Effective power analysis is vital in developing AC-powered applications. One reason is the need to demonstrate compliance with the IEC 1000-3 EMC standards that limit the harmonic currents and voltage fluctuations that can be injected back into the AC supply. But effective power analysis also benefits overall system development by helping designers accurately account for power losses and improve equipment efficiency.
To understand why effective power analysis and compliance with the IEC standard are so important, we must consider the problems that arise from equipment that is not IEC-compliant. At the heart of these problems is the single-phase, AC-powered equipment that can cause serious supply problems in the three-phase transmission network.
Basic AC theory shows that complex, nonlinear loads, including any equipment with a capacitively smoothed, bridge-rectified input, create harmonically rich current waveforms. This results in waveforms comprising a fundamental component and a series of even and odd harmonic components. Although the waveforms are symmetrical, even harmonics are not significant.
The useful current is the fundamental component because this generates useful power. However, additional, nonuseful harmonic currents flow within the equipment power supply and the distribution cables, transformers, and switch gear of the transmission network.
Generally, a transmission network features distribution transformers providing power to the community via a three-phase, four-wire output (a star connection and a neutral line). Input to these transformers is three-phase, three-wire power (delta-connected) taken from the grid.
To ensure balanced load demand, each phase of a distribution transformer is wired to one-third of the community it serves. As the fundamental voltage components of each phase of a three-phase system are displaced by 120°, they cancel each other out, giving zero neutral current. That’s why the neutral line in a four-wire transmission system has a much smaller current rating than each phase conductor.
However, odd harmonics that are divisible by three, such as the 3rd and the 9th harmonics, can cause problems. Figure 1 shows a basic, symmetrical, three-phase supply in which each phase is shifted by 120°. If we introduce the 3rd harmonic of each phase, we can see that they are significant—they are exactly in phase with each other and do not cancel each other out. As each phase draws its 3rd, 9th, and higher harmonic current from the neutral line, rather than carrying zero current, this line carries three times the phase harmonic current.
The presence of these nonuseful harmonic currents drawn from the transmission network via the neutral line can create problems. The power resulting from neutral currents, for instance, can cause neutral lines to overheat or burn out.
Similar problems can occur at the distribution transformer as it delivers neutral 3rd, 9th, and higher harmonics on its secondary windings when its primary is delta- configured (no neutral). These currents also reduce transmission efficiency because real power (watts) decreases as harmonic current increases. At the same time, increases in reactive energy (VAr) can raise the distribution system’s copper losses.
Finally, large current peaks drawn from a supply with finite impedance result in the voltage waveform itself becoming flat-topped, leading to problems with loads connected to the supply. Motors, for example, can overheat or vibrate. Capacitors for power-factor correction applications may be damaged because they provide a low-impedance path for harmonic components of the distorted voltage.
Except for products such as electric heaters or incandescent light bulbs, almost any piece of electronic equipment generates distortion on an AC supply. The main offender is the switch-mode power supply (SMPS) used in the majority of consumer, computing, telecommunications, and industrial systems. However, lighting ballasts for controlling fluorescent and sodium lamps and pulse-width modulated (PWM) motor drives also are major culprits. As a result, these applications demand rigorous power analysis.
Analyzing the Power
To perform effective power analysis, it is important to understand the key voltage, current, and power measurements. The main waveform measurements that must be taken include the rms values, the average values, the real and apparent power, the power factor, the crest factor, and the harmonic distortion (see sidebar). Accurately measuring each of these parameters gives raw data that not only facilitates IEC analysis, but also supplies information on key design and environmental issues such as power consumption and efficiency.
One important consideration for successful power analysis is the frequency bandwidth of the equipment used to measure the waveforms. For instance, consider the example of a PWM motor drive with a fundamental component of 50 or 60 Hz and a 12-kHz carrier frequency. A standard 20-kHz power analyzer might read 200 Vrms on the output. However, measuring the same signal on an instrument with a 1-MHz bandwidth might give an rms value of 240 V, the difference of 40 V—20% of the reading—being the contribution of harmonic components above 20 kHz.
Another important criterion is the capability to perform multiple, simultaneous measurements. This ensures synchronization of current and voltage waveform sampling which, in turn, allows vector analysis to be used for interphase calculations.
