Machine Modeling and Power System Study Applications...pscad.com Powered by Manitoba Hydro International Ltd. Simulation setup –Synchronous machine Tm0 D + F + 1.0 w Wref Cv Steam

Machine Modeling and Power System Study Applications

Presented by: Dharshana Muthumuni

pscad.comPowered by Manitoba Hydro International Ltd.

Outline - Machine Modeling and Applications

• Mathematical representation of machine windings and rotor dynamics

• Machine models and controls models available in PSCAD

• Setting up a PSCAD simulation case

o Synchronous machine (initialization of machine and control models)

o Induction machine (starting example)

• Illustration of Simulation examples

o Model setup and data entry and model response

o Model Benchmarking

o Black start restoration studies

o Voltage flicker due to compressor load driven by a synchronous machine

o Sub synchronous resonance and torsional interactions

o Voltage dips due to induction motor starting and mitigation options

o Applications in wind generation (DFIG)


Machine windings and the mathematical representation


Machine windings and the mathematical representation

𝑉 = 𝑅 𝑖 +𝑑

𝑑𝑡([𝐿][𝑖])

Representation of the machine coils and the direction of their magnetic axes


Kd F

if

Vf

VaIa

A

B

C

Kq

𝑽 = 𝑹 𝒊 +𝒅

𝒅𝒕( 𝑳 𝒊 )

𝑳𝒂 = 𝑳𝟏 + 𝑳𝟐 + 𝑳𝟑𝑪𝒐𝒔(𝟐𝜭)

𝑴𝒂𝒇 = 𝑴𝒇𝑪𝒐𝒔(𝟐𝜭)

Position dependent (time dependent) elements.


Kd F

if

Vf

VaIa

A

B

C

Kq

𝑽 = 𝑹 𝒊 +𝒅

𝒅𝒕( 𝑳 𝒊 )

𝑳𝒂 = 𝑳𝟏 + 𝑳𝟐 + 𝑳𝟑𝑪𝒐𝒔(𝟐𝜭)

𝑴𝒂𝒇 = 𝑴𝒇𝑪𝒐𝒔(𝟐𝜭)

Position dependent (time dependent) elements of Inductance matrixa

a

A

a

a


Synchronous Machine Equations in d-q reference frame

Stator Side Rotor Side

Dampers – 2 on Q-axis

Mechanical rotation

𝑇𝑚 − 𝑇𝑒 = 𝐽𝑑𝜔

𝑑𝑡+ 𝐵𝜔

Speed - Wk

LPHP GIP J


Synchronous Machine Equations in d-q reference frame

[ABC] [dq0]

Direct linear relationship

Examples:

Field open time constant: 𝑻𝒅𝟎ˈ =

𝑳𝒇

𝑹𝒇

Parameter

Stator leakage Inductance Xl

Synchronous ReactanceXd

Xq

Transient ReactanceX'd

X'q

Sub transient ReactanceX''d

X''q

Transient OC Time ConstantT'do

T'qo

Sub transient OC Time ConstantT''do

T''qo

La,Lb..Mab,..Lf, Maf, Lkd…..


Machine Models in PSCAD

STe

3

AV

Tm

Ef0

Tmw

Ef Ifw

S

TL

I M

W

W

Te

Synchronous Machine

Induction Machine

Permanent Magnet Machine

PSCAD Machine models are accurate and reliable.

• In use for over 30 years

• Almost all major power system projects (HVDC, large generation) were studied using these models

• In recent times, the wind turbine models of all vendors use PSCAD machine models


Machine control models

VTIT 3

IfEfEf0

Vref

Exciter_(AC1A)VTIT 3

EfEf0

Vref

Exciter (DC1A)VTIT 3

IfEfEf0

Vref

Exciter (ST1A)

w

Wrefz0

z

Hydro Gov 1

w Tm

Wref

z

zi Hydro Tur 1

w

Wref

Cv

Steam Gov 1 Steam_Tur_2

w Tm1

Tm2WrefIv

Cv

Vs

PSS1A

VsPSS1A

Vt

Efw

& DEC1A

VsPSS1A

Vt Vk

& DEC2A

VsPSS1A

Vt

& DEC3A

Exciter models

Governor/Turbine models

PSS models

IEEE Standard exciter type AC1A

Non standard generator control systems


Simulation setup – Synchronous machine

© Manitoba HVDC Research Centre | a division of Manitoba Hydro International

ParameterThermal Units

(Typical values)

