354CHAPTER 11. POWER FACTORcurrent phase-angle somewhere between the inductor and capacitor currents. Moreover, that totalcurrent (Itotal) was forced to be in-phase with the total applied voltage (Vtotal), by the calculationof an appropriate capacitor value.Since the total voltage and current are in phase, the product of these two waveforms, power,will always be positive throughout a 60 Hz cycle, real power as in Figure 351,11.2. Had the phase-anglenot been corrected to zero (PF=1), the product would have been negative where positive portionsof one waveform overlapped negative portions of the other as in Figure 354,11.6. Negative power is fedback to the generator. It cannont be sold; though, it does waste power in the resistance of electriclines between load and generator. The parallel capacitor corrects this problem.Note that reduction of line losses applies to the lines from the generator to the point wherethe power factor correction capacitor is applied. In other words, there is still circulating currentbetween the capacitor and the inductive load. This is not normally a problem because the powerfactor correction is applied close to the oﬀending load, like an induction motor.It should be noted that too much capacitance in an AC circuit will result in a low power factor justas well as too much inductance. You must be careful not to over-correct when adding capacitanceto an AC circuit. You must also be very careful to use the proper capacitors for the job (ratedadequately for power system voltages and the occasional voltage spike from lightning strikes, forcontinuous AC service, and capable of handling the expected levels of current).If a circuit is predominantly inductive, we say that its power factor is lagging (because the currentwave for the circuit lags behind the applied voltage wave). Conversely, if a circuit is predominantlycapacitive, we say that its power factor is leading. Thus, our example circuit started out with apower factor of 0.705 lagging, and was corrected to a power factor of 0.999 lagging.• REVIEW:• Poor power factor in an AC circuit may be “corrected”, or re-established at a value closeto 1, by adding a parallel reactance opposite the eﬀect of the load’s reactance. If the load’sreactance is inductive in nature (which is almost always will be), parallel capacitance is whatis needed to correct poor power factor.11.4Practical power factor correctionWhen the need arises to correct for poor power factor in an AC power system, you probably won’thave the luxury of knowing the load’s exact inductance in henrys to use for your calculations. Youmay be fortunate enough to have an instrument called a power factor meter to tell you what thepower factor is (a number between 0 and 1), and the apparent power (which can be ﬁgured by takinga voltmeter reading in volts and multiplying by an ammeter reading in amps). In less favorablecircumstances you may have to use an oscilloscope to compare voltage and current waveforms,measuring phase shift in degrees and calculating power factor by the cosine of that phase shift.Most likely, you will have access to a wattmeter for measuring true power, whose reading you cancompare against a calculation of apparent power (from multiplying total voltage and total currentmeasurements). From the values of true and apparent power, you can determine reactive power andpower factor. Let’s do an example problem to see how this works: (Figure 364,11.13)First, we need to calculate the apparent power in kVA. We can do this by multiplying loadvoltage by load current: