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An Introduction to PLECS
Introducing Plexim
An Introduction to
Key Features of PLECS Modeling, Simulation and the Operation of PLECS Thermal modeling Special Features of PLECS Solvers
electrical engineering software
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WHO IS PLEXIM?
Independent company Spin-off from ETH Zurich Privately owned by founders Software PLECS sold since December 2002
Introducing PLEXIM
Now in Release 3.2 September 2011 PLECS Blockset or PLECS Standalone
Customers in more than 40 countries
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SOME OF OUR CUSTOMERS TODAY
Aerospace:
Goodrich Saab GE Aviation US Air Force
Academia:
Aachen Aalborg Nottingham Virginia Tech
Automation & Drives:
Danfoss Hilti Rockwell Woodward SEG
Automotive:
Bosch Chrysler Opel Skoda
Key Features of PLECS
Electronics:
Infineon Panasonic Philips Tyco
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High Power:
ABB Bombardier GE Energy Siemens
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KEY FEATURES OF PLECS
Fast and efficient simulation Simple to use Open component library Accurate thermal modeling The PLECS Scope The two versions of PLECS:
PLECS Blockset PLECS Standalone
FAST AND EFFICIENT SIMULATION
Instantaneous switching
Analysis tools
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SIMPLE TO USE
Drag and drop components
OPEN COMPONENT LIBRARY
Models are open for customization
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THERMAL MODELING
Look-up table approach for speed
PLECS SCOPE
Cursors RMS, Mean, Max, Min, Absolute Max Delta, THD, Fourier Analysis X-Y plot Export to .bmp, .pdf, .csv Copy to Clipboard: Traces and Data
DTC_scope.plecs
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PLECS SCOPE Curve Tracer
X-Y Plot of Solar Panel
PV_model_1.plecs PV_model_2.plecs
PLECS BLOCKSET/STANDALONE
Available as Standalone or as a toolbox in Simulink
Current characteristic of a single BP365 PV module.
Plot of 22 series-connected BP365 PV modules
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PLECS STANDALONE
An independent simulation tool. Compatible with PLECS blockset Key Features:
Control and circuit components Faster simulation thanks to an optimized solver Lower overall investment and maintenance cost
IMPORT FROM BLOCKSET INTO STANDALONE
Blockset Standalone
Faster than PLECS Blockset!
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IMPORT FROM BLOCKSET INTO STANDALONE
Blockset Standalone
EXPORT FROM BLOCKSET INTO STANDALONE
Standalone Blockset
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BLOCKSET AND STANDALONE MODEL COMPATIBILITY
Blockset
Standalone
Simulink Solver & Control blocks
PLECS Solver
MATLAB/Simulink
PLECS Control blocks Circuit editor Scope
PLECS Control blocks Circuit editor Scope
Modeling, Simulation and the Operation of PLECS
Analysis tools and M/L Script editor
Analysis tools and Script editor
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MODELING, SIMULATION AND THE OPERATION OF PLECS
Modeling, Simulation, Emulation The Challenges and the Different Simulation Types Ideal Switches Basic Solver Types
FAILURE TO DO QUALIFIED SYSTEM MODELING ...
