Symmetry

An active symmetry support control method based on model predictive control and incorporating transient synchronization security boundaries is developed for a grid-following (GFL)/grid-gorming (GFM) hybrid renewable-energy station comprising GFL wind energy and GFM energy storage. The control objective is to suppress disturbance-induced departures from the dynamic balance between generation-side support and grid/load demand, which are referred to here as power asymmetry rather than phase-domain three-phase imbalance, and to restore a power-symmetric operating state through coordinated active- and reactive-power support. Reduced-order transient synchronization models are established separately for the GFL phase-locked loop and the GFM virtual synchronous generator without explicitly constructing a transient coupling model between the two converter types. For the GFM converter, damping energy is incorporated into the fault-stage transient-energy balance. The resulting transient-energy functions and critical-energy criteria are used to determine the synchronization-stability boundaries, which are then mapped into dynamically updated P-Q feasible regions. A frequency–voltage prediction model combining a system frequency-response model and a point-of-common-coupling voltage-sensitivity model is then established. The GFL/GFM transient-energy constraints, dynamic P-Q security regions, power-regulation capability limits, and command-direction constraints are embedded in the receding-horizon optimization to coordinate active- and reactive-power support while preserving transient synchronization security. Local linearization of the transient-energy constraints and second-order-cone reformulation of the dynamic P-Q regions are adopted to improve online computational efficiency. Simulation results show that, compared with MPC without transient synchronization security boundaries, the proposed strategy limits power-angle excursions, enhances active- and reactive-power support, and mitigates frequency and voltage deviations. A sensitivity analysis is further conducted to examine how uncertainties in grid impedance, inertia, damping, and filter inductance affect the calculated critical energies and P-Q security regions. The results highlight the distinct effects of these parameters on the critical-energy thresholds and dynamic energy margins.

Deep-buried tunnels excavated in soft-hard interbedded rock masses under high in-situ stresses frequently suffer from severe asymmetric squeezing. To elucidate the multi-scale controlling mechanism of the bedding dip angle ($\beta$), a finite–discrete element method (FDEM) model was developed on the Abaqus platform using the Muzhailing Tunnel as an engineering prototype. The model couples the Mohr–Coulomb criterion for rock matrix plasticization with zero-thickness cohesive elements for interface debonding and shear slip. Following specimen-scale validation against multi-orientation uniaxial compression tests (average peak strength error of 4.67%) and a qualitative consistency check against field failure patterns, the model was employed to investigate the evolution of surrounding-rock deformation, interface damage, and matrix plastic zones across $\beta =0$–${90}^{\circ }$. Results demonstrate that maximum radial convergence responds non-monotonically to the bedding dip, peaking at $\beta ={45}^{\circ }$ (74.47 mm), which is approximately 52% larger than the minimum at $\beta ={60}^{\circ }$ (48.97 mm), defining a prominent deformation amplification window within $40$–${50}^{\circ }$. An asymmetry index ($AI$) quantifies the pronounced bias induced by inclined strata, reaching a maximum of 0.153 at ${75}^{\circ }$. Dominant deformation zones migrate systematically along the perimeter governed by the geometric tangency between bedding planes and the excavation profile; uniquely, intense interlayer shear slip at ${30}^{\circ }$ shifts the peak convergence anomaly to the right sidewall. Crucially, macroscopic convergence, interface damage, and matrix plasticization evolve asynchronously, where modest radial convergence may mask substantial subsurface interlayer slip. The asymmetric instability is fundamentally a progressive, cross-scale process driven by the synergy between discontinuous interface slip and continuous matrix shear yielding, providing theoretical guidelines for non-symmetric support design in deep stratified ground.

Oblique inflow breaks the nominal rotational periodicity of a geometrically symmetric propeller by introducing an azimuth-dependent velocity component across the rotor disk. This study develops a transparent reduced order blade element/momentum framework to examine the resulting once-per-revolution aerodynamic loading of a representative two-bladed small UAV propeller. The formulation combines blade element aerodynamics, momentum-based induction, Fourier decomposition, and advancing–retreating blade diagnostics over moderate oblique inflow conditions. Particular attention is given to distinguishing quantities that arise directly from the assumed harmonic structure from quantities that provide independent aerodynamic information. A first-order analytical expansion shows that, for small in-plane velocity, the normalized first-harmonic loading scales approximately with the in-plane velocity ratio and therefore with J sin(α), consistent with the numerical model. The analysis additionally reports the absolute first-harmonic load amplitude, spanwise development of the asymmetry, cross-plane hub load components, circulation imbalance, and sensitivity to aerodynamic model assumptions. Published axial and non-axial propeller data are used to establish the range over which the reduced order trends can be interpreted. The results indicate that advance ratio and inflow angle govern the modeled cyclic asymmetry, whereas quantitative magnitudes remain sensitive to sectional aerodynamic assumptions and induced flow representation. The framework is therefore intended as a computationally inexpensive screening and interpretation tool for oblique inflow symmetry breaking rather than as a substitute for phase-resolved CFD or experimental measurements.