Graph theory within power electronics, developed over a 50-year span, is continually evolving, necessitating ongoing research endeavors. Facing with the never-been-seen explosion of graph-structured data, the state-of-the-art deep learning technique-Graph Neural Networks (GNNs), becomes the leading trend in machine learning within just recent five years and demonstrated surprisingly broad and prominent benefits covering from new drug discovery to better IC design. However, its promising applications in Power Electronics are still rarely discussed and its full potential remains unexplored. Addressing this gap, this review paper is the first to outline GNNs’ general workflow in power electronics, laying the groundwork and examining current GNN methodologies within the field. To bridge the gap in the sparse GNN literature within this domain, we also provide extended discussions on leveraging insights from GNN-aided circuit design to enrich power electronics research. Our work includes in-depth GNN-based case studies that demonstrate promising applications from converters to system-level power electronics, showcasing GNNs’ unique benefits and untapped possibilities (e.g., accurate component design, voltage predictions on IEEE-13 bus and 118 bus systems). Additionally, we provide a comprehensive survey of GNNs’ latest and successful applications, emphasizing their impact on energy-centric sectors, such as transportation electrification, smart grids. Considering the interdisciplinary nature of power electronics in modern energy systems, our review highlights the potential of GNNs emerge as a promising tool to decode the intricate behavior and dynamics of power electronics systems, and we hope such synergies between advanced AI methodologies like GNNs with the ever-evolving graph theory can lead to more powerful tools, novel methodologies, and advancements in the power electronics community.

Graph isomorphism phenomenon has been identified since the 1930s, which was firstly addressed in the graph-theoretical field and was thoroughly studied as a critical topic of computer science. In many research disciplines, isomorphism theory and dual principles are identified as powerful tools in the study of related subjects. However, during the development of power converters, only dual principles have been adopted, such as in the study of relationships between voltage-source converter (VSC) and current-source converter (CSC), while the isomorphic relationship between them was never discovered. This indeed limits the understanding of relationships among converter topologies. In this paper, such isomorphic relationships are firstly revealed in the power converter field. Several topologies are discovered as isomorphic pairs, and the modulation isomorphism between single-phase three-level VSC and three-phase CSC is also demonstrated. The experimental results verify that the physical meaning of direct PWM for CSC is the modulation process of the DC-side voltage of three-phase CSC as its isomorphic pair shows. With the aid of isomorphic transformation, the existing knowledge of VSCs can be directly transformed into corresponding CSCs to deal with problems where dual principle has difficulties, which provides another opportunity for innovation of power converters.

Graph theoretical approaches have been widely applied in many disciplines, however, their implementation in power electronics converters and systems is still in the exploring stage. In this overview, we summarize the milestones and general applications of this powerful mathematical tool and illustrate its unique benefits in some emerging/challenging power electronics research topics, e.g., systematic converter derivation and modeling, advanced control, etc. Given the multidiscipline nature of power electronics, Graph Theory can serve as a bridge for experts in different disciplines with a universal framework for complex problems. With solid mathematical foundations, it can stimulate research of topological aspects in both converter and systematic level, fits well for nowadays power electronics converter. It is hoped this article can serve as a timely and handy summary for engineers/students who want to enter the field and promote the innovation of power-electronics-enabled applications.

This article presents a new artificial neural network (ANN)-based calibration mechanism for analog-to-digital converters (ADCs). The proposed mechanism applies ANN to realize the bijective vector recovery mapping (VRM) for nonlinearity calibration and thus effectively suppresses both harmonic distortions and spurs. A new ANN-based calibrator is designed to calibrate both single-channel nonlinearity and interchannel mismatches and significantly improve the performance of ADCs. Through signal-fitting-based training process and noise adding, the proposed mechanism and calibrator can calibrate the general nonlinearity and mismatches of ADCs, including but not limited to the typical nonideality that conventional calibration techniques commonly concern (such as interstage gain error, digital-to-analog converter (DAC) error, and timing mismatch). For verification, an on-chip ANN-based calibrator is implemented in a 12-bit 600-MS/s four-channel time-interleaved (TI) ADC prototype. The measurement results show that signal-to-noise-and-distortion ratio (SNDR) and spurious-free dynamic range (SFDR) are improved from 32.79 and 35.30 to 62.45 and 74.21 dB, respectively. Another off-chip ANN-based calibrator is applied to a commercial 12-bit 5.4-GS/s four-channel ADC, and the results show that the SNDR and SFDR are improved from 42.38 and 43.17 to 53.98 and 78.25 dB, respectively.

In this paper, topology transformations of power converters are realized through the dual and isomorphic principles for both the planar and nonplanar circuits. The topology cycling phenomenon is discovered in the topology transformation process and investigated in the power electronics field for the first time. It fills the gap between the dual converter and isomorphic converter and reveals the fundamental relationships among various power converters (existing and/or future ones). By utilizing this new discovery, the operation analysis, modulation/control design, topology derivation can be facilitated in a more comprehensive way. Numerous examples with both theoretical and experimental verifications show the feasibility and versatility of this work.