Iec tr 61000 1 7 2016

IEC TR 61 000 1 7 Edition 1 0 201 6 02 TECHNICAL REPORT Electromagnetic compatibility (EMC) – Part 1 7 General – Power factor in single phase systems under non sinusoidal conditions IE C T R 6 1 0 0 0[.]

IEC TR 61 000- 1 - 7

Edit io 1.0 2 16-0

Elect romagnetic compat ibi ity (EMC) –

Part 1- 7: General – Pow er factor in single- phase sy st ems under non- sinusoidal

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IEC TR 61000- 1 - 7

Edit io 1.0 2 16-0

Elect romagnetic compatibi it y (EMC) –

Part 1- 7: General – Pow er fact or in single- phase sy st ems under non- sinusoidal

CONTENTS

FOREWORD 4

INTRODUCTION 6

0.1 Series overview 6

0.2 Purp se of this doc ment 6

1 Sco e 8

2 Normative ref eren es 8

3 Terms an def i ition 8

4 General 14 5 Electric p wer q antities u der non-sin soidal con ition 15 5.1 Voltages an c r ents 15 5.1.1 In tantane u values 15 5.1.2 Ref eren e f un amental comp nents 16 5.1.3 Total distortion contents 16 5.1.4 RMS values of the voltage an c r ent 16 5.1.5 RMS values of total distortion contents 17 5.1.6 DC ratios 17 5.1.7 Total distortion ratios 17 5.2 In tantane u p wer 18 5.3 Def i ition related to the active p wer 18 5.3.1 Active p wer 18 5.3.2 DC p wer 18 5.3.3 Fu damental active power 19 5.3.4 Distortion active p wer 19 5.4 Def i ition related to the a p rent p wer 19 5.4.1 Ap arent p wer 19 5.4.2 Fu damental a p rent p wer 2

5.5 Def i ition related to the p wer f actor 2

5.5.1 Power f actor 2

5.5.2 Fu damental p wer f actor 21

5.5.3 Non-f un amental p wer f actor 21

5.6 Summary 21

6 Electric p wer q antities with a sin soidal voltage an a c r ent distorted only with harmonic 22 6.1 Voltages an c r ents 2

6.1.1 In tantane u values 2

6.1.2 Fu damental comp nents 2

6.1.3 Harmonic content of the c r ent 2

6.1.4 RMS values of the voltage an c r ent 2

6.1.5 RMS value of the harmonic content of the c r ent 2

6.1.6 Total harmonic ratio of the c r ent 2

6.1.7 Fu damental f actor 2

6.2 In tantane u p wer 2

6.3 Active p wer 2

6.4 Def i ition related to the a p rent p wer 2

6.4.1 Ap arent p wer 2

6.4.2 Fu damental a p rent p wer 2

6.5 Def i ition related to the p wer f actor 2

6.5.1 Power f actor 2

6.5.2 Fu damental p wer f actor 2

6.5.3 Non-f un amental p wer f actor 2

6.6 Summary 2

An ex A (normative) Electric p wer q antities u der sin soidal con ition 2

A.1 In tantane u values of the voltage an c r ent 2

A.2 In tantane u p wer 2

A.3 Active p wer 3

A.4 Re ctive p wer 3

A.5 Ap arent p wer 3

A.6 Power f actor 30 An ex B (inf ormative) Fu damental active f actor 3

B.1 Fu damental active f actor an its u e 3

B.2 Con umer con ention 3

Bibl ogra h 3

Fig re A.1 – Il u tration of the displacement an le (φ) when the voltage le d the c r ent, φ > 0 2

Fig re A.2 – Il u tration of the displacement an le (φ) when the voltage lag the c r ent, φ < 0 2

Fig re B.1 – Con umer sig con ention of the f un amental active f actor, f un amental active p wer an f un amental re ctive p wer 3

Ta le 1 – Summary of the p wer q antities u der non-sin soidal con ition 21

Ta le 2 – Summary of the p wer q antities with a sin soidal voltage an a c r ent

distorted only with harmonic 27

INTERNATIONAL ELECTROTECHNICAL COMMISSION

1 Th Intern tio al Ele trote h ic l Commis io (IEC) is a worldwid org niz tio for sta d rdiz tio c mprisin

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this e d a d in a ditio to oth r a tivitie , IEC p bls e Intern tio al Sta d rd , Te h ic l Sp cific tio s,

