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Abstract: In this paper, the traditional automatic generation control loop with modifications is incorporated for simulating automatic generation control (AGC) in restructured power system. Federal energy regulatory commission (FERC) encourages an open market system for price based operation. FERC has issued a notice for proposed rulemaking of various ancillary services. One of these ancillary services is load following with frequency control which comes broadly under Automatic Generation Control in deregulated regime. The concept of DISCO participation matrix is used to simulate the bilateral contracts in the three areas and four area diagrams. Hybrid particle swarm optimization is used to obtain optimal gain parameters for optimal transient performance. [Copyright &y& Elsevier]

In this paper, we solve the classic problem of computing the average number of decomposed quadtree blocks (quadrants, nodes, or pieces) in quadtree decomposition for an arbitrary hyperrectangle aligned with the axes. We derive a closed-form formula for general cases. The previously known state-of-the-art solution provided a closed-form solution for special cases and utilized these formulas to derive linearly interpolated formulas for general cases individually. However, there is no exact and uniform closed-form formula that fits all cases. Contrary to the top-down counting approach used by most prior solutions, we employ a bottom-up enumeration approach to transform the problem into one that involves the Cartesian product of d multisets of successive 2's powers. Classic combinatorial enumeration techniques are applied to obtain an exact and uniform closed-form formula. The result is of theoretical interest since it is the first exact closed-form formula for arbitrary cases. Practically, it is nice to have a uniform formula for estimating the average number since a simple program can be conveniently constructed taking side lengths as inputs. [ABSTRACT FROM AUTHOR]