*Welcome to EC&M's monthly forum where Mark McGranaghan, vice president of Electrotek Concepts, and Mike Lowenstein, president of Harmonics Limited, address your PQ problems and concerns*.

**Q.** The figures in the article “Harmonic Current and Voltage Distortion,” on page 32 in the November 2002 issue listed 1st, 5th, 7th, and 11th harmonic categories, along with respective current and voltage measurements at various points noted. What happened to the 3rd harmonic? Isn't this the one that gives us the most grief and distortion due to our switching power supplies?

**Lowenstein's answer:** The third harmonic does cause the most grief for single-phase (phase-to-neutral connected) switching power supplies. I discuss this issue in the “Ask the Experts” column of this same issue (page 44). However, the article you are questioning is about 3-phase loads, for which there is *no* 3rd harmonic current formation. If you look closely at **Fig. 1** and **Fig. 2** from that article (reprinted at right for reference), you'll see the load is labeled “3-phase, nonlinear.” Everything noted in that article about voltage distortion, current distortion, and energy is true, no matter what the electrical system or load connection. I elected to use a 3-phase example for the article.

**Q.**My harmonic analyzer gives two values for power factor, PF and DPF. What is the difference between the two, and which one does my utility use in determining power factor penalties?

**Lowenstein's answer:**Power factor (PF) is defined as real power (the power that does work) divided by apparent power (the power that must be delivered in order to get the work done). Real power is measured in kilowatts (kW), and apparent power is measured in kilovolt amperes (kVA). Values of PF range from 1, where all the power delivered does useful work, to 0, where no useful work is done for the power delivered.

Put another way, PF is a measure of the efficiency of utilization of a power distribution system. The closer the PF is to 1, also referred to as unity, the more of the electrical system capacity is being used to do useful work. With linear loads, the PF depends on the phase relationship between the current and voltage sine waves. When these two waves are in phase, the PF is unity and no system capacity is wasted.

Linear loads, such as resistance heaters and incandescent lights, are 100% efficient in converting real power to heat and therefore have a PF of unity. Induction motors require real power and reactive power, which is measured in kilovolt amperes reactive (kVAR). The reactive current that flows in the system creates a magnetic field that enables the motor to operate, but doesn't contribute to the work done by the motor. Reactive current also causes the current wave to lag the voltage wave, a process called displacement.

The apparent power for a motor can be calculated using the equation,

kVA=√(kW^{2}+kVAR^{2})

Since the apparent power for a motor is larger than the active power, the PF is less than unity. The PF for a system powering only linear loads is called the displacement power factor — the DPF on your meter. Unless the loads are pure resistance, this PF will be less than unity.

Nonlinear loads draw harmonic currents, which are similar to reactive currents in that they use up system capacity but don't do real work. The harmonic currents can be represented by a term called harmonic reactive power (kVAH). The apparent power for a nonlinear load can be calculated using the equation,

kVA5=√(kW^{2}+kVAR^{2}+kVAH^{2})

The presence of harmonics increases the apparent power that must be delivered to do a certain amount of work, therefore lowering the PF. The PF term that describes a system with both linear and nonlinear loads is called the true power factor.

If harmonic currents are introduced into a system, the true PF will always be lower than the DPF. For example, the DPF for a computer is close to unity — usually about 0.95 — whereas the true PF, which includes harmonics, is around 0.7. For both linear and nonlinear loads, the result of extra current that does no real work — whether reactive current or harmonic current — is a reduced capability for the system to support useful loads. In effect, much of the transformer, wiring, and circuit breaker capacity is wasted carrying reactive or harmonic currents.

Many utilities make the customer pay for wasted system capacity by charging a power factor penalty. This penalty is based on the numerical PF, and the further it deviates from unity, and in turn the more system capacity being wasted, the larger the penalty. In the past, most utilities measured only the DPF in determining power factor charges. As a result, customers who had large numbers of nonlinear loads weren't paying the cost of the extra capacity necessary to deliver harmonic currents. However, with the advent of effective electronic utility meters that can measure true PF, some utilities are now charging customers penalties based on this value.

If your utility is measuring true PF and charging you accordingly, you could benefit from investigating harmonic mitigation techniques to increase your PF.