PSIM User Manual

-9

PSIM

Users Guide

Powersim Inc.

-8

PSIM Users GuideVersion 6.1

Release 3

February 2

Copyright

All rights remeans with

DisclaimPowersim Iaccuracy ofdirect or indindirect, incbusiness proany damage

Powersim

email: info@http://www005

2001-2005 Powersim Inc.

served. No part of this manual may be photocopied or reproduced in any form or by anyout the written permission of Powersim Inc.

ernc. (Powersim) makes no representation or warranty with respect to the adequacy or this documentation or the software which it describes. In no event will Powersim or itsirect suppliers be liable for any damages whatsoever including, but not limited to, direct,idental, or consequential damages of any character including, without limitation, loss offits, data, business information, or any and all other commercial damages or losses, or fors in excess of the list price for the licence to the software and documentation.

Inc.

powersimtech.com.powersimtech.com

Contents

1 General Information1.1

1.2

1.3

1.4

1.5

1.6

1.7

2 Po2.1

2.2

2.3

2.4 -7

Introduction 1

Circuit Structure 2

Software/Hardware Requirement 3

Installing the Program 3

Simulating a Circuit 3

Simulating a Circuit with the Command Line Option 4

Component Parameter Specification and Format 4

wer Circuit ComponentsResistor-Inductor-Capacitor Branches 72.1.1 Resistors, Inductors, and Capacitors 7 2.1.2 Rheostat 82.1.3 Saturable Inductor 9 2.1.4 Nonlinear Elements 10

Switches 11 2.2.1 Diode, DIAC, and Zener Diode 12 2.2.2 Thyristor and TRIAC 142.2.3 GTO, Transistors, and Bi-Directional Switch 15 2.2.4 Linear Switches 182.2.5 Switch Gating Block 19 2.2.6 Single-Phase Switch Modules 21 2.2.7 Three-Phase Switch Modules 22

Coupled Inductors 24

Transformers 26

i

-6

2.4.1 Ideal Transformer 262.4.2 Single-Phase Transformers 26 2.4.3 Three-Phase Transformers 29

2.5 Other Elements 31 2.5.1 Operational Amplifier 31

2.6

2.7

ii2.5.2 dv/dt Block 32

Motor Drive Module 33 2.6.1 Electric Machines 33

2.6.1.1 DC Machine 332.6.1.2 Induction Machine 372.6.1.3 Induction Machine with Saturation 412.6.1.4 Brushless DC Machine 422.6.1.5 Synchronous Machine with External Excitation 482.6.1.6 Permanent Magnet Synchronous Machine 502.6.1.7 Permanent Magnet Synchronous Machine with Saturation 542.6.1.8 Switched Reluctance Machine 57

2.6.2 Mechanical Loads 59 2.6.2.1 Constant-Torque Load 592.6.2.2 Constant-Power Load 602.6.2.3 Constant-Speed Load 612.6.2.4 General-Type Load 62

2.6.3 Gear Box 622.6.4 Mechanical-Electrical Interface Block 63 2.6.5 Speed/Torque Sensors 652.6.6 Position Sensors 67

2.6.6.1 Absolute Encoder 672.6.6.2 Incremental Encoder 672.6.6.3 Resolver 682.6.6.4 Hall-Effect Sensor 69

MagCoupler Module 70

3 Control Circuit Components3.1 Transfer Function Blocks 75

3.1.1 Proportional Controller 763.1.2 Integrator 773.1.3 Differentiator 78

3.2

3.3

3.4 -5

3.1.4 Proportional-Integral Controller 793.1.5 Built-in Filter Blocks 79

Computational Function Blocks 80 3.2.1 Summer 803.2.2 Multiplier and Divider 813.2.3 Square-Root Block 823.2.4 Exponential/Power/Logarithmic Function Blocks 82 3.2.5 Root-Mean-Square Block 833.2.6 Absolute and Sign Function Blocks 83 3.2.7 Trigonometric Functions 833.2.8 Fast Fourier Transform Block 84

Other Function Blocks 85 3.3.1 Comparator 853.3.2 Limiter 863.3.3 Gradient (dv/dt) Limiter 863.3.4 Trapezoidal and Square Blocks 87 3.3.5 Sampling/Hold Block 883.3.6 Round-Off Block 883.3.7 Time Delay Block 893.3.8 Multiplexer 903.3.9 THD Block 91

Logic Components 93 3.4.1 Logic Gates 933.4.2 Set-Reset Flip-Flop 93 3.4.3 J-K Flip-Flop 943.4.4 D Flip-Flop 953.4.5 Monostable Multivibrator 95

iii

-4

3.4.6 Pulse Width Counter 963.4.7 Up/Down Counter 963.4.8 A/D and D/A Converters 97

3.5 Digital Control Module 99 3.5.1 Zero-Order Hold 99

3.6

4 Oth4.1

4.2

iv3.5.2 z-Domain Transfer Function Block 100 3.5.2.1 Integrator 1013.5.2.2 Differentiator 1033.5.2.3 Digital Filters 103

3.5.3 Unit Delay 1063.5.4 Quantization Block 1073.5.5 Circular Buffer 1083.5.6 Convolution Block 1093.5.7 Memory Read Block 1103.5.8 Data Array 1103.5.9 Stack 1113.5.10 Multi-Rate Sampling System 112

SimCoupler Module 113 3.6.1 Set-up in PSIM and Simulink 1133.6.2 Solver Type and Time Step Selection in Simulink 116

er ComponentsParameter File 119

Sources 1204.2.1 Time 1204.2.2 DC Source 120 4.2.3 Sinusoidal Source 121 4.2.4 Square-Wave Source 1224.2.5 Triangular Source 1234.2.6 Step Sources 1244.2.7 Piecewise Linear Source 125

4.2.8 Random Source 1274.2.9 Math Function Source 1274.2.10 Voltage/Current-Controlled Sources 1284.2.11 Nonlinear Voltage-Controlled Sources 130

4.3 Voltage/Current Sensors 131

4.4

4.5

4.6

5 An5.1

5.2

5.3

6 Cir6.1

6.2

6.3 -3

Probes and Meters 132

Switch Controllers 134 4.5.1 On-Off Switch Controller 1344.5.2 Alpha Controller 1354.5.3 PWM Lookup Table Controller 136

Function Blocks 139 4.6.1 Control-Power Interface Block 1394.6.2 ABC-DQO Transformation Block 1404.6.3 Math Function Blocks 1414.6.4 Lookup Tables 1424.6.5 External DLL Blocks 145

alysis SpecificationTransient Analysis 151

AC Analysis 152

Parameter Sweep 156

cuit Schematic DesignCreating a Circuit 160

Editing a Circuit 160

Subcircuit 161 6.3.1 Creating Subcircuit - In the Main Circuit 1626.3.2 Creating Subcircuit - Inside the Subcircuit 1636.3.3 Connecting Subcircuit - In the Main Circuit 164

v

-2

6.3.4 Other Features of the Subcircuit 1656.3.4.1 Passing Variables from the Main Circuit to Subcircuit 1656.3.4.2 Customizing the Subcircuit Image 1666.3.4.3 Including Subcircuits in the PSIM Element List 167

6.4 Other Options 168

6.5

7 Wa7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

8 Err8.1

vi6.4.1 Running the Simulation 1686.4.2 Generate and View the Netlist File 1686.4.3 Define Runtime Display 1686.4.4 Set Path 1686.4.5 Settings 1696.4.6 Printing the Circuit Schematic 169

Editing PSIM Library 169

veform ProcessingFile Menu 172

Edit Menu 172

Axis Menu 173

Screen Menu 174

View Menu 175

Option Menu 177

Label Menu 178

Exporting Data 178

or/Warning Messages and Other Simulation IssuesSimulation Issues 1818.1.1 Time Step Selection 1818.1.2 Propagation Delays in Logic Circuits 1818.1.3 Interface Between Power and Control Circuits 182

8.1.4 FFT Analysis 182

8.2 Error/Warning Messages 183

8.3 Debugging 184 -1vii

0 viii

1 General Information

1.1 InPScosiman

ThCoMostuz-danSimele

In Th

Thsim

1. PSIM a2. Matlab 3. JMAG i Introduction 1

troductionIM is a simulation package specifically designed for power electronics and motorntrol. With fast simulation and friendly user interface, PSIM provides a powerful

ulation environment for power electronics, analog and digital control, magnetics,d motor drive system studies.

is manual covers both PSIM1 and its add-on Modules: Motor Drive Module, Digitalntrol Module, SimCoupler Module, and MagCoupler Module. The Motor Drivedule has built-in machine models and mechanical load models for drive systemdies. The Digital Control Module provides discrete elements such as zero-order hold,omain transfer function blocks, quantization blocks, digital filters, for digital control

alysis. The SimCoupler Module provides interface between PSIM and Matlab/ulink2, and the MagCoupler Module provides interface between PSIM and the

ctromagnetic field analysis software JMAG3 for co-simulation.

addition, PSIM supports links to third-party software through custom DLL blocks.e overall PSIM environment is shown below.

e PSIM simulation package consists of the circuit schematic program PSIM, theulator engine, and the waveform processing program SIMVIEW1. The simulation

nd SIMVIEW are copyright by Powersim Inc., 2001-2005and Simulink are registered trademarks of the MathWorks, Inc.s copyright by the Japan Research Institute, Ltd., 1997-2005

PSIMMatlab/Simulink

JMAG- Control systems

- Finite element analysis

- Power electronics- Analog/digital control- Motor drives

- Electric machines, and other magnetic devices

Third-partySoftware

2 General Info

process is illustrated as follows.

