Power measurement and its theoretical background ∫
Contents
1. ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 reer ZSS ZIMMER The power waveform can be described with following formula Das Beck ra a l 1 p t 1 sin at g u sin at 1 u G cos o P g S 0 Formula 16 power waveform of same frequent signals As told above see Formula 11 the active power is the average value of the power waveform While taking a look to the above formula you see that only the term aan l euS ROR P has an average value which can be different from zero This depends on the phase angles of the voltage and current signal The other term i a costar 9 can never produce an active power because it s average value over one period is zero The first term can be modified to give you a common known formula P siar coslo 2 J2 J2 P P I U cos g Formula 17 Active power of same frequent signals Pay attention that this formula is correct for voltage and current components with same frequency only 2 Rule Components with different frequencies will produce distortion reactive power Again the power waveform can be described with following formula p t i sin t 9 a sin a t anal l 1 arf eso t Q O CO t a Formula 18 power waveform of different frequent signals In this case you see that the first term as well as the second2. 1 U u t dt PE 2 Formula 1 General definition of the DC component t tl Of course this definition is also valid for pure DC signals By this definition the user can choose any time interval to get a DC value But in practice you have very often periodic signals These signals are repeated after the period time T So if T is included into Formula 1 for the time interval the commonly known formula appears 1 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 ante ZSS ZIMMER 1 T U u t dt ae 7 Ju Formula 2 DC component of periodic signals Conclusion e The DC component is the average value of a signal e In practice you have to define a time interval for a DC value Rectified values The rectified value is usually an historical value Today there are very few applications in which it is needed for example U is proportional to the magnetic flux B This is important in some transformer applications The rectified values were created when the first AC signals appeared At this time there were many moving coil meters used But they measure just the average value DC value which is zero for sinusoidal signals The first simple way to solve the problem was to rectify the signal and to take the average value of the rectified signal 1 t2 Unser mo dt Formul
3. All other total values are invalid Derivation Following you find the very much simplified deviation for the measuring method P U 1 U 1 U I U U U gives U U U likewise U U U gives you U U U If you insert this in above formula you get Pe ht U gt e047 h U htu P U 71 U l U 11 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER In a three wire system the vector sum of the currents must be zero 1 1 1 0 which gives you Pe 71 tUs h That s exactly the measuring condition which was described above Of course this derivation can be done in a universal way Special features in LMG450 As a special feature the LMG450 calculates the third not measured current in phase 2 and the third not measured voltage U This values are correct the power values and other derived values not see above With the option star to delta conversion the wrong values of aron circuit can be recalculated to really existing star or delta circuit values As a result you get active reactive and apparent power as well as power factor for each phase as well as for the total system Measuring delta voltages and star currents A very typical situation when measuring motors is that you have only L1 L2 and L3 to the motor but no neutral conductor So without addit
4. common factor E g for f 50 Hz and f 50 2 Hz the result is T 10 gcd 500 502 5 s 9 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER The total or sum active power is the simple sum of all phase active powers No problem so far With the apparent power we face the first problem This is not any vector Only the apparent power component which is caused by the phase shift see the dashed line in Figure 1 Graphical relation of the different powers could be added as two dimensional vectors But there is also a component caused by distortion reactive power which is not a vector So it s wrong to just add the apparent power of different phases It s also wrong to add them as a two dimensional vector The same problem happens with the reactive power There is an important difference between Qpe and Que A further problem and it s solution could be explained very easily by the power factor In general it can be said that the power factor is a value which expresses the usage of a power distribution system If you have any kind of reactive power independent if phase shift reactive power or distortion reactive power you will get a value smaller than 1 Also in a three phase system you will get a total power factor smaller than 1 if you have just ohmic loads which are not equal In this case you have not use
