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[cont from part 1]
4. THE EFFECTS OF HARMONICS
4.1 Heating Effects of Harmonics
Harmonic currents flowing in rotating machines cause heating effects both in the conductors and in the iron circuit. In particular, eddy current losses are proportional to the square of the frequency. Further, some harmonics are negative-phase sequence in nature and these give rise to additional losses by inducing higher frequency currents and negative torques in machine rotors.
Harmonic currents will tend to flow into the system capacitance and this can give rise to overloading of power factor correction capacitors and to the derating of cables.
The only meaningful way to sum harmonic currents is by their heating effect, that is, by their root mean square (r.m.s.) value. Thus the effectiveness of, say, a group of harmonic currents and the fundamental current is given in terms of their r.m.s. values as follows:
FIG. 2 Harmonic current spectra, as a function of the firing angle
of a six-pulse thyristor-controlled reactor.
4.2 Harmonic Overvoltages
Harmonic voltages, generated by harmonic currents flowing against impedance to the harmonic, can lead to significant overvoltages. Such effects are known to cause equipment failures, and capacitors are particularly susceptible. These overvoltages can be enhanced by system resonances whereby a given harmonic current may generate a disproportionately large harmonic the changing phase relationship of the harmonics to the fundamental voltage.
Therefore it is recommended that the arithmetic sum of the peaks of the fundamental and harmonic voltages are calculated when assessing the stresses placed on equipment due to harmonics. Such a pessimistic approach will ensure that the equipment, particularly capacitors, are generously rated and be less susceptible to overvoltage failure.
4.3 Resonances
Any inductive capacitive resistance (LCR) circuit, such as a power system, will exhibit a resonant response to one or more frequencies. Resonance is defined by the circuit becoming resistive with the reactive components cancelling out. As a consequence the phase angle between the driving voltage and the current becomes zero. Either side of the resonant frequency the circuit becomes inductive or capacitive.
There are two types of resonant response. Series resonance is characterized by the circuit impedance tending towards a small residual, largely resistive, impedance. Consequently, in this response the circuit current will tend to be high when the circuit is fed from a voltage source and large voltages will appear across the reactive circuit components. Parallel resonance exhibits a high impedance response which is still resistive. This response gives rise to the generation of relatively high voltages across reactive components when the circuit is fed from a constant current source. These characteristics are put to good use in filter circuits.
An inspection of the frequency response (Figs. 3 and 4) of a typical power system impedance against increasing frequency shows a variable non linear response with peaks and troughs. These peaks and troughs are due to resonances caused by the system capacitive and inductive reactance. The peaks are parallel type resonance responses and the troughs are series resonance effects. The low impedance troughs will give rise to increased harmonic currents of the appropriate frequency and these in turn can cause increased harmonic voltages in other equipment.
Such natural system resonances are not in themselves necessarily a cause for concern. It is only when such system responses, coupled with significant harmonic current inputs from non-linear loads, lead to excessive harmonic voltages that steps must be taken to limit the response. Nevertheless on some (high Q) systems with low damping, potentially huge harmonic voltages can be generated. Overvoltages as high as 120% or more have been encountered in studies and in actuality on some systems.
FIG. 3 Typical power system harmonic impedance plot as a function
of frequency.
FIG. 4 Typical power system harmonic impedance polar plot in the
XR plane corresponding to Fig. 3.
4.4 Interference
Power system harmonics may cause interference with communication, signaling, metering, control and protection systems either by electromagnetic voltage. Since, from the point of view of electric stress, the peak value of applied voltage is important, it is not appropriate in this case to take the r.m.s. value of a given harmonic voltage spectra. It is not possible to be certain of induction or by the flow of ground currents. However, systems such as signaling circuits whose correct function is essential to safety should have any sensitivity to harmonic interference designed out of them at the outset. Also, standby earth fault relays connected in the neutral of transformer circuits may employ third harmonic filters. These filters are designed to prevent anomalous relay operation from large discharge lighting loads which may generate triplen harmonics flowing in the neutral conductor. Incorrect earth fault residual current relay element operation may also be prevented by connecting the supply transformers to converter equipment in a delta configuration thus blocking the flow of zero-sequence currents from converters to the power system. Other adverse effects of harmonics include:
_ Overstressing and heating of insulation.
_ Machine vibration.
_ The destruction by overheating of small auxiliary components, e.g. small capacitors and motors.
_ Malfunctioning of electronic devices.
5. THE LIMITATION OF HARMONICS
5.1 Harmonic Filters
Harmonic filters are series or parallel resonant circuits designed to shunt or block harmonic currents. They reduce the harmonic currents flowing in the power system from the source and thereby reduce the harmonic voltage distortion in the system. Such devices are expensive and should only be used when other methods to limit harmonics have also been assessed. The application of filters in a given situation is not always straightforward. The filters themselves may interact with the system or with other filters to produce initially unsuspected resonances. Hence in all but the most simple cases harmonic studies should be used to assist with the determination of the type, distribution and rating of the filter group. Classical shunt filter circuits and their associated characteristics are shown in Fig. 5. Note that when the filter forms the capacitive section of an SVC, it is essential for it to be capacitive at fundamental frequency so it will produce the reactive power required.
The selectivity or tuning response of the simple single resonant frequency filter circuit is defined by its Q or quality factor:
FIG. 5 Typical harmonic filter characteristics.
A high Q factor gives good selectivity (narrow frequency response) but the filter tuned circuit may be prone to drifting in its tuned frequency owing to changes in temperature or component ageing. Since slight changes in system frequency will cause detuning a less peaky filter response with a lower Q factor is more desirable to accommodate these changes. The tuned resonance frequency of a series LCR circuit is given by:
FIG. 6 A balancer and filter group schematic.
The more complex calculations associated with parallel high pass and C type filters are given in the references at the end of this section.
5.2 Capacitor Detuning
It is possible for power factor correction capacitors, particularly on thyristor controlled drives, to form a low impedance path or 'sink' for harmonics or to inadvertently resonate with one of the harmonics produced by the non-linear load. Symptoms are typically capacitor overheating, capacitor fuse protection operation or failure due to overstressing. A solution is to detune the capacitors from high harmonics by the insertion of a series reactor forming a tuned circuit with the resonant frequency typically around the fourth harmonic. The capacitor circuit then looks inductive to all harmonics above the fourth harmonic and resonance is quenched. This is a sufficiently common problem that power factor correction capacitor banks may be specified for installation with these detuning components at the outset. Examples of detuned power correction capacitor networks are shown in Fig. 7.
6. FERRORESONANCE AND SUBHARMONICS
6.1 Introduction
These phenomena involve real physical events and real practical problems on power systems. For example, when the British 275 kV and 400 kV trans mission systems were installed, a number of ferroresonance events occurred leading to outages and damages to grid transformers. The failure of a large generator in Mohave power station in the USA, caused by subsynchronous resonance with the turbine natural frequency mode, is also well documented.
FIG. 7 Detuned power factor correction capacitors.
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FIG. 8 Overvoltages arising from ferroresonance phenomena.
Normal transformer voltage scale 1.9 p.u./cm (a) (b) Transformer voltage and current during subharmonic oscillation showing 43% overvoltage V = 1.9 p.u./cm I = 2.0 p.u./cm (c) Transformer voltage and current during ferroresonance showing 70% overvoltage V = 1.9 p.u./cm, I = 4.0 p.u./cm
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FIG. 9 Double circuit line transformer feeders a possible condition
for the energization of ferroresonance.
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6.2 A Physical Description of Ferroresonance
Ferroresonance is characterized in a circuit by the sudden departure from sinusoidal conditions and the emergence of current spikes reaching magnitudes of typically 2 to 5 per unit values. These current spikes arise from the magnetic cores of transformers or reactors going into brief saturation excursions. Such large current spikes give rise to system overvoltages reaching values in excess of 1.5 per unit as illustrated in Fig. 8c.
Ferroresonance and subsynchronous resonance can arise in power sys tem circuits when capacitance is connected in series (and less commonly when connected in parallel) with non-linear inductive circuits such as trans formers and reactors and when the voltage is sufficient to drive the non-linear inductance to near the knee point of the B-H curve. As the inductance falls at the knee point a stage may be reached where the residual inductance is in resonance with the capacitance at the driving voltage frequency.
