Battery Storage Formulation for Faster Day-Ahead SCUC

The patent transforms the binary variable formulation into a continuous variable formulation by changing the parameter type. This is achieved by using complementarity constraints and valid inequalities to model the mutual exclusiveness of charging and discharging modes without requiring discrete binary variables, thereby maintaining physical constraints while improving computational performance

The patent replaces the mechanical binary variable switching mechanism with a mathematical formulation using complementarity constraints and valid inequalities. This substitution eliminates the need for discrete optimization while preserving the physical reality that a battery cannot charge and discharge simultaneously, thus resolving the contradiction between constraint satisfaction and computational efficiency

The patent changes the mathematical formulation from non-convex continuous constraints to a convex formulation by using valid inequalities and complementarity constraints. This transformation maintains the physical accuracy of mutual exclusiveness while ensuring the optimization problem remains computationally tractable through convex optimization techniques

The patent introduces valid inequalities as intermediary constraints that mediate between the physical requirement of mutual exclusiveness and the computational need for convexity. These inequalities act as a bridge, capturing the essential physical behavior while maintaining mathematical tractability for efficient optimization