5. larger you might get aliasing which means you see signals at wrong frequencies with wrong amplitudes In practice the standard IEC61000 4 7 defines a rejection of 50dB as sufficient to get no aliasing In principle there are two possible ways to meet this requirement 14 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER e The uncertain way is when a signal has a theoretically small bandwidth Typically AM radio stations transmit with low bandwidth This may cause aliasing due to coupling e The safe way is to use an anti aliasing filter inside the instrument This also rejects the components which are coupled externally into the signals The instrument itself is shielded so that no problems occur This anti aliasing filter in the instrument we call it a HF rejection filter is automatically used inside the instrument if you select a harmonic mode Of course this filter has not an infinite steepnes Odb lt 50kHz 50dB gt 50kHz So you can measure harmonics up to about 10kHz In the range from 10kHz to 50kHz the filter derates down to 50dB Reactive power of a non linear load supplied with a sinusoidal source Two methods of measuring reactive power are shown one using the original distorted current signal the other a filtered current signal In this example the device under test is a LMG95 mea
6. source This energy is reactive energy If you measure with cycles of 1s you measure the transfer to the motor while start up as well as the transfer from the motor while stopping as active energy because your defined time is not long enough to take the shut down into calculation So while measuring non periodic signals there is a possible error Of course you can measure many short sequences of TRMS and active power values This values are correct in the defined time which is the measuring time Only the user can decide if some of the power will return later Power factor The power factor is the ratio of active power to apparent power l S Formula 20 power factor A second value which is very often confound with the power factor is the cos It has the same definition but it is only valid if voltage and current are both sinusoidal Therefore the power factor is a more general definition Sometimes the cosine of the angle between the fundamental voltage and the fundamental current is sometimes called Displacement Power Factor DPF The above ratio between P and S is sometimes called True Power Factor TPF Multi phase systems Total sum values All the above values for a single phase are well defined For example in a three phase system the situation becomes more complex gcd is the greatest common divisor This function is only defined for integers If otherwise then the fraction has to be multiplied with a
7. source and so the same like in the first set up Filter 5 Crl 38Hz AC DC UI a e Extn Figure 5 Filter settings 16 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER To filter the distorted current input signal we selected the above shown filter settings paas kz2 x dive5 000 me Figure 6 Filtered current input signal Now the current wave form is now nearly sinusoidal because all harmonics with order gt 2 have been rejected Itrms 67 664 mA Utems 219 818 U 14 2390 U 14 6882 Ua 3 6647 var F B 96942 C 49 9997 HZ To 4 Figure 7 Measured values Due to the filter the fundamental components are a little bit smaller As you can see the active power P is nearly as large as the total absorbed apparent power S Now the only measured reactive power Q is caused by the phase shift between voltage and current This is nearly identical with the value Q 3 7961var calculated in section Measurement with a distorted current signal The distortion of one input signal may cause a very large apparent power To calculate the distortion reactive power D you need two different values of reactive power Q The first needs to be measured with the distorted input signals what means the total reactive power with the two parts
8. term will have an average value over one period of zero So both terms can never produce any active power just distortion reactive power The maximum period time of this signal can be calculated according to following formula 8 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER 1 1 7S gcd f fa Formula 19 power waveform period time of different frequent signals In all the above definitions we talked about a defined time With periodical signals this time is an integer number of complete periods because after a complete period the signal is periodical and the values of different measurements are identical If you would not measure for a complete period the resulting values are not the same in the next measurement If you use more than one period for measuring you can get an averaging over this measuring time For this reason you can set up a basic cycle time in the ZES ZIMMER instruments This cycle time determinates the average over some periods Non periodical signals like starting characteristics are not that easy to measure because it is very difficult to determine the defined time For example if you start up an elevator you transfer energy to the motor which is the load Now the motor runs for some minutes and is stopped then While stopping the motor recovers some energy to the
9. to the RECT value U aus Uy U pecr Formula 5 Definition of the form factor For sinusoidal signals it is about 1 11 RMS values If you have any voltage or current signal and apply it to an ohmic resistor you will have a loss power in this resistor The problem is that every different wave shape will produce another loss power so you would have to define endlessly allowed wave shapes which will not overload the resistor The definition of a wave shape might be quiet complex You need a drawing or a mathematical description For a more practical solution it was tried to describe a wave shape via the power This is the most general definition of the root mean square value The RMS value of a signal is the amplitude of a DC signal which will transfer the same energy like the applied signal into an ohmic resistor in the same time As a formula you could use in this example we use the voltage If you want to use the current you get the same result U aba u t RMS 2 1 us 22 11 tl dt 1 t2 U u t at a iat l Formula 6 General definition of the RMS value Using this definition you can choose any time interval of any signal to calculate the RMS value If you would apply in the same time interval a DC signal with the amplitude of the RMS value the same energy would have been pushed into the resistor In this definition the user can choose any time interval to get a RMS value But in practice
