UNDESIRABLE EFFECTS OF THE HARMONICS (POWER SYSTEM) BASIC INFORMATION

Different categories of harmonic-producing loads are supplied by the electric utilities such as

1. Domestic loads like fluorescent lamps, light dimmers, etc.

2. Ripple control systems for regulating hot-water loads

3. Medium-sized industrial loads like several adjustable speed drives in a cement mill, paper mill, etc.

4. Large loads like high-voltage direct current (HVDC) convertors, aluminum smelters, static var compensators, heavy single-phase ac traction loads for hauling coal trains, etc.

The undesirable effects of the harmonics produced by these loads are listed as follows:1–3
1. Capacitors: These may draw excessive current and prematurely fail from increased dielectric loss and heating. Also, under resonance conditions, considerably higher voltages and currents can be observed than would be the case without resonance.

IEEE Std 18-19924 gives limits on voltage, current, and reactive power for capacitor banks based on their ratings. These can be used to determine the maximum allowable harmonic levels.

2. Power Cables: In systems with resonant conditions, cables may be subjected to voltage stress and corona, which can lead to dielectric (insulation) failure. Further harmonic currents can cause heating.

3. Telephone Interference: Harmonics can interfere with telecommunication systems, especially noise on telephone lines. A “standard” human ear in combination with a telephone set has a sensitivity to audio frequencies that peaks at about 1 kHz.

Two systems with slightly different weighting systems are used to obtain a reasonable indication of the interference from each harmonic. The two systems are:

C-message weighting by Bell Telephone system (BTS) and Edison Electric Institute used in the United States and Canada

Psophometric weighting by the International Consultative Commission on Telephone and Telegraph System

HARMONICS IN ROTATING MACHINES AND ARC FURNACE BASICS AND TUTORIALS

HARMONICS IN ROTATING MACHINES
The distribution of the armature windings and the presence of slots in the machines cause spatial harmonics in them. These in turn produce time harmonics in the induced voltages, which appear at the terminals.

Most of the power station generators are wye-connected. In such machines, triplen harmonic voltages do not appear in line-to-line voltages. Also, triplen harmonics can be eliminated even in phase-to-neutral voltages by using two-third pitch winding.

Usually, the most significant harmonics to be minimized by the use of fractional pitch windings are the fifth and seventh. Higher harmonics than the ninth are so small that they require little attention except in rare cases.

HARMONICS IN ARC FURNACE LOADS
Voltage flicker is caused by arc furnace loads at the point of common coupling. For steel making, arc furnaces of the rating 100 MW and above are used.

Usually, a melting cycle can be divided into three distinct steps—drilling period, melting period, and reheating period. The full voltage is applied during the melting period, and the time required for melting is rather large compared with other steps.

Due to uneven arc length, the bus voltage fluctuates continuously during the melting cycle. For large arc furnaces, reactive voltage controllers such as SVCs are required to keep the voltage within the specified limits.

REFERENCES/ ADDITIONAL READING
1. Kimbark, E.W., Direct Current Transmission (1971). Vol. 1, John Wiley, New York.
2. Schlabbach, J., Blume, D., and Stephanblome, T. (2001). Voltage Quality in Electrical
Power Systems, IEE, London.
3. Mahmoud, Aly A. (1984). Power System Harmonics: An Assessment. IEEE Tutorial
Course Text, EHO221-2-PWR, 1–9.
4. Arrillaga, J., Bradley, J.D., and Bodger, P. (1985). Power System Harmonics, John
Wiley, Chichester, U.K.
5. Arrillaga, J. and Watson, N.R. (2003). Power System Harmonics, John Wiley,
Chichester, U.K.
6. Adamson, C. and Hingorani, N.G. (1960) High Voltage Direct Current Power Transmission,
Chapter 3, Garraway, London.
7. Dugan, R.C., McGranaghan, M.G., and Beaty, H.W., (1996). Electrical Power Systems
Quality, McGraw-Hill, New York.
8. Feature Article: “Reducing the Safety Hazard of Switchers,” Electronics Australia,
February 1990, 124–125.

HARMONICS IN POWER TRANSFORMERS BASIC INFORMATION AND TUTORIALS

HARMONICS IN NO-LOAD EXCITING CURRENT
Because transformer cores are made of ferromagnetic materials, the exciting current of the transformer under no-load conditions is not sinusoidal even though the applied voltage and flux are sinusoidal due to the nonlinear nature of the B-H curve, and similarly the relationship between flux and magnetomotive force (MMF).

For anyvalue of flux, there are two values of MMF, depending on whether the flux is increasing or decreasing. From these MMFs, the magnetizing current can be computed and plotted corresponding to these values of flux, depending on whether the flux is rising or falling.

With three-limb transformers, as the triplen harmonics return through air (or rather through oil and tank), the higher reluctance of the path reduces the third harmonics to a lower value (about 10% of the value in independent core phases). The fifth and seventh harmonics may also be large enough, around 5–10%.

