Block Diagrams GENSAL

Exciter AC7B and ESAC7B

CE

RsT+11

Σ Σ

REFV

SV

UELV

+

−

+

Σ1

EsT

EK

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

( )X E E EV V S V=

+

−

+

−

+

++

+

FEV

XV

EV

EXF

FDI

FDE

Σ Σ

Exciter AC7B and ESAC7B IEEE 421.5 2005 Type AC7B Excitation System Model

1IR DR

PRDR

K sKKs sT

+ ++

L FE-K V

+

CV

AC7B supported by PSSEESAC7B supported by PSLF with optional speed multiplier

RMAXVFEMAX D FD

E E E

V -K IK +S (V )

πIAPA

KKs

+

AMAXV

AV

Σ 2FK

1FK

+

+

3

1F

F

sKsT+

−

P TK V

EM INVAM INVRM INV

NI

E

t

IR

DR

A

1 - V2 - Sensed V3 - K4 - K5 - V6 - Feedback

States

12

3 4

5

6

Speed

10

Spdmlt

Exciter AC8B

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV

REFV SV

+−

+

+

Exciter AC8B IEEE 421.5 2005 AC8B Excitation System

RVΣ

Model supported by PSSE

COMPV

1

EsT

( )E E EK S V+

DK

( )EX NF f I=

C FDN

E

K IIV

=

−

+

+

EXF

FDI

FDE

Σ

NI

Σ π

FEV

52

E

t

R

1 - V2 - Sensed V3 - PID 14 - PID 25 - V

States

3

1

4

FEMAX D FD

E E E

V -K IK +S (V )

EM INV

1IR DR

PRDR

K sKKs sT

+ ++

++

+

UELV OELV

PIDMAXV

PIDMINV

Exciter BPA_EA

TV

RsT+11

1

11 AsT+Σ

REFV

+

−+

Σ1

EsT

E ES K+

+

−

Exciter BPA_EA Continuously Acting DC Rotating Excitation System Model

1A

A

KsT+

1F

F

sKsT+

Model in the public domain, available from BPA

STBV

FDE

Σ−

+

RMAXV

RMINV

RegulatorExciter

Filter

Stabilizer

FD

t

R

R1

F

1 - E2 - Sensed V3 - V4 - V5 - V

States

3 4

5

12

Exciter BPA EB

RsT+11

1

11 AsT+Σ

REFV

+

−+

Σ1

EsT

E ES K+

+

−

Exciter BPA EB Westinghouse Pre-1967 Brushless Excitation System Model

1A

A

KsT+

1F

F

sKsT+


STBV

FDEΣ

−

+

RMAXV

RMINV

Regulator Exciter

Filter

Stabilizer

1

11 FsT+

FD MAXE

FD MINE 0=

TV

FD

t

R

R1

F

F1

1 - E before limit2 - Sensed V3 - V4 - V5 - V6 - V

States

3 4

5

12

6

Exciter BPA EC

1

11 AsT+Σ

REFV

+

−

+

Σ1

EsT

E ES K+

+

−

Exciter BPA EC Westinghouse Brushless Since 1966 Excitation System Model

1A

A

KsT+

1F

F

sKsT+


STBV

FDEΣ−

+

RMAXV

RMINV

Regulator Exciter

Stabilizer

FD MAXE

FD MINE 0=

E ES K+

TV3

4

12

FD

R

R1

F

1 - E before limit2 - V3 - V4 - V

States

Exciter BPA ED

Exciter BPA ED SCPT Excitation System Model


RsT+11

Σ

REFV

SV

+

−+

Σ1

EsT+

+

FDE

RVΣ−

+

20.78

If 1, 0

FD

THEV

B

IAV

A V

⎛ ⎞⋅= ⎜ ⎟⎝ ⎠> =

1F

F

sKsT+

0

BMAXV

BV

THEV P T I TV K V jK I= +

1 A−FDI

Σ+

−

EK

π

1A

A

KsT+

RMAXV

RMINV

1

11 AsT+

Stabilizer

Regulator Exciter

'TV

TV

TITHEVV

3 4

5

12

t

A

R

1 - EField2 - Sensed V3 - V4 - V5 - Feedback

States

Exciter BPA EE

'TV

REFV

−

+

Σ1

EsT

E ES K+

+

−

Exciter BPA EE Non-Continuously Active Rheostatic Excitation System Model

'

1A

RH

KsT

∗

+


FDE+

RMAXV

RMINV

Regulator Exciter

FD MAXE

FD MINE

Σ

If:, , ,

T V R RMAX

T V R RH

T V R RMIN

V K V VV K V VV K V V

Δ ≥ =

Δ < =

Δ ≤− =

RV

'TV

'TOV

−

+

Σ TVΔ

RHV

RH'

* NOTE:If the time constant T is equal to

zero, this block is represented as K /sA

1

2

RH

1 - EField before limit2 - V

States

Exciter BPA EF

Σ

REFV

+

−

+

Σ1

EsT

E ES K+

+

−

Exciter BPA EF Westinghouse Continuous Acting Brushless Rotating Alternator

Excitation System Model

1F

F

sKsT+


SOV

FDEΣ−

+

RMAXV

RMINV

Regulator Exciter

Stabilizer

FD MAXE

FD MINE 0=

E ES K+

( )TV

T 0R =

(1 )A AK sTs+

3

12

R

F

1 - EField before limit2 - V3 - V

States

Exciter BPA EG

Exciter BPA EG SCR Equivalent Excitation System Model


Σ

REFV

SOV

+

−

+

FDE

RVΣ−

+

1F

F

sKsT+

1A

A

KsT+

RMAXV

RMINV

1

11 AsT+

Stabilizer

Regulator

TV

3

12

A

F

1 - EField2 - V3 - V

States

Exciter BPA EJ

1

11 AsT+

REFV

+

+

Exciter BPA EJ Westinghouse Static Grand Couple PP#3 Excitation System Model

1A

A

KsT+

1F

F

sKsT+


'TV

FDEΣ

−

+

RMAXV

RMINV

Regulator

Stabilizer

FD MAXE

FD MINE

SOV

11 RsT+ − Σ

Filter

π3

4

12

t

R

F

1 - EField before limit2 - Sensed V3 - V4 - V

States

Exciter BPA EK

1

11 AsT+Σ

REFV

+

−

+

Σ1

EsT

E ES K+

+

−

Exciter BPA EK General Electric Alterrex Excitation System Model

1A

A

KsT+

1F

F

sKsT+


SOV

FDEΣ−

+

RMAXV

RMINV

Regulator Exciter

Stabilizer

FD MAXE

FD MINE 0=

T

R

V(T =0)

3

4

12

R

R1

F

1 - EField before limit2 - V3 - V4 - V

States

Exciter BPA FA

Exciter BPA FA WSCC Type A (DC1) Excitation System Model


FV

SV

1

EsTFDE

−

+

1F

F

sKsT+

VR( )C T C C TV V R jX I= + +TV

TI Σ+

−

E ES K+

11

C

B

sTsT

++

RMAXV

RMINV

1A

A

KsT+

ERRV +

FEV

RsT+11CV

Σ

REFV

−

+

Σ3

4

5

1

2

t

B

R

F

1 - EField2 - Sensed V3 - V4 - V5 - V

States

Exciter BPA FB

Exciter BPA FB WSCC Type B (DC2) Excitation System Model


FV

SV

1

EsTFDE

−

+

1F

F

sKsT+

VR( )C T C C TV V R jX I= + +TV

TI Σ+

−

E ES K+

11

C

B

sTsT

++

T RMAXV V

T RMINV V

1A

A

KsT+

ERRV +

FEV

RsT+11CV

Σ

REFV

−

+

Σ3

4

5

1

2

t

B

R

F


States

Exciter BPA FC

1A

A

KsT+

RMAXV

RMINV

1F

F

sKsT+

0

SV

+Σ

FV

1

EsT

EK

DK

( )EX NF f I=

C FDN

E

K IIV

=

+

−−

+

+

FEV

RVEV

EXF

FDI

FDE

Σ

NI

( )C T C C TV V R jX I= + +TV

TI

ERRV

RsT+11CV

REFV

−

+

Exciter BPA FC WSCC Type C (AC1) Excitation System Model


π11

C

B

sTsT

++

Σ

Σ+

34

5

1

2

E

t

R

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter BPA FD

1A

A

KsT+

RMAXV

RMINVSV

+

+Σ

1

EsT

EK

+

−

FDE

Exciter BPA FD WSCC Type D (ST2) Excitation System Model

1F

F

sKsT+

FV 0

π

+

BV

E P T I TV K V jK I= +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

MAXEFD

+−

EV If 0. and 0., 1.P I BK K V= = =

RV



TI

ERRV

RsT+11CV

REFV

−

+

Σ

Σ

Σ3

4

1

2

t

R

F

1 - EField2 - Sensed V3 - V4 - V

States

Exciter BPA FE

Exciter BPA FE WSCC Type E (DC3) Excitation System Model

ERRV RMAX RMIN

V RH

V VsK T

−

RMAXV

RMINV

If , If , If ,

ERR V R RMAX

ERR V R RH

ERR V R RMIN


≥ =

< =

≤− =

RHV

VK−

VK

Σ1

EsT

E EK S+

FDE+

−RV



TI RsT+11CV

REFV

−

+

Σ

FEV

3

1

2

t

RH

1 - EField before limit2 - Sensed V3 - V

States

Exciter BPA FF

11

C

B

sTsT

++

SV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

FDE

Σ

Exciter BPA FF WSCC Type F (AC2) Excitation System Model

1A

A

KsT+

AMAXV

AMINV

1F

F

sKsT+

0−

FV LV

LVGateΣ

AV

+

RMINV

RMAXV

BK

LK

HK

Σ −

+

LRVHV

NI

−



TI RsT+11CV

REFV

−

+

Σ

ERRV

Σ+ 34

5

1

2

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter BPA FG

1A

A

KsT+

Exciter BPA FG WSCC Type G (AC4) Excitation System Model

11

C

B

sTsT

++


FDE+

IMIMV

IMAXV


TI RsT+11CV

REFV

−

+

Σ

VS

ERRV

ΣRMIN C FD(V K I )−

RMAX C FD(V K I )−

+

3 1

2

t

LL


States

Exciter BPA FH

11

C

B

sTsT

++

SV+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

Σ

Exciter BPA FH WSCC Type H (AC3) Excitation System Model

1A

A

KsT+

AMAXV

AMINV

1 F

ssT+

0−

FV

+AV

RK

NI

HVGate π

LVK −

+

LVV

Σ

EFD

NV

FK

NK

FDNE


FDE


TI RsT+11CV

REFV

−

+

ERRV

Σ

Σ34

5

1

2

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter BPA FH

11

C

B

sTsT

++

SV+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

Σ

Exciter BPA FH WSCC Type H Excitation System Model

1A

A

KsT+

AMAXV

AMINV

1 F

ssT+

EMINV−

FV

+AV

RK

NI

π

EFD

NV

FK

NK

FDNE


FDE


TI RsT+11CV

REFV

−

+

ERRV

Σ

Σ34

5

1

2

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter BPA FJ

1A

A

KsT+

Exciter BPA FJ WSCC Type J Excitation System Model

11

C

B

sTsT

++


FDE+

RMAXV

RMINV


TI RsT+11CV

REFV

−

+

Σ

SV

ERRV

T FDMAX C FD(V E K I )−

+

1F

F

sKsT+

T FDMIN C FD(V E K I )−

Σ−

FV

3

4

1

2

t

LL

F


States

Exciter BPA FK

1A

A

KsT+

Exciter BPA FK WSCC Type K (ST1) Excitation System Model

11

C

B

sTsT

++


FDE+


TI RsT+11CV

REFV

−

+

Σ

VS

ERRV

T RMAX C FD(V V K I )−

+

1F

F

sKsT+

T RMIN C FD(V V K I )−

Σ−

IMIMV

IMAXV

FV

3

4

1

2

t

LL

F


States

Exciter BPA FL

SV

REFV

+

+

+Σ+

FDE

Exciter BPA FL WSCC Type L (ST3) Excitation System Model

IMINV

IMAXV

J1K1

C

B

sTsT

++

−

GV

AV

GK

1A

A

KsT+

RMAXV

RMINV

RVπ

π( )PE T I P L TV K V j K K X I= + +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

EV

BV

FDMAXE

GMAXV

jP PK K e pθ=


TI RsT+11CV

REFV

−

+

ERRV

Σ

Σ


3 1

2

M

t

LL

1 - V2 - Sensed V3 - V

States

Exciter BPA FM through BPA FV

Exciter BPA FM through BPA FV

No block diagrams have been created

Exciter DC4B

RsT+11

UEL(UEL=1)

V

REFV

+−+

FDE

Exciter DC4B IEEE 421.5 2005 DC4B Excitation System Model

1A

A

KsT+

T RMAXV V

T RMINV V

1F

F

sKsT+

−

OEL(OEL=2)

V

HVGate

LVGate

Alternate UEL Inputs

Alternate OEL InputsOEL

(OEL=1)

V

+

Model supported by PSSEModel supported by PSLF with optional speed multiplier

CE

UEL(UEL=2)

V

SV

1I D

PD

K sKKs sT

+ ++Σ

RMAX AV K

RMIN AV K

1

EsT

EMINV

π Σ π

EK

( )X E E EV V S V=

−

Σ

RV

TV

+

+

−+

FV

FD

t

R

1 - E2 - Sensed V3 - PID14 - PID25 - V6 - Feedback

States

3 4

5

6

12

Speed

1 0 Spdmlt

Exciter ESAC1A

CE

RsT+11 1

1C

B

sTsT

++Σ

REFV

+

−

+

Σ1

EsT

EK

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

( )X E E EV V S V=

+

−

+

++

+

FEV

RV

XV

EV

EXF

FDI

Σ Σ

Exciter ESAC1A IEEE Type AC1A Excitation System Model

1A

A

KsT+

AMAXV

RMINV

RMAXV

1F

F

sKsT+

0−

UELV

HVGate

OELV

LVGate

FV


SV

AMINV

FDE3

4

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Speed

10

Spdmlt

Exciter ESAC2A

E

1sTR

11+sT

C

B

1+sT1+sT BK

HK

F

F

sK1+sT EK

X E E EV =V S (V ) EX NF =f(I )

DK

C FDN

E

K II =V

CE REFV

FV

++

−

−

AV+

−

UELV OELVAMAXV

AMINV HV

RV −

+

RMINV

RMAXV

0

EV

FEMAX D FD

E E E

V -K IK +S (V )

FDE

EXF

XV NI

FEV

+

+

+

+

FDI



A

A

K1+sT

SV

34

5

1

2Σ Σ Σ

Σ

Σ

πHVGate

LVGate

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Speed

10

Spdmlt

Exciter ESAC3A

CE

RsT+11 1

1C

B

sTsT

++Σ Σ 1

A

A

KsT+

AMAXV

AMINV

1 F

ssT+

FEMAX D FD

E E E

V -K IK +S (V )

EMINV

REFV

SV

UELV

HVGate

+

−

+

π Σ

FV

1

EsT

RK

EK

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

( )X E E EV V S V=

+

−

+

−

+

++

+

FEV

AV RV

XV

EV

EXF

FDI

FDE

EFD

NV

FK

NK

NV

Σ Σ


CV

NI


3

4

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Speed

10

Spdmlt

Exciter ESAC4A

CERsT+1

1 11

C

B

sTsT

++Σ 1

A

A

KsT+

RMAX C IFDV -K I

RMINV

REFV

SV

UELV

HVGate

+

−

+

FDE


IM INV

IM AXV

IV

FD

Model supported by PSLF and PSSEPSSE uses nonwindup limit on E

3 12

t

LL


States

Exciter ESAC5A

CE

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV 0

REFV

SV

+

−

+

Σ1

EsT

EK

( )X E E EV V S V= ⋅

+

−

+

+

XV

FDE

F2 F3If T =0, then sT =0. Σ


( )( )( )

3

1 2

11 1

F F

F F

sK sTsT sT

++ +

−

Model supported by PSLF and PSSE

3

4 5

12

t

R

1 - EField2 - Sensed V3 - V4 - Feedback 15 - Feedback 2

States

Exciter ESAC6A

CE

RsT+11 1

1C

B

sTsT

++Σ Σ

REFV

SV

UELV

+

−+

ΣAV

1

EsT

EK

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

( )X E E EV V S V=

+

−

+

−

+

++

+

FEV

RV

XV

EV

EXF

FDI

FDE

Σ Σ


( )11

A K

A

K sTsT+

+

AMAXV

AMINV T RM INV V

T RM AXV V

HK11

J

H

sTsT

++

HMAXV

0

0HV Σ +

FELIMV−

+

CV


NI

3 4

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - T Block4 - V5 - V

States

Speed

10

Spdmlt

Exciter ESAC8B_GE

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV

REFV

SV

+−

+

+

Exciter ESAC8B_GE IEEE Type AC8B with Added Speed Multiplier.