10. very often you have periodic signals These signals are repeated after the period time T So if T is included into Formula 6 for the time interval the commonly known formula appears T 1 Uprus uty at T t 0 Formula 7 RMS definition for periodic signals 3 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 evi ZSS ZIMMER The advantage of this formula is that you get the same value for each period So it is sufficient to give one single value to describe a signal concerning it s power consumption in an ohmic resistor This is valid for 99 of all measuring applications Keep in mind that this is a simplified definition for periodic signals Sometimes it is difficult to find the correct time interval of a signal or the questions arises What is the true time interval This depends very much on your application Conclusion e The RMS value is proportional to the power consumption in an ohmic resistor e Usually it is defined over one period of the signal e Other time intervals might be possible TRMS values In theory the RMS and the TRMS true RMS value are of course the same In practice there are different measuring methods e Some older analogue instruments just measure the rectified value and multiply it with the form factor 1 11 to get the RMS value of the signal This is only valid when t
11. 0 9371 usa zes com Application Note 105 anid ZSS ZIMMER Crest factor The crest factor is the ratio between peak value and TRMS value of a signal U Uy a TRMS Formula 8 Definition of the crest factor For analogue instruments a maximum crest factor is defined If the signal has a larger one you might get measuring errors For digital instruments usually you find two values for a measuring range in the technical data of the user manual The nominal value e g 250V This can be used to select easily the correct range The other value is the allowed peak value in this range e g 400V With these two values you can calculate your actual allowed crest factor In this example it would be 400V 250V 1 6 If you apply in the same range only a 180V signal a crest factor of 400V 180V 2 2 is allowed So the crest factor is not that important for digital instruments as for the older analogue ones because you can influence it Definitions of power For power measurement it is important to take first a look at the energy In a simple system you have a source and a load Now you can transfer electrical energy from the source to the load This energy can be absorbed or converted to another kind of energy light heat rotation This is called active energy Beside of this it can be stored and returned to the source later This is called reactive energy Power is defined by energy transfer per time So in a defined time you can transfer powe
12. Application Note 105 peer ZSS ZIMMER Power measurement and its theoretical background This is a short description of some well known values which are very often used but in fact only very few people can remember where they come from and what is their exact definition DC values Pure signals The most simple case of a signal is a signal which doesn t change it s amplitude in any time interval The definition of a DC signal is quiet simple A DC signal has always the same amplitude In theory the always is running for an infinite time So in practice you define a time interval and say A DC signal has during a time interval the same amplitude For example this time interval is defined by the time a signal is applied or by the time you need to measure the signal Mixed signals There is another possible definition for a DC signal or better the DC component of a signal As you know you can split every signal according to Fourier into many sinusoidal signals of different frequencies amplitudes and phase shifts One special case of this sinusoidal signals is the DC part of a signal which could be described as a cos function with frequency 0Hz According to this the definition of the DC component is just the average value of a signal As a formula this can be written as in this and all other example we use the voltage If you want to use the current you will get to the same result t2
13. IMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER The fastest time is the time between two sample values This time depends on the number of conversions per second For example at the LMG95 we have about 100000 conversions per second for each voltage and current channel and so every 10us we see a new sample value Synchronisation You have to choose which signal you want to synchronise Why do you have to synchronise at all As described for example in section RMS values were the values are defined for a defined observation time For periodic signals this is the period time of the signal or multiple of period times So the instrument has to measure for a multiple number of periods of the signal In the LMG series usually the positive zero crossings are used to detect the end of a signal period Cycle time The cycle time defines after which time you want to get measuring results As written above the instruments measures for a multiple number of periods How you can handle this Let s assume you have a 50Hz signal 20ms period time and a 50ms cycle time Exactly when the cycle time starts you have the start of a 20ms period too The instrument starts measuring After 50ms the cycle ends The instrument has measured from t 0 to t 40ms exactly 2 periods of the signal This values are calculated to all displayed values