... results in tragedy
correct modeling correct simulation
system thermal
Basic PLECS Operation Behavioral Models in PLECS
behavioral
(Thorough real-time controls testing (HIL))
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MODELING VERSUS SIMULATION
Modeling
Find essential functionality of target system Describe components as simple as possible (model component details only as needed at this stage) Enter the design using the modeling language
CHALLENGES WITH NUMERICAL SIMULATION
Power semiconductors introduce extreme non-linearity
program must be able to handle switching
user
Time constants differ by several orders of magnitude
e.g. in electrical drives small simulation time steps long simulation times
Simulation
PLECS
Transforming the model into mathematical equations Solving the equations with specified tolerances Providing numerical results
Accurate models are not always available
e.g. semiconductor devices, magnetic components behavioral models with sufficient accuracy are required
Controller modeled along with electrical circuit
e.g. digital control mixed signal simulation
The accuracy of the simulation results depend on the model
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DIFFERENT DEGREES OF SIMULATION DETAIL
Power circuit modeled as linear transfer function
small signal behavior no switching, no harmonics controller design
DIFFERENT DEGREES OF SIMULATION DETAIL
Controls
PLECS Blockset & Simulink
Power circuit modeled with ideal components
large signal behavior, voltage and current waveforms overall system performance circuit design and controller verification
PLECS Standalone
Power circuit with manufacturer specific components
parasitic effects (magnetic hysteresis) switching transitions (diode reverse recovery) component stress (electrical or thermal) choice of components
Power input vi ii Power converter Control signals Controller Power output vo i
o
Circuit
Heat
Load
Component
Measurement
Reference
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HIGH SPEED SIMULATIONS WITH IDEAL SWITCHES
Conventional continuous diode mode
arbitrary static and dynamic characteristic snubber often required
COMPARISON: DIODE RECTIFIER
Simulation with conventional and ideal switches
Ideal diode model in PLECS
instantaneous on/off characteristic optional on-resistance and forward voltage
Simulation steps:
1160 153
Computation time:
0.6s 0.08s
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Saber & Spice
Simplorer
Psim
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STATE SPACE MODEL: BUCK CONVERTER
OPERATING PRINCIPLE OF PLECS
Circuit transformed into state-variable system One set of matrices per switch combination
Switch conducting
Diode conducting
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VARIABLE VS FIXED TIME-STEP SIMULATION
Variable Time-Step
highest accuracy time-step automatically adapted to time constants can get slow for systems with many independently operating switches
VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER
Transistor conducts Diode blocks
Fixed Time-Step
can speed up simulation for large systems hardware controls are often implemented in fixed time-step non-sampled switching events (diodes, thyristors) require special handling
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VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER
Transistor opens Impulsive voltage across inductor
VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER
Impulsive voltage closes diode
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VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER
VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER
Switch timing Problem:
diode opens too late impulsive voltage across inductor
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VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER
Zero-crossing detection:
Time-step is reduced Diode opens at the zero-crossing
HANDLING OF NON-SAMPLED SWITCHING EVENTS
Diode currents
zero-crossing zero-crossing Backward interpolation, Forward step Backward interpolation Forward step sync. with sampleBackward time interpolation, Forward step Backward interpolation, Forward step Diode 3 starts conducting Forward step sync. with sample Diode 2 stops conducting time
Non-sampled Non-sampled
Diode voltage
Non-sampled zero-crossing
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DIFFERENT DIODE MODELS IN PLECS
Diode turn-off
DYNAMIC DIODE MODEL WITH REVERSE RECOVERY
Reverse recovery effect under different blocking conditions
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DYNAMIC IGBT MODEL WITH FINITE DI/DT
DIFFERENT LEVELS OF SIMULATION
System simulation
waveforms resolved up to switching frequency response times, controller behaviour dead times, currents and voltages (peak, RMS etc) harmonic content (Fourier, THD)
Thermal simulation
efficiency, junction & heat-sink temperatures
3_L_3Ph_IGCT.plecs
semiconductor cooling, average and peak temperatures, temperature cycles, choice of devices, average power dissipation
Circuit simulation (single commutation cell)
waveforms resolved to transient response stray inductances and capacitances common-mode currents semiconductor tail-times, recovery times, spreading times.
Clamp_Rep_Real.plecs
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THERMA L SIMULATIONS
Semiconductor Losses Ideal Switches vs Continuous Switches Look-up Tables
Thermal Modeling
Electrical-Thermal Simulation Thermal Equivalent Networks Steady-State Thermal Calculations
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SEMICONDUCTOR LOSSES
Switching Loss Conduction Loss
Gate signal
SWITCHING LOSSES
Switching energy loss dependent on:
blocking voltage, device current, junction temperature, gate drive EON = f(VCE, IC, TJ, RG)
Turn on
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Turn off
EXAMPLE IGCT TURN-OFF: VARYING STRAY INDUCTANCE
kV 4.5
300 nH (10.5 Ws) 800 nH (12 Ws) 1500 nH (13.5 Ws)
SWITCHING LOSS CALCULATION FROM TRANSIENTS
kA 3.0
Accurate physical device models required
generally unavailable
VPK = 3800V
Physical parameters often unknown during design phase.
