FIELD OF THE INVENTION

The present invention relates to a method and a system for measur- ing an electrical quantity in an electrical network.

BACKGROUND OF THE INVENTION

Nowadays the utility companies are committed to keep the power quality of the supplied power at a certain level. The utility companies are also committed to pay reimbursement for customers suffering from long power out- ages. Among other things these commitments increase the demand to monitor higher order current or voltage harmonics than previously needed for network protection and control purposes, as well as to locate the fault location in the electrical network quickly in order to minimize the outage time of the power supply or to prevent a build-up of total outage of the power supply due to oc- casional, incipient faults.

Protection and control lEDs (Intelligent Electronic Devices) used nowadays for distribution network protection and control have a quite moderate sampling frequency, typically between 1 kHz and 2 kHz. This sampling frequency is suitable in that purpose that at present most of the functionality in the lEDs is based on phasor measurements, calculated from the nominal frequency components of the electrical quantities, such as zero voltage, zero current or phase currents and voltages, of the electrical network. For calculating 50 Hz or 60 Hz components of the measurement signals a higher sampling frequency would not really bring any benefits.

However, for monitoring the higher order harmonics the sampling frequency of 1 to 2 kHz may be too low. This is also the case for the fault location purposes, especially when the fault location calculation is based on a transient phenomenon occurring at an early stage of the fault. The frequency of the transient, which may be used for earth fault location purposes, for example, lies typically between the 100 Hz and 800 Hz, i.e. notably under the 1 kHz limit frequency defined by the Nyqvist theorem when the sampling frequency is 2 kHz. Therefore the sampling frequency of 2 kHz used at present would theoretically be adequate for transient analysis, but in practice, due to a very short duration of the transient, typically only a few milliseconds, the sampling fre- quency of 2 kHz is not adequate for acquiring enough transient data points for accurate fault location calculation.

In order to measure higher order harmonics or in order to measure a bigger amount of transient data points from the transient occurring at the early stage of the fault, the sampling frequency of the intelligent electronic devices could be increased. This, however, will increase the cost of the intelligent electronic devices, the increase of the costs rising to an unacceptable level especially if the intelligent electronic devices usable as such should be replaced by new ones only for providing a higher sampling frequency. Therefore, in order to fulfil the commitments relating for example to the monitoring of the higher order harmonics or to minimize the outage times of the power supply by quicker fault location other ways to provide appropriate measuring data should be provided.

BRIEF DESCRIPTION OF THE INVENTION

An object of the present invention is thus to provide a novel solution for measuring electrical quantities in an electrical network.

The method according to the invention is characterized by measuring samples of the electrical quantity at different feeders or locations of the electrical network in turns at different time instants and creating a value sequence on the basis of the measured samples, an individual value of the value sequence corresponding to a measured sample or a value calculated on the basis of at least one measured sample, the values in the value sequence being arranged into an order corresponding to the chronological order of the measured samples.

The system according to the invention is characterized in that the system comprises at least two intelligent electronic devices arranged at differ- ent feeders or locations of the electrical network for measuring the electrical quantity of the electrical network, each intelligent electronic device being arranged to measure samples of the electrical quantity in turns at different time instants than any other intelligent electronic device and that the system comprises an intelligent electronic device arranged to create a value sequence on the basis of the measured samples, an individual value of the value sequence corresponding to a measured sample or a value calculated on the basis of at least one measured sample, the values in the value sequence being arranged into an order corresponding to the chronological order of the measured samples.

In a method for measuring an electrical quantity in an electrical net- work, samples of the electrical quantity are measured at different feeders or locations of the electrical network at different time instants. On the basis of the measured samples a value sequence is created, wherein an individual value of the value sequence corresponds to a measured sample or a value calculated on the basis of at least one measured sample. The values of the value sequence are arranged into an order corresponding to the chronological order of the measured samples.

By measuring the same electrical quantity at different feeders or locations of the electrical network such that the samples of the electrical quantity are taken in turns at different feeders at different time instants, the actual sampling frequency of the measured electrical quantity may be increased without increasing the sampling frequency of any individual measurement point. At hardware level this means, that the sampling frequency relating to the above mentioned value sequence containing all the measured samples or values cal- culates on the basis of the measured samples, is higher than the sampling frequency of any individual intelligent electronic device. Thereby the sampling frequency of the measurement may be increased without increasing the sampling frequency of any individual intelligent electronic device.