14. Qy D and Qpa The second measurement needs to be performed with filtered input signals Now the distortion reactive power Q or rather D becomes zero no harmonics what means Q is equal to Q With the following formula you get the correct value of D 4 Q Qin Q measured without filter Qng Measured with filter shift Note This works while only Q remains after filtering An example in which this does not work follows below With the LMG95 you can measure the correct value for D directly with the HARM100 option refer Figure 4 Power values in HARM100 mode 17 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER Measuring of a burst firing control signal of a heat gun The following breadboard will describe the difficulties of measuring the correct values of the different kinds of power You will find a lot of the above theoretical explanations here in a practical application Experiment The breadboard set up is shown in the picture below Hot Air Fan LMG95 Mains Supply Figure 8 Breadboard set up Time signal The following figure shows the time signal of the absorbed current The peaks show the current which is needed to heat the heating coil The signal before and after heating is the one way rectification current of the fan motor The signal c
15. a 3 General definition of the rectified component By this definition the user can choose any time interval to get a RECT value But in practice you have very often periodic signals This signals are repeated after the period time T So if T is included into Formula 3 for the time interval the commonly known formula appears 1 T Urr fluc ar t 0 Formula 4 RECT component of periodic signals The disadvantage of the rectified value is For many applications you need a value which is proportional to the power which will be absorbed in a resistor see RMS Values For this you can calculate a proportional factor between the RECT value of a signal and the RMS value of a signal This factor is called the form factor The form factor depends very much on the wave shape of the signal So in the scale of the moving coil instruments the form factor for sinusoidal signals was integrated For other wave shapes you get measuring errors 2 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 ania ZSS ZIMMER Conclusion e The RECT component is the average value of the rectified signal e In practice you have to define a time interval for the RECT value e For every wave shape the RECT value has another proportional factor to get the RMS value Form factor The form factor is just the ratio of RMS value of a signals
16. an be interpreted as an amplitude modulated 1 5Hz rectangular signal with a 50Hz carrier frequency with neglect of the one way rectified current 0 45009 5 x2 50 xdi 200 0 Curs dx dyi B 63897 5 S21731m Figure 9 Measured time signal Optimal equipment for measuring the different kinds of power is the ZES ZIMMER LMG series with option HARM100 The cycle time is the largest issue you can face while using ordinary instruments The rectangular signal above has a period of 639ms measurements with a cycle time of 1s which means 1 to 2 beats will get very fluctuating measurement values of the power The problem was the trigger on U or I frequency Because of the amplitude modulated signal the baseband signal 1 5Hz is not existing hence triggering with common used filters is impossible The LMG series provides a special trigger setup to allow measuring AM demodulation Measure menu set up The following adjustments must be set up in measure menu Important Xtrig 18 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 peer ZSS ZIMMER 5 CF1 AC DC Figure 10 Measure menu set up XTrig menu set up To measure the correct values of the different powers the amplitude modulated signal must be squared and filtered with a 30Hz filter the 100Hz squared carrier frequency will be eliminated It is imp
17. c of 1 5Hz fundamental frequency Figure 17 64th harmonic 100Hz means the 2nd harmonic of the fan motor The harmonic analysis shows that the signal will have a very high content of distortion reactive power D because the voltage is about sinusoidal and the current has many spectral components between 0 50Hz and also between 50 100Hz Difference to the normal measurement Line triggered The following figures show the harmonic analysis of the signal triggered with line frequency The first figure was shot while the heating coil was not in operation The DC component is caused by the fan motor 20 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 Rev 20 red azne5 5 eae 59 Figure 18 Measured harmonics triggered with line frequency ZZS ZIMMER E B 13425 kh Q 8 12178 kua VF 6 155606 kVA D 6 13176 kuak mmo m sn 1E 0 00018 ki 8 66878 KUA 1 6 19496 ki 8 19436 KUA 2 6 68885 ki 8 68885 KUA 3 4 88868 ki 8 66861 KUA 4 8 86065 ki 8 68885 kUA Figure 19 Active and apparent power while the heating coil is not in operation In the second figure the ed coil started to heat the current increases Me to 8A gAx 4545 mAediw in oe arga Hz j YZMEo 0 6 24686 A Figure 20 Heating coil in operation Lozak a f 5 LYorB
