This paper proposes modified Second-Order Generalized Integrators (mSOGIs) for a fast estimation of all harmonic components of arbitrarily distorted single-phase signals such as voltages or currents in power systems. The estimation is based on the internal model principle leading to an overall observer system consisting of parallelized mSOGIs. The observer is tuned by pole placement. For a constant fundamental frequency, the observer is capable of estimating all harmonic components with prescribed settling time by choosing the observer poles appropriately. For time-varying fundamental frequencies, the harmonic estimation is combined with a modified Frequency Locked Loop (mFLL) with gain normalization, sign-correct anti-windup and rate limitation. The estimation performances of the proposed parallelized mSOGIs with and without mFLL are illustrated and validated by measurement results. The results are compared to standard approaches such as parallelized standard SOGIs (sSOGIs) and adaptive notch filters (ANFs). ; for more details see [1]) *** This long version includes (i) more detailed explanations, (ii) more simulation and measurement results and (iii) a thorough theoretical analysis in its Appendix.CONTENTS ‡ C.M. Hackl is with the Munich University of Applied Sciences (MUAS) and head of the "Control

This paper presents a method for online detection of symmetrical components of arbitrarily distorted and biased three-phase input signals. This method is based on Second-Order Generalized Integrators (SOGIs), for which a new tuning based on a gradient search is presented to achieve the fastest possible estimation. Frequency estimation is achieved by a Frequency Locked Loop (FLL) with Gain Normalization (GN) for which an Output Saturation (OS) is applied; this OS guarantees stability of the overall system. Offset detection is implemented by a combination of High-Pass Filter (HPF) and HPF-Amplitude Phase Correction (APC); the HPF filters out any offset, where the APC reconstructs the original offset-free signal. An identical method (APC) can be used for the implemented Low-Pass Filter (LPF) used for noise filtering. The resulting estimates are then used for Harmonic Sequence Detection (HSD) of each harmonic. For the overall system, stability is proven. The estimation performances of the proposed overall system are verified by simulation results. The improvements in tuning and offset detection are compared to standard approaches.

A unified method is presented which allows to estimate dc-offset, all harmonic components and fundamental frequency in arbitrarily distorted single-phase grids using a Frequency Adaptive Observer (FAO) consisting of modified Second-Order Generalized Integrators (mSOGIs), an adaptive DC-Integrator (DCI) and a modified Frequency Locked Loop (mFLL). DCI and mSOGIs are tuned by pole placement which allows for an arbitrarily fast detection of dc-offset and harmonic components if the fundamental frequency is known. If the fundamental frequency must be estimated as well, an mFLL with Gain Normalization (GN), Rate Limitation (RL), Anti-Windup (AW) strategy and low-pass filters (LPF) must be employed. The effectiveness of the proposed FAO is validated by experimental results and its enhanced performance is shown and compared to existing estimation methods. INDEX TERMS dc-offset estimation, frequency adaptive observer; frequency estimation; frequency locked loop; harmonics estimation; second-order generalized integrator.

Within a disruptively changing environment, design of power systems becomes a complex task. Meeting multi-criteria requirements with increasing degrees of freedom in design and simultaneously decreasing technical expertise strengthens the need for multi-objective optimization (MOO) making use of algorithms and virtual prototyping. In this context, we present Gaussian Process Regression based Multi-Objective Bayesian Optimization (GPR-MOBO) with special emphasis on its profound theoretical background. A detailed mathematical framework is provided to derive a GPR-MOBO computer implementable algorithm. We quantify GPR-MOBO effectiveness and efficiency by hypervolume and the number of required computationally expensive simulations to identify Pareto-optimal design solutions, respectively. For validation purposes, we benchmark our GPR-MOBO implementation based on a mathematical test function with analytically known Pareto front and compare results to those of well-known algorithms NSGA-II and pure Latin Hyper Cube Sampling. To rule out effects of randomness, we include statistical evaluations. GPR-MOBO turnes out as an effective and efficient approach with superior character versus state-of-the art approaches and increasing value-add when simulations are computationally expensive and the number of design degrees of freedom is high. Finally, we provide an example of GPR-MOBO based power system design and optimization that demonstrates both the methodology itself and its performance benefits.