Along with the wide-ranging addition of wind power into power systems

multiple uncertainties are produced due to continuous changes of wind power

which in turn will affect the dispatching and operational process of the power grid. In this process

excessive pursuit of the lowest risk of wind energy may bring an apparent influence on the economic effect of the multi-energy complementary power generation system because a continuous imbalance between demand and supply may lead to wind curtailment. To solve these issues

a new model that couples the multi-dimensional uncertainty model with the day-ahead complementary operation model is developed for a wind-hydro-thermal system. A multi-dimensional uncertainty model (MU) is used to deal with wind uncertainty because it can quantitatively describe the complex features of error distribution of hourly day-ahead wind power forecasting. The multi-dimensional interval scenes attained by the MU model can reflect hour-to-hour uncertain interaction in the day-ahead complementary operation for the wind-hydro-thermal system. This new model can make up for the shortcomings of the day-ahead operation model by reducing wind power risk and optimizing the operational costs. A two-layer nested approach with the hierarchical structure is applied to handle the wind-hydro-thermal system's complex equality and inequality constraints. The new model and algorithm's effectiveness can be evaluated by applying them to the Shaanxi Electric Power Company in China. Results demonstrated that: compared with the conventional operation strategies

the proposed model can save the operational cost of the units by 7.92 % and the hybrid system by 0.995 %

respectively. This study can offer references for the impact of renewable energy on the power grid within the context of the day-ahead electricity market.