TechRef_DoublyFed

DIgSILENT PowerFactoryTechnical Reference Documentation

Doubly-Fed Induction MachineElmAsmsc, TypAsmo

DIgSILENT GmbH

Heinrich-Hertz-Str. 972810 - Gomaringen

Germany

T: +49 7072 9168 00F: +49 7072 9168 88

http://[email protected]

r1018

Copyright ©2011, DIgSILENT GmbH. Copyright of this document belongs to DIgSILENT GmbH.No part of this document may be reproduced, copied, or transmitted in any form, by any meanselectronic or mechanical, without the prior written permission of DIgSILENT GmbH.

Doubly-Fed Induction Machine (ElmAsmsc, TypAsmo) 1

http://www.digsilent.de

mailto:[email protected]

Contents

Contents

1 General Description 3

1.1 Load-Flow Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Short-circuit Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Transient Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Rotor Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Input/Output Definitions of Dynamic Models 6

3 Input Parameter Definitions 9

3.1 Induction Machine type (TypAsmo) . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Induction Machine Element (ElmAsmsc) . . . . . . . . . . . . . . . . . . . . . . . 11


1 General Description


Figure 1.1: Equivalent Circuit of the Doubly-Fed Induction Machine Model

Figure 1.2: Rotor-Side PWM-Converter

The doubly-fed induction generator (DFIG) is a rotor-voltage controlled, slip-ring induction ma-chine. The PWM converter connected to the slip-rings controls the rotor voltage in magnitudeand phase angle, why active and reactive power output of the DFIG can be controlled.

As shown in Figure 1.1, the doubly-fed induction machine model of PowerFactory includes therotor-side converter. Hence, the doubly-fed induction machine is a model with two terminals,an AC and a DC terminal. The induction machine model is identical to the standard inductionmachine model of PowerFactory , including a very detailed approximation of Zrot with up to threeR-L ladder circuits.

The converter according to Figure 1.2 is modelled by a fundamental frequency approach. TheAC- and the DC-voltages are related to each other by the modulation index (Pm) that can bedefined by magnitude and phase angle or in cartesian co-ordinates, by real- and imaginary part:

UACr =

√3

2√2PmrUDC

UACi =

√3

2√2PmiUDC

(1)

The AC rotor-voltage is expressed in a rotor reference frame. It is assumed that the modulationcorresponds to a sinusoidal pulse-width modulation (PWM).

The relationship between AC and DC currents can be found by assuming that the PWM con-verter is loss-less:

PAC = Re(UACI∗AC) = UDCIDC = PDC (2)



If relevant, switching losses can be considered as no-load losses by an equivalent resistanceconnected between the DC-node and ground.

However, the detailed PWM-converter model of PowerFactory integrates no-load losses, why itis recommended to consider all switching losses in the grid-side converter model.

The model is completed by the open-loop rotor voltage. The winding ratio between stator androtor is directly calculated from the open-loop rotor voltage without considering the voltage dropacross the leakage reactance due to no-load currents. Hence, if both parameters are available,the winding ratio and the actually measured nominal rotor voltage, the input parameter Urot“rated slip ring voltage” should be calculated from the winding ratio.

1.1 Load-Flow Calculation

For load flow analysis, active and -reactive power and the steady state slip have to be specified.All other variables, including the corresponding modulation index are calculated during the loadflow iteration.

The specified active and reactive power defines the stator active- and reactive power, not thetotal active power of the doubly-fed induction machine.

For many applications, it is useful to specify the power at a different point, e.g. at the HV-side ofa three-winding transformer fed by a DFIG. This is currently not possible but will be implementedin future versions of PowerFactory

1.2 Short-circuit Calculations

Figure 1.3: Short-Circuit Model of the Doubly-Fed Induction Machine

For short circuit analysis, the doubly-fed induction machine is modelled by the subtransientequivalent Protective actions, such as under-voltage tripping or bypassing of the rotor-side con-verter cannot be directly considered in the subtransient model. However, if the rotor bypass isideal, with no additional resistance or reactance, the subtransient model is still correct.

1.3 Harmonic Analysis

For harmonics analysis, the doubly-fed induction machine model is the same as the standardinduction machine model that is based on the subtransient model according to Figure 1.3.



