Power Systems Formulae
3
Electric Power Systems – Formula Sheet Formula Sheet – Electric Power Systems The allowed tools at the exam are: this formula sheet, TEFYMA (or equivalent) and a pocket calculator. = 2 1 0 9 9 9 $ 9 9 9 where = = = − D D D D $ H D D D D D $ 2 2 1 3 2 2 2 1 1 1 1 1 3 1 ; with 1 1 1 1 1 π Three-phase per-unit base definitions according to Glover-Sarma: EDVH EDVH EDVH EDVH// EDVH EDVH/1 EDVH EDVH/1 EDVH EDVH// EDVH/1 EDVH// EDVH EDVH/1 EDVH EDVH EDVH EDVH = < 6 9 6 9 , 9 = 9 9 9 6 9 6 , 6 6 / 1 3 / 3 3 3 2 1 2 3 1 1 3 = = = = = = = = φ φ φ φ φ φ Zero sequence networks of transformers, neglecting phase shift and shunt admittance: Z n1 Z n2 3Z n1 3Z n2 Z eq Z n 3Z n Z eq Z eq
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Transcript of Power Systems Formulae
Electric Power Systems – Formula Sheet
Formula Sheet – Electric Power Systems
The allowed tools at the exam are: this formula sheet, TEFYMA (or equivalent) and a pocket calculator.
=
2
1
0
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F
E
D
where
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= −
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2
213
2
2
2
1
1
111
31
; with
1
1
111 π
Three-phase per-unit base definitions according to Glover-Sarma:
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/1
3/
33
3
2
1
2
3113
=
====
===
φφ
φφφφ
Zero sequence networks of transformers, neglecting phase shift and shunt admittance:
Z n1 Z n2
3Z n1 3Z n2 Z eq
Z n
3Z n Z eq Z eq
Electric Power Systems – Formula Sheet
Zero, positive and negative sequence fault currents (In-0, In-1, In-2) for a fault at bus n
Three-phase fault 0 ; 201
1 === −−−
)
Q��
�
�
Single line-to-ground, phase a )QQQQQQ
)
QQQ �
���3210
210 +++===
−−−−−−
Line-to-line fault, phases b and c 0 ; 021
21 =++
=−= −−−
−− Q
)QQQQ
)
QQ�
�
��
Double line-to-ground fault, phases b and c
( )
++−=
+++−=
++++
=
−−
−−−
−−
−−−
−−
−−−
−
)QQQQ
)QQQQ
)QQQQ
)QQQQ
)
Q
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��
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3
33
33
02
210
02
012
02
021
1
Znn-0, Znn-1 and Znn-2 denote element (n,n) of zero, positive and negative sequence bus impedance matrix Zbus.
If prefault currents are neglected, bus voltages during fault at bus n,
Vbus = VF − Z bus IF
where IF only has one nonzero element being In – the fault current leaving bus n.
rms short-circuit current unloaded synchronous machine
Symmetrical (ac) ( )
+
−+
−= −−
G
7W
GG
7W
GG
JDF �
�
��� GG
11
’
1
’
1
"
1 ’/"/
Asymmetrical (ac+dc) ( ) ( ) ( )22 ������GFDFUPV
+=
Asymmetrical (ac+maximum dc) ( ) ( ) [ ]G
J7W
DFUPV
�������� $
"" where"2
2/2 =+= −
Electric Power Systems – Formula Sheet
Salient pole rotor synchronous generator
( )
( )
+−=
−+=
GTG
T
H
GTG
T
H
�
���
�
���
δδδδ
δδδ
222
2
sincoscos
2sin11
2sin
Newton-Raphson solution of y=f(x) , iteration i: ( ) ( ) ( ) ( )[ ]{ }
( ) ( )L[[
Q
P
PQ ��
��
����������
=
−
=
−+=+
∂∂
element Matrix
1 1
Complex Power injected at bus k calculated using bus admittance matrix, bus voltage vector:
−−=
−−=⇒=+=
∑
∑
=
=
)sin(
)cos(
1
1*
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θδδ
θδδ
where ),( ��� EXV
M
NQNQ=θ and )(���� EXV
M
NN =δ
∆-Y transformation
ZAB = ZAZB + ZBZC + ZAZC
ZC
ZBC =ZA ZB + ZBZC +Z AZC
ZA
ZAC =Z AZB + ZB ZC +Z AZC
ZB
ZA =Z ABZAC
Z AB +Z BC + ZAC
ZB =Z ABZBC
Z AB +ZBC + ZAC
ZC =ZACZ BC
ZAB + ZBC + ZAC