Stator leakage Inductance xl 0.1-0.2

Synchronous reactance

Xd 1.0-2.3

Xq 1.0-2.3

Transient Reactance

X’d 0.15-0.4

X’q 0.3-1.0

SubtransientReactance

X”d 0.12-0.25

X”q 0.12-0.25

Transinet OC time constant

T’do 3.0-10.0 s

T’qo 0.5-2.0 s

Subtransient OC Time constant

T”do 0.02-0.05 s

T”qo 0.02-0.05 s


Simulation setup – Synchronous machine

Tm0

D+

F

+

1.0

w

Wref

Cv

Steam Gov 2

Iv

Steam_Tur_2

w Tm1

Tm2WrefIv

Cv

VTIT 3

IfEfEf0

Vref

Exciter_(AC1A)

Vref0

LRR

S2M

TIME

TIME

#1#2

STe

3

AV

Tm

Ef0

Tmw

Ef If

Tm0

S / Hinhold

out

Ef

If

S2M

P = 42.46Q = 0.4006V = 0.9993

V

A

RL

RRL

W

Ef0

T imedFaultLogicABC->G

Ia

Technical note available on how to set up the machine model and controls.


Steady state operation:

Hand calculations confirm PSCAD model response


Transient response: PSCAD model follows expected response (see technical note)

Fault Current - Isc

time(s) 0.0 2.0 4.0 6.0 8.0 10.0

-30

-20

-10

0

10

20

30

kA

PhaseA

-20

-10 0

10 20

30 40

50

kA

PhaseB

-50

-40 -30

-20 -10

0 10

20

kA

PhaseC

Field Current

time(s) 0.0 2.0 4.0 6.0 8.0 10.0

0.0

1.0

2.0

3.0

4.0

5.0

PU

If - Field Current ExpCurve

msTdoXd

XdTd 7.34039.0

314.0

280.0__

_

__"

Sub Transient response

Transient response

Field current decay time constant

PUIXd

XdI fofo 23.31

314.0

014.1

_

'

'

'' dTt

fofofof eIIII

'

123.31 dTt

e

=

sTdoXd

XdTd 03.255.6

014.1

314.0_

_'


Induction machine

Machine response can be represented in the form of six mutually coupled winding


Induction machine

Steady state equivalent circuit and torque-slip characteristics

1X

1V

1I 1R

mX

'

2X'

2I

s

R '

2agP

Speed(w)

time

Synchronous speed - ws

Rotor mechanical speed - wm

Slip (s)

T s( )3 V

2 R2

s w0 R1

R2

s

2

Xeq( )2

Torque

T-Rated

T-s Curve

Torq

ue

7.368 104

8.541 105

T s( )

Trat s( )

0.990 Speed s( )


Induction machine

Induction machine response during fault recovery – High reactive power absorption can lead to voltage stability concerns

1X

1V

1I 1R

mX

'

2X'

2I

s

R '

2agP

Direct connected IM response to a fault

1.50 2.50 3.50 4.50 5.50 6.50 ...

...

...

0.20

1.00

pu

Vrms

0.9900

1.0400

pu

W

0.00

0.20

0.40

0.60

0.80

1.00

1.20

pu

P1

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

pu

Q1

Machine speeds up (assume a Type 1 wind unit) during the fault• At fault clearance, slip is larger (compared to normal

operation)• Stator and rotor current will be high as a result of high

slip• Increased reactive power absorption in leakage fields


Simulation setup – Induction machine

CROMER_A_94372

V

A

0.994868

S

TL

I M

W

TIME

1.0

#1 #2

0.96

WX2*

1

0

0.0

S

TL

I M

W

TimedBreaker

LogicOpen@t0

BRK

+

Rext

#1 #2E1 V

A

0.96Iins

Technical note available on how to set up the machine model and controls

Title

Simulation examples


Simulation examples

• Illustration of Simulation examples

o Model setup and data entry

o Model Benchmarking

o Black start restoration studies

o Voltage flicker due to compressor load driven by a synchronous machine

o Sub synchronous resonance and torsional interactions

o Voltage dips due to induction motor starting and mitigation options

o Applications in wind generation (DFIG)