RVΣ+

+

+

IRKs

PRK

1DR

DR

sKsT+

TMULT RMAX T RMAX RMIN T RMIN

Model supported by PSLFIf V 0, V V V and V V V<> = =

COMPV

1

EsT

( )E E EK S V+

DK

( )EX NF f I=

C FDN

E

K IIV

=

−

+

+

EXF

FDI

FDE

Σ

NI

Σ π

FEV

52

E

t

R

1 - V2 - Sensed V3 - PID 14 - PID 25 - V

States

3 1

4

FEMAX D FD

E E E

V -K IK +S (V )

EM INV

Speed

10

Spdmlt

Exciter ESAC8B_PTI

RsT+11

1A

A

KsT+

RMAXV

RMINV 0

REFV

SV

+

−

+

Σ1

EsT

EK

( )X EV EFD S EFD= ⋅

+

−

+

+

XV

FDE

Σ

Exciter ESAC8B_PTI Basler DECS Model

RV

+

+

+

IRKs

PRK

1DR

D

sKsT+


CV

3

4 5 12

FD

t

R

1 - E2 - Sensed V3 - Derivative Controller4 - Integral Controller5 - V

States

ΣΣ

Exciter ESDC1A

CE

RsT+11

Σ 1A

A

KsT+

RMAXV

0

REFV

SV

+

−

+

Σ1

EsT

EK


+

−

+

+

XV

FDE

Σ

Exciter ESDC1A IEEE Type DC1A Excitation System Model

RV

11F

F

sKsT+

11

C

B

sTsT

++CV

UELV

HVGate

FV FEV

Model supported by PSSEModel supported by PSLF includes spdmlt, exclim, and UEL inputs that are read but not utilized in the Simulator implementation

−

RMINV

3

4

5

12

FD

t

R

F

1 - E2 - Sensed V3 - V4 - V5 - Lead-Lag

States

Exciter ESDC2A

RsT+11

Σ 1A

A

KsT+

T RMAXV VREFV

SV

+

−

+

Σ1

EsT

EK


+

−

+

+

XV

FDE

Σ

Exciter ESDC2A IEEE Type DC2A Excitation System Model

RV

11F

F

sKsT+

11

C

B

sTsT

++CV

HVGate

Model supported by PSSEModel supported by PSLF includes spdmlt, exclim, and UEL inputs that are read but not utilized in Simulator

CEUELV

FV

T RMINV V

FEV

−

3

4

5

12

FD

t

R

F

1 - E2 - Sensed V3 - V4 - V5 - Lead-Lag

States

Exciter ESDC3A

Exciter ESDC3A IEEE Type DC3A with Added Speed Multiplier

ERRVRMAX RMIN

V RH

V VsK T

−

RMAXV

RMINV

If , If , Else

ERR V R RMAX

ERR V R RMIN

R RH

V K V VV K V V

V V

≥ =≤− =

=

RHVVK−

VK

Σ1

E EK sT+FDE

+

−

RV

Model supported by PSLF

RsT+11CV

REFV

−

+

Σ

π

( )X EV EFD S EFD= ⋅XV Speed

10

Spdmlt

t

RH

1 - EField2 - Sensed V3 - V

States

31

2

If exclim 0 then 0 else unlimited<>

Exciter ESST1A

RsT+11

Σ

S(VOS=1)

V

REFV

+

−

+

Σ+

−AV FDE

Exciter ESST1A IEEE Type ST1A Excitation System Model

1A

A

KsT+

AMAXV

AMINV

1F

F

sKsT+

0

−

HVGate

IM INV

IM AXV( )( )( )( )

1

1

1 11 1

C C

B B

sT sTsT sT

+ ++ +

HVGate

OELV

LVGate

IV

T RM INV V

T RMAX C FDV V -K I

LRK Σ FDI

LRI

AlternateStabilizer

Inputs

AlternateUEL Inputs

+

+−

+


CE

FV

3 4

5

12

S(VOS=2)

V

UEL(UEL=1)

V UEL(UEL=3)

V

UEL(UEL=2)

V

A

t

1 - V2 - Sensed V3 - LL4 - LL15 - Feedback

States

Exciter ESST2A

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV

REFV

SV

+

−+

Σ1

EsT

EK

+

−

FDE


1F

F

sKsT+

UELV

HVGate

FV 0

π

BV

E P T I TV K V jK I= +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

MAXEFD

−

EV If 0 and 0, 1P I BK K V= = =

Model supported by PSSEModel supported by PSLF includes UEL input that is read but not utilized in Simulator

CE

CVRV

11

C

B

sTsT

++

3

4

12 π

FD

t

R

F

1 - E2 - Sensed V3 - V4 - V

States

Exciter ESST3A

RsT+11

Σ

SV

REFV

+

−

+Σ+

AV FDE


1A

A

KsT+

RMAXV

HVGate

IM INV

IM AXV11

C

B

sTsT

++IV

−

GV

RV

GK

1M

M

KsT+

MMAXV

MMINV

MVπ

π( )PE T I P L TV K V j K K X I= + +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

EV

BVBMAXV


CEUELV

GMAXV

RMINV

PjP PK K e θ=

34 12

M

t

R

1 - V2 - Sensed V3 - V4 - LL

States

Exciter ESST4B

RsT+11

Σ

SV

REFV

+

−

+Σ+

FDE

Exciter ESST4B IEEE Type ST4B Potential- or Compound-Source Controlled-Rectifier Exciter Model

11 AsT+

−

RV

GK

IMPM

KKs

+

MMAXV

MMINV

π

π( )E P T I P L TV K V j K K X I= + +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

EVBVBMAXV

RMAXV

RMINVOELV

LVGate

IRPR

KKs

+

+

GMAX

Model supported by PSSEModel supported by PSLF includes V input that is read but not utilized in Simulator

UELV

PjP PK K e θ=

COM PV34 12

M

t

A

R

1 - V2 - Sensed V3 - V4 - V

States

Exciter EWTGFC

Exciter EWTGFC Excitation Control Model for Full Converter GE Wind-Turbine Generators

∑


+− 1

1 FVsT+

RFQV

11 PsT+

elecP

1

Nf

1PV

V

KsT+

+

∑RsT+1

1

IVKs

M INQ

M AXQ

π

tanFAREFP

REFQ

1

1−

0

Reactive Power Control Model

M INQ

M AXQ

varflg

−genQ

QIKs

MINV

+

−∑

REFVVIKs

QMAXI

QMINI

QCMDI

CV

3

4

5

1

2

ref

qppcmd

PV

regMeas

IV

ORD

Meas

1 - V2 - E

3 - K4 - V

5 - K6 - Q7 - P

States

6

7MAXV

TERMV

+

elecP

dbrK

∑

∑1s

÷PMAXI

−

++

−TERMV

PCMDI

∑

+

pfaflg

REFQ

01

ORDP

Converter Current Limitpqflag

∑

+

−

dbrP

0

1

0 BSTE

Exciter EX2000

RsT+11

Σ Σ IAPA

KKs

+

AMAXV

AMINV

1FK

EMAXV

EMINV

−+

π Σ

FV

1

EsT

PK ETRM⋅

EK

DK

π

( )EX EF f I=

C FDN

E

K IIV

=

( )X E E EV V S V=

+

−

+

−

+

++

+

FEV

AV

XV

EV

EXF

FDI

Σ Σ

Exciter EX2000 IEEE Type AC7B Alternator-Rectifier Excitation System Model

MinimumGate 1

IRPR

KKs

+

RMAXV

RMINV L FEK V−

ReferenceSignal

Field CurrentLimiter

2FKΣ +

+


EMAX

FEMAX D FDEMAX

E E E

If field current limiter is included, V is off.V -K IIf field current limiter is excluded, V =K +S (V )

CE

FDE

REF 34

12

1st PI Controller 2nd PI Controller

E

t

API

RPI

PI

1 - V2 - Sensed V3 - V4 - V5 - LL6 - IFD

States

Exciter EX2000 REFERENCE SIGNAL MODEL

REF

Exciter EX2000 Reference Signal Model

MinimumGate 2

KRCCSBASE

Machine MVA BASEELECQ1

ETERM

KVHZ

Σ

REFV

UELV

STBV

++

+

−LIMPREF

Frequency

ReactiveCurrent

Reference Signal Model


Exciter EX2000 FIELD CURRENT LIMITER MODEL

KIIFDKPIFDs

+

REF2IFD

LIMNIFD

Exciter EX2000 Field Current Limiter Model

LevelDetector

LatchGate 1

LatchGate 2

O R

ADVLIMIFD11

LEAD

LAG

sTsT

++

Σ

Advance Limit

( 1, 1)I T

( 3, 3)I T

( 2, 2)I T

( 4, 4)I T

Inverse Timing

A

B

C

D

A

B

C

D

LIMPIFD

REF3IFD

REF4IFD

REF1IFD

FDI

+

−

ToMinimum

Gate 1

Output =1 if level exceeded

Output =1 iftiming expired

Sw itch O peration O utput D = B if C =0O utput D = A if C =1

Field Current Lim iter Model(Over Excitation Lim iter)


3rd PI Controller

5

6

Exciter EXAC1

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

FDE

Σ

Exciter EXAC1 IEEE Type AC1 Excitation System Model

1A

A

KsT+

RMAXV

RMINV

1F

F

sKsT+

0−

FV

Σ+

−+

CV

AMIN AMAX

AMIN RMIN RMIN AMIN

AMAX RMAX

Model supported by PSSEModel supported by PSLF also uses V and V

Simulator will narrow the limit range as appropriate when loading the DYD fileIf V V then V VIf V V the

> =

< RMAX AMAXn V VModel supported by PSLF includes speed multiplier that is not implemented in Simulator

=

CE

E

t

R

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

34

5

12

Exciter EXAC1A

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

FDE

Σ

Exciter EXAC1A Modified Type AC1 Excitation System Model

1A

A

KsT+

RMAXV

RMINV

1F

F

sKsT+

0−

FV

Σ+

−+

CV

Model supported by PSSEModel supported by PSLF includes speed multiplier that is not implemented in Simulator

CE

34

5

12

E

t

R

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter EXAC2

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

FDE

Σ


1A

A

KsT+

AMAXV

AMINV

1F

F

sKsT+

0−

FV

Σ+

− +

CVLV

LVGateΣ

AV

+

RM INV

RM AXV

BK

LK

HK

Σ −

+

LRV

HV

NI

−


CE 34

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter EXAC3

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

Σ


1A

A

KsT+

AMAXV

AMINV

1 F

ssT+

0−

FV

Σ+

−

+CV AV

RK

NI

HVGate π

LVK −

+

LVV

Σ

EFD

NV

FK

NK

NEFD


CE

FDE34

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

FEMAXV

Exciter EXAC3A

RsT+11 1

1C

B

sTsT

++ Σ

SV

REFV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

RVEV

EXF

FDI

Σ

Exciter EXAC3A IEEE Type AC3 Excitation System Model

1A

A

KsT+

AMAXV

AMINV

1 F

ssT+

EMINV−

FV

Σ+

−+

AV

NI

π

RK

EFD

NV

FK

NK

NEFD

CEFDE

EMAXV Speed


( )

( )

L1 C S REF C FFEMAX

FA L1

FEMAX D FDEMAX

E E

LVEMIN

EX

K V +V +V -V -VV =

K KV -K I

V =S +K

VV =F

34

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - V4 - V5 - V

States

CV

Exciter EXAC4

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

FDE


1A

A

KsT+Σ

+−

+ERRV

IM INV

IM AXV

RM IN C IFDV -K I

RM AX C IFDV -K I


CE3 12

t

LL


States

Exciter EXAC6A

Exciter EXAC6A IEEE Type AC6A Excitation System Model


RsT+11 1

1C

B

sTsT

++ Σ

SV

REFV

+

Σ1

EsT

E EK S+

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

FEV

EV

EXF

Σ

(1 )1A k

A

K sTsT+

+

T RMAXV V

AMINV

11

J

H

sTsT

++

0−

HV

Σ+

− +

NI

HK

CE

FDE

Speed

HM AXV

AMAXV

AV

0

+

−Σ

FELIMV

T RMINV V

DK FDI

RV3 4

5

12

E

t

A

LL

F

1 - V2 - Sensed V3 - T Block4 - V5 - V

States

Exciter EXAC8B

Exciter EXAC8B Brushless Exciter with PID Voltage Regulator


RsT+11

Σ1

1 AsT+

RMAXV

RMINV

REFV

SV

+−+

+Σ+

++

VIKs

VPK

1VD

VD

sKsT+

CE

Σ1

EsT

E EK S+

π

( )EX NF f I=

C FDN

E

K IIV

=

−

+

+

FEV

EV

EXF

Σ

0

NI

FDE

Speed

DK FDI

IM AX-V

IM AXV3

4

5 12

E

t

R

1 - V2 - Sensed V3 - V4 - Derivative5 - Integral

States

Exciter EXBAS

RsT+11 1

1C

B

sTsT

++Σ

STBVREFV

+

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+

−

+

+

EV

EXF

FDI

Σ

Exciter EXBAS Basler Static Voltage Regulator Feeding DC or AC Rotating Exciter Model

1A

A

KsT+

RMAXV

RMINV

1F

F

sKsT+

−

Σ+

− +

UELV

NI1

2

11

F

F

sTsT

++

IP

KKs

+

OELV

+ +


CE

FDE3

4 5

12

E

t

R

1 - V2 - Sensed V3 - V4 - PI5 - LL6 - Feedback LL7 - Feedback

States

67

Exciter EXBBC

3

4

11

sTsT

++ Σ

REFV

Σ1

1 EsT+

EX

+

−

FDI

Exciter EXBBC Transformer-fed Excitation System

RMAXV

RMINV+

Σ+

− +

1

2 2

1 111

TK T sT⎛ ⎞

−⎜ ⎟ +⎝ ⎠

2

1

TKT+

Model supported by PSLF but not yet implemented in Simulator

CE

FDEΣ

T FDMINE E

T FDMAXE E

Switch 0= Switch 1=

SupplementalSignal

+

−

11 FsT+

Exciter EXDC1

Exciter EXDC1 IEEE DC1 Excitation System Model


RsT+11

Σ

SV

REFV

+

+1

A

A

KsT+

RMAXV

RMINV

Σ1

EsT

E EK S+

+

−

11F

F

sKsT+

RV−

CE

− π

Speed

FDE11

C

B

sTsT

++

FV

3 4

5

1

2

FD

t

B

R

F

1 - E2 - Sensed V3 - V4 - V5 - V

States

Exciter EXDC2_GE

RsT+11 1

1C

B

sTsT

++

SVREFV

+

Exciter EXDC2_GE IEEE Type DC2 Excitation System Model

Σ+

−1

A

A

KsT+

RMAX TV V

Σ1

1 EsT+

E EK S+

FDE+

−

( )( )1 21 1F

F F

sKsT sT+ +

−


RMIN TV V

compV

π

Speed

3 4

5

1

2

FD

t

B

R

F1

F2

1 - E2 - Sensed V3 - V4 - V5 - V6 - V

States

6

Exciter EXDC2_PTI

RsT+11 1

1C

B

sTsT

++

SVREFV

+

Exciter EXDC2_PTI IEEE Type DC2 Excitation System Model

Σ+

−

1A

A

KsT+

RMAX TV V

Σ1

1 EsT+

E EK S+

FDE+

−

11F

F

sKsT+

−

Model supported by PSEE

RMIN TV V

compV

π

Speed

Σ+ERRV

3 4

5

1

2

FD

t

B

R

F

1 - E2 - Sensed V3 - V4 - V5 - V

States

Exciter EXDC2A

RsT+11 1

1C

B

sTsT

++Σ

+

Exciter EXDC2A IEEE Type DC2 Excitation System Model

−

1A

A

KsT+

RMAX TV V

Σ1

EsT

E EK S+

+

−

11F

F

sKsT+

RV−


CE

FV

SV

REFV+

π

Speed

FDE34

5

1

2

RMIN TV V

FD

t

B

R

F

1 - E2 - Sensed V3 - V4 - V5 - V

States

Exciter EXDC4

Σ+

Exciter EXDC4 IEEE Type 4 Excitation System Model

− 1

RHsT

RMAXV

Σ1

E EK sT++

−RHV


CE

RMINV

SV

REFV+

π

Speed

FDE

ESRMAXV

RMINVVK

V-K

RV

π

1

-1RK

R-K

1

2

FD

RH

1 - E2 - V

States

Exciter EXELI

11 FVsT+ Σ

REFV

+Σ

+

−

+

+

FDE

Exciter EXELI Static PI Transformer Fed Excitation System Model

PUV

Σ +

Σ1

NUsT

+

11 FIsT+

EX

FDI

F M INE

F M AXE

PIV

PNFV

−

−

+

PNFD

GENP3

1W

W

sTsT

⎛ ⎞⎜ ⎟+⎝ ⎠

2

21s

s

sTsT

−+Σ

+

+

1sK

2

11s

s

KsT+

MAXS−

MAXS


CE

− Σ

3

4 5

12

NU

t

FLD

GEN

GEN

GEN

1 - T2 - Sensed V3 - Sensed I4 - P Washout15 - P Washout26 - P Washout37 - Lag Stabilizer8 - Washout Stabilizer

States

6 7

8

Exciter EXPIC1

RsT+11

Σ

REFV

Exciter EXPIC1 Proportional/Integral Excitation System Model

Σ+

−

+

( )11A AK sTs+

R1V

R2V

1

EsT

E EK S+

FDE+

−

( )( )1 21 1F

F F

sKsT sT+ +

RVTE

SV

AV( )

