Mathworks SIMPOWERSYSTEMS 5 Reference

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SimPowerSystems™ 5

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SimPowerSystems™ Reference

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Revision History

January 1998 First printing Version 1.0 (Release 10) September 2000 Second printing Revised for Version 2.1 (Release 12) June 2001 Online only Revised for Version 2.2 (Release 12.1) July 2002 Online only Revised for Version 2.3 (Release 13) (Renamed from Power

System Blockset User’s Guide) February 2003 Third printing Revised for Version 3.0 (Release 13SP1) June 2004 Online only Revised for Version 3.1 (Release 14) October 2004 Fourth printing Revised for Version 4.0 (Release 14SP1) March 2005 Online only Revised for Version 4.0.1 (Release 14SP2) May 2005 Online only Revised for Version 4.1 (Release 14SP2+) September 2005 Online only Revised for Version 4.1.1 (Release 14SP3) March 2006 Online only Revised for Version 4.2 (Release 2006a) September 2006 Online only Revised for Version 4.3 (Release 2006b) March 2007 Online only Revised for Version 4.4 (Release 2007a) September 2007 Online only Revised for Version 4.5 (Release 2007b) March 2008 Online only Revised for Version 4.6 (Release 2008a) October 2008 Online only Revised for Version 5.0 (Release 2008b) March 2009 Online only Revised for Version 5.1 (Release 2009a) September 2009 Online only Revised for Version 5.2 (Release 2009b) March 2010 Online only Revised for Version 5.2.1 (Release 2010a)

Block Reference

Electrical Sources ................................. 1-2

Contents

Elements

Power Electronics

Machines

Applications

Electric Drives Flexible AC Transmission Systems (FACTS) Distributed Resources (DR)

Measurements

Extras

Signal Measurem ents Signal and Pulse Sources

Powergui

.......................................... 1-2

................................. 1-5

......................................... 1-5

...................................... 1-7

.................................... 1-7

......................... 1-10

..................................... 1-10

............................................ 1-11

............................. 1-11

........................... 1-11

......................................... 1-13

........... 1-9

Blocks — Alphabetical List

Function Reference

Technical Conventions

International System of Units ....................... A-2

Per Unit

What Is the Per Unit System? Example 1: Three-Phase Transformer Example 2: Asynchronous Machine Base Values for Instantaneous Voltage and Current

Why Use the Per Unit System Instead of the Standard SI

.......................................... A-3

....................... A-3

................. A-5

................... A-6

Waveforms

Units?

..................................... A-8

........................................ A-8

Bibliography

Index

vi Contents

Block Reference

Electrical Sources (p. 1-2) Generate electric signals

Elements (p. 1-2)

Power Electronics (p. 1-5) Machines (p. 1-5) Applications (p. 1-7 ) Access electric drives, F ACTS, and

Measurements (p. 1-10) Current and voltage measurements Extras (p. 1-11) Additional useful blocks, such as

Powergui (p. 1-13) Opens graphical user interface for

Linear and nonlinear circuit elements

Power electronics devices Power machinery models

distributed resources

specialized measurement and control blocks

steady-state analysis of electrical circuits

1 Block Reference

Electrical Sources

Eleme

nts

AC Current Source AC Voltage Source Battery Controlled Current Source Controlled Voltage Source DC Voltage Source Implement DC voltage source Three-Pha

Source

Three-P

Break

Conn

se Programmable Voltage

hase Source

ection Port

Implement sinusoidal current source Implement sinusoidal voltage source Implement generic battery model Implement co Implement c

Implement source wit variatio frequenc

Implement three-phase source with internal R-L impedance

ment circuit breaker opening

Imple

rrent zero crossing

at cu

te Physical Modeling connector

Crea

for subsystem

port

ntrolled current source

ontrolled voltage source

three-phase voltage

h programmable time

nofamplitude,phase,

y, and harmonics

1-2

Distributed Parameter Line Implement N-phase distributed

parameter transmission line model

with lumped losses Ground Grounding Transformer

Linear Transformer

Provide connection to ground

Implement three-phase grounding

transformer providing a neutral in

three-wire system

Implement two- or three-winding

linear transformer

Elements

Multi-Winding Transformer

Implement multi-windin g

transformer with taps Mutual Inductance Implement inductances with mutual

coupling Neutral Implement common node in circuit Parallel RLC Branch Implement parallel RLC branch Parallel RLC Load Implement linear parallel RLC load PI Section Line

Implement single-phase

transmission line with lumped

parameters Saturable Transformer

Implement two- or three-winding

saturable transformer Series RLC Branch Implement series RLC branch Series RLC Load Implement linear series R LC load Surge Arrester

Implement metal-oxide surge

arrester Three-Phase Breaker Implement three-phase circuit

breaker opening at current zero

crossing Three-Phase Dynamic Load Im pleme nt three-phase dynamic

load with active power and reactive

power as function of voltage or

controlled from external input Three-Phase Fault Implement programmable

phase-to-phase and phase-to-ground

fault breaker system Three-Phase Harmonic Filter

Implement four types of three-phase

harmonic filters using RLC

components Three-Phase Mutual Inductance

Z1-Z0

Implement three-phase impedance

with mutual coupling among phases Three-Phase Parallel RLC Branch Implement three-phase parallel RLC

branch

1-3

1 Block Reference

Three-Phase Parallel RLC Load Implement three-phase parallel RLC

load with selectable connection Three-Phase PI Section Line

Three-Phase Series RLC Branch Implement three-phase series RLC

Three-Phase Series RLC Load Implement three-phase series RLC

Three-Phase Transformer (Three Windings)

Three-Phase Transformer (Two Windings)

Three-Phase Transformer 12 Terminals

Three-Phase Transformer Inductance M atrix Type (Three Windings)

Three-Phase Transformer Inductance Matrix Type (Two Windings)

Implement three-phase transmission

line section with lumped parameters

branch

load with selectable connection

Implement three-phase transformer

with configurable winding

connections

Implement three-phase transformer

with configurable winding

connections

Implement three single-phase,

two-winding transformers where all

terminals are accessible

Implement three-phase

three-winding transform er with

configurable winding connections

and core geometry

Implement three-phase two-winding

transformer with configurable

winding connections and core

geometry

1-4

Zigzag Phase-Shifting Transformer Implement zigzag phase-shifting

transformer with configurable

secondary winding connection

Power Electronics

Diode Implement diode model GTO Implement gate turn off (GTO)