stray inductance of buss-bars
3.0
2.0
Small simulation steps required
large computation times
VDC = 2 kV 1.5 TJ = 125 C 1.0
0.0
Courtesy ABB 5 10 tf 2.5s, ttail 7s
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0.0
15 s
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LOOKUP TABLE APPROACH FOR SWITCHING LOSSES
Instantaneous switching maintained for speed Switching losses are read from a database after switching event
Esw = F(TJ, VBLOCK, ION) (RG = constant)
EXAMPLE LOOK-UP TABLE
Turn-off loss is a function of:
current before switching voltage after switching temperature at switching RG is assumed constant
Exact loss found using interpolation Note the voltage and current polarities! Only data-sheet losses used in thermal calculations Same procedure for EON, EREC and on-state Report generation for reliable documentation
5SNA 1500E330305_report.pdf
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SEMICONDUCTOR CONDUCTION LOSSES
On-state loss
conduction profile is nonlinear: vON = f(iON, TJ). conduction profile stored in lookup table exact voltage found using interpolation conduction power loss: PLOSS(t) = vON(t), iON(t)
SIMULATION OF AN ELECTRICAL-THERMAL MODEL
Off-state loss
negligible - low leakage current
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SEMICONDUCTOR THERMAL BEHAVIOR
OBTAINING SWITCHING LOSS DATA
Experimental measurements
switching losses highly dependent on gate drive circuit and stray parameters use a switching loss setup to characterize loss dependency on voltage and current for two temperatures
Datasheets
given for a specific gate resistance and stray inductance good approximations can be made by extrapolating manufacturers data (or asking for complete loss measurements)
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POINTS TO NOTE
Thermal and electrical domains not coupled
Semiconductor losses from lookup tables dont appear in the electrical circuit Energy conservation may be achieved with extra feedback
THERMAL DOMAIN
Thermal circuit analogous to electrical circuit Thermal and electrical circuits solved simultaneously
The only legal way is to use datasheet values !
Measurements only represent a few devices Datasheets represent all devices over the lifetime of the component and over its production life Transient simulations do not represent datasheet values
Only when you design your equipment using data-sheet values can you ask for help from your supplier ! Otherwise, if you are not respecting his data-sheet he wont be willing to discuss your problem!
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A COMPLETE ELECTRICAL-THERMAL MODEL
The heat-sink is the interface between the two domains
automatically absorbs component losses propagates temperature back to semiconductors
DIFFERENT THERMAL EQUIVALENT NETWORKS
Cauer equivalent
Physics based thermal equivalent circuit Each Rth and Cth pair represents a physical layer in the thermal circuit
Foster equivalent
Curve fitting approach based on heating and cooling characteristics No correspondence between Rth,n or Cth,n and the physical structure! Any modification of the system requires recalculation of all values
Thermal impedance modeled with RC elements
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MEASURING AVERAGE DEVICE LOSSES
Concept
Calculate total switching and conduction energy lost during a switching cycle Output as an average power pulse during the next cycle Implementation: based on a C-Script block conduction and switching losses measured with a Probe
JUNCTION-CASE THERMAL IMPEDANCE
Define in semiconductor thermal description to observe junction temp fluctuations Foster coefficients usually given in data-sheet
Foster network coefficients
Example junction-case thermal impedance
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FOSTER NETWORK PITFALLS
Only accurate if reference point x is a constant temperature Cannot be arbitrarily extended beyond point x
TJ is immediately affected by temperature changes at x
SOLUTION 1 - USE FIRST ORDER CAUER NETWORK
Calculate from 63% R value C = /R
VC reaches 63.2% VFINAL after
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COMBINED ELECTRICAL-THERMAL SIMULATION
CYCLE-AVERAGE LOSSES
Calculate average device losses for each device
Semiconductor losses dont appear in electrical circuit Conservation of energy can be maintained by subtracting thermal losses from electrical circuit
Average device losses
Apply to external resistive-only thermal circuit
Average device losses
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EXAMPLE IGBT CONDUCTION LOSSES
CALCULATING THE STEADY-STATE OPERATING POINT
Challenge: Large thermal time-constant of heat-sink - simulation can take hours! Newton-Raphson analysis
Instantaneous loss thermal capacitances left in circuit Jacobian matrix must first be calculated system must be periodic and all states must converge Cycle average loss
