Formulating a quadratic frequency nadir constraint in unit commitment based on energy conservation law

Abstract

This paper proposes a quadratic formulation for the frequency nadir constraint (FNC) based on the energy conservation law. Incorporating the formulation into the unit commitment (UC) model, a mixed-integer quadratically constrained programming (MIQCP) model for frequency nadir constrained UC can be obtained, which can be solved efficiently by the MIQCP solver. The distinct feature of the formulation is that it considers the inertia difference among generators, which has a significant effect on the on/off schedule of generators. Besides, the formulation has a clear physical meaning and does not have to be linearized. The test on the WSCC 3-machine 9-bus benchmark system validates the accuracy of the formulation, and the case studies on a New England 10-machine 39-bus system confirm the effectiveness of the proposed formulation.