Power Electronics

thyristor model

Machines

Ideal Switch IGBT

IGBT/Diode Implements

MOSFET Implement Three-Level Bridge Implement three-level neutral point

Thyristor Implement thyristor model

rsal Bridge

Unive

Asynchronous Machine Model the dynamics of three-phase

Implement ide

Implement in

transistor (

MOSFET and

clamped (NPC) power converter

with selectable topologies and power

switching devices

ment universal power

Imple

rter with selectable topologies

conve

ower electronic devices

and p

asynchronous machine, also known

as induction machine

al switch device

sulated gate bipolar

IGBT)

ideal IGBT, GTO, or

antiparallel diode

MOSFET model

DC Machine Implement wound-field or

permanent magnet DC machine Excitation System Provide excitation system for

synchronous machine and regulate

its terminal voltage in generating

mode

1-5

1 Block Reference

Generic Power System Stabilizer

Hydraulic Turbine and Governor

Machine Measurement Demux

Multiband Power System Stabilizer

Permanent Magnet Synchronous Machine

Simplified Synchronous Machine Model the dynamics of simplified

Single Phase Asynchronous Machine Model the dynamics of single

Steam Turbine and Governor Model the dynamics of speed

Implement generic power system

stabilizer for synchronous machine

Model hydraulic turbine and

proportional-integral-derivative

(PID) governor system

Split measurement signal of machine

models into separate signals

Implement multiband power system

stabilizer

Model the dynamics of three-phase

permanent magnet synchronous

machine with sinusoidal or

trapezoidal back electromotive force

(back EMF)

three-phase s ynchronous machine

phase asynchronous machine with

squirrel-cage rotor

governing system, steam turbine,

and multimass shaft

1-6

Stepper Motor Switched Reluctance Motor Model the dynamics of switched

Synchronous Machine Model the dynamics of three-phase

Implement stepper motor mo de l

reluctance motor

round-rotor or s alient-po le

synchronous machine

Applications

Electric Drives (p. 1-7) AC and D C electric drives models Flexible AC Transmission Systems

(FACTS) (p. 1-9) Distributed R esources (DR) (p. 1-10)

FACTS models

Wind turbine models

Electric Drives

DC Drives (p. 1-7) DC electric drives AC Drives (p. 1-8) AC electric drives Shafts and Speed Reducers (p. 1-8) Shafts and speed reducers Extra Sources (p. 1-9)

DC Drives

Four-Qu

Four-Q Rectif

Four-Quadrant Three-Phase Rectifier DC Drive

adrant Chopper DC Drive

uadrant Single-Phase

ier DC Drive

Extra electrical sources

Impleme

DC drive

Implement single-phase

dual-converter DC drive with

circulating current

Implement three-phase

dual-converter DC drive with

circulating current

nt four-quadrant chopper

One-Quadrant Chopper DC D rive

o-Quadrant Chopper DC Drive

lement one-quadrant chopper

Imp

ck converter topology) DC drive

(bu

Implement two-qua dra n t chopper

(buck-boost converter topology) DC

drive

1-7

1 Block Reference

Two-Quadrant Single-Phase Rectifier DC Drive

Two-Quadrant Three-Phase Rectifier DC Drive

Implement two-quadrant

single-phase rectifier DC drive

Implement two-quadrant

three-phase rectifier DC drive

AC Drives

Brushless DC Motor Drive Implement brushless DC motor

drive using Permanent Magnet

Synchronous Motor (PMSM) with

trapezoidal back electromotive force

(BEMF) DTC Induction M otor Drive Implement direct torque and flux

control (DTC) induction motor drive

model Field-Oriented Control Induction

Motor Drive PM Synchronous Motor Drive

Self-Controlled Synchronous Motor Drive

Implement field-oriented control

(FOC) induction motor drive model

Implement P ermanent Magnet

Synchronous Motor (PMSM) vector

control drive

Implement Self-Controlled

Synchronous Motor Drive

1-8

Six-Step VSI Induction Motor Drive Implement six -ste p inverter fed

Induction Motor Drive Space Vector PWM VSI Induction

Motor Drive

Implement space vector PWM VSI

induction motor drive

Shafts and Speed Reducers

Mechanical Shaft Implement mechanical shaft Speed Reducer

Implement speed reducer

Extra Sources

Applications

Battery Fuel Cell Stack Implement generic hydrogen fuel

Implement generic battery model

cell stack model

Flexible AC Transmission Systems (FACTS)

Power-Electronics Based FACTS (p. 1-9)

Transformers (p. 1-10) Transformer models

Power-Electronics Based FACTS

Static Synchronous Compensator (Phasor Type)

Static Synchronous Series Compensator (Phasor Type)

Static Var Compensator (Phasor Type)

Power-electronics based models

Implement phasor model of

three-phase sta tic synchronous

compensator

Implement phasor model of

three-phase sta tic synchronous

series compensator

Implement phasor model of

three-phase static var compensator Unified Power Flow Controller

(Phasor Type)

Implement phasor model of

three-phase unified power flow

controller

1-9

1 Block Reference

Transformers

Three-Phase OLTC Phase Shifting Transformer Delta-Hexagonal (Phasor Type)

Three-Phase O LTC Regulating Transformer (Phasor Type)

Distributed Resources (DR)

Wind Turbine

Wind Turbine Doubly-Fed Induction Generator (Phasor Type)

Wind Turbine Induction Generator (Phasor Type)

Implement phasor model of

three-phase OLTC phase-shifting

transformer using delta hexagonal

connection

Implement phasor model of

three-phase OLTC regulating

transformer

Implement model of variable pitch

wind turbine

Implement phasor model of variable

speed doubly-fed induction generator

driven by wind turbine

Implement phasor model of

squirrel-cage induction generator

driven by variable pitch wind turbine

Measurements

1-10

Current Measurement Impedance Measurement

Multimeter Measure v oltages and currents

Three-Phase V-I Measurement Measure three-phase currents and

Voltage Measurement Measure voltage in circuit

Measure current in circuit

Measure impedance of circuit as

function of frequency

specified in d i al og boxes of

SimPowerSystems™ blocks

voltages in circuit

Extras

Signal Measurements (p. 1-11) Specialized measurement blocks Signal and Pulse Sources (p. 1-11) Specialized source blocks

Signal Measurements

abc_to_dq0 Transformation Perform Park transformation from

three-phase (abc) reference frame to

dq0 reference frame Active & Reactive Power

dq0_to_abc Transformation Perform Park transformation from

Fourier RMS Measure root mean square (RMS)

Three-Phase Sequence Analyzer

Total Harmonic Distortion Measure total harmonic distortion

Measure active and reactive powers

of voltage-current pair

dq0 reference frame to abc reference

frame

Perform Fourier analysis of signal

value of signal

Measur

and zer

three

(THD)ofsignal

e positive-, negative-, o-sequence components of

-phase signal

Signal and Pulse Sources

PWM Generator Generate pulses for carrier-based

two-level pulse width modulator

(PWM) in converter bridge Synchronized 12-Pulse Generator

Implement synchronized pulse

generator to fire thyristors of

twelve-pulse converter

1-11

1 Block Reference

Synchronized 6-Pulse G enerator

Timer

Implement synchronized pulse

generator to fire thyristors of

six-pulse converter

Generate signal changing at

specified transition tim es

1-12

Powergui

Environment block for

SimPowerSystems models

1-13

1 Block Reference

1-14

Blocks — Alphabetical List

abc_to_dq0 Transformation

Purpose Perform Park transformation from three-phase (abc) reference frame to

dq0 reference frame

Library Extras/Measurements

A discrete version of this block is available in the Extras/Discrete Measurements library.

