Estimating the Frequency Coupling Matrix From Network Measurements

Abstract

Power converters are present in increasing numbers in the electric power grid. They are a major source of harmonic currents and voltages, which can reduce power quality and trip protection devices. The frequency coupling matrix (FCM) is a general technique for modeling converter harmonics. It can be obtained through experimental characterization or, given a converter's internal parameters, direct calculation. In this paper, we estimate FCMs from network measurements. We give a novel harmonic reduction theorem for computing equivalent, virtual FCMs for unobservable portions of a network. We estimate FCMs and harmonic line admittances from PMU measurements, and give an efficient online version for the FCM problem. We test our approaches on a numerical example, and show that the estimation error is low under noisy observations.

Waveform Variation Defined Model for Harmonic Current Emissions Including Cross-Order Supply Voltage Harmonics Influence

“…From the result plots (Figure 5, Figure 7) it is evident that base harmonic current vector I * x,Base does not lie in the centre of ellipse, and with the non-symmetric part included, the average of |dIx,y@Ix,MAX| and |dIx,y@Ix,MIN| is used to determine the Gxy using equation (17). The phase variation margins are well symmetrical to the ellipse centre, and to determine the initial proposed value of coefficient of phase angle change (kxy), the measurement-derived dφIx,Uy@φIx,MAX is used as in (18) 𝑘 𝑥𝑦 = 𝑑𝜑𝐼𝑥,𝑈𝑦@𝜑𝐼𝑥,𝑀𝐴𝑋 𝑈 𝑦 (18) The magnitude of the harmonic current difference vectors is linearly dependent on the Uy.…”