During power system restoration, the maximum load amount that a substation can pick up at one time is a critical parameter to be determined. Many factors should be considered, such as frequency constraint, transient v...
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During power system restoration, the maximum load amount that a substation can pick up at one time is a critical parameter to be determined. Many factors should be considered, such as frequency constraint, transient voltage-dip constraint, steady-state voltage constraint and cold load pickup. This paper proposes a mathematical model for calculating the maximum restorable load amount, in which proper checking methods are presented to deal with these constraints. Frequency deviation is calculated by the average system frequency model. The transient voltage-dip constraint is dealt with by a fast estimation. Cold load pickup characteristics are addressed according to a simple guideline. And a modified bisection algorithm is proposed to solve the complex problem efficiently. The effectiveness is demonstrated by case studies performed on the IEEE 14-bus system and a practical power system. (C) 2012 Elsevier Ltd. All rights reserved.
We consider an identification (inverse) problem, where the state u is governed by a fractional elliptic equation and the unknown variable corresponds to the order s(0,1) of the underlying operator. We study the existe...
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We consider an identification (inverse) problem, where the state u is governed by a fractional elliptic equation and the unknown variable corresponds to the order s(0,1) of the underlying operator. We study the existence of an optimal pair (s) and provide sufficient conditions for its local uniqueness. We develop semi-discrete and fully discrete algorithms to approximate the solutions to our identification problem and provide a convergence analysis. We present numerical illustrations that confirm and extend our theory.
In this paper, we consider the linearly constrained multiobjective minimization, and we propose a new reduced gradient method for solving this problem. Our approach solves iteratively a convex quadratic optimization s...
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In this paper, we consider the linearly constrained multiobjective minimization, and we propose a new reduced gradient method for solving this problem. Our approach solves iteratively a convex quadratic optimization subproblem to calculate a suitable descent direction for all the objective functions, and then use a bisection algorithm to find an optimal stepsize along this direction. We prove, under natural assumptions, that the proposed algorithm is well-defined and converges globally to Pareto critical points of the problem. Finally, this algorithm is implemented in the MATLAB environment and comparative results of numerical experiments are reported.
An important class of generalized eigenvalue problems Ax = lambdaBx is those in which A and B are Hermitian and some real linear combination of them is definite. For the quadratic eigenvalue problem (QEP) (lambda(2)A ...
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An important class of generalized eigenvalue problems Ax = lambdaBx is those in which A and B are Hermitian and some real linear combination of them is definite. For the quadratic eigenvalue problem (QEP) (lambda(2)A +lambdaB + C)x = 0 with Hermitian A, B and C and positive definite A, particular interest focuses on problems in which (x*Bx)(2) - 4(x*Ax)(x*Cx) is one-signed for all non-zero x-for the positive sign these problems are called hyperbolic and for the negative sign elliptic. The important class of overdamped problems arising in mechanics is a sub-class of the hyperbolic problems. For each of these classes of generalized and quadratic eigenvalue problems we show how to check that a putative member has the required properties and we derive the distance to the nearest problem outside the class. For definite pairs (A, B) the distance is the Crawford number, and we derive bisection and level set algorithms both for testing its positivity and for computing it. Testing hyperbolicity of a QEP is shown to reduce to testing a related pair for definiteness. The distance to the nearest non-hyperbolic or non-elliptic n x n QEP is shown to be the solution of a global minimization problem with n - 1 dearees of freedom. Numerical results are given to illustrate the theory and algorithms. (C) 2002 Published by Elsevier Science Inc.
A numerical model is presented for the optimal vulcanization of 2D extruded polar rubber with microwaves and peroxides. Magnetron power and curing time are used as the input production parameters, and the output mecha...
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A numerical model is presented for the optimal vulcanization of 2D extruded polar rubber with microwaves and peroxides. Magnetron power and curing time are used as the input production parameters, and the output mechanical property selected for optimization is the average tensile strength of the item. A 2D thick weather strip is analyzed to validate the model. The electric field is evaluated by means of Yee cells (FDTD approach) and suitably inserted in Fourier's heat transmission law, thus allowing point-by-point temperature profiles to be determined. The temperature is then used to evaluate the degree of peroxidic reticulation, and thus the final tensile strength. A so-called alternating tangent approach based on the bisection method is finally proposed to estimate the optimal magnetron power and curing time.
We present the PFix algorithm for the fixed point problem f (x) = x on a nonempty domain [a, b], where d greater than or equal to 1, a, b epsilon R-d and f is a Lipschitz continuous function with respect to the infini...