Chancirac Ch

1.2 CA an

Thcodono

PSIM Schematic Circuit Schematic Editor (input: *.sch)rmation

apter 1 of this manual describes the circuit structure, software/hardware requirement,d parameter specification format. Chapter 2 through 4 describe the power and controlcuit components. Chapter 5 describes the specifications of the transient analysis andanalysis. The use of the PSIM schematic program and SIMVIEW is discussed inapter 6 and 7. Finally, error/warning messages are discussed in Chapter 8.

ircuit Structurecircuit is represented in PSIM in four blocks: power circuit, control circuit, sensors,d switch controllers. The figure below shows the relationship between these blocks.

e power circuit consists of switching devices, RLC branches, transformers, andupled inductors. The control circuit is represented in block diagram. Components in smain and z domain, logic components (such as logic gates and flip flops), andnlinear components (such as multipliers and dividers) are used in the control circuit.

PSIM Simulator

SIMVIEW

PSIM Simulator (output: *.txt)

Waveform Processor (input: *.txt)

Power Circuit

Control Circuit

Sensors Switch Controllers

Sensors measure power circuit voltages and currents and pass the values to the controlcircuit. Gating signals are then generated from the control circuit and sent back to thepower circuit through switch controllers to control switches.

1.3 Software/Hardware RequirementPSmi

1.4 InA RO

So

Fil

1.5 SiTo Software/Hardware Requirement 3

IM runs in Microsoft Windows environment 98/2000/XP on personal computers. Thenimum RAM memory requirement is 32 MB.

stalling the Programquick installation guide is provided in the flier PSIM - Quick Guide and on the CD-M.

me of the files in the PSIM directory are shown in the table below.

e extensions used in PSIM are:

mulating a Circuit simulate the sample one-quadrant chopper circuit chop.sch:

- Start PSIM. Choose Open from the File menu to load the file chop.sch.

Files Description

psim.dll PSIM simulator

psim.exe PSIM circuit schematic editor

simview.exe Waveform processor SIMVIEW

psim.lib, psimimage.lib PSIM libraries

*.hlp Help files

*.sch Schematic files

*.sch PSIM schematic file (binary)

*.cct PSIM netlist file (text)

*.txt PSIM simulation output file (text)

*.fra PSIM ac analysis output file (text)

*.smv SIMVIEW waveform file (binary)

4 General Info

- From the Simulate menu, choose Run PSIM to start the simulation. Thesimulation results will be saved to File chop.txt. Any warning messagesoccurred in the simulation will be saved to File message.txt.

- If the option Auto-run SIMVIEW is not selected in the Options menu, fromthe Simulate menu, choose Run SIMVIEW to start SIMVIEW. If the optionAuto-run SIMVIEW is selected, SIMVIEW will be launched automatically.

1.6 SiPSto file

or

This

Infprosimfileof "m

W

1.7 CThOtrmation

In SIMVIEW, select curves for display.

mulating a Circuit with the Command Line OptionIM simulation can also be launched through the command line option. For example,simulate the circuit "chop.sch" which is stored in the folder "c:\programs\psim6.1\examples", go to the PSIM folder, and run the command:

psim /c c:\program files\PSIM6.1\examples\chop.sch

psim /c "c:\program files\PSIM6.1\examples\chop.sch"

e parameter "/c" refers to the command line option. The quotes around the file nameoptional, but is recommended.

ormation on each simulation run will be saved to the file "psim.log" in the PSIMgram folder. The log file will show the date, file name, simulation time, and theulation status (whether the simulation has succeeded or failed). The content of the "psim.log" is retained, and information of new simulation run is appended at the endthe file. Any warning messages generated in the simulation will be saved to the fileessage.txt" in the PSIM program folder.

ith the command line option, one can run several circuits automatically in a batch run.

omponent Parameter Specification and Formate parameter dialog window of each component in PSIM has three tabs: Parameters,her Info, and Color, as shown below.

The parameters in the Parameters tab are used in the simulation. The information in theOther Info tab, on the other hand, is not used in the simulation. It is for reportingpurposes only and will appear in the parts list in View | Element List in PSIM.Information such as device rating, manufacturer, and part number can be stored underthe Other Info tab.

The component color can be set in the Color tab.

Paex

wh4.1

Posup

A ma Component Parameter Specification and Format 5

rameters under the Parameters tab can be a numerical value or a mathematicalpression. A resistance, for example, can be specified in one of the following ways:

12.512.5k12.5Ohm12.5kOhm25./2.OhmR1+R2R1*0.5+(Vo+0.7)/Io

ere R1, R2, Vo, and Io are symbols defined either in a parameter file (see Section), or in a main circuit if this resistor is in a subcircuit (see Section 6.3.4.1).

wer-of-ten suffix letters are allowed in PSIM. The following suffix letters areported:

G 109

M 106

k or K 103

m 10-3

u 10-6

n 10-9

p 10-12

mathematical expression can contain brackets and is not case sensitive. The followingthematical functions are allowed:

+ addition- subtraction* multiplication/ division^ to the power of [Example: 2^3 = 2*2*2]

6 General Info

SQRT square-root functionSIN sine functionCOS cosine functionASIN sine inverse functionACOS cosine inverse functionTAN tangent functionrmation

ATAN inverse tangent functionATAN2 inverse tangent function [-

2 Power Circuit Components

2.1 Re

2.1.1 ReBoprode

ToRvo

Im

ThexR

Fo

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P

R

I

C Resistor-Inductor-Capacitor Branches 7

sistor-Inductor-Capacitor Branches

sistors, Inductors, and Capacitorsth individual resistor, inductor, capacitor branches and lumped RLC branches arevided in PSIM. Initial conditions of inductor currents and capacitor voltages can be

fined.

facilitate the setup of three-phase circuits, symmetrical three-phase RLC branches,3, RL3, RC3, RLC3, are provided. Initial inductor currents and capacitorltages of the three-phase branches are all zero.

ages:

e names above the element images are the netlist names of the elements. Forample, a resistor appears as Resistor in the library menu, and the netlist name is.

r three-phase branches, the phase with a dot is Phase A.

tributes:

arameters Description

esistance Resistance, in Ohm

nductance Inductance, in H

apacitance Capacitance, in F

R L C RL RC

R3 RL3 RC3 RLC3

RLC

LC

8 Power Circu

Ththe

2.1.2 RhA

Im

At

Parameters Description

Initial Current Initial inductor current, in A

Initial Cap. Voltage Initial capacitor voltage, in V

Current Flag Flag for branch current output. If the flag is zero, there is

CCC

P

T

T

Cit Components

e resistance, inductance, or capacitance of a branch can not be all zero. At least one of parameters has to be a non-zero value.

eostatrheostat is a resistor with a tap.

age:

tributes:

no current output. If the flag is 1, the current will be saved to the output file for display in SIMVIEW. The current is positive when it flows into the dotted terminal of the branch.

urrent Flag_A; urrent Flag_B; urrent Flag_C

Flags for Phase A, B, and C of three-phase branches, respectively.


otal Resistance Total resistance of the rheostat R (between Node k and m), in Ohm

ap Position (0 to 1) The tap position Tap. The resistance between Node k and t is: R*Tap.

urrent Flag Flag for the current that flows into Node k.

RHEOSTAT

k m

t

2.1.3 Saturable InductorA saturable inductor takes into account the saturation effect of the magnetic core.

Image:

At

Thfluproas

ThsatL2Nomo

Alseg

In

P

C

C

L_SAT Resistor-Inductor-Capacitor Branches 9

tributes:

e nonlinear B-H curve is represented by piecewise linear approximation. Since thex density B is proportional to the flux linkage and the magnetizing force H isportional to the current i, the B-H curve can be represented by the -i curve instead,shown below.

e inductance is defined as: L = / i, which is the ratio of v.s. i at each point. Theuration characteristics can then be expressed by a series of data points as: (i1, L1), (i2,), (i3, L3), etc. te that the defined saturation characteristics must be such that the flux linkage isnotonically increasing, that is, L1*i1 < L2*i2 < L3*i3, etc.

so, similar to the saturation characteristics in the real world, the slope of each linearment must be monotonically decreasing as the current increases.

certain situations, circuits that contain saturable inductors may fail to converge. In


urrent v.s. Inductance Characteristics of the current versus the inductance (i1, L1), (i2, L2), etc.

urrent Flag Flag for the current display

i (H)

(B)

i1 i2 i3

123

Inductance L = / i

10 Power Circ

such a case, connecting a very small capacitor across the saturable inductor will helpthe convergence.

2.1.4 Nonlinear ElementsFour elements with nonlinear voltage-current relationship are provided:

Th

Im

AtFo

Fo

P

E

E

I

L

U

P

Efuit Components

- Resistance-type (NONV) [v = f(i)]

- Resistance-type with additional input x (NONV_1) [v = f(i,x)]

- Conductance-type (NONI) [i = f(v)]

- Conductance-type with additional input x (NONI_1) [i = f(v,x)]

e additional input x must be a voltage signal.

ages:

tributes:r resistance-type elements:

r conductance-type elements:


xpression f(i) or f(i,x) Expression v = f(i) for NONV and v = f(i,x) for NONV_1

xpression df/di The derivative of the voltage v versus current i, i.e. df(i)/di

nitial Value io The initial value of the current i

ower Limit of i The lower limit of the current i

pper Limit of i The upper limit of the current i


xpression f(v) or (v,x)

Expression i = f(v) for NONI and i = f(v,x) for NONI_1

NONV / NONI NONV_1 / NONI_1

Input x

A

Ex

Thcuspe

2.2 SwThtheop

Sw


Expression df/dv Derivative of the current i versus voltage v, i.e. df(v)/dv

Initial Value vo The initial value of the voltage v

Lower Limit of v The lower limit of the voltage v

U Switches 11

good initial value and lower/upper limits will help the convergence of the solution.

ample: Nonlinear Diode

e nonlinear element (NONI) in the circuit above models a nonlinear diode. The dioderrent is expressed as a function of the voltage as: i = 10-14 * (e 40*v-1). In PSIM, thecifications of the nonlinear element will be:

itchesere are two basic types of switches in PSIM. One is switchmode. It operates either in cut-off region (off state) or saturation region (on state). The other is linear. It canerates in either cut-off, linear, or saturation region.

itches in switchmode include the following:

- Diode (DIODE) and DIAC (DIAC)