This causes a drop in the circuit impedance to the value of the residual resistance and a spike of current results that drives the inductive reactance well into saturation. The inductance then becomes very low, the resonance condition is destroyed, and since the voltage wave is now falling, the cur rent rapidly falls to a low value. This whole process is repeated in the next half cycle yielding another current spike in the opposite direction. This is a simplistic explanation of a complex phenomenon since sometimes two spikes of current occur each half cycle. The potential for ferroresonance problems has ironically increased with the introduction of low-loss square law characteristic transformer and reactor steels. Such materials increase the inherent non-linearity of transformers and reduce system damping.
Hence, ferroresonance is basically a fundamental system frequency event, but, because of the current spikes and voltage distortion a rich harmonic spectrum is generated.
A typical situation that arose on the British 275 kV grid system involved a double circuit line feeding two grid transformers as shown in Fig. 9. If one circuit was tripped out for whatever reason, that circuit should have been dead and was initially expected to be so. However, it transpired that if the double circuit line was long enough then there was sufficient inter-circuit capacitance between the live and apparently dead circuits for a ferroresonance response to be excited in the transformer feeder circuit that had been switched out of service. The transformer was continuing to be fed by energy through the inter-circuit mutual capacitance. The resulting spiky currents caused an alarming noise from the transformer core and some transformer failures resulted from overvoltage flashover effects. Such phenomena are now avoided by the use of operational rules that require the transformer to be initially switched off and isolated from its circuit and earthed, before the overhead line circuit is switched out.
Another well-documented case occurred in the USA on the Detroit-Edison Company electrical supply system. A 40 kV transformer had lost a phase and gone into ferroresonance with the system capacitance. The resulting overvoltages caused the failure of 39 surge arresters on the network.
In summary, the following parameters are important:
_ The characteristics of the iron of the transformer core.
_ The designed flux level of the transformer.
_ The level of the supply voltage compared to the nominal.
_ The inductance of the relevant transformer winding when saturated.
_ The load on any other windings on the transformer, and the coupling between the windings.
_ The instantaneous flux in the transformer when the initiating incident occurs.
_ The point on wave at which the switching event occurs.
Problems can be avoided by tackling these criteria, and by operational actions such as ensuring sufficient load remains connected to the system being switched and eliminating single-phase switching.
6.3 Sub-harmonics
Consider the same LCR circuit involving non-linear inductance as described above but energized by a voltage below the value sufficient to cause ferroresonance. As might be expected the circuit will behave in a linear manner.
However, if this current is suddenly disturbed by, say, a switching event or a transient voltage fluctuation, the circuit may jump into a subharmonic response characterized again by spiky currents and overvoltages but at a frequency that is a sub-multiple of the fundamental frequency. The subsynchronous frequency may be typically one third (16 2/3 Hz for a 50 Hz fundamental power frequency system) or less likely one fifth of the fundamental frequency.
A transformer undergoing this subharmonic response will exhibit a waveform typically as shown in Fig. 8b and generate loud audible vibrations.
6.4 Inter-harmonics
Between the harmonics of the power frequency voltage and current, further frequencies can be found which are not an integral multiple of the fundamental.
These can appear as discrete frequencies or as a wide-band spectrum. Summation effects are not likely and need not be considered (IEC 61000-2-1). The main sources of interharmonics are static frequency converters, cyclo-converters, induction motors, welding machines and arc furnaces. One effect of interharmonics is the disturbance of ripple control systems, another is a flicker effect. The latter occurs with discrete frequencies close to the fundamental.
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TABLE 3 Terms Relating to Power System EMC (From IEC 61000-3-6) Term Explanation
Level of harmonic distortion that can be used for planning purposes in evaluating the impact on the supply system of all consumer loads.
They are set by the utility and can be considered as internal quality objectives. They are equal to or lower than compatibility levels.
The reference value for coordinating the emission and immunity of equipment that is part of, or supplied by, a supply network to ensure the EMC in the whole network. Compatibility levels are generally based upon the 95% probability levels of entire systems using distributions which represent both time and space variations of disturbances.
The maximum level of a given electromagnetic disturbance incident on a particular device, equipment, or system for which it remains capable of operating at the required degree of performance.
At each (inter)harmonic frequency, the emission level from a distorting load is the (inter)harmonic voltage or current that would be caused by the load into the power system if no other distorting load were present.