According to an embodiment at least two sample sequences of a same electrical quantity are measured such that samples of each sample sequence are measured at a different feeder of the electrical network than the samples of any other sample sequence and that the samples of different sample sequences are measured in turns one sample at a time at different time instants and a value sequence is created on the basis of the samples of the sample sequences, wherein an individual value of the value sequence corresponds to a sample of a sample sequence or a value calculated on the basis of at least one sample of at least one sample sequence, and the values of the value sequence are arranged into an order corresponding to the chronological order of the samples of the sample sequences. BRIEF DESCRIPTION OF THE DRAWINGS

In the following the invention will be described in greater detail by means of preferred embodiments with reference to the accompanying drawings, in which

Figure 1 is a schematic illustration of an electric station; Figure 2 is a schematic illustration of an intelligent electronic device; Figure 3 is a schematic illustration of a measurement principle of an electrical quantity in an electrical network;

Figure 4 is a schematic illustration relating to the operation of the measurement principle relating to Figure 3;

Figure 5 is a schematic illustration of a substation computer;

Figure 6 and 7 are schematic illustrations of a measurement principle of an electrical quantity in an electrical network,

Figure 8 is a schematic illustration of the effect of a gain error of an intelligent electronic device on a signal-to-noise-ratio,

Figure 9 is a schematic illustration of the effect of an offset error of an intelligent electronic device on a signal-to-noise-ratio,

Figure 10 is a schematic illustration of the effect of a timing error on a signal-to-noise-ratio,

Figures 1 1 and 12 are schematic illustrations of a gain and timing error on a signal-to-noise-ratio,

Figure 13 is a schematic illustration of an effect of additional intelligent electronic devices on a signal-to-noise-ratio and

Figure 14 to 17 show schematically an example of an effect of a sampling frequency relating to earth fault location estimation. DETAILED DESCRIPTION OF THE INVENTION

Figure 1 shows schematically an electric station ES or a substation ES, illustrated by a dashed line. The substation 1 of Figure 1 comprises five feeders, one incoming feeder F1 and four outgoing feeders F2, F3, F4 and F5, the feeders F1 to F5 constituting an electrical network EN. For the sake of clar- ity only one phase, i.e. only one line denoted by F1 , F2, F3, F4 or F5 of each feeder is shown in Figure 1 . Each one of the feeders F1 to F5 comprise an intelligent electronic device lED, the incoming feeder F1 comprising intelligent electronic device IED1 and the outgoing feeders F2 to F5 comprising intelligent electronic devices IED2, IED3, IED4 and IED5 correspondingly. The intelligent electronic device lED may for example be a data collector, which measures or collects data about an electrical quantity EQ of the electrical network EN. The electrical quantity EQ of the electrical network EN may be for example zero voltage Uo, zero current l ₀ , phase voltage U or phase current I. The intelligent electronic device lED may also be a network protection and control unit, such as a protection and control relay, which in addition to data collection functional- ity provides necessary electrical network protection and control functionalities known as such for a person skilled in the art. The internal structure and functionality of an intelligent electronic device IED in view of the measurement solution presented in this description is discussed more detailed later.

The substation ES according to Figure 1 further comprises a substation computer ESC. Each intelligent electronic device IED1 to IED5 is connected to the substation computer ESC by data transmission lines DL1 , DL2, DL3, DL4 and DL5 such that any data collected by the intelligent electronic devices IED1 to IED5 or determined by the intelligent electronic devices IED1 to IED5 may be transmitted to the substation computer ESC for further analysis. The internal structure and functionality of the substation computer ESC in view of the measurement solution presented in this description is discussed more detailed later. The substation computer ESC forms or constitutes one kind of an intelligent electronic device too and it is also possible that the functionality of the substation computer ESC may be included in any of the intelligent electronic device IED1 to IED5.

Figure 2 shows schematically an internal structure of an intelligent electronic device IED when it is assumed that the intelligent electronic device IED is a network protection and control unit. The internal structure of all the intelligent electronic devices IED1 to IED5 in Figure 1 may be the same or may vary from each other depending on the purpose of use of each intelligent electronic device IED1 to IED5.

Intelligent electronic device IED according to Figure 2 comprises an input line IL for receiving an input or measurement signal describing or corre- sponding the electrical quantity EQ of the electrical network EN to be measured. The intelligent electronic device IED comprises further a low pass filter LPF and a sampling circuit SC. The sampling circuit SC comprises typically a sample and hold circuit and an analog-to-digital -converter for measuring or collecting or taking samples of the low pass filtered input signal with a sam- pling frequency f _s , the time interval At or sampling interval At between the consecutive samples being thus 1/f _s . The low pass filter LPF is used to filter away or remove those frequencies of the input signal which are above a border frequency set for the low pass filter LPF. The border frequency set for the low pass filter LPF is typically about half of the sampling frequency f _s of the sam- pling circuit SC. The sampling frequency f _s of the sampling circuit SC of the intelligent electronic device IED may vary depending on the purpose or use of the intelligent electronic device, but in the examples below it is assumed that the sampling frequency f _s of each intelligent electronic device IED1 to IED5 is 2 kHz, unless otherwise informed, whereby the border frequency of the low pass filter LPF is about 1 kHz.

