Power system harmonics Part 41 Interharmonics.pdf

power system harmonics part 4 1 interharmonics the fourth part of this tutorial series deals with interharmonics those frequencies generated by large converters which are not integer harmonics of the supply frequency previous parts of the series have covered harmonic sources measurements calculations harmonic problems and harmonic reduction by r yacamini lnterharmoniics the term interharmonics covers a wide range of frequencies generated by converters which are not integer harmonics of the fundamental frequency part 1 of this series august 1994 pej dealt in some detail with the integer or characteristic harmonics which are often 3rd 5th 7th 11 th and 1 3th harmonics of the fundamental interharmonics cover all other frequencies present in the spectrum of for example large variable speed drives the presence of interharmonics has become of increasing importance as motor drives and converters have been developed into the megawatt range such frequencies have been found in for example large variable speed drives of the dc link type be they current fed or voltage fed inverters cycloconverters kramer drives traction drives especially those using three phase ac motors and also high voltage direct current transmission systems appear where two ac systems running at different frequencies are joined together through some form of dc link the problem arises if the systems are not perfectly decoupled through the dc link a critical parameter in the level of decoupling is the dc side reactor the interharmonics will be present in both ac systems so that in for example a drive the feeding ac system and the motor will experience interharmonics another feature of such circuits is that frequencies can be generated which are below the fundamental these are sometimes wrongly called subharmonics a quick test which can be carried out to determine the presence of interharmonics is to set up the system to run in the steady state and to examine the ac currents using an oscilloscope not a digital storage scope see part 2 february 1995 pej if the current is not steady on the screen if its amplitude in the majority of cases the interharmonics appears to be changing and if you can see a ripple running across the tops of the current pulses then there is a good chance that the converter system is producing interharmonics the other possibilities are control system instability or poor measurement techniques i nterha rmon ic generation the rippkwhich is seen on the ac current associated with a converter can also be seen on the dc sicle of the converters it is the non perfect dc side voltage generated by each converter which produces ripple on the dc current the ripple on the dc current mixed with the non linear nature of the ac current is the source of the interharmonics the method of describing these used in this tutorial is based on the fact well known to practising engineers that aydc converters when excited by a frequency on the dc side have the property of producing sidebands of the frequency on the other side an example is that a 200 hz ripple on the dc side of a 50 hz converter will produce 1 conventionalview of six pulse converter power engineering journal august 1996 185 2 six pulseconverter predominantly 150 and 250 hz on the ac with direct current and firing pulses as input 3 switching function and modulating function input to converter side this can be shown experimentally it can also be shown experimentally that this single harmonic on the dc side will in fact produce other harmonics as sidebands of the theoretical harmonics on the ac side i e sidebands of the harmonics of order 6k 1 for a six pulse bridge these facts lead to the idea that the bridge is in fact acting as a modulator of a type which has been well known to telecommunications engineers for a long time it is conventional to draw a three phase bridge as shown in fig 1 the bridge operates synchronously with the ac system using the firing order as shown in the figure the bridge produces a current waveshape on the ac side which contain harmonics of order 6k i 1 and the current on the dc side is smooth assuming an infinite dc reactor the ac is in fact synchronously sampled portions of the dc current inputs produce an alternating current as illustrated in fig 2 it should be noted that any overlap angle will tend to reduce the amplitude of the higher order harmonics the same figure can be redrawn as a telecommunications engineer would understand it as being a combination of a switching function amplitude unity and a modulating function which in this case is the smooth direct current this is illustrated in fig 3 if now the dc has ripple superimposed on it the diagram would be as in fig 4 the alternating current now does not have the previous smooth appearance but contains ripple as sampled from the direct current the output is said to be modulated the system illustrates the case which was described in the introduction where the naturally commutated converter is fed with a direct current containing ripple analysed using a fourier series and can be shown to be represented by the series the switching function s t shown can be 1 1 1 11 13 17 where k 2 3 z and w is the angular velocity of the commutating ac system the modulating function i t can be expressed in general form as the sum of the direct current and superimposed sine waves cos1 icolt cosl301t cos1701t 4 1 1 wherea is the peak magnitude of sinusoidal components on the dc side w can have any value and is not necessarily an integer multiple of wl by modulation theory the output of the bridge in this case the alternating current can be found by multiplying the switching function by the modulating function ia these include cycloconverters kramer drives and traction locomotives fed both from high voltage ac lines or dc trackside systems cycloconverter interharmonics are well explained in the book by pelly4 which is the standard text on the subject the book contains charts which show that the input and output interharmonics will vary as the motor frequency varies a simplified version of this type of chart is shown in fig 9 this shows the interharmonics present in the motor as the output or motor frequency is varied as an example if the output frequency were 10 hz and the input frequency 50 hz the ratio horizontal axis would be 0 2 the interharmonics can be identified by drawing a vertical line there is group arouncl 300 hz and another group of sidebands around 600 hz all of which will give oscillating torques on the motor shaft similar charts can be found for a wide range of pulse numbers in reference 4 both input and output interharmonics are shown the normal range of output frequency ratio of a cyclo is 0 to 0 33 approx variable frequency drive which will produce interharmonics fig 10 shows a simplified equivalent circuit the rotor winding is connected to a rectifier through a set of slip rings and slip energy is fed back to the ac system through the three phase inverter because the rotor will be running at variable speed the frequency of voltage supply to the the previous section described the the kramer drive is another form of power engineering journal august 1996 