Simulation setup – Synchronous Machine

Tm0

D+

F

+

1.0

w

Wref

Cv

Steam Gov 2

Iv

Steam_Tur_2

w Tm1

Tm2WrefIv

Cv

VTIT 3

IfEfEf0

Vref

Exciter_(AC1A)

Vref0

LRR

S2M

TIME

TIME

#1#2

STe

3

AV

Tm

Ef0

Tmw

Ef If

Tm0

S / Hinhold

out

Ef

If

S2M

P = 42.46Q = 0.4006V = 0.9993

V

A

RL

RRL

W

Ef0

T imedFaultLogicABC->G

Ia


Fault Response– Synchronous Machine

Fault Current - Isc

time(s) 0.0 2.0 4.0 6.0 8.0 10.0

-30

-20

-10

0

10

20

30

kA

PhaseA

-20

-10 0

10 20

30 40

50

kA

PhaseB

-50

-40 -30

-20 -10

0 10

20

kA

PhaseC

Transient response: PSCAD model follows expected response (see technical note)

msTdoXd

XdTd 7.34039.0

314.0

280.0__

_

__"

Sub Transient response

Transient response

sTdoXd

XdTd 03.255.6

014.1

314.0_

_'


Model Benchmarking– Synchronous Machine

Comparing response with RMS simulation results

Synchronous generator fault ride through

The results (even RMS quantities) are derived from two different methods of mathematical circuit solution techniques – There can be minor differences



The results (even RMS quantities) are derived from two different methods of mathematical circuit solution techniques

• The test circuits are simplified (ideal like) • Note network dynamics such as DC offset in fault current• In EMT, currents are interrupted at ‘zero crossings’



The results (even RMS quantities) are derived from two different methods of mathematical circuit solution techniques

Zero fault resistance

Low fault resistance


Black Start Restoration Example

Steam_Tur_1

w Tm1

Tm2Wref

Cvw

Wref

Cv

Steam Gov 4

STe

3

AV

Tm

Ef0

Tmw

Ef If

Tm0

1.0

D+

F

+

System Blackstart Study - 900 MVA generating plant

VTIT 3

IfEfEf0

Vref

Exciter_(AC1A)

Vref0

#1#2

S / Hinhold

out

S2M

TM0

W

V

A

W

90 MVA Machine

1 unit of the plant being used for black start

A B

E_A1

E_B1

Sub Station -01

4.8

4.8

B_B1

B_A1

B1

#1 #2

Ef

Ia

Ea

#1 #2Ib

B2

375 km line

E_B2

E_A2

Sub Station -02

Example: Self Excitation when energizing a long line


Example: Flicker due to a synchronous motor driven compressor

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250 300 350 400

T

Compressor load torque characteristicsVoltage flicker measured at transmission level


Example: SSTI studies - Mechanical shaft-mass system

• Rotor of a Turbine Generator is a complex system of masses connected by shaft sections

• The total length can be as much as 50 m.

• A single lumped inertia representation is typically considered in system transient stability studies

– Assumption: Rigid shafts

Gen

Speed - W

http://www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCIGz1pLyncgCFdI1iAodAZEOUQ&url=http://emadrlc.blogspot.com/2014/12/balancing-of-rotating-equipment.html&bvm=bv.104226188,d.cGU&psig=AFQjCNELEccQ7SjbXgr2Vys8hFTEC1x0iQ&ust=1443672714917806


Mechanical shaft-mass system

• Torsional Interaction studies require a more detailed representation of the shaft (compared to lumped mass representation)

– A Multi-Mass representation

o Main rotor components represented as separate (rigid) masses

o The masses are connected to each other with ‘elastic’ shaft sections

Speed - Wk

LPHP GIP

δ

Multim

ass

Te

Wra

dTm

Tm

iTei

( SyncM

/c)


Induction Machine Response

Title

Thank you

Documents

Machine Modeling and Power System Study Applications...pscad.com Powered by Manitoba Hydro International Ltd. Simulation setup –Synchronous machine Tm0 D + F + 1.0 w Wref Cv Steam