Capacitors for Power Factor Correction

Capacitors for Power Factor Correction and Filtering (MKK)

Page

Siemens Matsushita Components

Product advantages

298

Applications

300

General technical information and formulas

302

Thermal calculation

306

Symbols and terms

309

PhaseCapTM series B 25 667 (MKK)

312

297

Capacitors for Power Factor Correction and Filtering

PhaseCapTM po powe werr capa capaci cito tors rs of the the MKK MKK ser series ies are de desi sign gned ed for for AC app ppli lica cati tio ons in the the ran range of 230 23 0 to 10 1000 00 V. In ad addi diti tion on to po powe werr fact factor or corr correc ecti tion on,, Phas PhaseC eCap apTM capaci capacitor tors s are becomi becoming ng increa increassingl ingly y po popu pula larr in filt filter er circ circui uits ts to impr improv ove e en ener ergy gy qu qual alit ity. y. The The comp compac actt de desi sign gn,, extr extrem emel ely y high high stab stabililit ity y of cap capacit acitan anc ce, highe ighest st pu puls lse e curr curre ent with withst stan and d cap apab abil ilit ity y of mo more re tha than 300 time times s rate rated d cur current rent,, ease ea se of inst instal alla lattion ion an and d ser service vice life life of mo more re tha than 10 100 0 00 000 0 h are are indi indisp spe ensab nsable le ad adva vant nta age ges s in ap appl pliication cations s like like reacti reactiveve-pow power er compen compensat sation ion equ equipm ipment ent,, wind wind farms, farms, high-p high-powe owerr conver converter ters s and uninuninterruptible power supplies. 1

Product advantages

Compact design for low height, low weight and small dimensions The PhaseC PhaseCap apTM MKK MKK capa capaci cito torr in comp compac actt de desi sign gn is a me meta talllliz ized ed po poly lypr prop opyl ylen ene e film film capa capaci cito torr with with self self-h -hea eali ling ng prop proper erti ties es.. The The curr curren entt carr carryi ying ng me meta tall laye layerr of an MKK MKK capa capaci cito torr is vapo vaporr-de depo posi site ted d onto one side of the polypropylene film. Thre Three e elec electr tric ical ally ly sepa separa rate ted d pa part rtia iall capa capaci cito tors rs are are wo woun und d conc concen entr tric ical ally ly in a sing single le op oper erat atio ion n on an insu insula late ted d me meta tall core core tube tube,, wh whic ich h gu guar aran ante tees es exce excell llen entt wind windin ing g prec precis isio ion. n. The The elec electr trod odes es are are conconnected by metal spraying (schooping) at the front surface of the winding element. The partial capa capaci cito tors rs can can be conn connec ecte ted d in star star,, de delt lta a or seri series es circ circui uits ts.. The The comp compac actt MKK MKK wind windin ing g elem elemen entt is housed in a cylindrical aluminum case with a metal lid, press-rolled onto it. Extended Extended service service life of more more than 100000 h After an extended drying period impregnation (filling the capacitor case with protection gas) is carried out under high igh vacuum to reduce moisture at the active element. Fina inally, the case is hermeti me tica call lly y seal sealed ed an and d the the ga gas s proo proofn fnes ess s is insp inspec ecte ted d in rout routin ine e test tests s usin using g a spec specia iall leak leakag age e test tester er.. This This de desi sign gn avoi avoids ds oxid oxidat atio ion n as we well ll as pa part rtia iall disc discha harg rges es,, an and d en ensu sure res s ther theref efor ore e capa capaci cita tanc nce e stastability over an extended period of time, which is essential especially in filter circuit applications.

You You can can find find ou outt all all ab abou outt Phas PhaseC eCap apTM MKK MKK seri series es from from your your loca locall Siem Siemen ens s sale sales s offi office ce for for pa pass ssiv ive e components or direct from Siemens Matsushita Components GmbH & Co. KG KO PM L Postfach 80 17 09 D-81617 München 636 - 2 38 17 ¤ +49 89 636 Fax: +49 89 89 636- 2 27 48 E-Mail: [email protected] [email protected] mens.de For information on our entire product range look in on internet under http://www.siemens.de/pr/inf/20/55/d00 http://www.siemens.de/pr/inf/20/55/d0000000.htm 00000.htm