- Thyristor (THY) and TRIAC (TRIAC)

pper Limit of v The upper limit of the voltage v

Expression f(v) 1e-14*(EXP(40*v)-1)

Expression df/dv 40e-14*EXP(40*v)

Initial Value vo 0

Lower Limit of v -1e3

Upper Limit of v 1

12 Power Circ

- Self-commutated switches, specifically:

- Gate-Turn-Off switch (GTO)

- npn bipolar junction transistor (NPN)

- pnp bipolar junction transistor (PNP)

Th

SwneSn

Lin

2.2.1 DiThtur

Im

At

P

D

I

Cuit Components

- Insulated-Gate Bipolar Transistor (IGBT)

- n-channel Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) and p-channel MOSFET (MOSFET_P)

- Bi-directional switch (SSWI)

e names inside the bracket are the netlist names used in PSIM.

itch models in PSIM are ideal. That is, both turn-on and turn-off transients areglected. A switch has an on-resistance of 10 and an off-resistance of 10M.ubber circuits are not required for switches.

ear switches include the following:

- npn bipolar junction transistor (NPN_1)

- pnp bipolar junction transistor (PNP_1)

ode, DIAC, and Zener Diodee conduction of a diode is determined by circuit operating conditions. A diode isned on when it is positively biased, and is turned off when the current drops to zero.

age:

tributes:


iode Voltage Drop Diode conduction voltage drop, in V

nitial Position Flag for the initial diode position. If the flag is 0, the diode is open. If it is 1, the diode is closed.

urrent Flag Flag for the diode current output. If the flag is 0, there is no current output. If the flag is 1, the diode current will be saved to the output file for display in SIMVIEW.

DIODE

A DIAC is a bi-directional diode. A DIAC does not conduct until the breakover voltageis reached. After that, the DIAC goes into avalanche conduction, and the conductionvoltage drop is the breakback voltage.

Image:

At

A

Im

At

If

P

B

B

C

P

B

F

C

DIAC Switches 13

tributes:

zener diode is modelled by a circuit as shown below.

ages:

tributes:

the zener diode is positively biased, it behaviors as a regular diode. When it is reverse


reakover Voltage Voltage at which breakover occurs and the DIAC begins to conduct, in V

reakback Voltage Conduction voltage drop, in V

urrent Flag Current flag


reakdown Voltage Breakdown voltage VB of the zener diode, in V

orward Voltage Drop Voltage drop of the forward conduction (diode voltage drop from anode to cathode)

urrent Flag Flag for zener current output (from anode to cathode)

ZENERCircuit Model

A

K

A

K

VB

14 Power Circ

biased, it will block the conduction as long as the cathode-anode voltage VKA is less thanthe breakdown voltage VB. When VKA exceeds VB, the voltage VKA will be clamped toVB. [Note: when the zener is clamped, since the diode is modelled with an on-resistanceof 10, the cathode-anode voltage will in fact be equal to: VKA = VB + 10 * IKA.Therefore, depending on the value of IKA, VKA will be slightly higher than VB. If IKA isvery large, V can be substantially higher than V ].

2.2.2 ThA

A sam

Im

At

TR

Th(GTR

Th

P

V

H

L

I

Cuit Components

KA B

yristor and TRIACthyristor is controlled at turn-on. The turn-off is determined by circuit conditions.

TRIAC is a device that can conduct current in both directions. It behaviors in thee way as two thyristors in the opposite direction connected in parallel.

ages:

tributes:

IAC holding current and latching current are set to zero.

ere are two ways to control a thyristor or TRIAC. One is to use a gating blockATING), and the other is to use a switch controller. The gate node of a thyristor orIAC, therefore, must be connected to either a gating block or a switch controller.

e following examples illustrate the control of a thyristor switch.


oltage Drop Thyristor conduction voltage drop, in V

olding Current Minimum conduction current below which the device stops conducting and returns to the OFF state (for THY only)

atching Current Minimum ON state current required to keep the device in the ON state after the triggering pulse is removed (for THY only)

nitial Position Flag for the initial switch position (for THY only)

urrent Flag Flag for switch current output

THY

A KGate

TRIAC

Gate

Examples: Control of a Thyristor Switch

Thgathede

2.2.3 GTSe(B1Vemthewhsou

A cappa

A ga

Nobesenno

Im

Gating Block Switches 15

is circuit on the left uses a switching gating block (see Section 2.2.5). The switchingting pattern and the frequency are pre-defined, and will remain unchanged throughout simulation. The circuit on the right uses an alpha controller (see Section 4.5.2). The

lay angle alpha, in deg., is specified through the dc source in the circuit.

O, Transistors, and Bi-Directional Switchlf-commutated switches in the switchmode, except pnp bipolar junction transistorJT) and p-channel MOSFET, are turned on when the gating is high (when a voltage of or higher is applied to the gate node) and the switch is positively biased (collector-itter or drain-source voltage is positive). It is turned off whenever the gating is low or current drops to zero. For pnp BJT and p-channel MOSFET, switches are turned onen the gating is low and switches are negatively biased (collector-emitter or drain-rce voltage is negative).

GTO switch is a symmetrical device with both forward-blocking and reverse-blockingabilities. An IGBT or MOSFET switch consist of an active switch with an anti-

rallel diode.

bi-directional switch (SSWI) conducts currents in both directions. It is on when theting is high and is off when the gating is low, regardless of the voltage bias conditions.

te that a limitation of the BJT switch model in PSIM, in contrary to the devicehavior in the real life, is that a BJT switch in PSIM can block reverse voltage (in thisse, it behaviors like a GTO). Also, it is controlled by a voltage signal at the gate node,

t a current.

ages:

Alpha Controller

16 Power Circ

At

A Thillu

Ex

Thco

ExThco

P

I

C

NPN PNP SSWIGTO IGBTMOSFET_PMOSFETuit Components

tributes:

switch can be controlled by either a gating block (GATING) or a switch controller.ey must be connected to the gate (base) node of the switch. The following examplesstrate the control of a MOSFET switch.

amples: Control of a MOSFET Switch

e circuit on the left uses a gating block, and the one on the right uses an on-off switchntroller (see Section 4.5.1). The gating signal is determined by the comparator output.

ample: Control of a npn Bipolar Junction Transistor e circuit on the left uses a gating block, and the one on the right uses an on-off switchntroller.


nitial Position Initial switch position flag. For MOSFET and IGBT, this flag is for the active switch, not for the anti-parallel diode.

urrent Flag Switch current flag. For MOSFET and IGBT, the current through the whole module (the active switch plus the diode) will be displayed.

On-off Controller

ThlefVBcu

ThDbthein wico Switches 17

e following shows another example of controlling the BJT switch. The circuit on thet shows how a BJT switch is controlled in the real life. In this case, the gating voltage is applied to the transistor base drive circuit through a transformer, and the base

rrent determines the conduction state of the transistor.

is circuit can be modelled and implemented in PSIM as shown on the right. A diode,e, with a conduction voltage drop of 0.7V, is used to model the pn junction between base and the emitter. When the base current exceeds 0 (or a certain threshold value,which case the base current will be compared to a dc source), the comparator outputll be 1, applying the turn-on pulse to the transistor through the on-off switchntroller.

18 Power Circ

2.2.4 Linear SwitchesLinear switches include npn bipolar junction transistor (NPN_1) and pnp bipolarjunction transistor (PNP_1). They can operate in either cut-off, linear, or saturationregion.

Images:

At

A thepro

whco

Nobeco

WAwethi

P

C

B

VPuit Components

tributes:

linear BJT switch is controlled by the base current Ib. It can operate in either one of three regions: cut-off (off state), linear, and saturation region (on state). Theperties of these regions for NPN_1 are:

- Cut-off region: Vbe < Vr; Ib = 0; Ic = 0

- Linear region: Vbe = Vr; Ic = Ib; Vce > Vce,sat- Saturation region: Vbe = Vr; Ic < Ib; Vce = Vce,sat

ere Vbe is the base-emitter voltage, Vce is the collector-emitter voltage, and Ic is thellector current.

te that for NPN_1 and PNP_1, the gate node (base node) is a power node, and must connected to a power circuit component (such as a resistor or a source). It can not bennected to a gating block or a switch controller.

RNING: It has been found that the linear model for NPN_1 and PNP_1 worksll in simple circuits, but may not work when circuits are complex. Please uses model with caution.


urrent Gain beta Transistor current gain , defined as: =Ic/Ibias Voltage Vr Forward bias voltage between base and emitter for

NPN_1, or between emitter and base for PNP_1

ce,sat [or Vec,sat for NP_1]

Saturation voltage between collector and emitter for NPN_1, and between emitter and collector for PNP_1

NPN_1 PNP_1

Examples: Circuits Using the Linear BJT SwitchExamples below illustrate the use of the linear switch. The circuit on the left is a linearvoltage regulator circuit, and the transistor operates in the linear mode. The circuit onthe right is a simple test circuit.

2.2.5 SwA gatex

Nocan

Im

At

P

F

N

S

F

NPN_1 Switches 19

itch Gating Blockswitch gating block defines the gating pattern of a switch or a switch module. Theting pattern can be specified either directly (with the gating block GATING) or in at file (with the gating block GATING_1).

te that a switch gating block can be connected to the gate node of a switch ONLY. It not be connected to any other elements.

age:

tributes:


requency Operating frequency of the switch or switch module connected to the gating block, in Hz

o. of Points Number of switching points (for GATING only)

witching Points Switching points, in deg. If the frequency is zero, the switching points is in second. (for GATING only)

ile for Gating Table Name of the file that stores the gating table (for GATING_1 only)

NPN_1

GATING / GATING_1

20 Power Circ

The number of switching points is defined as the total number of switching actions inone period. Each turn-on or turn-off action is counted as one switching point. Forexample, if a switch is turned on and off once in one cycle, the number of switchingpoints will be 2.