18. d the system in an optimum way because the load is not symmetrical and one phase has to drive more current than the other ones The power factor of each phase is of course 1 Example Phase 1 230V 1A ohmic load P 230W S 230VA A 1 Phase 2 230V 2A ohmic load P 460W S 460VA A 1 Phase 3 230V 3A ohmic load P 690W S 690VA A 1 Collective sum voltage according DIN40110 2 173 trms Uns YU Legg FU 2 trms trms Formula 21 Collective sum voltage U 398 37V Collective sum current according DIN40110 2 or eee Dame cy trms trms trms Formula 22 Collective sum current L 3 742A Total system 398 37V 3 742A ohmic loads P 1380W S 1490 7VA A 0 926 At this system the total power factor is smaller than 1 because the phases drive different loads Modern ZES ZIMMER measuring instruments work according to DIN40110 2 It s the only standard which describes this kind of systems in a sufficient way Sometimes values like sum voltage or sum current are requested in the meaning like U14 U2 U3 resp I11 12 13 This values have no physical background in opposite to the collective sum current according DIN40110 2 A customer can calculate this values with the implemented formula editor Special wirings star to delta conversion 10 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes co
19. eactive power is calculated as Q y5 P Formula 12 Definition of reactive power The reactive power can have two causes e a phase shift between voltage and current components with the same frequency causes the phase shift reactive power called Qni and calculated as follows Qsit gt I sing i l Formula 13 Definition of phase shift reactive power Phase shift reactive power can only be generated by same frequent voltage and current components e the combination of voltage and current components with different frequencies causes the distortion reactive power called D or Q 6 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 anid ZSS ZIMMER The geometrical addition of this two kinds of reactive power is the total reactive power Q VQ Qin Qin D Formula 14 Definition of total reactive power which is also calculated with the above formula For a better understanding the following figure is maybe useful Figure 1 Graphical relation of the different powers The distortion reactive power D of a system can be calculated with the formula D yS P Qin Formula 15 Definition of distortion reactive power Two simple rules 1 Rule Same frequent voltage and current components can produce active power and phase shift reactive power only 7 22
20. f 200Hz You sample the first period of the sinewave with following results phase angle amplitude 0 0 90 1 180 0 and 270 1 So the sum is zero Now let s take the same signal but a sampling frequency of 40Hz and we take several periods Here are the results period phase angle amplitude 1 0 0 2 90 1 3 180 0 4 270 1 You see you need 4 periods but you get exactly the same sample values Now let s assume a sampling frequency of 28 6Hz 1 0 035s and again we take several periods Here are the results period phase angle amplitude 1 0 0 2 270 1 4 180 0 6 90 1 You see that the order of the sampling values has changed but the sum is the same again You will get the same statistical values of a wave shape independent of the sampling frequency Important is that each point of the wave shape was sampled which might take several signal periods to get this This working principle is called undersampling Coming back to the question the shortest cycle time is 50ms So a 500kHz signal 2us period time is sampled for at least 25000 periods With longer cycle times you also have more signal periods included As mentioned above you have to meet the Shannon theorem if you want to perform a Fourier transformation for example In principle the bandwidth of your signal has to be smaller than half of the sampling frequency So with 100kHz sampling frequency the signal bandwidth should not exceed 50kHz If it is
21. he signal is sinusoidal For non sinusoidal signals you need another form factor e Some instruments measure the AC part of a signal only The DC component produces a power consumption in a resistor too These instruments might display a wrong value if a DC component exists To indicate that an instrument measures the RMS value independent from the wave shape of the signal this instruments call their value the true RMS TRMS value Peak values The definition of the peak value is simple the peak value is the largest amplitude of a signal In practice there are some further definitions usual e positive peak value in fact the largest value of the signal even if it should be negative e negative peak value in fact the smallest value of the signal even if it should be positive e the peak value the largest value of the amounts of the positive negative peak values e the peak peak value the difference between positive and negative peak value The peak value is important for measuring instruments If it is too large for the chosen measuring range it could happen that e analogue instruments could come into saturation which would cause measuring errors e the full scale of the ADC digital instruments could be reached Thereby the signal is cut off which cause distortions and measuring errors 4 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 55
