Current Transformers Effects on the Measurement of Harmonic Active Power in LV and MV Networks

The harmonic active power is used to determine the location of polluting loads, the direction of harmonic power flow and to estimate how consequential a certain current harmonic source is. The highest uncertainties, when measuring harmonic active power, are introduced by the current and voltage transducers. This paper presents experimental results which show the impact of current transformers (CTs) on the accuracy of the harmonic power measurements. An expression for the evaluation of the power error in distorted conditions was developed which can be easily utilized in the case of linear current transducers. It is shown how CTs cannot be considered linear transducers and how the higher the absolute value of the CT phase angle error is, the higher becomes the harmonic power error. The harmonic power error reaches maximum value when the phase shift between the voltage and current harmonic nears . Even high accuracy class CTs may not be adequate enough to assist on harmonic power measurement, while linear current transducers will perform satisfactorily.

I. Introduction

Different approaches for harmonic sources detection have been presented in literature. They can be mainly divided in single-point and multi-point methods (i.e., based on measurement performed in one metering location or in multiple metering locations, respectively) [1]–[7]. Most of the described techniques are based on the measurement of the sign of the harmonic active power. When the sign is positive, the harmonic disturbances are due to nonlinear loads external to the monitored load, and the dominant harmonic source is located within the power grid upstream the metering station; otherwise, when its value is negative, the harmonic disturbance is predominantly due to the load, thus the dominant harmonic source is located downstream the metering station. This method is also suggested by the modern standards concerning the definitions for the measurement of electric power quantities in distorted conditions [8]. The -order harmonic active power [8] is

$$P_{h} = {1\over kT}\int_o^{kT} {v_{h} i_{h} dt} = V_{h} I_{h} \cos (\theta _{h}) \eqno{\hbox{(1)}}$$ where is a positive integer number, is the cycle (s), $$v_{h} = \sqrt 2 V_{h} \sin (h\omega t + \beta _{h}) \eqno{\hbox{(2)}}$$ is the instantaneous -order harmonic voltage $$i_{h} = \sqrt 2 I_{h} \sin (h\omega t + \alpha _{h}) \eqno{\hbox{(3)}}$$ is the instantaneous -order harmonic current and is the phase shift between the harmonic phasors voltage and current. and are the rms value and the phase angle of the -order harmonic voltage; and are the rms amplitude and the phase angle of the -order harmonic current. The total harmonic active power is: $$P_{H} = \sum_{h \ne 1} {P_{h}} = P - P_{1} \eqno{\hbox{(4)}}$$ where is the total active power in the circuit [8].