Modeling and Analysis of SOGI-PLL/FLL-based Synchronization Units: Stability Impacts of Different Frequency-feedback Paths

— Second-order Generalized Integrator (SOGI)-based quadrature-signal-generator (QSG) together with either a phaselocked-loop (PLL) or a frequency-locked-loop (FLL) constitute two types of typical synchronization units (i.e., SOGI-PLL and - FLL) that have been widely used in grid-tied converter systems. This paper will reveal and clarify the stability issue of these two synchronization units arising from different implementations of the frequency-feedback-path (FFP) connecting the SOGI-QSG and the PLL/FLL. In this regard, four types of FFP implementations that are frequently seen in the literature will be discussed. Although different implementations of the FFP will not affect the steady-state frequency adaptation, their dynamical effects on the small-signal stability of SOGI-PLL/FLL remain concealed. To this end, this paper will present a comprehensive stability assessment and comparative analysis of SOGI-PLL/FLL focusing on the FFP issue. To extend the applicability and accuracy of discussions, all the analyses will be fulfilled by using a parameter space-oriented stability assessment method formulated in the linear-time periodic (LTP) framework. The obtained results are verified by time-domain simulations, and the main findings are further interpreted by using appropriate analytical models. Index Terms— FLL, PLL, synchronization, SOGI, stability, LTP, frequency feedback.acceptedVersio

A signal analysis toolbox for power system identification in Smart Grids

This thesis delves into the two fields of signal analysis and small-signal stability of power systems. Due to the extensive deployment of PMUs in today s Smart Grid, new possibilities arise to assess the small-signal stability by measurement based techniques. The benefits of this approach are many, the most compelling being that the power system has become too complex to be accurately modelled with a component-based approach. A whole range of methods are available for the purpose of signal analysis in power systems, all with various assumptions, strengths and weaknesses. Insight into the analysis methods and the measurement data in itself is important for choosing the appropriate techniques for a given signal. The methods described in this thesis are: Prony s method, Robust Recursive Least Squares (RRLS) and the FFT based Welch s method. Prony s method is known as a ringdown (post-disturbance transient) analyzer, while the two latter are known as ambient analyzers. To improve estimation robustness and accuracy, pre-filtering is implemented with the Empirical Mode Decomposition (EMD). This technique works as a non-linear and non-stationary band-pass filter, effectively extracting the desired frequency spectrum in the electro-mechanical range. This is validated using Welch s method, which reveals negligible change in the power spectral density of the investigated frequency range. Both Prony s method and RRLS assume an underlying parametric model, and require specifying a model order. This issue is transformed into a benefit, extracting the consistent information from multiple analyses with varying model order. Clustering is used as post-processing intelligence to identify the dominant modes of the estimation. The third technique, Welch s method, is used for validation purposes. The methods and data are contextualized; subsequently, the techniques are described with relevant theory, and thoroughly tested for both simulated and real-world data. The estimation from ringdown data is compared to the estimation from ambient data, which in real-time scenario often is the only option for evaluation. The three analyzers contribute to mutual validation of the modal content, improving the credibility of the estimates. For simulated data, the measurement based estimation is also evaluated against eigenvalue inspection of the linearized power system model. This thesis is based in part on a conference paper to be published at SPEEDAM 2018. This article describes theory of Prony s method, as well as the EMD and Clustering technique. Since then, the thesis has evolved in scope and depth. The results from detailed testing show that the investigated combination of methods performs well on real-world PMU-measurements. Prony s method identifies the modes of ringdown data and the RRLS method identifies the modal content in the ambient data. The damping ratio is in general slightly underestimated in the ambient data compared to ringdown data. However, both give a good indication of the modal content. A comprehensive toolbox of the methods mentioned above has been indigenously created (in Python) as a part of thesis work; the toolbox utilizes weaknesses of some methods, e.g. the model order selection problem in Prony s method and RRLS, as input to other methods, such as the clustering technique. The result is an autonomous algorithm, taking care of each submethod s deficiency

Prony's method as a tool for power system identification in Smart Grids

Abstract —This paper investigates the theory, intuition and performance of two known implementations of Prony’s method. Such methods are useful for identifying the individual modes of a system without constructing a component-based model. In the Smart Grid, Prony Analysis has been widely used on post-disturbance ring-down measurements, which have been increasingly available with the extensive deployment of PMU’s. Both methods decompose the signal into decaying sinusoidals, and estimate the frequency, damping, amplitude and phase of each modal component. The first method is based on the original Prony’s method, whilst the second method is based on the thought that the system can be viewed as a digital synthesis problem where the system has the properties of an infinite impulse response filter. Both methods employ EMD-based pre-filtering. Additionally, a cluster based approach is proposed for circumventing the issue of determining model order, so that the true modes of the estimation can be distinguished from the trivial modes. Index Terms —Prony Analysis, model order, modal analysis, signal processing, linear prediction model, linear time-invariant systems, clustering, empirical mode decompositio

