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1. INTRODUCTION
The term 'power quality' refers to the purity of the voltage and current waveform, and a power quality disturbance is a deviation from the pure sinusoidal form. Harmonics superimposed on the fundamental are one cause of such deviations, and this section describes the nature, generation and effects of harmonics on power supply systems, together with the limitation of such effects and harmonic studies.
The widespread and increasing use of solid state devices in power systems is leading to escalating ambient harmonic levels in public electricity supply systems.
These harmonic levels are subject in order to limitations to safeguard consumers' plant and installations against overheating and overvoltages. It is also incumbent upon individual consumers to ensure that their equipment does not produce harmonic levels that exceed such limits at the point of common coupling with other consumers. These are called 'emission limits.' Immunity standards set down the disturbance levels which equipment should be capable of tolerating without undue damage or loss of function. A third set of standards, for 'compatibility levels,' has the function of enabling co ordination and coherence of the emission and immunity standards (see Table 3).
In the UK, limits at the point of common coupling are detailed in the Electricity Councils Engineering Recommendation, G5/4, although where necessary a connection agreement may stipulate other limits for an individual consumer. Internationally, the subject is covered by various parts of IEC 61000 (see Table 1) and acceptable levels of voltage disturbance to be established in power supply systems in Europe are provided in EN 50160 (but these are not formal compatibility levels). In the USA, the appropriate standard is IEEE 519-1992.
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TABLE 1 Useful Selection of IEC Standards (See Also Section 20)
Document Number Document Title 61000-1-1 Electromagnetic compatibility (EMC) _ Part 1: General -- Section 1:
Application and interpretation of fundamental definitions and terms 61000-1-4 Electromagnetic compatibility (EMC) _ Part 1_4: General _ Historical rationale for the limitation of power frequency conducted harmonic current emissions from equipment, in the frequency range up to 2 kHz 61000-2-2 Electromagnetic compatibility (EMC) _ Part 2_2: Environment _ Compatibility levels for low-frequency conducted disturbances and signaling in public low-voltage power supply systems 61000-2-4 Electromagnetic compatibility (EMC) _ Part 2_4: Environment _ Compatibility levels in industrial plants for low-frequency conducted disturbances 61000-2-6 Electromagnetic compatibility (EMC) _ Part 2: Environment _ Section 6: Assessment of the emission levels in the power supply of industrial plants as regards low-frequency conducted disturbances 61000-2-12 Electromagnetic compatibility (EMC) _ Part 2_12: Environment _ Compatibility levels for low-frequency conducted disturbances and signaling in public medium-voltage power supply systems 61000-3-2 Electromagnetic compatibility (EMC) _ Part 3_2: Limits _ Limits for harmonic current emissions (equipment input current #16 A per phase 61000-3-4 Electromagnetic compatibility (EMC) _ Part 3_4: Limits _ Limitation of emission of harmonic currents in low-voltage power supply systems for equipment with rated current greater than 16 A 61000-3-6 Electromagnetic compatibility (EMC) _ Part 3: Limits _ Section 6:
Assessment of emission limits for distorting loads in MV and HV power systems _ Basic EMC publication 61000-3-12 Electromagnetic compatibility (EMC) _ Part 3_12: Limits _ Limits for harmonic currents produced by equipment connected to public low-voltage systems with input current .16 A and #75 A per phase 61000-3-14 Electromagnetic compatibility (EMC) -- Limits _ Part 3--14:
Assessment of emission limits for installations connected to LV power systems 61000-4-1 Electromagnetic compatibility (EMC) _ Part 4_1: Testing and measurement techniques _ Overview of IEC 61000-4 series (Note:
There are at the time of publication 34 Sections to Part 4, covering different aspects of testing & measurement; many are relevant to the present topic.)
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The major producers of harmonics are railway traction loads, large furnaces and large converter-controlled electric motor drives. Such harmonics are usually filtered on site so that they do not inject a harmful level of harmonic currents into the public electricity supply system. A further significant source of harmonics arises from the myriad of miscellaneous non-linear loads connected to the power system such as rectifiers, welders, discharge lamps, control systems, television sets, microwave ovens and computers, etc. It is fortunate that because of the arbitrary and independent nature of these loads a significant amount of harmonic cancellation occurs thus reducing the overall impact.
2. THE NATURE OF HARMONICS
2.1 Introduction
Power systems are generally linear and because of this each harmonic has an independent existence. For instance, there is no net power and energy generated between, say the fifth harmonic current and a seventh harmonic voltage, etc.
This is very convenient since it greatly simplifies the treatment of harmonics and allows superposition techniques to be used in harmonic analysis. However, in the case of weak systems a detailed representation of any system non-linearity may be required as in such systems there can be interactions between harmonics of different order that are not predicted by linear time-invariant models.
