GB2281629A - Measuring distortion in ac networks - Google Patents

Abstract

Distortion in an AC network may be quantified by integrating over time one or more kth harmonics of current. This involves taking (1, 2, 4, 5) N samples of current phase-locked (7, 8, 5) to the associated voltage; applying reference sine (kx) and cosine (kx) waveforms to the sampled current waveform, with arbitrary phase between them, to produce orthogonal components of the kth harmonic component; squaring and adding the components to produce a value for the square of the kth harmonic of current; and integrating this value, or its square root, over time to provide the quantitative measure of distortion in the AC network. Similar techniques may be used to determine energy consumption, imbalance current in a three-phase, four-wire system having three sensing elements and third phase current in a three-phase three-wire system having two sensing elements. <IMAGE>

Description

MEASURING DISTORTIONS IN AC NETWORKS The present invention relates to AC power supply/distribution networks. More particularly, the invention concerns the evaluation of distortion occurrinq within such networks and use of such measurements.

In theory a perfect sinusoidal waveform is supplied in AC power networks. In conventional electricity metering it is assumed that the loads used by a consumer are resistive or regular such that the current waveform will have the same shape as the voltage waveform. Thus the supplied current/voltaqe is expected to consist only of harmonics of odd order, even harmonics (including dOc.) being entirely absent.

However in practice this ideal sinusoid may be distorted by effects on the distribution side and on the consumer side. The distortion causes problems, not least in that it leads to incorrect metering of consumer's energy consumption which can result in undercharging.

Distortion may be caused on the distribution side by non-linearity of elements used in the network, notably transformers. On the consumer side distortion is caused by the use of non-linear and time-varying loads, such as rectifiers, convertors and phase-variable devices such as thyristor-controlled variable power drives.

Until now it has been necessary to use expensive and complicated equipment in order to monitor the level of distortion.

Embodiments of the present invention provide methods and apparatus for enabling distortion of an AC network to be quantified in a simple and relatively inexpensive manner by making use of a harmonic current measurement technique.

The new technique for evaluation of distortion stems from a realisation that it is not useful to evaluate voltage or power at a monitored location because the power level arisinq from the distorted waveform depends upon the distortion level in voltage, which in turn is proportional to the supply impedance.

Thus those factors do not give a true picture of the distortion being injected by that consumer.

The present invention provides methods and apparatus for quantifying the distortion introduced into an AC network at a monitored location making use of harmonic current measurement: A technique for quantifying distortion in an AC network is useful in a number of ways. For example, it enables distorting loads to be located so that, if feasible, they can be replaced by non-distorting loads.

Also, it enables consumers to be billed for distortion they introduce into the network, either to compensate for under-registration of energy consumption or on the principle that the polluter pays".

According to embodiments of the present invention distortion can be evaluated by measuring the integral over time of one or more selected harmonic components of current or the integral over time of the square thereof. These measures may be termed Distortion Ampere Hours or Distortion Ampere Squared Hours (DASH), respectively, in a manner analogous to kilowatthours.

Whilst it would, in theory, be possible to include a large number of harmonics in the measure of distortion this would involve lengthy calculations.

Thus, in practice, it is preferred to make a selection of particular harmonics to be included. This selection may be made beforehand based on the harmonics most likely to arise from distortion induced by the consumer.

Alternatively, the selection may be made adaptively based upon an assessment of which harmonics are having the greatest effect on the waveform at a given time.

The preferred method for quantifying distortion involves: taking samples of the current waveform in an AC network phase locked relative to an associated voltage waveform; multiplying successive samples of the current waveform by successive discrete values representing a reference sine(kx) waveform at phase e relative to the current waveform, summing the resulting products and squaring the sum to produce a first squared value; multiplying successive samples of the current waveform by successive discrete values representing a reference cosine(kx) waveform at arbitrary phase e relative to the current waveform, summing the resulting products and squaring the sum to produce a second squared value; processing the first and second squared values whereby to produce a value indicative of the kth harmonic component of current; and integrating said value with respect to time.

The new technique can be built into fixed apparatus to be installed at a consumer's premises.

This could be either as a separate monitoring apparatus or as part of an electricity meter. Equally, the new evaluation technique may be built into testing equipment that may be brought on-site and used to monitor an installation.

In the basic embodiments discussed above a value is produced which represents the distortion found in the a.c. supply as sampled at a consumer's installation. However, this measure is affected by distortion introduced on the distribution side and introduced by other consumers. For example, even if the consumer's load is perfectly regular a distorted current waveform will be seen if the voltage waveform has been distorted by other consumers or by the distribution network. It would be preferable to obtain a value which represents the distortion caused by each consumer alone.

Then the consumer could be billed more fairly for the distortion he is causing.