Te h ic l Re orts, Pu lcly Av ia le Sp cific tio s (PAS) a d Guid s (h re fter refere to a “IEC

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a re me t b twe n th two org niz tio s

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The main tas of IEC tec nical commit e s is to pre are International Stan ard However, a

tec nical commite may pro ose the publ cation of a tec nical re ort when it has col ected

data of a dif f erent kin f rom that whic is normal y publ s ed as an International Stan ard, f or

example "state of the art"

IEC TR 610 0-1-7, whic is a Tec nical Re ort, has b en pre ared by s bcommit e 7 A:

c mp tibility

The text of this tec nical re ort is b sed on the f ol owin doc ments:

En uiry draft Re ort o v tin

Ful inf ormation on the votin f or the a proval of this tec nical re ort can b f ou d in the

re ort on votin in icated in the a ove ta le

This publ cation has b en draf ted in ac ordan e with the ISO/IEC Directives, Part 2

A l st of al p rts in the IEC 610 0 series, publ s ed u der the general title Electroma n tic

c mp tibility (EM C), can b f ou d on the IEC we site

The commite has decided that the contents of this publ cation wi remain u c an ed u ti

the sta i ty date in icated on the IEC we site u der "ht p:/we store.iec.c " in the data

related to the sp cif i publcation At this date, the publcation wi b

Mitigation method an devices

Part 6: Ge eric sta dards

Part 9: Mis el a eous

Eac p rt is f urther s bdivided into section whic are to b publ s ed either as international

stan ard , tec nical sp cif i ation , or as tec nical re orts

ac ordin ly (f or example, 610 0-6-1)

0.2 Purpose of this document

The prevalen e of lo d drawin non-sin soidal c r ent f rom p wer s stems req ires

impl ed as umption of sin soidal voltage an c r ent This doc ment sp cif i al y ad res es

the terms related to the p wer f actor of eq ipment that are a pl ca le regardles of the

voltage an c r ent wavef orms

When voltages an c r ents on p wer s p ly network are p rf ectly sin soidal, cos ϕ

cor esp n s to the p wer f actor But this is not true an more when electric q antities are

distorted In some existin doc ments, cos ϕ is sti u ed as p wer f actor, le din to an

in or ect as es ment of the eq ipment imp ct to s p ly network

The purp se of this Tec nical Re ort is to give cle r inf ormation on b th comp nents in the

p wer f actor:

• the f un amental p wer f actor, whic is d e to the phase dif f eren e b twe n the voltage

an c r ent at the f un amental f req en y (cos ϕ

1, an

• the non-f un amental p wer f actor, whic is related to the distortion of the voltage an /or

c r ent

ELECTROMAGNETIC COMPATIBILITY (EMC) –

Part 1-7: General – Power f actor in single-phase systems

under non-sinusoidal conditions

This p rt of IEC 610 0, whic is a Tec nical Re ort, provides def i ition of variou electrical

p wer q antities an the relation hip b twe n them u der non-sin soidal con ition , in order

to give cle r inf ormation on b th comp nents in the p wer f actor: the f un amental p wer

f actor, whic is d e to the phase dif f eren e b twe n the voltage an c r ent at the

f un amental f req enc , an the non-f un amental p wer f actor, whic is related to the

distortion of the voltage an /or c r ent This Tec nical Re ort is a pl ca le only to sin l

e-phase s stems

This Tec nical Re ort provides def i ition f or the thre f ol owin cases:

• the general case where the voltage an c r ent are b th distorted (Clau e 5),

• the case where the voltage is as umed to b sin soidal an the c r ent is only distorted

with harmonic comp nents (Clau e 6),

• the p rtic lar case where the voltage an c r ent are b th sin soidal (An ex A)

An ex B gives inf ormation on the f un amental active f actor, whic is u ed to des rib the

b haviour of a piece of eq ipment as a lo d or a generator

2 Normative ref erences

The f ol owin doc ments, in whole or in p rt, are normatively ref eren ed in this doc ment

an are in isp n a le f or its a pl cation For dated ref eren es, only the edition cited a pl es