Description The abc_to_dq0 Transformation block computes the direct axis,

quadratic axis, and zero sequence quantities in a two-axis rotating reference frame for a three-phase sinusoidal signal. The following transformation is used:

2-2

where ω = rotation speed (rad/s) of the rotating frame. The transformation is the same for the case of a three-phase current;

you simply replace the V I

c,Id,Iq

,andI0variables.

a,Vb,Vc,Vd,Vq

,andV0variables with the Ia,Ib,

This transformation is commonly used in three-phase electric machine models, where it is known as a Park tran sf orm a tion [1]. It allows you to eliminate time-varying indu c tances by referring the stator and rotor quantities to a fixed or rotating reference frame. In the case of a synchronous machine, the stator quantities are referred to the ro tor. I

and Iqrepresent the two DC currents flowing in the two equivalent

rotor windings (d winding directly on thesameaxisasthefieldwinding, and q winding on the quadratic axis), producing the same flux as the stator I

,andIccurrents.

a,Ib

You can use this block in a control system to measure the positive-sequence component V

of a set of three-phase voltages or

abc_to_dq0 Transformation

currents. The Vdand Vq(or Idand Iq) then represent the rectangular coordinates of the positive-sequence component.

You can use the Math Function block and the Trigonometric Function block to obtain the modulus and angle of V

Dialog Box and Parameter

Inputs and Outputs

This measure Fourier anal harmonics a

ment system does not introduce any delay, but, unlike the

ysis done in the Sequence Analyzer block, it is sensitive to

nd imbalances.

abc

Connect to the first input the vectorized sinusoidal phase signal to be converted [phase A phase B phase C].

sin_cos

Connect to the second input a vectorized signal containing the [sin(ωt) cos(ωt)] values, where ω is the rotation speed of the reference frame.

dq0

The output is a vectorized signal containing the three sequence components [d q o].

2-3

abc_to_dq0 Transformation

Example The power_3phsignaldq demo uses a Discrete Three-Phase

Programmable Source block to generate a 1 pu, 15 degrees positive sequence voltage. At 0.05 second the positive sequence voltage is increased to 1.5 pu and at 0.1 second an imbalance is introduced by the addition of a 0.3 pu negative sequence component with a phase of -30 degrees. The magnitude and phase of the positive-sequence component areevaluatedintwodifferentways:

• Sequence calculation of phasors using Fourier analysis

• abc-to-dq0 transformation

2-4

Start the simulation and observe the instantaneous signals Vabc (Scope1), the signals returned by the Sequence Analyzer (Scope2), and the abc-to-dq0 transformation (Scope3).

abc_to_dq0 Transformation

2-5

abc_to_dq0 Transformation

2-6

Note tha immune t is a oneHoweve

r, an imbalance produces a ripple at the V1 and Phi1 outputs.

t the Sequence Analyzer, which uses Fourier analysis, is

o harmonics and imbalance. However, its response to a step

cycleramp.Theabc-to-dqotransformation is instantaneous.

abc_to_dq0 Transformation

References [1] Krause, P. C. Analysis of Electric Machinery.NewYork:

McGraw-Hill, 1994, p.135.

See Also dq0_to_abc Transforma tion

2-7

AC Current Source

Purpose Implement sinusoidal current source

Library Electrical Sources

Description The AC Current Source block implements an ideal AC current source.

The positive current direction is indicated by the arrow in the block icon. The generated current I is described by the following relationship:

Negative values are allowed for amplitude and phase. A zero frequency and a 90 degree phase specify a DC current source. You cannot enter a negative frequency; the software returns an error in that case, and the block displays a question mark in the block icon. You can modify the first three block parameters at any time during the simulation.

Dialog Box and Parameters

2-8

Peak a

The p

mplitude

eak amplitude of the generated current, in amperes (A).

AC Current Source

Phase

The phase in degrees (deg). Specify a frequency of 0 and a p hase of 90 degrees to implement a DC current source.

Frequency

The source frequency in hertz (Hz). Specify a frequency of 0 and a phase of 90 degrees to implement a DC current source.

Sample time

The sample period in seconds (s). The default is to a continuous source.

Measurements

Select Current Source block.

Place a Multimeter block in your m ode l to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurement is identified by a label followed by the block name.

Current to measure the current flowing through the AC

0, corresponding

Measurement Label

Current

Isrc:

Example The power_accurrent demo uses two AC Current Source blocks in

parallel to sum two sinusoidal currents in a resistor.

2-9

AC Current Source

See Also Controlled Current Source, M ultimeter

2-10

Active & Reactive Power

Purpose Measure active and reactive pow ers of voltage-current pair

Library Extras/Measurements

A discrete version of this block is available in the Extras/Discrete Measurements library.

Description The Active & Reactive Power block measures the active power P and

reactive power Q associated with a periodic voltage-current pair that can contain harmonics. P and Q are calculated by averaging the V I product with a running average window over one cycle of the fundamental frequency, s o that the powers are evaluated at fundamental frequency.

where T = 1/(fundamental frequency). A current flowing into an RL branch, for example, produces positive

active and reactive powers. As this block uses a running window, one cycle of simulation has to be

completed before the output gives the correct active and reactive powers. The discrete version of this block, a vailable in the Extras/Discrete

Measurements library, allows you to specify the initial input voltage and current (magnitude and phase). For the first cycle of simulation the outputs are held constant using the values specified by the initial input parameters.

2-11

Active & Reactive Power

Dialog Box and Parameters

Fundamental freq uency (Hz)

The fundamental frequency, in hertz, of the instantaneous voltage and current.

Inputs and Outputs

The first input is the instantaneous voltage.

The secon

The outp

d input is the instantaneous current.

ut is a vector [P Q] of the active and reactive powers.

Example The power_transfo demo simulates a three-winding distribution

transformer rated at 75 kVA:14400/120/120 V. The transformer primary winding is connected to a high-voltage source of 14400 Vrms. Two identical inductive loads (20 kW-10 kvar) are connected to the two secondary windings. A third capacitive load (30 kW-20 kvar) is fed at 240 V.

2-12

Active & Reactive Power

Initially, the circuit breaker in series with Load 2 is closed, so that the system is balanced. When the circuit breaker opens, a current starts to flow in the neutral path as a result of the load imbalance.

The active power computed from the primary voltage and current is measured by an Active & Reactive Power block. When the breaker opens, the active power decreases from 70 kW to 50 kW.

2-13

Active & Reactive Power

2-14

AC Voltage Source

Purpose Implement sinusoidal voltage source

Library Electrical Sources

Description The AC Voltage Source block implements an ideal AC voltage source.

