5-1 Power Factor Correction The power factor (pf) is the ratio of real power to apparent power. It is dimensionless and between 0 and 1: i) a pure resistance has unity pf ii) a pure inductance has zero pf (lagging) iii) a pure capacitance has zero pf (leading)

Almost all industrial loads are lagging. Low pf results in unnecessarily high currents (requiring larger conductors and resulting in unnecessary losses) and in too much being dropped across the feeders—the power lines feeding the load.

If a power source is required to deliver power—average power—to a load which has a low pf (pf =cos q), the required current will be higher than it would be if the power factor were larger.

This excess current causes excessive losses in the power lines and in the entire power system. The power company is then required to devote capacity to this excess current that is present only because the load power factor is small—that is, because the load appears too strongly inductive.

What is physically going on is that energy is being temporarily stored at the load during one part of the cycle and then sent back to the source during another part. A low pf indicates a significant transfer of stored energy with respect to energy dissipation—the transfer of stored energy does no useful work. Energy is just transferred between the source and load.

lecture 5 outline 5-2 Almost all industrial load are inductive because of motors and other electric machines. This provides a practical way to “correct” a low power factor nearer to one.

By adding a —a power factor-correcting capacitor—in parallel with the inductive load, we may improve efficiency and save a great deal of money.

Power companies encourage power factor correction so that taking care to maintain a high power factor can easily result in savings in the million of dollars per year for a large plant.

It’s usual to correct the power factor to 0.9-0.95. Adding too much capacitance is wasteful and if we overcorrect, the power factor becomes leading and its magnitude to decrease with additional capacitance.

General Analysis

lecture 5 outline 5-3 Example i) Given 13.2 kV, 60 Hz source find the pfc capacitor required to correct a load of 3.6 MW at pf = 0.707 lag to pf = 0.95 lag. ii) Compare the line current (just magnitude) before and after installing the pfc capacitor. iii) Compare the apparent power before and after installing the pfc capacitor. iv) Suppose the power company charges $9 /KVA/month in “demand charges.” How much money do we save by installing pfc ?

What is going on physically with power factor correction is that less energy is being swapped between the load and source. Much of the stored energy is now being swapped between the inductive elements in the original load and the power factor correction capacitor.

lecture 5 outline 5-4 A very common way to measure power is via an , a voltmeter, and a as shown below.

The scheme is this, with the voltmeter measuring voltage (rms), the ammeter measuring current (rms), and the wattmeter measuring power (average power, in W). We can quickly determine all quantities of interest for power measurement.

Example: Suppose I = 20 A, V = 120 V, and P = 2 kW. Find: i) apparent power ii) power factor (assume lagging) iii) complex power iv) reactive power v) v(t) and i(t), assume 60 Hz with v(t) taken as reference.

lecture 5 outline 5-5 More sophisticated power meters, like those in the power lab, measure phasor current and phasor voltage. These meters measure current, voltage, power factor, power, apparent power, and reactive power.

The meter assumes current and voltage polarities as shown below (that is, the polarities that result in power flowing from the source to the load). So, for example, if the load is inductive, the reactive power will be positive.

Would the readings be affected if the meter voltage polarity were reversed? How?

lecture 5 outline