Harmonics in India

by - Mr D M Tagare, MD, Madhav Capacitors Pvt Ltd

A Power Generator rotating at a synchronous speed produces electric voltage which varies as a perfect sine wave at 50 cycles/second. As this power flows along different systems to the ultimate apparatus, the perfect sine wave gets distorted. The distorted wave can be mathematically considered as the basic sine wave with numerous other sine waves of differing frequencies & amplitudes super imposed upon it. If this analysed portion has a frequency which is an integral multiple say 'n' of the fundamental frequency i.e. 50 Hz, then this frequency is called the nth harmonic & so on. This harmonic has distinct disadvantages & can be segregated to get rid of its ill effects. The predominant harmonics which occur frequently & are trouble some are the 3rd, 5th, 7th, 11th & 13th. We also run into the second harmonic occasionally.

Let us next consider the basic factors which contribute to the generation of these harmonics. Of the four basic electric components, resistances & capacitors are passive components i.e. they do not generate e.m.f.s. They modify the outputs of the applied voltages in phase & applitude. On the other hand, Inductances & Switches are active components. The magnetic fields associated with inductances influence the output due to applied voltages to the extent they can produce distortions in phase, amplitude as well as in frequencies. In other words they can act as harmonic generators. Under electrical switching, we can group all aparata hich can disrupt an applied voltage at any instant on the sine wave e.g. Rectifiers, Thyristors, Solid state switching devices, an arc in an arc furnace which will break-down at any instant, uncontrolled arcing between contacts & between live points & earth & so on. Thus a square wave generated by a solid state circuit or a sine wave started & cut off at its intermediate points, can be analysed as so many harmonic waves superimposed on one another to give a final output, such as a square wave etc. A sharp rising & diminishing surge across a line, can be considered as a grouping of very high frequency sine waves superimposed on one another.

One might conclude that the superimposed group of harmonic sine waves which produce in practice a distorted, sliced or spiked wave exist only on paper - as a theoretical explanation. Not quite so. In practice, the effect on various electrical apparata is, as if a separate harmonic distinctly existed.Consider a capacitor, for example, subjected to a distorted wave shape with a large proportion of 3rd harmonic. The output of a capacitor is given by

kVAR = KV2 x 2nfC x 10-3 where C is in Mfd.

For the same voltage, if f becomes 3f, then kVAR 3f is 3kVARf. The losses in a capacitor are given by KW = kVAR x Tan Delta. Thus for a 3rd harmonic, the losses will become 3 times. The capacitor will get much hotter if a considerable 3rd harmonic exists - since it now produces a basic kVAR at 50 Hz plus a high kVAR due to the 3rd harmonic. Its life will be reduced & it will fail peraturely.

Let us further consider the case of a spike or a surge entering a capacitor. The capacitor has a very low, limited life against this abuse, since the dielectric cannot withstand the high rate of dv/dt repeatedly. As we traverse from 50 Hz to very high frequencies, the capacitor life reduces. This logic should hold good for higher harmonics as well.

Similarly a HRC Fuse will blow much more frequently if the current contained fairly large harmonics. One can safely take frequent blowing up of fuses on apparently healthy capacitors as a sign of existence of large harmonics.

Nowadays computerised controls are being extensively used in steel mills, chemical plants & almost every industry which can drive economic benefits from these. Many circuits in these are beased on detecting the start of a voltage/current! wave on the 50 Hz scale. Should a harmonic exist, which at any instant on a 50 Hz sine wave, has a magnitude equal to or greater than that of the fundamental at that instant, the actual voltage/current will cross zero & come up again. This will trigger the computer circuitry falsely & lead to chaos. Thus filtering out all types of harmonics on the supply lines to computerised controls becomes a high priority.

In a rotating machine the slot insulation is a critical factor due to very limited space available. Harmonic currents raise the conductor temperatures to uncomfortable levels for the partition to withstand on a long term basis.

Thus excessive harmonics into or out of a rotating machine will lead to frequent & permature winding failures. The harmonics must be filtered out.

A summary of other major ill effects due to harmonics is given below :

1) Inductive coupling with unshielded or open telephone carries can make conversions impossible due to harmonics in the power carrier.

2) Interference with video signals as evidenced by bright light shafts traverse slowly upwards. Voltage flicker due to operation of induction furnaces makes it impossible to view TVs.

