Harmonics Analysis and Remedy

Power distribution systems are designed to function at 50 or 60 Hz frequencies. But some types of connected loads generate current and voltage with different frequency which may be in multiples of the 50 or 60 Hz basic frequency. These abnormal frequencies cause electrical distortion which is called power system harmonics.

Power quality problems can produce equipment malfunctioning, voltage fluctuations, power outage and system distortions. It’s prime responsibility of maintenance engineer to understand the causes of these problems and to find out the solution to prevent them.

The sources of harmonics generation are power electronic loads such as variable frequency drives (VFDs), computers, printers and switching power supplies. The abundant use of non-linear (such as a rectifier) loads also results harmonics. 

Introduction:

Usually the voltage varies sinusoidal at a fundamental frequency of 50 or 60 Hz. While we connect linear load it draws a sinusoidal current but in case of non-liner load it is not perfectly sinusoidal.

Generally because of the third harmonics, the neutral conductor current increases so an electrical engineer should take care in the design of an electric system considering non-linear load. Besides the increased line current, other part of electrical machine may bear ill effects because of harmonics in the power system. Normally 1^st to 25^th harmonics are considered, in which the majority problems are due to 3^rd, 5^th and 7th harmonics.

Generation of Harmonics in power system:

At the point of power generation, the power distortion may be very less i.e 1% to 2% only.

Linear loads: When a sinusoidal voltage is connected with a load, the current drawn by the load is proportional with the voltage. e.g. resistive heaters, incandescent bulbs, constant speed motors etc.

Nonlinear loads: The non-sinusoidal current and voltage waveforms

In contrast, some loads cause the current to vary disproportionately with the voltage during each half cycle. These loads are classified as nonlinear loads, and the current and voltage have waveforms that are non-sinusoidal, containing distortions, whereby the 60-Hz waveform has numerous additional waveforms superimposed upon it, creating multiple frequencies within the normal 60-Hz sine wave. The multiple frequencies are harmonics of the fundamental frequency.

Motors:

Electric motors experience hysteresis loss caused by eddy currents set up in the iron core of the motor. These are proportional to the frequency of the current. Since the harmonics are at higher frequencies, they produce more core loss in a motor than the power frequency would. This results in increased heating of the motor core, which (if excessive) can shorten the life of the motor. The 5th harmonic causes a CEMF (counter electromotive force) in large motors which acts in the opposite direction of rotation. The CEMF is not large enough to counteract the rotation, however it does play a small role in the resulting rotating speed of the motor.

VFD (Variable Frequency Drives):

There is an increasing use of variable frequency drives (VFDs) that power electric motors. The voltages and currents emanating from a VFD that goes to a motor are rich in harmonic frequency components. Voltage supplied to a motor sets up magnetic fields in the core, which create iron losses in the magnetic frame of the motor. Hysteresis and eddy current losses are part of iron losses that are produced in the core due to the alternating magnetic field. Hysteresis losses are proportional to frequency, and eddy current losses vary as the square of the frequency. Therefore, higher frequency voltage components produce additional losses in the core of AC motors, which in turn, increase the operating temperature of the core and the windings surrounding in the core. Application of non-sinusoidal voltages to motors results in harmonic current circulation in the windings of motors. The net rms current is [I.sub.rms] = [square root of [([I.sub.1]).sup.2] + [([I.sub.2]).sup.2] + [([I.sub.3]).sup.2] +] ..., where the subscripts 1, 2, 3, etc. represent the different harmonic currents. The [I.sub.2]R losses in the motor windings vary as the square of the rms current. Due to skin effect, actual losses would be slightly higher than calculated values. Stray motor losses, which include winding eddy current losses, high frequency rotor and stator surface losses, and tooth pulsation losses, also increase due to harmonic voltages and currents.

The phenomenon of torsional oscillation of the motor shaft due to harmonics is not clearly understood, and this condition is often disregarded by plant personnel. Torque in AC motors is produced by the interaction between the air gap magnetic field and the rotor-induced currents. When a motor is supplied non-sinusoidal voltages and currents, the air gap magnetic fields and the rotor currents contain harmonic frequency components.

