Harmonics 
The Effect of HarmonicsORIGINS OF HARMONIC DISTORTIONThe ever increasing demand of industry and commerce for stability, adjustability and accuracy of control of electrical equipment led to the development of relatively low cost power diodes and thyristors. Now used widely for rectifier circuits for U.P.S. systems, static converters, and D.C. motor control, these modern devices replace the Mercury Arc Rectifiers of earlier years and in consequence create new and challenging conditions for the power engineer of today. Although solid state devices such as the thyristor have brought significant improvements in control techniques, they have the disadvantage that they produce harmonic currents. Harmonic currents can cause an unacceptable disturbance on the supply network and adversely affect the operation of other electrical equipment including power factor correction capacitors. WAVEFORMAll complex waveforms can be resolved into a series of sinusoidal waves of various frequencies, hence any complex waveform is the sum of a number of odd or even harmonics of lesser or greater value. Thyristor convertors or rectifiers are usually referred to by the number of DC current pulses they produce each cycle, the most commonly used being 6 pulse and 12 pulse. There are many factors that can influence the harmonic content but typical harmonic currents, shown as a percentage of the fundamental current are given in the following table. Some content of the harmonics not listed will always be present to some degree but for practical reasons they have been ignored.
HARMONIC OVERLOADING OF CAPACITORSThe impedance of a circuit dictates the current flow in that circuit. As the supply impedance is generally considered to be inductive, the network impedance increases with frequency while the impedance of a capacitor decreases. This encourages a greater proportion of the currents circulating at frequencies above the fundamental supply frequency to be absorbed by the capacitor, and all equipment associated with the capacitor. In certain circumstances such currents can exceed the value of the fundamental (50Hz) capacitor current. These currents in turn cause increased voltage to be applied across the dielectric of the capacitor. The harmonic voltage due to each harmonic current added arithmetically to the fundamental voltage dictates the voltage stress to be sustained by the capacitor dielectric and for which the capacitor must be designed. Capacitors of the correct dielectric voltage stress must always be used in conditions of harmonic distortion to avoid premature failure. HARMONIC RESONANCEAs freqency varies, so reactance varies and a point can be reached when the capacitor reactance and the supply reactance are equal. This point is known as the circuit or selective resonant frequency. Whenever power factor correction is applied to a distribution network, bringing together capacitance and inductance, there will always be a frequency at which the capacitors are in parallel resonance with the supply. If this condition occurs at, or close to, one of the harmonics generated by any solid state control equipment, then large harmonic currents can circulate between the supply network and the capacitor equipment, limited only by the damping resistance in the circuit. Such currents will add to the harmonic voltage disturbance in the network causing an increased voltage distortion. This results in an unacceptably high voltage across the capacitor dielectric coupled with an excessive current through all the capacitor ancillary components. The most common order of harmonics are 5th, 7th, 11th and 13th but resonance can occur at any frequency. AVOIDING RESONANCEThere are a number of ways to avoid resonance when installing capacitors. On larger systems it may be possible to reposition the proposed capacitor installation onto another part of the system. The same value of kvar installed at high voltage rather than at low voltage may eliminate a resonant difficulty, or there may be other low voltage busbars where there is no harmonic generating load. Varying the output rating of the capacitor bank will alter the resonant frequency. With multi stage capacitor switching there will be a different resonant frequency for each stage. Changing the number of switching stages may avoid resonance at each stage of switching. OVERCOMING RESONANCEIf resonance cannot be avoided an alternative solution is required. A reactor must be connected in series with each capacitor switching section such that the capacitor/reactor combination is inductive at the dangerous frequencies but capacitive at fundamental frequency. To achieve this the capacitor and series connected reactor must have a tuning frequency below the lowest order of harmonic to be experienced, which is usually the 5th. This means the tuning frequency is usually in the range of 175Hz to 230Hz, althouth the actual frequency will depend upon the magnitude of the harmonic currents present. The actual tuning frequency will be varied to suit the specific needs of each case. The inclusion of a reactor in the capacitor circuit increases the fundamental voltage across the capacitor in the order of 5 to 9% in addition to the harmonic voltages previously mentioned. COST EFFECTIVENESSDue to varying site conditions, it is not always possible to determine with certainty that resonance will occur. Adding series reactors to power factor correction equipment is expensive and can increase the cost to uneconomic levels. If later found not to be required, then unnecessary expenditure is incurred. An intermediate step is to install appropriate capacitors with facilities for the addition of reactors if found to be necessary at a later date, thus lowering considerably the initial capital cost. When capacitors are used in series with reactors they are rated at higher than system voltage, so when used without reactors they have the ability to withstand higher levels of harmonic overload, which alone may resolve the situation. If resonance does actually occur reactors can be added to the existing power factor correction equipment at minimum extra cost LIMITS OF HARMONIC DISTORTIONHarmonic distortion can cause severe disturbance to certain electrical equipment and as it is the duty of the electric utility to provide a “clean” supply, many countries now set limits to the harmonic distortion allowed on the distribution networks. In the U.K. the Electricity Council Engineering Recommendation G5/3 provides for three levels of acceptance for the connection of harmonic generating equipment, defined as stages.
Before accepting harmonic generating loads, the existing harmonic voltage distortion on the supply network is taken into consideration in setting the individual limits of Stage 3, and may also restrict the maximum limits as tabulated for Stage 2. Where these limits are exceeded, it may be necessary to reduce or eliminate the harmonics produced. REDUCTION OF HARMONIC DISTORTIONHarmonic currents can never be totally eliminated from an electrical system. They can, however, be very significantly reduced by using a harmonic filter. In its basic form a filter comprises a capacitor connected in series with a reactor tuned to the frequency to be eliminated. In theory the impedance of the filter is zero at the tuning frequency and therefore all of the particular harmonic current is absorbed by the filter. In practice, however, the capacitor and reactor are usually tuned slightly below the harmonic frequency. This together with the natural resistance of the circuit means that only a small acceptable level of harmonic current will flow in the network. When it is necessary to reduce more than one harmonic, a multi arm filter may be required. TYPES OF FILTERThe effectiveness of any filter scheme depends on the nett reactive output of the filter, filter tuning accuracy and the impedance of the network at the point of connection. Harmonics below the filter tuning frequency will be amplified. The experience of the filter designer is therefore important to ensure that insignificant distortion is not amplified to unacceptable levels. Where there are several harmonics present, a single arm filter may reduce some harmonics whilst increasing others, e.g. a filter for 11th harmonic may create resonance in the vicinity of 7th harmonic and high magnification of any 5th harmonic already on the network In these cases it may be necessary to use a multiarm filter where each arm is tuned to a different frequency Experience is paramount in the design of such filters to ensure:
LOAD ALTERATIONWhenever load expansion is considered, with or without additional power factor correction equipment, the network impedance is likely to change and existing filter equipment must be reappraised in conjunction with the new load condition and be suitably uprated. It is not recommended to have two or more filters fine tuned to the same frequency connected on the same busbar system. Slight tuning differences may cause one filter to take a much larger share of the harmonic distortion, or even cause a harmonic resonance condition leading to amplification of the very harmonic order for which the equipment has been designed to reduce. When there is a need to vary the power factor correction component of a harmonic filter, careful consideration of all parameters is necessary. HARMONIC ANALYSISTo determine capacitor and filter requirements to meet specific harmonic conditions, it is necessary to establish with accuracy the impedance of the supply network and the value of each harmonic current experienced at the point of intended connection of any filter or power factor correction capacitor.

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