| Due to the increasing power load, a lot of generators are required to provide electrical energy. Among them, the energy produced by thermal units accounts for up to 80.8 percent of China’s energy output, but hydro energy accounts for only about 16.5 percent. Thermal units not only need to consume a large amount of primary energy, but also cause serious pollution when they provide electrical energy. Therefore, in order to support the national call of "energy conservation and emissions reduction", this dissertation has studied unit commitment (UC) problems in order to achieve the targets of priority scheduling renewable generation resources, minimizing energy consumption and pollutant emissions. It will not only be conductive to the safe and stable operation of power system, but also can create significant economic and social benefits.UC problems are high-dimensional, discrete, non-convex mixed integer nonlinear programming problems, which belong to NP-hard problems. According to the existing technology, it is difficult to direct solve quickly. Due to limitations of mathematical theory and solving techniques, the mixed integer non-linear programming solvers are developing slowly, which are even unable to find the optimal solution for small-scale systems. But the performance of mixed-integer linear programming (MILP) solvers has improved dramatically. Therefore, building MILP models of UC problems to solve has become one of the mainstreams. However, the MILP models of UC problems for large-scale systems still need very long computational time. In addition, for convenient calculation, the modeling of UC problems has done a lot to simplify. Therefore, in order to improve the solving efficiency and create more realistic models, this dissertation will use a variety of theories and methods such as MILP theory, linearization theory, algebraic modeling technology, to in-depth study and improve MILP models of traditional UC, hydrothermal coordination and short-term hydro scheduling problems.Aiming at UC problems which consider and not consider the influence of ramp limits on the spinning reserve, this dissertation presents more compact and tighter MILP models using four sets of binary variables. By introducing auxiliary binary variables to represent the cold start-up status, the start-up cost is formulated as a linear expression, which improves the compactness and tightness of the MILP model simultaneously. Combining with the ramp rate and the minimum uptime limits, new expressions of generation limits are proposed as well, which can shrink the feasible region of the power output significantly with a much tighter model. The efficiency of solving linear programming relaxations of the proposed models is higher because of the more compact characteristic. Their linear programming relaxed solutions are nearer to the MILP optimal solutions due to the tighter characteristic, since the search space to find the optimal solutions is reduced. The results indicate that the proposed models can obtain high-quality solutions, and also improve the solving efficiency by several even hundreds of times, especially for large-scale systems.This dissertation presents a more realistic model for the operating states of thermal units considering the start-up and shut-down power trajectories. The curve of the unit power output is modelled as a piecewise linear model from the traditional staircase curve, and then it is smoothed. Therefore, the traditional energy schedule is transformed into the power schedule. The model considers four operating phases of a coal-firing unit, which are consisted of warming up, starting-up ramp, dispatching and shuting-down ramp. The electrical energy produced in the phases is also considered. The model can support any number of the startup types. The start-up cost, warming up time, start-up ramp time and start-up power output trajectories of different types are all dependent on the unit’s prior reservation time. The results indicate that the proposed model is correct and reasonable, and is closer to the realistic calculation.This dissertation builds an MILP model for the hydrothermal and reserve coordination problem which considers the start-up and shut-down power trajectories of thermal units. Since the hydro unit ramps fast, its power output is modelled as a staircase curve. The model considers the start-up and shut-down cost, and also the water required to start-up and shut-down a unit. For reservoirs with large water storage, ignoring the head effect, a linear expression of hydroelectric conversion function considering vibration area is proposed. Combined with electricity market, a more precise model for the ancillary services is proposed, including regulation down, regulation up, ten-minute spinning reserve and ten-minute non-spinning reserve. The results indicate that the proposed model is correct and reasonable, and is conducive to the frequent call of system reserves in electricity market.Logarithmic convex combination method, the latest achievement of the piecewise linearization, is applied to power system problems for the first time. This method uses a Gray code to encode the segmentation where the variable locates in. The number of binary variables and constraints increases logarithmically as the number of total segments. It is used to linearize the univariate nonconvex nonlinear function, such as the forebay level and the water storage of the reservoir, the tailrace level and the total water release of the reservoir. The quadrilateral and logarithmic quadrilateral linear interpolation methods are proposed for the linear interpolation of the bivariate nonconvex nonlinear function, which are used for the power production function. Therefore, a more realistic high-efficient MILP model for the hydro generation scheduling problem is built. The results indicate that logarithmic convex combination and the proposed methods can reduce the binary variables and constraints significantly, therefore, can effectively improve the solving efficiency of the hydro generation scheduling model. |
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