According to the present invention a more representative value can be produced by comparing the harmonic content of the voltage waveform with the harmonic content of the current waveform. If the consumer's loads are regular then the current waveform will follow the voltage waveform. If the loads are not regular then (except in extremely unusual circumstances) a discrepancy will be seen between the form of the two.

The analysis of the harmonic content of the voltage waveform may be made in an analogous manner to the above-described preferred method for the analysis of the harmonic content of current.

By a technique related to the preferred embodiments mentioned above, a further aspect of the invention enables imbalance current to be evaluated in a three-phase four-wire system using three sensors, or the third phase current to be evaluated in a three-phase three-wire system using two sensors. This is further described below.

Features and advantages of the invention will become clear from the following description of embodiments thereof, given by way of example, and illustrated by the accompanying drawing which indicates one embodiment of apparatus according to the invention for metering both electricity consumption and distortion.

In the embodiment illustrated in the drawing, distortion current is sensed using a shunt 1 and an amplifier 2. The output of the amplifier 2 is fed to an analog to digital convertor (ADC) 4 which in turn sends data to a microprocessor 5.

The microprocessor is arranged to take samples of the current waveform which are phase locked relative to the voltage waveform. This may be achieved, for example, by changing the microprocessor clock frequency as described by Fielden and Peddie in UK Patent 2040051. The sampling is arranged to take a set of N samples equally spaced over the waveform, for example 60 samples. In order to obtain sufficiently high resolution it is preferable to use a high resolution ADC or to use a ramp technique to average over a longer period, say 1 second, as described by Fielden at al in UK Patent 2083306. Alternatively, or additionally, a number of sets of current samples may be taken during a time period, T, and, for each sample position within the waveform, the values summed over that time period.

As shown in the drawing a measurement of voltage is made using a voltage divider 7 feeding an ADC 8 which in turn supplies the microprocessor 5. In this embodiment the voltage measurements are used in calculating energy consumption and may also be used in the distortion measurement as described below.

It is to be understood that the shunt and amplifier shown in the drawing could be replaced by other known means for current sensing, for example a current transformer. Similarly, the voltage divider 7 may be replaced by known means.

For a single phase system the general technique used by the microprocessor 5 to evaluate distortion is, as follows. The microprocessor takes its phase locked sampled current data (either a single set or a set summed over an averaging period as mentioned above) and stores the data for processing. Reference waveforms are applied to the sampled current data in order to extract sine and cosine components of a selected, kth, harmonic component of the current. These sine and cosine components are squared and the squared values added to give a value for the square of the kth harmonic component of current (Ik2). This value can be used as the measure of distortion or its square root may be taken, I . Other ways of combining the sine and cosine components of the kth harmonic to produce a measure of distortion may also be envisaged. The calculated value is corrected for constants of multiplication introduced by the hardware and the detailed calculation process.

Further reference waveforms may be applied to the sampled current data in order to extract sine and cosine components of any further selected harmonic components of the current. These sine and cosine components will also be processed to produce measures of the respective harmonics. These measures too are corrected to take into account the constants of multiplication.

For each harmonic, the current measure is multiplied by the time period over which the samples were taken (or over the averaging period). The resultant values are summed over the harmonics of interest in order to give a measure of distortion.

In embodiments of the invention which meter both electricity consumption and distortion it is convenient to use a corresponding technique to extract also the first harmonic component of current (fundamental). This can be used, together with phase and voltage information, to measure power and hence the energy at the fundamental frequency. The fundamental component is not essential for distortion measurement but can be useful for that and other purposes. For example, instead of measuring distortion ampere squared hours or distortion ampere hours one could measure the ratio between the harmonic components of current and the fundamental component. This would give a "distortion ratio" and could be used to obtain a "percentage distortion1,.

The harmonic evaluation technique described above may be extended to two-phase and polyphase systems by applying the reference waveforms and correction factors separately to sampled current values taken for each phase. The current measures produced are summed over the harmonics of interest and over all phases in order to obtain a value for distortion.

In a multiphase system there may not be sufficient time to take a full set of samples simultaneously for each phase in a single cycle of the supply waveform. In practice it is convenient to interleave the sampling of each phase and to build up the full sets of samples over a number of cycles of the supply waveform. Thus, for example, in the first cycle sample positions (1,4,7,10,13..) would be taken for phase 1, sample positions (2,5,8,11,15,...) taken for phase 2 and sample positions (3,6,9,12,15,...) taken for phase 3; in the second cycle sample positions (2,5,8,11,14,...) would be taken for phase 1, etc. This technique is suitable in the general case where the successive cycles of the waveform remain approximately the same over the time period required for taking a full set of samples for all phases.

The steps of the distortion evaluation process for a single phase will now be considered in greater detail.

In order to extract a measure of the kth harmonic of current the microprocessor 5 multiplies the sampled current waveform by a reference sine(kx) waveform, by a reference cosine(kx) waveform, squares the two results and adds the squared values together.