For u dated ref eren es, the latest edition of the ref eren ed doc ment (in lu in an

for a time-de en ent q antity, p sitive s uare ro t of the me n value of the s uare of the

q antity taken over a given time interval

Note 1 to e try: Th ro t-me n-s u re v lu of a p rio ic q a tity is u u ly ta e o er a inte ratio interv l

th ra g of whic is th p rio multiple b a n tural n mb r

Note 2 to e try: For a sin s id l q a tity a( = Âc s(ωt

+ϑ

0), th ro t-me n-s u re v lu is A

ef

= Â/√2

Note 3 to e try: Th ro t-me n-s u re v lu of a q a tity ma b d n te b a din o e of th s b cripts ef or

rms to th s mb l of th q a tity

Note 4 to e try: In ele tric l te h olo y, th ro t-me n-s u re v lu s of ele tric c re t i( a d v lta e u( are

u u ly d n te I a d U, re p ctiv ly

[SOURCE: IEC 6 0 0-10 :2 0 , 10 -0 -0 ]

3.2

dire t compone t

me n value of a q antity taken over a given time interval

[SOURCE: IEC 6 0 0-10 :2 0 , 10 -0 -0 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

3.3

sinusoidal adj

p rtainin to an alternatin q antity re resented by the prod ct of a re l con tant an a sine

or cosine f un tion whose arg ment is a l ne r f un tion of the in e en ent varia le

Note 1 to e try: Th re l c n ta t ma b a s alar, v ctor or te s r q a tity

Note 2 to e try: Ex mple are a( = Âc s(ωt +ϑ

0) a d a(x) = Âc s[k (x –x )]

value of the phase of a sin soidal q antity when the value of the in e en ent varia le is zero

Note 1 to e try: For th q a tity a( = Âc s(ωt +ϑ

0), th initial p a e is ϑ

0

[SOURCE: IEC 6 0 0-10 :2 0 , 10 -0 -0 ]

3.5

periodic conditions

state of an electric circ it element or electric circ it that is c aracterized by the electric

c r ents an voltages al b in p riodic f un tion of time with the same p riod T

[SOURCE: IEC 6 0 0-131:2 0 , 131-1 -2 , modif ied – ad ition of s mb l T f or the p riod

3.6

sinusoidal conditions

state of a l ne r electric circ it element or electric circ it that is c aracterized by the electric

c r ents an voltages al b in sin soidal f un tion of time with the same f req en y

where u

AB

is the l ne integral of the electric f ield stren th f rom A to B, an where the electric

c r ent in the element or circ it is taken p sitive if its direction is f rom A to B an negative if

its direction is f rom B to A

Note 1 to e try: Th dire tio of ele tric c re t is a d fin d in IEC 6 0 0:2 0 , 131 1 -2

Note 2 to e try: In circ it th ory th ele tric field stre gth is g n raly n n-otatio al a d th s u

B

= v

A– v

B,

wh re v

A

a d v

Bare th ele tric p te tials at termin ls A a d B, re p ctiv ly

Note 3 to e try: Th c h re t SI u it of in ta ta e u p wer is wat, W

Note 4 to e try: A two-termin l eleme t or circ it refers to a sin le-p a e e uipme t or s stem

[SOURCE: IEC 6 0 0-131:2 13, 131-1 -3 , modif ied – in note 2, the term ir otational is

re laced by non- otational an a new note 4 has b en ad ed

3.8

S

prod ct of the r.m.s voltage U b twe n the terminals of a two-terminal element or

two-terminal circ it an the r.m.s electric c r ent I in the element or circ it

S = UI

Note 1 to e try: Th c h re t SI u it for a p re t p wer is v ltamp re, V

Note 2 to e try: A two-termin l eleme t or circ it refers to a sin le-p a e e uipme t or s stem

[SOURCE: IEC 6 0 0-131:2 13, 131-1 -41, modif ied – the existin note 1 has b en removed

dttp

TP

0)(1

Note 1 to e try: Th c h re t SI u it for a tiv p wer is wat, W

Note 2 to e try: Wh n th v lta e or c re t c ntain interh rmo ic c mp n nts, ofte th ir wa eforms are n

more p rio ic In this d c me t, th a tiv p wer is a pro imate b th me n v lu of th in ta ta e u p wer,

ta e o er a inte er n mb r of p rio s of th a.c p wer s p ly s stem (s e 5.3.1 a d 5.1.4) This d finitio is

als u e u d r p rio ic c n itio s in this d c me t (s e 6.3 a d Cla s A.3)

