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Transient analysis of transformersTransient analysis of transformers and cables for offshore wind

tiBjørn Gustavsen

connectionBjørn Gustavsen

SINTEF Energy ResearchTrondheim, Norway

Wind power R&D seminar – deep sea offshore wind: Trondheim, Norway, 20-21 January, 2011.

SINTEF Energy Research

1

, y, y,

OutlineOutline

Modeling of transformers and cablesModeling of transformers and cables

High-frequency transformer-cable resonanceHigh frequency transformer cable resonance

Wind powerWind power

SINTEF Energy Research 2B. Gustavsen, 2010

PART I :Modeling of transformers and cables


High-frequency transformer modelingHigh frequency transformer modeling(black box)

1. Characterize the transformer by its frequency domain behavior at its external terminals

2. Identify a model which emulates the behavior of the transformer, as seen from the terminals.transformer, as seen from the terminals.


Terminal characterization by admittance

t l t i l

ymatrix

external terminals

n=i Y v

1 11 12 1 1( ) ( ) ( ) ( ) ( )nI Y Y Y Vω ω ω ω ω⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥

1( )I ω 1( )V ω

2 21 22 11 2( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

I Y Y Y V

I Y Y Y V

ω ω ω ω ω

ω ω ω ω ω

⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

2 ( )I ω

( )I ω

2 ( )V ω

( )nV ω: Transformer

1 2( ) ( ) ( ) ( ) ( )n n n nn nI Y Y Y Vω ω ω ω ω⎣ ⎦ ⎣ ⎦ ⎣ ⎦( )nI ω ( )n


Measurement of admittance matrixeasu e e t o ad tta ce at

Network analyzerConnection boxCoaxial cablesCoaxial cablesCurrent sensor

SINTEF Energy Research 6

Built-in current sensor (Pearson)B. Gustavsen, 2010

Modeling via rational functions g

1 11 12 1 1( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )

nI Y Y Y VI Y Y Y V

ω ω ω ω ω⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥

1( )I ω 1( )V ω( )V Measurement

2 21 22 11 2

1 2

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

I Y Y Y V

I Y Y Y V

ω ω ω ω ω

ω ω ω ω ω

⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

2 ( )I ω

( )nI ω

2 ( )V ω

( )nV ω: Transformer

Measurement

1 2( ) ( ) ( ) ( ) ( )n n n nn nI Y Y Y Vω ω ω ω ω⎣ ⎦ ⎣ ⎦ ⎣ ⎦( )n

Yn

Model extraction(fitting)

1( )

Nm

nm mj a

ωω=

≅ +−∑ RY D

Rational model

The rational model is compatible with EMTP type circuit simulators


The rational model is compatible with EMTP-type circuit simulators

Procedure for rational fittingProcedure for rational fitting

1 Calculate a rational model using Vector Fitting1. Calculate a rational model using Vector Fitting

1( )

Nm

j aω

ω≅ +

−∑ RY D

2. Enforce passivity by residue perturbation

1m mj aω=

1

Nm

m ms a=

Δ= + Δ ≅

−∑ RΔY D 0

N Δ∑ R1

(Re{ })m

m m

eigs a=

Δ+ >

−∑ RY 0

( )eig + Δ >D D 0

Matrix Fitting Toolboxh // i f / d k /VECTFIT/i d


http://www.energy.sintef.no/produkt/VECTFIT/index.asp

High frequency cable modelingHigh-frequency cable modeling

1 Characterize the cable by its per-unit-length series1. Characterize the cable by its per unit length series impedance matrix Z and shunt admittance matrix Y

( ) ( ) ( )jω ω ω ω= +Z R L

2 F Z d Y l l t t f f

( ) ( ) ( )jω ω ω ω= +Z R L

( ) ( ) ( )jω ω ω ω= +Y G C

2. From Z and Y, calculate parameters for a frequency-dependent traveling wave model.

This modeling capability is available in EMTP-type programs

Main challenge: calculate Z− Analytical expressions

Fi it El t


− Finite Element

PART II :Cable-transformer high-frequency resonance

B. Gustavsen, “Study of transformer resonant overvoltages caused by cable-transformer high-frequency interaction” IEEE Trans Power Delivery vol 25 no 2 pp 770-779 April


high frequency interaction , IEEE Trans. Power Delivery, vol. 25, no. 2, pp. 770 779, April 2010.

Demonstrate that transients on the high voltage side of aDemonstrate that transients on the high-voltage side of a transformer can cause excessive overvoltages on the low-voltage side.

Identify critical cable-transformer configurations that lead t hi h ltto high overvoltages


Voltage ratio from high to lowVoltage ratio, from high to low

41230 V11 kV

4411230 V11 kV

456

123

456

456

123

123

300 kVA

At high frequencies, the voltage ratio is governed by stray capacitances and inductances, not ampere-winding balance.

50 Hz voltage ratio ≈0.022MHz voltage ratio ≈ 2

A 2 MH i id l lt ld d 100 lt


A 2 MHz sinusoidal voltage would produce a 100 p.u. overvoltage

B. Gustavsen, 2010

Laboratory measurementLaboratory measurementHigh-voltage

Low-voltage30 Ω

High-voltage

Low-voltage30 Ω

Step voltage

voltage voltage30 Ω456

123

Step voltage

voltage voltage30 Ω456

456

123

123

Cable (27 m)Cable (27 m)

Before connecting cable to transformer After connecting cable to transformer

24 p u overvoltage !!~24 p.u. overvoltage !!