The harmonics are grouped into positive (+), negative (-) and zero (0) sequence components. Positive sequence harmonics (harmonic numbers 1,4,7,10,13, etc.) produce magnetic fields and currents rotating in the same direction as the fundamental frequency harmonic. Negative sequence harmonics (harmonic numbers 2,5,8,11,14, etc.) develop magnetic fields and currents that rotate in a direction opposite to the positive frequency set. Zero sequence harmonics (harmonic numbers 3,9,15,21, etc.) do not develop usable torque, but produce additional losses in the machine. The interaction between the positive and negative sequence magnetic fields and currents produces torsional oscillations of the motor shaft. These oscillations result in shaft vibrations. If the frequency of oscillations coincides with the natural mechanical frequency of the shaft, the vibrations are amplified and severe damage to the motor shaft may occur. It is important that for large VFD motor installations, harmonic analyses be performed to determine the levels of harmonic distortions and assess their impact on the motor.

Transformers:

The harmful effects of harmonic voltages and currents on transformer performance often go unnoticed until an actual failure occurs. In some instances, transformers that have operated satisfactorily for long periods have failed in a relatively short time when plant loads were changed or a facility's electrical system was reconfigured. Changes could include installation of variable frequency drives, electronic ballasts, power factor improvement capacitors, arc furnaces, and the addition or removal of large motors.

Application of non-sinusoidal excitation voltages to transformers increase the iron losses in the magnetic core of the transformer in much the same way as in a motor. A more serious effect of harmonic loads served by transformers is due to an increase in winding eddy current losses. Eddy currents are circulating currents in the conductors induced by the sweeping action of the leakage magnetic field on the conductors. Eddy current concentrations are higher at the ends of the transformer windings due to the crowding effect of the leakage magnetic fields at the coil extremities. The eddy current losses increase as the square of the current in the conductor and the square of its frequency. The increase in transformer eddy current loss due to harmonics has a significant effect on the operating temperature of the transformer. Transformers that are required to supply power to nonlinear loads must be de-rated based on the percentages of harmonic components in the load current and the rated winding eddy current loss.

One method of determining the capability of transformers to handle harmonic loads is by k factor ratings. The k factor is equal to the sum of the square of the harmonic currents multiplied by the square of the frequencies.

k = [([I.sub.1]).sup.2]([1.sup.2]) + [([I.sub.2]).sup.2]([2.sup.2]) + [([I.sub.3]).sup.2]([3.sup.2]) + . . . + [([I.sub.n]).sup.2]([n.sup.2]).

where [I.sub.1] = ratio of fundamental current to total rms current, [I.sub.2] = ratio of second harmonic current to total rms current, [I.sub.3] = ratio of third harmonic current to total rms current, etc., and 1,2,3, ... n are harmonic frequency numbers. The total rms current is the square root of the sum of square of the individual currents.

By providing additional capacity (larger-size or multiple winding conductors), k factor rated transformers are capable of safely withstanding additional winding eddy current losses equal to k times the rated eddy current loss. Also, due to the additive nature of triplen harmonic (3, 9, 15, etc.) currents flowing in the neutral conductor, k rated transformers are provided with a neutral terminal that is sized at least twice as large as the phase terminals.

Capacitor banks:

Many industrial and commercial electrical systems have capacitors installed to offset the effect of low power factor. Most capacitors are designed to operate at a maximum of 110% of rated voltage and at 135% of their kvar ratings. In a power system characterized by large voltage or current harmonics, these limitations are frequently exceeded, resulting in capacitor bank failures. Since capacitive reactance is inversely proportional to frequency, unfiltered harmonic currents in the power system find their way into capacitor banks, these banks act like a sink, attracting harmonic currents, thereby becoming overloaded. A more serious condition, with potential for substantial damage, occurs as a result of harmonic resonance. Resonant conditions are created when the inductive and capacitive reactance become equal in an electrical system. Resonance in a power system may be classified as series or parallel resonance, depending on the configuration of the resonance circuit. Series resonance produces voltage amplification and parallel resonance causes current multiplication within an electrical system. In a harmonic rich environment, both types of resonance are present. During resonant conditions, if the amplitude of the offending frequency is large, considerable damage to capacitor banks would result. And, there is a high probability that other electrical equipment on the system would also be damaged. If the protective device does not operate to protect the capacitor bank, serious damage will occur.