The complexity of modern power grids, caused by integrating renewable energy sources, especially inverter-based resources, presents a significant challenge to grid operation and planning, since linear models are unable to capture the complex nonlinear dynamics of power systems with coupled muti-scale dynamics, and it necessitate an alternative approach utilizing more advanced and data-driven algorithms to improve modeling accuracy and system optimization. This study employs the sparse identification of nonlinear dynamics method by leveraging compressed sensing and sparse modeling principles, offering robustness and the potential for generalization, allowing for identifying key dynamical features with relatively few measurements, and providing deeper theoretical understanding in the field of power system analysis. Taking advantage of the this method in recognizing the active terms (first and high order) in the system’s governing equation, this paper also introduces the novel Volterra-based nonlinearity index to characterize system-level nonlinearity. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise is adopted to clearly show the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to inverter-based resources, revealing system-level (second-order) nonlinearity compared to module-level (first order) nonlinearity in conventional synchronous generators. The proposed index quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the profile of the proposed index.

Real‐time estimating harmonic distortion levels near the Point of Interconnections of grid‐connected inverter‐based resources (IBRs) is critical for maintaining the operational reliability and security of the power grid, particularly during transients when IBRs generate excessive harmonics. Traditional methods like Total Harmonic Distortion (THD) are unsuitable for time‐varying waveforms as they suffer from aliasing, spectral leakage, and picket‐fence effects. This paper proposes a novel approach that utilizes convolution‐based measures for estimating harmonic distortion, which offers a more suitable way for ongoing real‐time applications. The first measure uses a 60 Hz sinusoidal function as the convolution kernel, while an enhanced measure employs the Gaussian function as the kernel. Two convolution‐based measures are proposed and compared with THD. The comparison criteria are based on the two significant features describing the variation of harmonics: min/max values and variation curvature of harmonics showing the accurate performance of proposed measures. Moreover, short‐term estimations of harmonic distortion are used to validate the effectiveness of the proposed measures, while long‐term estimations are used to determine the ability of the proposed measures to determine harmonic distortion contributions among power network components. The proposed technique's intrinsic characteristics provide a sampling window with low sensitivity to deviations in the fundamental frequency and signal's stationary condition to prevent aliasing and spectral leakage and rule out the impact of the picket‐fence effect on the harmonic distortion level estimation.

The increasing level of harmonics in the power grid, driven by a substantial presence of coupled inverter-based energy resources (IBRs), poses a new challenge to power grid transient stability. This paper presents the findings from experiments and analytical studies on the impact of the topological configuration of coupled IBRs on the level of power flow harmonics in a distribution grid: (i) our findings report that the impact of grid topology on harmonics is nonlinear, which is in contrast to the common perception that the power grid operates as a large linear low-pass filter for harmonics; (ii) importantly, this study highlights that the influence of the topological configuration of inverters on the reduction of system-level harmonics is more substantial than the effect of line impedance, emphasizing the significance of grid topological configuration; (iii) furthermore, the observed reduction in harmonics is attributed to a harmonic cancellation effect achieved through self-compensation by all the coupled inverters without affecting the active power flow in the power grid. These findings propose a new approach to limit the penetration of complex IBR harmonics in the power grid from a system-wide perspective. This approach significantly differs from the component-level or localized solutions used today, such as inverter control, power filtering, and transformer tap changes.

The complexity of modern power grids, exacerbated by integrating diverse energy sources, espe-cially inverter-based resources (IBRs), presents a significant challenge to grid operation and plan-ning since linear models fail to capture the intricate IBR dynamics. This study employs the Sparse Identification of Nonlinear Dynamics (SINDy) method to bridge the gap between theoretical un-derstanding and practical implementation in power system analysis. It introduces the novel Volterra-based Nonlinearity Index (VNI) to examine system-level nonlinearity comprehensively. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise elucidates the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to IBRs, revealing system-level nonlinearity compared to module-level nonlinearity in conventional syn-chronous generators. The VNI quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a versatile tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the proposed VIN profile.

Artificial Intelligence is revolutionizing education by enabling adaptive, personalized, and scalable learning systems across domains. This review encapsulates the recent advancements in AI architectures-convolutional neural networks, recurrent neural networks, transformer models, generative adversarial networks, and reinforcement learning-and evaluates their applications across STEM, language learning, art education, and lifelong learning. We examine domain-adaptations, scalability issues, interpretability, fairness, and ethical deployment, and propose design principles in the spirit of cognitiveaffective-social learning theories. Cross-modal data fusion, hybrid neuro-symbolic, and teacher-interactive explainability methods are identified as key enablers for secure AI integration. To bridge the gap between algorithmic innovation and the real-world classroom effect, we recommend a multidimensional assessment framework that considers predictive reliability, pedagogical value, ethical compliance, and deployability. We also emphasize the importance of standardized metrics and longitudinal studies. Ultimately, we argue that AI's transformative power in schools relies as much on pedagogical alignment, cultural sensitivity, and human-AI collaboration as it does on technological advancements.

This research presents a novel Multi-scale PAramorphic Kernel (MPAK) learning framework that is designed to enable autonomous, context-adaptive STEM learning for electrical and renewable energy topics. By employing distributed multi-agent kernel cores, recursive kernel reweighting, and entropy-guided abstraction modulation, this system dynamically adapts instructional content and sequencing based on the specific cognitive state of individual learners. Concept learning history is maintained in persistent memory buffers to facilitate individualized reinforcement and remediation in asynchronous, informal environments. Grounded in physics-informed knowledge graph, the system offers epistemic coherence and domain consistency at multiple levels of abstraction. Evaluated across multiple, underrepresented student groups in community and laboratory implementations, MPAK demonstrated a 45% rate increase in concept recall, a 3.2× improvement in student-led project completion, and sustained 68% learner interest over 12 weeks. These results emphasize the effectiveness of this architecture in delivering scalable, culturally sensitive, and high-fidelity STEM education without human interaction. The paper also discusses system deployment, statistical validation, longitudinal deployment settings, informal education problem-solving, cultural adaptation, and learning assessment. MPAK provides an extensible blueprint for inclusive, technology-driven workforce development in clean energy sectors, fueling inclusive participation and expertise in advanced technical fields.