Special Issue: Symmetry/Asymmetry Studies in Modern Power Systems

Tao Zhou; Cheng Wang

doi:10.3390/sym17122154

and

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

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Author to whom correspondence should be addressed.

Symmetry2025, 17(12), 2154;https://doi.org/10.3390/sym17122154

This article belongs to the Special Issue Symmetry/Asymmetry Studies in Modern Power Systems

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Abstract

This Special Issue, “Symmetry/Asymmetry Studies in Modern Power Systems,” presents a curated collection of research addressing the critical and evolving role of symmetry in the context of energy transition. The contributions, selected through a rigorous review process, collectively advance the understanding and management of power system balance, stability, and resilience amidst the increasing integration of renewables and power electronics. The published papers offer innovative solutions across several interconnected areas, including advanced control for active power symmetry, optimized renewable integration and inertia support, intelligent equipment operation, system-wide dynamic analysis, scheduling under uncertainty, and enhanced protection and power quality. By synthesizing advanced computational techniques with core power engineering challenges, this issue provides both theoretical insights and practical methodologies. It underscores a paradigm shift towards actively orchestrating system stability within inherently asymmetric conditions, laying a foundation for the design of more resilient, efficient, and sustainable future grids. Finally, key future research directions are outlined to further integrate adaptive control, physics-informed machine learning, and standardized metrics for holistic system design.

Keywords:

power system symmetry; renewable energy integration; power system stability; power symmetry and balance control; power system optimization and scheduling

1. Introduction

Concepts of symmetry and asymmetry have long been recognized as fundamental to the analysis and operation of power systems [1]. However, with the increasing integration of renewable energy sources, widespread adoption of power electronic devices, and the emergence of complex grid architectures, the roles of symmetry and asymmetry have become more pronounced and multifaceted [2]. This Special Issue, “Symmetry/Asymmetry Studies in Modern Power Systems,” addresses this evolving landscape by presenting cutting-edge research that explores the intricate relationship between symmetry principles and modern power system performance. The contributions in this issue provide valuable insights into how symmetry and asymmetry influence fault diagnosis, system planning, operational efficiency, and stability in contemporary power systems. By examining these phenomena across various dimensions—from fundamental theory to practical applications in renewable integration and grid-forming control—this Special Issue offers a comprehensive perspective that is essential for advancing the design and operation of resilient, efficient, and sustainable power systems in the era of energy transition. The collected research not only deepens our theoretical understanding but also provides actionable methodologies for addressing the complex challenges posed by modern power system dynamics.

2. Thematic Overview of Contributions

Following a rigorous peer-review process, this Special Issue “Symmetry/Asymmetry Studies in Modern Power Systems” received a total of about 20 high-quality submissions from researchers across the globe. After thorough evaluation by experts in relevant fields, 12 papers were accepted for publication, reflecting the diversity of approaches and perspectives in the field. These selected contributions present significant advancements in understanding the critical role of symmetry and asymmetry in modern power system operations, analysis, and design. The accepted papers included different symmetry/asymmetry studies on techniques for modern power systems:

Power symmetry and balance control (contributions 1, 2, 8, and 9);
Symmetry and asymmetry in renewable energy integration (contributions 6 and 12);
Power equipment operation optimization (contributions 3 and 5);
Power system dynamic analysis and stability (contribution 4);
Power system optimization and scheduling (contribution 7);
Power system protection and power quality (contributions 10 and 11).

The integration of renewable energy sources and power electronic devices has significantly reduced system inertia, resulting in unstable frequency and threatening the active power symmetry and balance essential for grid reliability [3]. Maintaining power symmetry—ensuring balanced generation and load dynamics—is critical for preventing frequency deviations, oscillations, and cascading failures, particularly in modern systems with the high penetration of variable resources [4]. This direction addresses these challenges by developing advanced control strategies that enhance dynamic stability, optimize resource coordination, and support the transition to resilient, low-carbon power networks [5]. Contribution 1 proposes a knowledge-aggregation-based deep reinforcement learning method for load frequency control in isolated microgrids, combining improved whale optimization with LSTM and self-attention mechanisms to optimize power symmetry and balance under uncertainties. Contribution 2 introduces a coordinated control strategy for multi-type flexible resources and under-frequency load shedding, leveraging voltage variation effects to improve active power balance and frequency support capabilities. Contribution 8 develops an adaptive voltage reference-based multi-objective optimal control approach for multi-terminal DC systems, employing normal boundary intersection to ensure power flow symmetry with large-scale offshore wind integration. Contribution 9 presents a stability control method using grid-forming converters and virtual synchronous generator technology to achieve active symmetry in distribution grid elastic balance regions, enhancing inertia and damping under disturbances.