298



Highest inrush current withstand capability is crucial Capaci Capa cito tors rs used used in po powe werr fact factor or corr correc ecti tion on syst system ems s are are freq freque uent ntly ly swit switch ched ed.. The The rela relate ted d inru inrush sh curcurrent rents s mu must st be ha hand ndle led d with withou outt affe affect ctin ing g the the serv servic ice e life life.. The The pu puls lse e ha hand ndli ling ng capa capabi bili lity ty of this this tech tech-nolo no logy gy de dep pen ends ds mainl ainly y on the the con contact tact zone zone area area.. Enlar nlarge gem men entt of the the sens sensib ible le cont conta act zone zone is of major ajor impo imporrtanc tance e. The The S+M pa pate ten nt, the the “wav “wave e cut” cut”,, ha has s brou brough ghtt the the brea breakt kthr hro oug ugh h in this this crit critic ical al matter. Inrush currents of 300 times rated current and above can be easy handled. Highest inrush current withstand capability is crucial in the following applications: q q q

Parallel switching of capacitors Non-detuned capacitors Capacitor banks using “standard contactors”

Customer-oriented output range q q

25 kvar units units over all all voltage voltage ranges ranges (above 230 230 V) available available Outputs adapted for detuned capacitor banks

The MKK capacitor offers a triple safety system q

q q

DryDry-ty type pe de desi sign gn.. Du Due e to the the fact fact that that the the asse assemb mbly ly is free free of liqu liquid id impr impreg egna nati ting ng ag agen ents ts,, such such as oil oil or PC PCB, B, the the risk risk of fire fire caus caused ed by spur spurti ting ng or leak leakin ing g oil oil is elim elimin inat ated ed.. In ecol ecolog ogic ical ally ly sens sensit itiv ive e applications as well as for insurance aspects the dry-type design is a must. Self-healing technology. The The over overpr pres essu sure re tear tear-o -off ff fuse fuse prev preven ents ts the the capa capaci cito torr from from bu burs rsti ting ng at the the en end d of serv servic ice e life life,, or due to inadmissible electrical or thermal overloads.

Innovative and reliable connection technology: SIGUT ® The The SIGU SIGUT T term termin inal al en ensu sure res s a reli reliab able le an and d ea easy sy conn connec ecti tion on also also for for pa para rall llel el conn connec ecti tion on of a nu nummber of capacitor units. Major customer benefits are: q q q q q

Parallel connection of connection cable Protection against electric shock hazard (IP20, according VDE 0106 part 100) Separate connection of discharge resistors increases reliability Clamping principle prevents loosening of the screws Cable cross cross sections sections up up to 16 mm2

Easy mounting and grounding q

q

Any Any mo moun unti ting ng po posi siti tion on of the the capa capaci cito torr is po poss ssib ible le.. The The mo moun unti ting ng po posi siti tion on is chos chosen en to ob obta tain in op op-timum cost effectiveness and ease of engineering for the intended application. A threaded stud (M12) at the bottom of the case serves for both grounding and mounting.


299


2

Applications

2 .1

Power fa factor co correction

Indu Induct ctiv ive e de devi vice ces s like like mo moto tors rs or tran transf sfor orme mers rs load load ge gene nera rato tors rs,, supp supply ly line lines s an and d elec electr tric ical al dist distri ribu bu-TM tion tion syst system ems s with with reac reacti tive ve curr curren entt as we well ll as acti active ve curr curren ent. t. Phas PhaseC eCap ap MKK capaci capacitor tors, s, specia specially lly deve de velo lope ped d for for po powe werr fact factor or corr correc ecti tion on an and d use use in filt filter ers, s, are are ab able le to prev preven entt mo most st of this this reac reacti tive ve curcurrent from reaching power generation/transmission plant.

PFC controller

Contactor M

M

M

~3

~3

~3

Capacitor

Figu Figure re 1 Standard power factor correction

KLK1652-4

Benefits of power factor correction: q

q

q

q

q

q

Amortization in 8 to 24 months Power factor correction equipment reduces the amount of reactive power in an installation. As a result electricity bills drop in proportion. Generally investment in PFC equipment pays off within 8 to 24 months of installing it. Effective utilization of electrical power An impr improv oved ed po powe werr fact factor or me mean ans s high higher er acti active ve po powe werr for for the the same same ap appa pare rent nt po powe wer. r. This This ma make kes s an electrical system more economical. Reduction of losses Cabl Ca bles es carr carry y less less reac reacti tive ve curr curren entt wh when en the the po powe werr fact factor or is impr improv oved ed.. This This redu reduce ces s the the cond conduc uc-tion losses in a cable. Optimum dimensioning of cables The The requ requir ired ed cabl cable e size size redu reduce ces s with with the the impr improv ovem emen entt of po powe werr fact factor or.. In an exis existi ting ng ap appl plic icat atio ion n the same cable can be used to serve an additional load. Reduction of transmission losses Sinc Since e the the tran transm smis issi sion on an and d swit switch chge gear ar eq equi uipm pmen entt carr carry y redu reduce ced d curr curren ent, t, on only ly the the acti active ve curr curren ent, t, electrical losses will be reduced. Improvement of power quality