( ) ( )3

2 4

11 1

A

A A

sTsT sT+

+ +

RM INV

RM AXV

FD M INE

FD M AXE

Σπ0E

−

πTV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI

NI

EXF

BV

0

If 0 and 0, then 1If 0, then

P I B

E

K K VT EFD E

= = == =

E P T I TV K V jK I= +


CE3

4 51

2

FD

t

A

R1

R

F1

F

1 - E2 - Sensed V3 - V4 - V5 - V6 - V7 - V

States

6 7

Exciter EXST1_GE

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

FDE

Exciter EXST1_GE IEEE Type ST1 Excitation System Model

1A

A

KsT+

+

−

IM INV

IM AXV

T RM IN C IFDV V -K I

T RM AX C IFDV V -K I

1F

F

sKsT+

−


compV

1

1

11

C

B

sTsT

++

AMAXV

AMINV

Σ+−

EX

lrK

Σ

FDIΣ

lrI

+

−

+−

3

4

5 12

0

A

t

LL

F

LL1

1 - V2 - Sensed V3 - V4 - V5 - V

States

Exciter EXST1_PTI

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

FDE

Exciter EXST1_PTI IEEE Type ST1 Excitation System Model

1A

A

KsT+

+

−

IM INV

IM AXV

T RM IN C IFDV V -K I

T RM AX C IFDV V -K I

1F

F

sKsT+

−


cE

ERRV+ Σ

3

4

12

FD

t

LL

F

1 - E before limit2 - Sensed V3 - V4 - V

States

Exciter EXST2

RsT+11

Σ

REFV

Exciter EXST2 IEEE Type ST2 Excitation System Model

Σ+

−+

1A

A

KsT+

RMAXV

RMINV

1

EsT

EK

FDE+

−

1F

F

sKsT+

RV Σ−

πE P T I TV K V jK I= +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI

EXF

If 0 and 0, then 1P I BK K V= = =

Σ++ERRV

BV

FD MAXE

0

SV

+

EV

B C

Model supported by PSLFModel supported by PSSE does not include T and T inputs

CE3

4

5 12

FD

t

R

F

LL

1 - E2 - Sensed V3 - V4 - V5 - V

States

11

C

B

sTsT

++

Exciter EXST2A

RsT+11

Σ

REFV

Exciter EXST2A Modified IEEE Type ST2 Excitation System Model

Σ+

−+ 1

A

A

KsT+

RMAXV

RMINV

1

EsT

EK

FDE+

−

1F

F

sKsT+

RV Σ−

πE P T I TV K V jK I= +TV

TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

If 0 and 0, then 1P I BK K V= = =

ERRV

FD MAXE

0

SV

+

EV

π

B C

Model supported by PSLFModel supported by PSSE does not include T and T inputs

FVBV

COMPV11

C

B

sTsT

++

3

4

5 12

FD

t

R

F

LL

1 - E2 - Sensed V3 - V4 - V5 - V

States

Exciter EXST3

RsT+11

Σ

REFV

Exciter EXST3 IEEE Type ST3 Excitation System Model

Σ+−

+

11

CJ

B

sTKsT

++

FDEAV π


TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

ERRV

BV

F D M A XE

SV

+

EV

∑ 1A

A

KsT+

RMAXV

RMINV

RV+

IM INV

IM AXV

GK

−GV

GMAXV


CE

PjP PK K e θ=

3 12

R

t

1 - V2 - Sensed V3 - LL

States

Exciter EXST3A

Exciter EXST3A IEEE Type ST3 Excitation System Model

11

CJ

B

sTKsT

++

FDEAV π


TI

( )EX NF f I=C FDN

E

K IIV

=FDI NI EXF

BV

EV

∑ 1A

A

KsT+

RMAXV

RMINV

+

IM INV

IM AXV

GK

−GV

GMAXV


RsT+11

Σ+

−

CESV

REFV+

BMAXV

SpeedPj

P PK K e θ=

3 12

R

t

1 - V2 - Sensed V3 - LL

States

Exciter EXST4B

Exciter EXST4B IEEE Type ST4B Excitation System Model

FDEπ

π( )E P T I P L TV K V j K K X I= + +

( )EX NF f I=C FDN

E

K IIV

=FDI NI

EXF

BV

EV

∑ IMPM

KKs

+

MMAXV

MMINV

+

RM INV

RM AXV

GK

−


RsT+11

Σ+

−

CESV

REFV+

BMAXV

11 AsT+

IRPR

KKs

+MV

TV

TI

PjP PK K e θ=

34 12

MInt

t

A

R

1 - V2 - Sensed V3 - V4 - V

States

Exciter EXWTG1

Exciter EXWTG1 Excitation System Model for Wound-Rotor Induction Wind-Turbine Generators

∑

MAXR

MINR

+


+−Rω 1

1 AsT+ EXT FDR (E )

REFω

1DP

DP

sKsT+EP

WK 1

2

11

W

W

sTsT

++ +

+

EXTR

∑

3

12

external1 - R2 - SpeedReg3 - Washout

States

Exciter EXWTGE

Exciter EXWTGE Excitation System Model for GE Wind-Turbine Generators

∑


+− 1

1 CsT+ORDQ

RFQ REFV (V )

11 PsT+

EP

1

Nf

1PV

V

KsT+

+

+∑

RsT+11

IVKs

M INQ

M AXQ

π

tan( )⋅FAREF REFP (V ) REF

REF

Q(V ) Switch 0=

Switch 1=

ORDQ

Switch 1= −

Switch 1=

Switch 0=

ORD

REF

Q from separate model(V )

WindVAR Emulation

OpenLoop Control

M INQ

M AXQ

CMDQ

pfaflg

varflg

+−GENQ

∑QIKsCMDQ

MAXV

MINV

+−

TERMV

∑REFV VIKs

TERM QMAXV + XI

TERM QMINV + XI

Q CMD FDE '' (E )

÷ORD SFrom Wind Turbine Model

P (V ) PCMD FDI (I )

PM AXI

To Generator M odel

R E GV

3

4

5

1

2

ref"QCMD

PV

regMeas

IV

ORD

Meas

1 - V

2 - E3 - K4 - V

5 - K6 - Q7 - P

States

6

7

Exciter IEEET1

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV

REFV

SV

+

−+

Σ1

EsT

EK

E E FDV S E= ⋅

+

−

+

+

EV

FDE

Σ

Exciter IEEET1 IEEE Type 1 Excitation System Model

RVΣ−

+

1F

F

sKsT+


CE

3

4

1

2

t

R

F


States

Exciter IEEET2

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV

REFV

SV

+

−+

Σ1

EsT

EK

E E FDV S E= ⋅

+

−

+

+

EV

FDE

Σ


RVΣ−

+

11F

F

sKsT+2

11 FsT+


CE

3

45

1

2

t

R

F1

F2


States

Exciter IEEET3

RsT+11

Σ 1A

A

KsT+

RMAXV

RMINV

REFV

SV

+

−+

Σ1

E EK sT+

+

+

FDE


RVΣ−

+

20.78

If 1, 0

FD

THEV

B

IAV

A V

⎛ ⎞⋅= ⎜ ⎟⎝ ⎠> =

1F

F

sKsT+

0

BM AXV

BV

πTHEV P T I TV K V jK I= +TV

TI

1 A−FDI


CE

3

4

12

t

R

F


States

Exciter IEEET4

Σ1

RHsT

RMAXV

RMINV

REFV

+

− Σ1

E EK sT+

+ FDE


RVRHVVΔV K<ΔV

π

ψ

ES

−


CE

RMAXV

RMINVKV

-KV

1

-1RK

R-K

VΔV K>

12

RH

1 - EField2 - V

States

Exciter IEEET5

Σ1

RHsT

+

− Σ1

E EK sT+

+

Exciter IEEET5 Modified IEEE Type 4 Excitation System Model

RMAXV

π

ψ

ES

−


CE

RMAXV

RMINVKV

-KV

RMAXV

RMINV

REFV

FDE

RVRHV

VΔV K<ΔV

VΔV K>

12

RH

1 - EField2 - V

States

Exciter IEEEX1

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Exciter IEEEX1 IEEE Type 1 Excitation System Model

Σ+

−+

ERRV 1A

A

KsT+

RMAXV

RMINV

Σ1

EsT

E EK S+

FDE+

−

11F

F

sKsT+

FVRV

Regulator

D am ping

−


CE3 4

5

12

t

B

R

F


States

Exciter IEEEX2

Exciter IEEEX2 IEEE Type 2 Excitation System Model IEEEX2


RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Σ+

−

+ERRV 1A

A

KsT+

RMAXV

RMINV

Σ1

EsT

E EK S+

FDE+

−FV

RV

Regulator

D am ping

−

CE

( ) ( )1 21 1F

F F

sKsT sT+ +

3 4

5

12

t

R

F1

F2

1 - EField2 - Sensed V3 - LL4 - V5 - V6 - V

States

6

Exciter IEEEX3

RsT+11

Σ

SVREFV

+


Σ+

− +

ERRV 1A

A

KsT+

RMAXV

RMINV

Σ1

E EK sT+FDE+

+

1F

F

sKsT+

FV

Regulator

Damping

−

0

THEV P T I TV K V jK I= +TV

TI0

BM AXV

( )22 0.78TH FDV I−THV

FDI

BV


CE

RV

3

4

12

t

R

F


States

Exciter IEEEX4

RsT+11

REFV


Σ+

− ERRV RMAX RMIN

V RH

V VsK T

−

RMAXV

RMINV

If , If , If ,

ERR V R RMAX

ERR V R RH

ERR V R RMIN


≥ =

< =

≤− =

RHV

VK−

VK

Σ1

EsT

E EK S+

FDE+

−RV


CE

3

1

2

t

RH

1 - EField2 - Sensed V3 - V

States

Exciter IEET1A

Σ

REFV

Exciter IEET1A Modified IEEE Type 1 Excitation System Model

Σ+

− +

1A

A

KsT+

RMAXV

RMINV

Σ1

EsT

E EK S+

FDE+

−

1F

F

sKsT+

−

SV

FD M AXE

FD M INE+


CE

3

12

R

F

1 - EField2 - V3 - V

States

Exciter IEET1B

Σ

M AGI

+

+Σ

1

EsT+ FDE

Exciter IEET1B Modified IEEE Type 1 Excitation System Model

RV

π

ψ

ES

−

EK−

+RsT+1

1

EX

TV Σ

REFV

+SM AXV

SM INV

Σ− +

Bias

SV

Σ+

++

11A

A

KsT+

RMAXV

RMINV

2

11 AsT+ REGV

1

11F

F

sKsT+

−

Switch=0

Switch=1

Model supported by PSSE but not implemented yet in Simulator

CE

Exciter IEET5A

Σ 1A

RH

KsT+

RMAXV

RMINV

REFV

+

− Σ1

E EK sT+

+FDE

Exciter IEET5A Modified IEEE Type 4 Excitation System Model

RV

*

π

ψ

ES

−

Σ

TOV

+

− TΔV

FD M AXE

FD M INE

* If equals zero, block becomes ARH

KTs


CE

RMAXV

RMINVKV

-KV

VΔV K<

VΔV K>

12

RH

1 - EField2 - V

States

Exciter IEEX2A

RsT+11 1

1C

B

sTsT

++Σ

SVREFV

+

Exciter IEEX2A IEEE Type 2A Excitation System Model

Σ+

−+

ERRV 1A

A

KsT+

RMAXV

RMINV

Σ1

EsT

E EK S+

FDE+

−

11F

F

sKsT+

FVRV−

0


CE3 4

5

12

t

B

R

F


States

Exciter REXS

RsT+11

ΣSV

REFV

+

Exciter REXS General Purpose Rotating Excitation System Model

Σ+

−+

ERRV 1A

A

KsT+

RMAXV

RMINV

1

2

11

F

F

sTsT

++

FV

Regulator

−

0

RMIN RMAX FMIN FMAX TERMModel supported by PSLF. If flimf = 1 then multiply V ,V ,V , and V by V .

CE

IM AXV−

IM AXV

1F

F

sKsT+

VIVP

KKs

+ 1 2

1 2

(1 )(1 )(1 )(1 )

C C

B B

sT sTsT sT

+ ++ +

ΣΣ IIIP

KKs

++

RV

11 PsT+

FMAXV

FMINVHK

Σ1

EsT

E EK S+

DK

π

( )EX NF f I=

C FDN

E

K IIV

=

+−

+

+

EV

EXF

FDI

Σ

NI

FDE+

0

Speed

CXTERMI

CMAXV

EFDK

RV

−

+ +

FEI0

1

2

Fbf

34

5

1

2 E

T I

F I

R

1 - V 6 - Voltage PI2 - Sensed V 7 - V LL13 - V 8 - V LL24 - Current PI 9 - Feedback5 - V 10 - Feedback LL

States6

87

10

9

Exciter REXSY1

Exciter REXSY1 General Purpose Rotating Excitation System Model


RsT+11

Σ

SV

REFV

+

Σ+

−+

11 AsT+

RMAXF V⋅

RMINF V⋅1

2

11

F

F

sTsT

++

FV−

IM AXV−

IM AXV

1F

F

sKsT+

VIVP

KKs

+ 1 2

1 2

(1 )(1 )(1 )(1 )

C C

B B

sT sTsT sT

+ ++ + RV

0

1

2FEI

FDE

0II

IPKKs

+1

1 PsT+

FMAXF V⋅

FMINF V⋅HK

Σ1

EsT

E EK S+

π

( )EX NF f I=

C FDN

E

K IIV

=

−

+

+

EV

EXF

FDI

ΣNI

FDE+

CXTERMI

CMAXV

+

FEI

RV

DK

Σ+

−

[ ]1IMF T E D EF= 1.0 + F (E -1.0) (K +K +S )⋅CE

Exciter Field Current Regulator

Fbf

34

5

1

2

Voltage Regulator

E

T I

F I

R


States

6

7 8

910

Exciter REXSYS

Exciter REXSYS General Purpose Rotating Excitation System Model


RsT+11

Σ

SV

REFV

+

Σ+

−+

11 AsT+

RMAXF V⋅

RMINF V⋅1

2

11

F

F

sTsT

++

FV−

IM AXV−

IM AXV

1F

F

sKsT+

VIVP

KKs

+ 1 2

1 2

(1 )(1 )(1 )(1 )

C C

B B

sT sTsT sT

+ ++ + RV

0

1

2FEI

FDE

0II

IPKKs

+1

1 PsT+

FMAXF V⋅

FMINF V⋅HK

Σ1

EsT

E EK S+

π

( )EX NF f I=

C FDN

E

K IIV

=

−

+

+

EV

EXF

FDI

ΣNI

FDE+

+

FEI

RV

DK

Σ+

−

[ ]1IMP T E D EF= 1.0 + F (E -1.0) (K +K +S )⋅CE

Exciter Field Current Regulator

Fbf

34

5

1

2

Voltage Regulator

E

T I

F I

R


States

6

7 8

910

Exciter SCRX

REFV

Exciter SCRX Bus Fed or Solid Fed Static Excitation System Model

Σ+

−1 E

KsT+

FDMAXE

FDMINE

πFDE1

1A

B

sTsT

++

SV

+

TE 1SWITCHC =0 SWITCHC =1

SWITCH

Model supported by PSLFModel supported by PSSE has C 1=

CE

1 2

E

1 - Lead-Lag2 - V

States

Exciter SEXS_GE

compV

REFV

Exciter SEXS_GE Simplified Excitation System Model

+

−1 E

KsT+

MAXE

MINE

11

A

B

sTsT

++

StabilizerOutput

+


RsT+11 FDE( )1C C

C

K sTsT+

Σ

FDM INE

FDM AXE34 12

t

1 - EField2 - Sensed V3 - LL4 - PI

States

Exciter SEXS_PTI

CE

REFV

Exciter SEXS_PTI Simplified Excitation System Model

Σ+

−1 E

KsT+

FDMAXE

FDMINE

FDE11

A

B

sTsT

++

SV

+


12

1 - EField2 - LL

States

Exciter ST6B

RsT+11

UELVREFV

−FDE

Exciter ST6B IEEE 421.5 2005 ST6B Excitation System Model

RMAXV

RMINV

1G

G

sKsT+

−

OEL(OEL=2)

V

HVGate

LVGate

Alternate OEL Inputs

OEL(OEL=1)

V

+

RMULT

ST6B supported by PSSEESST6B supported by PSLF with optional V

CV

1IA DA

PADA

K sKKs sT

+ ++Σ

AMAXV

AMINV

Σ

π

CLK

GV

AV

TV

FD

t

G

1 - E2 - Sensed V3 - PID14 - PID25 - V

States

3 4

5

1

2

10 RMULTV

Σ

SV

+

+−

Σ MK Σ

FFK

LRK

BV

RMINV

LRI

FDI

+

−

+

−

++

RVΣ

11 SsT+

Exciter ST7B

RsT+11

REFV

FDE

Exciter ST7B IEEE 421.5 2005 ST7B Excitation System Model

1IA

IA

sKsT+

OEL(OEL=2)

V

LVGate

Alternate OEL Inputs

OEL(OEL=1)

V

+

ST7B supported by PSSEESST7B supported by PSLFNot implemented yet in Simulator

CV

++

−

LK

HK

Σ

11 SsT+

11

G

F

sTsT

++

HVGate

Alternate UEL Inputs

UEL(UEL=1)

V UEL(UEL=2)

V

MAXV

MINVΣ

+++

+

DROOPV

SCLVΣ Σ

REF_FBV

SV

PAK

HVGate

LVGate

11

C

B

sTsT

++

Σ Σ

Σ LVGate

HVGate

T RMAXV V

T RMINV V

OEL(OEL=3)

V UEL(UEL=3)

V

T RMAXV VT RMINV V

+

−

+

+

Exciter TEXS

CE

REFV

Exciter TEXS General Purpose Transformer-Fed Excitation System Model

Σ+

−FDE

1G

G

KsT+

SV

+


11 RsT+

IM AXV−

IM AXVVI

VPKKs

+

1VD

VD

sKsT+

RMAXV

RMINV

Σ++

Σ−

Σ+

+ Σ+

−

FFK

MK

RM INV

RM AXVLVGate π

CX

Σ+−

CLKLRI LRK

0

FDI

1 0

GeneratorTerminal Voltage

ConstantSource Voltage

RV EV+

3

4

1

2

t

1 - Feedback2 - Sensed V3 - Derivative Controller4 - Integral Controller

States

Exciter URST5T

CE

RsT+11

Σ

REFV

−+

Σ

CK

+

+

STBV FDI

FDE

Exciter URST5T IEEE Proposed Type ST5B Excitation System Model

UELV

HVGate

OELV

LVGate Σ

−

1

1

11

C

B

sTsT

++

RMAX RV /K

RMIN RV /K

2

2

11

C

B

sTsT

++

RMAX RV /K

RMIN RV /K

RMAXV

RMINV1

11 sT+

RMAX TV V

RMIN TV V

RK +


3 4 12

R

t

1 - V2 - Sensed V3 - LL14 - LL2

States

Exciter WT2E1

−

+

Exciter WT2E1 Rotor Resistance Control Model for Type 2 Wind Generator

elecP

MAXR

MINR


external

elec

1 - R2 - Speed3 - P

States

11 SPsT+

11 PCsT+

Σ1

PI

KsT

+

Speed

Power-Slip Curve

1

2

3

Exciter WT3E and WT3E1

Exciter WT3E and WT3E1 Electrical Control for Type 3 Wind Generator

∑

MAX wrat MIN wrat FV C

QCMD QMAX QMIN

WT3E supported by PSLF with RP P and RP -P , T TWT3E1 supported by PSSE uses vltflg to determine the limits on E . When vltflg > 0 Simulator always uses XI and XI .

