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Vector Analysis in Electrical EngineeringIntroduction to AC Power and Power Factor Improvement

Franz Xyrlo Tobias, Jayson Bryan Mutuc, Joy Andrew Rondilla, Nahdiya Zaheer BetonioMS Electrical Engineering, Mapua Institute of Technology

Abstract- Power factor indicates how efficient weutilize energy. Having a low value of it would yield tohigh electricity consumption and losses in the system.Thus, by power factor improvement, such problemscan be resolved. However, methods like using PowerSaver may not actually help in reducing electricityconsumption cost.

This paper focuses on the application of vectoranalysis in the field of electrical engineering throughpower saving.

I. I NTRODUCTION

The concepts of advanced mathematics areimportant in the field of electrical engineering and inmany other engineering and scientific disciplines aswell. They form the foundation for further studies inareas such as Electric Circuits, Power SystemAnalysis and other electrical concepts. Almost all thetopics discussed in MATH220 are applicable to theelectrical engineering discipline, such as LaplaceTransform, Fourier Series, Power Series and themost basic Vector Analysis.

Vector analysis is a mathematical tool with whichsome electrical concepts are most convenientlyexpressed and best comprehended. In electricalengineering, vectors are also termed as phasors inrepresenting voltage, current and other parameters.

The group has chosen this topic for it has oneapplication in electrical engineering that is importantin our daily lives, that is, regarding power saving.

II. T YPES OF POWER

In a power system, two types of power are actually

transmitted, which are the real power and reactive power.

Real power measured in kW and the second is thereactive power measured in kVAR. Ordinary loadssuch as heaters and incandescent bulbs consume real

power (kW). Real power can perform work. Utilitymeters on the side of our houses measure thisquantity and distribution companies charge for it.

Motors and transformers require reactive power(kVAR) in addition to kW. Unlike real power, thiscannot perform work. Residential customers do not

pay for kVAR, and utility meters on houses do notrecord it as well.

The vector sum of kW and kVAR is calledapparent power measured in kVA. Also, by the useof multimeters, we can measure the current andvoltage and then multiply these readings together inorder to get the apparent power.

The relationship between the three power valuesis shown in Figure 1.

Figure 1. Relationship between real, reactive and apparent power.

Figure 1 is also referred to as Power Triangle. Fromthis relationship, power factor can be obtained.

III. P OWER FACTOR

Power factor (cos ) is the ratio of working powerto apparent power. It measures how effectively

electrical power is being used. To illustrate theanalogy of power factor, consider a boy dragging aheavy load, shown in Figure 2. His working power(kW) is in the horizontal direction, where he wantsthe load to travel. Unfortunately, he cannot drag hisload on a perfect horizontal, so his shoulder adds alittle reactive power (kVAR) by pulling the load atan angle to the direction of travel.


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Figure 2. Power factor analogy.

Ideally, we want kVAR to be very small(approaching zero) thus kW and kVA would almost

be equal (the boy wouldn't have to waste any poweralong his body height). Also, the angle ( ) formed

between kW and kVA would approach zero.Therefore, cos approaches one, as well as the power

factor.

IV. T YPES OF POWER FACTOR

Power factor is commonly classified into threetypes, namely unity, lagging or leading. Power factorvalue ranges from zero to one.

A. Unity Power Factor For this type, the voltage and current are in-phase

as in the case of purely-resistive loads (See Figure 3).The value of the power factor is one.

Figure 3. Phasor diagram for the resistive circuit showing thatthe current is in phase with the voltage.

B. Lagging Power Factor For this type of power factor, the current lags the

voltage by an acute angle as in the case of Resistor-

Inductor (RL) or inductive loads such as inductionmotors (See Figure 4 below). The value of powerfactor is between 0 to 1.

Figure 4. Phasor diagram for the inductive circuit, showing

that the current lags behind the voltage by 90.

C. Leading Power Factor For this type of power factor, the current leads the

voltage by an acute angle as in the case of R-C orcapacitive loads such as synchronous condenser (SeeFigure 5). The value of this power factor is also

between 0 to 1.

Figure 5. Phasor diagram for the capacitive circuit, showingthat the current leads the voltage by 90.


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V. S HOULD W E BE CONCERNED WITH LOW POWER FACTOR ?

Low power factor means your're not fullyutilizing the electrical power you're paying for. Thus,we should be concerned about it.

This low value is caused by inductive loads (suchas transformers, electric motors, and high-densitydischarge lighting), which are a major portion of the

power consumed in industrial complexes. Unlikeresistive loads that create heat by consumingkilowatts, inductive loads require the current tocreate a magnetic field, and the magnetic field

produces the desired work. Reactive power required by inductive loads increases the amount of apparent power (kVA) in your distribution system. Theincrease in reactive and apparent power causes the

power factor to decrease.In order to have a more efficient energy usage, the

system power factor must be improved.

VI. P OWER FACTOR IMPROVEMENT

Power factor should be improved due to manyreasons. Some of the benefits of improving your

power factor include lower utility fees, increasedsystem capacity and reduced system losses in yourelectrical system,

Correcting your power factor can be done through

the following strategies:1. Minimize the operation of idling or lightly

loaded motors2. Avoid operation of equipment above its rated

voltage3. Replace standard motors as they burn out with

energy-efficient motors4. Install capacitors in your AC circuit to decrease

the magnitude of reactive power.Regarding capacitor installation, the interesting

factor that exists in AC power systems is that

inductive kVARs are opposite of capacitive kVARsand can cancel each other out if they are of the samevalue. The vector representation of this relationship

between the real, reactive and apparent powerassociated with resistor, inductor and capacitors isshown in Figure 6. Note how the inductive andcapacitive kVARs oppose each other and can cancel,yet resistive kW remain independent.

Figure 6. Electrical Power Relationships

Figure 7 shows the power triangle with thecapacitive kVAR cancelling the inductive kVAR.The result is net in kVAR, which is positive in thiscase (the circuit is inductive), since not all of theinductive kVAR was cancelled by the capacitivekVAR.

Figure 7. Power Factor Correction by Installing Capacitor

VII. P OWER SAVERS IN DOMESTIC LOAD

Manufacturers claim that the problem in low power factor may be solved by installing a well-calculated inductor/capacitor network and switchingit automatically. Using power savers allows to bringthe power factor level close to unity, thus improvingthe apparent power at a great extent. Having animproved kVA would mean less currentconsumption by all the domestic appliances.

Though this may look fine, however, the

MERALCO bill that we pay is never based onapparent power (kVA) but rather on real power(kW). Commercially available power savers arereally just saving the reactive power produced byinductive loads, which implies that there is noreduction in real power required by the appliances tofunction.


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Thus, any savings in energy demand will notdirectly result in lowering a residential user'selectricity bill. Power savers, though, are useful inimproving power quality and helps in enhancing thelife-span of household appliances.

R EFERENCES

Technical Data SA02607001E. Power factor correction: a guide for the plant engineer . August 2014.

Motor Challenge. Reducing Power Factor Cost . 2001

Electrical Engineering Portal. The real truth behind household power savers . (electrical-engineering-portal.com)

Serway, R.A. and J. W. Jewett. Physics for Scientists and Engineers .

Do Power Savers Really Save Power? www.efymag.com
http://www.efymag.com/http://www.efymag.com/http://www.efymag.com/http://www.efymag.com/

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