300



2 .2

Harmonics fi filter in in po power el electronics

Powe Powerr conv conver erte terr curr curren entt is actu actual ally ly a curr curren entt mix, mix, with with a fund fundam amen enta tall comp compon onen entt of line line freq freque uenc ncy y and an d a nu numb mber er of ha harm rmon onic ics s wh whos ose e freq freque uenc ncie ies s are are inte integr gral al mu mult ltip iple les s of line line freq freque uenc ncy. y. The The ha harm rmon on-ic curr curren ents ts are are impr impres esse sed d on the the thre threee-ph phas ase e line line.. This This resu result lts s in ha harm rmon onic ic volt voltag ages es on the the ne netw twor ork k imp imped edan ance ces s tha hatt are supe superrimpo impose sed d on the fund fundam amen enta tall an and d cau cause disto istort rtio ion n of the the line line volt voltag age e. This can lead to disturbance in the network and to outage of other loads. PhaseCapTM MKK MKK capa capaci cito tors rs,, used used in ha harm rmon onic ics s filt filter ers, s, redu reduce ce the the ha harm rmon onic ics s an and d impr improv ove e en ener ergy gy quality. Frequency converter 1

EMC filter

_

Ι c

~

Line

Ι dc

+U dc/2 U dc

_

~

EMC output filter

M

~3

_ U

dc/2

KLK1653-C

2

4

3 Phase Cap

1 2 3

Figu Figure re 2 Filter for reduction of harmonic currents

2.3 2.3

4

Commutating choke Filter choke KLK1653-C Harmonics filter, e.g. for 250, 350 and an d 550 550 Hz Alum Alumin inum um elec electr trol olyt ytic ic for for DC link link circ circui uitt

Dam Da mpin ping of harm harmon onic ics s in in power ower elec electr tron onic ics s

PWM conv conver erte ters rs ge gene nera rate te harm armon onic ics s in the the ran ange ge of 3 to 12 kHz. kHz. This his ha has s a ne neg gativ ative e effe effect ct on en en-TM ergy ergy qua qualit lity. y. Harmon Harmonic ic curren currents ts cause cause consid considera erable ble distur disturban bance ce in oth other er loads. loads. PhaseC PhaseCap ap capacitors are used in filters to keep disturbing harmonic currents away from supply networks. PWM converter

Ι N

Phase Cap

Ι L

C

Line

LCL filter

Load

KLK1654-K

Figu Figure re 3 Damping of harmonic currents


301


3

Gene Genera rall tec techn hnic ical al info inform rmat atio ion n and and form formul ulas as for for pow power er fact factor or corr correc ecti tion on

3 .1

Definitions

Active power The The am amou ount nt of inpu inputt po powe werr conv conver erte ted d into into ou outp tput ut po powe werr is term termed ed acti active ve po powe werr an and d ge gene nera rall lly y reprepresented by P . Active power is defined by the following formula: P

=

U ⋅ I ⋅ cos ϕ

The formula P =

[W] 3 ⋅ U ⋅ I ⋅ cos ϕ applies to three-phase systems.

Ideally the entire input, i.e. apparent power, should be converted int into useful output, i.e. active ive powe po wer, r, e.g e.g.. the the mo moto torr outpu utputt on a shaf shaft. t. In such such a case case cos cos ϕ is un unit ity y an and d the the syst system em is said said to wo worrk at unity power factor. Reactive power Elec Electr tric ic ma mach chin ines es wo work rk by conv conver erti ting ng elec electr trom omag agne neti tic c en ener ergy gy (e.g. (e.g. elec electr tric ic mo moto tors rs,, tran transf sfor orme mers rs). ). Part art of the the inpu inputt en ener ergy gy is used used to crea creatte an and d maint aintai ain n the the ma magn gnet etic ic fiel field. d. This This pa parrt of the the inpu inputt en en-ergy ergy cann cannot ot be conv conver erte ted d into into acti active ve en ener ergy gy an and d is retu return rned ed to the the elec electr tric ical al ne netw twor ork k up upon on remo remova vall of the magnetic field. This power is therefore called reactive power Q and defined as follows: Q

=

U ⋅ I ⋅ sin ϕ

The formula Q =

[var] 3 ⋅ U ⋅ I ⋅ sin ϕ applies to three-phase systems.