For GATING_1, the file for the gating table must be in the same directory as theschematic file. The gating table file has the following format:

wh

ExAspe

Th

Than

If

Thuit Components

nG1G2... ...Gn

ere G1, G2, ..., Gn are the switching points.

ample:sume that a switch operates at 2000 Hz and has the following gating pattern in oneriod:

e specification of the gating block GATING for this switch will be:

e gating pattern has 6 switching points (3 pulses). The corresponding switchinggles are 35o, 92o, 175o, 187o, 345o, and 357o, respectively.

the gating block GATING_1 is used instead, the specification will be:

e file test.tbl will contain the following:

Frequency 2000.

No. of Points 6

Switching Points 35. 92. 175. 187. 345. 357.

Frequency 2000.

File for Gating Table test.tbl

0 180 360

9235 175 187 345 357

(deg.)

635.92.175.187.345.

2.2.6 SiBu(Bare

Im

At

NoSwTh

Simga

P

DV

I

C

A

A Switches 21

357.

ngle-Phase Switch Modulesilt-in single-phase diode bridge module (BDIODE1) and thyristor bridge moduleTHY1) are provided in PSIM. The images and internal connections of the modules shown below.

ages:

tributes:

de Ct at the bottom of the thyristor module BTHY1 is the gating control node foritch 1. For the thyristor module, only the gatings for Switch 1 need to be specified.e gatings for other switches will be derived internally in PSIM.

ilar to the single thyristor switch, a thyristor bridge can also be controlled by either ating block or an alpha controller, as shown in the following examples.


iode Voltage Drop or oltage Drop

Forward voltage drop of each diode or thyristor, in V

nit. Position_i Initial position for Switch i

urrent Flag_i Current flag for Switch i

+

-

BDIODE1 BTHY1DC+

DC-

A+

A-

DC+

DC-

1 3

4 2 24

1 3

Ct

A+

A-

DC+

DC-

A+

A-

DC+

DC-

Ct

22 Power Circ

Examples: Control of a Thyristor Bridge

Thrigcoco

2.2.7 ThThcoMOcuIG

Im

A

B

Cuit Components

e gatings for the circuit on the left are specified through a gating block, and on theht are controlled through an alpha controller. A major advantage of the alphantroller is that the delay angle alpha of the thyristor bridge, in deg., can be directlyntrolled.

ree-Phase Switch Modulese following figure shows three-phase switch modules and the internal circuitnnections. The three-phase voltage source inverter module VSI3 consists of

SFET-type switches, and the module VSI3_1 consists of IGBT-type switches. Therrent source inverter module CSI3 consists of GTO-type switches, or equivalentlyBT in series with diodes.

ages:

BTHY3H BTHY6HA1

1

2

6

1

2

3

A6

A

B

C

NN N N

Ct

Ct

Ct

Ct

B

A

C

BDIODE3 BTHY3DC+

DC-

A

B

C

DC+

DC-

1 3 5

4 6 2

1 3 5

4 6 2

A AB BC C

DC-

DC+

DC-

DC+

Ct

Ct

At

Simthrhasw

Th

P

O

S

V

D

I

C

VSI3 / VSI3_1

A

B

C

1 3 5

DC-

DC+DC+

CBA

Ct

VSI3 Switches 23

tributes:

ilar to single-phase modules, only the gatings for Switch 1 need to be specified foree-phase modules. Gatings for other switches will be automatically derived. For thelf-wave thyristor bridge (BTHY3H), the phase shift between two consecutiveitches is 120o. For all other bridges, the phase shift is 60o.

yristor bridges (BTHY3 / BTHY3H / BTHY6H) can be controlled by an alpha


n-Resistance On resistance of the MOSFET switch during the on state, in Ohm (for VSI3 only)

aturation Voltage Conduction voltage drop of the IGBT switch, in V (for VSI3_1 only)

oltage Drop Conduction voltage drop of the switch, in V (for CSI3 only)

iode Voltage Drop Conduction voltage drop of the anti-parallel diode, in V (for VSI3 and VSI3_1 only)

nit. Position_i Initial position for Switch i

urrent Flag_i Current flag for Switch i

CSI3

DC+

DC-

A

B

C

24 6

1 3 5

24 6

DC-

DC-

DC+

CBA

Ct

Ct

Ct

CSI3

24 Power Circ

controller. Similarly, voltage/current source inverters can be controlled by a PWMlookup table controller (PATTCTRL).

The following examples illustrate the control of three-phase thyristor and voltage sourceinverter modules.

Example: Control of Three-Phase Thyristor and VSI Modules

Thzeris co

ThstomoanPW

2.3 CCosho

Leuit Components

e thyristor circuit on the left uses an alpha controller. For a three-phase circuit, theo-crossing of the voltage Vac corresponds to the moment when the delay angle alphaequal to zero. This signal is, therefore, used to provide synchronization to thentroller.

e circuit on the right uses a PWM lookup table controller. The PWM patterns arered in a lookup table in a text file. The gating pattern is selected based on thedulation index. Other input of the PWM lookup table controller includes the delay

gle, the synchronization, and the enable/disable signal. A detailed description of theM lookup table controller is given in Section 4.5.3.

oupled Inductorsupled inductors with two, three, and four branches are provided. The followingws coupled inductors with two branches.

t L11 and L22 be the self-inductances of Branch 1 and 2, and L12 and L21 the mutual

PWM ControllerVac

i1

i2

v1

v2

+ -

+ -

inductances, the branch voltages and currents have the following relationship:

The mutual inductances between two windings are assumed to be always equal, i.e.,L1

Im

At

In res

ExTwindthe

P

L

L

i

I

v1v2

L11 L12L21 L22

ddt----- i1

i2= Coupled Inductors 25

2=L21.

ages:

tributes:

the images, the circle, square, triangle, and plus refer to Inductor 1, 2, 3, and 4,pectively.

ample: o mutually coupled inductors have the following self inductances and mutualuctance: L11 = 1 mH, L22 = 1.1 mH, and L12 = L21 = 0.9 mH. The specification of element MUT2 will be:


ii (self) Self inductance of the inductor i, in H

ij (mutual) Mutual inductance between Inductor i and j, in H

i_initial Initial current in Inductor i

flag_i Flag for the current printout in Inductor i

L11 (self) 1m

L12 (mutual) 0.9m

L22 (self) 1.1m

MUT2 MUT3 MUT4

26 Power Circ

2.4 Transformers

2.4.1 Ideal TransformerAn ideal transformer has no losses and no leakage flux.

Im

Th

At

Sinrep

2.4.2 SiTh

A

P

N

Nuit Components

ages:

e winding with the larger dot is the primary and the other winding is the secondary.

tributes:

ce the turns ratio is equal to the ratio of the rated voltages, the number of turns can belaced by the rated voltage at each side.

ngle-Phase Transformerse following single-phase transformer modules are provided in PSIM:

- Transformer with 1 primary and 1 secondary windings (TF_1F / TF_1F_1)

- Transformer with 1 primary and 2 secondary windings (TF_1F_3W)


- Transformer with 1 primary and 4 secondary windings (TF_1F_5W /TF_1F_5W_1)




single-phase two-winding transformer is modelled as:


p (primary) No. of turns of the primary winding

s (secondary) No. of turns of the secondary winding

TF_IDEAL

Np Ns

TF_IDEAL_1

Np Ns

whpriindpri

Im

In

Ththebo

Fo

Lp Ls

Lm

Ideal

Rp Rs Np:Ns

SecondaryPrimary Transformers 27

ere Rp and Rs are the primary and secondary winding resistances; Lp and Ls are themary and secondary winding leakage inductances; and Lm is the magnetizinguctance. All the values are referred to the primary winding side. If there are multiplemary windings, all the values are referred to the first primary winding.

ages:

the images, p refers to primary, s refers to secondary, and t refers to tertiary.

e winding with the largest dot is the primary winding or first primary winding. For multiple winding transformers, the sequence of the windings is from the top to thettom.

r the transformers with 2 or 3 windings, the attributes are as follows.

TF_1F_5W

p

s_1

s_4

TF_1F_5W _1

p_1

p_2

s_1

s_3

TF_1F_4W

p_1

p_2

s_1

s_2

TF_1F_8W

p_1

p_2

s_1

s_2

s_6

TF_1F TF_1F_3W TF_1F_7W

p st

p

p

ss_1

s_6

s_2

sp

TF_1F_1

TF_1F_6W

p_1

p_2

s_1

s_4

28 Power Circ

Attributes:

Al

Fowi

At

Al

ExA leaare


Rp (primary); Rs (secondary);Rt (tertiary)

Resistance of the primary/secondary/tertiary winding, in Ohm

LLL

L

NNN

P

RR

LL

L

NNuit Components

l the resistances and inductances are referred to the primary side.

r the transformers with more than 1 primary winding or more than 3 secondaryndings, the attributes are as follows.

tributes:

l the resistances and inductances are referred to the first primary winding side.

ample: single-phase two-winding transformer has a winding resistance of 0.002 Ohm andkage inductance of 1 mH at both the primary and the secondary side (all the values referred to the primary). The magnetizing inductance is 100 mH, and the turns ratio

p (pri. leakage); s (sec. leakage);t (ter. leakage)

Leakage inductance of the primary/secondary/tertiary winding, in H (seen from the primary)

m (magnetizing) Magnetizing inductance, in H

p (primary); s (secondary);t (tertiary)

No. of turns of the primary/secondary/tertiary winding


p_i (primary i); s_i (secondary i)

Resistance of the ith primary/secondary/tertiary winding, in Ohm

p_i (pri. i leakage); s_i (sec. i leakage)

Leakage inductance of the ith primary/secondary/tertiary winding, in H (referred to the first primary winding)

m (magnetizing) Magnetizing inductance, in H (seen from the first primary winding)

p_i (primary i); s_i (secondary i)

No. of turns of the ith primary/secondary/tertiary winding

is Np:Ns = 220:440. In PSIM, the transformer will be TF_1F with the specifications as:

2.4.3 ThPSTh

Im

Rp (primary) 2m

Rs (secondary) 2m

Lp (primary) 1m Transformers 29

ree-Phase TransformersIM provides two-winding and three-winding transformer modules as shown below.ey all have 3-leg cores.

