Measurement of the steady-state power-quality factors on the power system is usually justified by the need to assess the level of the stresses they impose on equipment. These stresses, which in most cases take the form of overheating of electronic and electrical components, reduce the useful life of the end user’s equipment. This section addresses the basic concepts in measuring the steady-state  harmonic voltage level.

Type of instrument

Analyzers come in two general types: analog and digital. The analog concept and the digital concept provide two different design strategies. Analog equipment works with continuously variable voltages or currents, whereas digital equipment works with voltage samples that represent binary numbers observed during a short interval called the observed window.

Analog analyzers are composed of several adjustable filters which display or plot the amplitude of a specific harmonic component versus time during the recording. These types of analyzers are called frequency-domain instrumentation. The filters should be selected to attenuate neighboring frequency according the following table:

The use of microprocessors in digital analyzers with the DFT algorithm began to replace the analog analyzers at the beginning of the 1980s. The data processing units used in this new, so-called time-domain instrumentation, opened the door to multiple types of disturbance and the statistical analysis needed for power quality assessment. Since this capability continues to increase in popularity, this guide describes in greater detail the time-domain instrumentation.

Basic equation used to assess harmonic level

This section aims to provide basic equations for assessing harmonics, it is not intended to replace the specialized instrumentation using advance techniques but to introduce the digital Fourier-transform technique "DFT".

The voltage or the current to analyze f(t) is sampled every 12th cycle window.  According to Fourier theory, this signal can be replaced by the summation of several sinusoidal waves according the following equation:

                             [6.1]

where w  = 2 ´  p  ´ Frequency = 2 ´  p  ´  60 = 377

                    [6.2]

                       [6.3]

                                                      [6.4]

                                                                      [6.5]

S = sampling rate

Example to explain how to apply the basic DFT equations

This section aims to explain the basic equations for assessing harmonic while the reader constructs his personal harmonic analyser using his preferred spread sheet software. For example, the voltage or the current to analyse f(t) is sampled every 200 µs with a digital oscilloscope.  The most common voltage wave form which can be recorded in most business office using many personal computers is shown in Figure 6.1.

Figure 6.1: Voltage supply of most business office using personal computer

In this example, an oscilloscope is used to sample the wave form at the sampling rate S of 5000 samples per second (200-µs sample interval) and more then 1024 samples can be stored. According to IEC standard, at least 12 cycles should be sampled for the 60-Hz system (10 cycles on 50-Hz system). Most modern digital oscilloscopes include the serial communication port which allows the data to be transferred into PC. The reader can also approximate the wave form with the following equation:

where t = 1 to 1024 in this example,

The user should find the number NK of samples contained in the 12-cycle window. The data recorded (Fig 6.1) for this example revealed exactly 1000 samples are comprised in the 12 cycles. The frequency is calculated according to the following equation:

Frequency = S · number of cycles / NK

S = 5000 S/s for this example,

Number of cycles = 12 cycles specified in IEC 61000-4-7 and considered in IEC61000-4-30

NK = 1000 samples in 12 cycles for this example

Therefore, the fundamental frequency = 5000 · 12 / 1000 = 60 Hz

Therefore, the coefficient a_n, b_n, and c₀ become:

                  [6.6]

           [6.7]

                                            [6.8]

Now equations are defined, data should linked to the spread sheet. The table 6.1 gives the spread-sheet design which needs to be developed according equations 6.6 and 6.8 which are rewritten from Eq 6.9 to 6.16 for this specific application and for harmonic order 3, 5 and 7.

             [6.9]

             [6.10]

             [6.11]

           [6.12]

           [6.13]

          [6.14]

            [6.15]

         [6.16]

Table 6.1: Spread sheet to calculate the harmonic order 1 to 7 of a wave recorded

The summation of values in each colon divided by 500 gives the harmonic level of each order as shown in Table 6.2

Table 6.2: Amplitude of each harmonic order of the wave shape given as example

Therefore the wave recorded can be replaced by the following equation:

[6.16]

 Instrumentation specification:

Since the power system frequency fluctuates all the time, the fixed sampling rate should produce a new number of samples for almost each observation window analyzed to maintain the window width at exactly 12 cycles. Rather than count the samples in each window, some manufacturer prefer to change the sampling rate according to the power system frequency and to obtain a fixed number of samples. Using either method , the number of samples comprised in the observation window of 12 cycles should be accurate, otherwise, significant error will be added in the result. For this reason IEC specifies the accuracy of the number of samples analyzed to fit with the exact 12-cycle window. This specification is frequently forgotten. Few manufacturers test the number of cycle once in a while assuming that this parameter is constant between two tests. This technique works perfectly well when the signal generator controls the frequency during a laboratory test, but the instruments using this technique are not as accurate during a field test. Therefore IEC requires testing each window width for assessing the error in the number of cycles, this should not exceed 0.03%. 

