To address the key challenges of distributed generation and loads, insufficient edge computing capacity, significant data privacy risks among multiple participants, and immature market mechanisms in county-level distribution networks, this paper presents a transaction-driven two-tier distributed collaborative optimization approach for interconnected integrated energy systems. We develop a market-oriented architecture that combines upper-layer price coordination with lower-layer autonomous optimization. The overall system is decoupled using just two types of non-sensitive data—local electricity prices and regional net power—while preserving the operational independence and data privacy of all stakeholders. We further devise a Two-Stage Distributed Transactional Optimization (TSDTO) mechanism. This mechanism reformulates the intraday multi-variable collaborative optimization into a single-variable electricity price search problem, substantially reducing algorithm iterations and communication overhead. Simulations are conducted on three typical interconnected integrated energy systems in a county in northern China. The results demonstrate that the proposed method maintains main transformer power within safe limits, effectively lowers daily operating costs, and boosts the renewable energy accommodation rate. Compared with the conventional subgradient method, our algorithm offers higher computational efficiency, along with improved convergence and real-time performance. The proposed approach is capable of achieving a relatively satisfactory balance among privacy protection, low computational complexity, on-site renewable energy utilization, and rapid real-time operation. This paper provides theoretical references and guidance for the low-carbon, cost-effective, coordinated and sustainable operation of modern county-level power systems and integrated energy systems.

The torsional behavior of an extruded AZ31 magnesium alloy was investigated by combined axial-torsion mechanical testing with different stress ratios. The SEM-EBSD was used to analyze the microstructure and texture evolution of deformed samples. The results indicate that the axial tension results in a concave-down shape of shear stress–strain curves, while a concave-up shape after yielding is presented during combined compression-torsion loading due to twinning mechanism. Compared to pure shear, the yield strength decreases by 7 MPa and shear strain increases by 1% under σ:τ = −1:1 with same shear stress. Due to the Swift effect, a strain partitioning is displayed for axial strain during combined tension-torsion loading with low stress ratio. The twin volume fraction is 90% under σ:τ = −1:1, and the local dislocation density with a KAM value of 1.1 is maximum under σ:τ = 2:1. The primary twin type is {10-12} twins with axial compression. The main deformation mode changes from basal slip to prismatic slip with increase in axial tension stress. Both basal slip and twinning are activated and the interaction between dislocation slip and twinning contributes to the complex strain hardening behavior during combined compression-torsion loading.