= = =

+− 1

1 FVsT+

RFQV

11 PsT+

elecP

1

Nf

1PV

V

KsT+

+

∑RsT+1

1

IVKs

M INQ

M AXQ

π

tanFAREFP

REFQ

1

0

1−

Reactive Power Control Model

M INQ

M AXQ

varflg

−elecQ

QIKs

MINV

+−

∑REFV

QVKs

QMAXXI

QMINXI

QCMDE

CV

3

4

5

1 2

ref ORD

qppcmd Meas

PV

regMeas

IV ORD

1 - V 6 - Q2 - E 7 - P

3 - K 8 - PowerFilter4 - V 9 - SpeedPI

5 - K 10 - P

States

6

7

MAXV TERMVvltflg

+

0

0>

20( 20%, )PP ω=

100( 100%, )PP ω=

40( 40%, )PP ω=60( 60%, )PP ω=

( , )MIN PMINP ω

Speed

P

Active Power (Torque) Control Model

elecP1

1 PWRsT+∑ IP

PPKKs

+ π ∑1

FPsT ÷

M INRP

M AXRP PMAXIMAXP

MINP

1098

Speed Speed

−

++

−

TERMV

PCMDI

∑

+

Exciter WT4E1

Exciter WT4E1 Electrical Control for Type 4 Wind Generator

Model supported by PSSE but not yet implemented in Simulator

∑+

− 11 FVsT+

RFQV

11 PsT+

elecP

1PV

V

KsT+

+

∑1

1 RVsT+

IVKs

M INQ

M AXQ

π

tanFAREFP

10

M INQ

M AXQ

varflg

−elecQ

QIKs

MINCLV

+

−∑ VIK

s

QMAXI

QMINI

QCMDI

CV

MAXCLV

TERMV

+

elecP ∑ ÷PMAXI

−+

+

−

TERMV

PCMDI

∑

+

pfaflg

REFQ

01

ORDP

Converter Current Limitpqflag

∑

−

0.01

11 PWRsT+

IPPP

KKs

+

1F

F

sKsT+

REFP

MINdP

MAXdP

Machine Model CSVGN1


Σ−

Machine Model CSVGN1 Static Shunt Compensator CSVGN1

+

5

11 sT+

1.

/MINR RBASE

Other SignalsVOTHSG

REFV−

V ( ) ( )( )( )

1 2

3 4

1 11 1

K sT sTsT sT+ ++ +

MAXV

MINV

π+

−

/BASEC SBASE

YΣ

/MBASE SBASE

RBASE MBASE= is the voltage magnitude on the high side of generator step-up transformer if present.VNote :



Σ−


+

5

11 sT+

1.

π+

−

/MINR RBASE

Other SignalsVOTHSG

REFV−

/BASEC SBASE

YERRV

V ( ) ( )( )( )

1 2

3 4

1 11 1

K sT sTsT sT+ ++ +

MAXV

MINV

1, if / if

ERR OV

ERR OV

V VRMIN RBASE V V

>

<−

Σ

/MBASE SBASE

RBASE MBASE= is the voltage magnitude on the high side of generator step-up transformer if present.VNote :



Σ−


+

5

11 sT+

1.

π+

−

/MINR RBASE

Other SignalsVOTHSG

REFV−

/BASEC SBASE

YERRV

IBV ( ) ( )( )( )

1 2

3 4

1 11 1

K sT sTsT sT+ ++ +

MAXV

MINV

1, if / if

ERR OV

ERR OV

V VRMIN RBASE V V

>

<−

Σ

/MBASE SBASE

RBASE MBASE=



Machine Model CSVGN5 Static Var Compensator CSVGN5

−

6

11 sT+

MAXB

MINB

( )VREF I

+VOLT(IBUS)

VOLT(ICON(M ))or

EMAXV

EMAXV−

+

1

11 ssT+ Σ

+

( )VOTHSG I

Σ 2

3

11

S

S

sTsT

++

4

5

11

S

S

sTsT

++ SVSK

( )MBASE ISBASE ( )VAR L

( )' '

'

' '

If :If :

If :

ERR LO R MAX SD ERR

HI ERR LO R R

ERR HI R MIN

V DV B B K V DVDV V DV B B

V DV B B

> = + −< < =< =

ERRV RB

Fast Override

Thyristor Delay

'

'

If 0, /

/LO MAX SVS

HI MIN SVS

DVDV B K

DV B K

=

=

=

If 0,

LO

HI

DVDV DVDV DV

>==−

Filter

Regulator1st Stage 2nd Stage64444744448

'R

B SVSB



Machine Model CSVGN6 Static Var Compensator CSVGN6

−

6

11 sT+

MAXB

MINB

VREF

+VOLT(IBUS)

VOLT(ICON(M ))or

+

1

11 ssT+ Σ

+

OtherSignals

( )VOTHSG I

Σ 2

3

11

S

S

sTsT

++

4

5

11

S

S

sTsT

++ SVSK

( )' '

'

' '

If :If :

If :

ERR LO R MAX SD ERR

HI ERR LO R R

ERR HI R MIN

V DV B B K V DVDV V DV B B

V DV B B

> = + −< < =< =

ERRV RB

Fast Override

Thyristor Delay

'

'

If 0, /

/LO MAX SVS

HI MIN SVS

DVDV B K

DV B K

=

=

=

If 0,

LO

HI

DVDV DVDV DV

>==−

Filter

'R

B SVSB

MAXV

MINV

EMAXV

EMINV

++

Σ

Position 1 is normal (open)If 2, switch willclose after cycles.

ERRV DVTDELAY

>

1 2

BIAS

BSHUNT

+

RB

Machine Model GENCC

fdE+

−

Machine Model GENCC Generator represented by uniform inductance ratios rotor

modeling to match WSCC type F

−

+

−

'

1

dosT

'

' ''d d

d d

X XX X

−−


''

'd d

d d

X XX X

−−

' ''d dX X−

'qE '

qE''

1

dosTΣ

di

1EeS

q

d

XX

q axis

d axis

−Σ

π

Machine Model GENCLS

Machine Model GENCLS Synchronous machine represented by “classical” modeling or

Thevenin Voltage Source to play Back known voltage/frequency signal


R ecordedV oltage

R espondingS ystem0.03

on 100 M V A baseabZ =

A B

gencls

R espondingS ystem

ppdI

B

R espondingS ystem0.03

on 100 M V A baseabZ =

A Bgencls

ppdI

Machine Model GENROU

fdE+

Machine Model GENROU Solid Rotor Generator represented by equal mutual

inductance rotor modeling

+

+'

1

dosT

''

'd l

d l

X XX X

−−


''dP

di

−

fdP

' ''

'd d

d l

X XX X

−− Σ

'd lX X−

+ ''

1

d os T−

ΣkdP−

+

+

+

'd dX X−

Σ

''dP

+

+

Σ

''P

''

( )q l

qd l

X XP

X X−

−

eS

Σ

' ''

'( ) * *2d d

d l

X XX X

−−

d AXIS−

ad fdL i

*** , q AXIS identical swapping d and q substripts−

Machine Model GENSAL

fdE+

Machine Model GENSAL Salient Pole Generator represented by equal mutual

inductance rotor modeling

+

+'

1

dosT

''

'd l

d l

X XX X

−−


''dP

di

−

fdP ' ''

'd d

d l

X XX X

−− Σ

'd lX X−

+ ''

1

d os T−

ΣkdP−

++

+

'd dX X−

Σ

+

+

Σ

' ''

'( ) * *2d d

d l

X XX X

−−

d AXIS−

ad fdL iΣ

''

1

q os T−

Σ kdP−

''q qX X−

''qP

qiq AXIS−

e fdS P

Machine Model GENTPF

fdE+

−

Machine Model GENTPF Generator represented by uniform inductance ratios rotor

modeling to match WSCC type F

−

+

−

'

1

dosT

'

' ''d d

d d

X XX X

−−


''

' ''d d

d d

X XX X

−−

' ''d dX X−

'qE '

qE''

1

dosT

di

−Σ

eS

eS Σ''dϕ

( )

( )

1 .

A x is S im ilar ex cep t:

1 .

e ag

qe ag

d

S fsa t

QX

SX

ϕ

ϕ

= +

−

= +

Machine Model GENTRA

fdE+

Machine Model GENTRA Salient Pole Generator without Amortisseur Windings

+


di

−

'dX

'd dX X−+

+

d AXIS−

ad fdL i

qX qiq AXIS−

eS

'

1

d os T Σ−

Σ

Σ

Machine Model GENWRI

MECHP+

−

Machine Model GENWRI Wound-rotor Induction Generator Model with Variable External

Rotor Resistance

−

+1

2Hs


rω slip0ω÷Σ

ELECP

Σ

Sf

( )( )

( )( )( )

( )( )

'0

'0

'

'0

'

'0

'

'

2

22 2

( )

( )

s l

s

fd d s dfd fq

fq q s qfq fd

d fd

q fq

L LR T p o

L L

R T p oTR ex R

S L L is l ip

T

S L L is l ip

T

−=

−

=+

+ + −= − +

+ + −= − +

=

=

&

&

ω

ϕϕ ϕ

ϕϕ ϕ

ϕ ϕ

ϕ ϕ

( ) ( )( )( )( )

' '

' '

2 2' ' '

'

'

'

q s d d a q

d s q q a d

d q

e sat

d e d

q e d

e Li R i

e Li R i

S f

S S

S S

= − −

= − + −

= +

=

=

=

ω ϕ

ω ϕ

ϕ ϕ ϕ

ϕ

ϕ

ϕ

'0R 2 T p o i s a c o n s t a n t w h i c h i s e q u a l t o T t i m e s

t h e t o t a l r o t o r r e s i s t a n c e . R 2 i s t h e i n t e r n a l r o t o r r e s i s t a n c e R 2 e x i s t h e i n t e r n a l r o t o r r e s i s t a n c e

Machine Model GEWTG

''

( )q cmdEefd

Fromexwtge

Machine Model GEWTG Generator/converter model for GE wind turbines – Doubly Fed Asynchronous Generator (DFAG) and

Full Converter (FC) Models

11 0.02s+


0s

1''X

−

PlvI11 0.02s+

1s

( )PcmdI

ladifdFrom

exwtge

sorcI

''jX

H igh V oltageR eactive C urrent

M anagem ent

Low V oltageA ctive C urrentM anagem ent

11 0.02s+

2sV

LVPL

xerox(0.5pu)

brkpt(0.9pu)

LowVoltage Power Logic

1.11

LVPL

& LVLP rrpwr

VtermV

Figure 1. DFAG Generator / Converter Model

''

( )q cmdEefd

Fromexwtge

Machine Model GEWTG Generator/converter model for GE wind turbines – Doubly Fed Asynchronous Generator (DFAG) and

Full Converter (FC) Models

11 0.02s+


0s

1−

PlvI11 0.02s+

1s

( )PcmdI

ladifdFrom

exwtge

sorcIH igh V oltageR eactive C urrent

M anagem ent

Low V oltageA ctive C urrentM anagem ent

11 0.02s+

2sV

LVPL

xerox(0.5pu)

brkpt(0.7pu)

LowVoltage Power Logic

1.11

LVPL

& LVLP rrpwr

VtermV

Figure 1. Full Converter Generator / Converter Model

Machine Model MOTOR1

Machine Model MOTOR1 “Two-cage” or “one-cage” induction machine


1

1

o r

lr

RL

ω

o SL IPω1drψ

Σ1

1 .

lrL

+

−+

+1qrψ

2

2

o r

lr

RL

ω

o SL IPω

Σ

2drψ

Σ2

1 .

lrL

+

−+

−2qrψ

''m satLΣ

+

+

'' ''d qE ψ− =

''m satL qsi

Σ

eS

mψ

1. ( )sat e mK S ψ= +

''

1 2

1./ 1. / 1. /m sat

sat m lr lr

LK L L L

=+ +

Σ

2

2

o r

lr

RL

ω

o SL IPω2qrψ

Σ2

1 .

lrL

+

−+

+2drψ

1

1

o r

lr

RL

ω

o SL IPω

Σ Σ1

1 .

lrL

+

−+

+1drψ

Σ

1qrψ

''m satL

+

+ Σ

+

−

2 2md mqψ ψ+

''m satL dsi

−Σ+

'' ''q dE ψ=

' '1

'' ''1 2

' '1 1 1 1

'' ' '' '2 2 2 2

1. / (1. / 1. / )

1. / (1. / 1. / 1. / )

/ ( ) ( ) / ( )

/ ( ) ( ) / ( )

m s l

m m lr l

m m lr lr l

o lr m o r m lr m o r

o lr m o r m lr m o r

L L L

L L L L L

L L L L L L

T L L R L L L R

T L L R L L L R

ω ω

ω ω

= −

= + = −

= + + = −

= = +

= = +

mqψ

mdψ

Machine Model SVCWSC

Machine Model SVCWSC Static Var device compatible with WSCC Vx/Wx models

+

+Σ

11

S12

1+sT1+sT

S13

S14

sT1+sT

S3K

Input 1

Input 2


EM INV

EM AXV

RETV

SVSBC

S1

1+sT1+sTΣ+

−

CX

S2

S3

1+sT1+sT

S4

S5

1+sT1+sT SVSK

1MAXV

1MINV

2*VC MAXK V

2*VC MINK V

Σ Σ

SCS S

S

V VV (from external PSS)

+

S6

11+sT

F as tO v e rR id e

MAXB

MINB

π

BUSV

S1

S7

K1+sT

8

S9

1+ sT1+sT

S2

S10

K1+sT

+

+ +

−

SCSM INV

SCSM AXV

SCSV

if Vbus<V1vcl, Kvc = 0.if Vbud>V2vcl for Tdvcl sec., Kvc =1.

Voltage Clamp Logic

Generator Other Model LCFB1

Turbine Load Controller Model LCFB1

mwsetP 1Ks

++

PK

−

+

bFMAXe

MAXe−db

db−

11 PELECsT+

Σ

genP

rmaxL

rmaxL−

rmaxL

rmaxL−

Σ +

+

0refP

Σ refP


Σ

Frequency Bias Flag - fbf, set to 1 to enable or 0 to disablePower Controller Flag - pbf, set to 1 to enable or 0 to disable

Freq

1.0 +

−

−

elec

I

1 - P Sensed2 - K

States

1

2

Governor BPA GG

Governor BPA GG WSCC Type G Governor Model


mech1 - P2 - Lead-Lag 13 - Integrator 34 - Integrator 4

States

'1K Δω 2

1

11

sTsT

++ Σ

+

−

M OP

MAXP+

−3

11 sT+ 4

11 sT+

5

5

11

sFTsT

++

MPM eP -P

eP

Σ2 3 4 1

Governor BPA GH

Governor BPA GH WSCC Type H Hydro-Mechanical Governor Turbine Model


1(1 )G PT sT+

UPP&

−−

1s /2

11

W

W

sTsT−+

'1K Δω

DOWNP&

0P XRMAX(P.U.)P

MINP =0

R

Σ+

+

1d d

d

SD TsT+

Σ+

PILOT VALVE GATE SERVO TURBINE

MP23

4

1

mech1 - P2 - P gate valve3 - y34 - Feedback

States

Governor BPA GIGATB, BPA GJGATB, BPA GKGATB, and BPA GLTB

Governor BPA GIGATB, BPA GJGATB, BPA GKGATB, and BPA GLTB


Governor BPA GSTA

Governor BPA GSTA WSCC Type S Steam System Governor

And Nonreheat Turbine (Type A) Model


−−

1s

1K Δω

0PMAX(P.U.)P

MIN(P.U.)P

+GVP

2

1

11

sTsT

++ 3

1T

UPP&

DOWNP&

Σ1

1 CHsT+MP23 1

mech1 - P2 - P gate valve3 - Lead-lag

States

Governor BPA GSTB

Governor BPA GSTB WSCC Type S Steam System Governor and Tandem Compound

Single Reheat Turbine (Type B) Model


−−

1s

1K Δω

0PMAX(P.U.)P

MIN(P.U.)P

+

GVP2

1

11

sTsT

++ 3

1T

UPP&

DOWNP&

Σ

MP

11 CHsT+

11 RHsT+

11 COsT+

HPF IPF LPF

++

++

ΣΣ

2

3 4 5

1

1 - P gate valve2 - Lead-lag3 - y34 - y45 - y5

States

Governor BPA GSTC

Governor BPA GSTC WSCC Type S Steam System Governor and Tandem Compound

Double Reheat Turbine (Type C) Model


−−

1s

1K Δω

0PMAX(P.U.)P

MIN(P.U.)P

+

GVP2

1

11

sTsT

++ 3

1T

UPP&

DOWNP&

Σ

MP

11 CHsT+ 1

11 RHsT+ 2

11 RHsT+

VHPF HPF IPF

++

++

Σ

11 COsT+

LPF

++

Σ Σ

2

3 4 5 6

1

1 - P gate valve2 - Lead-lag3 - y34 - y45 - y56 - y6

States

Governor BPA GWTW

Governor BPA GWTW WSCC Type W Hydro Governor System

And Hydro Turbine (Type W) Model


−

KΔω

0P

+GVP

2

1 3

1(1 )(1 )

sTsT sT+

+ +

MAX/100P

MIN/100P

Σ1

1 0.5W

W

sTsT

−+

MP

2 3

1

mech1 - P2 - y03 - y1

States

Governor CCBT1

Governor CCBT1 Steam Plant Boiler/Turbine and Governor Model

MIN4

Σ

Model supported by PSLFProportional-integral blocks 1-6 also have rate limits not shown in the block diagram

Σ

11 WsT+

1

DsT

11 FsT+

11

IP

KKs

+

77

71D

PD

sKKsT

++

Σ

44

IP

KKs

+

Σ

Σ

33

IP

KKs

+

Σ1 r

rpelec

rvalve

ΣBK

-dbd

+dbd Σ

MAX4

MIN3

MAX3

Σ

MIN7

MAX7

Σ

MIN2

22

IP

KKs

+

MAX2

MIN5

55

IP

KKs

+

MAX5

1.0

MIN6

66

IP

KKs

+

MAX6

MIN1

MAX1

Σ

π

πPK

π

1 ah−

ah

1

RHsT

1PLM

PLM

KsT+

Σ

Σ

11 GsT+

IGOVPGOV

KKs

+

MINV

MAXV

Σ Σ

11 PelecsT+

-1

0

refω Speed

1.0

Speed

mechP

Valve Bias

mechP

refL

Bias

refPresslmref refP •Press

genP

Σ

+

−

−

−

++

−

− −

−−

−

−

−

−−

−−

+

+

+

+

++

++

++

+

++

++

2

3

4

5

6

1

7

8 9

10

11

12

+

13

14 1550PLMT =

Σ

Governor CRCMGV

(HP)Speed ( )

