Instantaneous frequency tracking of harmonic distortions for grid impedance identification based on Kalman filtering

Abstract

Abstract-This paper presents a non-invasive approach for real-time grid impedance identification based on the principle of instantaneous frequency tracking of voltage and current harmonics already present in the system, by the use of Kalman Filter (KF). The KF based technique is compared to the FFT frequency domain approach highlighting the advantages and disadvantages of each method. The main limitation of the KFbased identification lies in its intrinsic model based nature, which in this case will limit its scope to the system steady state and to stationary signals. The KF based approach presented in this paper, can be useful as a basis for real-time grid stability assessment based on the impedance identification. I. INTRODUCTIONKnowledge of the source and load impedances in an electrical grid is essential to estimate the stability of the grid using the impedance-based method with the generalized Nyquist stability criterion, first described in [1], with an application for AC systems in [2]. The impedance-based method requires, however, the injection of small signals in a wide range of frequencies to obtain a good estimate of the stability of the grid. This frequency scanning technique does not allow for a real-time estimation of the impedances and stability. The real-time identification of the impedances of the grid can be relevant considering the non-stationary environment where the impedance may vary with the operating conditions and with parameter variations over time [3]. This paper is proposing a non-invasive method to identify the impedances of the grid based on the use of the information of the distortions already present in the current and voltage waveforms, without resorting to any small-signal injection.Modern electrical systems are including more and more non-linear loads that are a frequent source of harmonic distortions. Electrical grids that are already affected by distorted voltages and currents can readily benefit from a non-invasive approach of impedance identification that makes use of the information provided by such distortions and can lead to a straightforward grid stability assessment in time-domain. The tracking, at a given node, of each of the harmonic components present in the voltage and current, can enable the identification of the grid impedances in a non-invasive way, by simply calculating the ratio V (ω)/I(ω) = Z(ω) at each harmonic distortion.

Real-Time Grid Impedance Estimation Using a Converter

“…For the impedance estimation, grid converters have been utilized to inject an excitation signal to the grid [3]- [16]. On the contrary, the impedance has been estimated passively using existing power system disturbances [17], [18]. From these approaches, the active injection-based methods are more deterministic.…”

Online Impedance Estimation in AC Grids Considering Parallel-Connected Converters

“…The use of Kalman filters for grid estimation are other solutions within this approach. In [7] grid impedance is estimated based on the grid harmonics and the impedance at different frequencies, this study is only supported with simulations. In [8] a similar approach is presented; the estimated coefficients are online updated using an adaptive linear neuron (ADALINE) algorithm, this model requires to measure grid current and voltages but it is experimentally demonstrated under balanced conditions.…”

“…αβ e −(jωt+θ) From top to bottom: 1) Equivalent impedance for the converter under balanced situation at 50Hz; 2) Resistive part of the impedance at 50Hz; 3) Inductance part of the impedance at 50Hz (v cαβ ) Relationship between voltage and current, in frequency domain, according expression of the equivalent impedance ΣZ and ∆Z.Expanding the terms from (6), considering positive and negative sequence component, leads to equation(7) …”

Observer-Based Pulsed Signal Injection for Grid Impedance Estimation in Three-Phase Systems

“…From (11), the discrete approximation for the grid current αβ components using Tustin method with a sampling period T s can be expressed according to (12), (13).…”

“…The method looks appealing and it is well supported with experimental validation, but it does not include the operation under unbalanced grid conditions and does not show the response to sudden changes on the grid impedance, which is critical for islanding detection. In [13], the use of the existing grid harmonics is proposed for the impedance estimation at different frequencies using a Kalman filter. However, only simulation results are provided.…”