Contents – Electric Power T&D

Introduction

Power in AC systems, Three Phase Systems

Transformers

P.U. System

Power Lines

Fundamentals of Power Transmission

Symmetrical Components
1
Power line
2
Total # of real quantities:
8
One voltage angle as reference:
-1
2 complex equations = 4 real equations:
-4
# of independent quantities:
3
3
U1
P2+jQ2
G
U1 P1+jQ1
G
U1 ϕ 1
U2 ϕ =0
4
Lossless power line (R’=G’=0 )
U1
U2
Z2
5
Lossless power line (R’=G’=0 )
Surge Impedance Loading (Natürliche Last)
PSIL  Pnat
2
U

ZW
6
Lossless power line (R’=G’=0 )
Calculate P1 and Q1!
7
Lossless power line (R’=G’=0 )
For a load equal to the surge impedance loading at the receiving end of a line, i.e.
P2 =
2
U2
ZW
and Q2 = 0
then the active and reactive load at the sending end is
P1 =
U2
ZW
2
and Q1 = 0
and U 1 = U 2
8
∆Ql
1
∆Qc
2
1
∆Qc
2
P = PSIL ⇒ ∆Ql = ∆Qc
9
U
L′
2
Ql = Qc ⇒ U ωC ′ = I ωL′ ⇒ 2 =
= ZW
I
C′
2
2
2
10
11
Surge Impedance Loading for power line with losses
∈ℜ
12
No load conditions – Ferranti-Effect (Lossless line)
U1
U2 , P+jQ = 0
G
(5.107)
(6.13)
13
Ferranti effect
U1
U2 =
≥ U1
cos( βl )
The voltage is higher at the end of a open-circuited power line
14
∆Ql ∝ XI 2
1
∆Qc
2
1
∆Qc
2
1
1
∆Qc ∝ BcU 2
2
2
15
Power World (Fig_6_2_System_2006_400kV)
Ex. 1: Lossless line, length = 300 km, Voltage = 400 kV
16
Ferranti-Effect
17
Open ended lossless line
18
Power World(Resonance_2)
Ex. 2: Lossless line, length = 1 581 km, Voltage = 800 kV
19
Half wavelength power transmission lines
20
P1  jQ1
P2  jQ2
U1
U2
Lossless line: P1 = P2
21
22
P1  jQ1
P2  jQ2
U1
U2
P2+jQ2
G
U1 = ?
U2
23
24
25
26
27
R0
28
29
(δ is small)
30
U1
P2+jQ2
G
U2 = ?
31
32
stable
unstable
33
Efficiency of power lines, Sect. 6.6
34
Energy losses in the US T&D system were 7.2% in 1995.
Estimates of the UK system: 7.4%
Most of the losses occur in the distributions (MV and LV)
grids.
35
U1 θ 1
U2 θ 2
jωL = jX L ( R = 0)
36
37
U1U 2
sin δ
P1 = P2 =
XL
δ = θ1 − θ 2
δ
38
Abbildung 6.9 P - δ relationship for a power line (400 km)
39
40
The reactive power flows for short lines (shunt capacitance neglected):
U12 − U1U 2 cos δ
Q1 =
XL
δ = θ1 − θ 2
U1U 2 cos δ − U 22
Q2 =
XL
P1  jQ1
P2  jQ2
U1
U2
41
Reactive power flows
For short power lines (shunts neglected):
U − U1U 2 cos δ
Q1 =
XL
2
1
If U1 > U 2 ⇒ Q1 > 0
P1  jQ1
P2  jQ2
U1
U2
“Reactive power flows from higher voltage (magnitude) to lower”
42
43
Series Compensation
Pmax
U1U 2
=
XL
In order to increase Pmax one can series compensate the line.
That means that the effective line reactance is reduced :
X Leff = X L − X C
X Leff = X L − X C
44
45
46
Controllable Series Compensation
XL
ef f
= X L ¡ X C (®)
47
TSSC = Thyristor Switched Series Capacitor
TCSC = Thyristor Controlled Series Capacitor
C
L
TSSC
48
49
Limits for Power Transmission
St. Clair curves
50
51
Question to think about
Why is the power frequency 50 Hz? (or 60 Hz)
52