Apparent power App ppli lica cattions ions of elec electr tric ic eq equi uipm pme ent are are ba base sed d on conv conve ersio rsion n of elec electr tric ical al en ener ergy gy into into som some othe otherr for form of en ener ergy gy.. The The elec electr tric ical al pow ower er draw drawn n by the the eq equi uipm pme ent from from the the sour source ce is ter terme med d ap app paren arentt power and consists of active and reactive power. It is defined as follows: S

=

U ⋅ I

[VA]

The formula S =

3 ⋅ U ⋅ I applies to three-phase systems.

Power factor Electrica ically, the power factor of a circuit is defined as the cosine of the phase angle between the fundamental of the voltage and current waveforms. Power factor is also defined as the ratio of active power to apparent power: power factor

302

=

active power ----------------------------------------apparent power

=

P ---S

=

cos ϕ



3 .2

Inductive circuits

Most indu Most indust stri rial al load loads s are are indu induct ctiv ive e in na natu ture re,, e.g. mo moto tors rs an and d tran transf sfor orme mers rs.. Du Due e to the the indu induct ctiv ive e rereacta actanc nce e of the the load load,, the the curr curren entt draw drawn n by the the load load lags lags be behi hind nd the the volt voltag age e wa wave vefo form rm elec electr tric ical ally ly by an an angl gle e ϕ. The magnitude of ϕ is prop propor orti tion onal al to the the indu induct ctiv ive e reac reacta tanc nce. e. Sinc Since e the the curr curren entt lags lags behind the voltage, inductive loads are said to have a lagging power factor.

r e w o P ;

Power ϕ

Ι

; U

Current

Voltage Time

Figu Figure re 4 Lagging power factor condition

KLK1655-T

3.3 3.3

How How do ca cap pac acit itor ors s corre orrec ct powe ower fac acttor? or?

Capaci Capa cito tors rs are are char charac acte teri rize zed d by lead leadin ing g kvar kvar in the the ph phas asor or diag diagra ram m or po powe werr tria triang ngle le.. This This is op oppo po-site to the inductive kvar (refer to the following diagram). Reactive power (kvar) 2 _ 2 P Θ = S Q2

Q N Q 1

Active power 2 2 P = S _ Θ [kW]

S 2

ϕ2

Apparent power

ϕ1 S 1

S =

P

2

+ Θ 2

[kva]

KLK1656-2

cos ϕ sin ϕ Q Q

ϕ S1 S2

Figu Figure re 5 Phasor diagram for power factor correction

= P/S = Q/S = S sin ϕ = P ta n ϕ = phase displacement angle = uncompensated apparent power = compensated power with capacitors for compensation


303


The The an angl gle e ϕ is the the ph phas ase e an angl gle e be betw twee een n the the volt voltag age e an and d curr curren entt wa wave vefo form rms. s. The The reac reacti tive ve po powe werr is defined by Q

2

S

=

–

2

P

[var]

A capacitor of Q kvar will compensate for the inductive kvar and produce cos ϕ = 1. It is no nott com commo mon n prac practi tice ce to prod produc uce e cos cos ϕ = 1 with with capa capaci cito tors rs be beca caus use e this this ma may y resu result lt in over overco commpens pe nsat atio ion n du due e to load load chan chang ges an and d the the resp respon onse se tim time of the cont contrrolle oller. r. Gen Genera erally lly pu pub blic lic util utilit itie ies s specify a value (cos ϕ2) to which the existing power factor (cos ϕ1) should be corrected. The reactive power to be compensated is determined as follows. Q N

=

3 .4

P ⋅ ( tan ϕ 1 – tan ϕ 2 )

[var]

Connection an and ra rating of of ca capacitors

A general expression for the kvar rating of a capacitor (single-phase connection) is: Q N

=

U N ⋅ I N

Q N

=

U N U N ⋅ -------X N

X N

=

1 ---------------ω ⋅ C N

Q N

=

U N ⋅ ω ⋅ C N

3.4. 3.4.1 1

[var]

=

2

1 -----------------------------2 π ⋅ f N ⋅ C N =

2

U N ⋅ 2 π ⋅ f N ⋅ C N

Capa Ca paci cito torr in sing single le-p -pha hase se PFC PFC appl applic icat atio ion n

