How Accurate Are Your Power Measurements?

Energy efficiency is the most common discussion point in all forms of sustainable energy, and whenever the topic comes up, the importance of power measurement moves straight to the top of the priority list. Manufacturers today offer a wide range of power measuring instruments backed by seemingly impressive specifications, but how do potential users decide which parameters actually matter for their application? This article looks at the factors that affect the accuracy of power measurements and shows how users can address the challenges of accurate energy-efficiency testing.

Power Accuracy

Improving the energy efficiency of a product, even by a few decimal points, is both an important goal and a major challenge for manufacturers. To validate small efficiency gains, R&D teams need to understand the total accuracy, or uncertainty, of their power analyzers. As a manufacturer, it is important to know all of the factors that influence that uncertainty.

In many cases, customers evaluate power analyzers based on voltage and current uncertainty alone, but what they should really be looking at is power uncertainty. A full power accuracy evaluation should consider not just the basic parameters, but also factors such as crest factor, phase angle error, temperature range, warm-up time, stability period, and common mode rejection.

Understanding Manufacturers' Specifications

Manufacturers' specifications often include terms such as "guaranteed" and "typical" values. Yokogawa is the only manufacturer of power meters that guarantees the power measurement uncertainties published in its data sheets. Some manufacturers instead publish typical values, which can mislead customers.

A typical value is usually a reference figure based on what a manufacturer expects from a product, not a value that is 100% guaranteed. This is why many manufacturers' typical-value specifications look better than their guaranteed values, and it is also why Yokogawa power analyzers, once calibrated, provide accuracies that are five to ten times better than the published specifications.

Measurement Range

Measurement range is another factor that is often inadequately specified in manufacturers' data. Yokogawa is the only power analyzer manufacturer to specify the measurement range over which its accuracy figures apply. This matters because the uncertainty of a power measurement varies with the measurement range, so an accuracy value is only meaningful if the range it applies to is stated. For example, the power accuracy of the Yokogawa WT3000, the world's most accurate power analyzer, is valid from 1% to 130% of the measurement range. Without a stated range, users cannot know whether a published accuracy figure holds across the whole range or only at a single point within it.

High-Precision Harmonics

Harmonic measurement is another area where specifying accuracy in context matters. Every Yokogawa power analyzer includes an additional oscillator dedicated to phase-locked loop (PLL) measurement, which enables high-precision harmonic measurement. With this dedicated oscillator and powerful digital signal processing, the frequency spectrum can be analyzed up to the 500th order harmonic (depending on the instrument) simultaneously with the normal measurement. Because of this dedicated circuit, Yokogawa is able to specify the accuracy of its harmonic analysis, something that is not the case with many other manufacturers.

The Influence of Crest Factor

Accuracy calculations are usually performed using sine waves at 50 to 60 Hz and a power factor of one, meaning all of the energy supplied by the source is consumed by the load. Basic accuracy for voltage, current, and power is specified as a percentage of the measured value and a percentage of the measurement range, and that range can be defined with respect to either the peak or the RMS value. Understanding the resulting measurement range error requires understanding crest factor: the ratio of a waveform's peak value to its effective RMS value.

Crest factor matters to a power meter in two ways. First, it describes a specification of the meter itself, showing how well the instrument can measure correctly regardless of how distorted the input waveform is. Second, measuring the crest factor of an input voltage or current signal gives an indication of the quality of that signal.

For a measuring instrument, crest factor expresses the extent of the dynamic range available for an input signal. Yokogawa defines crest factor as the dynamic range value based on the rated range value, the RMS value. Yokogawa power meters are usually specified with a crest factor of three or six, meaning the instrument can measure an input signal with a peak value three or six times larger than the rated RMS range. For example, using 100 V RMS and 1 A RMS ranges, the available input voltage and current signals are as follows:

When CF=3, using 100 V RMS and 1 A RMS ranges, the instrument can measure input peaks of up to 300 V and 3 A.

When CF=6, using the same 100 V RMS and 1 A RMS ranges, the instrument can measure input peaks of up to 600 V and 6 A.

If the input RMS value is lower than the rated range value, the power meter can measure signals with an even larger crest factor. The WT series can display values when the signal is more than 0.5% of the rated range value; if the input RMS value sits at that 0.5% floor and the input peak value is three times the rated range value, the effective crest factor becomes 600. If an input exceeds the value shown in the specifications, the peak area of the waveform is clipped, causing a measurement error. A crest factor of three therefore means the maximum allowable input is three times the rated RMS value.