2.2 Three Phase Harmonics
The general expression for harmonic currents in a three phase system is given by: [...]
From Eq. (1), it is clear why the third and all triplen harmonics are zero-phase sequence in nature and must always have a neutral conductor to flow in or a delta-connected winding in which to circulate. Furthermore, the fifth harmonic is seen to be backward rotating and therefore negative-phase sequence in nature. The harmonic sequence is as follows:
For the general unbalanced case:
In this case all harmonics will exhibit positive, negative and zero-phase sequence components. That is, if the zero-sequence currents have a neutral path in which to exist.
3. THE GENERATION OF HARMONICS
3.1 General
Harmonic distortion needs to be defined as either 'current distortion' or 'voltage distortion.' Non-linear loads, unlike linear loads, draw a non-sinusoidal current from a sinusoidal voltage supply. The distortion to the normal incoming sinusoidal current wave can be considered to result from the load emitting harmonic currents that distort the incoming current. These emitted harmonic currents, like any generated current, will circulate via available paths and return to the other pole of the non-linear load. In doing so, they cause harmonic voltage drops in all the impedances through which they pass which distort the normal supply sinusoidal voltage. The aim must therefore be to shunt the emitted harmonic currents into low impedance paths as close to the non-linear load as possible to minimize the resulting voltage distortion, as the voltage distortion will cause harmonic currents to flow in other linear and non-linear connected loads, such as motors, with deleterious effects. Zero sequence triplen harmonic currents present a further problem as they are con strained to zero-sequence paths such as neutral conductors which can then become overloaded and present a serious risk as neutral conductors are not normally protected against overloading.
3.2 Transformers
Public electricity and industrial supplies are, to a first approximation, linear with the generated voltage being an almost pure sinusoidal wave. Virtually all harmonics are generated in non-linear loads and machine drives connected to the system. Exceptions to this are the magnetizing currents of transformers and the triplen currents that flow in generator neutral circuits. All other power system shunt equipment with non-linear characteristics, such as shunt reactors, static VAr compensators and static balancers, etc., can, from the point of view of harmonic generation be regarded as non-linear loads.
Magnetic circuits in transformers and rotating machines operating under varying conditions of saturation have, since the earliest days, been known to produce power system harmonics. Typically a transformer magnetizing current (I_mag) will contain small third, fifth and seventh harmonic components as given in per cent by the following formula for the older stalloy-type trans former core steels:
Modern cold rolled grain oriented silicon steel, which has a squarer magnetizing characteristic produces significantly less third harmonic current.
Normally transformers are designed to operate up to the knee point of their magnetizing curve, but under conditions of magnetic saturation (caused by overvoltage or ferroresonance) the harmonic content of the magnetizing current can increase dramatically. Equipment containing saturable reactors, which deliberately exploit the magnetic saturation phenomenon, will therefore probably require harmonic filtering.
Remanent magnetism in transformers (caused for example by circuit breaker interruption of a fault when there is still a significant DC component) can persist for months or longer and, by displacing the B-H curve can result in magnetizing asymmetry and even harmonics in the magnetizing current.
3.3 Converters
Converter is the generic name given to rectifier and inverter systems. These systems range from simple rectifiers through to AC-DC-AC systems for the interconnection of major power networks such as the UK/France cross Channel power link and frequency changer systems for soft start and speed control of AC machine drives. In addition, particularly with the advent of the gate turn off thyristor (GTO), Flexible AC Transmission Systems (FACTS) of great technical and operational sophistication are gaining widespread use for the control and conditioning of power systems. All these systems can produce copious harmonics. The principal harmonic numbers may be filtered out on site but significant harmonic currents may still emanate from these systems onto the power network.
FIG. 1 Three phase, six-pulse thyristor-controlled bridge rectifier
supplied from an infinite busbar.
3.4 The Thyristor Bridge
Thyristor rectifier_inverter bridges are the basis of all the systems described in Section 3.2 above. Fig. 1 shows a basic three phase six-pulse thyristor-controlled bridge together with the idealized DC side voltage and AC current of one phase. Applying Fourier analysis to the square wave of phase current yields the following harmonic series:
This indicates that the fifth and seventh are the principal or characteristic harmonics of the six-pulse bridge. These harmonics would be present on the primary side of a star-star configured transformer feeding the bridge, how ever, if the bridge was fed from a star-delta vector group transformer then a 30 degree phase shift would have to be taken into account together with some adjustment for the transformer ratio. The harmonic series for this connection then becomes:
If these two converters are supplied from the same AC source and connected in series on the DC side we have a 12 pulse connection. Notice that in this case the fifth and seventh harmonics cancel out yielding the following harmonic series:
In Eq. (.6), the eleventh and thirteenth are the principal harmonics, Eq. (.4) and (6) indicate that a polyphase bridge will produce harmonics of the order:
where p is the pulse order and k an integer. These harmonic series are idealized since in practice such converters will operate from supplies having a significant impedance. This will modify the converter response and waveforms.
