Grid Lecture 1

8/9/2019 Grid Lecture 1

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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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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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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


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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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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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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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:

Grid Lecture 1

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