Chapter 6. Harmonics and lters of LCC HVDC linksvct/elec0445/chap6.pdf · Chapter 6. Harmonics and lters of LCC HVDC links Introduction Introduction Thyristor converters generate

ELEC0445 - High Voltage Direct Current grids

Part 1. Line Commutated Converters

Chapter 6. Harmonics and filters of LCC HVDC links

Patricia Rousseaux Thierry Van [email protected] www.montefiore.ulg.ac.be/~vct

March 2018

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Chapter 6. Harmonics and filters of LCC HVDC links Introduction

Introduction

Thyristor converters generate harmonic voltages and currents on both the ACand the DC sides.

Undesirable effects of harmonics in the AC systemI higher currents, resulting in higher losses and heating in AC equipmentsI vibrationsI interference with electronic and telecommunication equipmentI resonance phenomena which could produce overvoltages and overcurrentsI control and stability issues in the HVDC system

Undesirable effects of harmonics in the DC systemI interference with the telecommunication link between both terminalsI DC cable insulation limits the allowable voltage distortion.

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Chapter 6. Harmonics and filters of LCC HVDC links Current harmonics generated in AC grids by HVDC converters

Current harmonics generated in AC grids by HVDCconverters

We first neglect the commutation overlap (µ = 0).

6-pulse bridge with Y-Y transformer connection

i6Y =√

2I1

[sinωt +

∞∑k=1

(−1)k

(1

6k − 1sin(6k − 1)ωt +

1

6k + 1sin(6k + 1)ωt

)]

where I1 =

√6

πId is the RMS value of the fundamental component.

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6-pulse bridge with Y-∆ transformer connection

i6∆ =√

2I1

[sinωt +

∞∑k=1

1

6k − 1sin(6k − 1)ωt +

∞∑k=1

1

6k + 1sin(6k + 1)ωt

]

12-pulse bridge with Y-Y and Y-∆ transformers : i12 = i6Y + i6∆

i12 = 2√

2I1

[sinωt +

∞∑k=1

(1

12k − 1sin(12k − 1)ωt +

1

12k + 1sin(12k + 1)ωt

)]

less harmonic components with 12 pulse bridgeessentially 5th and 7th harmonics are eliminated

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Taking into account the commutation overlap

The overlap angle “rounds off the square edges” of the current waves

this reduces the magnitude of each harmonic component

for n−th order harmonic :

ihih0

=

√H2 + K 2 − 2HK cos(2α + µ)

cosα− cos(α + µ)

H = (sin(n + 1)µ/2) /(n + 1)

K = (sin(n − 1)µ/2) /(n − 1)

where ih is the amplitude of the harmonic current with overlapih0 is the amplitude of the harmonic current with no overlap

the amplitude ih of the harmonic depends on the operating conditions

as µ increases, the harmonic component decreases

during faults, α is brought close to 90 and µ is reduced; for a given DCcurrent, the AC harmonics increase

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Chapter 6. Harmonics and filters of LCC HVDC links Non-characteristic harmonics

Non-characteristic harmonics

The above harmonics correspond to perfectly balanced conditions

under unbalanced conditions, more harmonics are present : 2nd, 3rd,...

sources of imbalance :I converter asymmetry : non equally spaced firing pulses, thyristor asymmetry,...I converter transformer asymmetryI imbalances on the AC side

a cautious design of converters is required !

Some HVDC links use special supplementary controls to reduce low ordernon-characteristic harmonics.

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Chapter 6. Harmonics and filters of LCC HVDC links Harmonic performance criteria

Harmonic performance criteria

Harmonic Factor (HF) : measure of individual harmonic magnitude

HFn =Vn

V1

Total Harmonic Distortion (THD) : measure of closeness between the actualwaveform and the fundamental sinusoidal component :

THD =1

V1

√√√√ ∞∑n=2

V 2n

where V1 is the RMS value of the fundamental componentVn is the RMS value of the n-th harmonic component.

Of course, the values of HF and THD should be as low as possible.

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Chapter 6. Harmonics and filters of LCC HVDC links Harmonic performance criteria

Standards specifying the limits tolerated on voltage harmonics

IEEE standard 519

IEC standard 61000 3-6

DC side : recommendation for XLPE cables : THD < 3%, for insulation reasons.

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Chapter 6. Harmonics and filters of LCC HVDC links Harmonic filters on the AC side

Harmonic filters on the AC side

Each HVDC station is provided with harmonics filters on the AC side

designed to reduce the harmonic distortion below the acceptable limits.