Prony's method as a tool for power system identification in Smart Grids

Abstract —This paper investigates the theory, intuition and performance of two known implementations of Prony’s method. Such methods are useful for identifying the individual modes of a system without constructing a component-based model. In the Smart Grid, Prony Analysis has been widely used on post-disturbance ring-down measurements, which have been increasingly available with the extensive deployment of PMU’s. Both methods decompose the signal into decaying sinusoidals, and estimate the frequency, damping, amplitude and phase of each modal component. The first method is based on the original Prony’s method, whilst the second method is based on the thought that the system can be viewed as a digital synthesis problem where the system has the properties of an infinite impulse response filter. Both methods employ EMD-based pre-filtering. Additionally, a cluster based approach is proposed for circumventing the issue of determining model order, so that the true modes of the estimation can be distinguished from the trivial modes. Index Terms —Prony Analysis, model order, modal analysis, signal processing, linear prediction model, linear time-invariant systems, clustering, empirical mode decompositionacceptedVersion© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Frequency Domain Modelling for Assessment of Hilbert and SOGI Based Single-Phase Synchronisation

Two different single-phase synchronisation schemes based on orthogonal system generation (OSG) are modelled in the linear, time-periodic framework. The frequency adaptive Hilbert phase locked loop (PLL) and the frequency-fixed second-order-generalised-integrator (SOGI) PLL fit smoothly into existing models for the synchronous reference frame PLL, due to the linear and decoupled nature of the orthogonal system generation. The harmonic transfer functions are established, and shown to accurately capture the frequency coupling properties of the synchronisation techniques. This modelling approach is a milestone towards the ultimate goal of assessing the impact of synchronisation on single-phase converter small-signal stability. The analytic models are compared to simulations, through use of a chirp input signal instead of the typical frequency sweeping technique. The conceptual differences between the Hilbert PLL and SOGI PLL are highlighted, yet without attempts at asserting superiority of either scheme

Modeling and Analysis of SOGI-PLL/FLL-based Synchronization Units: Stability Impacts of Different Frequency-feedback Paths

— Second-order Generalized Integrator (SOGI)-based quadrature-signal-generator (QSG) together with either a phaselocked-loop (PLL) or a frequency-locked-loop (FLL) constitute two types of typical synchronization units (i.e., SOGI-PLL and - FLL) that have been widely used in grid-tied converter systems. This paper will reveal and clarify the stability issue of these two synchronization units arising from different implementations of the frequency-feedback-path (FFP) connecting the SOGI-QSG and the PLL/FLL. In this regard, four types of FFP implementations that are frequently seen in the literature will be discussed. Although different implementations of the FFP will not affect the steady-state frequency adaptation, their dynamical effects on the small-signal stability of SOGI-PLL/FLL remain concealed. To this end, this paper will present a comprehensive stability assessment and comparative analysis of SOGI-PLL/FLL focusing on the FFP issue. To extend the applicability and accuracy of discussions, all the analyses will be fulfilled by using a parameter space-oriented stability assessment method formulated in the linear-time periodic (LTP) framework. The obtained results are verified by time-domain simulations, and the main findings are further interpreted by using appropriate analytical models. Index Terms— FLL, PLL, synchronization, SOGI, stability, LTP, frequency feedback

An Integrated Method for Generating VSCs’ Periodical Steady-state Conditions and HSS-based Impedance Model

This paper proposes an integrated method for generating the voltage-source-converters’ (VSCs’) periodical steady-state (PSS) conditions and the harmonic-state-space (HSS)-based impedance model. Since these two objectives can be realized in one unified frequency-domain iteration process, it is briefly referred to as the automatic model generation (AMG). Application of the AMG method to the impedance acquisition and stability analysis of a single-phase grid-VSC system with corresponding experimental verification is presented as an example. The presented results demonstrate how the AMG method facilitates parametric stability assessments (e.g., under varying control parameters) in an efficient and accurate manner. The AMG method is also applicable to other systems with PSS, aiming for effective and efficient frequency domain analysis with impedance

Harmonic-Domain SISO Equivalent Impedance Modeling and Stability Analysis of a Single-Phase Grid-Connected VSC

This article presents a harmonic-domain single-input single-output (SISO) equivalent modeling technique for the impedance modeling and stability analysis of a single-phase grid-connected voltage-source converter (VSC). The basis is a conversion technique that transforms a harmonic transfer function (HTF)-based model into a SISO equivalent model while preserving all the information of frequency couplings. The proposed SISO modeling concept is useful for understanding the meaning and consequence of SISO impedance measurement of an interconnected system with frequency couplings, which further enables a simpler impedance measurement and impedance-based analysis. Applications of this method for the VSC model reduction and stability characteristic analyses are presented. From these results, useful conclusions regarding the accuracy of three types of reduced-order VSC impedance models and the stability effects of the VSC control with and without compensation for dc voltage variation are obtained. The presented examples of applications demonstrate how the proposed SISO modeling technique facilitates a simpler and efficient impedance-based analysis. Finally, experimental results verify the validity of the proposed VSC-SISO admittance and corresponding analyses. © 1986-2012 IEEE. (33 refs