The generated voltage U is described by the following relationship:

Negative values are allowed for amplitude and phase. A frequency of 0 and phase equal to 90 degrees specify a DC voltag e source. Negative frequency is not allowed; otherwise the software signals an error, and the block displays a question mark in the block icon.

Dialog Box and Parameters

Peak amplitude

The peak amplitude o f the generated voltage, in volts (V).

Phase

The phase in degrees (deg).

Frequency

The source frequency in hertz (Hz).

2-15

AC Voltage Source

Sample time

The sample period in seconds (s). The default is to a continuous source.

Measurements

Select the AC Voltage Source block.

Voltage tomeasurethevoltageacrosstheterminalsof

Measurement Label

Voltage

Usrc:

Example The power_acvoltage demo uses two AC Voltage Source blocks at

different frequencies connected in series across a resistor. The sum of the two voltages is read by a Voltage Measurement block.

0, corresponding

See Also Controlled Voltage Source, DC Voltage Source, Multimeter

2-16

Asynchronous Machine

Purpose Model the dynamics of three-phase asynchronous machine, also known

as induction machine

Library Machines

Description The Asynchronous Machine block operates in either generator or motor

mode. The mode of operation is dictated by the sign of the mechanical torque:

• If Tm is positive, the machine acts as a motor.

• If Tm is negative, the machine acts as a generator.

The electrical part of the machine is represented by a fourth-order state-space model and the mechanical part by a second-order system. All electrical variables and parameters are referred to the stator. This is indicated by the prime signs in the machine equations given below. All stator and rotor quantities are in the arbitrary two-axis reference frame (dq frame). The subs cripts used are defined as follows:

Subscript Definition

d d axis quantity q r s

l Leakage inductance m

qaxisquantity Rotor quantity Stator quantity

Magnetizing inductance

2-17

Asynchronous Machine

Electrical System

2-18

Mechanical System

The Asynchronous Machine block parameters are defined as follows (all quantities are referred to the stator):

Parameter Definition

Rs,L R’r,L’ L

Ls,L’

Stator resistance and leakage inductance Rotor resistance and leakage inductance Magnetizing inductance Total stator and rotor inductances

Parameter Definition

Asynchronous Machine

Vqs,i V’qr,i’ Vds,i V’dr,i’

ϕqs, ϕ ϕ’qr, ϕ’

q axis stator voltage and current q axis rotor voltage and current d axis stator voltage and current d axis rotor voltage and current Stator q and d axis fluxes Rotorqanddaxisfluxes Angular velocity of the rotor Rotor angular position Number of pole pairs Electrical angular velocity (ωmxp) Electrical rotor angular position (Θmxp) Electromagnetic torque Shaft mechanical torque Combined rotor and load inertia coefficient. Set

to infinite to simulate locked rotor. Combined rotor and load inertia constant. Set to

infinite to simulate locked rotor. Combined rotor and load viscous friction

coefficient

Dialog Box and Parameters

You can choose between two Asynchronous M achine blocks to specify the electrical and mechanical parameters of the model, by using the pu Units dialog box or the SI dialog box. Both blocks are modeling the same asynchronous machine model. Depending on the dialog box y ou choose to use, SimPowerSystems software automatically converts the parameters you enter into per unit parameters. The Simulink

model of

the Asynchronous Machine block uses pu parameters.

2-19

Asynchronous Machine

Configuration Tab

2-20

Preset model

Provides a set of predetermined electrical and mechanical parameters for various asynchronous machine ratings of power (HP), phase-to-phase voltage (V), frequency (Hz), and rated speed (rpm).

Select one of the preset models to load the corresponding electrical and mechanical parameters in the entries of the dialog box. Note that the preset models do not include predetermined saturation parameters. Select preset model, or if you want to modify some of the parameters of a preset model, as des cribed below.

No if you do not want to use a

Asynchronous Machine

When you select a preset model, the e lectrical and mechanical parameters in the Parameters tab of the dialog box become unmodifiable (grayed out). To start from a given preset model and thenmodifymachineparameters,youhavetodothefollowing:

1 Select the desired preset model to initialize the parameters. 2 Change the Preset model parameter value to No.Thiswillnot

change the machine parameters. By doing so, you just break the connection w ith the particular preset model.

3 Modify the machine parameters as you wish, then click Apply.

Mechanical input

Allows you to select either the torque applied to the shaft or the rotor speed as the Simulink signal applied to the block’s input.

Select Torque Tm to specify a torque input, in N.m or in pu, and change labeling of the block’s input to determined by the machine InertiaJ(orinertiaconstantHforthe pu machine) and by the difference between the applied mechanical torque Tm and the internal electromagnetic torque Te. The sign convention for the mechanical torque is the following: when the speed is positive, a positiv e torque signal indicates motor mode and a negative signal indicates generator mode.

Tm. The machine speed is

Select Speed w to specify a speed input, in rad/s or in pu, and change labeling of the block’s input to is imposed and the mechanical part of the model (Inertia J) is ignored. Using the spee d as the mechanical input allows modeling a mechanical coupling between two machines and interfacing with SimMechanics™ and SimDriveline™ models.

The next figure indicates how to model a stiff shaft interconnection in a motor-generator set when friction torque is ignored in machine 2. The speed output of machine 1 (motor) is connected to the speed input of machine 2 (generator), while machine 2 electromagnetic torque output Te is applied to the mechanical torque input Tm of machine 1. The Kw factor takes into account

w. The machine speed

2-21

Asynchronous Machine

speed units of both machines (pu or rad/s) and gear box ratio w2/w1. The KT factor takes into account torque units of both machines (pu or N.m) and machine ratings. Also, as the inertia J2 is ignored in machine 2, J2 referred to m achine 1 speed must be added to machine 1 inertia J1.

Rotor type

Specifies the branching for the rotor windings.

2-22

Reference frame

Specifies the reference frame that is used to convert input voltag es (abc reference frame) to the dq reference frame, and output currents (dq reference frame) to the abc reference frame. You can choose among the following reference frame transformations:

•

Rotor (Park transformation) Stationary (Clarke or αβ transformation)

•

Synchronous

•

The following relationships describe the abc-to-dq reference frame transformations applied to the Asynchronous Machine phase-to-phase voltages.

Asynchronous Machine

In the preced reference frame, while

position of the reference frame and the position (electrical) of the rotor. Because the machine windings are connected in a three-wire Y configuration, there is no homopolar (0) component. This also justifies the fact that two line-to-line input voltages are used inside the model instead o f three line-to-neutral voltages. The following relationships describe the dq-to-abc reference frame transformations applied to the Asynchronous Machine phase currents.