Cycle-average losses with resistive thermal circuit
thermal capacitances are removed losses are averaged, TJ = constant at steady-state Moving average (20ms) system can be non-periodic and have non-convergent states
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THERMAL SIMULATIONS
Control Analysis Tools Newton-Raphson Analysis Magnetic Modeling
Special Features of PLECS
Custom Control Codes Simulation Scripting
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ANALYSIS TOOLS
Control analysis tools
AC sweep impulse response analysis loop gain analysis
BuckOpenLoop.plecs
NEWTON-RAPHSON ANALYSIS
Iterative method for finding the roots of an equation y = f(x):
If x is the initial state vector and FT(x) is the final state vector after time T, then to find the steady-state solution we must find the roots of f(x) = x FT(x)
Steady-state analysis
This is done iteratively in PLECS by the Newton-Raphson method: xk+1 = xk J-1f(xk) where J is the Jacobian (determinant) of the Jacobian matrix of the n state variables (requires n+1 simulation runs)
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NEWTON-RAPHSON ITERATION DEMO
NEWTON-RAPHSON ITERATION DEMO GUESS X1
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NEWTON-RAPHSON ITERATION DEMO
NEWTON-RAPHSON ITERATION DEMO TANGENT AT F(X1)
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NEWTON-RAPHSON ITERATION DEMO X2 FROM TANGENT
NEWTON-RAPHSON ITERATION DEMO
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NEWTON-RAPHSON ITERATION DEMO - SET X2 AS NEW ROOT
NEWTON-RAPHSON ITERATION DEMO TANGENT AT F(X2)
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NEWTON-RAPHSON ITERATION DEMO X3 FROM TANGENT
NEWTON-RAPHSON ITERATION DEMO
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NEWTON-RAPHSON ITERATION DEMO SET X3 AS NEW ROOT
NEWTON-RAPHSON ITERATION DEMO - TANGENT AT F(X3)
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NEWTON-RAPHSON ITERATION DEMO X4 FROM TANGENT
NEWTON-RAPHSON ITERATION DEMO
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NEWTON-RAPHSON ITERATION DEMO SET X4 AS NEW ROOT
NEWTON-RAPHSON ITERATION DEMO TANGENT AT F(X4)
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NEWTON-RAPHSON ITERATION DEMO X5 FROM TANGENT
NEWTON-RAPHSON ITERATION DEMO CONVERGENCE!
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NEWTON RAPHSON: CONVERGENCE
Typically converges in less then 10 iterations
NEWTON RAPHSON: REQUIREMENTS FOR CONVERGENCE
The system must be convergent Example Problem:
PLL model angle is a ramp signal towards infinity
Solution:
create a periodic signal with a self-resetting integrator
2-level IGBT Inverter.plecs
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MAGNETIC MODELING
Permeance-capacitance analogy
CUSTOM CONTROL CODE
Custom C-code External DLL
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SIMULATION SCRIPTING
Inbuilt scripting External scripting
Solvers
BuckParamSweep.plecs
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OUTLINE
What are Solvers? Discrete Solvers
trapezoidal rule
SOLVERS
In a digital simulation, integration is numerically performed by starting with known initial conditions
Continuous solvers
Taylor series polynomial step-size control acceptable error tolerances: relative and absolute refining the display output
A time step is taken and some assumptions are made about the way a variable changes within this time step; the algorithm for doing this is called a Solver
Step-size selection for Discrete Solvers Solver Comparisons Conclusions
The simplest solver is one which assumes a linear change of conditions within a time step; this is a reasonable assumption for a small step. This type is known as a Discrete Solver and it builds the computed function from a series of trapezoidal blocks
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TRAPEZOIDAL RULE FOR DISCRETE SOLVER
CONTINUOUS SOLVER
We will see later that discrete solvers have limitations with regards to speed and accuracy. A non-linear interpolation between two points might allow a larger time step, depending on how closely the interpolating function matches the real response. Any waveform may be emulated by the sum of a sufficient number of simple mathematical functions (e.g. by sine waves, in the case of Fourier). Continuous Solvers, in fact, use the Taylor Series
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TAYLOR SERIES EXPANSION
To perform a piece-wise simulation with a continuous solver requires the approximation of a continuous function with a higher order polynomial
CONTINUOUS SOLVER OPERATION
If y(t) is the (unknown) function, it can be constructed in a piece-wise fashion from (known) points p1(t) and p2(t) from Taylor series polynomials. A continuous solver determines the point yn+1 by calculating the equivalent Taylor series for p1(t). An nth order solver has the same accuracy as an nth order Taylor series.