3) Rotating Discs in a meter or a protective relay are influenced by the magnetic field produced by the mains currents at 50 Hz. Harmonic can cause phase unbalancing. All this leads to wrong meter readings/relay operations.

We have to study of two aspects of harmonics :-

1) How & where they are generated in practice &

2) How they are likely to be amplified. These two could be amplified.

Power Transformers are the single biggest contributors to harmonic generation in India today. The EMF generated in a transformer winding is equal to the line voltage minus the voltage drop in the primary impedance. On full load, this EMF lies on the straight portion of the B-H curve due to a sizeable voltage drop across the primary impedance & consequently a lower EMF. On no load, the voltage drop across the primary impedance is comparatively low & the EMF being higher, moves further up across the B-H curve. In a tightly designed transformer, the point lies in the saturation bend & this generates harmonics. In addition to this, if this transformer on no load has a few permanently connected capacitors, then the leading current of capacitors cancells out all the primary impedance voltage drop & the EMF tries to rise still further. While the voltage rise on secondary is marginal, haronics are produced in abundance, over loading the capacitors. Further if capacitance cancels out the transmission line impedance to some extent, then the short circuit MVA level at the capacitor point rises considerably, leading to instability. A chance surge on the line will get amplified & will vibrate for a longer period putting the capacitor- as well as the transformer in jeopardy. By arranging the transformer winding in star delta, the generation of the 3rd harmonic can be limited - but not of that other harmonis. In case of single phase transformers with one grounded terminal - as used in the railway A.C. traction, the situation on harmonics becomes worst.

The harmonic generation due to saturated cores of a transformer is voltage based - i.e. the harmonic voltages are constant - but not the power or the current amplitudes. Consequently accurately tuned filter capacitor banks will amplify the harmonics to uncomfortable levels here. A slight detuning will absorb the harmonics, at the same time not amplifying those.

The second most trouble- some source of harmonics are the steel-melting Arc-Furnaces in India. A number of phenomenon are heaped together. First there are the arcing frequencies. Secondly there are heavy surges when the entire currents are cut-off for example when a melting mass sinks down suddenly & losses arc contact or even when the electrode itself breaks or detaches.

Thirdly the transformer core in series with the inductance of the melting mass, gets saturated & produces harmonics. The spread of these harmonics to some extent depends on the composition & density of the melting mass as well. Well established furnace manufacturers have data collected & categorised on harmonic generation under various conditions & for different furnace designs.

This data is useful in designing the overall capacitor installation as well as the filter banks for an Industrial Arc Furnace. Here again, the harmonic generation is voltage based. This together with the presence of a no. of frequencies, leads one to prefer wide-band filter circuits as against accurately tuned filter circuits.

Although we have not gone in for solid state controlled equipments as extensively as the western countries have done, these drives are being set up in large sizes & more quantities now. These include electro-chemical power supplies, adjustable speed drives-both D.C. & A.C., uninterrupted power supplies & so on. By controlling the switching actions on a fundamental A.C. sine wave at 50 Hz., they affect the power factor in two ways :

1) The displacement component of the power factor gives the ratio of controlled active power to the total supplied apparent power at the 50 Hz. This introduces harmonics.

2) The distortion component of the power factor arises out of wave shaping of the voltage & current to be used further. It is associated with the harmonic voltages & current generated & transmitted backwards into the network.

Harmonic generation arising out of switching actions is mainly current based in that the maximum harmonic current supply in capacity of the source is limited.

This results in several characterstics :

1) The fixed reactive power requirment is determined by the operating point & can be predicted. Fixed capacitors can cater to this requirments.

2) The harmonic current requirment for various harmonics can be calculated. This helps in designing finely tuned filter capacitor banks for various harmonics accurately. The harmonics are not amplified beyond the capacity of the generating source. IEEE Specifications 519-1981 discuss the Hamonic Control & Reactive Compensation of Static Power Convertors in great detail.

The chokes of all varieties used on fluorescent tubes in Industry contribute perceptibly to voltage distortions. Their effect can distinctly seen on the oscilloscope voltage waveform - during evening as the lighting load keeps on coming.

We have presently only one HVDC transmission system in India. As these systems appear, they will have to be fitted with suitable, large filter capacitor banks to avoide system voltage distortions.

