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EG2040-Wind Power Systems,Grid lecture 1-2
Lennart Sder
Professor in Electric Power Systems
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Solution:
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New (?) words to be treatedin the lectures:
Voltage Weak grid
Short circuit capacity
Feeding grid is purely inductive
Voltage regulating equipment
Line capacitance
Line impedance
Power factor equal to 0.9 inductive
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Single-phase alternating voltage
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RMS-value of voltage and current
Sinusoidal voltage and current
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Complex power
The complex power is defined as
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which implies that
With phase angles on voltage and current
i.e. arg( ) = 0 and arg ( ) =
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Example: Two series connected impedancesare fed by a voltage having an RMS-value of
1 V according to the figure
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a) Calculate the power consumed by
as well as the power factor (cos) at
bus 1 and 2 where k
is the phase
angle between the voltage and thecurrent at bus k.
b) Calculate U2 when is capacitive :
= 0.7 -j0.5.
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Symmetrical three-phase alternating voltage
Time domain expressions
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Line-to-line voltage
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Three phase complex values
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Three phase complex values - 2
+ + = 0
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Symmetrical three-phase power
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Symmetrical three phase systems
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Connection to a network
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Example 7.1
At a bus with a short circuit capacity of 500
MVA and cosk= 0, inductive, an impedanceload of 4 MW, cosLD=0.8 at nominal voltage,
is
connected. Calculate the change in bus
voltage when the load is connected.
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Overhead transmission lines20 kV 220 kV
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Transmission line - 1
One phase equivalent of a transmission line at
symmetrical three phase transmission
Resistance
The resistance of a conductor with the cross-
section area A mm2 and the resistivity mm2/ km is
h
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Shunt conductance
The shunt conductance g is neglected in
this course.
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Transmission line - 2
Inductance:
where
Geometrical mean distance according to the figure below.
Diameter of the conductor, m
Number of conductors per phase
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Figure 4.2
Ground level
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Transposed three-phase overhead line
Locations of transposing
Transposing cycle
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Transposed line
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Alternativ to transposed line
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Transmission line - 3
Multiple conductor
Cross-section of a multiple conductor
with three conductors per phase
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Overhead transmission lines
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where
n = number of conductors per phase
D/2 = radius in the circle formed by the
conductors
Transmission line - 4
Multiple conductor
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Example 4.1
Determine the reactance of a 130 kV overheadline where the conductors arc located in a plane
and the distance between two closely located
conductors is 4 m. The conductor diameter is 20
mm. Repeat the calculations for a line with two
conductors per phase, located 30 cm from one
another.
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Example 4.1 One conductor/phase
phase
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Example 4.1 Multiple conductor
phase
The reactance is in this case reduced by
Multiple conductor
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Transmission line - 5
Shunt capacitance
For a transposed overhead line andsymmetrical conditions :
phase
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Figure 4.2
Ground level
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where
Geometrical mean height for
the conductors
Geometrical mean distance
between the conductors and their image
conductors.
The shunt susceptance of a line is
S/km, phase
Common value : 310-6 S/km,phase
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Approximatively it can be shown that
Where v = speed of light in vacuum in km/s.
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Transmission line - 6
Example
Assume that a line has a shunt susceptance of
310-6 S/km,phase. Use equation 4.6 to estimate
the reactance of the line
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Transmission line - 7
Model for a short line
Where s = length of line in km.
phase
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Model for a medium long line
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Power flow on a line - 1-model for a transmission line
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Example 8.1 Assume a line where the voltage inthe sending end is U1 = 2250 kV and in thereceiving end U2 = 213.08 3.572 kV. The linehas a length of 100 km and has x = 0.4 /km, r =
0.04 /km and b = 3 10-6 S/km. Calculate theamount of power transmitted from bus 1 to bus 2.
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Power flow on a line - 2At U > 70 kV, R
i.e. active power flows towards a lower angle
With the same phase for Ukand Uj
i.e. reactive power flows towards a lower
voltage
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Line losses
One phase losses
Symmetrical three phase system
The squared current can be expressed as
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The losses for a medium line can
now be expressed as
or
Line losses
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Load flow analysis - 1
Notation at bus kin a network
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Assume that voltage is known in oneend of a line and P+Q in the other.
Based on this information:
Calculate the voltage in the other end.
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Solution:
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