The intelligent electronic device IED of Figure 2 comprises further a memory MM, which may be used to store the samples of the input signal to be measured such that the stored samples form or constitute a sample sequence SS of the measured electrical quantity EQ. Further the intelligent electronic device IED comprises a central processing unit CPU provided with an internal clock CLK for controlling the operation of the intelligent electronic device IED, for example for controlling the operation of the sampling circuit SC through a control line CTRL, and, if necessary, for executing necessary protection and/or control functions on the basis of the measured input signal values read from the memory MM or straight from the sampling circuit CS through a command line CL for example for opening a circuit-breaker of a feeder in a case of a fault on the feeder. Figure 2 shows schematically also the data transmission line DL, through which the content of the memory MM of the intelligent electronic device IED may be transmitted to the substation computer ESC, for example. Figure 2 shows also another filter FD, which may be used to filter the sample sequence SS stored into the memory MM for further reducing disturbances present in the sample sequence before transmitting the sample sequence SS to the substation computer ESC for further analysis. The function of the filter FD is considered more detailed later.

Figure 2 discloses schematically the internal structure of an intelli- gent electronic device which may be used for taking, collecting or measuring samples of an electrical quantity EQ of an electrical network EN to be measured. The intelligent electronic device may also comprise the necessary measuring sensors for measuring the input signal or the measurement signal corresponding to the electrical quantity or the intelligent electronic device may be connected to the measurement sensors providing the input signal, as is the case in Figure 2. The internal structure of different kind of intelligent electronic devices may also vary in many other ways and, when considering the solution presented in this description, the only important ability of the intelligent electronic device is to take, collect or measure samples of an electrical quantity EQ of an electrical network EN.

Figures 3, 4 and 5 present a measuring principle for measuring an electrical quantity EQ according to the solution presented in this description, when the phase voltage U is the electrical quantity EQ to be measured. Figure 3 presents schematically phase voltage U, y axis of Figure 3 representing the value of the phase voltage U and x axis of Figure 3 representing time t. Figure 4 presents schematically the memory contents MM1 to MM5 of each intelligent electronic devices IED1 to IED5 after ten samples of phase voltage U have been measured. Figure 5, in turn, presents schematically the internal structure and functionality of the substation computer ESC for organizing the samples measured by each intelligent electronic device IED1 to IED5 into specific order for providing the phase voltage U measurement with higher sampling frequency than the sampling frequency f _s of any individual intelligent electronic device IED1 to IED5.

According to the solution each intelligent electronic device IED1 to IED5 is arranged to take, collect or measure samples of the phase voltage U at the same sampling frequency f _s as any other intelligent electronic device in the same electrical network EN. Each intelligent electronic device IED1 to IED5 is, however, arranged or synchronized to measure the phase voltage samples in turns such that only one intelligent electronic device at a specific feeder is arranged to take one sample of phase voltage U at a specific time instant, and after that, another intelligent electronic device at another feeder is arranged to measure one sample of phase voltage U, the other intelligent electronic devices being again idle at that time, when considering the sampling of the phase voltage U. The samples of the electrical quantity are thus measured in such a way that after one sample of the electrical quantity EQ is measured at a specif- ic feeder, a new sample of the same electrical quantity is measured at a different feeder, and so on.

So, in the example relating to Figures 3, 4 and 5, the intelligent electronic device IED1 at feeder F1 is arranged to measure at a time instant ti a sample of the phase voltage U, the value of this sample being U(ti) _F i and cor- responding the value of the phase voltage U at time instant ti and being stored into the memory MM1 of the intelligent electrical device IED1 as shown schematically in Figure 4. At the time instant ti the other intelligent electronic devices IED2 to IED5 are idle when considering the sampling of the phase voltage U. Next, at time instant t ₂ the intelligent electrical device IED2 at feeder F2 is arranged to measure a sample of the phase voltage U, the value of this sample being U(t ₂ )F2 and stored into the memory MM2 of the intelligent electronic de- vice IED2. Again, at the time instant t ₂ the other intelligent electronic devices IED1 and IED3 to IED5 are idle when considering the sampling of the phase voltage U.

After this, the next sample of the phase voltage U is measured at time instant t ₃ by intelligent electronic device IED3 at the feeder F3, the value of the sample being U(t ₃ ) _F 3 and stored into the memory MM3 of the intelligent electronic device IED3, the other intelligent electronic devices IED1 , IED2, IED4 and IED5 being again idle when considering the sampling of the phase voltage U. _. In a similar way, next samples of the phase voltage U are measured at time instant t ₄ by the intelligent electronic device IED4 at feeder F4, the value of this sample being U(t ₄ ) _F 4 and at time instant t ₅ by the intelligent electronic device IED5 at feeder F5, the value of this sample being U(t ₅ ) _F 5, the values of the samples being stored correspondingly into the memories MM4 and MM5 of the intelligent electronic devices IED4 and IED5. After this, the next sample of phase voltage U is measured again by the intelligent electronic device IED1 at feeder F1 , the value of this sample being U(t ₆ )F-i , and after this, the measurement of the phase voltage U continues as explained above.