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We present the PFix algorithm for the fixed point problem f (x) = x on a nonempty domain [a, b], where d greater than or equal to 1, a, b epsilon R-d and f is a Lipschitz continuous function with respect to the infinity norm, with constant q less than or equal to 1. The computed approximation (x) over tilde satisfies the residual criterion parallel tof ((x) over tilde) - (x) over tilde parallel to (infinity) less than or equal toepsilon, where epsilon > 0. In general, the algorithm requires no more than Sigma(i=1)(d) s(i) function component evaluations, where s equivalent to [ max(1, log(2) parallel tob - aparallel to(infinity) /epsilon))] +1 . This upper bound has order O([log(2)(d) as epsilon-->0. For the domain [0, 1] with epsilon<0.5 we prove a stronger result, i.e., an upper bound on the number of function component evaluations is ((d+r-1)(r-1)) +2((d+r)(r+1)) where r [log(2)(1/epsilon)]. This bound approaches O(r(d)/d!) as r-->infinity (epsilon-->0) and O(d(r+1)/r+1)!) as d-->infinity. We show that when q < 1 the algorithm can also compute an approximation (x) over tilde satisfying the absolute criterion parallel to(x) over tilde - x*parallel to(infinity) less than or equal toepsilon, where x* is the unique fixed point of f. The complexity in this case resembles the complexity of the residual criterion problem, but with tolerance epsilon(1 - q) instead of epsilon. We show that when q>1 the absolute criterion problem has infinite worst-case complexity when information consists of function evaluations. Finally, we report several numerical tests in which the actual number of evaluations is usually much smaller than the upper complexity bound. (C) 2003 Elsevier Inc. All rights reserved.
In this paper, we develop a bi-level transferable air pollutant price (TAPP) model, and use the model to find ways to mitigate China's interprovincial air pollution control problem. In this model, the leader is Ch...
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In this paper, we develop a bi-level transferable air pollutant price (TAPP) model, and use the model to find ways to mitigate China's interprovincial air pollution control problem. In this model, the leader is China's central government and the followers consist of China's 31 provinces. The leader aims to decrease the nation's total pollutant control costs, whereas each province attempts to minimize its pollution control costs by balancing its own pollutant reduction cost with transfer payments to or from other provinces, in the context of a transfer price set by the leader. We chose a Karush-Kuhn-Tucker approach with an embedded bisection algorithm to solve the model. We then applied the TAPP model to the seriously polluted Beijing-Tianjin-Hebei area of China. Compared with the current command-and-control regulation approach, the TAPP model for the Beijing-Tianjin-Hebei area decreased the total environmental cost by US$ 3 964.61x10(3) (10.5% of the current command-and-control regulation cost). This demonstrated that the TAPP model was superior because it both mitigated the problem of air pollution transport across regional boundaries and utilized the available resources of the study area more efficiently.
Design of microwave structures is a multiobjective task where several conflicting requirements have to be considered at the same time. For contemporary circuits characterized by complex geometries, multiobjective opti...
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Design of microwave structures is a multiobjective task where several conflicting requirements have to be considered at the same time. For contemporary circuits characterized by complex geometries, multiobjective optimization cannot be performed using standard population-based algorithms due to high cost of electromagnetic (EM) evaluations. In this work, we propose a deterministic approach for fast EM-driven multiobjective design of microwave structures. Our Pareto ranking bisection algorithm (PRBA) generates candidate designs by dividing the line segments connecting previously obtained Pareto optimal solutions and refining them by means of poll-type search involving Pareto ranking. Computational efficiency of the optimization process is ensured by a small number of objective function evaluations required by PRBA as well as by executing the algorithm using the low-fidelity EM model of the structure at hand. The algorithm is demonstrated using a compact impedance transformer. Experimental validation is also provided.
A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n3p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors ar...
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A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n3p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n2p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity.
This letter examines the robust beamforming design multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) downlink systems with imperfect channel state information (ICSI). Sparked by the worst-case ...
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ISBN:
(纸本)9781538645024
This letter examines the robust beamforming design multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) downlink systems with imperfect channel state information (ICSI). Sparked by the worst-case performance optimization framework, we consider to maximize the minimum of received signal-to-interference-plus-noise ratios (SINIRs) of users, which is not convex with regards of beamforming vectors. The formulated optimization problem is not convex so, to solve the challengeable problem, we first formulate a equivalent optimization problem based on semidefinite programming (SDP). By applying a rank one relaxation and a linear matrix inequality (LMI) the S-Procedure can be used, which leads to exploiting bisection algorithm in order to obtaining the robust optimal beamforming solution. Finally, simulation results demonstrate the proposed design.
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