The The capa capaci cito torr is conn connec ecte ted d acro across ss the the ph phas ase e an and d ne neut utra rall an and d is subj subjec ecte ted d to the the ph phas ase e volt voltag age. e. The The above equation, without any change, is applicable to such capacitors. 3.4. 3.4.2 2

Capa Ca paci cito torr in in thr three ee-p -pha hase se PFC PFC app appli lica cati tion on

Star connection

U N -------The partial capacitor is subjected to a voltage of 3 Thus total kvar compensation of all three partial capacitors: U N 2 2 Q N = 3 ⋅  -------- ⋅ ω ⋅ C STAR = U N ⋅ ω ⋅ C STAR  3  Q N Q N = -----------------------------C STAR = ---------------2 2 U N ⋅ ω U N ⋅ 2 π ⋅ f N Ι

Ι

C STAR

U N

Figu Figure re 6 Star connection KLK1657-A

304



Delta connection The capacitor is subjected to line voltage U N, phase to phase. Thus total kvar compensation: Q N

=

2

3 ⋅ U N ⋅ ω ⋅ C DELTA

C DELTA

=

Q N -----------------------2 3 ⋅ U N ⋅ ω

=

Q N -------------------------------------2 3 ⋅ U N ⋅ 2 π ⋅ f N

Ι Ι

C DELTA

3

U N

Figu Figure re 7 Delta connection KLK1658-I

From the above equations it follows that for the desired Q kvar: Q kvar: C STAR C DELTA = ----------------3 Thus Thus for for the the same same am amou ount nt of kvar kvar comp compen ensa sati tion on a star star conn connec ecti tion on requ requir ires es the the trip triple le capa capaci cita tanc nce e of a delta connection. On the other hand, for the same nominal voltage U N in de delt lta a conn connec ecti tion on a 3 thicker dielectric film is required to get similar values of electric field strength. 3.4.3 3.4 .3

Calcul Cal culati ation on of capaci capacitor tor rating ratings s usin using g stan standar dard d tabl tables es

Capaci Capa cito tors rs can can be rate rated d by mu mult ltip iply lyin ing g the the acti active ve po powe werr P g P given on the rating plate of the motor by the value in the table below. To find find the the righ rightt valu value, e, cho choose ose you your exis existi ting ng pow ower er facto actorr (he herre 0,7) 0,7),, then then mo move ve horiz orizo ontal ntally ly to the the colu column mn of the the de desi sirred po powe werr fact facto or (he (here 0,9) 0,9).. The valu value e you find find ther there e is the the on one e to multi ultipl ply y by the the active power of the motor (0,54). Thus, for the last example: Q N = P ⋅ 0,54 Capa Ca paci cito torr outp output ut in ca case se of oper operat atin ing g volt voltag age e and/ and/ or freq freque uenc ncy y diff differ eren entt to nomi nomina nall ratin ratings gs U NE W 2 f NE W Q NE W =  ---------------- ⋅ ------------- ⋅ Q N  U N  f N Note: 1)

U NEW < U N

2)

f NEW: 50 or 60 Hz; Hz; in case case of high higher er freq freque uenc ncie ies, s, loss losses es ha have ve to be take taken n into into cons consid ider erat atio ion, n, thermal data sheet can be used.


305


.Existing power factor (cos ϕ1) 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90