Instantaneous power at any point, for instance, can be obtained by sampling data points for voltage and current over a wide band. Also, the need for simultaneous measurements is explicitly stated in the documentation relating to IEC 1000-3-2 that demands that the AC source characteristics (voltage, frequency, and harmonics) are measured continuously at the same time as the current harmonics.
Analyzing the Waveform
Once the raw waveform data has been collected, separate it into fundamental and harmonic components. This typically requires Fourier analysis. Using sine and cosine calculations, Fourier analysis allows any complex waveform to be broken into a DC component, a fundamental component, and a series of harmonics.
For waveforms that are symmetrical for positive and negative half cycles, there will only be odd harmonics. However, when symmetry becomes distorted, even harmonics become relevant.
Fourier analysis offers two methods for breaking down the waveform: discrete Fourier transform (DFT) and fast Fourier transform (FFT). In principle, both DFT and FFT analysis use the same mathematical formulas. FFT analysis, however, combines formulas to produce simplified matrices which reduce the number of calculations to be performed. Despite this, DFT is the preferred method for harmonic analysis.
Both FFT and DFT methods require power-measurement equipment to sample input waveforms in line with Nyquist at a rate to avoid aliasing. An FFT-based system requires that the number of samples be a power of two, such as 256 or 1,024. Depending on the cycle times of the waveform measured, it is rare that a complete cycle or multiple cycles fit perfectly into the power of two sampling windows. This introduces errors that must be compensated for with filters or windowing functions.
DFT analysis has no sampling restrictions, and the number of samples can be selected to fit the cycle or cycles exactly. With a precise measurement of the fundamental frequency, multiples of the fundamental will provide the basis for accurate discrete computation of each harmonic. Given accurate samples, the accuracy of the results for a DFT-based computation is not dependent on precise control of the sampling rate or the use of frequency windows. Instead, it relies on the more easily achievable, accurate measurement of fundamental frequency.
To put power analysis into context, consider the requirements for a PWM motor drive. As Figure 2 shows, key power measurements break down into drive electronics input, DC bus, and drive electronics output measurements. Practically, there also is a need for motor output measurements.
Table 1 lists the measurements for each stage. The output waveform of the drive electronics will be a complex mixture of high- and low-frequency components that is difficult to measure accurately. Measurements at high frequencies, for example, may lose accuracy of the low-frequency content of the waveform, while filtering it to measure low frequencies eliminates the high-frequency data.
A particular problem here is measuring total power which demands sampling at very high frequencies over an integral number of cycles. The solution is to sample data at a high speed and compute parameters such as total rms volts and watts in real-time. Then, digitally filter the samples to provide low-frequency information such as the fundamental voltage and current and a measurement of the output frequency. This allows both high-frequency and low-frequency data to be obtained from the same samples and ensures that high-frequency measurements are synchronized to the low-frequency signal.
Generally, drive output measurements are made using the two-wattmeter method shown in Figure 3. This method provides identical total power measurements to the three-wattmeter method used in a three-wire system. The third channel of a typical power analyzer then is available for DC bus measurements, for example.
Measuring the input power of a PWM drive also is problematical because current taken from the supply may be modulated by components of the output frequency. One way around this is to synchronize the measurements to the AC line frequency over an integral number of cycles of the output waveform during a user-specified interval.
Conclusion
To obtain sensible and useful results, effective power analysis requires much more sophisticated equipment than basic multimeters. Fortunately, some of today’s power analyzers simplify power testing by combining wide-bandwidth, multichannel measurement capabilities with the high power processing required for analysis. Increasingly, such analyzers also offer control via a host PC with software packages that not only speed setup and analysis, but also simplify the key measurements demanded by the IEC standards.
About the Author
Stuart Chappell is the sales and marketing director at Voltech Instruments. Before joining the company in 1992, he spent nine years as an engineer with Farnell Instruments and a brief period as a senior sales engineer at Gould Electronics. Voltech Instruments Ltd., 65 Milton Park, Milton, Abingdon OX14 4RX, U.K., (011) 44 1235 861173.
Voltech Instruments, (919) 461-1701.
