**1. Introduction**

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In recent years, power quality analyzers and revenue meters with harmonic analyzing function have increasingly been used to monitor the state of the power supply network. The precise capability of revenue meters to measure electrical energy under non-sinusoidal conditions has been questioned on the basis of some IEC [IEC, 2003] standards and international recommendations. For EMC, harmonic tests are prescribed in the IEC documents [IEC, 2001, 2002] to ensure that appliances including televisions, computers, lamps, and motors do not produce harmonic currents that exceed allowable limits when they are operated under sinusoidal voltage. The harmonic measurement is an important task too in the background of the smart grid.

Many harmonic analyzers with variable levels and harmonic sources with determined accuracies have been offered in the market even as new instruments are being developed. At the same time, these have created a need for national laboratories to provide calibration facilities and traceability for harmonic quantities, including harmonic voltage, harmonic current, and harmonic power.

To respond to the changing needs of the industry for non-traditional electrical measurements, many national laboratories (NMIs) have developed standards for power measurements under non-sinusoidal waveform conditions. A harmonic power standard equipment was also developed at the National Institute of Metrology of China (NIM) in 2006. This equipment can accurately calibrate harmonic power analyzers and harmonic sources, and calibrate the harmonic-analyzing-function of the revenue meters, including its measuring capability for electrical energy under non-sinusoidal conditions. The uncertainties of the standard equipment are less than 30 μV/V, 36 μA/A, and 42 μW/VA for harmonic voltage, harmonic current, and harmonic power measurements, respectively, at fundamental frequencies of 50 and 60 Hz and operating ranges of up to 50 A, 500 V, and 60th order harmonics.

The harmonic power standard equipment is introduced in this chapter as an example. Its measurement functions for harmonic voltage, harmonic current, and harmonic power at industrial frequency are described, with aspects such as its principle, setup, uncertainty evaluation, and experimental validation also covered.

The digital sampling technique is widely adopted for commercial harmonic analyzers. For standard equipment, this technique must be developed to a higher level to satisfy calibration requirements. The standard equipment of the NIM is also based on digital sampling techniques. Unlike that proposed in general sampling theory, however, the synchronization between sampling rate and signal frequency is not a stringent requirement for the NIM equipment. The leakage effect that results from such an asynchronous case is compensated for by the introduction of a novel algorithm. The engineering practicality of this algorithm is demonstrated and its calculation is limited to a couple of seconds, without the need for an especially large computing space.

The uncertainty evaluation for the standard equipment is based primarily on experiments. The standard equipment is tested using the national AC voltage and AC current standards at variable frequency points to determine frequency characteristics. Some special factors for harmonic conditions are then considered; these include the small harmonic components, leakage between harmonics, noise, and nonlinear effect of frequency. Finally, some experiments are designed and implemented to validate the uncertainty.

The principles and methods of the algorithm are designed to achieve higher accuracy. The uncertainty evaluation is carried out from the frequency to the harmonic feature. These attributes would be of significant reference for researchers, engineers, and students in developing higher quality commercial instruments or in general study. Based on these principles and methods the readers can improve system and reach a higher accuracy and a better function.

Further investigation to extend the capability of the algorithm for impedance measurement, higher frequency measurement, or other AC measurements would also be valuable.

The equipment system is introduced in Section 2. The algorithm is described in Section 3. The uncertainty of harmonic measurement is conceptually shown in Section 4. The harmonic voltage and harmonic current, their phase shifts, and harmonic power are discussed in Sections 5, 6, 7, and 8, respectively. The experimental validation is presented in Section 9.

The core materials on which this chapter is based are taken from [Lu et al., 2010], and some concepts in [Lu et al., 2008a, 2008b, 2008c] are extended. A primary form of the algorithm is discussed in [Lu, 1988], and its detailed analysis and application can be found in [Lu, 1991].
