arXiv subjects

Andreas Martin Kettner

Publications and source records attributed to Andreas Martin Kettner.

12 recordsLinked to original sources

arXiv2024

Harmonic Stability Analysis of Microgrids with Converter-Interfaced Distributed Energy Resources, Part I: Modelling and Theoretical Foundations

This paper proposes a method for the Harmonic Stability Assessment (HSA) of power systems with a high share of Converter-Interfaced Distributed Energy Resources (CIDERs). To this end, the Harmonic State-Space (HSS) model of a generic power system is formulated by combining the HSS models of the resources and the grid in closed-loop configuration. The HSS model of the resources is obtained from the Linear Time Periodic (LTP) models of the CIDER components transformed to frequency domain using Fourier theory and Toeplitz matrices. Notably, the HSS of a CIDER is capable of representing the coupling between harmonic frequencies in detail. The HSS model of the grid is derived from the dynamic equations of the individual branch and shunt elements. The system matrix of the HSS models on power-system or resource level is employed for eigenvalue analysis in the context of HSA. A sensitivity analysis of the eigenvalue loci w.r.t. changes in model parameters, and a classification of eigenvalues into control-design variant, control-design invariant, and design invariant eigenvalues is proposed. A case of harmonic instability is identified by the HSA and validated via Time-Domain Simulations (TDS) in Simulink.

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arXiv2024

Harmonic Stability Analysis of Microgrids with Converter-Interfaced Distributed Energy Resources, Part II: Case Studies

In Part I of this paper a method for the Harmonic Stability Assessment (HSA) of power systems with a high share of Converter-Interfaced Distributed Energy Resources (CIDERs) was proposed. Specifically, the Harmonic State-Space (HSS) model of a generic power system is derived through combination of the components HSS models. The HSS models of CIDERs and grid are based on Linear Time-Periodic (LTP) models, capable of representing the coupling between different harmonics. In Part II, the HSA of a grid-forming, and two grid-following CIDERs (i.e., ex- and including the DC-side modelling) is performed. More precisely, the classification of the eigenvalues, the impact of the maximum harmonic order on the locations of the eigenvalues, and the sensitivity curves of the eigenvalues w.r.t. to control parameters are provided. These analyses allow to study the physical meaning and origin of the CIDERs eigenvalues. Additionally, the HSA is performed for a representative example system derived from the CIGRE low-voltage benchmark system. A case of harmonic instability is identified through the system eigenvalues, and validated with Time-Domain Simulations (TDS) in Simulink. It is demonstrated that, as opposed to stability analyses based on Linear Time-Invariant (LTI) models, the HSA is suitable for the detection of harmonic instability.

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arXiv2024

Ensuring Solution Uniqueness in Fixed-Point-Based Harmonic Power Flow Analysis with Converter-Interfaced Resources: Ex-post Conditions

Recently, the authors of this paper proposed a method for the Harmonic Power-Flow (HPF) calculus in polyphase grids with widespread deployment of Converter-Interfaced Distributed Energy Resources (CIDERs). The HPF problem was formulated by integrating the hybrid nodal equations of the grid with a detailed representation of the CIDERs hardware, sensing, and controls as Linear Time-Periodic (LTP) systems, and solving the resulting mismatch equations using the Newton-Raphson (NR) method. This work introduces a novel problem formulation based on the fixed-point algorithm that, combined with the contraction property of the HPF problem, provides insights into the uniqueness of its solution. Notably, the effectiveness of the fixed-point formulation and the uniqueness of the solution are evaluated through numerical analyses conducted on a modified version of the CIGRE low-voltage benchmark microgrid.

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arXiv2023

Harmonic Power-Flow Study of Hybrid AC/DC Grids with Converter-Interfaced Distributed Energy Resources

As the share of Converter-Interfaced Distributed Energy Resources (CIDERs) in power distribution systems increases, hybrid AC/DC distribution systems are drawing more interest. Indeed, CIDERs usually rely on DC power and hybrid AC/DC grids with few Network-Interfacing Converters (NICs) are a promising solution to decrease installation costs and conversion losses compared to a pure AC grid. However, interactions between the AC and DC subsystem of a hybrid AC/DC grid can lead to undesirable amplification and propagation of harmonics. The authors of this paper have recently proposed a Harmonic Power-Flow (HPF) method that accurately represents the AC power flows including the coupling between different harmonics. The HPF framework is formulated through the mismatch equations of the nodal equations between the grid and the resource models and solved by a Newton Raphson algorithm. This paper updates the HPF method to model hybrid AC/DC grids interconnected through NICs. To this end, the model of the NICs and the resulting coupling between the AC and DC subsystems is included in the mismatch equations and the Jacobian matrix of the algorithm. The updated HPF method is applied to a typical hybrid AC/DC grid, and its accuracy is validated through detailed time-domain simulations with Simulink.

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arXiv2022

Modelling of AC/DC Interactions of Converter-Interfaced Resources for Harmonic Power-Flow Studies in Microgrids

Power distribution systems experience a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). As acknowledged by recent literature, the interaction of individual CIDER components and different CIDERs through the grid can lead to undesirable amplification of harmonic frequencies and, ultimately, compromise the distribution system stability. In this context, the interaction of the DC and AC sides of CIDERs has been shown to have a significant impact. In order to analyze and support the mitigation of such phenomena, the authors of this paper recently proposed a Harmonic Power-Flow (HPF) framework for polyphase grids with a high share of CIDERs. The framework considers the coupling between harmonics, but ignores the DC-side response of the CIDERs. Modelling the DC side and AC/DC converter introduces a nonlinearity into the CIDER model that needs to be approximated for the numerical solution of the HPF. This paper extends the CIDER model and HPF framework to address this aspect, whose inclusion is non-trivial. The extended HPF method is applied to a modified version of the CIGRE low-voltage benchmark microgrid. The results are compared to (i) time-domain simulations with Simulink, (ii) the predecessor of the extended HPF which neglects the DC side, and (iii) a classical decoupled HPF.