Power-Analysis Measurements
RMS
This is the most useful means of specifying the value of both AC voltage and current because it indicates the level of power available from the AC waveform. The calculation of an rms value is best described by considering an AC current waveform and its associated heating effect as shown in Figure 4a.
If this current is flowing through a resistance, the heating effect at any instant is given by W = I2R. By dividing the current cycle into equally spaced coordinates, the variation of the heating effect with time can be determined as in Figure 4b. The average heating effect (power) is given by:
I12R + I22R + I32R + … + In2R
WAv = ———————————————-
n
To find the equivalent value of current that would produce the average heating- effect value, then the following applies:
Ieff = ————————————–
n
leff = the rms of the current
This value is the effective value of the AC waveform because it is equivalent to the direct current that produces the same heating effect in the resistive load.
Average Value
The average value of a waveform is the area enclosed by one half cycle divided by the length of the base of that half cycle. The average value can only have real meaning over one half cycle because, for a symmetrical waveform, the mean or average value over a complete cycle would be zero.
Most simple multimeters determine AC values using full wave rectification of the waveform followed by a calculation of the mean value. Such meters will be calibrated in rms and use the known relationship between rms and average for a sinusoidal waveform or rms = 1.11 × mean. For waveforms other than a pure sine wave, the readings from such meters will be invalid.
Real and Apparent Power
If a sinusoidal voltage is connected to a resistive load, then the voltage and current will be in phase, and the power into the load at any instant is given as the product of the voltage and current at that instant. This results in the power into the load fluctuating at twice the supply frequency. If the load is reactive, then the current is no longer in phase with the voltage.
Although the power continues to fluctuate at twice the supply frequency, it is dissipated in the load only during a part of each half cycle. During the remaining part, it is returned from the load to the supply. The apparent power (VA) delivered to the load is calculated as Vrms × Arms.
The real power delivered depends on the nature of the load, and it is not possible to determine the value of real power from the knowledge of rms voltage and current. When the real power is required (for instance, for assessing heat loss or efficiency), this can only be achieved through the use of a true AC power meter capable of computing the product of instantaneous voltage and current values and displaying the mean of the result.
Power Factor
When assessing power designs, it must be possible to assess the power factor (W/VA) which is defined as the ratio of useful power to apparent power. In the case of sinusoidal voltage and current waveforms, the power factor actually is equal to the cosine of the phase angle (f ) between the voltage and current waveforms. For this reason, the power factor often is referred to as cos f .
However, the power factor is only equal to cos f when the waveforms are perfectly sinusoidal. Power factor can change dramatically in the case of harmonically distorted waveforms. Unlike many power meters which merely calculate cos f , any power-analysis equipment must be able to calculate the actual rather than theoretical power factor by measuring real and apparent power. A universal definition for cos f which applies to all waveforms, whether distorted by phase or shape, derives from the fact that f always is the phase angle between the fundamental voltage and current.
Crest Factor
For a sinusoidal waveform, the peak value can be defined as the rms value multiplied bycrest factor = peak value/rms value
A sinusoidal waveform will have a crest factor ofHarmonic Distortion
Modern loads introduce complex distortion of the current waveform, and it is essential to accurately quantify the level of this distortion. Observation using general-purpose instrumentation may indicate the presence and level of the distortion but will not provide the high levels of accuracy needed for effective power analysis.
|
Motor Output Measurements |
Speed, Torque, and Shaft Power |
|
Drive Electronics Output Measurements |
Total Output Power and Power Factor Fundamental Output Power and PF RMS Output Voltage and Current Fundamental Output Voltage and Current Harmonic Voltages, Currents, and Powers Output Frequency |
|
Drive DC Bus Measurements |
DC Bus Voltage, Current, and Power |
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Drive Electronics Input Measurements |
Input Voltage and Current Input Power and Power Factor Input VA and VAr Input Harmonic Currents Including Checking to Harmonic Specifications such as IEC 555 |
|
Efficiency Measurements |
Efficiency of Each Section of PWM Drive, Motor Efficiency, and Overall Efficiency |
|
Measurements Under Dynamic Load Conditions |
Real-time Analog Outputs Representing Voltage, Current, Watts, and Power Factor of Drive Output |
Table 1
Copyright 1999 Nelson Publishing Inc.
June 1999