for the one chosen evaluation point in time. The output of a superposition calculation module in STARS for an Arbitrary Current Waveshape is illustrated in Figure 2 for the Powerex T9G0 (2400V, 1000A) SCR. Here the first two (or three) columns is a text input file and the junction temperature is calculated and placed in the 4th column.
A. SCR and Diode On-State Modeling: The model parameters described in References
1, 2 and 3. are illustrated in Figure 3. Under the Data menu
in STARS, there is a choice of the Vf, Vtm Model Parameters i.e., the ABCD
or MNOPQ… . The parameters are quickly evaluated and placed in a parameter
file with the format as illustrated. The range of anode current can also
be chosen (last two numbers in first row). B. Transient Thermal Impedance
Models: The transient thermal impedance can be modeled
from physical parameters of the SCR or Diode as described in [3].
The resulting ladder network however is too complex to be used as a model
but can be simplified with good accuracy by regression of the resulting
transient thermal impedance curve by four or five series connected
parallel RC stages.[2] The R(n), Tau(n) for the Transient Thermal
Impedance Model Parameters are also automatically calculated in STARS for
the selected device and placed into a file as displayed at the bottom of
Figure 3.
The newest generation of the STARS Visual Rating System, called STARSim, provides a transition from curve or table based data to the Vf, Vtm and Transient Thermal Impedance Models. The idea is to make calculations with the old tables and the new modeling equations to transfer the confidence from the old standard calculations to the new equation modeling methods. The first step is to compare the model generated curve, for transient thermal impedance, to the table of values curve as illustrated in Figure 4. This is actually two curves which provides, by the overlap of the curves, a quick evaluation as to how well the table generated curves match the model equation curves.
Figures 5a. and 5b. illustrate the STARSim Arbitrary Waveform Evaluation Module for the Powerex T9G0 SCR. This module takes an arbitrary wave shape and evaluates the junction temperature rise using the Vf, Vtm and transient thermal Modeling Equations. The arbitrary waveform data can be viewed in Figure 5b. by clicking on the curve in Figure 5a, Note this is the same current waveform used in Figure 2. which used the old Vf or Vtm and transient thermal impedance tables and superposition. Comparison of the peak junction temperatures which occurs at 4.5 msec is 369°C in STARS (Figure 2) compared to 353°C in STARSim (Figure 5b) indicating agreement of the two methods within 4%.
Next we will describe how the junction temperature is calculated in STARSim . This is done by hard coding in Microsoft Visual BASIC. While some readers may not be interested in tackling the time consuming task of hard coding this section will provide insight into: 1. How the modeling procedures are implemented and 2. How the SPICE modeling works which will be described in the next section of this paper.
Hard coding for circuit simulation consist of iterating very small steps of time, resulting in small steps in the applied source voltage. Next, depending upon the state of the SCR(s), (see the state diagram; Figure 6), calculations are made as to how this voltage step affects the other voltage and currents in the circuit. Equations will be presented in next section. Of interest here are the instantaneous anode current through the SCR(or Diode) and the resulting on-state forward voltage drop, VTM or VFM, using the ABCD or MNOPQ.. models. The product of the device voltage and current then represents the instantaneous power dissipation in the device. Finally, this power dissipation is used as a current in the equivalent analog thermal circuit of the device (several stages of parallel RC circuits) and the calculated voltage across the RC stages is analogous to the virtual junction temperature of the device. A. Modeling the Electrical
Circuit:
The code to model the SCR is given as Code
Fragment 1 in the Appendix. Note that line 1400 is the calculation of
instantaneous current as described by Equation (2). The EX variable is the
exponential term value for the fixed time step IL=IL*Ex + (VL/RL)*(1! - Ex) ‘SCR (Load) Current (3) B. Modeling the Thermal
Circuit: As we iterate with very small time increments, each time increment results in a new set of instantaneous temperatures(voltages), and switching from the electrical analog to thermal symbols the equation for the temperature contribution of a given RC section is:
The modeling waveforms in STARSim for an SCR in an AC switch are illustrated in Figure 7. The device is the TBK7 77mm 600 Volt SCR, The conditions are a two cycle 60,000 Ampere surge at a 90 degree conduction angle The source is 600 (peak) Volts and the load a 0.06 Ohm resistor in series with a 6µHenry di/dt inductor .The waveforms include: the applied AC line voltage(VdVr), SCR current(IL), SCR On-State Voltage drop(Vtm), instantaneous power dissipation(Pt) and last, but certainly not least: the instantaneous virtual junction temperature of the SCR (Tj). Note that the peak junction temperature occurs around 23.6 msec and is 121.6°C. This compares well with 122.9°C in STARSim Arbitrary Waveform Module at 23.9msec. The old superposition table look up in STARS resulted in 117.6°C. The agreement of the two approaches is 3.3%.
Next we switch our attention from Hard Coding in a higher level language to the simulation of the SCR and Diode in Power Electronic Circuits with PSPICE.
