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Content available remote Diagonals of Self-adjoint Operators with Finite Spectrum
Given a finite set X ⊆ R we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur–Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison’s theorem for orthogonal projections (2002) and the second author’s result for operators with three-point spectrum (2013).
This paper addresses a novel technique to solve non-convex economic load dispatch (NCELD) problem. Generator constraints,such as valve point loading, ramp rate limits and prohibited operating zones are taken into account in the problem formulation of NCELD.Few Variants of Differential Evolution (DE) and Differential Evolution with Random Scale Factor (DE-RSF)is applied for solving the above problem. The technique is tested with IEEE standard test systems.It is shown that, the presented technique for solving NCELD problem generates quality solutions reliably. Keywords: Differential Evolution, economic dispatch, prohibited operating zones, ramp-rate limits, valve-point effect.
W artykule opisano nową technikę optymalizacji rozmieszczenia jednostek wytwarzania energii elektrycznej na podstawie analizy ekonomicznej i analizy obciążenia. Zastosowano różne warianty algorytmu ewolucji różnicowej oraz ewolucji różnicowej o zmiennym współczynniku skali. Przeprowadzono badania weryfikujące skuteczność działania proponowanej techniki.
Department of Electrical Engineering, Anna University Regional Centre, Coimbatore, India This paper presents a new approach to solve economic load dispatch (ELD) problem in thermal units with non-convex cost functions using differential evolution technique (DE). In practical ELD problem, the fuel cost function is highly non linear due to inclusion of real time constraints such as valve point loading, prohibited operating zones and network transmission losses. This makes the traditional methods fail in finding the optimum solution. The DE algorithm is an evolutionary algorithm with less stochastic approach to problem solving than classical evolutionary algorithms.DE have the potential of simple in structure, fast convergence property and quality of solution. This paper presents a combination of DE and variable neighborhood search (VNS) to improve the quality of solution and convergence speed. Differential evolution (DE) is first introduced to find the locality of the solution, and then VNS is applied to tune the solution. To validate the DE-VNS method, it is applied to four test systems with non-smooth cost functions. The effectiveness of the DE-VNS over other techniques is shown in general.
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