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### Polish

Home ## PhD thesis - abstract

New stochastic optimization methods to the unit commitment problem are proposed. The mathematical model of the problem includes the cost function defined as the sum of variable production costs and start-up unit costs in 24-hour optimization period, the load  balance constraint, power generation limits of a single unit and set of units, and minimum up and down time constraints.

Methods of construction of variable cost and start-up cost characteristics are proposed. These characteristics include the costs of fuel, additional material costs, operating costs of the installations of combustion gases cleaning (desulphurization, denitrogenation), the cost of air pollution, waste storage costs and sewage costs.

Two approaches are proposed to the solution of the problem: (i) combined, using evolutionary algorithms, simulated annealing and a hybrid of both these algorithms and (ii) integrated, with comprehensive and sequential evolutionary algorithms.

In the first approach, the optimization problem is decomposed into the problem of generating unit selection (combinatorial), solved using stochastic methods, and the problem of determining the generation levels of selected units (continuous), solved using Lagrange multipliers. Several ways of variable definitions and  representation methods adapted to them are proposed. Some heuristic operators to modify solutions in the process of searching the solution space are proposed – mutation, recombination and transposition operators. In the simulated annealing algorithm the adaptive annealing schedule, that allows taking into account the problem constraints, is introduced, where the temperature is adapted to the stages of searching the solution space. The hybrid algorithm has the structure of simulated annealing, but there are many parallel processes of annealing. The solution space is searched by a population of points which are modified independently in the inner loop of the algorithm and exchange information among themselves in the outer loop.

In the integrated approach, the evolutionary algorithms solve the problems of generating unit selection and determining the unit generation levels simultaneously. The comprehensive evolutionary algorithm optimizes the cost function in the whole optimization period, while  the  sequential evolutionary algorithm optimizes the cost function in the subsequent whiles of the  optimization period. The floating-point representation of variables and specialized operators of mutation, transposition and crossover are applied.

The cost function constrains are eliminated using the repair strategy of infeasible solutions (random or deterministic) and penalty functions.

All variants of the developed optimization algorithms were tested in a practical task. Comparative calculations were made using other optimization algorithms, deterministic and stochastic. In all cases the proposed algorithms gave better solutions.

A statistical analysis of the accuracy and sensitivity of the presented optimization methods was performed.

The proposed methods of unit commitment can be applied in a single power station and in power systems as well. They can also be used in some models of the energy market.