2.2 Mixed-Integer Linear Formulations for Storage Dispatch
To evaluate the operational flexibility and economic value of mountain energy storage under structural transmission constraints, this methodological framework integrates mathematical dispatch optimization with empirical market scarcity assessment. The primary dispatch engine utilizes a Mixed-Integer Linear Programming formulation to simulate hourly plant operations under day-ahead electricity market conditions, explicitly incorporating technical operating parameters such as turbine and pump capacities, round-trip efficiency, reservoir energy storage limits, and startup frequency restrictions (crossref-10-3390-su18136805, 2026). This optimization structure captures the precise operational capacity of pumped storage assets to capitalize on short-term price volatility and negative pricing intervals, reflecting seasonal market dynamics where summer solar overproduction generates substantial spreads between charging and discharging phases (crossref-10-3390-su18136805, 2026). To link micro-level dispatch decisions with macro-level grid reliability and industrial cost exposure, the mathematical programming formulation is coupled with a generalized empirical framework that analyzes asset performance during historical scarcity events and grid stress (crossref-10-36227-techrxiv-174060198-84092808-v1, 2025). Because variable renewable energy resources tend to underperform during extreme weather episodes such as severe heatwaves and prolonged cold snaps, dispatchable hydroelectric resources become critical balancing assets when thermal generation faces operational limits or extreme fuel price spikes (crossref-10-36227-techrxiv-174060198-84092808-v1, 2025). Synthesizing deterministic linear programming with empirical scarcity evaluation provides a robust methodological foundation for quantifying how transalpine transmission bottlenecks restrict flexible power evacuation, thereby amplifying wholesale price divergence across interconnected bidding zones and eroding industrial competitiveness.