Sparse Ordered‐Binary Formulation for Committed‐Number‐Controlled Transmission Constraints in Security‐Constrained Unit Commitment

ABSTRACT

Security‐constrained unit commitment is a fundamental optimization problem in power system operations. Conditional transmission constraints, whose limit values dynamically depend on the number of online committed units, introduce computational challenges due to the binary variables required for level selection. This paper proposes a sparse formulation based on ordered binary variables to model these constraints. By representing the staircase function with an ordered binary sequence, the proposed formulation achieves the same linear programming relaxation tightness as the interval‐selection method while reducing binary variables and non‐zero entries. The ordered sequence associated with a given unit group is constructed only once and can be shared across multiple transmission sections controlled by the same committed‐number condition, which eliminates redundant auxiliary variables. Numerical results on three test systems show speedups over the conventional approach.