Symmetry

With the increasing integration of high-proportion renewable energy, power systems are exhibiting low-inertia and low-damping characteristics, posing severe challenges to frequency stability. This paper proposes a coordinated supplementary frequency regulation strategy utilizing electrolytic aluminum (EA) loads and a hybrid energy storage system (HESS). Firstly, a system frequency response model is established, incorporating EA, electrochemical energy storage, pumped hydro storage, and conventional generation units. Secondly, an improved variable filter time constant controller is designed, supplemented by fuzzy logic, to achieve adaptive power allocation under different disturbance magnitudes. Concurrently, regulation intervals are defined based on the area control error (ACE), enabling a tiered response from source-grid-load resources. Simulation results demonstrate that under a severe disturbance of 0.05 p.u., the proposed strategy reduces the maximum frequency deviation from 0.198 Hz to 0.054 Hz, achieving a 72.7% performance improvement, and shortens the system settling time by 59.5%. Furthermore, the state of charge (SOC) of the electrochemical storage is successfully maintained within the range of [0.482, 0.505], effectively balancing frequency regulation performance and device lifespan. The findings demonstrate the effectiveness of the proposed strategy in enhancing the frequency resilience of low-inertia power grids.

This paper presents a probabilistic, multi-layered framework designed to forecast the longevity and security of cryptographic systems under the dual pressures of classical and quantum computational threats. The model integrates thermodynamic decay analogies, stochastic transitions via Hidden Markov Models, and an adapted financial option pricing method to quantify cryptographic degradation, strategic risk, and transition readiness. This framework can guide standardization roadmaps, cipher retirement, or quantum-migration planning, guiding proactive, instead of reactive, crypto agility. Furthermore, it provides a quantitative methodology to complement the current opinions expressed in surveys, as well as a qualitative approach to cryptographic security risk projections.

To address the complex influencing factors, divergent stakeholder demands, and the challenge of quantitative comparison in alignment selection for highway expansion and reconstruction, we systematically reviewed the relevant factors. These factors were classified into four categories—economy, technology, safety, and environment—and comprise 16 subfactors in total. The symmetry of the route selection process is disrupted by the varying priorities of different stakeholders, leading to asymmetric evaluations of the alternatives. Using the G30 Lianhuo Expressway Jingqing section expansion and reconstruction project as a case study, we applied the Analytic Hierarchy Process (AHP) combined with expert judgment to derive weights for each factor. The results indicate that environmental factors carry substantial weight, reflecting increased awareness of environmental protection in contemporary projects. We then developed a comparative model based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Applying this model to alignment alternatives between the Jingjiadian and Huachacun sections indicates that Option 4 is the preferred alignment. Overall, the AHP–TOPSIS composite evaluation framework effectively integrates expert knowledge with objective quantitative analysis. It enables the scientific ranking of alternatives and provides decision support for alignment selection in mountainous highways and other linear engineering projects.