In the measurement solution above, each intelligent electronic device IED1 to IED5 at different feeders F1 to F5 in the electrical network EN are arranged to measure samples of the phase voltage U in turns, one sample at a time at different time instants t,, i = 1 , 10 in this example. When the sampling frequency f _s of each intelligent electronic device IED1 to IED5 is 2 kHz, the sampling interval At between the consecutive samples of the same intelligent electronic device being then At = 1/2000 = 500 s. However, when each of the intelligent electronic device IED1 to IED5 is arranged to collect samples of the same electrical quantity EQ as shown above, the sampling interval between the consecutive samples of all the collected samples is At/M = At/5 = 500/5 s = 100 s, M = 5 corresponding to the number of the intelligent electronic devices taken part in collecting the samples of the same electrical quan- tity EQ in this example. The sampling interval 100 s corresponds to a sampling frequency of 10 kHz, which is fivefold when compared to the original sampling frequency of each intelligent electronic device IED1 to IED5.

So, by arranging different intelligent electronic devices having the same sampling frequency f _s but configured to take samples at different time instants at different feeders or locations of the electrical network to measure the same electrical quantity, in this example phase voltage U, in turns one sample at a time, it is possible to increase the actual sampling frequency of the electrical quantity EQ to be measured without increasing the original sampling frequency f _s of the intelligent electronic devices. The measurement may thus take place at a feeder, for example at a connection point of the feeder at the substation, or at a location being in connection with the feeder, such as in an equipment like a motor, a transformer or a generator, connected to the feeder. At hardware level this means, that by only configuring the intelligent electronic devices already in use at different feeders or locations of the network to take samples at different time instants, the sampling frequency of the electrical quantity to be measured may be considerably increased without increasing the sampling frequency of any individual intelligent electronic device. Therefore the overall sampling frequency of the electrical quantity to be measured can be multiplied by the number of the intelligent electronic devices to be used for the measurement without creating any extra costs relating to hardware or its instal- lation. Further this means that it is possible to measure the higher order harmonics than before, as well as multiply the number of transient samples for fault location calculation and thereby increase the accuracy of fault location estimation.

Figure 4 shows schematically the contents of the memories MM1 to MM5 of the intelligent electronic devices IED1 to IED5 after measuring the samples of the phase voltage U at time instants ti to t-io shown in Figure 3. After the measurement the memory MM1 of the intelligent electronic device IED1 contains a sample sequence SS1 of two samples taken at time instants ti and t ₆ at feeder F1 , i.e. the samples U(ti) _F i and U(t ₆ )Fi - Further the memory MM2 of the intelligent electronic device IED2 contains a sample sequence SS2 of two samples taken at time instants t ₂ and t ₇ at feeder F2, i.e. the samples U(t ₂ )F2 and U(t ₇ ) _F 2- In a similar way, the memories MM3 to MM5 of the intelligent electronic devices IED3 to IED5 contain sample sequences SS3 to SS5 comprising the samples taken at the corresponding feeders F3 to F5. So, a number of sample sequences SS1 to SS5 of a same electrical quantity EQ, i.e. the phase voltage U, are measured by a number of intelligent electronic devices such that samples of each sample sequence SS1 to SS5 are measured at different feeders, of the electrical network EN than the samples of any other sample sequence SS1 to SS5. The samples of different sample sequences SS1 to SS5 are measured in turns one sample at a time at different time instants, and the individual samples are stored into the memories of the corresponding intel- ligent electronic devices in a form of a sample sequences SS1 to SS5. For the sake of clarity of the example presented in Figures 3 to 5 only two samples per each feeder F1 to F5 were measured but in practice the number of samples to be measured per each feeder is naturally much higher.

Figure 5 shows schematically the internal structure and operation of the substation computer ESC to the extent that it relates to the operation of the measurement solution described above. The substation computer ESC comprises a first memory MEM1 , into which the content of the memories MM1 to MM5 of the intelligent electronic devices IED1 to IED5 may be transmitted via the data transmission lines DL1 to DL5. The content of each memory MM1 to MM5 of the intelligent electronic devices IED1 to IED5 may be transmitted to the first memory MEM1 of the substation computer in such a way that the whole sample sequences SS1 to SS5 stored into the memories MM1 to MM5 are transmitted at a time. The central processing unit CPU of the substation computer ESC is arranged to create a value sequence VS on the basis of the samples of the sample sequences SS1 to SS5. An individual value of the value sequence VS corresponds to a specific sample of some sample sequence SS1 to SS5 such that the values of the value sequence VS are arranged into an order corresponding to the chronological order of the samples in the sample sequences SS1 to SS5. This means that the sample U(ti) _F i taken at time instant ti is arranged to be the first value in the value sequence VS, the sample U(t ₂ )F2 taken at time instant t ₂ is arranged to be the second value in the value sequence VS and so on. The value sequence VS may be stored for example into a second memory MEM2 of the substation computer ESC, which memory MEM2 may physically be in the same physical memory device as the first memory MEM1 . The value sequence VS stored in memory MEM2 may be utilized for example for fault location calculation, if the samples collected relate for example to a voltage transient phenomenon occurring at the beginning of an earth fault.

