Solutions. What You Should Know About Your Digital Power Meter. Volume 7, Issue 3

Transcription

1 Volume 7, Issue 3 What You Should Know About Your Digital Power Meter Introduction Digital power meters are very powerful tools that help manage your energy usage and ascertain the level of power quality in your facility. Generally, digital power meters have inputs for both voltage and current to measure the electrical characteristics of a specific point on the electrical system. Measuring and analyzing the voltage and current provides the basis for all other values calculated in a digital power meter. Before power system voltage and current signals can be analyzed in a digital power metering device, the signal must first be converted from an analog (continuous-time) signal into a digital (discrete-time) signal. Converting the analog signal into a digital signal requires a series of snapshots, or discrete samples, of the original analog signal (see Figure 1). As implied by the term sample, the resulting digital signal is only an estimate of the original analog signal. Transforming an analog signal into a faithful digital representation requires the use of hardware, specifically an ADC (analog-to-digital converter). The ADC samples (measures) the analog signal at a given discrete rate to approximate the original input signal. The rate at which the ADC samples PowerLogic is produced by Square D Company s Power Management Operation. Each issue presents a common power system problem, and offers guidance on how to solve it. the signal, called the sample rate, is expressed as samples per second. The sampling frequency is equal to the sample rate, but is expressed in Hertz. The intersample interval, typically specified in a manufacturer s literature, is the time between samples. The intersample interval is equal to 1/(sampling frequency) and is expressed in seconds. All other components being equal, the higher the sampling rate of the ADC, the more accurate the representation of the original signal. But how high should the sampling rate be? (... continued on page 2)

2 (... continued from page 1) A good analogy for sampling rate is the resolution of pictures taken by a digital camera. Figure 2 shows a picture taken at a low resolution (sampling rate), while Figure 3 shows the same picture taken at a higher sampling rate. Figure 3 has more clarity and is a truer representation of the subject. Similar to the resolutions of pictures, the resolution (or sampling rate) of a signal is important in telling the whole story. Another example that illustrates the effects of an inadequate sampling rate is the wagon wheel effect. This effect describes the optical illusion that occurs in old movies when the wheels of a fast-moving wagon appear to be turning slowly backwards. This effect is caused by the slower frame speed (sample rate) of the camera relative to the higher speed of the wagon wheel. Figure 2-Low resolution image Figure 3-High resolution image Sampling Theory Background A general discussion about analog signal sampling and processing in digital power meters requires that we lay some basic groundwork in the theory of digital signal processing. The Nyquist/Shannon Sampling Theorem states that an analog signal waveform may be uniquely reconstructed, without error, from samples taken at a rate slightly greater than twice the highest frequency component in the analog signal. For example, measuring the 11th harmonic on a 60 Hertz system (11 * 60 or 660 Hertz) requires a sampling rate of slightly greater than 1320 Hertz. Practical systems, which include non-ideal filters and other sources of error, require sampling rates considerably higher than twice the highest frequency components. The highest frequency component in the analog signal determines the bandwidth of the signal. The Nyquist frequency is equal to the highest frequency in the analog signal (660 Hertz in the discussion above). The Nyquist rate is equal to twice the highest frequency (1320 Hertz in the discussion above). One-half the sample rate is called the folding frequency, which will become important later in this article. A signal is said to be undersampled when the sampling rate of the ADC is less than the Nyquist rate. A rough estimate of the highest frequency that can reliably be measured by a meter is determined by dividing the sampling rate of the meter by 2. Some difficulties with discrete signal sampling Converting an analog signal into a digital signal is not as straightforward as taking discrete snapshots of the analog signal. There are several potential pitfalls in a meter s sampling techniques that can lead to conversion errors in the resulting digital signal or inadvertent filtering that can mask critical data. Financial considerations are typically a large determining factor when addressing the following constraints. Undersampling Some digital power meter manufacturers believe that there is no relevant information at higher frequencies, and, thus, that lower sampling rates are generally acceptable. This is not necessarily the case. As Figures 2 and 3 illustrate, undersampling a signal gives a poorer representation of the subject. A truer representation may be vital to properly analyze the intricacies of a waveform for the source of a disturbance. A true representation of the original signal Sampling analog signals at high rates in power quality meters is necessary to adequately represent signals that contain high-frequency components. By sampling the waveform at higher sample rates, a troubleshooter can conclusively determine the magnitude, duration, and initial polarity of extremely fast voltage events. The higher sampling rate also gives a troubleshooter a detailed profile of an event a higher and more accurate level of detail that is not available at normal sampling rates. This detail allows better diagnosis of (and solutions to) high speed events. In many cases, more damaging energy is behind high-speed events than would be assumed using normal sampling rates. Not only do high sample rates allow the characteristics of high-speed events to be accurately shown, but the meter is able to conclusively demonstrate that a chosen solution is effective in mitigating a problem at the load. The aliasing effect Loss of information is not the only concern when a signal is undersampled. Error in the conversion process can be introduced through a principle known as aliasing. Aliasing occurs when the highest frequency at the input of the ADC is greater than half the sample rate typically when the bandwidth of the analog signal is not limited by filters or when the sample rate is too slow. In short, aliasing occurs when a digital power meter tries to measure frequency components above its useful range.

