Adaptive Frequency Estimation in Smart Grid Applications: Exploiting Noncircularity and Widely Linear Adaptive Estimators

Abstract

Signal processing is a crucial technology for the efficient use of limited and intermittent power resources in the smart grid of the future, and a number of challenges remain to be met. One major issue, as we move towards distributed energy production and use (microgrid) is real time estimation of power quality parameters (frequency, voltages, power factor). The accurate knowledge of frequency is a key parameter of a power system, and its optimal estimation becomes critical in the future smart grid, where the generation, loading and topology are all dynamically updated. In this work, we first consolidate the existing approaches to real-time frequency estimation in a three phase system, and then provide a unified framework for the estimation of the instantaneous frequency in both balanced and unbalanced conditions of a three phase power system. This is achieved by using recent developments in the statistics of complex variables (augmented statistics), by employing the associated widely linear models, and by rigorously accounting for the different degrees of noncircularity associated with various natures of frequency variations in real-world conditions. The usefulness of the proposed framework for frequency tracking in smart grids is illustrated in the context of two major issues in power quality control, namely the tracking of false frequency perturbations in the presence of unbalanced voltage sags (here both synthetic and real-world) and in adaptive frequency tracking in microgrids and islands where there is mismatch between production and consumption. THE NEED FOR FREQUENCY ESTIMATION IN SMART GRIDGovernments, utilities and consumers are all interested in making the ways we produce and use energy more efficient and sustainable. For the electrical power grid this involves fundamental paradigm shifts as we build a smart grid, adopt more renewable energy sources, and promote more energy efficient practices. A smart grid delivers electricity from suppliers to users using digital technology and has a number of properties, including incorporating all forms of energy generation and storage, using sensor information, enabling active participation by end users, being secure and reliable, and using optimization and control to make decisions [1]. This will require the interplay between sensor networks, generation systems, and the power grid, with key technologies from signal processing.It is estimated that the financial loss due to outages in the US economy approaches USD $45.7 billion annually, with power quality issues costing USD $6.7 billion annually [2,3]. Among them, voltage sags, that is, an increase in load current over up to few hundred cycles, are the most frequent problem [4] that severely affects medical centres, semiconductor plants, and broadcasting stations, among others [5]. Voltage sags are typically followed by frequency variations and occur due to switching between the main grid and microgrids, short circuits, motor starting, transformer inrush, fast reclosing of circuit breakers, unexpectedly large or ...

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

“…Compared with some exisiting time-domain methods with simple implementations, such as delayed signal cancellation method and its generalised version [32], [33], and widely linear model based frequency estimators [42]- [45], [48], [49], the proposed ML frequency estimator generic considers noise measurements in its mathematical voltage modelling, and its derivation, which origins from the joint probability density functions of the unbalanced αβ-tramsformed voltages and measuremenet noises, enables ehnahced robustness agaist noisy polution in the sense that it approaches the theoretical CRLBs for all the system parameters by designed. However, this is achieved at an increased compulational complexity due to the involvement of the full DFT operation.…”

“…Based on the finding that under unbalanced conditions, the αβ-transformed voltage and its complex conjugate obey a first-order widely linear (WL) autoregressive model [39]- [41], augmented complex-valued and widely linear (WL) modeling have been recently used to exploit the second-order noncircular statistical nature of the unbalanced αβ-transformed voltage. This makes it possible to extend standard phase angle estimation algorithms so as to account naturally for the information contained in the negative phase-sequence component, in order to produce unbiased frequency estimates [42]- [47]. Other attempts along this direction employs a pre-linear combination of the the αβ-transformed voltage and its complex conjugate, so that strictly linear frequency estimators are adequate to achieve statistically unbiased frequency estimate of unbalanced three-phase power signals [48], [49].…”

A Harmonic Current Detection Method for APF Under Unbalanced Voltage Condition Using Complex LMS Estimation

“…Many factors, such as the mismatched frequency between microgrid and main electrical grid, single-phase fault [2], will cause unbalance of voltage and perturbation of voltage frequency within a power grid [3] . All these deteriorates the harmonic current detection performance.…”

An adaptive Clarke transform based estimator for the frequency of balanced and unbalanced three-phase power systems

“…This problem has become all the more important with the penetration of renewable energy sources and the advent of smart grids [3], [4]. In this work, we consider the general frequency estimation problem for a balanced or unbalanced three-phase system where the imbalance manifests as voltage sags [4].…”

“…However, the Clarke Transform and the algorithms that employ it are applicable only to balanced systems. When the voltages deviate from the assumed model, as in the case of voltage sags [4], significant degradation in the performance can result. Previous efforts, such as those of [4], [11], [12], to tackle this problem have focused on deriving the signal model and modifying the frequency estimators to handle it.…”