22. ional tools you can measure the voltage U U and U together with the currents I1 I2 and I3 only Similar like in the aron circuit you apply a linked voltage and a phase current to each measuring channel Just with an ohmic load the channel sees a phase shift of 30 With not ohmic loads the displayed active power of each channel can be larger smaller or even negative Worse then in the aron circuit here only the voltages and currents in each channel are correct but all other values also all total values are wrong The LMG instruments offer a so called star to delta conversion If you connect the instrument like mentioned above you can choose two special wirings a 3 1 UAI gt UAIA The values are recalculated in a way to get the values in a delta circuit b 3 1 UAI gt U I The values are recalculated in a way to get the values in a star circuit b is the more common one but both have the same positive result the LMG calculates now values which belong together U I U I and U I respective U L U I and U I Thereby it is possible that all values from all channels including the total values are correct Times In the above paragraphs it was told about a lot of times period time cycle time measuring time Here is the explanation of different times which run in an instrument Combined with this also the synchronisation and some other important things are explained Sampling time 12 22 ZES Z
23. like Utrms Idc P The exact measuring time in this cycle was just 40ms For the second cycle all sample values from t 40ms are taken our instruments measures without any gaps At t 100ms the second cycle ends At this time the period of the signal ends Now the instrument takes the sample values from t 40ms to t 100ms to calculate the values The exact measuring time in this cycle was 60ms Here 3 periods were measured This cycle has had another time interval For periodic signals it is not important because each period is exactly the same Fluctuating signals can have influences on the results You see The cycle time defines how often you want to get values in average The exact time is defined by the synchronisation signal Another important requirement is that the cycle time has to be bigger than the period time It is not possible to measure a 1Hz signal in 500ms Integration time To perform an energy measuring which usually takes a longer time some minutes to several weeks you have to define an energy measuring time too This time has always to be an integer of the cycle time because the instrument can take complete cycles into energy calculation only Observation time for harmonics When calculating harmonics you use the sample values over an integer number of periods The inverse value of this window width is the frequency step size in which the harmonics are calculated Example While measuring a 50Hz signal fo
24. m Application Note 105 anid ZSS ZIMMER While measuring phase to neutral conductor voltage of a phase and with the same power measuring channel the current in this phase you get the power consumption of this phase If you do this with several phases you can get the total values of this system like written above However there are some applications where you have no access to the neutral conductor For these applications you can use special wirings and features of ZES ZIMMER power meters Aron circuit This circuit can be used in three phase systems with three wires If you have a 4th wire it can t be used because currents could flow in this wire which are not taken into account Please note that in high frequent applications ground could be the 4th wire The main advantage of this circuit is that you just need 2 power meters to measure the total active power of the system You measure the current in phase 1 and 3 as well as the voltage of phase 1 resp 3 against phase 2 With this you apply a linked voltage and a phase current to each measuring channel Just with an ohmic load the channel sees a phase shift of 30 With not ohmic loads the displayed active power of each channel can be larger smaller or even negative The active power of each phase can t be displayed with this also the reactive and apparent power as well as the power factor Only the total active power is correct and of course the voltages and currents
25. ortant to set the trigger level to 10A 3 2A because of the DC component after the bate alle there are no zero crossings Signal i i Filter Level Hyst Figure 11 Filter settings in the measure menu for a squaring AM demodulator The values in the default menu The values shown in the default menu are correctly measured TRMS values of the burst firing control signal The basic frequency of the signal is 1 5Hz All values are stable This is an indication for a correct dai lanh like a stable signal on a scope Itrms 3 32087 A Utems 223 1710 38627 kW 71877 kU 66994 kuar 52905 56266 HZ To 4 aA BPs Figure 12 Values in the default menu 19 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 pon ZSS ZIMMER Harmonic analysis For getting a better understanding of the measured values the harmonic analysis is very helpful The following figures show the participation of the different current harmonics which have an influence on the TRMS of the measurement triggered on 1 5Hz fundamental f p ii nAediv fn B i YEM o 0 518 728 mA Figure 13 DC component cursor position caused by the fan motor driven with halfwave rectifier Figure 15 First frequency of the lower side band Figure 16 32nd harmonic is the 50Hz carrier that is the 31st harmoni