3 Figure 4 illustrates the concept of aliasing in the time domain. The signal (black line) is undersampled by 25% (sampled 1.5 times per cycle). The red line shows what the meter believes the signal to be a lower frequency than the real signal. Figure 5 illustrates how the higher frequencies are folded down to a lower frequency in the frequency domain. the 7th harmonic, an operator attempting to troubleshoot a power quality problem could easily be misled in this situation. Figure 4. Undersampled Analog Signal Figure 5. Illustration of Aliasing in the Frequency Domain Figure 8. Frequency Spectrum of Analog Signal with 9th Harmonic Sampled at 512 Samples per Cycle. Figures 6 and 7 illustrate a real-world example of aliasing. Figure 6 is a composite analog signal in the time domain, sampled at 512 samples per cycle. This signal includes a fundamental component (60 Hertz) and its 9th harmonic component (540 Hertz). The magnitude of the 9th harmonic component is 25% of the fundamental component. Figure 7 shows the same composite analog signal in the time domain, this time sampled at 16 samples per cycle. It is apparent by observation that the signals do not look the same. The question is: Why are they different? Figure 6. Analog Signal with 9th Harmonic Sampled at 512 Samples per Cycle Figure 7. Analog Signal with 9th Harmonic Sampled at 16 Samples per Cycle Earlier we stated that the highest frequency that a meter can reliably measure is roughly determined by its sample rate divided by two. The meter sampling at 16 samples per cycle can only measure up to slightly less than the 8th harmonic (< 480 Hertz). Then, why does the 16 samples/cycle waveform still show distortion, even though the 9th harmonic (540 Hertz) is above the meter s range? This is due to the phenomena of aliasing. Figures 8 and 9 show the harmonics in the frequency domain for each signal. When a frequency in the analog signal exceeds one-half the sample frequency (480 Hertz), that frequency is folded down into one of the frequencies that can be measured by the meter; hence the term folding frequency. The meter sampling at 16 samples per cycle can theoretically measure up to 480 Hertz. The 540 Hertz (9th harmonic) component in the signal is folded down an equal distance to the opposite side of the folding frequency: 420 Hertz (or the 7th harmonic of the fundamental) as shown in Figure 9. Since the meter reports what in reality is the 9th harmonic as being Figure 9. Frequency Spectrum of Analog Signal with 9th Harmonic Sampled at 16 Samples per Cycle. To further compound the complexity of aliasing in digital power meters, a phase shift in the aliased frequency components may also occur. The phase shift of a specific frequency component will depend on both the specific frequency component and the folding frequency for the meter. Thus, some frequency components will be subtracted and some will be added to the measured components below the folding frequency. Therefore, not addressing the problem of aliasing may result in unrecoverable error being introduced into the measurement results reported by a digital power meter. IEC (2002), a standard on measuring harmonics and interharmonics, is the first power standard to address the issue of aliasing. To comply with IEC (2002), a meter must include anti-aliasing filters. Non-synchronous Sampling Sampling a single cycle in a power monitor and returning a close approximation of that cycle would seem to be a simple task. But what if timing error in the meter allows the meter to sample a slightly longer or shorter period than one cycle?