Two kinds of LC filters :I tuned band-pass filter : rejects one specific harmonicI damped high-pass filter : attenuates all harmonics above a given order.

The penetration of harmonics in the AC system and resonance conditionsdepend on the system impedance at the harmonic frequency. The latter isnot easy to determine, and changes with operating conditions of the AC grid

At fundamental frequency, the filters have capacitive reactance. Hence, theyprovide part of the reactive power compensation at the converter buses

Reactive compensation is arranged in switchable banks

Banks are switched on and off by steps to follow the varying power

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Example of HVDC station filters

11-th (resp. 13-th) tuned filter : shows a minimal impedance at the 11-th(resp. 13-th) harmonic frequencyhigh-pass filter : small impedance at harmonics higher than 13.

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The AC-side filters are physically large.

Together with the switchgear,they can occupy over 50 % of the HVDC station footprint !

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Design of a tuned band-pass filter to attenuate the harmonic frequency ωf

Assumption :

the grid impedance at frequency ωf isinfinite.

Impedance of the (Rf , Lf ,Cf ) filter at frequency ω:

Zf = Rf + jωLf +1

jωCf= Rf − j

1− ω2Lf Cf

ωCf

At frequency ωf , the reactances of the capacitor and the inductor cancel eachother. Hence:

ωf =1√Lf Cf

and the impedance becomes simply : Zf = Rf .

The quality factor is defined as: qf =ωf Lf

Rf. Typical range of values : 10− 50.

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Frequency response Zf (ω) of an 11-th harmonic filter (ωf = 2π550 rad/s)

The band-pass (BP) of the filter is : BP = ± ωf

2 qf=

Rf

2 Lf 13 / 16


Rf should be as small as possible :

to attenuate the harmonic current more efficiently

to have the residual voltage at ωf , i.e. Vff = Rf Iff , as small as possible(voltage harmonic).

However, it is difficult to bring Rf close to zero :

there remains a parasitic resistance

section of conductors cannot be exaggerate.

Furthermore, a very small Rf is not desirable :

this means a small BP value

hence, if the capacitance Cf changes due to ageing, the filter gets de-tuned !

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Chapter 6. Harmonics and filters of LCC HVDC links Exercise 6-1

Exercise 6-1

A 500-MW, 250-kV, 2000-A, 12-pulse HVDC converter is equipped with 11th,13th and high-pass harmonics filters. The AC grid voltage is 220 kV, at 50 Hz.The ratio of the transformer is set to 0.4355 (= AC voltage on inverter side / AC

voltage on grid side).

The 11th-harmonic filter has the following parameters :

Cf = 3.91µF Lf = 0.0214 H Rf = 0.7 Ω

1 Verify that the filter is tuned to the 11th harmonics.2 Compute the reactive power it produces at the fundamental frequency.3 Compute the active losses in the filter at 50 Hz.4 Compute the same at 550 Hz.5 Compute the harmonic factor of the 11th harmonic of grid voltage.6 Compute the same after Cf has dropped by 10 %, due to ageing.

Assume that the impedance of the AC grid is zero at 50 Hz and infinite at 550 Hz.15 / 16

Chapter 6. Harmonics and filters of LCC HVDC links Harmonic filters of the DC side

Harmonic filters of the DC side

Harmonics are also present on the DC sideI they originate from the voltage waveform shown in slide # 20 of Chapter 4I voltage harmonics produce current harmonics in the DC line/cable

6-pulse bridge : produces voltage harmonics of order 6 k ; k = 1, 2, . . .

12-pulse bridge1 : produces voltage harmonics of order 12 k ; k = 1, 2, . . .I the 6th, 18th, 30th, ... harmonics are of opposite signs in the bridges and

cancel each other

the 12th harmonic is the most important one

the magnitudes of the voltage harmonics varies with α and µ.

some HVDC links are provided on the DC side with a (shunt) tuned filter toreject the 12th harmonic.

The smoothing reactor contributes to limiting harmonics on the DC slide.

In case of a DC cable, the higher shunt capacitance contributes to reducingharmonics.

1connected with YY and Y∆ transformers in parallel16 / 16

Documents

Chapter 6. Harmonics and lters of LCC HVDC linksvct/elec0445/chap6.pdf · Chapter 6. Harmonics and lters of LCC HVDC links Introduction Introduction Thyristor converters generate