RMS vs Peak Value for Crest Factor Evaluation

The measuring ranges of Yokogawa power meters are defined with respect to the RMS value, giving the analyzers a crest factor of three or six. If the range were instead defined using the peak value, as some other manufacturers do, the maximum crest factor of a Yokogawa power analyzer would be quoted as 300. For example, in the 100 V RMS range with a crest factor of three, peaks of plus or minus 300 V can be detected; dividing 300 V peak by 1 V RMS gives a result of 300. Note that this is still 1% of the range, so the accuracy specification remains valid.

Some power meters use RMS measurement ranges and others use peak measurement ranges. Relating an accuracy specification to peak values can look impressive at first glance, but it is not necessarily more meaningful. For example, an accuracy value of 0.1% from the peak measurement range corresponds to 0.3% of the RMS measurement range at a crest factor of three. For active power calculation, multiplying voltage and current (and power factor) together amplifies this effect dramatically. Yokogawa uses RMS values for both measurement range setting and tolerance calculation.

Zero-Crossing Detection

Accurate power measurement also depends on accurate zero-crossing detection. Yokogawa power analyzers use dedicated frequency-measuring hardware for zero-crossing detection, which identifies the fundamental frequencies within pulse-width-modulated (PWM) signals. This is achieved using a synchronization technique known as "average for the synchronous source period" (ASSP).

For complex PWM signals with many harmonics, alternative methods that determine the zero crossing in software cannot achieve high measurement accuracy for current, voltage, and active power. Precise measurement of effective power requires the current and voltage samples to be synchronized, particularly at low power factors and high frequencies. The instantaneous power values are then integrated over the defined measurement interval to obtain the effective electrical power, which can be displayed as a waveform or a numeric value depending on the customer's preference.

Phase Error

Every power meter has an associated phase error that cannot be ignored in uncertainty calculations. The voltage and current inputs fed to the A/D converters are not normally perfectly in phase, and the resulting phase error appears in the simple active power formula for pure sine waveforms as P = (Vrms) × (Irms) × cos(±δ), where δ is the phase error.

Phase angle error δ between the voltage and current waveforms directly affects the calculated active power.

Challenges in Current Measurement

One of the key challenges in current measurement arises when a current shunt is used. A current shunt is a relatively large component with low inductance and parasitic capacitance, which causes a small phase shift and an additional time delay in the current signal. Converting this signal into the digital domain without introducing further error requires careful hardware design.

This phase shift has no effect on RMS voltage, RMS current, or apparent power, but it does influence the measurement of active power and, in turn, power factor. A power factor of 0.1 causes a phase error of 0.1° and an additional active power error of 1.6%, which shows just how sensitive active power measurement is to small timing errors. This phase shift must be specified by the manufacturer of the power analyzer. Yokogawa specifications account for all possible boundary conditions that can lead to a phase angle error or measurement error, and these are included in the published calculations.

Common-Mode Rejection Ratio (CMRR)

The common-mode rejection ratio (CMRR) measures a device's ability to reject unwanted input signals that are common to both input leads of the voltage input. In this test, the two input terminals are connected to each other, with the device ground used as the reference point. Ideally, this configuration should have no influence on the measurement result, but in practice, leakage causes an interference voltage that depends on the symmetry of the input circuit.

In practical terms, the noise voltage superimposed on the signal being measured leads to measurement errors, so customers need to factor this into their uncertainty calculations. Common mode noise is especially present in inverter-style applications, because of the high-voltage potentials with high-frequency components present relative to ground. Yokogawa power analyzers have their CMRR specified, so it can be included directly in uncertainty calculations.

Temperature Effects

Temperature is another factor that affects the accuracy of a power analyzer. Yokogawa's uncertainty specifications are stated at 23°C ± 5°C. Some manufacturers specify a narrower temperature range, for example 23°C ± 2°C, a tighter figure that in practice adds significant uncertainty once the instrument operates outside that narrow band.

The Importance of Calibration

As this article has shown, understanding the true accuracy of a power analyzer requires understanding all of the factors that influence it. It is also always recommended to have the unit calibrated at regular intervals.

Yokogawa is the only industrial, that is non-government or national, organization to offer traceability up to 100 kHz, and it is the only power-meter manufacturer able to directly prove the performance of its own instruments.