In the example above the sample sequences SS1 to SS5 were transmitted from the intelligent electronic devices IED1 to IED5 to the substation computer ESC a sample sequence at a time, but it is also possible that the individual samples collected by the intelligent electronic devices IED1 to IED5 may be transmitted from each intelligent electronic device IED1 to IED5 to the substation computer ESC immediately after the sampling event so that no special sample sequences SS1 to SS5 are formed into the memories MM1 to MM5 of the intelligent electronic devices IED1 to IED5. In this case the value sequence VS may for example be created directly into the second memory MEM2 of the substation computer ESC without storing the samples temporarily into the memories MM1 to MM5 of the intelligent electronic devices IED1 to IED5.

With the measurement principle explained above the sampling frequency of the phase voltage U can easily be multiplied without increasing the actual sampling frequency f _s of any individual intelligent electronic device IED. The same measurement principle may be used for measuring the zero voltage Uo too because the phase voltages and the zero voltage of the electrical network are same in the whole galvanically interconnected electrical network.

Figure 6 and 7 show the measurement principle of the electrical quantity EQ in the electrical network EN in a case, wherein the electrical quantity to be measured is a phase current I. The structure of the intelligent elec- tronic device IED is same kind as disclosed in Figure 2 and the related description.

Because the phase current I is typically in practice different at every feeder F1 to F5, depending on the load connected to the feeder, the measurement method for measuring the phase current I is somewhat different when compared to the measurement method of phase voltage U. This limitation, however, can be at least partially compensated by applying Kirchhoff s current law, according to which at a specific point of an electrical network EN the sum of the incoming currents, i.e. current in incoming feeder F1 in this example, is equal to the sum of the outgoing currents, i.e. currents in the outgoing feeders F2 to F5. This leads to a measurement method of phase current I, in which at each time instant t, it is taken or measured one actual measurement value with one intelligent electronic device at one feeder. For the same time instant t, it is provided an estimated values for the phase currents I at the other feeders, the last measured sample at each feeder being a starting value for the estimation at each specific feeder. The estimated values may be provided for example by linear interpolation, i.e. linear interpolation is used for calculating virtual measurement points or values at each specific feeder between actual measurement points or values at that specific feeder. With this procedure there are obtained from each time instant t, one actual or real measurement at one feeder and several virtual interpolated measurements at the other feeders.

The above measurement method is shown by way of an example in Figures 6 and 7, wherein Figure 6 shows a phase current I with respect to time t, and Figure 7 shows the content of the memories MM1 to MM5 of the intelligent electronic devices IED1 to IED5 and the content of memory MEM2 of the substation computer ESC. At time instant ti the value of phase current I is measured at feeder F1 , this sample being denoted by and this value is stored into the memory MM1 of the intelligent electronic device IED1 . For the same time instant ti it is calculated, for example by using linear interpolation, estimated values for the phase current I at the other feeders F2 to F5 on the basis of the previously actually measured values (not shown) at each specific feeder F2 to F5, the calculated values being lc(ti )F2 at feeder F2, lc(ti )F3 at feeder F3, lc(ti )F at feeder F4 and lc(ti )F5 at feeder F5, these values being stored at the memories MM2 to MM5 of each specific intelligent electronic device IED2 to IED5. In the lower part of Figure 6 for each feeder F1 to F5 the actually measured values are schematically denoted by filled dots and the cal- culated values are denoted by circles for each time instant t,, wherein 1 = 1 , ... , 10. The period of time between successive time instants t, is Δί/Μ, where At is the sampling interval corresponding to the sampling frequency f _s of each intelligent electronic device and M is the number of active or operating intelligent electronic devices in the measurement system.

At time instant t ₂ the phase current I is measured at feeder F2, this measurement value being denoted by livi(t ₂ )F2 and this value is stored into the memory MM2 of the intelligent electronic device IED2. For the same time instant t ₂ it is again calculated or estimated, for example by using linear interpolation, values for the phase current I at the other feeders F1 and F3 to F5 on the basis of the previously actually measured values at each specific feeder F1 and F3 to F5. This means that the calculated value lc(t2)Fi at feeder F1 at time instant t ₂ is provided by using linear interpolation on the basis of the actually measured value at feeder F1 at time instant t-i. The arrow marked by reference mark C in the lower part of Figure 6 denotes that for all time instants t ₂ , t ₃ , and t ₅ the value of phase current I at feeder F1 is calculated or estimated on the basis of the last actually measured phase current value livi(ti )Fi for that specific feeder F1 . At the other feeders F3 to F5 values for the phase current I at time instant t ₂ is again interpolated on the basis of the last actually measured values (not shown in Figure 6) at each specific feeder F3 to F5, the calculated values being lc(t ₂ )F3 at feeder F3, lc(t ₂ )F4 at feeder F4 and lc(t ₂ )F5 at feeder F5, these values being stored at the memories MM3 to MM5 of each specific intelligent electronic device IED3 to IED5.