1.4 Transient Simulations

In time domain simulations (RMS- and EMT-simulation) the converter is controlled by the pulsewidth modulation factors Pmd and Pmq. It is important to remember that the AC voltage andhence the complex modulation factor is referred to the actual rotor reference frame and notto the field reference frame. It is therefore necessary to convert the d-q output of a controller(usually expressed in a field reference frame) to the rotor reference frame of the machine.

The model equations of the doubly fed machine can be derived from the normal, single-fedinduction machine equations by modifying the rotor-voltage equations:

us = rsis +dψ

s

ωndt+ j

ωref

ωnψs

uRej(ωR−ωref ]t = RRiR +

dψR

ωndt+ j

ωref − ωR

ωnψ

R

(3)

The per unit rotor voltage that appears in the above equation is related to the DC-voltage asfollows:

uRd =

√3

2√2Pmd

UDC

URnom

uRq =

√3

2√2Pmq

UDC

URnom

(4)

The nominal rotor voltage considers the winding ratio between stator and rotor.

All other equations, including mechanical equations are identical to the standard, single-fedinduction machine model.

In stability analysis (RMS-simulation), stator flux derivatives in the stator voltage equations areneglected, which is analogous to the standard, single-fed induction machine model.

1.4.1 Rotor Protection

For protecting the rotor side PWM-converter against high rotor currents and for avoiding loss ofsynchronism of the rotor-side converter with the network, the rotor can be bypassed during faultconditions.

Since in the current model, there is no specific parameter for bypassing the rotor-side con-verter, the pulse-width modulation factors Pmd and Pmq must be set to (approx.) zero, which isequivalent to bypassing the rotor.

For limiting the rotor current and for influencing the speed-torque characteristic of the machine,the rotor additional bypass-resistance and -reactance can be included. These can be insertedby setting the internal parameters rradd and xradd using “Parameter-Events”.

Additional protection, e.g. protection against under- or over-voltage can be implemented usingstandard PowerFactory relay models.


2 Input/Output Definitions of Dynamic Models


Figure 2.1: Input/Output Definition of Dynamic Models

The following per-unit systems are used:

• Rated Apparent Power, Rated Voltage:

Sr, Vr, Zb =V 2r

Sr

• Rated (Electrical) Active Power:Per = Srcos(ϕr)

• Rated Mechanical Power:Pmr = Perηr

ηr : Rated efficiency

• Rated Mechanical Torque:

Mr =Pmr

ωr=

Pmr

(1− sr)ωn

Sr : Rated slipωn : Nominal electrical angular velocity

• Rated Rotor Voltage, Urot



Table 2.1: Input Variables (signals)

Parameter Symbol/Equ. Description Unitpt Turbine power, (rated tomechanical power p.u.xmdm mm Mechanical Load Torque. (rated to mechanical torque) p.u.rradd Additional rotor resistance p.u.Pmd Pmd d-axis-modulation index (referred to rotor angle)Pmq Pmq q-axis-modulation index (referred to rotor angle)

Table 2.2: Output Variables (signals)

Parameter Symbol/Equ. Description Unitxspeed Mechanical Speed p.u.pgt Electrical Power p.u (rated

electrical activepower)

ird d-axis rotor current (referred to rotor angle) p.u.irq q-axis rotor current (referred to rotor angle) p.u.xphim rotor angle p.u.psis r Stator flux, real part p.u.psis i Stator flux, imaginary part p.u.cosphim cosine of rotor anglesinphim sin of rotor angle

Table 2.3: State Variables (signals)

Parameter Symbol/Equ. Description Unitspeed n Mechanical Speed p.u.phim Electrical Power radpsiA1 r ψ

RFlux of loop A1, real p.u.

psiA1 i ψR

Flux of loop A1, imaginary p.u.psiA2 r ψ

RFlux of loop A2, real p.u.

psiA2 i ψR

Flux of loop A2, imaginary p.u.psiB r ψ

RFlux of loop B, real p.u.

psiB i ψR

Flux of loop B, imaginary p.u.



Table 2.4: Additional Parameters and signals (calculation-parameter)

Parameter Description Unitslip Slip p.u.xme Electrical torque, based on rated mechanical torque p.u.xmem rated mechanical torque p.u.

rated mechanical torquexmt Mechanical Torque, based on rated mechanical torque p.u.xradd Additional rotor reactance p.u.addmt Additional mechanical torque, based on rated p.u.

mechanical torqueccomp Internal capacitance (for compensating reactive p.u.

power mismatch in case of PQ-load flow model)i star i star=1: Star Operation i star=0: Delta Operation p.u.