- 3-phase transformer (windings unconnected) (TF_3F)

- 3-phase Y/Y and Y/ connected transformer (TF_3YY / TF_3YD)- 3-phase 3-winding transformer (windings unconnected) (TF_3F_3W)

- 3-phase 3-winding Y/Y/ and Y// connected transformer (TF_3YYD / TF_3YDD)

- 3-phase 4-winding transformer (windings unconnected) (TF_3F_4W)

ages:

Ls (secondary) 1m

Lm (magnetizing) 100m

Np (primary) 220

Ns (secondary) 440

TF_3YY TF_3YD TF_3DD

TF_3YYD TF_3YDD

TF_3F

A

B

C

A+A-B+B-C+C-

A

B

C

a

b

c

A

B

C

a

b

c

a

b

c

N n

aa+

a+a-b+b-c+c-N

A

B

C

abc

aabbcc

A

B

C

abc

aabbcc

N

n

N

A+A-B+B-C+C-

a+a-b+b-c+c-

aa-bb+bb-cc+

cc-

TF_3F_3W TF_3F_4W

A+A-B+B-C+C-

AA+AA-BB+BB-CC+CC-

a+a-b+b-c+c-aa+aa-bb+bb-cc+cc-

30 Power Circ

Attributes:

In Alsid

Th


Rp (primary); Rs (secondary);Rt (tertiary)

Resistance of the primary/secondary/tertiary winding, in Ohm

LLL

L

NNNuit Components

the images, P refers to primary, S refers to secondary, and T refers to tertiary.l resistances and inductances are referred to the primary or the first primary windinge.

ree-phase transformers are modelled in the same way as single-phase transformers.

p (pri. leakage); s (sec. leakage);t (ter. leakage)

Leakage inductance of the primary/secondary/tertiary winding, in H

m (magnetizing) Magnetizing inductance, in H (seen from the primary side)

p (primary); s (secondary);t (tertiary)

No. of turns of the primary/secondary/tertiary winding

2.5 Other Elements

2.5.1 Operational AmplifierAn ideal operational amplifier (op. amp.) is modelled using power circuit elements, asshown below.

Im

wh

At

ThOPgro

P

V

V Other Elements 31

ages:

ere

tributes:

e difference between OP_AMP and OP_AMP_1 or OP_AMP_2 is that, for_AMP, the reference ground node of the op. amp. model is connected to the powerund, whereas in OP_AMP_1 and OP_AMP_2, the reference ground node of the

V+; V- - noninverting and inverting input voltages

Vo - output voltage

A - op. amp. gain (A is set to 100,000.)

Ro - output resistance (Ro is set to 80 Ohms)


oltage Vs+ Upper voltage source level of the op. amp.

oltage Vs- Lower voltage source levels of the op. amp.

V+

V-Vo

OP_AMP

Circuit Model of the Op. Amp.

V+

V-Vo

V+

V-

Vo

Vs+Vs-

Ro

A*(V+ - V-)

gnd

OP_AMP_1

gnd

V+

V-Vo

OP_AMP_2

gnd

32 Power Circ

model is accessible and can be floating.

Note that the image of an op. amp. OP_AMP is similar to that of a comparator. For theop. amp., the inverting input is at the upper left and the noninverting input is at the lowerleft. For the comparator, it is the opposite.

Example: A Boost Power Factor Correction CircuitThlooop

2.5.2 dvA thade

wht Imuit Components

e figure below shows a boost power factor correction circuit. It has the inner currentp and the outer voltage loop. The PI regulators of both loops are implemented using

. amp.

/dt Blockdv/dt block has the same function as the differentiator in the control circuit, exceptt it can be used in the power circuit. The output of the dv/dt block is equal to the

rivative of the input voltage versus time. It is calculated as:

ere Vin(t) and Vin(t-t) are the input values at the current and previous time step, andis the simulation time step.

age:

Comparator

VoVin t( ) Vin t t( )

t----------------------------------------------=

DV_DT

2.6 Motor Drive ModuleThe Motor Drive Module is an add-on module to the basic PSIM program. It providesmachine models and mechanical load models for motor drive system studies.

2.6.1 Electric Machines

2.6.1.1 DTh

Im

At

P

R

L

R

L

M

V

I Motor Drive Module 33

C Machinee image and parameters of a dc machine are as follows:

age:

tributes:


a (armature) Armature winding resistance, in Ohm

a (armature) Armature winding inductance, in H

f (field) Field winding resistance, in Ohm

f (field) Field winding inductance, in H

oment of Inertia Moment of inertia of the machine, in kg*m2

t (rated) Rated armature terminal voltage, in V

a (rated) Rated armature current, in A

DCM

+

-

+

-

ArmatureWinding

FieldWinding

Shaft Node

34 Power Circ

Wsav

A a mor theex

Threfdirme

In is theeleopSeSe

It


n (rated) Rated mechanical speed, in rpm

If (rated) Rated field current, in A

Torque Flag Output flag for internal torque Tem

Muit Components

hen the torque flag is set to 1, the internal torque generated by the machine will beed to the output file for display.

machine is set to either the master or slave mode. When there is only one machine inechanical system, this machine must be set to the master mode. When there are two

more machines in a system, only one must be set to the master mode and the rest to slave mode. The same applies to a mechanical-electrical interface block, as

plained later.

e machine in the master mode is referred to as the master machine, and it defines theerence direction of the mechanical system. The reference direction is defined as theection from the shaft node of the master machine along the shaft to the rest of thechanical system, as illustrated below:

this mechanical system, the machine on the left is the master and the one on the rightthe slave. The reference direction of the mechanical system is, therefore, from left to right along the mechanical shaft. Furthermore, if the reference direction enters anment at the dotted side, this element is along the reference direction. Otherwise it isposite to the reference direction. For example, Load 1, Speed Sensor 1, and Torquensor 1, are along the reference direction, and Load 2, Speed Sensor 2, and Torquensor 2 are opposite to the reference direction.

is further assumed the mechanical speed is positive when both the armature and the

aster/Slave Flag Flag for the master/slave mode (1: master; 0: slave)

Master SlaveReference direction of the mechanical system

Load 1 Load 2SpeedSensor 1

TorqueSensor 1

Speed TorqueSensor 2 Sensor 2TL2TL1

field currents of the master machine are positive.

Based on this notation, if the speed sensor is along the reference direction of themechanical system, a positive speed produced by the master machine will give apositive speed sensor output. Otherwise, the speed sensor output will be negative. Forexample, if the speed of the master machine in the example above is positive, SpeedSensor 1 reading will be positive, and Speed Sensor 2 reading will be negative.

ThmaamLotheis

Th

whresinttor

whbe Motor Drive Module 35

e reference direction also determines how a mechanical load interacts with thechine. In this system, there are two constant-torque mechanical loads with theplitudes of TL1 and TL2, respectively. Load 1 is along the reference direction, andad 2 is opposite to the reference direction. Therefore, the loading torque of Load 1 to master machine is TL1, whereas the loading torque of Load 2 to the master machine

-TL2.

e operation of a dc machine is described by the following equations:

ere vt, vf, ia, and if are the armature and field winding voltage and current,pectively; Ea is the back emf, m is the mechanical speed in rad./sec., Tem is theernal developed torque, and TL is the load torque. The back emf and the internalque can also be expressed as:

ere Laf is the mutual inductance between the armature and the field windings. It can calculated based on the rated operating conditions as:

vt Ea ia Ra Ladiadt-------++=

vf if Rf Lfdifdt------+=

Ea k m =

Tem k ia =

Jdmdt

---------- Tem TL=

Ea Laf if m =

Tem Laf if ia =

36 Power Circ

Note that the dc machine model assumes magnetic linearity. Saturation is notconsidered.

ExThthethepo

Th

ExThmawatra

LafVt Ia Ra( )

If m------------------------------=uit Components

ample: A DC Motor with a Constant-Torque Load e circuit below shows a shunt-excited dc motor with a constant-torque load TL. Since load is along the reference direction of the mechanical system, the loading torque to machine is TL. Also, the speed sensor is along the reference direction. It will give asitive output for a positive speed.

e simulation waveforms of the armature current and the speed are shown on the right.

ample: A DC Motor-Generator Set e circuit below shows a dc motor-generator set. The motor on the left is set to thester mode and the generator on the right is set to the slave mode. The simulationveforms of the motor armature current and the generator voltage show the start-upnsient.

Speed Sensor

Constant-

LoadTorque

Speed (in rpm)

Armature current

Motor Generator

Generator voltage

Motor armature current

2.6.1.2 Induction MachineTwo types of models are provided for both squirrel-cage and wound-rotor inductionmachines: linear and nonlinear model. The linear model is further divided into generaltype and symmetrical type. This section describes the linear models.

