# Power Measurement Techniques for Nonsinusoidal Conditions. The Significance of Harmonics for the Measurement of Power and other AC quantities

[Doktorsavhandling]

The increased application of power electronics and other non-linear loads makes it necessary to re-evaluate the measuring techniques used in the power system, and the measuring problems these loads cause. An instrument utilising digital sampling techniques has been built and evaluated at the Swedish National Testing and Research Institute (SP). The Digital Sampling Watt Meter (DSWM) is based on standard laboratory equipment: digital multimeters, voltage dividers, shunt resistors and a PC. The DSWM is versatile and can be used for calibrations of many quantities. The most basic ones are the (total) active power and the amplitude and phase angle of individual harmonics of non-sinusoidal voltages and currents.

The DSWM was first verified for sinusoidal signals. At 120 V and 5 A and power factor one, the DSWM has an estimated uncertainty (2s) of 60 ppm at 50 Hz and 600 ppm at 20 kHz. The wattmeter has also participated in three international comparison with satisfactory results. The most important additional feature, the input distortion, has been verified to be less than 800 ppm for all harmonics and lower than 100 ppm for most harmonics.

Some AC quantities, as the reactive power, are not properly defined for non-sinusoidal situations. Efforts are made in this work to understand and explain the problems of extending the reactive power definition to cover non-sinusoidal situations. The main conclusion is that reactive power is used to obtain information on more than one property of the power transmission mechanism, e. g. phase angle, transmission efficiency and line voltage drop. No single power definition can alone provide information on all these properties in a non-sinusoidal situation. Moreover, instrument designs may not comply with any of the extended definitions and these meters exhibit extra errors due to this non-compliance in non-sinusoidal situations.

Some conclusions on future demands on energy meters can be drawn, based on the error analysis of these meters and an analysis on how the responsibility for the harmonic currents and voltages in the power system can be determined and shared. One conclusion is that it is not possible to make a precise determination of the responsibility for harmonics based on any power measurement alone.

**Nyckelord: **sampling wattmeter, harmonics, reactive, power, non-sinusoidal

Denna post skapades 2006-08-28. Senast ändrad 2013-09-25.

CPL Pubid: 921