Measurement-based model of transformer230 V11 kV 230 V11 kV

300 kVA456

123

230 V11 kV456

456

123

123

230 V11 kV

– Frequency sweep measurements of Y(ω)

63 6633

– Model extraction by Matrix Fitting Toolbox

N R

1( ) m

mm j aω

ω=≈ +

−∑ RY D


Measurement-based model of 27-m cable

A AAAA AAA

v1 v2

CableSR

Cable50 Ω1̂v 2v̂

SRv1 v2

CableSR v1 v2

CableSRSR

Cable50 Ω1̂v 2v̂

SR

Cable50 Ω1̂v 2v̂

SRSR

ba

yy

a= −

( 1)b

bybR

=a( 1)R

a−

Model extraction by Matrix Fitting ToolboxN

ya , yb

1( )

Nm

mm j aω

ω=≈ +

−∑ RY D

ya , yb


Simulation vs. measurementHigh-voltage

Low-voltage30 Ω

1

High-voltage

Low-voltage30 Ω

11

Cable (27 m)

Step voltage 456

123

Cable (27 m)

Step voltage 456

456

123

123

Cable (27 m)Cable (27 m)

Before connecting cable to transformer After connecting cable to transformer


Max. overvoltage vs. cable lengthMax. overvoltage vs. cable length– State-of-the art frequency-dependent traveling-wave

type model obtained from geometry.

– Compute max. overvoltage on low-voltage side for alternative cable lengths


Ground fault.M lt bl l thMax. overvoltage vs. cable length

High-voltage

Low-voltage30 Ω

High-voltage

Low-voltage30 Ωideal

Step voltage

g g30 Ω456

123

Step voltage

g g30 Ω456

456

123

123

ideal

Cable (27 m)Cable (27 m)20 m cable (open LV)Overvoltage in p.u. of applied voltage

~43 p.u. overvoltage !!


Switching overvoltages (1)g g ( )

300 m 5000 m 20 mcablecable300 m 5000 m 20 mcablecable

cable

close@ t=0

overhead line1 p.u.

clos

cable

close@ t=0

overhead line1 p.u.

clos

– Several parallel cables connected to bus

– Combined characteristic impedance much lower than that of connection cable

– Bus appears as ”stiff” voltage seen from connection cable

Closing CB results in oscillating voltage on cable


Closing CB results in oscillating voltage on cable

B. Gustavsen, 2010

Switching overvoltages (1)g g ( )300 m cable

5000 m overhead line1 p u

20 mcablecable300 m

cable5000 m overhead line1 p u

20 mcablecableA

cable

close@ t=0

overhead line1 p.u.

clos

cable

close@ t=0

overhead line1 p.u.

clos



Switching overvoltages (2)g g ( )– Two cables of equal length coupled to the same busbar

One cable is liveT1

close@ 0clos

5000 m 20 m cableoverhead line

1 p.u.

T1

close@ 0clos


T1

close@ 0clos

5000 m 20 m cableoverhead line close

@ 0clos


1 p.u.

– One cable is live

@ t=0

20 m cable

T2@ t=0

20 m cable

T2@ t=0

20 m cable

@ t=0

20 m cable

T2

T1

~25 p u overvoltage !!~25 p.u. overvoltage !!


Switching overvoltages (3)g g ( )5000 m

20 m cableoverhead line1 p.u. 5000 m

20 m cableoverhead line1 p.u.

20 m cable

close@ t=0clos 1 µF

20 m cable

close@ t=0clos 1 µF@@



Note:Other transformers may have resonances at much lower frequenciesfrequencies.

Overvoltages will occur with longer cables.

Voltage ratio for a 410 MVA generator transformer (434 kV / 21 kV)


PART III :PART III :Relevance to wind power


Switching overvoltagesg g

Radials of nearly equal lengthEnergizing a branchEnergizing a branch

oscillating overvoltage on WT transformer HV sideIn the case of short radials (< 1km) the oscillatingIn the case of short radials (< 1km), the oscillating overvoltage has frequency above 50 kHzHigh overvoltages may result on WT transformer LV


High overvoltages may result on WT transformer LV side by resonance

B. Gustavsen, 2010

Ground fault initiation

Ground fault initiation can cause an oscillating overvoltage in the cableovervoltage in the cable. Frequency depends on fault locationHigh overvoltages may result on WT transformer LVHigh overvoltages may result on WT transformer LV side by resonance


Notes

The actual overvoltage on the WT LV side is stronglyThe actual overvoltage on the WT LV side is strongly dependent on the network on the LV side

A complete model must be developed


ConclusionsConclusionsHigh-frequency interaction between the wind turbineHigh frequency interaction between the wind turbine transformers and the cables can lead to excessive overvoltages the transformer LV side. The phenomenon can be triggered by ground fault initiation and by switching.


Electromagnetic Transients inElectromagnetic Transients inFuture Power Systems.Future Power Systems.

Phenomena, Component Stresses, Modeling

A JIP project (KMB) between SINTEF and industry partners(2011 2015)(2011-2015)

New partners are welcome !Contact: [email protected]


ObjectiveObjective

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