This produces a quantity which is directly related to the square of the kth harmonic component of current.

Before describing how the sampled current waveform is multiplied by the reference sine and cosine waveforms some comments on the reference waveforms are appropriate.

The reference waveforms are required in the form of series of discrete values. Discrete values representing a sine or cosine waveform may be generated in a number of different ways. For example, it is wellknown to program a microprocessor with an algorithm allowing it to calculate the values defining a sine or cosine waveform and certain integrated circuits have sine/cosine functions built into them (e.g. the Intel 80486 chip).

However, in preferred embodiments of the invention the reference sine and cosine waveforms are predetermined or precalculated and are stored in memory in the form of a lookup table. It is convenient for the first value in the table to correspond to the zero point (i.e. 0 ). The successive values in the lookup table could correspond to successive discrete samples of a sine or cosine waveform. Greatest flexibility in selection of the harmonics to be evaluated is obtained if the values stored in the look-up tables represent the basic sine(x) and cosine(x) functions in look-up tables and to derive values for sine(kx) and cosine(kx) by stepping through the table. For example, if successive values of the table represent successive values of sine(x) then successive values of the function sine(kx) may be obtained from the same lookup table by stepping through k places at a time in a circular fashion (i.e.

modulo N). In practice there is a limit on the highest harmonic that can be extracted arising from the number of current samples taken.

Furthermore, it is convenient to store values which are an integer multiple of the relevant sine/cosine values. For example, the discrete values representing the function 100 sine(x) may be expressed in digital terms in 7 bits with an additional sign bit.

This multiplication factor is taken into account in the later correction stage of the processing.

Also, where the number of current samples, N, is divisible by 4 it is possible to use the same look-up table to provide values for both the sine and cosine reference waveforms.

As mentioned above, in order to produce a measure of the kth harmonic component of current the sampled current waveform is first multiplied by discrete samples representing a reference sine(kx) waveform. In the multiplication the number of samples of the reference waveform that are used is the same as the number of samples N of the current waveform and the phase, &commat;, of the reference waveform is arbitrary relative to the phase of the sampled current waveform.

Each successive sample of the current waveform is multiplied by a successive sample of the reference sine waveform and the resulting products are added together.

In a similar fashion, the sampled current waveform is multiplied by a sampled reference cosine(kx) at phase &commat;. The two sums are squared and the squares added together to produce a value proportional to the square of the kth harmonic component of current.

If it is desired to work directly in terms of kth harmonic current then the square root of this measure should be taken. It is to be noted that this value is the line current and not the in-phase or quadrature component with respect to the voltage associated with the phase. If these two components are required then they can be obtained by analogous multiplication of the voltage waveform by reference sine and cosine waveforms and appropriate trigonometrical transformations.

In order to express the measure of kth harmonic component of line current (or square thereof) in terms of known physical units a correction must be made. This is to take into account multiplication factors introduced by the detailed calculation process and by the hardware.

The correction needed to combat factors introduced by the calculation depends upon the multiplication factor (if any) by which the reference waveforms differed from sine(kx) or cosine(kx), the magnitude of a particular voltage input to the ADC in digital terms and the number of samples taken. The correction needed to combat factors introduced by the hardware depends upon the hardware which controls the ADC reference voltage and the voltage at the ADC input corresponding to a particular input current. The "calculation factors" are known from the design of the apparatus whereas the "hardware factors" must normally be measured in order to calibrate the meter. This may be performed very simply by using a nominal correction factor in apparatus receiving a known current. The nominal value is updated taking into account the difference between the properties of the known current and the measured value. The updated correction factor is then stored in non-volatile memory.

In some cases the measurement hardware will have a varying frequency response. For example, in some circumstances the measurement circuitry will attenuate high frequencies. This can be taken into account by appropriate variation of the stored correction factor.

The desired variation can be achieved either by storing different correction factors for use with the different harmonics, or by arranging for the microprocessor to modify the correction factor for different harmonics based upon a pre-determined or downloaded law.

The above process produces a corrected measure of the kth harmonic component of current (or the square thereof). In order to convert the extracted harmonic current measures into a measure of distortion each current measure is integrated over time and the results summed over the selected harmonics. This is achieved by multiplying each measure by the period over which the samples were taken.

In the case where the processed current data represented a sum of several sets of current samples then the current measures are multiplied by the averaging period.

The relevant time periods are known either by assuming that the supply takes its nominal frequency value or, more accurately, from a knowledge of the microprocessor clock cycle time. In the latter case the number of microprocessor clock cycles can be measured conveniently with an on-board timer. The integrated values are in terms of ampere hours or ampere squared hours. These values are then summed over the harmonics of interest and over the various phases of the supply to produce a value for distortion in distortion ampere hours or distortion ampere squared hours.

