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It is envisioned that the future electric grid will be underpinned by a vast number of smart inverters linking renewables at the grid edge. These inverters' dynamics are typically characterized as impedances, which are crucial for ensuring grid stability and resiliency. However, the physical implementation of these inverters may vary widely and may be kept confidential. Existing analytical impedance models require a complete and precise understanding of system parameters. They can hardly capture the complete electrical behavior when the inverters are performing complex functions. Online impedance measurements for many inverters across multiple operating points are impractical. To address these issues, we present the InvNet, a machine learning framework capable of characterizing inverter impedance patterns across a wide operation range, even with limited impedance data. Leveraging transfer learning, the InvNet can extrapolate from physics-based models to real-world ones and from one inverter to another with the same control framework but different control parameters with very limited data. This framework demonstrates machine learning as a powerful tool for modeling and analyzing black-box characteristics of grid-tied inverter systems that cannot be accurately described by traditional analytical methods, such as inverters under model-predictive control. Comprehensive evaluations were conducted to verify the effectiveness of the InvNet., QC 20240828

Data-driven approaches are promising to address the modeling issues of modern power electronics-based power systems, due to the black-box feature. Frequency-domain analysis has been applied to address the emerging small-signal oscillation issues caused by converter control interactions. However, the frequency-domain model of a power electronic system is linearized around a specific operating condition. It thus requires measurement or identification of frequency-domain models repeatedly at many operating points (OPs) due to the wide operation range of the power systems, which brings significant computation and data burden. This article addresses this challenge by developing a deep learning approach using multilayer feedforward neural networks (FNNs) to train the frequency-domain impedance model of power electronic systems that is continuous of OP. Distinguished from the prior neural network designs relying on trial-and-error and sufficient data size, this article proposes to design the FNN based on latent features of power electronic systems, i.e., the number of system poles and zeros. To further investigate the impacts of data quantity and quality, learning procedures from a small dataset are developed, and K-medoids clustering based on dynamic time warping is used to reveal insights into multivariable sensitivity, which helps improve the data quality. The proposed approaches for the FNN design and learning have been proven simple, effective, and optimal based on case studies on a power electronic converter, and future prospects in its industrial applications are also discussed., QC 20240611

Multi-terminal HVDC projects are increasingly developed in recent years to enhance the flexibility of energy transmission. Differing from the point-to-point HVDC systems, it is more challenging to design the multi-terminal HVDC system and ensure stable interoperability among converter systems, especially when the converters are manufactured from different vendors. Although impedance-based stability analysis allows for analyzing such systems based on black-box models, it is still difficult to utilize those black-box models to identify the root cause of potential instability. To tackle this challenge, this paper proposes a multi-level sensitivity analysis approach using frequency-domain sensitivity functions based on the impedance-based stability criterion. The proposed method differs from the classical sensitivity analysis based on state-space or transfer-function models, as it is purely based on black-box impedance models. Case studies on a four-terminal HVDC system are carried out for stability and sensitivity analysis based on the impedance measurement in PSCAD, through which the most sensitive HVDC station can be identified. The proposed theory and the analyzed results are finally validated by electromagnetic transient simulations., QC 20230324

Power systems equipped with power electronic converters can be modeled by harmonic transfer functions (HTFs) in a black-box manner for dynamic analysis. This paper studies the truncation of HTFs. It is proposed to define the gain function of an HTF as the norm of its central-column vector. Then, the error bound of the gain function in relation to the truncation order is explicitly derived, which can be used as an indicator for the HTF truncation. Compared with existing solutions, the proposed method is practical in truncating black-box systems with unknown internal parameters, since the truncation error bound can be estimated by the central-column elements of the HTF, which can be easily measured through frequency scan. The truncation approach is finally verified on a three-phase electronic power system by electromagnetic transient simulations., QC 20220325

This letter proposes a frequency-domain participation analysis approach to identifying the root cause of small-signal instability for electronic power systems. Differing from the participation analysis based on state-space analysis, the proposed approach is implemented based on impedance models, which is, thus, readily applicable for large-scale systems only with black-box models. The theoretical analysis is finally verified by the simulations and experiments., QC 20230612

The frequency coupling and low-frequency oscillations are common challenges faced by PFC converters in data centers. To reveal their mechanism, this paper proposes the systematic harmonic state space (HSS) modeling of the single-phase PFC converters and conducts the stability analysis on that basis. The HSS model is based on the linear time-periodic (LTP) theory, which can accurately reveal the frequency-coupling interactions. Besides, the developed HSS model is validated by the frequency scan. The stability analysis is performed and is shown to be consistent with the simulation results. In addition, a SISO equivalent impedance model of the single-phase PFC converters is proposed considering the frequency-coupling dynamics and the interaction with grid impedance, based on the MIMO impedance model derived from the HSS modeling., QC 20230307

The future power grid will be supported by a large number of grid-tied inverters whose dynamics are critical for grid stability and power flow control. The operating conditions of these inverters vary across a wide range, leading to different small-signal impedances and different grid-interface behaviors. Analytical impedance models derived at specific operating points can hardly capture nonlinearities and nonidealities of the physical systems. The applicability of electromagnetic transient (EMT) simulations is often limited by the system complexity and the available computational resources. This paper applies neural network and transfer learning to impedance modeling of gridtied inverters. It is shown that a neural network (NN) trained by data automatically acquired from EMT simulations outperforms the one trained by traditional analytical models when unknown information exist in simulations. Pre-training the NN with analytically calculated data can greatly reduce the amount of simulation data needed to achieve good modeling results., QC 20230412

Impedance-based stability analysis has the potential to be adopted by transmission system operators (TSOs) for effectively assessing the stability of multi-terminal HVDC (MTDC) system. This paper introduces a PSCADcompatible software toolbox that enables the accurate frequency dependent AC/DC impedance (matrix) measurement of the MMC-HVDC converter stations. Case studies based on a generic MTDC model are given to demonstrate the effectiveness of using the toolbox for accurate impedance measurement as well as stability assessment., Part of ISBN 9781839534300, 9781839535048QC 20231106

The harmonic state-space (HSS), the dynamic phasor (DP), and the generalized dq (GDQ) modeling are three widely used methods for small-signal analysis of ac power electronic systems. By reviewing their principles and deriving their mathematical relationships, this paper proposes a unified framework for all the three approaches. The unified modeling reveals that the linearization and transformation can be exchanged flexibly in the modeling process, and the initial phase takes a role in transforming the GDQ model into the HSS or DP model. Case studies on a three-phase voltage-source converter in unbalanced power grids are provided for validation. The relationships of three modeling methods are verified by mathematical proofs and time-domain simulations. The unified frequency-domain model is further validated through the frequency scan in experiments. Insights of the unified modeling framework and recommendations from engineering perspectives are finally discussed., QC 20211027

Grid-forming converters can suffer from control interaction problems in grid connections that can result in small-signal instability. Their inner-loop voltage controller tends to interact with the outer-loop power controller, rendering the controller design more difficult. To conduct a design-oriented analysis, a control-loop decomposition approach for grid-forming converters is proposed. Combined with impedance-based stability analysis, the control-loop decomposition approach can reveal how different control loops affect the converter-grid interaction. This results in a robust controller design enabling grid-forming converters to operate within a wider range of grid short-circuit ratios. Finally, simulation and experimental results, which validate the approach, are presented., QC 20220825