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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 20211230

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. © 2022 IEEE., 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

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