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U

TL

IN

U

TL

INHarmonic distortion - What it is

Harmonic calculations and definitions

Harmonic limiting standards

Harmonic reduction techniques

Danfoss Solution

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Displacement power-factor, DPF

Voltage

Current

Displacement angle,

Apparent power:

S=Voltage * Current

Active power:

P= Voltage * Current * cosine(f)

Reactive power:

Q= Voltage * Current * sine(f)

P

S

Q

Displacement power-factor (DPF) = cos( )

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Total Harmonic Distortion, THD

( ) %100max)1(

)(

2

2

= =

h

hI

I hTHD

=

=max

1

2)(

h

h

hRMS II

2

)1(1 THDII

RMS+=

THD definition applies to current and voltage waveforms.

Current THD is defined as

The RMS value of a non-sinusoidal Current waveform is defined as

which relates to the THD as

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True power-factor, PF ( )

The basic power-factor definition is

For sinusoidal voltage and current the definition reduces to )(CosDPFPF ==

Power-factor relates to current THD as

For an VFD with dc-link inductor the displacement power-factor is almost 1

(typically 0.99) and therefore

21 THD

DPFPF

+=

21

1

THD

PF

+

RMSI

DPFIPF

=

)1(

S

PPF =

Power-factor is decreased by reactive power and harmonic currents

Low power-factor means high RMS current and thus higher losses in cable and transformer

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Illustrative way to understand PQ

Q = kVAR(nonwork

producing)

P = kW (work producing)

D = kVAH

(nonwork

producing)

S = kVA

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Illustrative way to understand PQ

FC

IM

Filter

THiD = 0

Cos ( ) = 0.9

THiD = 45%

Cos ( ) = 1

THiD = 0%

Cos ( ) = 1

Ip = 1

Irms =1.1Iq = 0.48

Ip = 1

Irms =1.1I

D= 0.45

Iq = 0

ID = 0 Ip = Irms = 1

PF = 1

2

1

1

THD

PF

+

=

PF = DPF= Cos (

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Total Demand Distortion, TDD

TDD = Current Harmonic Distortion in percentage of maximum demand load current

( ) %100max)1(

)(

2

2

= =

h

hI

I hTHD

TDD is a system level parameter as it depends upon the definition of IL.The definition of IL is crucial to this parameter.

( ) %100max)(

)(

2

2

= =

h

hI

I

L

hTDD

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Partial Weighted Harmonic Distortion,PWHD

( ) %100max

)1(

)(

14

2= =

h

hI

I hhPWHD

Partial weighted harmonic distortion is starting at h=14

and multiplying the harmonics with the order h

Higher harmonics are the the key to this index