This same principle is continued for the next time instants t,. After the measurement situation is over, the content of the memories MM1 to MM5 may be transmitted to the substation computer ESC, wherein, by the operation of central processing unit CPU, the value for the phase current l(tj) at each time stamp t, may be determined by a function f(l _M , lc, t,), i.e. I(tj) = f(l _M i, lei, t,), wherein l _M i denotes the actually measured phase current value at one feeder at time instant t,, l _C i denotes the calculated or estimated phase current values at the other feeders at time instant t,. When determining the phase current l(tj) by using the function f(l _M , lc, t,) it is applied in the function the Kirchhoffs current law according to which the sum of the actually measured phase current value at one feeder and the calculated or estimated phase current values at the same time instant t, should be zero for every time instant t, by adding to the interpolated values possible residual errors caused by the interpolation. The residual error may be added to the interpolated values for example on the basis of the magnitudes of the phase currents at each feeder such that the higher the magnitude of the phase current at the feeder, the higher portion of the residual error is added to the interpolated values relating to that specific feeder. For example the RMS-value of the phase current may describe the magnitude of the phase current. The phase current values l(t-i), l(t ₂ ) and so on determined for every time instant t, are then stored for example in the second memory MEM2 of the substation computer ESC.

In the example above the calculation or estimation of the phase current values was executed in the central processing unit CPU of each specific intelligent electrical device IED1 to IED5, but it could be done also in the central processing unit CPU of the substation computer ESC, if only the actually measured phase current values are transmitted to the substation computer ESC.

Instead of calculating any estimated values by using for example linear interpolation it is also possible to add zeros between the actually measured phase current values. In this example four zeros should be added between the actually measured phase current values for increasing the sampling frequency to be fivefold, i.e. 10 kHz, at each feeder F1 to F5, and then use a low pass filter to remove the signal having the frequency of 2 kHz, i.e. the fre- quency of the original sampling frequency, originating from the adding of zeros between the originally measured values. This general type of raising the sam- pling frequency of an individual measurement signal is known as such and it is not described more detailed here.

Linear interpolation and raising of the sampling frequency by adding zeros are presented in Oppenheim, Alan V.; Schafer, Ronald W. Discrete-Time Signal Processing. Prentice Hall. 1989. ISBN 0-13-216771-9.

In the embodiment shown for the measurement of the phase current I measuring samples of the electrical quantity to be measured, i.e. the phase current I, are measured or collected at different feeders of the electrical network EN in turns one sample at a time at different time instants. Thereafter value sequence VS is created on the basis of the actually measured phase current samples, and also on the basis of the calculated or estimated phase current values, such that an individual value in the value sequence VS corresponds to a value calculated on the basis of one measured sample at one feeder and one or more estimated values at the other feeders, wherein each estimated value is may be provided by using linear interpolation, the linear interpolation using the last measured sample as a starting value for interpolating the estimated value at each specific feeder. The values in the value sequence VS are arranged into an order corresponding to the chronological order of the measured samples. Same measurement principle may be used for measuring the zero current l ₀ too.

So, with the measurement solution described above a sampling frequency of 10 kHz may be produced with five intelligent electronic devices each having a sampling frequency of 2 kHz. However, each measurement chain, even with identical intelligent electronic devices and sensors, has some unique measurement error which may need to be compensated before the signal is used for analysis. If for example one intelligent electronic device has a small scaling error or an offset error in the measurement, it creates an additional frequency component equal to the sampling frequency, 2 kHz in the above example, which may be filtered out with a low-pass filter incase compensation is not possible. This second low-pass filter is schematically shown in Figure 2 with a reference mark FD.

In the following it is presented calculations for assessing the effect of different mismatches, i.e. gain, offset and timing mismatches between different intelligent electronic devices, for understanding the possible compensa- tion needs of the measurements. If gain, offset and timing mismatches are assumed to have Gaussian distribution, the combined effect to signal-to-noise- ratio SINAD may be determined by the following equati

SINAD

A is an amplitude of the input signal,

M is an amount of intelligent electronic devices,

μ is an expected value of the gain of an analog-to-digital converter in an intelligent electronic device,

a ₀ is an input signal frequency relative to the sampling frequency of one intelligent electronic device,

o _g is a standard deviation from the expected gain,

a _rl is a standard relative timing deviation of an analog-to-digital converter in an intelligent electronic device,

σ is a standard deviation of the offset.