Harmonics can easily be detected with an oscilloscope probes across the ammeter terminals inside a metering panel. There is no need for opening out any circuits. The voltage harmonics can be detected by putting the probes across a voltmeter & adjusting the oscilloscope range. This show the wave shapes & a preliminary idea of distortions.

Accurate measurments can be made with a calibrated oscilloscope or on a regular harmonic analyser equipment. These measure the 3rd, 5th, 7th, 11th & 13th harmonic contents independently.

This brings us to various definitions so that we can define & tackle the harmonic problems.

The current & voltage parameters are generally measured as percentages of harmonics RMS to the basic RMS values on a harmonic analyser. These can also be measured as abolute RMS values. On an oscilloscope these can e measured as peak values.

The filter bank balances the capacitive & inductive voltage drops at the tuned frequency. As a result if one measures the input voltage to a filter bank. It will mainly read the fundamental voltage & lead us no where with respect to the harmonics. Therefore the starting point has to be the current measurment.

The total current

IF = V (I21 + I2h)I1 = Fundamental RMS current &

Ih = Total harmonic current at the tuned frequency = sum of Ih of all convertors connected.

Let Xc = 1 = Reactance of the capacitor at the fundamental frequency.

XL = 2"fL = Reactance of the inductor(reactor) at the fundamental frequency.

Then I1 = Vs/Xc=X1 Where Vs = System Voltage at fundamental frequency.

Then Voltage across the capacitor = I1 Xc1 + Ih Xcn = Vc.

& Voltage across the reactor = V1 = I1 Xl1 = Ih Xln

I & H suffices indicating fundamental & harmonic frequenncy values. Then kVAR rating of the capacitor = Vc x IF x 10-3/phase at the given current IF.

Similarly, the kVAR rating of the series reactor is given by VLIF x 10-3/Phase.

1) As per IS-2834, the above rated kVAR can be upgrated by 135% to comply with the requirments of overload capacity of a capacitor.

2) Unlike the fixed p.f. improvement capacitors, where IS-2834 standardises voltage & kVAR ratings on the basic units, this cannot be done w.r.t. capacitors designed for a filter bank.

3) The filter capacitors cannot be designed accurately at the rated voltages since this will have a bearing on the nearest dielectric thicknesses, commertially available. Then if the revised design voltage under the considerations (for a safe volts/micron stress) is Vd, the kVAR rating of the capacitor will become Vd/Ve2 x kVAR as calculated (i.e. Ve x IF). The costs will go up if compared on the previously rated kVAR basis (i.e. Ve x IF).

4) While carrying out the factory testing for thermal stability, one will have to superimpose the fundamental testing voltage with the designated harmonic at 1.2 times the rated value. This is impractical. Hence the testing voltage at 50 Hz will have to be so adjusted that it will give the required total kVAR load on capacitors. If Vt/1.2 is equal to or less than Vd under (3) above, then there is no problem. Otherwise Vd will have to be upgraded so that Vd = Vt/1.2. This contingency should not normally arise - uless the high harmonic currents are very large w.r.t. the current It.

5) The filter bank contributes a kVAR at fundamental frequency to the system. This value must be deducted from the requirment of the fixed capacitor bank. It is given by kVAR = I2l (Xcl - Xll) x 10-3.

6) IEEE std.519 lays down the maximum, theoretically possible harmonic current in the power supply feeding a 6-pulse convertor as below :

Harmonic Order	5	7	11	13	17	19	23	25
Harmonic Current magnitude	0.200	0.1429	0.0909	0.0769	0.0568	0.0526	0.0436	0.0400

 

The convertor, acting as a source of constant current for a given harmonic & given set of load conditions, establishes a harmonic voltage Vh = 1h x Zc at its terminal. This voltage has several branches in parallel as shown in the above diagram.

Let us first consider the incoming line to the installation, represented by two impedance ZTRL & ZTX in series. These are mainly inductive. The voltage V1 will send a harmonic current Vh(ZTX + ZTRL) into the supply & cause nuisance to other consumers on the line.

In case the filter impedance Zf(Lf + Cf) tune to this harmonic, its value is almost zero & Vh will fall to zero - putting out maximum possible current into the filter. In that case, no harmonic current will flow into ZTX + ZTRL. Let us consider a likely condition where ZTX + ZTRL resonates with the impedance of the capacitor branch (Zf + Zc) in a parallel at a certain harmonic. Then very high harmonic currents will circulate between the two systems, causing serious consequences.

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