HARMONICS DUE TO INRUSH CURRENT
The transient current drawn by a transformer when it is first energized depends upon the instant of switching. If the transformer is energized when the applied sinusoidal voltage is at its peak, usually there is no transient.

If the transformer is energized when the applied voltage is zero and it has a residual flux fr with unfavorable polarity, then the total flux that would be required to counteract the applied voltage according to Lenz’s law would be 2 fm + fr.

To produce such a flux, the transformer may have to draw many times (say, 100 times) the normal exciting current of the transformer. In actual practice, the inrush current may be 8 to 10 times the full-load current of the transformer, depending upon the instant of switching and polarity of the applied voltage.

Depending upon the transformer, the inrush current phenomenon may persist for a few seconds, thus creating harmonics during this period.

DC MAGNETIZATION
Under unbalanced conditions, the transformer excitation current can contain odd and even harmonics. The transformers feeding half-wave rectifiers or supplying power to a three-phase converter with unbalanced firing fall into this category.

The magnitude of the harmonic components of the excitation current in the presence of the direct current on the secondary side of the transformer increase almost linearly with the dc content. The linearity is better for the lower-order harmonics.

As the harmonics generated by the transformer under dc magnetization are largely independent of the ac excitation, there appears to be no advantage in designing a transformer to run “underfluxed” in the presence of direct current.

HARMONIC FILTERS, APLCS, AND UPQCS

One means of ensuring that harmonic currents of nonlinear components will not unduly interact with the remaining part of the power system is to place filters near or close to nonlinear loads. The main function of a filter is either to bypass harmonic currents, block them from entering the power system, or compensate them by locally supplying harmonic currents.

Due to the lower impedance of the filter in comparison to the impedance of the system, harmonic currents will circulate between the load and the filter and do not affect the entire system; this is called series resonance. If other frequencies are to be controlled (e.g., that of arc furnaces), additional tuned filters are required.

Harmonic filters are broadly classified into passive, active, and hybrid structures. These filters can only compensate for harmonic currents and/or harmonic voltages at the installed bus and do not consider the power quality of other buses. New generations of active filters are active-power line conditioners that

are capable of minimizing the power quality of the entire system.

Passive filters are made of passive components (inductance, capacitance, and resistance) tuned to the harmonic frequencies that are to be attenuated. The values of inductors and capacitors are selected to provide low impedance paths at the selected frequencies. Passive filters are generally designed to remove one or two harmonics (e.g., the 5th and 7th).

They are relatively inexpensive compared with other means for eliminating harmonic distortion, but also suffer from some inherent limitations, including:

1. Interactions with the power system;

2. Forming parallel resonance circuits with system impedance (at fundamental and/or harmonic frequencies). This may result in a situation that is worse than the condition being corrected. It may also result in system or equipment failure;

3. Changing characteristics (e.g., their notch frequency) due to filter parameter variations;

4. Unsatisfactory performance under variations of nonlinear load parameters;

5. Compensating a limited number of harmonics;

6. Not considering the power quality of the entire system; and

7. Creating parallel resonance. This resonance frequency must not necessarily coincide with any significant system harmonic.

Passive filters are commonly tuned slightly lower than the attenuated harmonic to provide a margin of safety in case there are some changes in system parameters (due to temperature variations and/or failures). For this reason filters are added to the system starting with the lowest undesired harmonic.

For example, installing a seventh-harmonic filter usually requires that a fifth-harmonic filter also be installed. Designing passive filters is a relatively simple but tedious matter. For the proper tuning of passive filters, the following steps should be followed:

8. Model the power system (including nonlinear loads) to indicate the location of harmonic sources and the orders of the injected harmonics. A harmonic power (load) flow algorithm should be used; however, for most applications with a single dominating harmonic source, a simplified equivalent model and hand calculations are adequate;

9. Place the hypothetical harmonic filter(s) in the model and reexamine the system. Filter(s) should be properly tuned to dominant harmonic frequencies; and

10. If unacceptable results (e.g., parallel resonance within system) are obtained, change filter location(s) and modify parameter values until results are satisfactory.

In addition to power quality improvement, harmonic filters can be configured to provide power factor correction. For such cases, the filter is designed to carry resonance harmonic currents, as well as fundamental current.

Active filters rely on active power conditioning to compensate for undesirable harmonic currents. They actually replace the portion of the sine wave that is missing in the nonlinear load current by detecting the distorted current and using power electronic switching devices to inject harmonic currents with complimentary magnitudes, frequencies, and phase shifts into the power system.

Their main advantage over passive filters is their fine response to changing loads and harmonic variations. Active filters can be used in very difficult circumstances where passive filters cannot operate successfully because of parallel resonance within the system.

They can also take care of more than one harmonic at a time and improve or mitigate other power quality problems such as flicker. They are particularly useful for large, distorting nonlinear loads fed from relatively weak points of the power system where the system impedance is relatively large. Active filters are relatively expensive and not feasible for small facilities.

