Cad é an Fachtóir Cumhachta: Forbairt Foirmle agus Debhreathnú

Cad é an Fachtóir Phearsanta?

I réamhainneolaíocht, is é an fachtóir phearsanta (FP) de chóras feidhmeachta AC é an ráta idir an cumhacht oibre (mearbhuil i kilowatts, kW) a ghlactar ag an lód agus an chumhacht soiléir (mearbhuil i kilovolt amperes, kVA) a thiteann trí an circuit. Is uimhir gan dimensíon é an fachtóir phearsanta sa raon dúnta -1 go 1.

Is é an "ideal" fachtóir phearsanta ná ceann (freisin a thiomsaigh mar "unity"). Seo nuair nach bhfuil aon chumhacht eadrúcháin ag teacht trí an circuit, agus mar sin tá an chumhacht soiléir (kVA) cothrom leis an gcumhacht mearbhuil (kW). Is é an lód le fachtóir phearsanta 1 an lód is éifeachtaí ar an soláthar.

Sin á rá, níl sé seo realistiúil, agus beidh an fachtóir phearsanta in am féin níos lú ná 1. Úsáidtear roinnt teicnící fachtóir phearsanta chun cabhrú le hárdaíocht an fhachtóir phearsanta go dtí an staid ideal seo.

Chun é seo a mhíniú níos fearr, bheidh sé againn dul siar ar chúpla céim agus labhairt faoi cad atá i gceist le cumhacht.

Is é an cumhacht an t-úsáid chun oibriú a dhéanamh. Sa réimse reamhanach, is é an cumhacht reamhanach an méid cumhachta reamhainge a d'fhéadfaí a thabhairt chuig form sciliúil eile (heat, light, etc) sa phointe ama.

Matamaiticiúil, is é an fachtóir phearsanta an t-iontar den voltage drop ar an eilimint agus current ag teacht trí é.

Ag smaoineamh ar an DC circuits, ag baint amach sábháil DC voltage sources, the inductors and capacitors behave as short circuits and open circuits respectively in steady-state.

Hence the entire circuit behaves as a resistive circuit and the entire electrical power is dissipated in the form of heat. Here the voltage and current are in the same phase and the total electrical power is given by:

Now coming to the AC circuit, here both inductor and capacitor offer a certain amount of impedance given by:

The inductor stores electrical energy in the form of magnetic energy and the capacitor stores electrical energy in the form of electrostatic energy. Neither of them dissipates it. Further, there is a phase shift between voltage and current.

Hence when we consider the entire circuit consisting of a resistor, inductor, and capacitor, there exists some phase difference between the source voltage and current.

The cosine of this phase difference is called the electrical power factor. This factor (-1 < cosφ < 1 ) represents the fraction of the total power that is used to do the useful work.

The other fraction of electrical power is stored in the form of magnetic energy or electrostatic energy in the inductor and capacitor respectively.

The total power in this case is:

This is called apparent power and its unit is VA (Volt-Amp) and denoted by ‘S’. A fraction of this total electrical power that does our useful work is called active power. We denote it as ‘P’.

P = Active power = Total electrical power.cosφ and its unit is watt.

The other fraction of power is called reactive power. Reactive power does no useful work, but it is required for the active work to be done. We denote it with ‘Q’ and mathematically is given by:

Q = Reactive power = Total electrical power.sinφ and its unit is VAR (Volt-Amp Reactive). This reactive power oscillates between source and load. To help understand this better all these power are represented in the form of a triangle.

Mathematically, S2 = P2 + Q2, and the electrical power factor is active power / apparent power.

Meastachán Fachtóir Phearsanta

Tá an téarma fachtóir phearsanta ann i gcircuits AC amháin. Matamaiticiúil, is é an cosaín den difríocht phhasa idir an voltage agus an current. Tá sé ag tagairt don ráta de chumhacht iomlán (apparent power) a úsáideann chun oibriú mearbhuil a dhéanamh a théann ar a dtugtar active power.

Níos Mór Meastachán Fachtóir Phearsanta

• Tá an cumhacht mearbhuil le feiceáil ag P = VIcosφ. Is é an current inversely proportional to cosφ for transferring a given amount of power at a certain voltage. Hence higher the pf lower will be the current flowing. A small current flow requires a less cross-sectional area of conductors, and thus it saves conductors and money.

• From the above relation, we see having a poor power factor increases the current flowing in a conductor, and thus copper loss increases. A large voltage drop occurs in the alternator, electrical transformer, and transmission, and distribution lines – which gives very poor voltage regulation.

• The KVA rating of machines is also reduced by having a higher power factor, as per the formula:

Hence, the size and cost of the machine are also reduced.

This is why the electrical power factor should be maintained close to unity – it is significantly cheaper.

Modhanna Meastachán Fachtóir Phearsanta

Tá trí modh príomha chun an fachtóir phearsanta a fheabhsú:

• Banc Capacitors

• Synchronous Condensers

• Phase Advancers

Banc Capacitors

Tá an fachtóir phearsanta a fheabhsú ag ciallú an difríocht phhasa idir an voltage agus an current a laghdú. Mar go bhfuil formhór na lód de chineál inductive, tá rogha de chumhacht eadrúcháin ag teastáil ón lód chun gníomhú.

A capacitor or bank of capacitors installed parallel to the load provides this reactive power. They act as a source of local reactive power, and thus less reactive power flows through the line.

Capacitor banks reduce the phase difference between the voltage and current.

Synchronous Condensers

Synchronous condensers are 3 phase synchronous motors with no load attached to their shaft.