The following table shows the values taken by Θ and β in ea ch reference frame (Θ reference frame).

ing equations, Θ is the angular position of the

is the difference between the

is the position of the synchronously rotating

2-23

Asynchronous Machine

Reference Frame

Rotor Stationary Synchronous Θ

The choice of reference frame affects the waveforms of all dq variables. It also affects the simulation speed and in certain cases the accuracy of the results. The following guidelines are suggested in [1]:

• Use the stationary reference frame if the stator voltages are either unbalanced or discontinuous and the rotor voltages are balanced (or 0).

• Use the rotor reference frame if the rotor voltages are either unbalanced or discontinuous and the stator voltages are balanced.

• Use either the stationary or synchronous reference frames if all voltages are balanced and continuous.

-Θ

Θe- Θ

2-24

Mask units

Specifies the units of the electrical and mechanical parameters of the model. This parameter is not modifiable; it is pr ovided for information purposes only.

Parameters Tab

Asynchronous Machine

Nominal power, voltage (line-line), and frequency

The nominal apparent power Pn (VA), RMS line-to-line voltage Vn (V), and frequency fn (Hz).

Stator resistance and inductance

The stator resistance Rs (Ω or pu) and leakage inductance Lls (H or pu).

Rotor resistance and inductance

The rotor resistance Rr’ (Ω or pu) and leakage inductance Llr’ (H or pu), both referred to the stator.

Mutual inductance

The magnetizing inductance Lm (H or pu).

2-25

Asynchronous Machine

Inertia constant, friction factor, and pole pairs

For the SI units dialog box: the combined machine and load inertia coefficient J (kg.m (N.m.s), and pole pairs p. The friction torque Tf is proportional to the rotor speed ω (T f = F.w).

For the pu units dialog box: the inertia constant H (s), combined viscous friction coefficient F (pu), and pole pairs p.

Initial conditions

Specifies the initial slip s, electrical angle Θe (degrees), stator current magnitude (A or pu), and phase angles (degrees):

), combined viscous friction coefficient F

[slip, th, i

as,ibs,ics

,phaseas,phasebs,phasecs]

For the wound-rotor machine, you can also specify optional initial values for the rotor current magnitude (A or pu), and phase angles (degrees):

[slip, th, ias,ibs,ics, phaseas, phasebs, phasecs,iar,ibr,icr,

, phasebr, phasecr]

phase

For the squirrel cage machine, the initial conditions can be computed by the load flow utility in the Powergui block.

Simulate saturation

Specifies whether magnetic saturation of rotor and stator iron is simulated or not.

Saturation parameters

Specifies the no-load s aturation curve parameters. Magnetic saturation of stator and rotor iron (saturation of the mutual flux) is modeled by a nonlinear function (in this case a polynomial) using points of the no-load saturation curve. You must enter a 2-by-n matrix, where n is the number of points taken from the saturation curve. The first row of this matrix contains the values of stator currents, while t he second row contains values of corresponding terminal voltages (stator voltages). The first point

2-26

Asynchronous Machine

(first column of the matrix) must correspond to the point where the effect of saturation begins.

You must select the Simulate saturation check box to simulate saturation. If the Simulate saturation is not selected, the relationship between the stator current and the stator voltage is linear.

Advanced Tab

le time (-1 for inherited)

Samp

ifies the sample time used by the block. To inherit the sample

Spec

specified in the Powergui block, set this parameter to

time

-1.

2-27

Asynchronous Machine

Inputs and Outputs

The Simulink input of the block is the m echanical torque at the machine’s shaft. When the input is a positive Simulink signal, the asynchronous machine behaves as a motor. When the input is a negative signal, the asynchronous machine behaves as a generator.

When you use the SI parameters mask, the input is a signal in N.m, otherwise it is in pu.

The alternative block input (depending on the value of the Mechanical input parameter) is the machine speed, in rad/s.

The Simulink output of the block is a vector containing 21 signals. You can demultiplex these signals by u sing the Bus Selector block provided in the Simulink library. Depending on the type of mask you use, the units are in SI, or in pu.

Signal Definition Units Symbol

1 2 3 4 5 6 7 8 9 10 11

Rotor current ir_a Rotor current ir_b Rotor current ir_c Rotor current iq Rotor current id Rotor flux phir_q Rotor flux phir_d Rotor voltage Vr_q Rotor voltage Vr_d

Aorpu i’ Aorpu i’ Aorpu i’ Aorpu i’ Aorpu i’ V.s or pu V.s or pu Vorpu

Vorpu Stator current is_a A or pu Stator current is_b A or pu

ϕ’ ϕ’

v’ v’ i i

2-28

Asynchronous Machine

Signal Definition Units Symbol

12 13 14 15 16 17 18 19 20 21

Stator current is_c A or pu Stator current is_q A or pu Stator current is_d A or pu Stator flux phis_q Stator flux phis_d Stator voltage vs_q Stator voltage vs_d

V.s or pu V.s or pu Vorpu

Vorpu Rotor speed rad/s Electromagnetic torque Te

N.m or pu T Rotor angle thetam rad

The s tator terminals of the Asynchronous Machine block are identified by the A, B, and C letters. The rotor terminals are identified by the a, b, and c letters. Note that the neutral connections of the stator and rotor windings are not available; three-wire Y connections are assumed.

Limitations 1 The Asynchronous Machine block does not include a representation

of the saturation of leakage fluxes. You must be careful when you connect ideal sources to the machine’s stator. If you choose to supply the stator via a three-phase Y-connected infinite voltage source, you must use three sources connected in Y. However, if you choose to simulate a delta source connection, you must use only tw o sources connected in series.

2-29

Asynchronous Machine

2 When you use Asynchronous Machine blocks in discrete systems, you

might have to use a small parasitic resistive load, connected at the machine terminals, in order to avoid numerical oscillations. Large sample times require larger loads. The minimum resistive load is proportional to the sample time. As a rule of thumb, remember that with a 25 μs time step on a 60 Hz system, the minimum load is approximately 2.5% of the machine nominal power. For example, a 200 MVA asynchronous machine in a power system discretized with a50μssampletimerequiresapproximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 μs, a resistive load of 4 MW should be sufficient.

Examples Example 1: Use of the Asynchronous Machine Block in

Motor Mode

The power_ pwm demo illustrates the use of the Asynchronous Machine block in motor mode. It consists of an asynchronous machine in an open-loop speed control system.

The machine’s rotor is short-circuited, and the stator is fed by a PW M inverter, built with Simulink blocks and interfaced to the Asynchronous Machine block through the Controlled Voltag e Source block. The inverter uses sinusoidal pulse-width modulation, which is described in [2].Thebasefrequencyofthesinusoidal reference wave is set at 60 Hz and the triangular carrier wave’s frequency is set at 1980 Hz. This

2-30

corresponds to a frequency modulation factor m

1980). It is recommended in [2] that m that the value be as high as possible.

be an odd multiple of three and

of 33 (60 Hz x 33 =

Asynchronous Machine

The3HPmachineisconnectedtoaconstant load of nominal value (11.9 N.m). It is started and reaches the set point speed of 1.0 pu at t = 0.9 second.