1( )

1 /1

HP

HP

RsT+ Σ

+

mech(HP)P

Governor CRCMGV Cross Compound Turbine-Governor Model

( )( )( )( ) 5( )

3( ) 4( ) 5( )

11 1 1

HP HP

HP HP HP

sF TsT sT sT

+

+ + +−

Reference

MAX(HP)P

0

+

( )

1( )

1 /1

LP

LP

RsT+ Σ

+

( )( )( )( ) 5( )

3( ) 4( ) 5( )

11 1 1

LP LP

LP LP LP

sF TsT sT sT

+

+ + +−

ReferenceMAX(LP)P

0

+

( )( )2( )H HP T HPD E −

Σ−

+

( )( )2( )H LP T HPD E −−

Σ−

(LP)SpeedΣ

High-Pressure Unit

Low-Pressure Unit

mech(LP)P−


2 3 4

5

6

1

1 - HPInput2 - HPState13 - HPState24 - HPState35 - LPInput6 - LPState17 - LPState28 - LPState3

States

7 8

Governor DEGOV

Governor DEGOV Woodward Diesel Governor Model

( )( )( )

4

5 6

11 1

Actuator

K sTs sT sT

++ +

144424443

MAXT

MINT

π( )32

1 2 1

11

Electric Control Box

sTsT s T T− ++ +

1442443

1+Speed

{Engine

DsTe−mechP


2

3 4 5

1

1 - Control box 12 - Control box 23 - Actuator 14 - Actuator 25 - Actuator 3

States

ΔωSpeed

Governor DEGOV1

Governor DEGOV1 Woodward Diesel Governor Model

( )( )( )

4

5 6

11 1

Actuator

K sTs sT sT

++ +

144424443

MAXT

MINT

πΔωSpeed

1+Speed

{Engine

DsTe−mechP( )3

21 2 1

11

Electric Control Box

sTsT s T T− ++ +

1442443

+

−

11 EsT+

SBASEMBASE

elecPDROOP

Σ−

refP

1

0


6

Droop Control

1 - Control box 12 - Control box 23 - Actuator 14 - Actuator 25 - Actuator 36 - Droop Input

States

21

3 4 5

Governor G2WSCC

Governor G2WSCC Double Derivative Hydro Governor and Turbine

Represents WECC G2 Governor Plus Turbine Model

G VN

Δω(Speed) eps

1db

11 DsT+

1

1 F

sKsT+

22

2(1 )F

s KsT+

+

+

+

R1

1 TsT+elecP

1G

P

KsT+

OPENVEL

CLOSEVEL

1s

MAXP

MINP

2d b

GV 11

tu r b tu r b

tu r b tu r b

s A Ts B T

++

GVPmechP

+−

Σ

T(T =0)

refP


+−Σ IK

s−

Σ2 3

4 5

6

1

mech

D

1

2

2

elec

1 - P2 - T3 - K4 - K first5 - K second6 - Integrator7 - P Sensed8 - Valve9 - Gate

States

8 9

7

GV1, PGV1...GV6, PGV6 are the x,y coordinates of blockGVN

Governor GAST_GE

Governor GAST_GE Gas Turbine-Governor Model

refP ( )4

5

11

AK sTsT+

+

+

+

+


+

−

2

2

11

AsTBsT

++

−

eps

0db

Δω(Speed)

3

11 sT+

1

1sT

MAXV

MINV

LIMR

1R

Σ

IDLEF

TK

Σ

ΣIDLEF

MAXL

Σ +−

VG

GVP d b b

mechP

11 LTRsT+

+

−

V INC LIM TRAT

LIM MAX

if (D >L ) R =L else R =R Σ

VD

Σ

−

2

3

4

5

1 LVGATE

1 - Input LL2 - Integrator3 - Governor LL4 - Load Limit5 - Temperature

States

GV1, PGV1...GV6, PGV6 are the x,y coordinates of vs. blockGVP GV

Governor GAST_PTI

Governor GAST_PTI Gas Turbine-Governor Model

MAXV

refLoad mechP−

+

turbD

−

1R

Σ

MINV

1

11 sT+ 2

11 sT+

LVGate Σ+

Speed

3

11 sT+TK+ −

+

ΣΣ+

TA (Load Limit)


2

3

1

1 - Fuel Valve2 - Fuel Flow3 - Exhaust Temperature

States

Governor GAST2A

Governor GAST2A Gas Turbine-Governor Model

LowValueSelect

( )1W sXsY Z

++

+Σ−

ReferencesTe−

MAX

MINSpeed

GovernorSpeed

Control

3K +

FuelControl

AC sB+

11 Fsτ+

CRsEe−

FK

6K

Σ+

−

ValvePositioner

FuelSystem fW

FuelFlow

TDsEe−

51

T

sTsτ+

MAX

+

4

11 sT+

54

31KKsT

++ 1fΣ −

TurbineExhaust

Turbine

RadiationShieldThermocouple

TemperatureControl*

CT

11 CDsT+

2fMBASE

RATET

+

Δω

1.0 +

π

Σ

π

mechP

( )1 R f1 f1f1f =T -A 1.0-w -B Speed⎛ ⎞

⎜ ⎟⎝ ⎠

( ) ( )f22 f2 f2 f2f =A -B w -C Speed

f2wTurbine

Gas TurbineDynamics

* Temperature control output is set to output of speed governor when temperature control input changes from positive to negative


2 3

45

7

1

f1w

1 - Speed Governor2 - Valve Positioner3 - Fuel System4 - Radiation Shield5 - Thermocouple6 - Temp Control7 - Turbine Dynamics

States

6

Governor GASTWD

Governor GASTWD Woodward Gas Turbine-Governor Model

LowValueSelect+

−

SpeedReference

sTe−

MAX

MIN

SpeedControl

3K +

FuelControl

AC sB+

11 Fsτ+

CRsEe−

FK

6K

Σ+

−

ValvePositioner

FuelSystem

fWFuelFlow

TDsEe−

5 1

T

sTsτ+

MAX

+ 4

11 sT+

54

31KKsT

++ 1fΣ −

TurbineExhaust

Turbine

RadiationShieldThermocouple

TemperatureControl*

11 CDsT+

2fMBASE

RATET

+

Δω

1.0 +

π

Σ

π

mechP

( ) ( )f =T -A 1.0-w -B Speed1 R f1 f1 f1 ( ) ( )f =A -B w -C Speed2 f2 f2 f2 f2

f2wTurbineGas Turbine

Dynamics

* Temperature control output is set to output of speed governor when temperature control input changes from positive to negative

IKs

PK

DsK

+

Σ++

SBASE

RATET

1DROOP

D

KsT+

Σ

elecP

eP

−

T Setpoint for CTemperature Control


2 3

45

6

1

f1w

1 - Power Transducer2 - Valve Positioner3 - Fuel System4 - Radiation Shield5 - Thermocouple6 - Temp Control7 - Turbine Dynamics8 - PID 1 9 - PID 2

States

78 9

Governor GGOV1

Governor GGOV1 – GE General Governor-Turbine Model

( / )dref turb fnlL K w+ +1

1 FloadsT+11

SA

SB

sTsT

++

mD**Dmm <If D 0, (Speed+1)m >If D 0, (Speed)

−

11

C

B

sTsT

++

engsTe−

turbK

Σ

PloadK

IloadKs

Σ

Σ

−

++

+

1.0

AK tΔ +

+ΣΣ

+

1 A

ssT+

−

drefL mechP

Speed

PgovK

IgovKs

1Dgov

Dgov

sKsT+

+

++

−+

maxerr

minerr

-dbdb

++

π

11 ACTsT+

MAXV

MINV

refPΣ

LowValueSelect

r

Σ

IMWKs

Σ

Σ+ −

11 PelecsT+

elecP

−Σ

fnlw

π

1.0 (Speed+1)governor outputvalve stroke

aset

−

IMW

UP DOWN CLOSE OPEN

Model supported by PSLFModel supported by PSSE does not include non-windup limits on K blockR , R , R , and R inputs not implemented in Simulator

+

2

3

4

5

6

1

Flag0 1

Rselect

11−

2−

mwsetP

1.1r

-1.1r

Timestep

elec1 - P Measured 5 - Turbine LL2 - Governor Differential Control 6 - Turbine Load Limiter3 - Governor Integral Control 7 - Turbine Load Integral Control4 - Turbine Actuator 8 - Supervisory Load Co

States

ntrol9 - Accel Control10 - Temp Detection LL

7

8

9

10

M INV

M AXV

Governor GGOV2

Governor GGOV2 - GE General Governor-Turbine Model

mwsetP


1 floadsT+11

sa

sb

sTsT

++

mD−

11

c

b

sTsT

++

engsTe−

turbK

Σ

ploadK

iloadKs

Σ

Σ

−

++

+

1.0

aK tΔ

5s 9s

6s

+

+ΣΣ

+

1 a

ssT+

8s

4s

−

drefL MECHP

Speed

pgovK

igovKs

1dgov

dgov

sKsT+

+2s+

+

−

1s

+

++

π

11 actsT+

ropenvmax

vminrclose

refPΣ

LowValueSelect

r

Σ

imwKs

Σ

Σ+ −

11 P elecsT+

ELECP

7s

0s

−Σ

fnlw3s

π

1.0

aset

−

+

M INV

M AXV

Frequency-dependent

limit

Speed

fsrt

fsra

fsrn

2 3 4 5 61

1.1r

-1.1r

Flag0 1

Timestep

**Dmm <If D 0, (Speed+1)m >If D 0, (Speed)

(Speed+1)

Rselect

11−

2−governor output

valve stroke

maxerr

minerr

-dbdb


Governor GGOV3

11

cd

bd

sTsT

++


mwsetP


1 floadsT+11

sa

sb

sTsT

++

mD −

11

c

b

sTsT

++

engsTe−

Σ

ploadK

iloadKs

Σ

Σ

−

+

+

+

1.0

aK tΔ +

+ΣΣ

+

1 a

ssT+

−

drefL MECHP

PercievedSpeed

pgovK

igovKs

1dgov

dgov

sKsT+

++

+

−+

++

π

11 actsT+

refPΣ

LowValueSelect

R

Σ

imwKs

Σ

Σ+ −

11 P elecsT+

ELECP

−

fnlw

π

1.0

aset

−

+

Σ

turbK

2

3 4

56

1

7

8

9

10

11

**Dmm <If D 0, (Speed+1)m >If D 0, (Speed)

1.1r

-1.1r

Flag0 1

Timestep

MAXV

MINV

UP DOWN CLOSE OPEN dnrate, R , R , R , and R inputs not implemented in Simulator

Rselect

11−

2−(Speed+1)governor output

valve stroke

MINV

MAXV

elec1 - P Measured 5 - Turbine LL 9 - Accel Control2 - Governor Differential Control 6 - Turbine Load Limiter 10 - Temp Detection LL3 - Governor Integral Control 7 - Turbine Load Integral Contro

States

l 11 - Fuel System Lead Lag4 - Turbine Actuator 8 - Supervisory Load Control

M a x err

Minerr

-dbdb



dnlo

PercievedSpeed

dnhi

ffa

ffb

slope = 1

slope = ffc

MeasuredSpeed

Nonlinear Speed Filter

FilteredSpeed

Rate limit dnrate not used in SimulatorModel supported by PSLF

Governor GPWSCC

Governor GPWSCC PID Governor-Turbine Model

G VN

err

1db

11 DsT+

1Ks

1D

f

sKsT+

+

+

+

R 11 tsT+

( 0)tT >

1G

P

KsT+

1s 2d b

GV 11

tu r b tu r b

tu r b tu r b

s A Ts B T

++

+ −

Σ

PK

Σ+

−

− CVΣ

GVP

0tT =

176

5

3

4

2

mechP

elecP

Δω(Speed)

refP

OPENVEL

CLOSEVEL

MAXP

MINP


mech elec

D

1 - P 5 - P Sensed2 - T 6 - Valve3 - Integrator 7 - Gate4 - Derivative

States


Governor HYG3

Governor HYG3 PID Governor, Double Derivative Governor, and Turbine

Δω1db

11 DsT+

IKs

1

1 f

sKsT+

+

+

+

11 tsT+

1G

P

KsT+

1s

MAXP

MINP

2d bGV

+−

2K

Σ+

−

−

g a teR

−

1db

11 DsT+

1

1 f

sKsT+

( )2

22

1 f

s K

sT+

+

+

e le cR1

1 tsT+

++

Σ IKs

Σ

−

−−

g a teR

Δω (speed-1)pu=

Δω

cflag>0

Σcflag<0

G VN GVP 1

WsT0H

π tA Σ

tu rbD

GVq/PqNL

Σ÷ πΣ+

− +

−

+−

H q

ΔωπΣ

G VPmechP

refP

refP

elecP

CV

CV

1

2

4 5

7

6

3

8

9

1

7

2

OPENVEL

CLOSEVEL


e le cR

Note: cflag determines numbering of states

D

1

i

W

elec

2

2

1 - T2 - K3 - K4 - Valve5 - Gate6 - T7 - P Sensed8 - K First9 - K Second

States

elecP

3


G V

Governor HYGOV

Governor HYGOV Hydro Turbine-Governor Model

+1

1 fsT+−

R

1 r

r

sTrT s+ 1

1 gsT+

turbD

−

tA Σ

πg

+−

2d b

G VP GV

11

n

np

sTsT

++

MAXG

MING

elmrate limit - V

1db

refP

1 2 3

G VN

G V

Δω

Δω

mechP1

WsTHdam=1

πqNL

Σ÷ πΣ+

− +

−

H 4GVP

GVq/P

Model supported by PSSE and PSLFRperm shown as R, Rtemp shown as r

Ttur, Tn, Tnp, db1, Eps, db2, Bgv0...Bgv5, Bmax, Tblade not implemented in SimulatorGV0, PGV0...GV5, PGV5 are the x,y coordinates of blockGVN

1 - Filter Output2 - Desired Gate3 - Gate4 - Turbine Flow

States

Governor HYGOV2

Governor HYGOV2 Hydro Turbine-Governor Model

MAXP

GM AXV

GMAX-V

−

−

+I PK sK

s+

1

3

1A

sTKsT

⎛ ⎞+⎜ ⎟⎝ ⎠

2

4

11

sTsT

++

1s

R 1temp R

R

sR TsT+

5

6

11

sTsT

−+

Σ −

1 2 3

4

5

6

1 - Filter Output2 - Governor3 - Governor Speed4 - Droop5 - Gate6 - Penstock

States

MING

mechP

refP

Model supported by PSSEMAX MINThe G G limit is modeled as non-windup in PSSE but as a windup limit in Simulator.

MAXGΔωSpeed

Governor HYGOV4

G VN

GVP

GV

Governor HYGOV4 Hydro Turbine-Governor Model

+ 11 psT+

−

1

gT1s

+

+−

1dbΔω ΣCU

OU

2d b

permR+

1r temp

r

sT RT s+

Σ

−

turbD

Σ

π

tA


mechP

refP MAXP

MINP

G V

1

WsTHdam

πqNL

Σ÷ πΣ+

− +

−

H 4

GVP GVq/P

q

3

21


W

1 - Velocity2 - Gate3 - Rtemp4 - T

States

Bgv0...Bgv5, Bmax, Tblade not implemented in Simulator

Governor HYST1

Governor HYST1 Hydro Turbine with Woodward Electro-Hydraulic PID Governor,

Surge Tank, and Inlet Tunnel

− ip

KKs

+Σ+

11 asT+

1d

a

sKsT+

Σ+

+

11 asT+

1perm

reg

RsT+

Σ +

−

11 bsT+

MAXG

MING

( )G s +

turbD

Σ−

GVP

GV

refP

genP

Δω

mechP

4

3

21

5

6

9

7

8

Model supported by PSLFNot yet implemented in Simulator

Governor IEEEG1

Governor IEEEG1 IEEE Type 1 Speed-Governor Model

−

−

HPΔω

SPEED

4

11 sT+

2

1

(1 )1

K sTsT++ 3

1T

CU

OU1s

MAXP

MINP

Σ

1K

5

11 sT+

3K

6

11 sT+

5K

7

11 sT+

7K

Σ Σ

2K 4K 6K 8K

Σ Σ

Σ

Σ

HPPMECH

LPPMECH

+

+

+

+

+

+

+

++

++

+

M1P

M2P

+

Model supported by PSLF includes hysteresis that is read but not implemented in SimulatorModel supported by PSSE does not include hysteresis and nonlinear gain

GVP

GV

1db

2db

3 4 5

12

1 - Governor Output2 - Lead-Lag3 - Turbine Bowl4 - Reheater5 - Crossover6 - Double Reheat

States

6refP


Governor IEEEG2

Governor IEEEG2 IEEE Type 2 Speed-Governor Model

− 4

4

11 0.5

sTsT

−+

2

1 3

(1 )(1 )(1 )

K sTsT sT+

+ +

MAXP

MINP

Σ+


3

2 1

refP

mechP

mech1 - P2 - First Integrator3 - Second Integrator

States

ΔωSpeed

Governor IEEEG3_GE

Governor IEEEG3_GE IEEE Type 3 Speed-Governor Model IEEEG3

−

−

( )11

TURB TURB W

TURB W

K A sTB sT+

+

REFP

11 PsT+

1s

MAXP

MINP

+

1TEM P R

R

R sTsT+

+

+Σ

ΣCU

OU1

GT

GVP

GV

1db2db

GV GVP


32

1

mechP

PERMR

4

mech1 - P2 - Servomotor position3 - Gate position4 - Transient droop

States

PSLF model includes db1, db2, and Eps read but not implemented in Simulator

ΔωSpeed

Governor IEEEG3_PTI

Governor_IEEEG3_PTI IEEE Type 3 Speed-Governor Model IEEEG3

−

−

13 2123 11

23

11

1

1

W

W

a aa a sTa

a sT

⎡ ⎤⎛ ⎞+ −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦+

1(1 )G PT sT+

1s

MAXP

MINP

+

OU

CU

PERMR

1TEMP R

R

R sTsT+

+

+Σ

Σ


REFP

mechP32 1

4

mech1 - P2 - Servomotor position3 - Gate position4 - Transient droop

States

ΔωSpeed

Governor IEESGO

Governor IEESGO IEEE Standard Model IEEESGO

−Speed4

11 sT+

OP

1 2

1 3

(1 )(1 )(1 )

K sTsT sT

++ +

MAXP

MINPΣ+

21 K−

21 K−

3

61KsT+

2

51KsT+

Σ+

+ +

3

2

1

4 5

mechP

1 - First Integrator2 - Second Integrator3 - Turbine T44 - Turbine T55 - Turbine T6

States


Governor PIDGOV

Governor PIDGOV - Hydro Turbine and Governor Model PIDGOV

− ip

KKs

+Σ+

11 asT+

1d

a

sKsT+

Σ+

+

11 asT+

1perm

reg

RsT+

SBASEMBASE

Σ +

−

0

1

1

bT1s

MAXG

MING

MAXVel

MINVelGate

Power

12

3

11 2

Z

Z

sTsT−+

+

( )Z tw wT = A *T

turbD

Σ−

+

−Σ

Feedback signal

Model supported by PSSEModel supported by PSLF

3

2

1

4

5

6

7 mechP

REFP

elecP

(G0,0), (G1,P1), (G2,P2), (1,P3) are x,y coordinates of Power vs. Gate function

1 - Mechanical Output2 - Measured Delta P3 - PI4 - Reg15 - Derivative6 - Reg27 - Gate

States

ΔωSpeed

Governor TGOV1

Governor TGOV1 Steam Turbine-Governor Model TGOV1

1

11 sT+

MAXV

MINV

1R+

tD

−

2

3

11

sTsT

++

+

−Σ ΣREFP mechP2 1

1 - Turbine Power2 - Valve Position

States

Model supported by PSSEModel supported by PSLF

ΔωSpeed

Governor TGOV2

Governor TGOV2 Steam Turbine-Governor with Fast Valving Model TGOV2

1

11 sT+

MAXV

MINV

Reference MECHP1R+

tD

− 3

11

KsT−+

+

−Σ 1 t

vsT+

K

Σ+

I

A A

B B

T : Time to initiate fast valving.