4 This pitfall is known as non-synchronous sampling. Non-synchronous sampling along the time axis occurs when the meter samples a noninteger number of cycles of the frequency(s) of interest in the sample window (Figure 12). When a frequency is cut off in the middle of its period, other higher order frequencies are inadvertently introduced into the digital signal. Since these other frequencies are not really there, error is introduced into the digital power meter. Figure 13. Frequency Spectra of Signal in Figure 12. Figure 10. Synchronously Sampled Signal The worst case scenario for a nonsynchronous sampling period would be sampling over an additional half cycle. Figures 14 and 15 illustrate the time-domain and frequency-domain waveforms of a 1½ cycle sample period (90 Hertz in this case) where the sample rate was not adjusted to sample an integer number of cycles. This exaggerated example of non-synchronous sampling conveys some important information: Figure 11. Frequency Spectra of Signal in Figure 10 Figure 10 shows a single cycle that was sampled by a digital power meter for analysis. The frequency domain of this waveform is shown in Figure 11. The frequency spectrum of the signal is a pure 60 Hertz sine wave. Non-synchronous sampling introduces false even harmonic components and a dc component into the metering data that normally are limited in a power system. The odd harmonic components that are introduced will produce an error in a digital power meter s harmonic data (especially at lower frequencies). The fundamental frequency component will actually be higher than the meter states. All of these factors can add up to erroneous readings in the metered data. Figure 12 illustrates the case in which the power frequency has changed from 60 Hertz to 63 Hertz, but the sample rate in the meter was not changed accordingly to sample an integer number of cycles. Many additional frequencies appear in the frequency spectrum (Figure 13), because it takes all these frequency components to rebuild the truncated signal. This condition also introduces error into the final metering data. Figure 14. Non-synchronously Sampled Signal (90 Hertz) Figure 12. Non-synchronously Sampled Signal (63 Hertz)

5 Hertz in North America). As a rule of thumb, a higher folding frequency results in fewer errors in the data. However, many digital power meters available on the market today do not offer sample rates high enough to effectively mitigate the aliasing effect. Figure 15. Frequency Spectra of Signal in Figure 14 IEC (2002) also addresses the issue of synchronous sampling. IEC (2002) states these limits for synchronous sampling in Class I or Class II digital power metering devices: ±0.03% over a 200 millisecond window on all voltage channels. This equates to a maximum deviation of ±60 microseconds ( x 200 milliseconds) over the 200 millisecond window. Recommendations Now that some of the pitfalls of converting analog signals to digital signals have been discussed, how can these errors be minimized? High Sample Rates Sampling an analog signal at a high sample rate is important for several reasons. First, it provides a higher resolution image of the waveform that is being sampled (see Figures 2 and 3). This, in turn, provides more conclusive information about the characteristics of highspeed events. Magnitudes in lower sample rates are inaccurate by more than three times the actual values. Higher frequency components, associated with a high-speed event, may not even be measured. Initial polarity of an event could be missed as well. This information gives the user the ability to better diagnose transient events by helping locate the source of a transient based on that transient s characteristics. Another benefit of digital power meters that use high sample rates is that they can be used to better evaluate the true effectiveness of mitigation equipment such as SPDs or filters. High sample rates in digital power meters also push the folding frequency further out on the frequency spectrum. This minimizes the error due to aliasing, because frequencies in power spectra tend to attenuate as they increase beyond the fundamental frequency (60 Filtering Filtering the input analog signal before it is sampled by the digital power meter eliminates the problem of aliasing. A low-pass filter, or anti-aliasing filter, is placed on the input of the digital power meter to eliminate high frequency components that might be aliased. The anti-aliasing filter only passes frequency components that are lower than the power meter s folding frequency. Stated another way, the purpose of an anti-aliasing filter is to eliminate any frequency that may alias, and thus introduce an error into the converted digital signal within the digital power meter. Many digital power meters do not use antialiasing filters. This is largely due to cost constraints and the assumption that the inaccuracies due to aliasing will be minimal. When anti-aliasing filters are not employed in a digital power meter, higher sample rates can compensate as described earlier in this paper. Synchronous Sampling Minimizing the error in how a meter determines the length of a period is the key to improving a meter s accuracy. As shown in Figures 12 and 13, non-synchronous sampling can introduce significant errors in power system spectra. There are various ways of combating these errors. One method is to use an analog phase lock loop (PLL) to control the sample rate of the ADC. The PLL can be designed to produce a rectangular or square wave output, the frequency of which is a multiple of the fundamental of the power system frequency. This signal then controls the ADC sample rate. Once the signal is sampled, there are various algorithms available to measure the frequency of the power system fundamental. Once the actual frequency is known, the sample rate of the ADC can be adjusted by varying the frequency of the sample clock. The end result of all these methods is to cause the ADC sample rate to always be a multiple of the power system fundamental frequency.