Maintaining the delicate balance between variable renewable generation and load demand is paramount for modern power systems, as inherent asymmetries can severely compromise frequency stability and grid reliability [6]. This research direction focuses on developing advanced control and evaluation frameworks to enhance active power symmetry, mitigate the impacts of source–load imbalances, and harness the innate support capabilities of inverter-based resources [7]. Contribution 6 systematically evaluates the inertia support capability of wind turbine generators operating symmetrically, quantifying their potential to provide crucial grid stabilization services comparable to conventional synchronous machines. Contribution 12 introduces a distributed active support method for photovoltaic systems, utilizing a state–disturbance observer and a dynamic surface consensus algorithm to ensure robust frequency stability amid source–load asymmetry.

The optimization of power equipment operation is critical for enhancing the reliability, efficiency, and longevity of electrical systems, particularly as the integration of renewable energy sources and fluctuating loads introduces new challenges to grid stability [8]. Transformers, as key components in power networks, require advanced control and prediction methods to maintain power symmetry and prevent failures under dynamic conditions [9]. This direction focuses on developing intelligent strategies for transformer capacity regulation and temperature monitoring, which are essential for reducing operational costs, ensuring safety, and supporting the transition to sustainable energy systems [10]. Contribution 3 proposes an on-load capacity-regulating control method for power transformers that combines load forecasting with hesitant fuzzy control to dynamically adjust transformer output based on real-time demand, optimizing resource utilization and minimizing losses. Contribution 5 introduces a predictive model for transformer top-oil temperature using an LSTM neural network enhanced with a self-attention mechanism and optimized by an improved whale optimization algorithm, improving accuracy in temperature forecasting to prevent overheating and extend equipment life.

The research direction of power system dynamic analysis and stability is pivotal for ensuring the reliable operation of modern power systems, particularly as the integration of renewable energy sources introduces greater variability and reduces system inertia, leading to increased frequency deviations and instability risks [11]. This field focuses on modeling, analyzing, and controlling dynamic behaviors to maintain active power symmetry and balance between generation and demand, which is essential for preventing blackouts and enhancing grid resilience under disturbances such as load fluctuations or faults [12]. Contribution 4 addresses this by proposing a small-signal modeling approach for power-load frequency response that incorporates voltage variation effects, enabling a more accurate analysis of how loads can contribute to frequency support and improve system stability under dynamic conditions.

The research direction of power system optimization and scheduling is critically important in the era of energy transition, addressing the challenges posed by the large-scale integration of intermittent renewable energy sources and the increasing complexity of multi-energy flows in modern grids [13]. Its significance lies in enhancing the economic efficiency, reliability, and sustainability of power systems by achieving optimal resource allocation and maintaining active power balance between generation and demand under various uncertainties [14]. Contribution 7 specifically advances this field by developing a bi-level optimization scheduling strategy for Park-Level Integrated Energy Systems (PIESs) that effectively tackles the uncertainties associated with price-based demand response to improve scheduling decisions.

The research direction of power system protection and power quality is fundamental to ensure the security, reliability, and stability of modern electrical grids, especially with the increasing integration of power-electronics-interfaced resources like renewables and electric vehicles that introduce new types of faults and harmonic distortions [15]. Its significance lies in developing advanced methods to quickly isolate faults, prevent equipment damage, and maintain voltage and current waveforms within strict standards, thereby guaranteeing the safe operation of critical infrastructure and the delivery of clean power to end-users [16]. This field is pivotal for mitigating the risks of cascading failures and enhancing the overall resilience of the power system against disturbances [17]. Contribution 10 proposes a quantitative state evaluation method for relay protection equipment using an improved Conformer model optimized by a two-stage Artificial Physics Optimization (APO) algorithm to accurately assess equipment health and predict failures. Contribution 11 introduces an integrated approach combining an I-ADALINE neural network with selective filtering techniques to effectively mitigate harmonics and improve power quality in electrically distorted networks.

3. Conclusions and Future Perspectives

The accepted papers of this issue collectively advance the theoretical and practical understanding of symmetry and asymmetry in contemporary power systems, delivering comprehensive solutions to critical challenges arising from renewable integration, grid modernization, and power electronics proliferation. These contributions establish a unified framework for maintaining power symmetry and balance across diverse operational scenarios—from microgrid frequency control and multi-terminal DC system optimization to transformer management, renewable inertia support, and fault resilience. By integrating advanced computational techniques with system-level stability analysis, these papers provide actionable methodologies to enhance grid reliability, operational efficiency, and resilience under increasing asymmetry induced by variable renewable generation and complex grid topologies. This body of work not only deepens the foundational knowledge of symmetry principles in power systems but also offers implementable strategies for transitioning toward sustainable, stable, and intelligent power networks in the energy transition era.