In practice, noise causes non-zero values for assessed distortion even in a regular system. These would add over time, especially so when the measure of distortion represents I (which can never take a negative value). In preferred embodiments of the invention measures are taken to ensure that the sum does not "creep". A simple method for avoiding the problem is to apply a threshold below which values of assessed distortion are ignored.

In preferred embodiments of the invention an adaptive technique is used to select the harmonics for inclusion in the computation of distortion. A simple way of establishing which harmonics should be included is periodically to sample the evaluated harmonic current levels. The largest one, or largest few, harmonic components can then be included in the distortion computation until the time when the magnitude of the harmonic components is next checked. This avoids unnecessary lengthy computation.

As mentioned above, if it is desired to produce a quantitative measure of distortion introduced by a particular consumer the harmonic content of the voltage waveform may be compared with the harmonic content of the current waveform. Any given harmonic of each waveform may be evaluated by sampling voltage and current and applying the techniques described above.

For each harmonic of interest the comparison between the two waveforms amounts to assessing what current the measured voltage quantity would have produced in an imaginary resistive load and comparing that value with the observed magnitude of the corresponding current harmonic. The magnitude of the imaginary resistor is the ratio of the voltage fundamental to the current fundamental. If the load truly was equal to this imaginary resistance then the following expression would hold: Ikth Harmonic = Vkth harmonic fun am.n a 1 f un amer1 a I Thus deviation from this relationship indicates distortion. The difference between the expected and observed values can be accumulated, either as a proportion or as an absolute value, and used as a measure of the distortion introduced by that consumer.

As a practical matter it may be decided to ignore low level distortion and to meter only that distortion greater than a set level, e.g. 5% distortion in a harmonic. This level can be set differently for different harmonics.

In practice the impedances involved vary with frequency. It is a simple matter to factor this variation into the value of the imaginary resistor used when calculating distortion for any given harmonic. This correction factor can be set differently for each harmonic, as appropriate.

As indicated above, in embodiments of the invention where both distortion and electricity consumption are evaluated it is convenient to use similar methods to evaluate both items. Usually it is only the first harmonic which is significant for metering energy consumption The resulting measurement is in kilowatthours at the supply frequency.

In order to meter energy in this embodiment the following method may be used. The sine and cosine components of the fundamental component of current are extracted using the initial steps of the general harmonic extraction technique according to the present invention. The voltage waveform may be sampled and the sine and cosine components of the fundamental extracted using techniques corresponding to the current sample processing.

If the reference waveforms used to extract the components of fundamental voltage are applied at the same phase, e, relative to the sampled voltage waveform as was used in extracting the current components, then subsequent processing is simplified. In this case the respective sine and cosine components of voltage and current will be expressed in the same frame of phase reference. The magnitude of the voltage vector, Vo, may be obtained by squaring the cosine and sine components, adding the squared values and taking the square root.

Real power may be calculated by multiplying the cosine component of voltage by the cosine component of current, multiplying the sine component of voltage by the sine component of current, and adding the two sums.

Imaginary, or reactive, power may be calculated by multiplying the cosine component of voltage by the sine component of current, multiplying the sine component of voltage by the cosine component of current, and subtracting the second sum from the first sum. Apparent power may be calculated by multiplying the magnitude of the voltage by the magnitude of the current.

If the reference waveforms used to extract the components of fundamental voltage are applied at a phase, , relative to the sampled voltage waveform which is different from that used in extracting the current components then a vector rotation is required in order to place the voltage and current components in the same frame of reference. This may be performed in a straightforward manner using the appropriate trigonometric calculations.

It is to be appreciated that the abovedescribed techniques may be extended to allow the measurement of reactive power and energy and that import/export metering can readily be accommodated.

Furthermore, corresponding techniques can be used if it should be desired to evaluate the power/energy in a given harmonic.

As mentioned above, another aspect of the present invention provides a related technique for evaluating imbalance current in a three-phase four-wire system in which three current and/or voltage sensors are used and for evaluating third phase current in a threephase three-wire system in which two sensors are used.

In this technique current on each sensed phase of the system is sampled and multiplied by reference sine(x) and cosine(x) waveforms as when evaluating the fundamental component of current in the embodiment of Fig.l. These calculations amount to resolving the current vectors for each phase into orthogonal components. A simple way of ensuring that all of the resolved components are in the same frame of reference is to phase-lock the sampling of all current phases to a single one of the voltage waveforms and to extract the resolved components by applying reference waveforms at the same phase, e, relative to each sampled waveform.

However, neither of these steps is essential because straightforward trigonometric calculations can transform values into a common frame of reference.

Once resolved components in a common frame of reference have been produced for all of the phases it is a simple matter to find the magnitude of the resultant imbalance or third phase current vector. This is achieved by adding the respective cosine and sine coordinates together. The magnitude of the resultant vector is found by squaring the summed cosine values, squaring the summed sine values, adding the sums and taking the square root of the result.

