This paper presents a new approach with Muller method for solving profit based unit commitment (PBUC). In deregulated environment, the generation companies (GENCOs) schedule their generators to ...maximize their profit rather than satisfying the power demand. The PBUC problem is solved by the proposed approach in two stages. Initially, the information of committed units is obtained by a simple approach and finally non linear programming sub problem of economic dispatch is solved by Muller method. The proposed approach has been tested on a power system with 3 and 10 generating units. Simulation results of the proposed approach have been compared with existing methods and also with traditional unit commitment. It is observed from the simulation results that the proposed algorithm provides maximum profit with less computational time compared to existing methods.
This paper presents equal embedded algorithm to solve the economic load dispatch problem of thermal units with generator constraints and transmission losses. The equal embedded algorithm involves the ...selection of the lambda values, then the individual output power of generators are determined in terms of the lambda by interpolation and finally the lambda is evaluated from the power balance equation by Muller method. The proposed algorithm was applied to solve economic load dispatch problem of a power system having 3, 6 and 15 generating units. The proposed method results were compared with genetic algorithm and particle swarm optimization method. In our approach, the qualitative solution is achieved with less computational time and it converges within few iterations. (6 pages)
•The well-known methods for solving the scalar nonlinear equation f(x)=0 have been criticized, which use the conditions |xi+1−xi|≤ε,|f(xi+1)−f(xi)|≤δ, for stopping the iterative process, where ε,δ ...are a small positive numbers, i is the iteration number. On the examples of the solution of equations, it is shown that this widespread opinion is erroneous, since from the fact that these conditions are met, it does not follow that |xi+1−x*|≤ε, where x⁎ is the exact solution of the problem.•An improved parabolic method is proposed, which first uses the condition |xi+1−xi|≤ε, confirms or refines solution, using the condition f(xi+1)·f(xi)≤0 to guarantee accuracy.•The method is not inferior and even slightly exceeds the methods of Brent, Ridders and Müller, each of which, however, does not always guarantee accuracy when finding the roots of equations.
An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method.
This paper presents a novel method of pseudo-white noise jamming signal digital generation. Noise signal is generated only in parts of frequency spectrum based on Box-Müller algorithm. Thus necessary ...emission power of barrage jamming is decreased while jamming effectiveness is increased comparing to classical sweep jamming. It is analyzed how the jamming signal frequency spectrum is managed. The method is simpler for the application than classical barrage jamming, especially when jamming frequency bandwidth is limited.
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