Sampling Rate Impact on Electrical Power Measurements Based on Conservative Power Theory

Abstract

This article presents a study of the sampling rate effect on electrical power measurements whose definitions are based on the Conservative Power Theory (CPT). The definitions of active power and reactive power of the CPT were applied in the MATLAB® software by varying the sampling rate and using a digital power meter as a reference. The measurements were performed in scenarios with linear and non-linear loads. Due to the usage of an integral in the CPT calculus, an error was verified associated with the reactive power being inversely proportional to the sampling rate. From the present study, it is possible to conclude that depending on the sample rate, the errors associated with the reactive power measurements are unacceptable and make the CPT implementation unfeasible. The results also presented effective information about the minimal sampling rate needed to make these errors neglected and to assist in choosing suitable microprocessors for the digital implementation of the CPT. It is worth mentioning that this paper was limited to assess how accurate the measurements of active and reactive powers were and important to highlight that the CPT has the additional contribution of dealing with distortion currents and consequently new portions of powers. For the latter, the influence of sampling rate may be crucial and new lines of investigation are motivated.

A Method of Reducing Errors Due to Sampling in the Measurement of Electric Power

“…Rigorous identity between the components on each phase is not required, as a software calibration of the entire assembly can be performed in the first phase. The calibration consists in finding weighting coefficients for each size, so that the displayed value corresponds to the measured value [9][10][11][12][13].…”

“…Any method to approximate the signal variation between two successive samples could be used (polynomial, logarithmic, etc. ), but due to the small distance between the samples and the ease of calculation, the linear approximation was chosen [9][10][11]. Of course, other sequences of the quantities of interest can be used, but in order to have close voltage and current on each phase, this arrangement was preferred [17].…”

“…Any method to approximate the signal variation between two successive samples could be used (polynomial, logarithmic, etc. ), but due to the small distance between the samples and the ease of calculation, the linear approximation was chosen [9][10][11].…”

“…Considering that the signal variations were linear between two successive moments, it is proposed to determine the studied values at the same moment in time by interpolation/extrapolation, obtaining intermediate values, with the necessary changes at the ends of the acquired value vectors. [ [9][10][11].…”

A Novel Power Measurement Method Using Lock-In Amplifiers with a Frequency-Locked Loop

“…With the development of technology, the analog method using an operational amplifier circuit is replaced by the digital method. In the digital method, the voltage and current waveforms are sampled and processed digitally in the microcontroller unit (MCU) to calculate power [16,23,24]. However, the non-sinusoidal grid conditions, harmonics, and frequency fluctuations combined to cause an error in zero-crossing detection even in the digital power measurement method.…”