Harmonics in the imbalance current or third phase current can be derived in a corresponding manner.

Thus, in each sensed phase the current is sampled, multiplied by reference sine(kx) and cosine(kx) waveforms so as to resolve the kth harmonic component of current in each sensed phase into orthogonal components.

If necessary, these components are manipulated so as to be in the same frame of reference. Then, as above, the magnitude of the resultant vector is produced by summing the respective cosine and sine components, squaring each sum, adding the two values and taking the square root of the result. When calculating harmonics in this way some care is required in ensuring that any phase shifts introduced by the external measurement circuitry are fairly closely matched between the phases.

Other techniques are known for evaluating the imbalance or third phase current. For example, samples of current from each phase can be added either instantaneously or by sampling the waveforms, storing the sampled values and subsequently adding them together. However, the technique of the present invention has a number of advantages. Firstly, it is very convenient and simple to perform. Secondly, the hardware calibration corrections required for each phase are simpler to perform in the present invention than in the known systems. In the prior art systems more calibration arithmetic is needed or more closely matched hardware must be used in the various phases.

Claims (67)

CLAIMS:

1. A method of quantifying distortion in an AC network comprising evaluating the integral over time of one or more kth harmonic components of current, k being an integer other than 1.

2. The method of claim 1 and comprising the steps of: taking at least one set of N samples of a current waveform in an AC network, said samples being phase locked relative to an associated voltage waveform; multiplying successive samples of the current waveform by successive discrete values representing a reference sine(kx) waveform at arbitrary phase e relative to the current waveform and summing the resulting products to produce a value indicative of a first resolved component of the kth harmonic of current; and multiplying successive samples of the current waveform by successive discrete values representing a reference cosine(kx) waveform at phase e relative to the current waveform and summing the resulting products to produce a value indicative of a second resolved component of the kth harmonic of current; processing the first and second resolved components to produce a measure indicative of the magnitude of the kth harmonic of current; and multiplying the current measure for the kth harmonic by the time period over which the current samples were taken.

3. The method of claim 2, wherein the processing step comprises squaring the first and second resolved components and adding the squared values whereby to produce a value proportional to of the square of the kth harmonic of current, Ik2.

4. The method of claim 3, and further comprising the step of comparing the value proportional to 12 against a threshold value and disregarding the measure if it is below the threshold value.

5. The method of claim 3, and further comprising the step of calculating the square root of the value proportional to I 2 whereby to produce a value proportional to the kth harmonic current, I .

6. The method of claim 3, 4 or 5, and further comprising the step of scaling the measure of kth harmonic component of current by reference to a stored correction factor.

7. The method of claim 6, wherein the scaling step is adapted to scale the measure of kth harmonic using a correction factor which differs for different harmonics whereby to compensate for the frequency response of the hardware being employed.

8. The method of claim 6 or 7, and further comprising a calibration step to generate one or more values for the correction factor and a storing step for storing the evaluated correction factor(s) in nonvolatile memory.

9. The method of any previous claim, and further comprising the steps of: providing a lookup table storing successive discrete values representing an integer multiple of a sine(x) function; and deriving the reference sine waveform values by lookup within said table, successive reference values being derived for use in the multiplication by stepping through the lookup table k places at a time.

10. The method of claim 9, and further comprising the steps of: providing a lookup table storing successive discrete values representing an integer multiple of a cosine(x) function; and deriving the reference cosine waveform values by lookup within said table, successive reference values being derived for use in the multiplication by stepping through the lookup table k places at a time.

11. The method of claim 9 wherein, in the case where N is a multiple of 4, both reference sine and cosine values are derived by lookup within the same table.

12. The method of claim 9, 10 or 11, wherein: the values contained in the lookup table or tables are precalculated using sine and cosine approximation hardware or sine and cosine approximation functions implemented by a microprocessor; and the method further comprises the step of storing the lookup table or tables in alterable memory.

13. The method of any of claims 2 to 8, and further comprising the step of deriving the reference sine and cosine values using sine and cosine approximation functions calculated by a microprocessor.

14. The method of any of claims 2 to 8, and further comprising the step of deriving the reference sine and cosine values using sine and cosine approximation hardware.

15. The method of any of claims 2 to 8, and further comprising the step of deriving the reference sine and cosine values by downloading sine and cosine approximation values from an external source.

16. The method of any of claims 2 to 15, wherein the steps of multiplying current samples by reference sine and cosine values and adding resultant squared values are repeated to produce measures indicative of a plurality of harmonic components of current, the current measure for each harmonic is multiplied by the time over which the current samples were taken and the resultant products are added together to produce a value indicative of distortion.

