Abstract: This paper presents a hydro-thermal unit commitment model that fully considers the influence of the forbidden zone and the low-carbon operation of the power system. Furthermore, on the basis of the model, a computationally efficient mixed-integer linear programming (MILP) algorithm is established. First, inspired by the relationship between the roots of a function and its coefficients, high dimensional polynomial functions are used to simulate the forbidden zone constraints of hydropower plants. Meanwhile, coherent function (CF) is put forward to uniformly represent multiple forbidden zone constraints simulated by high dimensional polynomial functions. Then, by using groups of step functions, a transformation algorithm is proposed to approximate the high dimensional nonlinear coherent function constraints, which transforms the problem into a mixed-integer linear programming (MILP) problem and extremely improves the solve efficiency. Finally, the proposed model and algorithm are verified by the improved IEEE39 node system and a practical large-scale case.