Four linear models are provided:

Th

Im

Motor Drive Module 37

- Symmetrical 3-phase squirrel-cage induction machine (INDM_3S / INDM_3SN)

- General 3-phase squirrel-cage induction machine (INDM3_S_LIN)

- Symmetrical 3-phase wound-rotor induction machine (INDM3_WR)

- General 3-phase wound-rotor induction machine (INDM3_WR_LIN)

e images and parameters are shown as follows.

ages:

as+as-bs+bs-cs+cs-

INDM3_S_LININDM_3S INDM_3SN

as

bs

cs

ns

as

bs

cs

as

bs

cs

ns

nr

as+as-bs+bs-cs+cs-

ar br cr ar+ br+ cr+ar- br- cr-

INDM3_WR INDM3_WR_LIN

38 Power Circ

Attributes:

Al

AgSewh

Thacc

Th

wh


Rs (stator) Stator winding resistance, in Ohm

Ls (stator) Stator winding leakage inductance, in H

R

L

L

N

N

M

T

Muit Components

l the parameters are referred to the stator side.

ain, the master/slave flag defines the mode of operation for the machine. Refer toction 2.6.1.1 for detailed explanation. It is assumed the mechanical speed is positiveen the input source sequence is positive.

e model INDM_3SN is the same as INDM_3S, except that the stator neutral point isessible.

e operation of a 3-phase induction machine is described by the following equations:

ere

r (rotor) Rotor winding resistance, in Ohm

r (rotor) Rotor winding leakage inductance, in H

m (magnetizing) Magnetizing inductance, in H

s/Nr Turns Ratio Stator and rotor winding turns ratio (for wound-rotor machine only)

o. of Poles Number of poles P of the machine (an even integer)

oment of Inertia Moment of inertia J of the machine, in kg*m2

orque Flag Flag for internal torque (Tem) output. When the flag is set to 1, the output of the internal torque is requested.


vabc s, Rs iabc s, Lsddt----- iabc s, Msr

ddt----- iabc r,++=

vabc r, Rr iabc r, Lrddt----- iabc r, Msr

T ddt----- iabc s,++=

For squirrel-cage machines, va,r = vb,r = vc,r= 0. The parameter matrices are defined as:

whme

Th

wh

vabc s,

va s,vb s,vc s,

= vabc r,

va r,vb r,vc r,

= iabc s,

ia s,ib s,ic s,

= iabc r,

ia r,ib r,ic r,

= Motor Drive Module 39

ere Msr is the mutual inductance between the stator and rotor windings, and is thechanical angle. The mutual inductance is related to the magnetizing inductance as:

e mechanical equation is expressed as:

ere the developed torque Tem is defined as:

Rs

Rs 0 00 Rs 00 0 Rs

= Rr

Rr 0 00 Rr 00 0 Rr

=

Ls

Ls Msr+Msr2

--------Msr2

--------

Msr2

-------- Ls Msr+Msr2

--------

Msr2

--------Msr2

-------- Ls Msr+

= Lr

Lr Msr+Msr2

--------Msr2

--------

Msr2

-------- Lr Msr+Msr2

--------

Msr2

--------Msr2

-------- Lr Msr+

=

Msr Msr

cos 23

------+ cos 23

------ cos

23

------ cos cos 23

------+ cos

23

------+ cos 23

------ cos cos

=

Lm32---Msr=

Jdmdt

---------- Tem TL=

40 Power Circ

For a symmetrical squirrel-cage induction machine, the steady state equivalent circuit isshown below. In the figure, s is the slip.

ExThpothr

Thloa

Tem P iabc s,T d

d------ Msr iabc r, =

Rs RrLs Lruit Components

ample: A VSI Induction Motor Drive System e figure below shows an open-loop induction motor drive system. The motor has 6les and is fed by a voltage source inverter with sinusoidal PWM. The dc bus is fedough a diode bridge.

e simulation waveforms of the mechanical speed (in rpm), developed torque Tem andd torque Tload, and 3-phase input currents show the start-up transient.

Lm Rr(1-s)/s

InductionMotorBridge

Diode

VSI

SpeedSensor

TorqueSensor

SPWM

Speed

Tem

Tload

3-phase currents

2.6.1.3 Induction Machine with SaturationTwo models of induction machines with saturation are provided:

- 3-phase squirrel-cage induction machine (INDM3_S_NON)

- 3-phase wound-rotor induction machine (INDM3_WR_NON)

Im

At

P

R

L

R

L

N

N

M

T

M

I Motor Drive Module 41

ages:

tributes:


s (stator) Stator winding resistance, in Ohm

s (stator) Stator winding leakage inductance, in H

r (rotor) Rotor winding resistance, in Ohm

r (rotor) Rotor winding leakage inductance, in H

s/Nr Turns Ratio Stator and rotor winding turns ratio (for wound-rotor machine only)

o. of Poles Number of poles P of the machine (an even integer)


orque Flag Flag for internal torque (Tem) output. When the flag is set to 1, the output of the internal torque is requested.


m v.s. Lm (Im1,Lm1) ... Characteristics of the magnetizing current Im versus the magnetizing inductance [(Im1,Lm1) (Im2,Lm2) ...]

as+as-bs+bs-cs+cs-

as+as-bs+bs-cs+cs-

ar+ br+ cr+ar- br- cr-

INDM3_WR_LININDM3_S_LIN

42 Power Circ

All the parameters are referred to the stator side.

The operation of a 3-phase induction machine with saturation is described by thefollowing equations:

wh

In cu

2.6.1.4 BA wipe

Th

vabc s, Rs iabc s, Lsddt----- iabc s,

ddt----- abc s,++=

uit Components

ere

this case, the inductance Msr is no longer constant, but a function of the magnetizingrrent Im.

rushless DC Machine3-phase brushless dc machine is a type of permanent magnet synchronous machineth trapezoidal waveform back emf. It has 3-phase windings on the stator, andrmanent magnet on the rotor.

e image and parameters of the 3-phase brushless dc machine are shown as follows.

vabc r, Rr iabc r, Lrddt----- iabc r, ddt----- abc r,++=

abc s, Msr

1 12--- 1

2---

12--- 1 1

2---

12--- 1

2--- 1

iabc s, Msr+

cos 23

------+ cos 23

------ cos

23

------ cos cos 23

------+ cos

23

------+ cos 23

------ cos cos

iabc r,=

abc s, Msr

cos 23

------ cos 23

------+ cos

23

------+ cos cos 23

------ cos

23

------ cos 23

------+ cos cos

iabc s, Msr+1 1

2--- 1

2---

12--- 1 1

2---

12--- 1

2--- 1

iabc r,=

Image:

At

P

R

L

M

V

V

N

M

M

BDCM3

a

b Shaft Node Motor Drive Module 43

tributes:


(stator resistance) Stator phase resistance R, in Ohm

(stator self ind.) Stator phase self inductance L, in H

(stator mutual ind.) Stator mutual inductance M, in HThe mutual inductance M is a negative value. Depending on the winding structure, the ratio between M and the stator self inductance L is normally between -1/3 and -1/2. If M is unknown, a reasonable value of M equal to -0.4*L can be used as the default value.

pk / krpm Peak line-to-line back emf constant, in V/krpm (mechanical speed)

rms / krpm RMS line-to-line back emf constant, in V/krpm (mechanical speed).The values of Vpk/krpm and Vrms/krpm should be available from the machine data sheet. If these values are not available, they can be obtained through experiments by operating the machine as a generator at 1000 rpm and measuring the peak and rms values of the line-to-line voltage.

o. of Poles P Number of poles P


ech. Time Constant Mechanical time constant mech

c

sa sb sc6-pulse Hall Effect Position Sensor

n

44 Power Circ

ThterNosha

NoPhanco

Th


theta_0 (deg.) Initial rotor angle r, in electrical deg.The initial rotor angle is the rotor angle at t=0. The zero rotor angle position is defined as the position where Phase A back emf crosses zero (from negative to positive) under a

t

CW

T

Muit Components

e node assignments of the image are: Nodes a, b, and c are the stator windingminals for Phase A, B, and C, respectively. The stator windings are Y connected, andde n is the neutral point. The shaft node is the connecting terminal for the mechanicalft. They are all power nodes and should be connected to the power circuit.

de sa, sb, and sc are the outputs of the built-in 6-pulse hall effect position sensors forase A, B, and C, respectively. The sensor output is a bipolar commutation pulse (1, 0,d -1). The sensor output nodes are all control nodes and should be connected to thentrol circuit.

e equations of the 3-phase brushless dc machine are:

positive rotation speed.

heta_advance (deg.) Position sensor advance angle advance, in electrical deg.The advance angle is defined as the angle difference between the turn-on angle of Phase A upper switch and 30o in an 120o conduction mode. For example, if Phase A is turned on at 25o, the advance angle will be 5o (i.e. 30 - 25 = 5).

onduction Pulse idth

Position sensor conduction pulse width, in electrical deg.Positive conduction pulse can turn on the upper switch and negative pulse can turn on the lower switch in a full bridge inverter. The conduction pulse width is 120 electrical deg. for 120o conduction mode.

orque Flag Output flag for internal developed torque Tem (1: output; 0: no output)

aster/Slave Flag Flag for the master/slave mode (1: master; 0: slave).The flag defines the mode of operation for the machine. Refer to Section 2.6.1.1 for detailed explanation.

va R ia L M( ) diadt------- Ea++=

where va, vb, and vc are the phase voltages, ia, ib, and ic are the phase currents, R, L, andM an

Thele

Thideis

wh

an

Th

Th

vb R ib L M( ) dibdt------- Eb++=

vc R ic L M( ) dicdt------- Ec++=

Kp Motor Drive Module 45

are the stator phase resistance, self inductance, and mutual inductance, and Ea, Eb,d Ec are the back emf of Phase A, B, and C, respectively.

e back emf voltages are a function of the rotor mechanical speed m and the rotorctrical angle r, that is:

e coefficients ke_a, ke_b, and ke_c are dependent on the rotor angle r. In this model, anal trapezoidal waveform profile is assumed, as shown below for Phase A. Also shown

the Phase A current.

ere Kpk is the peak trapezoidal value, in V/(rad./sec.), which is defined as:

. Given the values of Vpk/krpm and Vrms/krpm, the

gle is determined automatically in PSIM. e developed torque of the machine is:

e mechanical equations are:

Ea ke_a m=

Eb ke_b m=

Ec ke_c m=

r

ke_a

Kpk

-Kpk

180o

360o

ia

kVpk krpm

2------------------------- 1

1000 2 60---------------------------------=

Tem Ea ia Eb ib Ec ic++( ) m=

46 Power Circ

where B is a coefficient, Tload is the load torque, and P is the no. of poles. Thecoco

MoA ma

Thwhtheis usicloimbrumo

Thmamashaof wh

ExThbysen

Thde

Jdmdt

---------- Tem B m Tload=

drdt

-------- P2--- m=uit Components

efficient B is calculated from the moment of inertia J and the mechanical timenstant mech as below:

re Explanation on the Hall Effect Sensor:hall effect position sensor consists of a set of hall switches and a set of triggergnets.

e hall switch is a semiconductor switch (e.g. MOSFET or BJT) that opens or closesen the magnetic field is higher or lower than a certain threshold value. It is based on hall effect, which generates an emf proportional to the flux-density when the switchcarrying a current supplied by an external source. It is common to detect the emfng a signal conditioning circuit integrated with the hall switch or mounted verysely to it. This provides a TTL-compatible pulse with sharp edges and high noisemunity for connection to the controller via a screened cable. For a three-phaseshless dc motor, three hall switches are spaced 120 electrical deg. apart and areunted on the stator frame.

e set of trigger magnets can be a separate set of magnets, or it can use the rotorgnets of the brushless motor. If the trigger magnets are separate, they should have thetched pole spacing (with respect to the rotor magnets), and should be mounted on theft in close proximity to the hall switches. If the trigger magnets use the rotor magnetsthe machine, the hall switches must be mounted close enough to the rotor magnets,ere they can be energized by the leakage flux at the appropriate rotor positions.

ample: Start-Up of an Open-Loop Brushless DC Motor e figure below shows an open-loop brushless dc motor drive system. The motor is fed a 3-phase voltage source inverter. The outputs of the motor hall effect positionsors are used as the gatings signals for the inverter, resulting a 6-pulse operation.

e simulation waveforms show the start-up transient of the mechanical speed (in rpm),veloped torque Tem, and 3-phase input currents.