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arXiv2021

Harmonic Power-Flow Study of Polyphase Grids with Converter-Interfaced Distributed Energy Resources, Part I: Modelling Framework and Algorithm

Power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). This complicates the analysis and mitigation of harmonics, whose creation and propagation are facilitated by the interactions of converters and their controllers through the grid. In this paper, a method for the calculation of the so-called Harmonic Power-Flow (HPF) in three-phase grids with CIDERs is proposed. The distinguishing feature of this HPF method is the generic and modular representation of the system components. Notably, as opposed to most of the existing approaches, the coupling between harmonics is explicitly considered. The HPF problem is formulated by combining the hybrid nodal equations of the grid with the closed-loop transfer functions of the CIDERs, and solved using the Newton-Raphson method. The grid components are characterized by compound electrical parameters, which allow to represent both transposed or non-transposed lines. The CIDERs are represented by modular linear time-periodic systems, which allows to treat both grid-forming and grid-following control laws. The method's accuracy and computational efficiency are confirmed via time-domain simulations of the CIGRÉ low-voltage benchmark microgrid. This paper is divided in two parts, which focus on the development (Part I) and the validation (Part II) of the proposed method.

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arXiv2021

Harmonic Power-Flow Study of Polyphase Grids with Converter-Interfaced Distributed Energy Resources, Part II: Model Library and Validation

In Part I, a method for the Harmonic Power-Flow (HPF) study of three-phase power grids with Converter-Interfaced Distributed Energy Resources (CIDERs) is proposed. The method is based on generic and modular representations of the grid and the CIDERs, and explicitly accounts for coupling between harmonics. In Part II, the HPF method is validated. First, the applicability of the modeling framework is demonstrated on typical grid-forming and grid-following CIDERs. Then, the HPF method is implemented in Matlab and compared against time-domain simulations with Simulink. The accuracy of the models and the performance of the solution algorithm are assessed for individual resources and a modified version of the CIGRÉ low-voltage benchmark microgrid (i.e., with additional unbalanced components). The observed maximum errors are 6.3E-5 p.u. w.r.t. voltage magnitude, 1.3E-3 p.u. w.r.t. current magnitude, and 0.9 deg w.r.t. phase. Moreover, the scalability of the method is assessed w.r.t. the number of CIDERs and the maximum harmonic order ($\leqslant$25). For the maximum problem size, the execution time of the HPF method is 6.52 sec, which is 5 times faster than the time-domain simulation. The convergence of the method is robust w.r.t. the choice of the initial point, and multiplicity of solutions has not been observed.

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arXiv2019

Performance Assessment of Kron Reduction in the Numerical Analysis of Polyphase Power Systems

This paper investigates the impact of Kron reduction on the performance of numerical methods applied to the analysis of unbalanced polyphase power systems. Specifically, this paper focuses on power-flow study, state estimation, and voltage stability assessment. For these applications, the standard Newton-Raphson method, linear weighted-least-squares regression, and homotopy continuation method are used, respectively. The performance of the said numerical methods is assessed in a series of simulations, in which the zero-injection nodes of a test system are successively eliminated through Kron reduction.

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arXiv2019

A Generalized Index for Static Voltage Stability of Unbalanced Polyphase Power Systems including Thévenin Equivalents and Polynomial Models

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., compound hybrid parameters), and the aggregate behavior of the devices in each node by Thévenin Equivalents (TEs) and Polynomial Models (PMs), respectively. The proposed VSI is a generalization of the known L-index, which is achieved through the use of compound electrical parameters, and the incorporation of TEs and PMs into its formal definition. Notably, the proposed VSI can handle unbalanced polyphase power systems, explicitly accounts for voltage-dependent behavior (represented by PMs), and is computationally inexpensive. These features are valuable for the operation of both transmission and distribution systems. Specifically, the ability to handle the unbalanced polyphase case is of particular value for distribution systems. In this context, it is proven that the compound hybrid parameters required for the calculation of the VSI do exist under practical conditions (i.e., for lossy grids). The proposed VSI is validated against state-of-the-art methods for voltage stability assessment using a benchmark system which is based on the IEEE 34-node feeder.

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arXiv2018

On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysis

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arXiv2017

On the Properties of the Power Systems Nodal Admittance Matrix

This letter provides conditions determining the rank of the nodal admittance matrix, and arbitrary block partitions of it, for connected AC power networks with complex admittances. Furthermore, some implications of these properties concerning Kron Reduction and Hybrid Network Parameters are outlined.

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arXiv2017

Sequential Discrete Kalman Filter for Real-Time State Estimation in Power Distribution Systems: Theory and Implementation

This paper demonstrates the feasibility of implementing Real-Time State Estimators (RTSEs) for Active Distribution Networks (ADNs) in Field-Programmable Gate Arrays (FPGAs) by presenting an operational prototype. The prototype is based on a Linear State Estimator (LSE) that uses synchrophasor measurements from Phasor Measurement Units (PMUs). The underlying algorithm is the Sequential Discrete Kalman Filter (SDKF), an equivalent formulation of the Discrete Kalman Filter (DKF) for the case of uncorrelated measurement noise. In this regard, this work formally proves the equivalence the SDKF and the DKF, and highlights the suitability of the SDKF for an FPGA implementation by means of a computational complexity analysis. The developed prototype is validated using a case study adapted from the IEEE 34-node distribution test feeder.

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