(used for Star-Delta start-up)usr Rotor Voltage, real part, referred to standard p.u.

reference system and rated rotor voltageusi Rotor Voltage, imaginary part, referred to standard p.u.

reference system and rated rotor voltageurd d-Axis Rotor Voltage, referred to rotor angle and p.u.

rated rotor voltageurq q-Axis Rotor Voltage, referred to rotor angle and p.u.

rated rotor voltageura Slip-Ring Voltage, phase A, referred to rated rotor voltage p.u.urb Slip-Ring Voltage, phase B, referred to rated rotor voltage p.u.urc Slip-Ring Voltage, phase C, referred to rated rotor voltage p.u.ird d-Axis Rotor Current, referred to rotor angle p.u.iq q-Axis Rotor Current, referred to rotor angle p.u.Ira Rotor Current, Phase A kAIrb Rotor Current, Phase B kAIrc Rotor Current, Phase C kAIrot Rotor Current, Instantaneous Phasor Magnitude kA


3 Input Parameter Definitions


3.1 Induction Machine type (TypAsmo)

• All rotor resistances and reactances are expressed in p.u. referred to the stator side.

• Rotor impedances given in Ohm, referred to the stator side have to be divided by the baseimpedance of the machine (Zbase = U2

rated/Srated)



Parameter Description Unitloc name Nameugn Rated Voltage kVsgn Power Rating: Rated Apparent Power kVApgn Power Rating: Rated Mechanical Power kWcosn Rated Power Factoreffic Efficiency at nominal Operation %frequ Nominal Frequency Hzanend Nominal Speed rpmnppol No of Pole Pairsnslty Connectioni cage Rotor Modelaiazn Locked Rotor Current (Ilr/In) p.u.amazn Locked Rotor Torque p.u.rtox R/X Locked Rotoramkzn Torque at Stalling Point p.u.aslkp Slip at Stalling Pointamstl Torque at Saddle Point p.u.asstl Slip at Saddle Pointrstr Stator Resistance Rs p.u.xstr Stator Resistance Xs p.u.xm Mag. Reactance Xm p.u.xmrtr Rotor Leakage Reac. Xrm p.u.i cdisp Operating Cage/Rotor data: Consider Current

Displacement (Squirrel Cage Rotor)rrtrA Operating Cage/Rotor data: Rotor Resistance RrA p.u.xrtrA Operating Cage/Rotor data: Rotor Reactance XrA p.u.rrtrA0 Operating Cage/Rotor data: Slip indep. Resistance RrA0xrtrA0 Operating Cage/Rotor data: Slip indep. Reactance XrA0r0 Operating Cage/Rotor data: Resistance RrA1x0 Operating Cage/Rotor data: Reactance XrA1r1 Operating Cage/Rotor data: Resistance RrA2x1 Operating Cage/Rotor data: Reactance XrA2rrtrB Starting Cage: Rotor Resistance RrB p.u.xrtrB Starting Cage: Rotor Reactance XrB p.u.i trans Consider Transient Parameter p.u.aiaznshc For short-Circuit Analysis: Locked Rotor Current (Ilr/In) p.u.iinrush Inrush Peak Current: Ratio Ip/In p.u.Tinrush Inrush Peak Current: Max. Time sTcold Stall Time: Cold sThot Stall Time: Hot strans Consider Transient Parameterxdssshc For Short-Circuit Analysis: Locked Rotor Reactancertoxshc For Short-Circuit Analysis: R/X Locked Rotorxtorshc For Short-Circuit Analysis: X/R Locked Rotor



3.2 Induction Machine Element (ElmAsmsc)

Parameter Description Unitloc name Nametyp id Type(TypAsmo∗)bus1 Terminal AC (StaCubic)bus1 bar Terminal ACbus2 Terminal DC (StaCubic)bus2 bar Terminal DCoutserv Out of Servicengnum Number of: parallel Machinesi mot Generator/Motorc pmod Modelpgini Active Power MWqgini Reactive Power Mvarslipset Slip %Urot Rated Slip Ring Voltage (open rotor, standstill) Vtstart Starting Time sIcrow Rotor-Bypass Settings: Max Rotor Current kArcrow Rotor-Bypass Settings: Crow-Bar Resistance p.u.xcrow Rotor-Bypass Settings: Crow-Bar Reactance p.u.mdmlp Mechanical Load: Proportional Factor p.u.mdmex Mechanical Load: Exponent


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