3.4. 3.4.4 4

Desired power factor cos ϕ2 1 ,0

0,98

0 ,9 6

0,94

0,92

0,90

0,85

0 ,8 0

0,75

0,70

2,29 1,99 1,73 1,52 1,33 1,17 1,02 0,88 0,75 0,62 0,48

2,09 1,79 1,53 1,32 1,13 0,97 0,82 0,68 0,55 0,42 0,28

2,00 1,70 1,44 1,23 1,04 0,88 0,73 0,59 0,46 0,33 0,19

1,93 1,63 1,37 1,16 0,97 0,81 0,66 0,52 0,39 0,26 0,12

1,86 1,56 1,30 1,09 0,90 0,74 0,59 0,45 0,32 0,19 0,05

1,81 1,51 1,25 1,04 0,85 0,69 0,54 0,40 0,27 0,14 –

1,67 1,37 1,11 0,90 0,71 0,55 0,40 0,26 0,13 – –

1,54 1,24 0,98 0,77 0,58 0,42 0,27 0,13 – – –

1,41 1,11 0,85 0,64 0,45 0,29 0,14 – – – –

1,27 0,97 0,71 0,50 0,31 0,15 – – – – –

Gene Genera rall rule rules s for for rati rating ng cap capac acit itor ors s

In a plant that is still in the design phase an average power factor of cos ϕ1 = 0,7 can be assumed for for the the reac reacti tive ve po powe werr load loads. s. To comp compen ensa sate te to cos cos ϕ = 0,9, the value 0,54 for (tan ϕ1 –tan ϕ2) can be take taken n from from the the tabl table e ab abov ove e. In this this case case a capa capac citor itor ratin ating g of ab abou outt 50 % of the the acti active ve pow ower er ratrating would be selected. Q N = P ⋅ 0,5 With existing operating plant the necessary values can be taken by measurements. To de dete term rmin ine e the the corr correc ectt capa capaci cito torr rati rating ng,, accu accura rate te valu values es of the the conn connec ecte ted d po powe werr an and d op oper erat atin ing g times should be known. This his calc calcul ulat atio ion n is on only ly vali valid d wh whe ere the the load load con conditi dition ons s are mo more re or less less cons consta tant nt.. Un Und der extr extrem eme e loa load vari variat atio ions ns,, e.g e.g.. he heav avy y mo moto torr load loads s (indu induct ctiv ive e) du durring ing pro produ duct ctio ion n ho hour urs s and on only ly he hea ating ting an and d ligh lighti ting ng du duri ring ng the the nigh night, t, the the aver averag age e valu values es used used to de dete term rmin ine e capa capaci cito torr rati rating ngs s wo woul uld d no nott be sufsuffici ficien entt for for pe peak ak indu induct ctiv ive e load loads. s. In suc such case cases s it is recom ecomme mend nded ed to take ake me mete terr read readin ing gs durin uring ga one-day period, for example, to obtain exact instantaneous values of current, voltage and cos ϕ. 4

Ther Therma mall desi desig gn of ca capa pac cito itors for for powe ower fac acttor corr correc ecttion ion

Capaci Capa cito tors rs of the the Phas PhaseC eCap ap seri series es can can ha hand ndle le a cert certai ain n am amou ount nt of ha harm rmon onic ic curr curren entt in ad addi diti tion on to the the no nom minal inal 50 Hz curr urren ent. t. Ho How w lar large the the ext extra curr curren ents ts may be de depe pend nds s on vari vario ous pa para ram meter eters s like like the the freq freque uenc ncy y of the the curr curren ent, t, the the type type of capa capaci cito torr an and d am ambi bien entt temp temper erat atur ure. e. The The ma maxi ximu mum m pe perrmissible currents can be determined with the aid of thermal data sheets.

306



The The tota totall po powe werr diss dissip ipat atio ion n P is P is comp compos osed ed of the the diel dielec ectr tric ic loss losses es P D an and d the the resi resist stiv ive e loss losses es P R: P = P D + P R 2

P D = U

⋅ 2 ⋅ π ⋅ f 0 ⋅ C ⋅ tan δ 0

U

rms value of AC voltage applied to capacitor (between two phases)

f 0

fundamental frequency

C

total capacitance (for delta connection 3 × C N, for star connection C N)

tan δ0

dielectric dissipation factor (2 · 10 –4 )

For For the the diel dielec ectr tric ic loss losses es it is no norm rmal ally ly suff suffic icie ient nt to cons consid ider er the the freq freque uenc ncy y an and d volt voltag age e of the the fund fundaamental for a nonlinear load. 2

P R = I

⋅ R S

I

rms value of capacitor current (for one phase)

R S

total series resistance of capacitor at maximum hot-spot temperature (refer to thermal data sheet)

For a no nonl nlin inea earr load load the the rms rms curr curre ents nts of the the harm armon onic ics s must ust be ad adde ded d to the the rms rms curr curren entt of the the funfundamental according to the following formula: I

=

I 0

2

+

I 0 I 1 ... I n

I 1

2

+

… + I n 2

rms current of fundamental rms current of 1st harmonic rms current of nth harmonic

Calculation example for MKK-440-D-18,8-01 (B25667-A4307-A365, (B25667-A4307-A365, refer to data sheet, pa page ge 32 328 8) use in in 400 V/ 50 Hz supply supply netwo network rk with with 5,67 5,67 % choke choke filter filtering ing Electrical operating point: C N = 3 × 103,1 µF U N = AC 440 V U = AC AC 424 424 V f 0 = 50 Hz I 0 = 25 A I 5 = 13, 13,5 5A I 7 = 4,5 A tan δ0 = 2 · 10 –4 R S (70 °C) = 13 mΩ

