Second-order cone programming for solving unit commitment strategy of thermal generators

• Second-order cone programming (SOCP) is proposed to solve unit commitment.
• Unit commitment is transformed to SOCP model with tight lower bounds.
• Conic quadratic constraints representation of UC problem is suggested.
• Effectiveness of the proposed method is verified with different test systems.
• SOCP is expanded to solve large-scale mixed integer nonlinear optimization problem.

The short-term unit commitment (UC) problem of hydrothermal generation systems is a mixed-integer nonlinear programming (MINLP), which is difficult to solve efficiently, especially for large-scale instances. The perspective relaxation (PR) is an effective approach to constructing tight approximations to MINLP with semi-continuous variables. In this paper, the PR of UC problem is formulated as a mixed integer second-order cone programming (SOCP) model because the quadratic polynomial cost function of the UC problem is SOCP-representable. The proposed model is implemented by using the commercial optimization software IBM CPLEX 12.4. Extensive numerical studies have been conducted to verify the advantages of our proposed method. Instances of the test system vary from 10 to 1000 units. Our results indicate that the proposed method performs better than the existing methods in terms of production cost savings and faster computational times, especially for large systems.