B Jmech------------=

ExThspethipu

ThPhpu

Brushless DC Motor Motor Drive Module 47

ample: Brushless DC Motor with Speed Feedbacke figure below shows a brushless dc motor drive system with speed feedback. Theed control is achieved by modulating sensor commutation pulses (Vgs for Phase A in

s case) with another high-frequency pulses (Vgfb for Phase A). The high-frequencylse is generated from a dc current feedback loop.

e simulation waveforms show the reference and actual mechanical speed (in rpm),ase A current, and signals Vgs and Vgfb. Note that Vgfb is divided by half for displayrpose.

Speed

Tem

3-phase currents

Brushless DC Motor

Speed

Phase A current

VgsVgfb/2

48 Power Circ

2.6.1.5 Synchronous Machine with External ExcitationThe structure of a conventional synchronous machine consists of three stator windings,one field winding on either a salient or cylindrical rotor, and an optional dampingwinding on the rotor.

Depending on the way the internal model interfaces with the external stator circuitry,thethetypsuiexthethista

Th

Im

At

P

R

L

L

L

R

Luit Components

re are two types of interface: one is the voltage-type interface (model SYNM3), and other is the current-type interface (model SYNM3_I). The model for the voltage-e interface consists of controlled voltage sources on the stator side, and this model istable in situations where the machine operates as a generator and/or the statorternal circuit is in series with inductive branches. On the other hand, The model for current-type interface consists of controlled current sources on the stator side, ands model is suitable in situations where the machine operates as a motor and/or thetor external circuit is in parallel with capacitive branches.

e image and parameters of the machine are shown as follows.

age:

tributes:


s (stator) Stator winding resistance, in Ohm

s (stator) Stator leakage inductance, in H

dm (d-axis mag. ind.) d-axis magnetizing inductance, in H

qm (q-axis mag. ind.) q-axis magnetizing inductance, in H.

f (field) Field winding resistance, in Ohm

fl (field leakage ind.) Field winding leakage inductance, in H

SYNM3 / SYNM3_I

a

b

c

Shaft Node

n

field-field+

Al

Th

wh

an

an


Rdr (damping cage) Rotor damping cage d-axis resistance, in Ohm

Ldrl (damping cage) Rotor damping cage d-axis leakage inductance, in H

Rqr (damping cage) Rotor damping cage q-axis resistance, in Ohm

L

N

N

M

T

M Motor Drive Module 49

l the parameters are referred to the stator side.

e equations of the synchronous machine can be expressed as follows:

ere

d [] = [L]*[I]. The inductance matrix is defined as follows:

d

qrl (damping cage) Rotor damping cage q-axis leakage inductance, in H

s/Nf (effective) Stator-field winding effective turns ratio

umber of Poles P Number of Poles P


orque Flag Output flag for internal developed torque Tem

aster/Slave Flag Flag for the master/slave mode (1: master; 0: slave).

V R Iddt----- +=

V va vb vc vf 0 0T

= I ia ib ic if idr iqrT

=

R diag Rs Rs Rs Rf Rdr Rqr= a b c f dr qrT

=

LL11 L12

L12T

L22

=

50 Power Circ

wh

Th

Th

2.6.1.6 PA anbru

Th

L11

Ls Lo L2 2r( )cos+ + Lo2----- L2 2r23

------ cos+Lo2----- L2 2r 23------+

cos+Lo2----- L2 2r 23------

cos+ Ls Lo L2 2r 23------+ cos+ + Lo

2----- L2 2r( )cos+

Lo 2 Lo 2

=uit Components

ere r is the rotor angle. e developed torque can be expressed as:


ermanent Magnet Synchronous Machine3-phase permanent magnet synchronous machine has 3-phase windings on the stator,d permanent magnet on the rotor. The difference between this machine and theshless dc machine is that the machine back emf is sinusoidal.


2----- L2 2r 3------+ cos+ 2----- L2 2r( )cos+ Ls Lo L2 2r 3------ cos+ +

L12

Lsf 2r( )cos Lsd 2r( )cos L sq 2r( )sinLsf 2r 23------

cos Lsd 2r 23------ cos L sq 2r 23------

sin

Lsf 2r 23------+ cos Lsd 2r 23------+

cos L sq 2r 23------+ sin

=

L22

Lf Lfdr 0Lfdr Ldr 0

0 0 Lqr

=

T P2--- I

ddr-------- L I =

Jdmdt

---------- Tem Tload=

drdt

-------- P2--- m=

Image:

At

P

R

L

L

V

N

M

M

T

M

PMSM3

a

b Shaft Node Motor Drive Module 51

tributes:


s (stator resistance) Stator winding resistance, in Ohm

d (d-axis ind.) Stator d-axis inductance, in H

q (q-axis ind.) Stator q-axis inductance, in H.The d-q coordinate is defined such that the d-axis passes through the center of the magnet, and the q-axis is in the middle between two magnets. The q-axis is leading the d-axis.

pk / krpm Peak line-to-line back emf constant, in V/krpm (mechanical speed).The value of Vpk/krpm should be available from the machine data sheet. If this data is not available, it can be obtained through an experiment by operating the machine as a generator at 1000 rpm and measuring the peak line-to-line voltage.



ech. Time Constant Mechanical time constant mechorque Flag Output flag for internal developed torque Tem (1: output; 0:

no output)


c

n

52 Power Circ

The node assignments of the image are: Nodes a, b, and c are the stator windingterminals for Phase a, b, and c, respectively. The stator windings are Y connected, andNode n is the neutral point. The shaft node is the connecting terminal for the mechanicalshaft. They are all power nodes and should be connected to the power circuit.

The equations of the permanent-magnet synchronous machine are:

whanare

wh

wh

Thuit Components

ere va, vb, vc, and ia, ib, and ic, and a, b, c are the stator phase voltages, currents,d flux linkages, respectively, and Rs is the stator phase resistance. The flux linkages further defined as:

ere r is the rotor electrical angle, and pm is a coefficient which is defined as:

ere P is the number of poles.

e stator self and mutual inductances are rotor position dependent, and are defined as:

vavbvc

Rs 0 00 Rs 00 0 Rs

iaibic

ddt-----

abc

+=

abc

Laa Lab LacLba Lbb LbcLca Lcb Lcc

iaibic

pm

r( )cosr 23------

cos

r 23------+ cos

+=

pm 60 Vpk krpm3 P 1000 ---------------------------------------=

Laa Ls Lo L2 2r( )cos+ +=

Lbb Ls Lo L2 2r 23------+ cos+ +=

Lcc Ls Lo L2 2r 23------ cos+ +=

Lab LbaLo2----- L2 2r 23------

cos+= =

where Ls is the stator leakage inductance. The d-axis and q-axis inductances areass

Th

Th

whcoco

Lac LcaLo2----- L2 2r 23------+

cos+= =

Lbc LcbLo2----- L2 2r( )cos+= = Motor Drive Module 53

ociated with the above inductances as follows:

e developed torque can be expressed as:


ere B is a coefficient, Tload is the load torque, and P is the no. of poles. Theefficient B is calculated from the moment of inertia J and the mechanical timenstant mech as below:

Ld Ls32---Lo

32---L2+ +=

Lq Ls32---Lo

32---L2+=

TemP2--- L2 ia ib ic

2r( )sin 2r 23------ sin 2r 23------+

sin

2r 23------ sin 2r 23------+

sin 2r( )sin

2r 23------+ sin 2r( )sin 2r 23------

sin

iaibic

=

P2--- pm ia ib ic

r( )sinr 23------

sin

r 23------+ sin

=

Jdmdt

---------- Tem B m Tload=

drdt

-------- P2--- m=

54 Power Circ

2.6.1.7 Permanent Magnet Synchronous Machine with SaturationA 3-phase PMSM machine with saturation differs from that of a linear 3-phase PMSMmaexfor

Th

Im

At

P

R

L

V

N

M

B Jmech------------=uit Components

chine in that the d-axis and q-axis magnetizing inductances Ldm and Lqm can bepressed as a nonlinear function of the d-axis and q-axis currents in the lookup tablem.


age:

tributes:


s (stator resistance) Stator winding resistance, in Ohm

s (stator leakage ind.) Stator d-axis inductance, in H

pk / krpm Peak line-to-line back emf constant, in V/krpm (mechanical speed).The value of Vpk/krpm should be available from the machine data sheet. If this data is not available, it can be obtained through an experiment by operating the machine as a generator at 1000 rpm and measuring the peak line-to-line voltage.