T : Intercept valve, , fully closed T seconds after fast valving initiation.

T : Intercept valve starts to reopen T seconds after fast va

v

C C

lving initiation.

T : Intercept valve again fully open T seconds after fast valving initiation.

ΔωSpeed


321

4

CT

BT

AT

IT ( )I AT T+ ( )I BT T+ ( )I CT T+

Time, seconds

1.

0.

Inte

rcep

t Val

ve P

ositi

on

1 - Throttle2 - Reheat Pressure3 - Reheat Power4 - Intercept Valve

States

Governor TGOV3

RMAXP

Governor TGOV3 Modified IEEE Type 1 Speed-Governor with Fast Valving Model

−

−4

11 sT+

REFP

2

1

(1 )1

K sTsT++ 3

1T

CU

OU1sΣ

1K 2K

6

11 sT+

3K

Σ+

+

+

+

+

Σ

MAXP

MINP5

1sT

+ vΣ−

I

A A

B B

T : Time to initiate fast valving.

T : Intercept valve, , fully closed T seconds after fast valving initiation.

T : Intercept valve starts to reopen T seconds after fast va

v

C C

lving initiation.

T : Intercept valve again fully open T seconds after fast valving initiation.

CT

BT

AT

IT ( )I AT T+ ( )I BT T+ ( )I CT T+

Time, seconds

1.

0.

Inte

rcep

t Val

ve P

ositi

on

MECHP

Model supported by PSLFModel supported by PSSE

0 0.3

0.8

Intercept Valve Position

Flow

321

4 56

1 - LL2 - StateT33 - StateT44 - StateT55 - StateT66 - Intercept Valve

States

Gv1,Pgv1 ... Gv6, Pgv6 are x,y coordinates of Flow vs. Intercept Valve Position function

ΔωSpeed

Governor TGOV5

Governor_TGOV5 - IEEE Type 1 Speed-Governor Model Modified to Include Boiler Controls

−

+HPSPEED

ωΔ4

11 sT+

OP

2

1

(1 )1

K sTsT++ 3

1T

CU

OU1s

MAXV

MINV

1K

5

11 sT+

3K

6

11 sT+

5K

7

11 sT+

7K

Σ Σ

2K 4K 6K 8K

Σ Σ

Σ

Σ

HPPMECH

LPPMECH

+

+

+

+

+

+

++

++

++

1MP

2MP

−sm

1MW

MW

KsT+ELECP

−

−

B

fΔ

14K1s

−

MINR

MAXRMAXL

MINL

Σ +++

−

Σ

OPLK

ΣΣMWDemand

DesiredMW2C Σ

+

12K

+

13K

Σ

3C

+

+

SPP DPE−DPE

Dead Band

EP(Pressure Error)

π

( )( )( )1

1 11

I I R

R

K sT sTs sT+ ++

MAXC

EP

π

( )( )1 1

DsT

F W

esT sT

−

+ +

Fuel Dynamics

Σ+

−

++

1

BsC

−+

Σ11K

10K

Σ

TP

DP 9K

1CΣ

Σ− +

−

+ +

πOP

π

sm

sm

SPP

π

DesiredMW

MINC


TP

2 3 4 5 61

Governor URGS3T

Governor URGS3T WECC Gas Turbine Model

G V

G VP

2d b1

1sT

refP err

1db+

−

+4

5

(1 )1aK sT

sT+

+LVGATE

+

MAXV

MINV

2

2

11

AsTBsT

++

LIMR

+ mechP

TK3

11 sT+ΣΣIDLEF

MAXL

++ −

+

−

turbD

ΣΣ

IDLEF−

1R

Σ

Speed

−

11 LTRsT+

+Σ−

V INC LIM TRAT

LIM MAX

If (D >L ), then R = L else, R = R

Σ

VD


2

3

4

5

1

1 - Input LL2 - Integrator3 - Governor LL4 - Load Limit5 - Temperature

States

−


Governor WT12T1

Governor WT12T1 Two-Mass Turbine Model for Type 1 and Type 2 Wind Generators

FromWT12AModel

Initial rotor slip

+−


Σ

Σ Σ

Σ

Σ

Σ

+

+

+

+ +

−

−

+

−

+

−

+

−

shaftD

Damp

12 tH s

12 gH s

1s

baseω

baseω

baseω Rotorangle

deviation

Σ shaftKs

elecT

mechT Speed

t tfrac

g t2

t gshaft

0

H =H×HH =H-H

2H ×H ×(2π×Freq1)K =

H×ω

1 - TurbineSpeed2 - ShaftAngle3 - GenSpeed4 - GenDeltaAngle

States

3

2

1

4

Governor W2301

Governor W2301 Woodward 2301 Governor and Basic Turbine Model

Speed

11 VsT+Valve Servo

+ Σ−

−GammaΣ

+

1 2Beta s+ ⋅

Σ+

−

11 psT+

1 0.5(1.05 )

Rho sBeta s Alpha

+ ⋅⋅ −

SpeedRef

+ Σ

gnl

−Turbine

PIController

+

mechP3

21

4

1 - PelecSensed2 - PI3 - Valve4 - Turbine

States

D

11

t turb

turb

sKTsT

++

refP

Model supported by PSLFGain, Velamx read but not implemented in Simulator.

Gmax

Gmin

elecP

Governor WEHGOV

Governor WEHGOV Woodward Electric Hydro Governor Model

0 (S p e e d d e a d b a n d )( ) (S p e e d d e a d b a n d ) (S p e e d d e a d b a n d )( ) (S p e e d d e a d b a n d ) (S p e e d d e a d b a n d )

O u t if E R RO u t E R R I if E R RO u t E R R I if E R R

= <= − >= + < −

Governor and Hydraulic Actuators


(*)

(*)

1

WsT0H =1

π÷ πΣ+

−H 4

ssq/q

Turbine Flow, qFlow

mssPGate position, g

Gate

Flow

ss

Steady-StateFlow, q mssP

+

−Σ mechP

g πturbDSpeed

−

IKs

Gmin-DICN

6

Gmax+DICN

Σ++

+

PKERR

Speed deadband

Σ Σ 1

DVsT11

1 PsT+

Gmin-DPV

Gmax+DPVPilot Valve

1D

D

sKsT+

Feedbacksignal=1 Feedback

signal=0

+

−

gGTMXCL*T

gGTMXOP*T

2

Gate position, g1s

3

Gmax

Gmin

1

gT1 PE

RpermPEsT+

7

−

Distribution Valve

RpermGate

0

Feedbacksignal

SBASEMBASE

elecP

Turbine Dynam ics

5

1 - Pilot Valve2 - DistributionValve3 - Gate4 - Turbine Flow5 - Derivative6 - Integrator7 - PelecSensed

States

(Gate 1, Flow G1)...(Gate 5, Flow G5) are x,y coordinates of Flow vs. Gate function(Flow P1, PMECH 1)...(Flow P10, PMECH 10) are x,y coordinates of Pmss vs. Flow function

+−

1−10

refP

Governor WESGOV

Governor WESGOV Westinghouse Digital Governor for Gas Turbine Model

*

Droop

ΔωSpeed

PK

+1

IsT ( )( )1 2

11 1sT sT+ +Σ+

11 pesT+

**

+

−

Σ

Reference

−

Digital Control ***

lim

* Sample hold with sample period defined by Delta TC.**Sample hold with sample period defined by Delta TP.

***Maximum change is limited to A between sampling times

.

mechP

elecP

32

1

4

1 - PEMeas2 - Control3 - Valve4 - PMech

States

Model supported by PSSElimA read but not implemented in Simulator

Governor WNDTGE

Governor WNDTGE Wind Turbine and Turbine Control Model for GE Wind Turbines


++

−

11 psT+

11 5s+

+

RotorModel

Over/UnderSpeed Trip

TripSignalω

rotorω

/pp ipK K s+

20.67 1.42 0.51elec elecP P− + +refω

cmdθ

WindPowerModel

BladePitch

θ

Σ

/ptrq itrqK K s+1

1 pcsT+π

ω

ordP

+

−/pc icK K s+ Σ

Σ

ω

Power ResponseRate Limit

Apcflg is set to zero. Limits on states 2 and 3 and trip signal are not implemented.

Anti-windup onPitch Limits

mechP

elecP

elecP

Anti-windup onPower Limits

Anti-windup on Pitch LimitsTorqueControl

Pitch Control

PitchCompensation

PIMax & PIRat

PImin & -PIRat

errω PWmax & PWrat

PWmin & -PWrat

1 2

4

5

7

6

3

8

91 - Pitch2 - Pitch Control3 - Torque Control4 - Pitch Compensation5 - Power Control6 - Speed Reference7 - Mech Speed8 - Mech Angle9 - Elect Speed10- ElectAngle11- Washout12- Active Power

States10

WindPowerModel

if (fbus < fb ORfbus > fc)

FrequencyResponse

Curve

Active PowerControl

(optional)

avlP

avfP

To gewtgTrip Signal

(glimit)

WTG TerBus Freq

AuxiliarySignal(psig)

fbusΣ+

+

setp0

1

fflg

apcflg minP

maxP

stlp

setAPCP

1

MAX

ReleaseP

if fflg set

WindSpeed

(glimv)

1

12

11 pavsT+

+

− 1W

W

sTsT+

Σ+

+

11

wshoΣ perr

plim

Spdwl

Simulator calculates initial windspeed Spdwl.

ordP

ΣdbrP +

+

Governor WNDTGE Wind Turbine and Turbine Control Model for GE Wind Turbines

1s

Two - Mass Rotor Model

1s

1s

1s

12H

12 gH

tgD

baseω

baseω

mechT

elecT

tgK

++

ΣΣ

Σ

Σ

Σ

Σ

0ω+

+rotorω

shaftT

++

−−

−

ωΔ

0ω+

+

7 8

9 10

−

Turbine Speed

ω Generator Speed

mechmech

mech 0

PTω ω

=+

mechω

elecω

elecelec

elec 0

PTω ω

=+

Wind Power Model( )3

mechP ,2 r w pAv Cρ λ θ=

( / )b wK vλ ω=

( )4 4

0 0

, i jp ij

i j

C λ θ α θ λ= =

=∑∑See charts for curve fit values


Governor WNDTRB

Governor WNDTRB Wind Turbine Control Model

1s

90

0

r

Rotor speedω

mechP1

2

(1 )1PK sT

sT+

++−

11 asT+

refω

Σ

woP

πMXBPR

MX-BPR


1 2 3cos

1 - Input2 - Blade Angle (Deg)3 - Blade Pitch Factor

States

Governor WPIDHY

Governor WPIDHY Woodward PID Hydro Governor Model

−+

+

PK

DsK

iKs

+

+ ( )21

1 AsT+Σ 1s

M AXVel

11 BsT+Σ

1 REG

REGsT+

+ Σ−

MAXG

MING

MAXP

MINP

1

12

W

W

sTTs

−

+PG

D

+

Σ

0( , 0)G

1 1( , )G P

2 2( , )G P

3(1, )P

Gate Position (pu)

0 1.0


REFP

ΔωSpeed

−

MECHP

ELECP Per U

nit O

utpu

t (M

BA

SE)

1

2

45

763

1 - Mechanical Output2 - Measured Delta P3 - PID14 - PID25 - PID36 - Velocity7 - Gate

States

MINVel

Governor WSHYDD

Governor WSHYDD WECC Double-Derivative Hydro Governor Model

G VN

Δω(Speed) err

1db

11 DsT+

1

1 F

sKsT+

( )

22

21 F

s KsT+

+

+

+ Σ IKs

refP

R

Σ+

−

−

11 TsT+( 0)TT >

elecP

1G

P

KsT+

OPENVEL

CLOSEVEL

1s

MAXP

MINP

2d b

GV 11

tu r b tu r b

tu r b tu r b

s A Ts B T

++

r a teTM V A

GVP mechP+

−

Σ


0TT =

2 3

7

8

6

1

mech

D elec

1

2

2

1 - P 6 - Integrator2 - T 7 - P Sensed3 - K 8 - Valve4 - K first 9 - Gate5 - K second

States

4 5

9

Inputs GV1, PGV1...GV5, PGV5 are the x,ycoordinates of blockGVN

Governor WSHYGP

Governor WSHYGP WECC GP Hydro Governor Plus Model

G VN

err

1db

11 DsT+

IKs

1D

f

sKsT+

+

+

+

R 11 tsT+( 0)tT >

1G

P

KsT+

1s 2d b

GV 11

tu r b tu r b

tu r b tu r b

s A Ts B T

++

r a teTM V A

GVP+

−

Σ

PK

Σ+

−

−

0tT =

CVΣ


176

5

3

4

2

mechP

elecP

Δω(Speed)

refP

OPENVEL

CLOSEVEL

MAXP

MINP

mech elec

D

1 - P 5 - P Sensed2 - T 6 - Valve3 - Integrator 7 - Gate4 - Derivative

States


Governor WSIEG1

Governor WSIEG1 WECC Modified IEEE Type 1 Speed-Governor Model

Δω err

1db

4

11 sT+

1K

5

11 sT+

3K

6

11 sT+

5K

7

11 sT+

7K

Σ Σ

2K 4K 6K 8K

Σ Σ

Σ

Σ

HPPMECH

LPPMECH

+

+

+

+

+

+

++

++

++

M1P

M2P

G VN

OU

CU

1s

MAXP

MINP

2d b

GV GVP−

−3

1T

K 2

1

11

sTsT

++

CV Σ

0GV

+

Model supported by PSSEGV1, PGV1...GV5, PGV5 are the x,y coordinates of blockGVN

1

653 4

2

1 - Lead-lag2 - Governor Output3 - Turbine 14 - Turbine 25 - Turbine 36 - Turbine 4

States

MIN MIN

MAX MAX

MIN MIN

MAX MAX

Iblock 1 : if P =0, P =PinitialIblock 2 : if P =0, P =PinitialIblock 3 : if P =0, P =Pinitial

: if P =0, P =Pinitial

===

Governor WT1T

Governor WT1T Wind Turbine Model for Type-1 Wind Turbines


+ 12H

1sΣ

−

÷

shaftD

−

12 tH

1s

12 gH

1s

1s

K

÷

÷

Σ

Σ

Σ

Σ

Σt tfrac

g t2

t g

H =H×HH =H-H


H

tω

gω

mechP

genP

Type 1 WTG Turbine Two - mass Model

Type 1 WTG Turbine One - mass Model

mechT

elecT

FromGovernor

M odel

FromGenerator

M odel

tω

gω

0ω

0ω

tωΔ

gωΔ

tgωΔtgωΔ

−

−

−

+

+

+

+

−

accT

FromGenerator

M odel

FromGovernor

M odel

mechP

genP

ToGenerator M odel andGovernor

M odel

ω

1

2

3 4


States

1

Damp

1s

Governor WT3T

Governor WT3T Wind Turbine Model for Type-3 (Doubly-fed) Wind Turbines

t tfrac

g t2

t g

H =H×HH =H-H


H

Type 3 WTG Turbine Two - mass Model


States

+ 12H

1sΣ

−

÷−

Type 3 WTG Turbine One - mass Model

accT

FromGenerator

M odel

FromPitch Control

M odel

mechPgenP

To Pitch Control M odel and Converter Control M odel

ω1+Σ−+

−

SimplifiedAerodynamic M odel

π

moP

aeroKΣ+

Blade Pitchθ

0θ


2

2 1When windspeed > rated windspeed, blade pitch initialized to 10.75 W

ThetaV

θ⎛ ⎞

= −⎜ ⎟⎝ ⎠

Damp

shaftD

12 tH

1s

12 gH

1s

1s

K

÷

÷

Σ

Σ

Σ

Σ

Σ

tω

gω

mechP

genP

mechT

elecT

tω

gω

0ω

0ω

tωΔ

gωΔ

tgωΔtgωΔ

−

−

−

+

+

+

+

−

1

2

3 41s

Governor WT3T1

Governor WT3T1 Mechanical System Model for Type 3 Wind Generator


+−Σ

Σ

Σ

Σ

Σ

+

+

+

+ +

−

−

+ +

−

+

−

shaftD

12 tH s

12 gH s

1s

baseω

Σ shaftKs

elecT

mechT

t tfrac

g t2

t gshaft

0

H =H×HH =H-H


H×ω

3

2

1

4

Damp

+ Σ−+−

InitialPitchAngle

π aeroP initialaeroKΣ

+Blade Pitchθ

0θ1

1 State 1+

baseω

baseω

From W T3P1 M odel

−

0ω

Rotor Angle

Deviation

Initial rotor slip

mechTΣ

tωΔ

gωΔ

tgωΔ

gω

Governor BBGOV1

European Governor Model BBGOV1

−

−

OP

+

+

11P

NK

sT⎛ ⎞⎜ ⎟+⎝ ⎠

−

+Speed

ωΔ

PELEC

cutf

cutf

SK

LSK

LSK−

G

LS

KK

1s

Σ

1

11 sT+

Σ 1D

D

sKsT+

MAXP

MINP

0SWITCH =

0SWITCH ≠

4

11 sT+ 21 K−

31 K−

2

51K

sT+

3

61K

sT+

+

+ +Σ PM ECH

2 3 4 5 61

Governor IVOGO

IVO Governor Model IVOGO

MECHP( )5 5 5

6 6

K A sTA sT

++

( )3 3 3

4 4

K A sTA sT

++

3MAX

3MIN

( )1 1 1

2 2

K A sTA sT

++

1MAX

1MIN

5MAX

5MIN

SPEEDΣ

REF

+

−

2 3 4 5 61

Governor TURCZT

Czech Hydro and Steam Governor Model TURCZT

+

PK

1

IsT

TMAXN

+

Power Regulator

TMINN

+

−

BSFREQ

REFdF

Σ

SBASEMBASE

PELEC

MAXf

MINfDEADf

Frequency Bias

KORK

11 CsT+ MK

−

−+

TREFN

Measuring Transducer

Σ 11 EHPsT+Σ

−

+

Hydro Converter

DEADs

Frequency Bias

STATK

ΣREGY

Governor

+

−

REGY

Regulation Valves

HPK

Turbine

1

UT1s

MAXG

MING

MAXV

MINV

Σ1SWITCH =

0SWITCH =

11 HPsT+

11 RsT+

1 HPK−

1

MKΣ+

+

HP Part

Reheater

Steam Unit

PM ECH

311 2Hs T+

2 1

MK+

− ΣPM ECH

Hydro Unit

2 3 4 5 61

Governor URCSCT

Combined Cycle on Single Shaft Model URCSCT

( , )STOUT A POUT A

Steam Turbine Output (MW)

( )

PlantOutputMW

( , )STOUT B POUT B

( , )STOUT C POUT C(Steam Turbine Rating, Steam & Gas Turbine Rating)

2 3 4 5 61

Governor HYGOVM

Hydro Turbine-Governor Lumped Parameter Model HYGOVM

( )TAILHV

( )LAKEHV

BSCHH

( )SCHH

V

SCHQ

TUNQ

PENQ

TUNNELTUNL / A, TUNLOS

SCHARE

SURGECHAMBER

PENSTOCKPENL / A, PENLOS

TURBINE

Hydro Turbine Governor Lumped Parameter Model

SCHLOS

Governor HYGOVM


INPUT OUTPUT

Gate +Relief Valve

π 2O ÷

PENLOS2

2PEN tQ AO gv

sPENL A

π

tA

Σ

2PENQ

+

+ − +

gvsTUNL A

TUNLOS

Σ ΣBSCHH

TAILH

−

Σ −+LAKEH

BSCHH

gvsTUNL A

ΣSCHH

+

+

SCHLOS

−

+

π2SCHQ

SCHQ

Σ TUNQ+

−

PENQ

π

2TUNQ

PENQ

gv Gravitational accelerationTUNL/A Summation of length/cross section of tunnel SCHARE Surge chamber cross section PENLOS Penstock head loss coeficient FSCH

LEGEND :

Surge chamber orifice head loss coeficientPENL/A Summation of length/cross section of penstock, scroll case and draft tube

tA Turbine flow gainO Gate + relief valve opening HSCH Water level in surge chamber QPEN Penstock flow QTUN Tunnel flowQSCH Surge chamber flow

Hydro Turbine Governor Lumped Parameter Model

2 3 4 5 61

Governor HYGOVM


SpeedReference

11 fsT+

+

−

+−

−

Speed

+

R

1s

RVLMAX

0

1 r

r

sTrsT+

MAXG

MING

0.01

+

+ Σ

1

gT1s

MXJDOR

MXJDCR

Σ−

DeflectorPosition

1

gT1s

MXGTOR orMXBGOR

MXGTCR orMXBGCR

GateOpening

Σ

Σ−

+

Σ

RVLVCR

Governor Gate Servo

Relief ValveOpening

Jet Deflector

Relief Valve

r

f

R Permanent droopr Temporary droopT Governor time constant T Filter time constantT Servo time constant MXG

g

LEGEND :

TOR Maximum gate opening rateMXGTCR Maximum gate closing rateMXBGOR Maximum buffered gate opening rate

MXBGCR Maximum buffered gate closing openingGMAX Maximum gate limitGMIN Minimum gate limit RVLVCR Relief valve closing rateRVLMAX Maximum relief valve limit MXJDOR Maximum jet deflector opening rateMXJDCR Maximum jet deflector closing rate

2 3 4 5 61

Governor HYGOVT

Hydro Turbine-Governor Traveling Wave Model HYGOVT

( )TAILHV

( )LAKEHV

BSCHH

( )SCHH

V

SCHQ

TUNQ

PENQ

TUNNEL

SCHARE

SURGECHAMBER

PENSTOCK

TURBINE

SCHLOS

( , , , )TUNNEL

TUNLGTH TUNSPD TUNARE TUNLOS

Time

Tunnel InletConstraint

TUN

BSCH

VAR(L + 45 + ICON(M + 2)) = QVAR(L + 65 + ICON(M + 2)) = H

Space

Surge ChamberConstraints

/ ( ( 2) 1)TUNLGTH ICON M + +144424443)

)VAR(L + 46VAR(L + 66

FlowsHeads

* ( 3)DELT ICON M⎧⎪+ ⎨⎪⎩

Hydro Turbine Governor Traveling Wave Model

Governor HYGOVT


+ +1

sSCHARE SCHH

SCHLOS

+

2SCHQ

SCHQTUNQ

PENQ

Surge Chamber

BSCHHΣ

π

Σ

( , , , )PENSTOCK

PENLGTH PENSPD PENARE PENLOS

Time

TurbineConstraint

VAR(L + 55 + ICON(M))VAR(L + 25 + ICON(M))

Space

Surge ChamberConstraints

/ ( ( ) 1)PENLGTH ICON M +144424443

))

PEN

BSCH

VAR(L + 6 QVAR(L + 26 H

==

FlowsHeads

* ( 1)DELT ICON M⎧⎪+ ⎨⎪⎩


Governor HYGOVT


SpeedReference

11 fsT+

+

−

+−

−

Speed

+

R

1s

RVLMAX

0

1 r

r

sTrsT+

MAXG

MING

0.01

+

+ Σ

1

gT1s

MXJDOR

MXJDCR

Σ−

DeflectorPosition

1

gT1s

MXGTOR orMXBGOR

MXGTCR orMXBGCR

GateOpening

Σ

Σ−

+

Σ

RVLVCR

Governor Gate Servo

Relief ValveOpening

Jet Deflector

Relief Valve

r

f

R Permanent droopr Temporary droopT Governor time constant T Filter time constantT Servo time constant MXG

g

LEGEND :

TOR Maximum gate opening rateMXGTCR Maximum gate closing rateMXBGOR Maximum buffered gate opening rate

MXBGCR Maximum buffered gate closing openingGMAX Maximum gate limitGMIN Minimum gate limit RVLVCR Relief valve closing rateRVLMAX Maximum relief valve limit MXJDOR Maximum jet deflector opening rateMXJDCR Maximum jet deflector closing rate


2 3 4 5 61

Governor TGOV4

Modified IEEE Type 1 Speed-Governor Model with PLU and EVA Model TGOV4

Generator Power1

REVA

REVA

sTsT+

EVA RateLevel>

EVAUnbalance

Level

>

AN D

Y

Y−

1RPLU

RPLU

sTsT+

Σ

Reheat Pressure

+

Generator CurrentPLU Rate

Level> Timer

AN D LATCH

1IVT

2IVT

#1IV

# 2IVOR

1CVT

2CVT

3CVT

4CVT

#1CV

# 2CV

# 3CV

# 4CVPLU

UnbalanceLevel

> YΣ+

−

Y

N

PLU and EVA Logic Diagram2 3 4 5 61

Governor TWDM1T

Tail Water Depression Hydro Governor Model TWDM 1T

Speed

11 fsT+

1 rsT+

−

+REFN

R

1s

1

rrT1

1 gsT+

GATE MAX

GATE MIN

VELM OPEN

VELM CLOSE

Σ

+

+Σ

e c

1

WsT tA 1.0π π÷ Σ+

−

−

+

−

+Σ Σh q

1 qNL turbD

Speed

PMECH

0.

g

Tail Water Depression Model 1

2s f sFΔ <

2f FΔ <

1f FΔ <

Measured Frequency

FREQΔ 11 ftsT+ 2FT LATCH

1FT LATCH

AN DOR

Trip TailWater

Depression

Tail Water Depression Trip Model

fΔ

2 3 4 5 61

Governor TWDM2T

Tail Water Depression Hydro Governor Model TWDM 2T

+

−SPEEDωΔ

1s

11 BsT+

ATMXG

ATMNG

ELMXV

ELMNV

+

1

WsT tA 1.0π π÷ Σ+

−

−

+

−

+Σ Σh q

1 qNL

turbD

PMECH

0.

Tail Water Depression Model 2

2s f sFΔ <

2f FΔ <

1f FΔ <

Measured Frequency

FREQΔ 11 ftsT+ 2FT LATCH

1FT LATCH

AN DOR

Trip TailWater

Depression

Tail Water Depression Trip Model

fΔ

( )21

1 AsT+LOGIC

1s

TWD Lock MAX

TWD Lock MIN TwoTrip

PK

DsK

Σ+

++

1 REG

RegsT+

ELECTP

−

REFP

Σ

Σ

2 3 4 5 61

2 CR

HVDC Two Terminal DC Control Diagram

1

2 3

(1 )(1 )(1 )

K sTsT sTα− +

+ +

ΣD E SP M O DPR E C T+ +

DESDES

MEAS

PIV

=11 vsT+

DCV MEASVDESIC O N S T A N T

P O W E RC O N S T A N TC U R R E N T

MEASVMINV

MAXI

MINI

If If , If ,

MIN DES MAX

ORD DES

MIN DES ORD DES

MAX DES ORD MAX

I I II II I I II I I I

≤ ≤=> =< =

11 CsT+

DCIMAXI

+

−

− +

MARGINSWITCHLOGIC 10%*

*MIN MAX

MIN LIM RATED

I IV V V

==

ORDI−LIM

0

Σ'Vα +

+

Σcoscos

R

I

αα

11 DsT+

1.35 CE

Vαcos cos

cos cos

R oOR

IOR

VEVE

α

α

α γ

α γ

= −

= −

OR OIE E

( )MEASI

RECTIFIER ( )MEASI

INVERTER

( )MODI

RECTIFIER

( )

CURRENTMARGIN

INVERTER

V O L T A G ET R A N S D U C E R

C U R R E N TT R A N S D U C E R

0 min(cos cos ) 2 ( )(cos cos ) 2 ( )

OR MEAS C

OI STOP MEAS C

LIM E I R RECTLIM E I R IVERT

γ γγ γ

= + −= + −

MEASI


HVDC WSCC Stability Program Two-Terminal DC Line Model

A rV A iV

'rD '

iDrV iV p iV

crX crR srL R L siL ciRviV ciX

1 2

3

vrV

p rV

rP iP

I

r rP G E N jQ G E N+

1 : rNi iP G E N jQ G E N−

: 1iN

' '

'

3 2 3 2 co s co s2

3co s P G E N

co s

crr r A R p r r r

p r

r r cr r r

rr

r

IXE N V VV

ID E X D I

DE

γ θπ π

απ

θ

= = = −

= − =

=

' '

'

3 2 3 2 co s co s2

3co s P G E N

co s

c ii i A i p i i i

p i

i i c i i i

ii

i

IXE N V VV

ID E X D I

DE

β θπ π

απ

θ

= = = −

= − =

=

''

'''

( c o s c o s ) /

( c o s c o s ) /3W H E R E ( )

r M I N i M I N v r v i T O T

r M I N i S T O P v r v i T O T

T O T c r c i c r c i

I E E V V R

I E E V V R

R R R R X X

α γ

α γ

π

= − − −

= + − −

= + + + −


6 CXπ

HVDC-MTDC Control System for Rectifiers and Inverters without Current Margin

1

2 3

(1 )(1 )(1 )

K sTsT sTα− +

+ +

DESDES

MEAS

PIV

=11 vsT+

DCV LAGVDESIC O N S T A N T


VDV

MAXI

MINI

If If , If ,

MIN D MAX

ORD D

D MAX ORD MAX

D MIN ORD MIN


≤ ≤=

> =< =

11 CsT+

DCI

−

ORDILIM

0.0

3V

11 LIMsT+

doV

cos cos ONdoL

VV

αα γ= −

MEASI

REFI

0 min

0

(cos cos ) (cos cos )

doL

doL STOP

RECT LIM VINV LIM V

γ γγ γ

= += +

MEASI


+

Σ

1V Vα GREATEROF THE

TWO

CV

doLV

+1.

1.−

cosα

'MAXI

−

6 CXπ

HVDC-MTDC Control System for Terminals with Current Margin

1

2 3

(1 )(1 )(1 )

K sTsT sTα− +

+ +

+

ORDI

LIM

0.0

3V

11 LIMsT+

doV

cos cos ONdoL

VV

αα γ= −

MEASI

MARGI

(cos cos )doL ON STOPLIM V γ γ= +

MEASI


+

1V Vα GREATEST

OF THETWO

CV

doLV

+1.

1.−

cosα

−

DCI 11 CsT+

1ORDI2ORDI

3ORDI

-1ORD NI

... Σ

Σ

2 ( )cos cosC MARGON o

do INITIAL

R FRAC IV

γ γ= +

(cos cos ) 2CORD do ON o C ORDV V R Iγ γ= − +

CORDV

0.25FRAC =

HVDC Detailed VDCL and Mode Change Card Multi-Terminal

DES

MEAS

PV


DES

MEAS

PV

1MEAS CV V>

ORDI

MEASV NO

YES

DESI

VDCL

1

Mode Change PU rated DC Voltage below

which mode is changed to constant from constant

CV

I P

1.0

1Y

0Y

1V 2V

CURRENT

VOLTAGE

1 0

1 2

VDCL, PU Current on rated Current base, V PU Voltage on rated Voltage base

Y YV

HVDC Equivalent Circuit of a Two Terminal DC Line

d rV d iV ciE

rX crR LR ciR iX

crE

dI, r rP Q

1 : T


+

−

+

−

rR eq rR eq iR iR

, i iP Q

rE α iE αco sd o r rV α co sd o i iV α−

1 : T

D rV D iV

2 CR

HVDC BPA Converter Controller

1

2 3

(1 )(1 )(1 )

K sTsT sTα− +

+ +

ΣD E SP M O DPR E C T+ +

DESDES

MEAS

PIV

=11 vsT+

DCV MEASVDESIC O N S T A N T


MEASVMINV

MAXI

MINI

If If , If ,

MIN DES MAX

ORD DES

MIN DES ORD DES

MAX DES ORD MAX


≤ ≤=> =< =

11 CsT+

DCIMAXI

+

−

− +

MARGINSWITCHLOGIC 10%*

*MIN MAX

MIN LIM RATED

I IV V V

==

ORDI−LIM

0

Σ'Vα +

+

Σcoscos

R

I

αα

11 DsT+

1.35 CE

Vαcos cos

cos cos

R oOR

IOR

VEVE

α

α

α γ

α γ

= −

= −

OR OIE E

( )MEASI

RECTIFIER ( )MEASI

INVERTER

( )MODI

RECTIFIER

( )

CURRENTMARGIN

INVERTER

V O L T A G ET R A N S D U C E R

C U R R E N TT R A N S D U C E R

0 min(cos cos ) 2 ( )(cos cos ) 2 ( )

OR MEAS C

OI STOP MEAS C

LIM E I R RECTLIM E I R IVERT

γ γγ γ

= + −= + −

MEASI


C U R R E N TC O N T R O L L E R

DESI

HVDC BPA Block Diagram of Simplified Model

11T DC

L

i IsT+

ΣD E SP( )

M O DPR+ +

DESDES

MEAS

PIV

=11 vsT+

drV MEASVdesIC O N S T A N T


MEASVMINV

MAXI

MINI

If If , If ,

MIN des MAX

ord des

MIN des ord MIN

MAX des ord MAX


< <=≥ =≤ =

11 CsT+

dIMAXI

+

+

MARGINSWITCHLOGIC

ORDI

ord rIΣMODI

d MEASI


C o n tro l S ch em eL o g ic

desI

+DI

DI +

+

IΔΣ

ord iI

0 0cos cos 2dor doi i

T

V V VR

α γ− −dorV

doiV

ordI

−( )cu rren t m a rg in

. IN V C o n tro lle r

DCI

ord iI

ord rI

dIcoscos

r

i

αα

C o n tro l S ch em e L o g ic

If: ; cos cos 2

T ordr d ordr

i o dor r doi o D T D

T ordi

i I CC CEAControl I IV V V R I

i I CIA CC Controlγ γ α γ

≥ → − → == = + +

≥ → − ; cos cos 2

d ordi

r o doi i do o D T D

ordi T ordr d T

I IV V V R I

I i I CIA CEAControl I iγ γ γ α

→ == = − −

< < → − → = ; r o i oα α γ γ= =



1 d

ssT+

11 fsT+

ss ε+

2

2

s sA Bs sC D+ ++ +

K

MINI

MAXIMODI

AC

AC

IP

Low Level Modulation

1 d

ssT+

11 fsT+

ss ε+

2

2

s sA Bs sC D+ ++ +

K*

MINP

*MAXP

MODPAC

AC

IP

High Level Modulation

11 d

ssT+ 1

11 fsT+ 1

ss ε+

21 1

21 1

s sA Bs sC D+ ++ +

1K1

RECTω

21 d

ssT+ 2

11 fsT+ 2

ss ε+

22 2

22 2

s sA Bs sC D+ ++ +

2K2

INVω

MINP

MAXP+

−

MODPΣ

Dual Frequancy Modulation

*MAX MAX DESIREDP P P= − *

MIN MIN DESIREDP P P= −



11ssT+

3

41A sT

sT++

5

61B sT

sT++

Kγ

MINγ

MAXγγ

ACV

Gamma Modulation

1 3 4 5

MAX

, , , are in secs. is in degrees/pu volts, are in degrees , must be 1 or zero

HILO must be 5MIN

T T T T KA B

γγ γ

REFV

+

−Σ +

+

Σ

0γ

Load Characteristic CIM5

Load Characteristic CIM5 Induction Motor Load Model


A AR jX+

mjX1jX

1Rs

2jX

2Rs

Type 1

A AR jX+

mjX 1Rs

2jX

2Rs

Type 2

Impedances on Motor MVA Base

1jX

2 2

DL

Model Notes: 1. To model single cage motor: set R = X = 0.

2. When MBASE = 0.; motor MVA base = PMULT*MW load. When MBASE > 0.; motor MVA base =MBASE 3. Load Torque, T = T(1+D ) 4. For mot

ω

nom 0

|

or starting, T=T is specified by the user in CON(J+18). For motor online studies, T=T is calculated in the code during initialization and stored in VAR(L+4). 5. V is the per unit vo

|

|

ltage level below which the relay to trip the motor will begin timing. To display relay, set

V=0

6. T is the time in cycles for which the voltage must remain below the threshold for t Bhe relay to trip. T is the

breaker delay time cycles.

Load Characteristic CIM6

Load Characteristic CIM6 Induction Motor Load Model


A AR jX+

mjX1jX

1Rs

2jX

2Rs

Type 1

A AR jX+

mjX 1Rs

2jX

2Rs

Type 2


( )

2 2

D2L 0


2. When MBASE = 0.; motor MVA base = PMULT*MW load. When MBASE > 0.; motor MVA base =MBASE

3. Load Torque, T = T A +B +C +D

4.

E

ω ω ω

nom 0

|

For motor starting, T=T is specified by the user in CON(J+22). For motor online studies, T=T is calculated in the code during initialization and stored in VAR(L+4). 5. V is the per

|

|

unit voltage level below which the relay to trip the motor will begin timing. To display relay, set

V=0

6. T is the time in cycles for which the voltage must remain below the threshol Bd for the relay to trip. T is the breaker delay time cycles.

1jX

Load Characteristic CIMW

Load Characteristic CIMW Induction Motor Load Model


A AR jX+

mjX1jX

1Rs

2jX

2Rs

Type 1

A AR jX+

mjX 1Rs

2jX

2Rs

Type 2


( )

2 2

D2L 0


2. When MBASE = 0.; motor MVA base = PMULT*MW load. When MBASE > 0.; motor MVA base =MBASE

3. Load Torque, T = T A +B +C +D where C0E

ω ω ω 0 0

2

0

|

=1 A B D .

4. This model cannot be used formotor starting studies. T is calculated in the code during initialization and stored in VAR(L+4). 5. V is the per unit voltage

Eω ω ω− − −

|

|

level below which the relay to trip the motor will begin timing. To display relay, set

V=0

6. T is the time in cycles for which the voltage must remain below the threshold for the rel Bay to trip. T is the breaker delay time cycles.

1jX

Load Characteristic CLOD

Load Characteristic CLOD Complex Load Model


P jQ+

Tap

O

R jXP+

Load MW input on system baseOP =

I

V

I

V

ConstantMVA 2

*

*

PKRO

RO

P P V

Q Q V

=

=

LargeMotors

SmallMotors

DischargeMotors

TransformerSaturation

RemainingLoads

M M

Load Characteristic EXTL

Load Characteristic EXTL Complex Load Model

PKs

PMLTMX

PMLTMN

1

initialP−

+

Σπ

initialP

MULTPactualPQK

s

QMLTMX

QMLTMN

1

initialQ−

+

Σπ

initialQ

MULTQactualQ

Load Characteristic IEEL

Load Characteristic IEEL Complex Load Model


( )( )

( )( )

31 2

5 64

1 2 3 7

4 5 6 8

1

1

nn nload

n nnload

P P av a v a v a f

Q Q a v a v a v a f

= + + + Δ

= + + + Δ

Load Characteristic LDFR

Load Characteristic LDFR Complex Load Model


m

OO

n

OO

r

p poO

s

q qoO

P P

Q Q

I I

I I

ωω

ωω

ωω

ωω

⎛ ⎞= ⎜ ⎟

⎝ ⎠

⎛ ⎞= ⎜ ⎟

⎝ ⎠

⎛ ⎞= ⎜ ⎟

⎝ ⎠

⎛ ⎞= ⎜ ⎟

⎝ ⎠

Load Characteristic BPA INDUCTION MOTOR I

Load Characteristic BPA Induction MotorI Induction Motor Load Model

S SR jX+

mjX

RjX

RRRs

= , MWST E

MECHANICALLOAD

2

2

Model Notes: Mechanical Load Torque, ( ) where C is calculated by the program such that 1.0 1

OT A B C T

A B C

ω ω

ω ωω ω

= + +

+ + == −


Load Characteristic BPA TYPE LA

Load Characteristic BPA Type LA Load Model

( )( )20 1 2 3 4 1 * DPP P PV PV P P f L= + + + +Δ


Load Characteristic BPA TYPE LB

Load Characteristic BPA Type LB Load Model

( )( )20 1 2 3 1 * DPP P PV PV P f L= + + +Δ


Stabilizer BPA SF, BPA SP, BPA SS, and BPA SG

Stabilizer BPA SF, BPA SP, BPA SS, and BPA SG Stabilizer Models

−

+

QV

QV

K1+sT

QS

QS

K1+sT

Q

Q

sT1+sT

'Q2

Q2

1+sT1+sT

'Q1

Q1

1+sT1+sT

T TO TV =V V−

SHAFT SLIP, FREQ. OR

ACCEL. POWERΔ

'Q3

Q3

1+sT1+sT

'CUTOFF S S

CUTOFF'

S S T CUTOFF

S T CUTOFF

T TO T

If V 0.0, then V =VIf V >0.0, then

V =V if V V

V =0.0 if V >V V =V V

≤

Δ ≤

Δ

Δ −

STV


SMAXV

SMINV

ΣQSKtse+

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

ZERO

'SV

TVΔ

CHOICE OFINPUT SIGNALS

QS

QV

Q

Q1

Q2

Q3

1 - K2 - K3 - T4 - T5 - T6 - T

States

1

2

3 4 5 6

Stabilizer BPA SH, BPA SHPLUS, and BPA SI

Stabilizer BPA SH, BPA SHPLUS, and BPA SI Stabilizer Models


Stabilizer IEE2ST

Stabilizer IEE2ST IEEE Stabilizing Model with Dual-Input Signals

+

+Σ

1

1

K1+sT

2

2

K1+sT

3

4

sT1+sT

7

8

1+sT1+sT

9

10

1+sT1+sT

SMINL

SMAXLS SS CU CT CL

S CT CL

S CT CU

V = V if (V > V > V )V = 0 if (V < V )V = 0 if (V > V )

5

6

1+sT1+sT

SSV

Output Limiter

Input Signal #1

Input Signal #2

STV


1

2

3 4 5

6

1 - Transducer12 - Transducer23 - Washout4 - LL15 - LL26 - Unlimited Signal

States

Stabilizer IEEEST

Stabilizer IEEEST IEEE Stabilizing Model

3

4

1+sT1+sT

5S

6

sTK1+sT

SMINL

SMAXLS SS CU CT CL

S CT CL

S CT CU

V = V if (V > V > V )V = 0 if (V < V )V = 0 if (V > V )

1

2

1+sT1+sT

SSV

Output Limiter

Input Signal2

5 62 2

1 2 3 4

1+A s+A s(1+A s+A s )(1+A s+A s )

Filter

Model supported by PSLF with time delay that is not implemented in SimulatorModel supported by PSSE

STV

1 2 3 4 5 6

1 - Filter 12 - Filter 23 - Filter 34 - Filter Out5 - LL16 - LL27 - Unlimited Signal

States

7

Stabilizer PFQRG

Stabilizer PFQRG Power-Sensitive Stabilizing Unit

-MAX

MAX+

+Σ I

PKKs

+


STV

ReactivePower

PowerFactor

J=1

J=0

Reference Signal,Reactive power or Power Factor

To VoltageRegulator

SupplementarySignal

1

1 - PIStates

Stabilizer PSS2A

Stabilizer PSS2A IEEE Dual-Input Stabilizer Model

+

+

Σ

STMINV

STMAXV

Input Signal #2

W1

W1

sT1+sT 6

11+sT

W2

W2

sT1+sT

W3

W3

sT1+sT

S2

7

K1+sT

W4

W4

sT1+sT

S3K

N

8M

9

1+sT(1+sT )⎡ ⎤⎢ ⎥⎣ ⎦

+

−S1K 1

2

1+sT1+sT

3

4

1+sT1+sT

STV

A B S4

Model supported by PSLFModel supported by PSSE without T ,T lead/lag block and with K 1=

A+sT1+sT

A

B

S4K

Σ

7 81 2 3

4 5 6

Input Signal #1

1 - WOTW1 11 - RampFilter32 - WOTW2 12 - RampFilter43 - Transducer1 13 - RampFilter54 - WOTW3 14 - RampFilter65 - WOTW4 15 - RampFilter76 - Transducer2 16 - RampFilter87 - LL1 17 - RampFilter98 - LL2 18

States

- RampFilter109 - RampFilter1 19 - LLGEOnly10 - RampFilter2

19

9 18−

Stabilizer PSS2B

Stabilizer PSS2B IEEE Dual-Input Stabilizer Model

+

+

Σ

STMINV

STMAXV

W1

W1

sT1+sT 6

11+sT

W2

W2

sT1+sT

W3

W3

sT1+sT

S2

7

K1+sT

W4

W4

sT1+sT

S3K

N

8M

9

1+sT(1+sT )⎡ ⎤⎢ ⎥⎣ ⎦

+

−

S1K 1

2

1+sT1+sT

3

4

1+sT1+sT

STV

10

11

1+sT1+sTΣS1V

S2V

S1MAXV

S1MINV

S2MAXV

S2MINV

7 81 2 3

4 5 6

20

19

A B S4

Model supported by PSLFModel supported by PSSE without T ,T lead/lag block and with K 1=

A+sT1+sT

A

B

S4K


States

- RampFilter109 - RampFilter1 19 - LLGEOnly10 - RampFilter2 20 - LL3

9 18−

Stabilizer PSSSB

Stabilizer PSSSB IEEE PSS2A Dual-Input Stabilizer Plus Voltage Boost Signal

Transient Stabilizer and Vcutoff

+

+

Σ

STMINV

STMAXV

Input 1

Input 2

W1

W1

sT1+sT 6

11+sT

W2

W2

sT1+sT

W3

W3

sT1+sT

S2

7

K1+sT

W4

W4

sT1+sT

S3K

N

8M

9

1+sT(1+sT )⎡ ⎤⎢ ⎥⎣ ⎦

+

−S1K 1

2

1+sT1+sT

3

4

1+sT1+sT

STV


S4K

Σ

7 81 2 3

4 5 6

19

KV

TΔV >Vcutoff

Sw1

01

0 d1

11+sT

d2

d2

sT1+sT

ΣVcutoff

tlV

0

0≤+

+

T T0 TΔV =V -V

20

9 18−


States

- RampFilter109 - RampFilter1 19 - TransducerTEB10 - RampFilter2 20 - WOTEB

Stabilizer PTIST1

Stabilizer PTIST1 PTI Microprocessor-Based Stabilizer

Δω 1 3

2 4

K(1+sT )(1+sT )(1+sT )(1 sT )+

+− Σ π

F

Ms1+sT

+

+Σ

+

−Σ

P

11+sT

MP' TapSelection

Table

tE

eP on machine MVA base

1


STV

Stabilizer PTIST3

Stabilizer PTIST3 PTI Microprocessor-Based Stabilizer

Δω 1 3

2 4

K(1+sT )(1+sT )(1+sT )(1 sT )+

+− Σ π

F

Ms1+sT

+

+

Σ+

−

Σ

P

11+sT

MP'

TapSelection

Table

tE


1

5

6

1+sT1+sT

AveragingFunction

2 20 1 2 3 4 5

2 20 1 2 3 4 5

(A +A s+A s )(A +A s+A s )(B +B s+B s )(B +B s+B s )

LimitFunction

DL−

DL

AL−

AL

Switch 0=

Switch 1=


STV

Stabilizer ST2CUT

Stabilizer ST2CUT Stabilizing Model with Dual-Input Signals

+

+Σ

1

1

K1+sT

2

2

K1+sT

3

4

sT1+sT

7

8

1+sT1+sT

SMAXLS SS CU TO T CL TO

S T TO CL

S CT TO CU

V = V if (V +V >V >V +V )V = 0 if (V < V +V )V = 0 if (V > V +V )

5

6

1+sT1+sT

SSV

Output Limiter

Input Signal #1

Input Signal #2

9

10

1+sT1+sT

SMINL

TO

T

V = initial terminal voltageV = terminal voltage


STV

1

2

3 4 5 6

1 - Transducer12 - Transducer23 - Washout4 - LL15 - LL26 - Unlimited Signal

States

Stabilizer STAB1

Stabilizer STAB1 Speed-Sensitive Stabilizing Model

Ks1+sT

1

3

1+sT1+sT

2

4

1+sT1+sTSpeed (pu)

LIM-H

LIMH


STV1 2 3

1 - Washout2 - Lead-lag 13 - Lead-lag 2

States

Stabilizer STAB2A

Stabilizer STAB2A Power-Sensitive Stabilizing Unit

3

2 2

2

K sT1+sT⎡ ⎤

− ⎢ ⎥⎣ ⎦

3

3

K1+sT


LIM-H

LIMH+

+Σ

4K

2

5

5

K1+sT⎡ ⎤⎢ ⎥⎣ ⎦


STV

4

1 3− 5 6−

3

1 - Input State 12 - Input State 23 - Input State 34 - T5 - Output State 16 - Output State 2

States

Stabilizer STAB3

Stabilizer STAB3 Power-Sensitive Stabilizing Unit


LIM-V

LIMV−

+ Σ X1

11+sT

X

X2

-sK1+sTt

11+sT

refP


STV1 2 3

t

X1

1 - Int T2 - Int T3 - Unlimited Signal

States

Stabilizer STAB4

Stabilizer STAB4 Power-Sensitive Stabilizer


L1

L2−

+Σ X

X2

sK1+sT

a

X1

1+sT1+sTt

11+sT

refP

b

c

1+sT1+sT d

11+sT e

11+sT


STV1

2 3 4 5 6

d

1 - Input2 - Reset3 - LL14 - LL25 - T6 - Unlimited Signal

States

Stabilizer STBSVC

Stabilizer STBSVC WECC Supplementary Signal for Static var Compensator

Input Signal #1

Input Signal #2

S1

S7

K1+sT

S3K+

+Σ S13

S14

sT1+sT

SCS-V

SCSV

S3K

S2

S10

K1+sT

S11

S12

1+sT1+sT

S8

S9

1+sT1+sT


STV

1 2

3 4

5

1 - Transducer12 - LL13 - Transducer24 - LL25 - Washout

States

Stabilizer WSCCST

Stabilizer WSCCST WSCC Power System Stabilizer

+

qv

qv

K1+sT

T0V

signal j

speed 1accpw 2freq 3

− − − − − −

SMAXV

SLOWV

+

Model supported by PSLFBlocks in gray have not been implemented in Simulator

q

q

sT1+sT

'q2

q2

1+sT1+sT

'q1

q1

1+sT1+sT

'q3

q3

1+sT1+sT

TVΣ+−

1

11+sT

2

2

sT1+sT qsK+f(U)

k

+

'Vs

qs

11+sT

3

3

sT1+sT 4

s1+sT

tK−

−

+

Σ Σ

ΣU

1

2

3 4 5 6

KV

Sw1

01

0

d1

11+sT

d2

d2

sT1+sT

tlV

SV

TΔV >Vcutoff

ΣVcutoff

0

0≤+

+

T T0 TΔV =V -V

1 - Transducer12 - Transducer23 - WashoutTq4 - LL15 - LL26 - LL3

States

Stabilizer WT12A1 and WT1P

Stabilizer WT12A1 and WT1P Pseudo Governor Model for Type 1 and Type 2 Wind Turbines

Speed

genP

2

11+sT

−+Σ

1s

MINPI

MAXPI

IK

PE

11+sT

1

11+sT

II

1WT12A1 supported by PSSE with K =T

WT1P supported by PSLF

12

3 4

gen

I

1

mech

1 - P

2 - K3 - T4 - P

States

refω

droopKΣ

Σ

PK

refP

mechP+

+

−+

+

Stabilizer WT3P and WT3P1

Stabilizer WT3P and WT3P1 Pitch Control Model for Type 3 Wind Generator

ORDP

+Σ

MAX-RTheta

MAXRTheta

P

1sT

P PI MAX MAX MIN MIN MAX RATE

WT3P supported by PSLF T =T , Theta =PI , Theta =PI , and RTheta PI

WT3P1 supported by PSSE with no non-windup limits on pitch control=

12

3

1 - Pitch2 - PitchControl3 - PitchComp

States

refω

Σ

Σ

setP

Pitch

−

+

+

ω IPPP

KK +s

ICPC

KK +s

Σ

MAXTheta

M INTheta

MAXTheta

M INTheta

0

− −

+ +

Block Diagrams GENSAL

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