Harmonic severity level

Hand sized meters and several other harmonic analyzers supply only the instantaneous value of the harmonic level. These meters supply very few measurements during a 10-min interval assuming that all values during short periods are all the same. This type of measurement, called a "snap shot" can give a good indication of the disturbance level only if the user knows exactly during which periods which the highest disturbance occurs. The user also needs to control precisely the phenomenon by turning on and off the disturbance load.

In most cases, the user is unaware of the phenomenon that causes the highest disturbance level and therefore, the snap shot technique is insufficient to assess accurately the actual severity level of disturbances. Most users do not control the phenomenon, so a snap shot can be performed while the disturbing loads are turned off or not synchronized. Even if the user succeeds in measuring the disturbance during the correct instant, he still needs to perform many measurements to assess the duration of the disturbance.

Instantaneous harmonic measurement is not accurate enough to supply the instantaneous severity level of a distorted voltage wave form. Zero-crossing, crest factor and voltage rise are more appropriate factors to consider for instantaneous-annoyance assessment. The real need for an harmonic analyzer is to assess the heating effect of the distortion on equipment. For assessing the severity level that the stress harmonics impose on equipment, IEC 1000-4-7 recommends use of the following time intervals;

IEC 1000-3-6 selects the rms assessment in every 3-s interval to assess the harmonic level of the power system. Tests performed in several laboratories (LTEE, PEAC, NRC …) have demonstrated that heat in equipment is influenced by the square of the disturbance. This rms output value in 3-s intervals supplies several other inputs such as the assessment of 10-min and 2-h intervals. The final result gives a complete set of ranges which allow severity level evaluation for electric and electronic apparatus. The sought measured value should give significant information to compare the emission level and the planning level with the disturbance level used for resting the equipment immunity.

For the short-term effects (thermal) assessment of harmonics, the rms value:

[6.17]

of all M single calculated values C_n shall be determined over the time interval T_VS for selectable individual harmonics.

For assessing the severity level of the stresses imposed on power electronic equipment such as power supplies used in computers, TV sets etc… the (thermal) rms value:

[6.18]

of the 200 single calculated C_nVs during the last 10-min interval shall be determined for selectable individual harmonics.

For assessing the severity level of the stresses imposed on power electric equipment such as motors and transformers the (thermal) rms value:

[6.19]

of the 12 single calculated C_nSh during the last 2-h interval shall be determined for selectable individual harmonics.

Preliminary investigation

A handheldmeter can be used during the preliminary investigation of a specific problem. These meters may be not accurate for field tests but they can be useful to detect resonance problems. The user should read the harmonic level before and after turning off the power capacitor used for correcting the power factor. If resonance occurs, then each disturbing load will need to be switched on and off during the resonance condition.

A handheld meter may fail to correlate the problem with the harmonic level or the user may not want to turn off loads. Several meters available offer a strip chart feature which continuously records each order of harmonic. The continuous recorder provides a level profile printed on a 24 h chart for each order of harmonic. Recent recorders give the option of 3-s, 10-min and 2-h interval assessment. The user should select 10 min or 2 h which cover the severity level for most electrical equipment.

As soon the disturbing load is located and the phenomenon is well known, the user may need the complete co-ordination graph to design the mitigation system. The design specification requires the correction level to achieve. Levels of instantaneous, very short, short and long intervals as defined in IEC 1000-4-7, should be recorded continuously during at least one week. Data recorded during each interval serve to perform the statistical analysis to assess the probability not to be exceeded. The user should select the probability at which the design will succeed in maintaining the harmonic level below the desired level. The higher the probability that is chosen, the more costly the mitigation system will be. As example, figure 6.2 provides one co-ordination graph matching the 99% probability that the fifth harmonic level recorded on a power system, is not exceeded. The red curve identified as "fixed intervals" is provided by the steady-state rms value of the disturbance levels occurring in standard intervals of 3 s, 10 min and 2 h which are equal to five times the heating time constant TC of equipment (see Tutorial on 3-s interval rms value assessment). These results are valid for the specific interval during which the measurement is performed. The technique of measurement by predefined intervals does not take account of energy accumulated in electrical equipment as a result of disturbances preceding the interval assessed. The blue curve shown as energy-related interval, is provided by the rms value of the disturbance level occurring in standard intervals, whose value is related to the heat flowing in equipment characterized by heating time constants of 600 ms, 2 min and 24 min. In this case, the measurement technique considers disturbance levels prior to the interval analyzed (see tutorial on Voltage Imbalance assessment).

Figure 6.2: Co-ordination graph matching 99% probability that the fifth harmonic level is not exceeded

The user can find the design goal by plotting on the graph the desired level and then measuring the margin between that level and the actual disturbance level.

There is a recorder which assesses the severity level by considering the disturbance previous to each interval measured. This type of measurement give the so called energy related level (see Fig. 6.2). This value is very useful for specifying the stresses which the mitigation system should handle.