The higher the order, the more accurate the solution
The Taylor series is of the form:
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REPRESENTATION OF EXPONENTIAL BY TAYLOR SERIES
REPRESENTATION OF SINE-WAVE BY TAYLOR SERIES
Exponential 5th order Taylor series representation At n = 8, perfect fit for -3 < x < 3 For -4 < x <4, a Taylor series to the 13th order is an accurate representation of y = sin(x)
1st order 3rd order 5th order 7th order 9th order 11th order 13th order y = sin(x)
Source: Wikipedia Source: Wikipedia
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CONTINUOUS SOLVER STEP-SIZE CONTROL
Step-size is automatically controlled by the solver (variable step)
goal: keep the error within acceptable limits advantages: accuracy directly specified by the user and fewer steps (faster simulation)
ACCEPTABLE ERROR
Local error
difference between 4th and 5th order solutions
Acceptable error
defines the local error limit determined by tolrel except for small state values
Step size, h, is calculated using where:
is relative or local error
tolrel is relative tolerance hold is previous time step
Result is valid if:
Local error
Acceptable error
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STEP SIZE CONTROL
Step size automatically controlled by solver (variable step)
Goal: Keep error within acceptable error limits Key advantage: Accuracy directly specified by the user
TOLERANCES
Relative tolerance (tolrel) determines acceptable error limit when x approaches 0
start with 10-3 (0.1%) numerical limit is 10-16
Step size calculated using
Relative error, (or local error) Relative tolerance, tolrel Previous time step, hold
hold
Absolute tolerance (tolabs)
best to set to auto
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LC CIRCUIT - SCOPE OUTPUT
Analytical solution:
LC CIRCUIT - COMPARISON WITH ANALYTICAL SOLUTION
Analytical response
Display uses linear interpolation used between time-steps
Solver response
(tolrel = 1e-3)
Resonant LC circuit VC(0) = 1 V
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LC CIRCUIT - SOLVER OUTPUT
OPTIONS FOR A FINER DISPLAY
Resonant LC circuit VC(0) = 1 V
Calculated points for tolrel = 1e-3
Option 1: Reduce tolrel or time-step
solver must recalculate polynomial coefficients at each time step less efficient
Option 2: Increase refine factor
solver uses existing polynomial coefficients to calculate additional points. more efficient
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TRAPEZOIDAL RULE FOR DISCRETE SOLVER
FIXED SOLVER TIME-STEP SELECTION
Accuracy is indirectly determined by the time-step
to ensure accuracy, reduce the time-step and observe any changes in the output, or: compare with a continuous simulation
Continuous waveform
highest transient frequency determines the sample time set tsample < ttransient/10 for a ratio of 10, the integration error is approx -3% (underestimation)
Switched system
switches must be turned on at sample instants set tsample < tsw/100
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COMPARISON - CONTINUOUS AND DISCRETE SOLVERS
Time steps: Underdamped RLC circuit
Continuous: tolrel = 10-6
SUMMARY
Variable solvers are in general faster and more efficient
use the Refine Factor for smoother displays rather than reducing tolrel or time-step tolrel is typically set to 1e-3 to start with tolabs is best set to auto
Fixed step solvers
do not require tolerance inputs (set by step-size)
Simulated current
Discrete: ts = 50s
Refine Factor is always one (set by step-size)
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CONCLUSIONS
Fast and efficient ideal switches Simple to use Drag & Drop Open component library customization of models Thermal modeling Look-up tables allow direct use of semiconductor data-sheets
Conclusions
Magnetic modeling Analysis tools fast calculation of steady state and frequency response Custom control code efficient controller design Simulation scripting fast performance analysis PLECS Scope high performance, user-friendly easy waveform and data export PLECS Blockset & PLECS Standalone simple model exchange (inter-company)
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electrical engineering software
Southeast-Asia Authorized Agents: Infomatic Pte. Ltd. Olivier WU TEL: +65 3158 2943 FAX: +65 3158 2190 Mobile: +65 8478 0572 Email: olivier.wu@infomatic.com.sg Web: www.infomatic.com.sg
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Vietnam Authorized Agents: Smart Green Solutions JSC 27/35 Cong Hoa Street, Ward 4, District Tan Binh Ho Chi Minh City, Vietnam. TEL: +84 8 38112941 FAX: +84 8 38112941 Email: info@sgs-jsc.com Web: www.sgs-jsc.com
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