As in substation automation an individual analog-to-digital-converter of an intel- ligent electronic device plays an important role, the equation (1 ) is arranged to take into account variations of each single intelligent electronic devices, thus making the results more descriptive. In equation (1 ), for example 1 s deviation with sampling frequency of 1 kHz per device, sampling interval being then 1 ms, means that the value a _rl is 0.001 , regardless of the amount of analog-to- digital converters used. Also when investigating the effect of multiple measurements, it should be considered the quantity a ₀ , i.e. the input signal frequency relative to the sampling frequency of one intelligent electronic device. In equation (1 ) a ₀ thus indicates the input signal frequency relative to the sampling frequency of one intelligent electronic device, a ₀ being 0.5 if the input signal frequency is 1 kHz with 2 kHz sampling frequency.

The effect of the deviations of individual components can be derived from equation (1 ) by setting other deviations to zero - e.g. the effect of timing deviation is well visible when both gain and offset deviations are set to zero. The graphical results of these derivations are visible in Figures 8, 9 and 10, wherein Figure 8 shows schematically the effect of the gain error, Figure 9 shows schematically the effect of the offset error and Figure 10 shows schematically the effect of the timing error on the measurement error indicated by the signal-to-noise-ratio SINAD and when it is assumed that M is 8, μ is 1 and a ₀ is 0.5.

Figures 8, 9 and 10 provide the maximum possible signal-to-noise- ratio SINAD if the error in one component is known. If the timing error can be 1 % of the sampling interval of one intelligent electronic device, the maximum possible SINAD according to Figure 10 is around 30 dB no matter how identi- cal the measurement chains otherwise are. In the measurement chain of an intelligent electronic device the offset error is normally negligible, and the effect of it can be skipped. The most interesting therefore is the combined effect of gain and timing mismatches, which are shown schematically in Figures 1 1 and 12, when M is 8, μ is 1 and a ₀ is 0.5. The combined effect is well visible in Figure 12 showing the contours of the combined effect. From the Figure 12 it can for example be seen that SINAD over 50 dB can only be achieved when both the timing deviation is below 0.001 and the gain deviation is below 0.003.

Figure 13 shows schematically the effect of additional intelligent electronic devices on the signal-to-noise-ratio when the number of intelligent electronic devices in the measurement system increases. In Figure 10 o _g is

0.005, o _rl is 0.001 , σ ₀ is 0 and μ _? is 1.

In Figure 13 it can be seen that the signal-to-noise ratio SINAD does get slightly worse when the amount of intelligent electronic devices, i.e. the amount of analog-to-digital-converters increases, but not greatly. This indi- cates that the signal quality would remain on the same level, which is the most important aspect with transient based algorithms. Transients last only few milliseconds, so the main aspect is that the amount of data points can be increased without a major affect to the SINAD -value.

According to calculations presented above the timing mismatch of samples should not exceed 0.1 % of the sampling interval At if gain accuracy is around 0.5 %. With the sampling frequency of 2 kHz the sampling interval is 0.5 ms which gives time accuracy requirements of 0.5 s with 0.1 % accuracy. This can be ensured by synchronizing the internal clock CLK in each intelligent electronic device with respect to the clocks CLK in other intelligent electronic devices such that each intelligent electronic device is arranged to take samples at its own turn at specific time instants. Therefore also the clock controlling the analog-to-digital controller, if the sampling circuit SC comprises a clock separate from the clock CLK in central processing unit, may be arranged in the same clock synchronization process. For synchronization purposes each intelligent electronic device comprises a settable time offset such that when one intelligent electronic device, for example intelligent electronic device IED1 , is running in sync with the synchronization master (offset = 0), which is typically the substation computer ESC, other intelligent electronic devices IED2 to IED5 must have an offset time with multiples of (1/M/f _s ) where M is the amount of intelligent electronic devices in the measurement system and f _s is the sampling frequency. For example if 5 intelligent electronic devices with 2 kHz sampling frequency are synchronized from the same synchronization master, the offset time for the intelligent electronic device IED1 at feeder 1 may be 0, the offset time for the intelligent electronic device IED2 is 1 / 5 / 2000 = 100 s, and the offset times for other intelligent electronic devices IED3 to IED5 are 200 s, 300 s and 400 s. The synchronization may be controlled by the substation computer ESC, which may send a synchronization control signal SYNC to each intelligent electronic device IED1 to IED5 when necessary. The system may, however, comprise a separate synchronization master which synchronizes also the substation computer ESC. By synchronization it is possible to com- pensate timing mismatches in the measurement system. The synchronization control signal SYNC is shown schematically in Figures 1 and 2 by an arrow.