189 7 equivalent circuit the transformers will therefore be comdex showing sources of harmonic voltage and will be a function of all three switching freauencies the 50 hz of the sinale dhase ac kystem the chopper frequenpy a ad the motor speed and hence frequency a more detailed discussion of the subject can be found in reference 6 again the size of the dc reactor will be a significant parameter in determining the level of the interharmonic interference other traction converter configurations such as pulse width modulated reversible rectifiers will also produce interharmonics as will chopper controlled three phase motors fed from dc third rail systems this is a specialised subject however and outside the scope of this power systems tutorial lnterharmonic difficulties elusive beast it is of low amplitude and the interharmonic in practice is rather an especially in variable speed drives can drift around the harmonic spectrum changing in amplitude and frequency with varying motor 8 harmonics and interharmonics at motor terminalsforvarying motor frequency operating conditions the maximum amplitude that the sidebands can have is half of the dc side current ripple which is carrying the coupling these are the sidebands of the fundamental see eqn 6 the sidebands of the harmonics have an even smaller amplitude the effects have however been around for some time and tend to manifest themselves in systems where there is resonance especially with low damping or high q factors an example of such a coincidence which put a 775 mva turbo alternator at risk can be found in reference 7 the kramer drive illustrated in fig io was being fed from a 10 5 kv busbar i n a power station to drive a boiler feed pump of 15 mw rating the inverter fed slip recovery energy back into the 10 5 kv bus which was also supplying the motor this recovered energy is rich in harmonics and interharmonics which will vary with pump speed it was found that some of the interharmonics were then penetrating the synchronous generator and producing sideband torques on the generator shaft8 again these are sidebands of the fundamental frequency in this and motor drive applications the converter can be thought of as a modulator and the machine as a demodulator normally torques of this type which are of low amplitude are of little consequence unless as occurred in this case they happen to coincide with one of the shaft natural frequencies in the turbine alternator system a feature of such systems is that because of the relatively high number of masses on the shaft and the length of the system there will be several natural frequencies typically in the 5 20 hz region another feature is that these mechanical resonances have an extremely high q factor in the example in question it is 190 power engineering journal august 1996 stated that an interharmonic of only 350 kw was sufficient to put the shaft of the 775 mva generator at risk due to fatigue failure recent work by the author and colleagues suggests that the damper cage of the generator will be the parameter which determines the level of stress experienced by the shaft the solution to this problem was to identify the pump speeds which coincided with excitation of the shaft resonance and to put narrow deadbands in the pump speed capability interharmonics concerns the possibility of shaft damage in drive motors this is one of the mechanisms by which shafts on for example large fans can be broken from the previous analysis it can be easily shown that harmonics of order another problem area caused by freauencies for a 2000 mw scheme this 9 lnterharmonics at woild be a potential interharmonic power of jed 2 mw this is much higher than the 350 kw motor generated by the kramer drive discussed previously which put a large turbo alternator at risk a more detailed algorithm which deals with the interharmonics caused by unbalanced ac systems and the effect of overlap can be found in reference 1 1 10 slip energy recovery kramer drive in a power station direct current as an interharmonic an interesting special case in the harmonic series is when a converter can produce direct n 6kz 1 fi i 6k1 f l 9 will be generated at the motor terminals where k and kz are integers and f l and f i are the frequencies of the ac system and the motor respectively as shown in fig 12 an example from an actual operating system is shown in fig 13 this shows the richness of current spectrum when a motor is fed at 39 4 hz if the torque associated with one of the harmonics or interharmonics should coincide with the natural frequency of the motor shaft load mechanical system then shaft damage is a possibility a possible source of interharmonics in reference 10 it is suggested that interharmonics of 0 1 of rated current can be expected in hvdc schemes where the two ends are working at even slightly different power engineering journal august 1996 high voltacie dc transmission systems are 191 11 power electronics on a tgv atlantique locomotive feeding two three phase svnchronous motors 12 naturally commutated motor drive current at its ac terminal due to modulation of ripple current examples of this can be seen in fig 8 four of the interharmonics will produce direct current at the terminals of the dc reactor co variaole freqwncy moior o h ac system rcctlfler invefier motor all at different motor fundamental frequencies the easiest to analyse is that described by line 1 this shows that if the rectifier is at 50 hz and the motor fed at 60 hz the 300 hz rectifier dc ripple will give a sideband of the 5th motor harmonic also 300 hz this sideband will have zero frequency modulation products k jand h will similarly produce dc at the motor terminals it is a simple exercise to show that dc can also be produced at the rectifier terminals it is well known that direct current can be used for the rapid braking of ac motors it is unlikely that the dc produced by intermodulation will ever brake a motor but reduced performance is a possibility hvdc schemes have in the past produced small values of direct current at their ac terminals due to this and other reasons this has resulted in saturation of the converter transformers and the resulting production of non characteristic harmonics including all the even harmonics modern transformers especially amorphous core types have very high levels of permeabilitywhich will make them very sensitive to even very small levels of dc a detailed examination of the subject is outside the scope of this tutorial reduction of interharmonics the following will reduce the interharmonics produced by dc link systems 192 power engineering journal august 1996 1 av 0 overlap fundamental frequency 39 375 hz loo i 0 6 d 0 6 m z x n i ro cu w u n 50 100 150 200 250 300 350 400 450 500 hz june 1994 pp 143 152 december 1994 pp 275 286 sabate v electrical disturbances generated by railway traction gecalsthom review 6 1991 5j pp 11 2 conclusions 7 fick h excitation of subsynchronous as conventional six pulse and 12 pulse converters get larger there is a possibility that interharmonic problems will increase using conventional rnodulation theory it is possible to predict the frequency of interharmonics accurately amplitude calculations will b