17. The method of any of claims 2 to 15, wherein the steps of multiplying current samples by reference sine and cosine values and adding resultant squared values are repeated to produce measures indicative of a plurality of harmonic components of current, these current measures are summed and are multiplied by the time period over which the current samples were taken to produce a value indicative of distortion.

18. The method of claim 16 or 17, wherein the particular harmonic components included in the calculation of the measure of distortion are selected by adaptive sampling of the harmonic current levels.

19. The method of any of claims 2 to 15 and further comprising the steps of: taking samples of a voltage waveform in the AC network; multiplying successive samples of the voltage waveform by successive discrete values representing a reference sine(kx) waveform at arbitrary phase ç relative to the voltage waveform and summing the resulting products to produce a value indicative of a first resolved component of the kth harmonic of voltage; multiplying successive samples of the voltage waveform by successive discrete values representing a reference cosine(kx) waveform at phase ç relative to the voltage waveform and summing the resulting products to produce a value indicative of a second resolved component of the kth harmonic of voltage; processing the first and second resolved components whereby to produce a measure indicative of the kth harmonic of voltage of a type comparable with the measure of kth harmonic of current and in a common frame of reference; producing corresponding measures of the fundamental components of voltage and current in a common frame of reference; comparing the relationship between the measured kth harmonic and fundamental components of voltage and current with the theoretical relationship for a resistive load: Vkth harmonic = Ikth harmonic Vfundamental Ifundamental and producing a value indicative of the extent of the deviation from the theoretical relationship, as a measure of distortion.

20. The method of claim 19, wherein the comparing step is adapted to take into account the variation of impedance with frequency.

21. The method of claim 19 or 20, wherein the first and second resolved components of voltage and current are produced by multiplying the respective sampled waveforms by reference waveforms at a common phase relative to each sampled waveform whereby to ensure that the measures of voltage and current are in the same frame of reference.

22. The method of any previous claim applied in a two-phase or polyphase system, wherein measures of one or more harmonic components of current are produced for each phase, all of said measures being in or transformed into a common frame of reference, the current measure(s) for each harmonic are multiplied by the time over which the respective current samples were taken and the resultant values are summed over harmonics and phases to produce a value indicative of distortion.

23. The method of any previous claim, and further comprising the step of metering electrical energy.

24. The method of claim 23 and comprising the steps of: producing first and second resolved components of fundamental current; taking samples of the voltage in the AC network; multiplying successive samples of the voltage waveform by successive discrete values representing a reference sine(x) waveform at arbitrary phase ç relative to the voltage waveform and summing the resulting products to produce a value indicative of a first resolved component of the fundamental of voltage; multiplying successive samples of the voltage waveform by successive discrete values representing a reference cosine(x) waveform at the phase ç relative to the voltage waveform and summing the resulting products to produce a value indicative of a second resolved component of the fundamental of voltage; and processing the resolved components of fundamental current and fundamental voltage in a common frame of reference to produce a value for power in the AC network.

25. The method of claim 24, wherein the resolved components of current and voltage fundamental are produced by multiplying the respective sampled waveforms by reference waveforms at a common phase relative to each sampled waveform whereby to ensure that the measures of voltage and current are in the same frame of reference.

26. The method of claim 24 or 25, and comprising the step of integrating the calculated power with respect to time so as to measure energy.

27. Distortion quantifying apparatus comprising means for evaluating the integral over time of a measure indicative of one or more kth harmonic components of current, k being an integer other than 1.

28. The apparatus of claim 27, wherein the evaluating means comprises sampling means for taking at least one set of N samples of a current waveform in an AC network, said samples being phase locked relative to an associated voltage waveform; and processing means for multiplying successive samples of the current waveform by successive discrete values representing a reference sine(kx) waveform at arbitrary phase &commat; relative to the current waveform and summing the resulting products to produce a value indicative of a first resolved component of the kth harmonic of current, multiplying successive samples of the current waveform by successive discrete values representing a reference cosine(kx) waveform at phase e relative to the current waveform and summing the resulting products to produce a value indicative of a second resolved component of the kth harmonic of current, processing the first and second resolved components to produce a measure indicative of the kth harmonic component of current and multiplying said measure by the time period over which the current samples were taken.

29. The apparatus of claim 28, wherein the processing means is adapted to square the first and second resolved components and add the squared values whereby to produce a value proportional to the square of the kth harmonic of current, Ik2.

30. The apparatus of claim 29, wherein the processing means is adapted to compare the value proportional to I 2 against a threshold value and disregard the measure if it is below the threshold value.

31. The apparatus of claim 29, wherein the processing means is adapted to take the square root of the value proportional to I 2 whereby to produce a value proportional to the kth harmonic of current, I

32. The apparatus of claim 29, 30 or 31, wherein the processing means is adapted to scale the measure of kth harmonic component of current by reference to a stored correction factor.