A. PSPICE Model Electrical
Circuit: The SCR Electrical Model provides the correct instantaneous on-state forward voltage drop for any value of instantaneous anode current. This is achieved by sensing the anode current I*(V_Pwr_Sen) and using the ABCD or MNOPQ… Vtm Models to force the correct instantaneous Vtm by the Value statement in (E_Vtm). This is illustrated by the circuit in Figure 9. and the Net List Code Fragment 2. in the Appendix. B. PSPICE Thermal "Circuit": This circuit is easy to follow in Figure 9. and the Net List in Code Fragment 2. where R1,C1 connect from the Tj Node via Tj1 to R2,C2 etc. Note that the same forced charging and natural discharging of the thermal capacitors is occurring as described in the hard code section but now PSPICE is taking care of the differential equations. The PSPICE waveforms for the Powerex T9G0 withstanding a 17,000 Ampere single cycle surge is illustrated in Figure 8. Note that not only is the current waveshape through the SCR, I(Rload) displayed but also the Forward Voltage Drop, Vtm , Power Dissipation, Pt and the resulting Virtual Junction Temperature Waveforms. The power dissipation is displayed as a current where (1 Amp = 1 Watt). Temperature is shown as the analog voltage Vtj (1 Volt=1°C) at the node Tj . The peak junction temperature is 356°C at 4.25msec versus 353°C for the hard code Arbitrary Waveforms in Figures 5a and 5b resulting in an difference of 0.8%.
C. PSPICE Model Sub Circuit:
Circuit modeling is an important tool in the design of power electronic applications. This paper has demonstrated that the new mathematical models of forward voltage drop and transient thermal impedance are quite capable of providing quick accurate simulations of SCRs and Diodes in power electronic applications. The methodology to use these models, in both "digital" Hard Code, and "analog" PSPICE simulations have been described in detail including graphs of the output waveforms and quantitative evaluations of the overall accuracy. The agreement between the new mathematical models method and old, classical, but tedious, curve look up, superposition methods of calculating virtual junction was good. There was also shown to be excellent agreement between the Hard Code and the new Electro Thermal PSPICE SCR Model implementing the on-stat drop and thermal models. This information hopefully will assist the power electronic engineer achieve more innovative, challenging and reliable designs in the many areas where power the electronics can provide useful functions to the public.
[1] J. W. Motto Jr., William H. Karstaedt, Jerry M. Sherbondy, Scott G. Leslie, "Thyristor(Diode) On-State Voltage, The ABCD Modeling Parameters Revisited Including Isothermal Overload and Surge Current Modeling" IEEE-IAS Annual Meeting, San Diego, California, October 1996 [2] J. W. Motto Jr., William H. Karstaedt, Jerry M. Sherbondy, Scott G. Leslie, "Thyristor(Diode) Transient Thermal Impedance Modeling Including the Spatial Temperature Distribution During Surge and Overload Conditions", IEEE-IAS Annual Meeting, Orlando Florida, October 1995 [3] J. W. Motto Jr., "Thyristor(Diode) Transient Thermal Impedance Modeling and Verification for Inductive Load Applications" , IEEE-IAS Annual Meeting, Denver, Colorado, October 1994 [4] J. W. Motto Jr., "Thyristor Steady State Current Ratings Past, Present and Future" , IEEE-IAS Annual Meeting, Toronto, Canada, October 1993 [5] J. W. Motto Jr., "Computer Aided Analysis of Thyristor Current Ratings" I&GA, IEEE Group Meeting Pittsburgh Pennsylvania, October 1967 [6] F. W, Gutzwiller and T. P. Sylvan "Power Semiconductors Under Transient and Intermittent Loads", AIEE Winter General Meeting, New York, New York January 31, 1960 [7] W. E. Newell "Transient Thermal Analysis of Solid State Power Devices - Making the Dreaded Process Easy", IEEE Transactions on Industry and General Applications Vol IA-12 July August, 1976 [8] D.E. Piccone, L.D. Eriksson, Dr. D.J. Urbanek, W.H. Tobin and I.L. Somos, "A Thermal Analog of Higher Accuracy and Factory Test Method for Predicting Thyristor Fault Suppression Ratings" IEEE-IAS Annual Meeting October 1988 [9] A. R. Hefner Jr. "A Dynamic Electro.-Thermal Model for the IGBT" IEEE Transactions on Industry Applications Vol 30 No 2 March/April 1994 [10] C. D. Mohler, "Digital Computer Calculation of Rectifier and Silicon Controlled Rectifier Ratings", AIEE Winter General Meeting, , New York, New York, January 30, 1962
1000 Rem ***** Switch Model { S(N)=0 Switch
OFF - S(N)=1 Switch ON } ****
******************* POWEREX TBK7 SCR MODEL
**************************** ***************** Vtm Model *** ****** April
15, 1997 ************************ |
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(1)
(2)
t =K which
is calculated prior to the time iteration loop. The computer code
calculation of instantaneous current is:
(4)
(5)