The parameters of the machine are thos e found in the SI Units dialog box above, except for the stator leakage inductance, which is set to twice its normal value. This is done to simulate a smoothing inductor placed between the inverter and the machine. Also, the stationary reference frame was used to obtain the results shown.

Open the p ower _pwm demo. Note in the simulation parameters that a small relative tolerance is required because of the high switching rate of the inverter.

Run the simulation and observe the machine’s speed and torque.

2-31

Asynchronous Machine

2-32

The first graph shows the machine’s speed going from 0 to 1725 rpm (1.0 pu). The second graph shows the electromag netic torque developed by the machine. Because the stator is fed by a PWM inverter, a noisy torque is observed.

However, this noise is not visible in the spe e d because it is filtered out by the m achine’s inertia, but it can also be seen in the stator and rotor currents, which are observed next.

Asynchronous Machine

Finally, look at the output of the PWM inverter. Because nothing of interest can be seen at the simulation tim e scale, the graph concentrates on the last moments of the simulation.

2-33

Asynchronous Machine

2-34

Example 2: Effect of Saturation of the Asynchronous Machine Block

The power_asm_sat demo illustrates the effect of saturation of the Asynchronous Machine block.

Two identical three-phase motors (50 HP, 460 V, 1800 rpm) are simulated with and without saturation, to observe the saturation effects on the stator currents. Tw o different simulations are realized in the demo.

Asynchronous Machine

The first simulation, is the no-load steady-state test. The table below contains the values of th e Saturation Parameters and the measurements obtained by simulating different operating points on the saturated motor (no-load and in steady-state).

Saturation Parameters Measurements

Vsat (Vrms L-L) Isat (peak A) Vrms L-L Is_A (peak A)

-230 14.04 230 14.03

-322 27.

120 7.322

250 16.86 300 24.04 322 28. 351 35.22

2-35

Asynchronous Machine

Saturation Parameters Measurements

Vsat (Vrms L-L) Isat (peak A) Vrms L-L Is_A (peak A)

-414

-460 72.69 460 73.01

-506 97.98 506 100.9

-552 148.68 552 146.3

-598 215.74 598 216.5

-644 302.98 644 313.2

-690 428.78 690 432.9

53.79

382 43.83 414 426 58.58 449 67.94

472 79.12 488 88.43

519 111.6 535 126.9 546 139.1

569 169.1 581 187.4

620 259.6 633 287.8

659 350 672 383.7 681 407.9

54.21

2-36

Asynchronous Machine

The graph below illustrates these results and shows the accuracy of the saturation model. As you can se e, the measured operating points fit well the curve that is plotted from the Saturation Parameters data.

Running the simulation with a blocked rotor or with many different values of load torque will allow t he observation of other effects of saturation on the stator currents.

References [1] Krause, P.C., O. Wasynczuk, and S.D. Sudhoff, Analysis of Electric

Machinery, IEEE Press, 2002.

2-37

Asynchronous Machine

[2] Mohan, N., T.M. Undeland, and W.P. Robbins, Power Electronics: Converters, Applications, and Design, J ohn Wiley & Sons, Inc., New

York, 1995, Section 8.4.1.

See Also Powergui

2-38

Battery

Purpose Implement generic battery model

Library Electrical Sources, E lectric Drives/Extra Sources

Description The B attery block implements a generic dynamic model parameterized

to represent most popular types of rechargeable batteries. The equivalent circuit of the battery is shown below:

Lead-Acid Model

Discharge model (i* > 0)

Charge Model (i* < 0)

2-39

Battery

Lithium-Ion Model

Discharge Model (i* > 0)

Charge Model (i* < 0)

Nickel-Cadmium and Nickel-Metal-Hydride Model

Discharge Model (i* > 0)

Charge Model (i*< 0)

where,

2-40

= Nonlinear voltage (V)

Batt

=Constantvoltage(V)

Exp(s) = Exponential zone dynamics (V) Sel(s) = Represents the battery mode. Sel(s) = 0 during battery

discharge, Sel(s) = 1 during battery charging.

-1

K = P olarization constant (Ah

) or Polarization resistance (Ohms) i* = Low frequency current dynamics (A) i = Battery current (A) it = Extracted capacity (Ah) Q = Maximum battery capacity (A h) A = Exponential voltage (V) B = Exponential capacity (Ah)

-1

Battery

The parameters of the equivalent circuit can be modified to represent a particular battery type, based on its discharge characteristics. A typical discharge curve is composed of three sections, as shown in the next figure:

The first section represents the exponential voltage drop when the battery is charged. Depending on the battery type, this area is more or less wide. The second section represents the charge that can be extracted from the battery until the voltage drops below the battery nominal voltage. Finally, the third section represents the total discharge of the battery, when the voltage drops rapidly.

When the battery current is negative, the battery will recharge following a charge characteristic as shown below:

2-41

Battery

2-42

Note that the parameters of the model are deduced from discharge characteristics and assumed to be the same for charging.

The E xp(s) transfer function represents the hysteresis phenomenon for the Lead-Acid, NiCD and NiM H batteries during charge and discharge cycles. The exponential voltage increases when battery is charging, no matter the SOC of the battery. When the battery is discharging, the exponential voltage decreases immediately:

Battery

2-43

Battery

Dialog Box and Parameters

Parameters Tab

2-44

Battery type

Provides a set of predetermined charge behavior for four types of battery:

• Lead-Acid

• Lithium-Ion

• Nickel-Cadmium

• Nickel-Metal-Hydride

Nominal Voltage (V)

The nominal voltage (Vnom) of the battery (volts). The nominal voltage represents the end of the linear zone of the discharge characteristics.

Rated Capacity (Ah)

The rated capacity (Qrated) of the battery in ampere-hour. The rated capacity is the minimum effective capacity of the battery.

Initial State-Of-Charge (%)

The initial State-Of-Charge (SOC) of the battery. 100% indicates a fully charged battery and 0% indicates an empty battery. This parameter is used as an initial condition for the simulation and does not affect the discharge curve (when the option Plot Discharge Characteristics is used).

Battery

Use parameters based on Battery type and nominal values

Load the corresponding parameters in the entries of the dialog box, depending on the selected Battery type,theNominal Voltage and the Rated Capacity.

When a preset model is used, the detailed parameters cannot be modified. If you want to modify th e discharge curve, select the desired battery type to load the default parameters, and then uncheck the Use parameters based on Battery type and

nominal values checkbox to access the detailed parameters.

Maximum Capacity (Ah)

The maximum theoretical capacity (Q), when a d isco ntin uity occurs in the battery voltage. This value i s generally equal to 105% of the rated capacity.

Fully charged Voltage (V)

The fully charged voltage (Vfull), for a given discharge current. Note that the fully charged voltage is not the no-load voltage.