PMSM3_NON

a

b

c

Shaft Node

n

Thind

whco

Than


Mech. Time Constant Mechanical time constant mech, in sec. It is associated with the friction coefficient B as: B = J / mech.

Ld Lookup Table File File name of the lookup table for Ldm

L

d

T

T


e relationship between the d-axis/q-axis inductances Ld/Lq and the magnetizinguctances Ldm/Lqm is as follows:

ere Ls is the stator leakage inductance. Since Ls is normally very small, Ld can bensidered equivalent to Ldm, and Lq can be considered equivalent to Lqm.

e Transformation Flag defines the transformation convention between the abc framed the dq frame. When the Transformation Flag is 0:

q Lookup Table File File name of the lookup table for Lqm

q Flag Flag for the lookup table. When the flag is 0, Ldm and Lqm are function of Id and Iq. When the flag is 1, Ldm and Lqm are function of the current vector magnitude Im and the angle.

ransformation Flag Flag for the transformation convention (see details below)

orque Flag Output flag for internal developed torque Tem (1: output; 0: no output)


Ld Ls Ldm+=

Lq Ls Lqm+=

IdIq

23---

r( )cos r 23------ cos r 23------+

cos

r( )sin r 23------ sin r 23------+

sin

iaibic

=

Im Id2 Iq

2+=

m 2 Iq Id,( )atan=

56 Power Circ

The current vector angle is in deg., and is from -180o to 180o.

When the Transformation Flag is 1:

Th

Th

whVcCo

If inpto

Thloo

Th4,1-5.7-5.7 0.0

Id 2---r( )cos r 23------

cos r 23------+ cos ia

ib =uit Components

e current vector angle is in deg., and is from 0o to 360o.

e Ldm and Lqm lookup tables have the following format:

m, nVr,1, Vr,2, ..., Vr,mVc,1, Vc,2, ..., Vc,nL1,1, L1,2, ..., L1,nL2,1, L2,2, ..., L2,n... ... ...Lm,1, Lm,2, ..., Lm,n

ere m is the number of rows and n is the number of columns; Vr is the row vector and is the column vector; and Li,j is the Ldm or Lqm inductance value, in H, at Row i andlumn j. Note that Vectors Vr and Vc must be monotonically increasing.

the input is between two points, interpolation is used to calculate the value. If theut is less than the minimum or greater than the maximum value, the input will be setbe the same as the minimum or maximum value.

is PMSM model with saturation can also be used as the linear PMSM model if thekup tables are defined such that Ldm and Lqm are linear function of Id and Iq.

e following shows an example of the lookup table:5155 -4.8990 -4.0825 -3.2660 155 -4.8990 -4.0825 -3.2660 -2.4495 -1.6330 -0.8165 0 0.8165 1.6330 2.4495 3.2660 4.0825 4.8990 5.7155109 0.0109 0.0107 0.0104 0.0102 0.0100 0.0098 0.0098 0.0098 0.0100 0.0102 0.0104 0.0107 0.0109 0.0109

Iq 3 r( )sin r 23------ sin r 23------+

sin ic

Im23--- Id

2 Iq2+=

m 2 Id Iq,( )atan=

0.0109 0.0109 0.0109 0.0106 0.0109 0.0106 0.0105 0.0105 0.0105 0.0106 0.0109 0.0106 0.0109 0.0109 0.0109 0.0109 0.0109 0.0109 0.0109 0.0111 0.0108 0.0106 0.0106 0.0106 0.0108 0.0111 0.0109 0.0109 0.0109 0.0109 0.0110 0.0110 0.0111 0.0110 0.0110 0.0109 0.0108 0.0107 0.0108 0.0109 0.0110 0.0110 0.0111 0.0110 0.0110

2.6.1.8 Switched Reluctance MachineThe model of a 3-phase switched reluctance machine with 6 stator teeth and 4 rotor teethis

Im

At

Th2.6

P

R

I

I

M

T


provided. The images and parameters are shown as follows.

age:

tributes:

e master/slave flag defines the mode of operation for the machine. See Section.1.1 for detailed explanation on how to set the master/slave flag.


esistance Stator phase resistance R, in Ohm

nductance Lmin Minimum phase inductance, in H

nductance Lmax Maximum phase inductance, in H

r Duration of the interval where the inductance increases, in deg.


orque Flag Output flag for internal torque Tem. When the flag is set to 1, the output of the internal torque is requested.


SRM3

a+

b+

c+

a-

b-

c-

c1 c2c3 c4 c1 c4 c1 c4

Phase a Phase b Phase c

Shaft Node

58 Power Circ

The node assignments are: Nodes a+, a-, b+, b-, and c+, c- are the stator windingterminals for Phase a, b, and c, respectively. The shaft node is the connecting terminalfor the mechanical shaft. They are all power nodes and should be connected to thepower circuit.

Node c1, c2, c3, and c4 are the control signals for Phase a, b, and c, respectively. Thecontrol signal value is a logic value of either 1 (high) or 0 (low). Node is themeco

Th

whphthe

Thousta

If

weuit Components

chanical rotor angle. They are all control nodes and should be connected to thentrol circuit.

e equation of the switched reluctance machine for one phase is:

ere v is the phase voltage, i is the phase current, R is the phase resistance, and L is thease inductance. The phase inductance L is a function of the rotor angle , as shown in following figure.

e rotor angle is defined such that, when the stator and the rotor teeth are completelyt of alignment, = 0. The value of the inductance can be in either rising stage, flat-topge, falling stage, or flat-bottom stage.

we define the constant k as:

can express the inductance L as a function of the rotor angle :L = Lmin + k [rising stage. Control signal c1=1)L = Lmax [flat-top stage. Control signal c2=1)

L = Lmax - k [falling stage. Control signal c3=1)

v i R d L i( )dt

-----------------+=

r

Lmin

Lmax

L Rising Flat-Top Falling Flat-Bottom

kLmax Lmin

---------------------------=

L = Lmin [flat-bottom stage. Control signal c4=1)

The selection of the operating state is done through control signals c1, c2, c3, and c4which are applied externally. For example, when c1 in Phase a is high (1), the risingstage is selected and Phase a inductance will be: L = Lmin + k . Note that only one andat least one control signal out of c1, c2, c3, and c4 in one phase must be high (1).

Th

Ba

No

2.6.2 MSepo

2.6.2.1 CTh

Im Motor Drive Module 59

e developed torque of the machine per phase is:

sed on the inductance expression, we have the developed torque in each stage as:

Tem = i2*k / 2 [rising stage]

Tem = 0 [flat-top stage]

Tem = - i2*k / 2 [falling stage]

Tem = 0 [flat-bottom stage]

te that saturation is not considered in this model.

echanical Loadsveral mechanical load models are provided in PSIM: constant-torque, constant-wer, constant-speed, and general-type load.

onstant-Torque Loade image of a constant-torque load is:

age:

Tem12--- i2 dLd------ =

MLOAD_T

60 Power Circ

Attributes:

If aloOtex

A

Th

2.6.2.2 CTh

Im

At

Th


Constant Torque Torque constant Tconst, in N*m

Moment of Inertia Moment of inertia of the load, in kg*m2

P

M

B

Muit Components

the reference direction of a mechanical system enters the dotted terminal, the load isng the reference direction, and the loading torque to the master machine is Tconst.herwise the loading torque will be -Tconst. See Section 2.6.1.1 for more detailedplanation on the reference direction.

constant-torque load is expressed as:

e torque does not depend on the speed direction.

onstant-Power Loade image of a constant-power load is:

age:

tributes:

e torque-speed curve of a constant-power load is shown below:


aximum Torque Maximum torque Tmax of the load, in N*m

ase Speed Base speed nbase of the load, in rpm

oment of Inertia Moment of inertia of the load, in kg*m2

TL Tconst=

MLOAD_P

WW

wh

2.6.2.3 CTh

Im

At

A spe

P

C

M

Tmax

Torque

(N*m) Motor Drive Module 61

hen the mechanical speed is less than the base speed nbase, the load torque is:

hen the mechanical speed is above the base speed, the load torque is:

ere P = Tmax*base and base = 2nbase/60. The mechanical speed m is in rad./sec.

onstant-Speed Loade image of a constant-torque load is:

age:

tributes:

constant-speed mechanical load defines the speed of a mechanical system, and theed will remain constant, as defined by the speed constant.


onstant Speed (rpm) Speed constant, in rpm


Speed (rpm)0 nbase

TL Tmax=

TLP

m----------=

MLOAD_WM

62 Power Circ

2.6.2.4 General-Type LoadThe image of a general-type mechanical load is as follows.

Image:

At

A

wh

No

2.6.3 GeTh

Im

P

T

k

k

k

M

MLOADuit Components

tributes:

general-type load is expressed as:

ere m is the mechanical speed in rad./sec. te that the torque of the general-type load is dependent on the speed direction.

ar Boxe image is a gear box is shown below.

age:


c Constant torque term

1 (coefficient) Coefficient for the linear term

2 (coefficient) Coefficient for the quadratic term

3 (coefficient) Coefficient for the cubic term


TL sign m( ) Tc k1 m k2 m2 k3 m 3+++( )=

GEARBOX

Attribute:

If the numbers of teeth of the first gear and the second gear are n1 and n2, respectively,thege

2.6.4 MThsys

Im

At

SimdeWmemeintex

Lea mmo

wh

Parameter Description

Gear Ratio The gear ratio a

P


gear ratio a is defined as: a = n1 / n2. Let the radius, torque, and speed of these twoars be: r1, r2, T1, T2, 1, and 2, we have: T1 / T2 = r1 / r2 = 2 / 1= a.

echanical-Electrical Interface Blockis block allows users to access the internal equivalent circuit of the mechanicaltem of a machine.

age:

tribute:

ilar to electric machines, the mechanical-electrical interface block can be used tofine the reference direction of a mechanical system through the master/slave flag.hen the interface block is set to the master mode, the reference direction is along thechanical shaft, away from the mechanical node, and towards the rest of thechanica

PSIM User Manual

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