[SOURCE: IEC 6 0 0-131:2 13, 131-1 -4 , modif ied – the existin note 1 has b en removed

an a note 2 has b en ad ed

3.10

non-a tiv power

Q~

f or a two-terminal element or a two-terminal circ it u der p riodic con ition , q antity eq al

to the s uare ro t of the dif f eren e of the s uares of the a p rent p wer S an the active

p wer P

Q~

22

Note 2 to e try: A two-termin l eleme t or circ it refers to a sin le-p a e e uipme t or s stem

[SOURCE: IEC 6 0 0-131:2 13, 131-1 -4 , modif ied – the existin note 1 has b en removed

an a note 2 has b en ad ed

Q

f or a l ne r two-terminal element or two-terminal circ it, u der sin soidal con ition , q antity

eq al to the prod ct of the a p rent p wer S an the sine of the displacement an le φ

Q = S sinϕ

Note 1 to e try: Th c h re t SI u it for re ctiv p wer is v ltamp re, V Th s e ial n me v r a d its s mb l

v r are als u e Se IEC 6 0 0- 31:2 13, 131 1 -4

Note 2 to e try: A two-termin l eleme t or circ it refers to a sin le-p a e e uipme t or s stem

Note 3 to e try: Wh n th c n itio s are n t sin s id l th re is n intern tio al c n e s s o a d finitio of th

re ctiv p wer In te d, s v ral d finitio s of th re ctiv p wer e ist In s me d c me ts, th re ctiv p wer is

ta e a th n n-a tiv p wer, b t th re are ma y oth r formula

[SOURCE: IEC 6 0 0-131:2 13, 131-1 -4 , modif ied – the existin note 1 has b en removed

=λ

Note 1 to e try: Un er sin s id l c n itio s, th p wer fa tor is th a s lute v lu of th a tiv fa tor

[SOURCE: IEC 6 0 0-131:2 0 , 131-1 -4 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

3.13

displa eme t a gle

pha e dif f ere c a gle

φ

u der sin soidal con ition , phase dif f eren e b twe n the voltage a pled to a lne r

two-terminal element or two-terminal circ it an the electric c r ent in the element or circ it

Note 1 to e try: Th c sin of th dis la eme t a gle is th a tiv fa tor

Note 2 to e try: A two-termin l eleme t or circ it refers to a sin le-p a e e uipme t or s stem

[SOURCE: IEC 6 0 0-131:2 0 , 131-1 -4 , modif ied – a note 2 has b en ad ed

3.14

a tiv fa tor

f or a two-terminal element or a two-terminal circ it u der sin soidal con ition , ratio of the

active p wer to the a p rent p wer

Note 1 to e try: Th a tiv fa tor is e u l to th c sin of th dis la eme t a gle, a d c n v ry fom –1 to +1

Note 2 to e try: A two-termin l eleme t or circ it refers to a sin le-p a e e uipme t or s stem

[SOURCE: IEC 6 0 0-131:2 0 , 131-1 -4 , modif ied – a note 2 has b en ad ed

[SOURCE: IEC 6 0 0-10 :2 0 , 10 -0 -19]

3.16

ref ere c f undamental compone t

con entional y c osen sin soidal comp nent of a q antity, to the f req en y of whic al the

other comp nents are ref er ed

Note 1 to e try: Th term is u e wh n, for a p rio ic q a tity, th c o e c mp n nt difers fom th

fu d me tal c mp n nt, or wh n th q a tity is n t p rio ic d e to interh rmo ic c mp n nts

Note 2 to e try: In this d c me t, th c mp n nt h vin th fe u n y of th a.c s p ly s stem is c o e a th

refere c fu d me tal c mp n nt

[SOURCE: IEC 6 0 0-10 :2 0 , 10 -0 -2 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents an a note 2 ad ed

refere c fundamental fre ue c

f req en y of the ref eren e f un amental comp nent

Note 1 to e try: Th term is u e wh n, for a p rio ic q a tity, th refere c fu d me tal c mp n nt difers fom

th fu d me tal c mp n nt,or wh n th q a tity is n t p rio ic d e to interh rmo ic c mp n nts

[SOURCE: IEC 6 0 0-10 :2 0 , 10 -0 -2 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

3.19

harmonic f re u nc

f req en y whic is an integer multiple gre ter than one of the f un amental f req en y or of

the ref eren e f un amental f req en y

Note 1 to e try: Wh n a refere c fu d me tal fe u n y is d fin d, it is u e in pla e of th fu d me tal

harmonic compone t

sin soidal comp nent of a q antity havin a harmonic f req en y

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -0 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

interharmonic compone t

sin soidal comp nent of a q antity havin an interharmonic f req en y

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -0 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