2-45

Battery

Nominal Discharge Current (A)

The nominal discharge current, for which the discharge curve has been measured. For example, a typical discharge current for a 1.5 Ah N iMH battery is 20% of the rated capacity: (0.2 *

1.5 Ah / 1h = 0.3A).

Internal Resistance

The internal resistance of the battery (ohms). When a preset model is used, a generic value is loaded, corresponding to 1% of the nominal power (nominal voltage * rated capacity of the battery). The resistance is supposed to be constant during the charge and the discharge cycles and does not v ary with the amplitude of the current.

Capacity (Ah) @ Nominal Voltage

The capacity (Qnom) extracted from the battery until the voltage drops under the nominal voltage. This value should be between Qexp and Qmax.

Exponential zone [Voltage (V), Capacity (Ah)]

The voltage (Vexp)andthecapacity(Qexp) corresponding to the end of the exponential zone. The voltage s ho uld be between Vnom and Vfull. The capacity should be between 0 and Qnom.

2-46

View Discharge Characteristics Tab

Plot Discharge Characteristics

If selected, plots a figure c on tain in g two grap h s . The first graph represents the nominal discharge curve (at the Nominal Discharge Current) and the second graph represents the discharge curves at the specified discharge currents. When the checkbox is active, the graph remains on and updates itself when a parameter changes in the dialog box. To clear the figure, uncheck and close the figure.

Discharge current

Allows to specify different values of discharge current. The discharge characteristics for these currents are presented in the second part of the graph.

Units

Choose either

Time or A mpere-hour as the x-axis for the plot.

Battery Dynamics Tab

Battery

Battery response time (s)

The response time of the battery (at 95% of the final value).

This value represents the voltage dynamics and can be observed when a current step is applied:

2-47

Battery

In this example, a battery response time of 30 secs is used.

2-48

Battery

Extract Battery Parameters From Data Sheets

This section gives an example of detailed parameters e xtracted from the Panasonic NiMH-HHR650D battery data sheet:

From the specification tables, we obtain the rated capacity and the internal resistance. The other detailed parameters are deduced from the Typical Discharge Characteristics plot:

Param

Rated capacity Internal Resistance Nominal Voltage Rated Capacity 6.5 Ah

eter

Value

6.5 A 2mΩ

(a)

1.18 V

2-49

Battery

Parameter Value

Maximum Capacity Fully Charged voltage Nominal Discharge Current Capacity @ Nominal Voltage Exponential Voltage Exponential C apacity

(b)

7 Ah (5.38h * 1.3A)

(c)

(d)

(a)

(e)

1.39 V

1.3 A

6.25 Ah

1.28 V

1.3 Ah

These parameters are approximate and depend on the precision of the points obtained from the d is charg e curve. A tool, called ScanIt (provided by amsterCHEM, http://www.amsterchem.com) can be used to extract values from data sheet curves.

The parameters obtained from the data sheet are entered in the mask of the Battery block as in the following picture:

2-50

Battery

The discharge curves (the dotted line curves in the following plots) obtained with these parameters are similar to the data sheet curves.

2-51

Battery

2-52

Battery

Cells in Series and/or in Parallel

To model a series and/or parallel combination of c ells based o n the parameters of a single cell, the parameter transformation shown in the next figure can be used. The corresponds to the number of cells in series, and to the number of cell in parallel:

Nb_ser variable in mask below

Nb_par corresponds

2-53

Battery

Block Inputs and Outputs

Model Validation

Model Assumptions

The Simulink output of the block is a vector containing three signals. You can demultiplex these signals by using the Bus Selector block provided in the Simulink library.

Signal Definition Units

SOC The State-Of-Charge o f the battery

(between 0 and 100%). The SOC for a fully charged battery is 100% and for an empty battery is 0%. The SOC is calculated as:

Current Voltage The Battery voltage

Experimental validation of the model shown a m aximum error of 5% (when SOC is between 10% and 100%) for charge (current between 0 and 2C) and discharge (current between 0 and 5C) dynamics.

• The internal resistance is supposed constant during the charge and

the discharge cycles and doesn’t vary with the amplitude of the current.

The Battery current

A V

2-54

• The parameters of the model are deduced from discharge

characteristics and assumed to be the same for charging.

• The capacity of the battery doesn’t change with the amplitude of

current (No Peukert effect).

• The model doesn’t take the temperature into account.

• The Self-Discharge of the battery is not represented. It can be

represented by adding a large resistance in parallel with the battery terminals.

Battery

• The battery has no memory effect.

Limitations • The minimum no-load battery voltage is 0 volt and the maximum

battery voltage is equal to 2*E0.

• The minimum capacity of the battery is 0 Ah and the maximum capacity is Qmax.

Example The power_bat tery demo illustrates a 200 volts, 6.5 Ah NiMH battery

connected to a constant load of 50 A. The DC machine is connected in parallel with the load and operates at no load torque. When the State-Of-Charge (SOC) of the battery goes under 0.4 (40%), a negative load torque of 200 Nm is applied to the machine so it acts as a generator to recharge the battery. When the SOC goes over 80%, the load torque is removed so only the battery supplies the 50 amps load .

The simulation produces the followings results:

2-55

Battery

The battery is discharged by the constant DC load of 50 A. When the SOC drops under 0.4, a mechanical torque of -200 Nm is applied so the machine acts as a generator and provides a current of 100 amps. Hence, 50 amps goes to the load and 50 amps goes to recharge the battery. When the SOC g oes over 0.8, the mechanical torque is removed and the machine operates freely. And then the cycle restarts.

References [1]C.M.Shepherd,"DesignofPrimary and Secondary Cells - Part 2.

An equation describing battery discharge," Journal of Electrochemical Society, Volume 112, Jul. 1965, pp. 657-664

[2] Tremblay, O.; Dessaint, L.-A.; Dekkiche,A.-I.,"AGenericBattery Model for the Dynamic Simulation of Hybrid Electric Vehicles," Vehicle Power and Propulsion Conference, 2007. VPPC 2007. IEEE 9-12 Sept. 2007, pp. 284-289

2-56

Breaker

Purpose Implement circuit breaker opening at current zero crossing

Library Elements

Description The Breaker block implements a circuit breaker where the opening and

closing times can be controlled either from an external Simulink signal (external control mode), or from an internal control timer (internal control mode).

A series Rs-Cs snubber circuit is included in the model. It can be connected to the circuit breaker. If the Breaker block happens to be in series with an inductive circuit, an open circuit or a current source, you must use a snubber.

When the Breaker block is set in external control m ode , a Simulink input appears on the block icon. The control signal connected to the Simulink input must be either 0 or 1 (0 to open the breaker, 1 to close it).

When the Breaker block is set in internal control mode, the switching times are specified in the dialog box of the block.

When the breaker is closed, it is represented by a resistance Ron. The Ron value can b e set as small as neces sary in order to be negligible compared with external components (a typical value is 10 mohms). When the breaker is open, it has an infinite resistance.