(vol (volta tage ge ap appl plie ied d to to cap capac acit itor or,, due due to chok chokes es))

(ha harrmo moni nic c cur currren ents ts caus caused ed by no non nline linear ar load loads s lik like e pow powe er con conve vert rte ers, rs, uninterruptible power supplies)

Calculation of rms current: I

=

I 0

2

+

I 5

2

+

I 7

2

=

25

2

+

13, 5


2

+

2

4, 5 A

≈

29 A

307


a)

Diel Dielec ectr tric ic pow power er dis dissi sipa pati tion on P D

This can be read as a function of frequency from the top diagram of the thermal data sheet (the diag diagra ram m ap appl plie ies s to op oper erat atio ion n at U N, there is also a curve for 0,9 · U N) or calc calcul ulat ated ed by eq equa uati tion on.. The The volt voltag age e drop drops s caus caused ed by the the ha harm rmon onic ic curr curren ents ts are are comp compar arat ativ ivel ely y smal smalll an and d un unkn know own n for for mo most st ap ap-plications, so they can be ignored in this calculation. 2

P D = U

⋅ 2 ⋅ π ⋅ f 0 ⋅ C ⋅ tan δ 0 KLK1659-R

10 2

W P D

10 1

Dielectric power dissipation P D versus repetition frequency f 0 0,9 · U N = AC AC 440 440 V 0,9 · U N = AC AC 3 396 96 V

10 0 1 10

10 2

10 3

Hz

10 4

f 0

The result: P D = 3, 3,5 W b)

Resi Re sist stiv ive e powe powerr diss dissip ipat atio ion n P R

This his can can be rea ead d as a func functi tion on of curr curren entt (29 A in the the exa examp mple le)) fro from the the middl iddle e dia diagram gram of the the ther ther-mal data sheet or calculated by equation. 2

P R = I

⋅ R S KLK1660-U

10 2

W P R

10 1

Ohmic power dissipation P R versus rms current value I R S (70 °C) = 13 mΩ I max = 40 A

10 0 0 10

10 1

10 2

A

10 3

Ι

The result: P R = 11 W

308



c)

Permi Permiss ssib ible le ambi ambien entt tem tempe pera ratu ture re::

This can be read as a function of total power dissipation from the bottom diagram of the thermal data sheet. Total power dissipation: P = P D + P R

=

14 , 5 W KLK1661-3

100 C

Permissible ambient temperature versus total power dissipation P

ΘA

Θ A 80

60

(Upright mounting position) Natural cooling Forced cooling cooling 2 m/s Permissible capacitor temperature black painted

40 20 0

0

10

20

30

40

50

60 W 70 P

The result is the following permissible ambient temperature (for continuous operation): ΘAmax = 48 °C for natural cooling: for forced convecti convection on cooling (2 m/s): ΘAmax = 54 °C 5

Symbols and terms

5 .1

Characteristics

C N

[µF]

Rated (o (or no nominal) ca capacitance, the capacitance value for which the capacitor has been designed.

C DELTA [µF]

Capa Ca pacit citan ance ce val value ue of of one one par parti tial al cap capac acit itar ar in in del delta ta conn connec ecti tion on..

C STAR [µF]

Capa Ca pacit citan ance ce val value ue of of one one par parti tial al cap capac acit itar ar in in sta starr con conne nect ctio ion. n.

cos ϕ

Power factor

f N

[Hz]

Rated (o (or no nominal) fr frequency, the frequency for which the capacitor has been designed.

I N

[A]

Rated (or nominal) current, rms value of the alternating current resulting from rated output and rated voltage.

P

[W]

Active power

Q N

[var] [var]

Rated (or Rated (or nomi nominal nal)) outpu output, t, the the reac reactiv tive e power power derive derived d from from the the rate rated d value values s of voltage, frequency and capacitance.