HARMONICS IN POWER SYSTEM – WHAT ARE POWER HARMONICS?

Power system harmonics are not a new topic, but the proliferation of high-power electronics used in motor drives and power controllers has necessitated increased research and development in many areas relating to harmonics.

For many years, high-voltage direct current (HVDC) stations have been a major focus area for the study of power system harmonics due to their rectifier and inverter stations. Roughly two decades ago, electronic devices that could handle several kW up to several MW became commercially viable and reliable products.

This technological advance in electronics led to the widespread use of numerous converter topologies, all of which represent nonlinear elements in the power system.

Even though the power semiconductor converter is largely responsible for the large-scale interest in power system harmonics, other types of equipment also present a nonlinear characteristic to the power system. In broad terms, loads that produce harmonics can be grouped into three main categories covering (1) arcing loads, (2) semiconductor converter loads, and (3) loads with magnetic saturation of iron cores.

Arcing loads, like electric arc furnaces and florescent lamps, tend to produce harmonics across a wide range of frequencies with a generally decreasing relationship with frequency. Semiconductor loads, such as adjustable-speed motor drives, tend to produce certain harmonic patterns with relatively predictable amplitudes at known harmonics.

Saturated magnetic elements, like overexcited transformers, also tend to produce certain ‘‘characteristic’’ harmonics. Like arcing loads, both semiconductor converters and saturated magnetics produce harmonics that generally decrease with frequency.

Regardless of the load category, the same fundamental theory can be used to study power quality problems associated with harmonics. In most cases, any periodic distorted power system waveform (voltage, current, flux, etc.) can be represented as a series consisting of a DC term and an infinite sum of sinusoidal terms.

A vast amount of theoretical mathematics has been devoted to the evaluation of the terms in the infinite sum, but It is reasonable to presume that instrumentation is available that will provide both the magnitude Fi and the phase angle ui for each term in the series. Taken together, the magnitude and phase of the ith term completely describe the ith harmonic.

It should be noted that not all loads produce harmonics that are integer multiples of the power frequency. These noninteger multiple harmonics are generally referred to as interharmonics and are commonly produced by arcing loads and cycloconverters.

All harmonic terms, both integer and noninteger multiples of the power frequency, are analytically treated in the same manner, usually based on the principle of superposition.

HARMONIC FREQUENCIES BASIC DEFINITION & TUTORIALS

In the ideal case, alternating voltages and currents are sinusoidal functions having a single frequency f or w. This fundamental frequency, also known as the power frequency, is usually the lowest frequency component in the system.

In reality, there are a number of effects within the power system that may cause the cosine wave to become distorted or “polluted” to some extent. When we say distorted or polluted, we mean that the voltage and current no longer contain just the desired power frequency (50 or 60 Hz).

Any repeating AC waveform, no matter how distorted, may be represented by a combination of waveforms of the fundamental frequency plus one or more harmonics. A harmonic is a frequency which is an integer multiple of the power frequency, (h#, h#integer). In a 60 Hz system, examples of harmonics of the power frequency would be 180 Hz, 300 Hz, 420 Hz, 660 Hz, 780 Hz, etc.

These higher frequencies are called the third, fifth, seventh, eleventh, and thirteenth harmonics of 60 Hz, respectively. The relative magnitude of the fundamental waveform and the number, magnitude, and phase displacement of the harmonic components determine the resultant waveform’s shape.

For instance, Figure 4-23 shows a voltage waveform composed of a 100 V fundamental 60 Hertz waveform and a 20 Volt third harmonic. This waveform contains 100% or one per-unit 60 Hz and a 20% or .02 per-unit third-harmonic component.

The third harmonic crosses the x-axis at the same instant in time as the fundamental waveform. Harmonics can be displaced in time from the fundamental, depending on circuit characteristics. For example, Figure 4-23 shows the 3rd harmonic 180º out of phase with the fundamental.

Under certain circumstances, harmonics can be important and also troublesome. Electronic loads containing power semiconductor devices, which switch on and off to control the flow of energy between the source and load, typically cause power system harmonics.

This switching on and off, hundreds to thousands of times every second, directly modulates the current and corrupts the voltage. In other words, the current modulation causes voltage drops across the impedance of the lines and distribution equipment resulting in the voltage being modulated as well.

Thus, high-frequency harmonic components are injected into the power system. Examples include variable-speed motor drives, electronic lighting ballasts, and electronic equipment power supplies.

As a result, these loads can cause dangerous resonance conditions between the electronic load’s step down transformer and the utility’s power factor correction capacitors.

Harmonics will cause additional heating in wiring and other equipment, and will not be detected by most digital test meters unless they are true rms measuring devices.

In addition, electromechanical meters typically under-register the energy being absorbed by these electronic loads.

In general, solid-state meters do a better job of measuring the total energy being consumed by a customer’s electronic load.