26. r 20ms 1 cycle you got harmonics in 50Hz steps While measuring 16 cycles 320ms you get harmonics in 3 125Hz steps 13 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 peer ZSS ZIMMER By choosing a different observation time you can define how many inter harmonics you will get The observation period is derived from the synchronisation signal too Undersampling Shannon theorem anti aliasing filter Concerning the bandwidth and the sampling frequency there is a very frequently asked question How can you measure a 500kHz signal while having just 100kHz sampling rate Many people assume that the sampling theorem also called Nyquist or Shannon theorem has to be met to calculate values This is not true except for few purposes which are relevant for our kinds of measuring e you want to analyse the signal in the time domain Like in the scope function e you want to filter digitally e g IIR or FIR filter e you want to make a FFT or DFT For our purposes of measuring DC TRMS or power values is has not to be met The reason for that is simple All this values are in principle statistical values average value squared average value So it doesn t matter in which order you add the values to get the sum or square sum A simple example You have a sinewave of 50Hz amplitude 1 and a sampling frequency o
27. r to a load Parts of this power may return to the source reactive power others do not active power 5 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 peer ZSS ZIMMER Electrical power can be divided in four groups Instantaneous power This is the power at one point of time It is calculated by multiplying the instantaneous voltage and current value at this point of time A sequence of instantaneous power values creates the oscillation of the power The letter for this power is p t So the formula is p t u t 12 Formula 9 Definition of instantaneous power Apparent power This is the product of TRMS values of voltage and current A phase shifting or a distortion of this signals are not considered It s formula is S Utrms z Tums Formula 10 Definition of apparent power Active power This is the power which is transferred to the load and does not return while a defined time So the active power is the average value of the power oscillation It s formula is P aood Formula 11 Definition of active power u nm The sign of P is or depending on the direction of power flow Active power can only be generated by same frequent voltage and current components Reactive power This is the power which is transferred to the load and does return within a defined time The r
28. skvA D a E Pin s n 7m 4 88889 ku 8 88889 KUA 1 179963 kW 1 79963 KUA 2 8 68878 ki 8 68878 KUA 3 8 09004 ki 6 60684 kVA 4 8 66084 ki 6 66864 KUA Figure 21 Active and apparent power while heating The distortion reactive power is quiet constant independent of the heating coil is in operation or not In this cases D is caused by the one way rectification of the fan motor current P and also S change very much depending on the signal being analysed heating on off All measurements were done for 2 periods of line frequency Power analysis With X synchronisation to the frequency of the 1 5Hz modulation signal the following power values were measured B 24163kW Q B S B 67r252 kVA D a P N Sin 38 46 6808 kt 8 68812 KUA 1 6 888011 ki 8 46868 KUA 1H 8 09928 ki 6 78594 KUA 33 8 88813 kW 8 68815 KUA 34 8 68817 kW 8 68878 KUA Figure 22 Active power and apparent power at line frequency 32nd harmonic 21 22 ZES ZIMMER Electronic Systems GmbH ZES ZIMMER Inc Tel 49 0 6171 6287 50 Tel 1 760 550 9371 sales zes com usa zes com www zes com Application Note 105 peer ZSS ZIMMER Here the 50Hz power component is at the 32nd harmonic The distortion reactive power is larger because both sidebands are taken into the calculation The values P and S are stable Conclusion The integration time in which a measurement has been made is a very impor
29. suring its own consumption Measurement with a distorted current signal We used the following input signals OS080hse2 2 asa In Figure 2 Voltage input signal The voltage signal is taken from a ZES ZIMMER 5000i power source This voltage is a with a frequency of 50Hz Gabas x dive5 000 me more Figure 3 Unfiltered current input signal The current signal is unfiltered and distorted but contains only harmonic components 50Hz 100Hz 15 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com Application Note 105 rev 20 15 7497 bl a 5 31 5142 VA D 27 3503 va Pin s n 2m 4 00811 8 6886 UA 1 15 7561 16 2856 UA 2 6 6885 6 6885 UA 3 8 6638 W 6 64872 UA 4 8 6886 8 6886 UA Figure 4 Power values in HARM100 mode ZZS ZIMMER These are the values measured in HARM100 mode with the above shown input signals As you can see the apparent power S is very high caused by the distortion reactive power D and not by the phase shift You can calculate the phase shift reactive power Qpa which is only Qari Q D 3 7961 var Measurement with a filtered current signal Another way to get D is shown in following experiment We used the same set up with a digital 30Hz filter inside the LMG95 The voltage input signal is taken also from the ZES AMAR 5000i power
30. tant parameter to get correct values Also the interpretation of the measured signal is very important As you can see you can measure 3 different active powers 1 79 kW during the heating 0 13 kW during the fan motor running only 0 34 kW over one complete control cycle All measurements are correct for their special time Which power is the valid one for you depends on the time period you are interested in Usually the best synchronisation is on the signal with the lowest frequency Author Dipl Ing Thomas Jackle Development and Application 22 22 ZES ZIMMER Electronic Systems GmbH Tel 49 0 6171 6287 50 sales zes com www zes com ZES ZIMMER Inc Tel 1 760 550 9371 usa zes com
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