S

[kva]

Apparent power


309


tan δ0

Dielectric dissipation factor The The diss dissip ipat atio ion n fact factor or tan tan δ0 of the the diel diele ectri ctric c is assum ssume ed to be cons consttan antt for for all cacapaci pa cito tors rs in the their freq frequ uen ency cy ran ang ge of use. use. The fig figure ure stat state ed in da data ta she sheets ets app pply ly to rated operation

U i

[V] [V]

Insu Insula lati tion on lev level el,, only only for for uni units ts hav havin ing g all all term termin inal als s insu insula late ted d from from the the case case.. The insulation level shall be marked by means of two numbers separated by a stroke, the first number giving the rms value of the power frequency test voltage U TC (in (in kV) kV) an and d the the seco second nd nu num mbe berr givi giving ng the the cres crestt valu value e of the the lig lightni htning ng impulse impulse test voltage voltage (in kV), kV), e.g. 3/15 kV. Unit Un its s for for no non n-exp -expo osed sed inst instal alla lati tion on are are not test teste ed acco accorrding ding to IEC IEC 83 831 1 cla clause use 15 (“Li (“Ligh ghtn tnin ing g impu impuls lse e volt voltag age e test test be betw twee een n term termin inal als s an and d cont contai aine ner” r”). ). For For this this info inforrmation mation should should be e.g. 3/– kV.

U N

[V]

Rated (or nominal) voltage, the the rms rms valu value e of the the alte altern rnat atin ing g volt voltag age e for for wh whic ich h the the capa capaci cito torr ha has s be been en de desi sign gned ed..

X N 5 .2

Nominal reactance of capacitor

Maximum ratings

U max

Maximum permissible AC voltage of the capacitor. This This valu value e de depe pend nds s on the the du dura rati tion on an and d is spec specif ifie ied d in the the IEC IEC stan standa dard rd as foll follow ows: s: U N + 10 % (up to 8 hours hours daily) daily) U N + 15 % (up to 30 30 minutes minutes daily) daily) U N + 20 % (up to to 5 minutes) minutes) U N + 30 % (up to to 1 minute) minute)

I max

Maximu Maxi mum m pe perm rmis issi sibl ble e AC curr curren entt of the the capa capaci cito tor: r: Ca Capa paci cito tors rs shal shalll be suit suitab able le for for cont contin inuo uous us op ope erati ratio on at an rms line line curr curren entt of 1,3 1,3 tim times rated ated cur current rent that that occu occurrs at rated sinusoidal voltage and rated frequency, excluding transients. Taki Taking ng into into acco accoun untt the the capa capaci cita tanc nce e tole tolera ranc nces es of 1,15 1,15 · C N, the the ma maxi ximu mum m curr curren entt can reach 1,5 · I N.

I s

Maximum allowed inrush current.

(du (du /dt /dt )max

Maximum repetitive rate of voltage rise.

(du (du /dt /dt )s

Maximum non-repetitive rate of voltage rise. (The rate of voltage rise is limited by the peak current handling capability ity of the contacts or the self-inductance of a capacitor.)

310



5 .3

Test data

U TT

Test voltage between terminals; each capacitor shall be subject to an AC test at U i = 2,15 · U N for a minimum minimum time time of 2 s.

U TC

Test voltage between terminals and case; U N ≤660 V: 3000 Vac for a period of 10 seconds, U N >660 V: 6000 Vac for for a period of 10 seconds seconds

tan δ (50 Hz)

Tangent of the loss angle of a capacitor, the ratio between the equivalent series resi resist stan ance ce an and d the the capa capaci citi tive ve rea eact cta ance nce of the capa capaci cito torr at spe specifi cified ed sinu sinuso soid idal al alternating voltage and frequency.

5 .4

Climatic category

Θmin Θmax

Minimum ambient temperature

Humidity

Average relative humidity ≤ 75 %

t LD(co)

Life expectancy

Θstg

Storage and transport temperature range

5.5 5.5

Maximum ambient temperature (under forced cooling conditions higher ambient temperatures possible, see thermal data sheets)

Stan Standa dard rds s for for low low volt voltag age e powe powerr fact factor or corre correct ctio ion n ca capa paci cito tors rs

VDE VD E 0560 0560 p par artt 46 and and 47

Powe Powerr capa capaci cito tors rs of the the self self-h -hea eali ling ng type types s for for AC syst system ems s ha havi ving ng rate rated d voltages voltages up to and includin including g 1 kV. part part 1: Genera General-p l-perf erform ormanc ance, e, testin testing g and and rating rating – safety requirements – guide for installation i nstallation and operation part part 2: Aging Aging test test,, selfself-hea healin ling g test test and and distr distruct uction ion test test

IEC 831 part 1 and 2

Most common international accepted standard for low voltage PFC capacitors, issue date 1996; IEC = “International Electrotechnical Commission” in Geneve/Suisse

EN 6 608 0831 31 par partt 1 and and 2

Euro Europe pean an sta stand ndar ard, d, ide ident ntic ical al to to the the inte intern rnat atio iona nall stan standa dard rd IEC IEC 831 831-1 -1


311

Capacitors for Power Factor Correction

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