6 Conclusions Sampling the analog signal at a higher rate is necessary to ensure that the meter collects all relevant information for any event that occurs on the electrical system. Some standards recognize the effect of influence factors outlined in this paper; and one, IEC Standard , 2002 requires anti-aliasing filters and a specified level of synchronous sampling to meet a certain meter performance level. The purpose for these requirements in digital power meters is to help ensure the validity of the data. Required Sampling Rate for Power Systems Power quality events that include high frequency components occur routinely on power systems. Some of these events originate outside the end user s facility (such as lightning), while others originate inside the facility (such as load-switching events). A lightning event has an extremely fast rise-time as shown in Figure 16, taken from IEEE Standard : IEEE Standard for Insulation Coordination Definitions, Principles and Rules. In this case, the time-to-crest (T r ) is defined at µs, and the time-to-half value (T h ) is given as less than 300 µs. These lightning events are generally unidirectional and of very short duration. For example, assume a lightning strike produces a voltage with a T r of 0.4µs. To obtain three samples of the rising edge of the impulse, the required sampling rate can be calculated as follows: Figure 16: Lightning Overvoltages (T r = µs, T h < 300 µs, where T r is the time-to-crest value, T h is the time-to-half value) ( 0.4µ sec ) Intersample Interval = ( 3 1) where the first sample is assumed to be taken at t = 0 0.4µ sec Intersample Interval = = 0.2µ sec 2 Sampling rate = 1 Intersample = Interval 1 = 5 MHz 0.2µ sec This sampling rate is equivalent to 83,333 samples per cycle at the power system fundamental component (60 Hz.). Many transient events are missed or not accurately approximated because the meter uses fewer samples than are necessary to accurately depict the analog signal. Most meters sample between 64 and 512 samples per cycle. While this may be fast enough to detect the majority of longer duration events, faster events such as transients may either be missed completely or not accurately represented. IEEE defines a transient event lasting less than one cycle. This broad definition opens the door for some digital meter manufacturers to loosely interpret it qualitatively instead of quantitatively. Simply put, if a meter can capture an event shorter than a cycle, then it can detect transients. To truly meet the spirit of IEEE 1159, a meter should be able to capture any transient event that may disrupt the operation of end-use equipment. Because of their short duration and often unpredictable pattern of occurrence, capturing and analyzing transient events requires the use of more sophisticated digital power meters. These meters sample the analog signal at a much higher frequency than standard meters. With a faster sampling rate, these specialized meters more accurately reproduce the original analog signal by including the higher frequency components inherent in transient events. While longer duration events may be properly diagnosed using lower sampling rates, many transient events cannot.

7 Power Management Operation offers complete power quality consulting services to ensure that power problems do not impact your operation. Contact our power management experts for information about the following: Power Quality Consulting Energy Management Consulting Harmonic Filters Power Factor Correction Power Management Training and Technical Support Digital Simulation Studies Remote Monitoring Services Data Collection and Analysis Our number is Doc # 3000HO0407 October Schneider Electric All Rights Reserved