33. The apparatus of claim 32, wherein the processing means is adapted to scale the measure of kth harmonic using a correction factor which differs for different harmonics whereby to compensate for the frequency response of the hardware being employed.

34. The apparatus of claim 32 or 33, and further comprising a non-volatile memory storing one or more correction factors generated in a calibration process.

35. The apparatus of any of claims 28 to 34, and further comprising a lookup table storing successive discrete values representing an integer multiple of a sine(x) function; wherein the processing means derives the reference sine waveform values by lookup within said table, successive reference values being derived for use in the multiplication by stepping through the lookup table k places at a time.

36. The apparatus of claim 35, and further comprising a lookup table storing successive discrete values representing an integer multiple of a cosine(x) function; wherein the processing means derives the reference cosine waveform values by lookup within said table, successive reference values being derived for use in the multiplication by stepping through the lookup table k places at a time.

37. The apparatus of claim 35 wherein, in the case where N is a multiple of 4, the processing means derives both reference sine and cosine values by lookup in the same table.

38. The apparatus of claim 35, 36 or 37, wherein: the values contained in the lookup table or tables are precalculated using sine and cosine approximation hardware or sine and cosine approximation functions implemented by a microprocessor; and there is further provided an alterable memory storing the lookup table or tables.

39. The apparatus of any of claims 28 to 34, wherein the processing means is adapted to calculate the reference sine and cosine values using sine and cosine approximation functions.

40. The apparatus of any of claims 28 to 34, and comprising sine and cosine approximation hardware from which the processing means derives the reference sine and cosine values.

41. The apparatus of any of claims 28 to 34, and further comprising means for downloading sine and cosine approximation values from an external source.

42. The apparatus of any of claims 28 to 41, wherein the processing means is adapted to repeat the steps of multiplying current samples by reference sine and cosine values and adding resultant squared values to produce measures indicative of a plurality of harmonic components of current, to multiply the current measure for each harmonic by the time over which the current samples were taken and to add the resultant products together to produce a value indicative of distortion.

43. The apparatus of any of claims 28 to 41, wherein the processing means is adapted to repeat the steps of multiplying current samples by reference sine and cosine values and adding resultant squared values to produce measures indicative of a plurality of harmonic components of current, to add the current measures and multiply the sum by the time over which the current samples were taken to produce a value indicative of distortion.

44. The apparatus of claim 42 or 43, and comprising means for selecting which harmonic components are included in the calculation of the measure of distortion, the selecting means selecting harmonics on the basis of an adaptive sampling of the harmonic current levels.

45. The apparatus of any of claims 28 to 44, and comprising means for taking samples of a voltage waveform in the AC network; and wherein the processing means is adapted: to multiply successive samples of the voltage waveform by successive discrete values representing a reference sine(kx) waveform at arbitrary phase ç relative to the voltage waveform and to sum the resulting products to produce a value indicative of a first resolved component of the kth harmonic of voltage, and to multiply successive samples of the voltage waveform by successive discrete values representing a reference cosine(kx) waveform at phase ç relative to the voltage waveform and to sum the resulting products to produce a value indicative of a second resolved component of the kth harmonic of voltage; to process the first and second resolved components whereby to produce a measure indicative of the kth harmonic of voltage of a type comparable with the measure of kth harmonic of current and in a common frame of reference; to produce corresponding measures of the fundamental components of current and voltage in a common frame of reference; and to compare the relationship between the measured kth harmonic components and fundamental components of current and voltage with the theoretical relationship for a resistive load: Vkth harmonic = Ikth harmonic V I f damenLtal dam fundamental and to produce a value indicative of the extent of the deviation from the theoretical relationship as a measure of distortion.

46. The apparatus of claim 45, wherein the comparing means is adapted to take into account the variation of impedance with frequency.

47. The apparatus of claim 45 or 46, wherein the processing means is adapted to produce the first and second resolved components of voltage and current by multiplying the respective sampled waveforms by reference waveforms at a common phase relative to each sampled waveform whereby to ensure that the measures of voltage and current are in the same frame of reference.

48. The apparatus of any of claims 25 to 47 applied in a two-phase or polyphase system, adapted to produce measures of one or more harmonic components of current for each phase, all of said measures being in or transmformed into a common frame of reference, wherein the processing means is adapted to multiply the current measure(s) for each harmonic by the time over which the respective current samples were taken and to sum the resultant values over harmonics and phases to produce a value indicative of distortion.

49. The apparatus of any of claims 28 to 48 and adapted to meter electrical energy.

50. The apparatus of claim 49, and comprising means for taking samples of the voltage in the AC network, wherein the processing means is adapted: to calculate first and second resolved components of fundamental current; to multiply successive samples of the voltage waveform by successive discrete values representing a reference sine(x) waveform at arbitrary phase, e, relative to the voltage waveform and to sum the resulting products to produce a value indicative of a first resolved component of the fundamental of voltage; to multiply successive samples of the voltage waveform by successive discrete values representing a reference cosine(x) waveform at phase e relative to the voltage waveform and to sum the resulting products to produce a value indicative of a second resolved component of the fundamental of voltage; to process the resolved components of fundamental current and fundamental voltage in a common frame of reference to produce a value for power in the AC network.

