This paper develops a methodology for optimizing the hydro unit commitment (HUC) for the Three Gorges Project (TGP) in China. The TGP is the world's largest and most complex hydropower system in operation. The objective is to minimize the total operational cost. The decision variables are the startup or shutdown of each of the available units in the system and the power releases from the online units. The mathematical formulation must take into account the head variation over the operation periods as the net head changes from hour to hour and affects power generation. Additionally, the formulation must consider the operation of 32 heterogeneous generating units and the nonlinear power generation function of each unit. A three-dimensional interpolation technique is used to accurately represent the nonlinear power generation function of each individual unit, taking into account the time-varying head as well as the non-smooth limitations for power output and power release. With the aid of integer variables that represent the on/off and operation partition statuses of a unit, the developed HUC model for the TGP conforms to a standard mixed integer linear programming (MILP) formulation. We demonstrate the performance and utility of the model by analyzing the results from several scenarios for the TGP.
The analysis of spatio-temporal signals plays an important role in various fields including sociology, climatology, and environmental studies, etcetera. Due to the abrupt breakdown of the sensors in the sensor network, always there are missing entries in the observed spatio-temporal signals. In this paper, we study the problem of recovering spatio-temporal signals from partially known entries. Based on both the global and local correlated property of spatio-temporal signals, we propose a Low Rank and Differential Smoothness-based recovery method (LRDS), which novelly introduces the differential smooth prior of time-varying graph signals to the field of spatio-temporal signal analysis. The performance of the proposed method is analyzed theoretically. Considering the case where a priori information about the signal's global pattern is available, we propose Prior LRDS (PLRDS) to further improve the reconstruction accuracy. Such improvement is also verified by synthetic experiments. Besides, experiments on several real-world datasets demonstrate the improvement on recovery accuracy of the proposed LRDS over the state-of-the-art spatio-temporal signal recovery methods.