Mixed integer nonlinear programming model for solving combination problem of hydroelectric generating set

Abstract

The invention provides a mixed integer nonlinear programming model for solving the combination problem of a hydroelectric generating set, and belongs to the field of hydroelectric scheduling operation. The mixed integer nonlinear programming model for solving the combination problem of a hydroelectric generating set is characterized by utilizing a polynomial fitting technology to process the complicated power station nonlinear relation, providing a quartic equation polynomial fitting method of water level-capacity of reservoir-tailwater level-out flow, and based on a quadratic polynomial of head loss of the hydroelectric generating set, describing the generating head of the hydroelectric generating set as a multivariate quartic function of capacity of reservoir and flow; considering aboutthe influence of the head on the output, providing a binary quadratic polynomial method of accurately representing the output head and the generating flow of the hydroelectric generating set, introducing 0-1 variable, solving the startup-shutdown problem of the hydroelectric generating set, obtaining the head-flow-output relation three-dimensional fitting surface of the hydroelectric generating set, and satisfying the fine calculation demand of the output of the hydroelectric generating set under the variation head; and realizing calculation with high efficiency by means of a mature MINLP solver. The mixed integer nonlinear programming model for solving the combination problem of the hydroelectric generating set fully considers the complicated nonlinear relation of the hydroelectric systemand has the advantages of reducing the linear error and significantly improving the solution accuracy, compared with a classic MILP model. Besides, the obtained set combination and load distributionresult can preferably reflect the practical operation situation of the hydropower station.

Description

Technical field [0001] The invention belongs to the field of hydropower dispatching operation, and relates to a mixed integer nonlinear programming model for solving the combined problem of hydropower generating units. Background technique [0002] Unit combination optimization has always been one of the core issues of hydropower and power system dispatch. The purpose is to rationally arrange the start-stop mode and power generation plan of each unit to save power generation costs while meeting system load requirements, as well as complex constraints such as water power and power. , Improve unit operating efficiency. Hydropower unit combination is a typical complex non-linear mixed integer problem, presenting high-dimensional, discrete, and non-convex characteristics. Compared with thermal power combination optimization problems, it is more complex and more difficult to model and solve. [0003] In the past few decades, many researches have been committed to establishing mathemati...

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Problems solved by technology

The combination of hydropower units is a typical complex nonlinear mixed integer problem, which is high-dimensional, discrete, and non-convex. It is more complicated than the optimization problem of thermal power units, and it is more difficult to model and solve.

[0003] Over the past few decades, numerous studies have been committed to establishing mathematical models and methods that can reflect actual engineering needs and take into account computational efficiency, including prioritization methods, dynamic programming, Lagrangian relaxation, and intelligent algorithms such as genetic algorithms and simulated annealing. It is applied to the combinatorial optimization problem of hydropower units. However, due to the nonlinear and non-convex characteristics of hydropower systems, dynamic programming faces the "curse of dimensionality" problem when solving discretely; the Lagrangian relaxation method handles complex coupling constraints by introducing multipliers Conditions, but small changes in the multiplier will cause oscillation or singularity, and the convergence cannot be guaranteed; due to the random search characteristics of the intelligent algorithm, the stability of the result is poor, which also limits its wide application

With the rapid development of computers and commercial computing software, mathematical programming methods are more widely used in hydropower combination optimization problems. Among them, MILP is widely used because of its easy solution and global convergence characteristics. However, due to the linearization of nonlinear factors, it is inevitable The ground will affect the accuracy of the result. Although piecewise linearization can reduce the linear error, it will reduce the solution efficiency, and different linearization methods will produce different calculation results. How to perform linearization is also very critical.

Taking the most complex unit output characteristic curve in hydropower dispatching as an example, in order to avoid nonlinear problems, some studies use only one unit output-flow curve in the MILP model or select some local optimal points to replace all the power generation curves of different water heads. Ignoring the change of water head, which directly affects the actual power generation efficiency of the unit, British Columbia Company applied this linearization method to a power station with a total installed capacity of 4 units of 2700MW, resulting in an actual reduction of 15% in the power generation efficiency of the unit

In order to consider the influence of hydraulic head changes on output, an improved linearization method is further proposed. By converting multiple output-discharge curves into a series of one-dimensional functions or through triangular and grid three-point interpolation calculations, the variable hydraulic head is realized. The calculation of the output under the following method does improve the calculation accuracy, but the introduction of a large number of integer variables greatly affects the solution efficiency, and the error between the result and the actual output characteristic curve is still difficult to ignore

In fact, the unit combination is a typical nonlinear integer optimization problem, and the nonlinear model can describe the problem more accurately than the linear model, but the research and practical work on this aspect are extremely rare

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