3.2

harmonic order

ratio of the f req en y of an sin soidal comp nent to the f un amental f req en y or the

ref eren e f un amental f req en y

Note 1 to e try: Th h rmo ic ord r of th fu d me tal c mp n nt or th refere c fu d me tal c mp n nt is

total distortion conte t

q antity o tained by s btractin f rom a q antity its direct comp nent an its f un amental

comp nent or its ref eren e f un amental comp nent

Note 1 to e try: Th total distortio c nte t in lu e h rmo ic c mp n nts a d interh rmo ic c mp n nts if a y

Note 2 to e try: Wh n a refere c fu d me tal fe u n y is d fin d, th refere c fu d me tal c mp n nt is

u e in pla e of th fu d me tal c mp n nt

Note 3 to e try: Th total distortio c nte t is a time fu ctio

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -1 , modif ied – def i ition exten ed to q antities

containin interharmonic comp nents an note 4 deleted

3.2

harmonic conte t

s m of the harmonic comp nents of a q antity

Note 1 to e try: Th h rmo ic c nte t is a timefu ctio

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -12, modif ied – def i ition exten ed to q antities

containin interharmonic comp nents an notes 2 an 3 deleted

3.2

total harmonic ratio

total harmonic distortion

THD

ratio of the r.m.s value of the harmonic content to the r.m.s value of the f un amental

comp nent or the ref eren e f un amental comp nent of a q antity

Note 1 to e try: Wh n a refere c fu d me tal fe u n y is d fin d, th refere c fu d me tal c mp n nt is

u e in pla e of th fu d me tal c mp n nt

Note 2 to e try: Th total h rmo ic ratio c n b a pro imate b lmitin th c lc latio u to a c rtain h rmo ic

ord r

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -13, modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

total distortion ratio

ratio of the r.m.s value of the total distortion content to the r.m.s value of the f un amental

comp nent or the ref eren e f un amental comp nent of a q antity

Note 1 to e try: Wh n a refere c fu d me tal fe u n y is d fin d, th refere c fu d me tal c mp n nt is

u e in pla e of th fu d me tal c mp n nt

Note 2 to e try: Th total distortio ratio c n b a pro imate b lmitin th c lc latio u to a c rtain h rmo ic

ord r

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -14, modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

[SOURCE: IEC 6 0 0-5 1:2 01, 5 1-2 -17, modif ied – def i ition exten ed to q antities

containin interharmonic comp nents

This Tec nical Re ort provides def i ition of variou electrical p wer q antities an the

relation hip b twe n them, when a voltage u(t) is a pl ed to a sin le-phase eq ipment or

s stem, i t) b in the c r ent f lowin in the eq ipment or s stem

The f olowin cases are con idered:

• In Clau e 5, the general case is des rib d The voltage an c r ent are b th distorted an

can contain d.c harmonic an interharmonic comp nents

• In Clau e 6, the voltage is as umed to b sin soidal an the c r ent is only distorted with

harmonic comp nents

• In An ex A, the voltage an c r ent are b th sin soidal

In this doc ment, the ref eren e f un amental f req en y is the f req en y of the a.c s p ly

p wer s stem (as umed to b con tant, but not neces ari y eq al to the rated value of 5 Hz

or 6 Hz) an al harmonic or interharmonic f req en ies are related to this f req en y

In the p rtic lar case where the voltage is sin soidal an the c r ent do s not contain

interharmonic comp nents, these q antities are p riodic an their f un amental f req en y is

eq al to the f req en y of the a.c p wer s p ly s stem Theref ore, the term " ef eren e

f un amental f req en y" is re laced by the term "f un amental f req en y" in Clau e 6 an

An ex A

In this Tec nical Re ort, the harmonic order of harmonic or interharmonic comp nents is not

l mited But, in practical a pl cation , the harmonic order may b l mited to a sp cif ied order

5 Electric power quantities under non-sinusoidal conditions

5.1.1 Insta ta eous v lu s

For ste d -state con ition , the non-sin soidal in tantane u value of the voltage or c r ent

is the s m of a d.c comp nent, a sin soidal comp nent at the p wer s stem f req enc an

sin soidal comp nents at harmonic or interharmonic f req en ies

+

⋅+

=

1011

0

sin2sin

2)

(

mm

mm

tmU

tU

Ut

+

⋅+

=

1011

0

sin2sin

2)

