Research On The Non-convex Economic Dispatch Problem Of Power System By Mixed-integer Linear Programming And Non-linear Programming

In recent years,with the rapid development of our national economy,it is accompanied by the high consumption of energy.Under this background,on the one hand,we should advocate the development of new energy sources,on the other hand,we should improve energy utilization efficiency and reduce consumption of energy.Therefore,it is of great theoretical and practical significance for optimizing the current power generation dispatching model of the power system and reducing the energy consumption.Based on two important issues in the security and economic operation of power system,namely,economic dispatch and hydrothermal coordination,this dissertation studies the more accurate and practical non-convex economic dispatch problem of power system(for instance,considering the factors such as valve-point effects,transmission loss and prohibited operating zones).It aims at solving the model effectively,achieving a better power generation scheduling to reduce the energy consumption of the system.When the complicated factors such as valve-point effects,transmission loss and prohibited operating zones all are taken into account,the model of the problem becomes non-convex,non-smooth and non-continuous in nature,which will lead to the failure in applying the deterministic mathematical programming method directly.In this dissertation,with the aid of reformulation techniques,the complicated models are transformed into the corresponding mixed-integer linear programming formulations and non-linear programming formulations that can be solved by mathematical programming method directly.Based on such two formulations,effective solution strategies are designed.Numerical results show that the proposed strategies are competitive with most of the currently state-of-the-art approaches.The specific research contents and main results are as follows:1)Based on the mixed-integer linear programming formulation and the non-linear programming formulation,an effective solution strategy is proposed for solving the dynamic economic dispatch problem with valve point effects.Since valve point effects are taken into account,the objective function of the problem is highly non-convex and non-smooth,making the traditional gradient-based optimization method can not be utilized any more.By introducing some auxiliary variables,the non-smooth terms in the objective function are transferred to the constraints,and then a non-linear programming formulation for the problem is derived.Although this formulation can be solved using the non-linear programming method directly.However,the optimization can easily become trapped in a poor local optimum due to its highly non-convex nature.So based on the multiple choice model,piecewise linearization is utilized to approximate the non-convex and non-smooth objective function,and then an approximate model of the problem,namely,a mixed-integer linear programming formulation,is obtained to generate a good initial point.Solving the non-linear programming model based on such a good initial point,a high-quality solution for the original problem can be achieved.2)Based on the logarithmic size mixed-integer linear programming formulation and the non-linear programming formulation,an effective solution strategy is proposed f-or solving the hydrothermal coordination problem with valve point effects.For the non-convex and non-smooth objective function and the non-convex two-variable hydro-generating function,piecewise linearizations are carried out based on the convex combination model and the the "Union Jack" triangulation,respectively.And combining with the advanced modeling strategy,only a logarithmic size of binary variables and constraints are introduced in the modeling process.Based on such a mixed-integer linear programming formulation,a global optimal solution within a preset tolerance can be obtained quickly.However,due to the application of linearization,the solution may not fully satisfy the constraints of the original problem.To eliminate the linearization errors and deal with the transmission loss,a non-linear programming model for the original problem can be obtained by reformulation.So a high-quality feasible solution for the original problem can be obtained by solving the non-linear programming model.3)Based on the fully mixed-integer linear programming formulation and the non-linear programming formulation,an effective solution strategy is proposed for solving the economic dispatch with valve-point effects,transmission loss and prohibited operating zones.Because the loss constraint is a non-convex equality constraint,and there is a strong coupling relationship between variables in the high-dimensional space,it is usually difficult to linearize directly.To handle this difficulty,a reformulation trick is utilized,transforming it into a linear constraint and a group of tractable quadratic constraints.By taking full advantage of the variables coupling relationships among univariate and bivariate functions,the introduced binary variables and constraints in the approximation process of the non-convex bivariate function are greatly reduced.At this time,applying the advanced modeling technique,the additional binary variables and constraints can be further reduced.When the non-continuous prohibited operating zones restrictions are also considered,a distance-based technique is adopted to rebuild these constraints,making them compatible with the previous mixed-integer linear programming reformulation and the introducing variables and constraints as few as possible.And then,a fully mixed-integer linear programming formulation is obtained for the problem.Based on such a model,if the obtained solution is less than a given precision for the power balance equation,the optimal solution is considered to be an acceptable approximate global optimal solution for the original problem.Otherwise,a further search will be implemented by solving a non-linear programming model of the original problem to capture a feasible optimal strategy.