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7 HARMONIC STUDIES
7.1 The Requirement
The basis under which a utility will consider acceptance of a load which may further add to the harmonic distortion on its supply network is twofold:
a) The level of distortion already existing-- to which its customers are already subject (this may be expressed as the effect of other distorting loads).
b) The increase in disturbance which the subject load will cause.
This approach is inherent in the IEC 61000 standards, and in the UK's G5/4 guide. The utility will assess both these aspects in order to assess the likely harmonic content in its mains after connection of the load. A comparison is then made with the 'planning levels' (see Table 3) of the affected harmonics in the standard chosen, and if the G5/4 approach is used, acceptance normally given if the new level is lower than the planning level. If it is not, usually some mitigating action will be required before the load is accepted; if existing distortion levels are high this may result in very significant and expensive mitigation investment for the new consumer. The IEC approach sets an emission limit on the new connected load which, if achieved will ensure that the planning level is maintained provided other consumers are treated in the same way. It acknowledges that if existing net work distortion levels are low, a utility may exceptionally accept individual loads which exceed the emission limit. Guidance is also given on calculating the combined effect of other specific existing loads, and the effect of existing distortion introduced from higher voltage levels must be considered (IEC 61000-3-6).
In order to determine the level of distortion existing, it is necessary to take accurate measurements at key points in the system. To determine the effect of the additional load it is necessary to undertake system studies.
7.2 The Studies
To calculate the effect of a potentially distorting load it is necessary both to determine the characteristics of the load, and of the network to which it is connected. In a relatively simple case where one continuous industrial process is supplied through a rectifier, a computer model of the load and rectifier installation can determine the maximum level and spectrum of harmonics generated into a given impedance. A much more complex task is to set up a model of the harmonic impedance of the network to which the load will be connected, and into which its harmonics will be generated. It is not just that in old networks data is often unreliable; account must also be taken of all the different network configurations that might realistically be encountered, so that potentially a great many study scenarios have to be considered. To reduce the extent of the work, it is sometimes realistic to treat parts of a net work very remote from the subject investigation as 'lumped' impedances.
Guidance is given in Ref..
Once a network model, or suite of models, has been created, and the harmonic generating potential of the load has been determined, any one of a number of proprietary harmonic system study software packages can be used to find out the effect of connecting the load, taking account of the existing voltage and current distortion in the network. One methodology is broadly as follows: where Vhp predicted harmonic voltage distortion at harmonic order h Vhr calculated harmonic distortion caused by network reconfiguration Vhi calculated harmonic distortion due to new or incremental current injection Vhm measured existing harmonic distortion Vhs calculated spare margin for additional load Vhl the limit under the standard applied (e.g. G5/4) Zhf the future harmonic impedance Zhe the existing harmonic impedance
Greater complexity is encountered when the load is of a widely varying nature, because (for example) the level of harmonics generated in a rectifier depends on the load and electrical environment in a manner that is almost random and even more care has to be taken when the varying load appears over a number of different supply points, such as in a traction system, since the net effect on the networks and its connected customers will depend upon the combined effect of the different injections at each instant.
7.3 Measurements
Bearing in mind that the effect of the many distorting sources feeding into a supply network is to cause a rapidly fluctuating mix of harmonic spectra, it is necessary to undertake accurate measurements to determine the true maximum levels of harmonic pollution present. The technology of harmonic measuring equipment is undergoing rapid development, and it is wise to check the market and compare with the requirements of the project, before choosing instrumentation. In a recent project in London, the selected equipment simultaneously read phase currents and voltages, and digitized its readings into 256 segments of every fundamental cycle. It used a fast Fourier transform to calculate the harmonic currents and voltages. Analysis of readings over a significant period enabled the worst levels of pollution to be selected as the basis for system studies. Further testing was undertaken to check performance after connection of the new loads, both to ensure limits were maintained and to check the accuracy of the computer predictions of the design studies. In order to be sure that system performance could be correctly related to load behavior, the use of GPS techniques was necessary to ensure highly accurate timing of simultaneous readings.
Guidance on measuring techniques is provided in IEC 61000-4 and IEEE 1159.
8. CASE STUDIES
There are now many published case studies, examples of which are given in Refs. [13] and [15]. A whole series of worked examples are provided in IEC 61000-3-6.