Future research in symmetry/asymmetry studies for modern power systems should focus on three interconnected dimensions: (1) developing adaptive control frameworks that dynamically maintain power symmetry under extreme renewable variability and grid-forming converter interactions, particularly for multi-inverter systems operating in weak grid conditions; (2) integrating physics-informed machine learning with real-time stability assessment to overcome the computational bottlenecks in transient stability analysis during high-asymmetry events; and (3) establishing standardized metrics for quantifying symmetry degradation across diverse grid architectures—from distribution networks with high PV penetration to multi-terminal HVDC systems—enabling the holistic design of resilient, low-carbon power systems. These directions will be critical for enabling seamless grid integration of next-generation renewable resources while ensuring operational stability in the face of increasingly complex, asymmetric power flows.

Author Contributions

Conceptualization, T.Z. and C.W.; writing—original draft preparation, T.Z.; writing—review and editing, C.W.; project administration, T.Z.; funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Natural Science Foundation of Jiangsu Province (No. BK20241481) and the Fundamental Research Funds for the Central Universities (No. 30922010709).

Data Availability Statement

Data availability is not applicable to this article as it is an Editorial and no new data were generated or analyzed.

Conflicts of Interest

The authors declare no conflicts of interest.

List of Contributions

Wu, M.; Ma, D.; Xiong, K.; Yuan, L. Deep Reinforcement Learning for Load Frequency Control in Isolated Microgrids: A Knowledge Aggregation Approach with Emphasis on Power Symmetry and Balance. Symmetry 2024, 16, 322. https://doi.org/10.3390/sym16030322.
Zhang, J.; Wang, J.; Cao, Y.; Li, B.; Li, C. A Coordinated Control Strategy of Multi-Type Flexible Resources and Under-Frequency Load Shedding for Active Power Balance. Symmetry 2024, 16, 479. https://doi.org/10.3390/sym16040479.
Zou, D.; Sun, X.; Quan, H.; Yin, J.; Peng, Q.; Wang, S.; Dai, W.; Hong, Z. Power Transformer On-Load Capacity-Regulating Control and Optimization Based on Load Forecasting and Hesitant Fuzzy Control. Symmetry 2024, 16, 679. https://doi.org/10.3390/sym16060679.
Zhou, T.; Zheng, Y.; Wang, C.; Chen, L.; Liu, B.; Chen, Z. Small-Signal Modeling and Frequency Support Capacity Analysis of Power Load Considering Voltage Variation Effect. Symmetry 2024, 16, 918. https://doi.org/10.3390/sym16070918.
Zou, D.; Xu, H.; Quan, H.; Yin, J.; Peng, Q.; Wang, S.; Dai, W.; Hong, Z. Top-Oil Temperature Prediction of Power Transformer Based on Long Short-Term Memory Neural Network with Self-Attention Mechanism Optimized by Improved Whale Optimization Algorithm. Symmetry 2024, 16, 1382. https://doi.org/10.3390/sym16101382.
Chen, Z.; Li, Y.; Zhou, Q. Inertia Support Capability Evaluation for Wind Turbine Generators Based on Symmetrical Operation. Symmetry 2025, 17, 31. https://doi.org/10.3390/sym17010031.
Chen, X.; Lei, J.; Zhang, X. Bi-Level Optimization Scheduling Strategy for PIES Considering Uncertainties of Price-Based Demand Response. Symmetry 2025, 17, 43. https://doi.org/10.3390/sym17010043.
Zhang, Y.; Feng, Y.; Xu, T.; Li, Y.; Du, X.; Yuan, C.; Chen, H. An Adaptive Voltage Reference-Based Multi-Objective Optimal Control Method for the Power Flow Symmetry of Multi-Terminal DC Systems with the Large-Scale Integration of Offshore Wind Farms. Symmetry 2025, 17, 105. https://doi.org/10.3390/sym17010105.
Lv, Z.; Jia, B.; Song, Z.; Li, H.; Zhou, S.; Li, Z. Stability Control Method Utilizing Grid-Forming Converters for Active Symmetry in the Elastic Balance Region of the Distribution Grid. Symmetry 2025, 17, 263. https://doi.org/10.3390/sym17020263.
Li, Y.; Zhang, M.; Zhang, S.; Zhou, Y. Quantitative State Evaluation Method for Relay Protection Equipment Based on Improved Conformer Optimized by Two-Stage APO. Symmetry 2025, 17, 951. https://doi.org/10.3390/sym17060951.
Hoon, Y.; Chew, K.W.; Mohd Radzi, M.A. Integrated I-ADALINE Neural Network and Selective Filtering Techniques for Improved Power Quality in Distorted Electrical Networks. Symmetry 2025, 17, 1337. https://doi.org/10.3390/sym17081337.
Zhou, Y.; Gao, Y.; Tang, Y.; Liu, Y.; Tu, L.; Zhang, Y.; Liu, Y.; Zhang, X.; Yu, J.; Cao, R. Distributed Active Support from Photovoltaics via State–Disturbance Observation and Dynamic Surface Consensus for Dynamic Frequency Stability Under Source–Load Asymmetry. Symmetry 2025, 17, 1672. https://doi.org/10.3390/sym17101672.

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