51. The apparatus of claim 50, wherein the processing means is adapted to produce resolved components of current and voltage fundamental by multiplying the respective sampled waveforms by reference waveforms at a common phase relative to each sampled waveform whereby to ensure that the measures of voltage and current are in the same frame of reference.

52. A method for evaluating the kth harmonic component of current in the mth conductor of a multiphase m-wire system having m- elements for sensing current and/or voltage, m being an integer, the method comprising, for each of the m-l phases corresponding to the m-l sensing elements: taking at least one set of N samples of the current waveform, said samples being phase locked relative to a voltage waveform; multiplying successive samples of the current waveform by successive discrete values representing a reference sine(kx) waveform at arbitrary phase e relative to the current waveform and summing the resulting products to produce a value indicative of a resolved component of the kth harmonic of current; and multiplying successive samples of the current waveform by successive discrete values representing a reference cosine(kx) waveform at phase e relative to the current waveform and summing the resulting products to produce a value indicative of a second resolved component of the kth harmonic of current; wherein the resolved components of current in all phases are in or transformed into a common frame of reference; and further comprising the steps of: summing the first resolved components for the m-l phases; summing the second resolved components for the m-l phases; and processing the two sums to produce a value indicative of the magnitude of the resultant vector, said value being indicative of the magnitude of current in the mth conductor.

53. The method of claim 52, and comprising the step of scaling the values of the resolved components in each phase by reference to stored correction factors.

54. The method of claim 53, wherein the scaling step is adapted to use separate correction factors for each phase of the current.

55. The method of claim 52, 53 or 54, wherein the processing step comprises squaring the two sums, adding the squared values and taking the square root of the result.

56. The method of any of claims 52 to 55, wherein the sampling of each phase of current is phase locked to a common voltage waveform.

57. The method of any of claims 52 to 56, wherein the resolved components of current in each phase are produced by multiplying the respective sampled waveforms by reference waveforms at a common phase e relative to each sampled waveform whereby to ensure that the resolved components for all phases are in the same frame of reference.

58. Apparatus for evaluating the kth harmonic component of current in the mth conductor of a multiphase m-wire system having m-l elements for sensing current and/or voltage, m being an integer, the apparatus comprising: means for taking at least one set of N samples of the current waveform in each of the m-l phases corresponding to the m-l sensing elements, said samples being phase locked relative to a voltage waveform; processing means adapted, for each sampled phase, to multiply successive samples of the current waveform by successive discrete values representing a reference sine(kx) waveform at arbitrary phase &commat; relative to the current waveform and to sum the resulting products to produce a value indicative of a first resolved component of the kth harmonic of current for each sampled phase, to multiply successive samples of the current waveform by successive discrete values representing a reference cosine(kx) waveform at phase e relative to the current waveform and to sum the resulting products to produce a value indicative of a second resolved component of the kth harmonic of current for each sampled phase, the resolved components of current in all phases being in or transformed into a common frame of reference, and adapted to sum the first resolved components for the m-l phases, to sum the second resolved components for the m-l phases and to process the two sums to produce a value indicative of the magnitude of the resultant vector, said value being indicative of the magnitude of current in the mth conductor.

59. The apparatus of claim 58, and comprising means for scaling the values of the resolved components in each phase by reference to stored correction factors.

60. The apparatus of claim 59, wherein the scaling means is adapted to use separate correction factors for each phase of the current.

61. The apparatus of claim 58,59 or 60, wherein the processing means is adapted to square the two sums, to add the squared values and to take the square root of the result.

62. The apparatus of any of claims 58 to 61, wherein the sampling means is adapted to sample each phase of current phase locked to a common voltage waveform.

63. The apparatus of any of claims 58 to 62, wherein the processing means is adapted to produce the resolved components of current in each phase by multiplying the respective sampled waveforms by reference waveforms at a common phase e relative to each sampled waveform whereby to ensure that the resolved components for all phases are in the same frame of reference.

64. A method of evaluating distortion in an AC network substantially as hereinbefore described with reference to the accompanying drawing.

65. Apparatus for evaluating distortion in an AC network substantially as hereinbefore described with reference to the accompanying drawing.

66. A method for evaluating current in the mth conductor of a multiphase m-wire system having m-l sensors for sensing current and/or voltage, m being an integer, substantially as hereinbefore described.

67. Apparatus for evaluating current in the mth conductor of a multiphase m-wire system having m-l sensors for sensing current and/or voltage, m being an integer, substantially as hereinbefore described.