(

mm

mm

tmI

tI

It

is the r.m.s value of the ref eren e f un amental comp nent of the voltage;

ω is the an ular f req en y cor esp n in to the ref eren e f un amental f req en y;

t is the time;

α

1

is the initial phase of the ref eren e f un amental comp nent of the voltage;

m is the harmonic order (m is a p sitive re l n mb r dif f erent f rom 0 an 1 It is an integer

n mb r f or harmonic comp nents an a non-integer n mb r f or interharmonic

comp nents);

U

m

is the r.m.s value of the voltage harmonic or interharmonic comp nent of order m;

α is the initial phase of the voltage harmonic or interharmonic comp nent of order m;

i() is the in tantane u value of the c r ent at time t;

is the r.m.s value of the c r ent harmonic or interharmonic comp nent of order m;

β is the initial phase of the c r ent harmonic or interharmonic comp nent of order m

The non-sin soidal in tantane u value of the voltage or c r ent can also b writen as the

s m of thre terms:

)()()

(

D10

tutuUt

)()()

(

D10

titiIt

() is the total distortion content of the voltage at time t (se 5.1.3);

i ( ) is the ref eren e f un amental comp nent of the c r ent at time t (se 5.1.2);

i

D

( ) is the total distortion content of the c r ent at time t (se 5.1.3)

5.1.2 Ref ere c f und me tal compone ts

The ref eren e f un amental comp nent of the voltage (c r ent is def i ed as the sin soidal

comp nent of the voltage (c r ent havin the f req en y of the a.c p wer s p ly s stem:

11

sin2)

u

11

sin2)

i

5.1.3 Total distortion conte ts

The total distortion content of the voltage (c r ent is o tained by s btractin the direct

comp nent an the ref eren e f un amental comp nent f rom the in tantane u value of the

voltage (c r ent :

)()

()(

10D

tuUtut

)()

()(

10D

tiItit

sin2)

(

mm

mm

tmU

sin2)

(

mm

mm

tmI

t

5.1.4 RMS v lue of the volta e a d c r e t

In this doc ment, the r.m.s value of the voltage U (c r ent I) is def i ed as the p sitive

s uare ro t of the me n value of the s uare of the voltage (c r ent taken over an integer

n mb r of p riod of the a.c p wer s p ly s stem:

∫+

=

kT

dttu

kTU

t

t

2

)(1

∫+

=

kT

dtti

kTI

t

t

2

)(1

where

T is the reciprocal of the ref eren e f un amental f req en y;

k is an integer n mb r;

τ is the time when the me s rement starts

NOT If th v lta e a d c re t are o ly distorte with h rmo ic c mp n nts, th n a me s reme t time interv l

k T e a le th c re t me s reme t of r.m.s a d p wer v lu s If th v lta e or th c re t c ntain interh rmo ic

c mp n nts, r.m.s a d p wer v lu s are in ore tly me s re , u le s th me s reme t time interv l k T in lu e

a inte er n mb r of th p rio of e c interh rmo ic c mp n nt For pra tic l situ tio s wh n th b lk of th

p wer is c rie b th refere c fu d me tal c mp n nts, s c er ors are smal Th larg r th me s reme t

time interv l k T, th le s sig ific nt th erors c u e b interh rmo ic c mp n nts b c me For more

informatio , s e IE E Std 14 9-2 10 Pra tic l meth d to e alu te sig als th t c ntain interh rmo ic or

These q antities are the s m of several terms:

2

D2

12

02

UUU

2

D2

12

02

III

is the r.m.s value of the total distortion content of the c r ent (se 5.1.5)

5.1.5 RMS v lu s of total distortion conte ts

Ac ordin to the def i ition given in 5.1.3, the r.m.s value of the total distortion content of the

voltage (c r ent is def i ed as f ol ows:

2

12

022

D

UUU

2

12

022

D

III

22

D

mmmUU

22

D

mmmII

5.1.6 DC ratios

The d.c ratio of the voltage DCR

U(c r ent DCR

I) is def i ed as the ratio of its d.c comp nent

to the r.m.s value of its ref eren e f un amental comp nent:

10

U

UU

10

I

II

5.1.7 Total distortion ratios

The total distortion ratio of the voltage TDR

U(c r ent TDR

I) is def i ed as the ratio of the

r.m.s value of its total distortion content to the r.m.s value of its ref eren e f un amental

comp nent: