8690889 Synchronous Machines

7/22/2019 8690889 Synchronous Machines

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Synchronous machines:

Protection relevant basics



Copyright © Siemens Australia & NZ 2007. All rights reserved. Siemens. Innovation for generations.

Synchronous Machine without Load

~

Xd IG

Vp V

Vp = V + j·IG·XdTurbine

ExcitationSystem

AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG

VP V

1/xd

IExc 0

IG= 0

Im

Re




Synchronous Machine connected to the Net:inductive Load

~

Xd

IG

Vp V

Vp = V + j·IG·Xd

TurbineExcitationSystem

AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG

Re

φ = +90°δ=0°

1/xd

IExc

IG

VP j·IG·Xd

V

Im

(Different scales for IExc and IG)

V= VN, f = fN


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Synchronous Machine connected to the Net:capacitive Load

~

Xd

IG

Vp V

Vp = V + j·IG·Xd

φ = -90°δ=0°

1/xd

IExc

IG

VP

j·IG·Xd V

Re

Im


AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG


V= VN, f = fN



Synchronous Machine connected to the Net:active Load

~

Xd IG

Vp V

Vp = V + j·IG·Xd

φ = 0°

δ

1/xd

IExc IG

Re

VP

j·IG·Xd

V

Im


AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG


V= VN, f = fN



Synchronous Machine connected to the Net:rated Load

~

Xd

IG

Vp V

Vp = V + j·IG·Xd


AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG

φNδ

1/xd

IExc N

ING

VP

j·IG·Xd

V

Im

Re

(Different scales for IExc and ING)

V= VN, f = fN



Synchronous Machine in Island operationat VN and fN , partial loaded

~

Xd

IG

Vp V

Vp = V + j·IG·Xd


AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG

φδ

1/xd

IExc

IG

VP

j·IG·Xd

V=VN

Im

Re


V= VN, f = fN



Synchronous Machine in Island operation

~

Xd

IG

Vp V

Vp = V + j·IG·Xd


AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG

φδ

1/xd

IExc

IG

VP

j·IG·Xd

V

Im

Re


V= >VN, f = fN

VN



Synchronous Machine in Island operation

~

Xd

IG

Vp V

Vp = V + j·IG·Xd


AVRn

n+n-

Speed-Control

V+V-

50 HzS →∞

V

IG

φδ

1/xd

IExc

IG

VP

j·IG·Xd

V=VN

Im

Re


V= VN, f = >fN




Synchronous Machines: P-Q-Equations describing the Theoretical Stability Limit

sinx

UE

Pd

ϑ

⋅

=

Salient-pole machine

ϑ ϑ sin2xx

x-x

2

U sin

x

UE P

qd

qd2

d

+⋅

=

)sinx

x-x (1

x

U cos

x

UE Q 2

q

qd

d

2

d

ϑ ϑ +−⋅

=

P active power [p.u.]Q reactive power [p.u.]E (VP) pole wheel voltage (e.m.f.) [p.u.]U (V) terminal voltage of the generator [p.u.]xd synchronous direct axis reactance [p.u.]x

qsynchronous quadrature axis reactance [p.u.]

ϑ pole wheel angle

Cylindrical-rotor machine (xd ≈≈≈≈ xq)

x

U cosx

UE Q

d

2

d−

⋅= ϑ




Construction of the Stability Limitsfor a Salient-Pole Machine

3.5 3 2.5 2 1.5 1 0.5 0 0.5 1

0.5

0.5

1

1.5

22.0

0.5

P 1i

P 3i

P 5i

P 6i

P dy1i

P dy2i

Sthya

Sprya

Stdya

cosφ

13.5 Q 1iQ 3i, Q 5i

, Q 6i, Q dy1i

, Q dy2i, Sthx

a, Sprx

a, Stdyx

a, Q N,

Theoretical staticstability limit

Dynamicstability limit

Practical staticstability limit

P[p.u]

1/xd

1/xq

Q[p.u]

1/x’d

E=0

E’=0

E=1,68

E’=0,25

E=1,0

E=0,5




Capability Curve of a Salient-Pole Generator (1/2)




Capability Curve of a Salient-Pole Generator (2/2)




Construction of the Stability Limitsfor a Cylindrical-Rotor Machine

3 2.5 2 1.5 1 0.5 0 0.5 1

0.5

0.5

1

1.5

22.0

0.5

P 1i

P 3i

P 6i

P dy1i

P dy2i

Sthya

Sprya

Stdya

cosφ

Theoretical staticstability limit

Dynamicstability limit Practical static

stability limit

P[p.u]

1/xd Q[p.u]

1/x’d

E=0,8

E’=0

E’=0,4

E=2,51




Capability Curve of a Turbo Generator

type of generator: TLRI 108/46

nominal apparent powerS N = 200 MVA

nominal voltage V N = 15.750 kVnominal current I N = 7.331 kAnominal frequency f N = 50.0 Hzpower factor cos ϕN = 0.8cold-air temperature T x = 40.00 °C

MVAr 140 120 MVAr100 80 60 40 20 0 20 40 60 80 100 120 140 160 180

underexcited overexcited

Q

P

MW

220

200

180

160

140

120

100

80

60

400,2

0,4

0,6

0,7

0 , 8

0 , 8

5

0 , 9

0 , 9

5

0 , 9

7 5

0 , 9

7 5

0 , 9

5

0 , 9

0,2

0,4

0,6

0,7

0,8

0,85

C o s φ

C o s φ

8690889 Synchronous Machines

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