In addition, imperfections and unbalance in the power supply system and in the converter itself will increase the harmonic spectra produced. Table 2 shows the actual current spectra of a 70 kVA, six-pulse converter motor drive operating on an electrically weak system. Here phase unbalance has caused the individual phase harmonics to be dissimilar in magnitude and a third harmonic has appeared. Further, slight imperfections in the converter's firing angle control have given rise to small even harmonic terms in the spectra.
Therefore it should be appreciated that harmonic spectra encountered in practice may be significantly different from the idealized spectra anticipated from a particular installation.
TABLE 2 Practical Harmonic Current Spectra: Produced by a 70 kVA, 415 V, Six-Pulse Thyristor-Controlled Converter Supplied from an Electrically Weak Source
3.5 Railway and Tramway Traction Systems
3.5.1 Introduction
Rail traction locomotives can produce high power harmonics and it is normally impractical to completely filter these on the rolling stock. Filtering, if required must therefore be carried out at the traction substations. The pragmatic approach is to supply the traction substations from a strong (high fault level) high voltage grid connection point if studies show that harmonics may be a problem at a lower voltage level on the network. Use of such a connection must be checked for economic viability since the higher the system volt age the higher the capital costs of the associated equipment.
3.5.2 AC Traction
The motive power units of trains taking an AC supply comprise onboard single-phase transformers supplying the axle drive motors through one of a variety of converter systems. Older AC trains with diode/thyristor convertor systems produce lower range harmonics (100-750 Hz). More modern trains with GTO drives, pulse-width-modulated (PWM) systems and synthesized driving voltages produce harmonics in the higher ranges centered around, say, 1,800 Hz, but of a lower pro rata magnitude. Although the harmonic spectra generated by modern rolling stock have improved, (reduced) significant third harmonics remain a feature of these systems.
Rail traction systems are rich in harmonics and the difficult assessment of the filtering requirements has to take into account that several trains of varying vintage and type operating at different duties will be supplied from any one traction substation at any given time. Further, since the traction load is essentially single phase it creates an unbalance on the three phase supply source. The effect of phase unbalance is to impose both positive and negative fundamental harmonic phase-sequence currents on the supply system. For further discussion and an example of this see the next section. In practice, this unbalance is partially reduced by connecting the different traction substations along the route of the railway line from different selected phase pairs of the three phase supply system. However, this has only partial success because the loads on each substation traction transformer will be varying with time throughout the day. In addition, different substation transformers may be taken out of service at different times for maintenance and this may exaggerate the overall state of unbalance. Because of the phase pair connection no zero-sequence components will be present but triplen harmonics with positive and negative sequence components will exist in the traction load current spectrum brought about by the phase unbalance.
3.5.3 DC Traction
DC traction systems are normally supplied through three phase rectifier banks, often combined in one piece of plant with a transformer, to comprise trans former rectifiers which take supply at 11 kV or 20 kV and convert to a traction supply at 500 V, 650 V or even 1,500 V DC. The problem of unbalance is avoided, because supply is taken equally from all three phases, but a harmonic distortion problem is created by the rectifiers. A six-pulse rectifier bank will generate 5th and 7th harmonics in the supplying system, while a 12-pulse bank will generate mainly 11th and 13th harmonics and a 24-pulse rectifier produces 23rd and 25th harmonics. Most public supply systems are already distorted with significant levels of the 5th harmonic, so any new DC traction rectifier system will probably be at least 12 pulse. The cost of a 24-pulse system may be difficult to justify; the cost of a 12-pulse system can be reduced in substations where there are pairs of transformer rectifiers. This is achieved by installing six-pulse units, but specifying the transformers of each pair to have a vector group with a 30_ displacement between them, thus achieving an overall 12-pulse system while both transformer rectifiers are in operation and sharing load equally.
It should be noted that while a three phase rectifier bank is a balanced load, where it is subject to unbalanced system voltages (e.g. unbalance already existing in the supplying power system) additional triplen harmonics are generated.
3.6 Static VAr Compensators and Balancers
These devices are discussed in more detail in Sections 25 and 28. Their ability to control voltage by compensating for rapid changes in reactive power loading has resulted in their widespread use as elements in power transmission systems. They typically include in their assembly thyristor control equipment that inevitably generates its own harmonic currents which are very sensitive to the thyristor firing angle delay as shown in Fig. 2. They also contain capacitor banks, which are often split into sub units that double as the necessary harmonic filters (either shunt filters tuned to the characteristic frequencies of the converter or high pass filters) as shown in Fig. 6.