Measurements can also be performed to assess the expected level after the installation of a disturbing load. For this type of assessment, the user will need a recorder that supplies data for the co-ordination graph as used for specifying the mitigation system. (see IEC1000-3-6 for the recommended level)

IEC 1000-2-2 deals with conducted steady-state disturbances including harmonic distortion in the frequency range up to about 10 kHz^§, and up to 150 kHz for mains signaling systems. IEC 1000-4-7, which is based on conventional measurement practices, specifies that measuring instruments for harmonics up to 2000 Hz (3 kHz in IEEE) are still adequate for assessing the so-called low-frequency steady-state distortion level at most points of common coupling (PCC). However, with new power electronic equipment, such as pulse width modulated (PWM) drives, harmonic distortions have been observed at frequencies up to 12 kHz and even exceeding 20 kHz when notches occur, which justifies the measurement of so-called high-frequency steady-state distortion levels. Instrumentation characterized by a limited bandwidth below the 150th harmonic cannot provide a reliable assessment of harmonics up to 9 kHz, apart from ascertaining that disturbances occurring on the power system do not exceed that particular bandwidth. This can be done using an analog circuit designed to measure the period of time in each hour monitored that the total rms level of the disturbance components of frequencies beyond the upper limit of the instrumentation bandwidth exceeds by more than 0.5% the nominal voltage or current amplitude. When that time does not exceed 1 minute per hour monitored, the recorded disturbance is considered valid for comparison with IEC planning levels up to 9 kHz; otherwise, the disturbance assessment is incomplete.

Time-domain instrumentation performs synchronized sampling of the voltages and currents by means of a phase-locked loop (PLL) in each group of rectangular windows. In event of a malfunction of the PLL, the instrumentation should flag and count each event. The 3-s assessment value assessed with Equation 6.17 should avoid any corrupted data resulting from incorrect PLL operation, transients, and phase shift and so gaps between observation windows are needed.

Consequently, power spectral analysis is recommended for every consecutive period of less than 500 ms that includes gaps up to 300 ms between windows. Each cycle of the signal in a sampled window is compared with the previous cycle to make sure infrequent transients do not appear in the data. Windows without any transients are then analyzed using the appropriate DFT algorithm, as explained in IEC 1000-4-7. The results of spectral analysis are subjected to the error study explained in the next section to check that the gaps between each observation windows are not too wide.

The instantaneous voltage harmonic C_n values of order n, used to calculate rms value over a 3-s interval Cn_Vs (Eq 6.17) serve also to assess the sampling error x n_3s according to Eq. 6.20:

[6.20]

where

[6.21]

K = maximum possible number of consecutive windows to be analyzed in the 3-s interval:

K = 30, for example, when a 200-ms window width is considered, since all possible moving windows in a 200 ms are redundant. When windows are not free of transients, moving windows cannot be redundant and the following equation should be considered:

where:

T = interval = 3 s

f = fundamental frequency = 50 or 60 Hz

cycles/window = number of cycles per window (8 to 12)

samples/cycle = number of samples per cycle (128 to 1024)

M = number of DFTs performed in each 3-s interval (M ³  6)

Cn_Vs = 3-s rms synchronized quality factor level

Cn_i = ith term of the M Cn values used to assess Cn_Vs in Equation 1

The variable x n_3s gives an indication of the error caused by data losses when increasing the gap between windows. Assessment of x n_3s using Equation 6.20 can give differences of up to ± 5 times the actual error, which means that this equation is of no use in assessing the accuracy of any particular Cn_Vs. However, experience has shown that a daily cumulative frequency of x n_3s tends toward the daily cumulative frequency of the actual error, which can be used as an accuracy criterion. This criterion states that the accuracy of the rms disturbance level is adequate when the error introduced by increasing the gap does not exceed 5% during 95% of the time that the power quality survey is being conducted at one service entrance. This criterion is tested daily and, when the recorded measurements do not satisfy it, the measurement technique is no longer reliable and errors exceeding 5% can occur in more than 5% of the measurements^§. Unless the power quality survey supplies quality factor levels five times lower than the compatibility level or error levels within the adequate margin, new measurements with a reduced gap width are recommended.

 

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References

20. Roger Bergeron, "Voltage Unbalance on Dstribution Systems - Phase I", Canadian Electrical Association, Project No. 231 D 488, Montréal, Québec, January 1989.

21. Westinghouse Electric Corporation. "Applied Protective Relaying", Silent Sentinels publication, Newark, New Jersey.

22. Cumming, P.G. "Protection of Induction Motors Against Unbalance Voltage Operation", IEEE-PCI, September 1983, IEEE-PIT, June 1984 and IEEE-IAS October 1984.

23. Roger Bergeron, "A Measurement Protocol for Power Quality Coordination", CIRED 1991, paper 2.17, April 1991.

24. IEC 27-1 (1992).- Letter Symbols To Be Used in Electrical Technology. Part 1: General.

25. IEC 146. Parts 1 to 6 .- Semiconductors Convertors.

26.     IEC 375 (1972).- Conventions Concerning Electric and Magnetic Circuits.

27. Roger Bergeron, "Power Quality Measurement Protocol, CEA Guide to Performing Power Quality Surveys," CEA report 220 D 711, Canadian Electrical Association 1 Westmount Square, Suite 1600 Montréal, Québec, Canada H3Z 2P9, 1996, 216 pp.