The settable offset times of intelligent electronic devices IED1 to IED5 ensure also that the measurement system is applicable also in situations where the network topology changes, in which case if an intelligent electronic device is behind a circuit breaker, a change in network topology e.g. due to a fault can remove one intelligent electronic device from the measurement chain or system. Because of this, centralized logic must be implemented to the substation which takes this aspect into account. If one intelligent electronic device measurement is missing, new timing offset values must be calculated and pro- vided to the remaining intelligent electronic devices so that the measurement system can resume operation with M-1 -measurements. In this case the sampling interval At of an individual intelligent electronic device remains same but the period of time between the samples taken by different intelligent electronic devices increases. As indicated earlier, this does not, however, affect greatly to the SINAD of the measurement signal, but the amount of data points for transient analysis is reduced. The measurement system is therefore arranged to take the network topology changes into account and to change the functionality of the measurement system, such as the number of intelligent electronic devices used for the measuring, the period of time between the samples taken by different intelligent electronic devices and the sampling order of different intelli- gent electronic devices accordingly.

As disclosed above, the timing mismatches can be minimized by synchronizing the intelligent electronic devices as exactly as possible by using settable offset times in each intelligent electronic device. This is one way to compensate the possible measurement errors during the measurement of the electrical quantity EQ. Because in a substation the measurement signal of one intelligent electronic device is needed for protection purposes also, an extensive signal processing, such as RMS (Root-Mean-Square) -Calculation or DFT (Discrete Fourier Transform) -calculation is already done to it. This brings new possibilities especially to the gain mismatch compensation because the gain mismatch can for example be compensated by comparing the fundamental frequency phasors of the measured electrical quantity obtained by different intelligent electronic devices at different feeders.

An example relating to Figures 14 to 17 illustrates an effect of the measurement solution presented above. The example relates to a transient analysis for earth fault location estimation. When an earth fault occurs in a network with an isolated neutral, there is always a fast transition, called a transient, present. When the voltages on phases change, the charge in them has to change too. During the transient there is a current flowing from one phase to another to compensate the change in the network. When the charge of supply lines reaches the new equilibrium, the transient slowly decays.

The transient consists mainly of two components which are called a discharge component and a charge component. In addition there are interline compensating components, the function of which is to equalize the voltages of parallel lines at their substation terminals. In compensated networks there is also a decaying DC-component (Direct Current), which is due to a compensation coil. The discharge component results from the decrement of the voltage in faulted phase. When the voltage in the faulted phase decreases, the electric charge in the cables has to decrease as well. Simultaneously the voltages in sound phases rise, and these cables can reserve more energy. This shows in the voltage as a charge component. Because the charge component flows through a substation transformer, the frequency of it is much less than of the discharge component. The amplitude of the charge component dominates the transient, which makes it more suitable for fault location estimation purposes. The frequency of the discharge component is normally 500...2500 Hz and the one of the charge component 100...800 Hz. Because of the higher amplitude and the lower frequency of the charge component earth fault location algorithms used are typically based on charge component analysis. In Figure 14 it is presented an example of phase voltages u-i , u ₂ and u ₃ at a beginning of an earth fault in an electrical network having an isolated neutral point. Figure 14 shows clearly, how the phase voltages change during a low resistance earth fault - the voltage of the faulted phase ui drops close to zero whereas the voltages of the sound phases u ₂ and u ₃ rise to phase-to-phase voltage.

Figures 15 to 17 show an example of the effect of the sampling frequency of the phase current I and phase voltage U measurements on the performance of an earth fault location algorithm, which determines the distance to fault by analyzing the charge transient. Figures show the error of the calculated distance to fault reported by the algorithm, when the fault distance varies between 1 and 40 km in an example network. The algorithm also reports the deviation of the calculated distance, which describes the accuracy of the result. In Figure 15 the sampling frequency applied was 10 kHz by using one measure- ment instrument and in Figure 16 the sampling frequency applied was 2 kHz by using one measurement instrument too. In Figure 17, however, five measurement instruments were used, each measurement instrument having a sampling frequency of 2 kHz and arranged to take samples in turns according to the measurement solution described above.

As the Figures show, with 5 streams of 2 kHz sampled signal the results are very similar to the results with single measurement instrument with 10 kHz sampling frequency. Using only one stream of 2 kHz sampled signal gives very poor results with short fault distances. The shorter the distance to fault is, the higher is the frequency of the charge transient. Therefore algo- rithms with low sampling frequency give bad results.

The example proves that by combining, as explained above, the measurements made by measurement instruments having low sampling frequencies it is possible to increase the sampling frequency of a measurement signal in an electrical network such that high quality measurement data to be used for power quality and fault location analysis, for example, may be provided. It will be obvious to a person skilled in the art that, as the technology advances, the inventive concept can be implemented in various ways. The invention and its embodiments are not limited to the examples described above but may vary within the scope of the claims. In the example above there are one incoming feeder and four outgoing feeders and therefore the example discloses five intelligent electronic devices. It is however evident that the number of the feeders or locations, where the samples of the electrical quantity are measured, and correspondingly the number of the intelligent electrical devices arranged to measure the electrical quantity, may vary such that there are at least two intelligent electrical devices and at least two different feeders or locations, where the samples of the electrical quantity are measured.