The arc extinction process is simulated by opening the breaker device when its current passes through 0 at the first current zero crossing following the transition of the Simulink control input from 1 to 0.

Operation Conditions

The Breaker closes when

The Breaker opens when

Control signal goes to 1 (for discrete systems, control signal must stay at 1 for at least 3 times the sampling period)

Control signal goes to 0 Breaker current passes through 0

2-57

Breaker

Dialog Box and Parameters

Note The Breaker block may not be the appropriate switching device to

use for DC circuits. For such applications, it is recommende d t hat you use the Ideal Switch block as a switching device.

2-58

Breaker r esistance Ron

The internal breaker resistance, in ohms (Ω). The Break er resistance Ron parameter cannot be set to 0.

Initial state

The initial state of the breaker. A closed contact is displayed in the block icon when the Initial state parameter is set to an open contact is displayed when it is set to

1,and

If the breaker initial state is set to 1 (closed), the software automatically initializes all the states of the linear circuit and the Breaker block initial current, so that the simulation starts in steady state.

Snubber resistance Rs

The snubber resistance, in ohms (Ω). Set the Snubber resistance Rs pa ra m eter to

Snubber capacitance Cs

The snubber capacitance, in farads (F). Set the Snubber capacitance Cs parameter to

inf to get a resistive snubber.

Switching times

Specifies the vector of switchin g times when using the Bre ak er block in internal control m ode. At each switching time the Breaker block opens or closes depending on its initial state. For example, if the Initial state parameter is closes at the first switching time, opens at the second switchin g time, and so on. The Switching times para m eter is not visible in the dialog box if the External control of switching times parameter is selected.

inf to eliminate the snubber from the model.

0 to eliminate the snubber, or to

0 (open), the breaker

Breaker

External control of switching times

If selected, adds a Simulink input to the Breaker block for external control of the switching times of the breaker. The switching times are defined by a logical signal ( to the Simulink input.

Measurements

Select block terminals.

Select the Breaker block. If the snubber device is connected to the breaker model, the measured current is the one flowing through the breaker contacts only.

Branch voltage to measure the voltage across the B reaker

Branch current to measure the current flowing through

0 or 1) connected

2-59

Breaker

Select Branch voltage and current to measure the breaker voltage and the breaker current.

Place a Multimeter block in your m ode l to display the selected measurements during the simulation.

In the Available Measurements list box of the Multimeter block, the measurement is ide ntified by a label followed by the block name:

Measurement Label

Branch voltage Branch current

Limitations When the b lock is connected in s eries with an inductor or another

current source, y ou must add the snubber circuit. In most applications you can use a resistive snubber (Snubber capacitance parameter set to

inf) with a large resistor value (Snubber resistance para m eter set

1e6 or so). Because of modeling constraints, the internal breaker

inductance Ron cannot be set to 0.

Ub:

Ib:

You must use a stiff integration a lg orithm to simulate circuits with the Breaker block. best simulation spe ed.

For discretized models, the control signal must stay at 1 for a minimum of 3 sampling time periods to correctly close the Breaker block, otherwise the device stays open.

ode23tb with default parameters usually gives the

Example The power_breaker demo illustrates a circuit breaker connected in

series with a series RL circuit on a 60 Hz voltage source. The switching times of the Breaker block are controlled by a Simulink signal. The breaker device is initially closed and an opening order is given at t =

1.5 cycles, when current reaches a maximum. The current stops at

2-60

Breaker

the next zero crossing, then the breaker is reclosed at a zero crossing of voltage at t = 3 cycles.

Simulation produces the following re sults.

2-61

Breaker

Note that the breaker device opens only when the load current has reached zero, after the opening order.

3 HP Drive Specifications

Drive Input Voltage

Amplitude Frequency 60 Hz

Motor Nominal Values

Power Speed Voltage 300 Vdc

220 V

3hp 1650 rpm

Example The ac7_example demo illustrates an AC7 motor drive simulation with

standard load condition. At time t = 0 s, the speed set point is 300 rpm.

2-77

Brushless DC Motor Drive

There are two design tools in this example. The first block calculates the gains of the speed regulator in accordance with your specifications. The second block plots the operating regions of the drive. Open these blocks for more information.

As shown in the following figure, the speed precisely follows the acceleration ramp. At t = 0.5 s, the nominal load torque is applied to the motor. At t = 1 s, the speed set point is changed to 0 rpm. The speed decreases to 0 rpm. At t = 1.5 s., the mechanical load passes from11N.mto-11N.m. Thenextfigureshowstheresultsforthe detailed converter and for the average-value converter. Observe that the average voltage, current, torque, and speed values are identical for both models. Notice that the higher frequency signal components are not represented with the average-value converter.

2-78

AC7 Example Waveforms (Blue: Detailed Converter, Red: Average-Value Converter)

Brushless DC Motor Drive

References [1] Bose, B. K., Modern Power Electronics and AC Drives,Prentice-Hall,

N.J., 2002. [2] Krause, P. C., Analysis of E lectric Machinery, McGraw-Hill, 1986. [3] Tremblay, O., Modélisation, simulation et commande de la machine

synchrone à aimants à force contre-électromotrice trapézoïdale,École de Technologie Supérieure, 2006.

2-79

Connection Port

Purpose Create Physical Modeling connector port for subsystem

Library Elements

Description The Connection Port block, placed inside a subsystem composed of

SimPowerSystems blocks, creates a Physical Modeling open round connector port connection line, the port becomes solid the solid port

You connect individual SimPowerSystems blocks and subsystems made of SimPowerSystems blocks to o ne another with SimPowerSystems connection lines, instead of regular Simulink signal lines. These are anchored at the open, round connector ports of SimPowerSystems blocks automatically have such open round connector ports. You can add additional connector ports by adding Connection Port blocks to your subsystem.

Dialog Box and Parameters

on the boundary of the subsystem. Once connected to a

. O nce you begin the simulation,

becomes a n electrical terminal port, an open square .

. Subsystems constructed

2-80

Port n

Port

umber

ield labels the subsystem connector port created by the

This f

. Multiple connector ports on the boundary of a single

block

ystem require different numbers as labels. The default value

subs

hefirstportis

for t

location on parent subsystem

se which side of the parent subsystem boundary the port is

Choo

ced on. The cho ices are

pla

Left or Rig ht. The default is Left.

Mathworks SIMPOWERSYSTEMS 5 Reference

Specifications and Main Features

Frequently Asked Questions

User Manual

Block Reference

Electrical Sources

Power Electronics

Machines

Applications

Electric Drives

DC Drives

AC Drives

Shafts and Speed Reducers

Extra Sources

Flexible AC Transmission Systems (FACTS)

Power-Electronics Based FACTS

Transformers

Distributed Resources (DR)

Measurements

Extras

Signal Measurements

Signal and Pulse Sources

Powergui

Blocks — Alphabetical List

3 HP Drive Specifications