Quadratic approximation and visualization of online contract-based available transfer capability region of power systems

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July 2008, 4(3): 553-563. doi: 10.3934/jimo.2008.4.553

Quadratic approximation and visualization of online contract-based available transfer capability region of power systems

Xiaojiao Tong ^1, , Felix F. Wu ^2, and Jifeng Su ^2,

1.	Mathematics and Computing Science, Changsha University of Science and Technology, China
2.	Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China

Received November 2007 Revised April 2008 Published July 2008

Abstract
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This paper develops the available transfer capability (ATC) concept to available transfer capability region (ATCR). Based on the steady-state security, the ATC of a single-contract is reformulated to a system of semismooth equations. Along the line of the methodology, the ATC of a combination of multi-contracts is presented. The combination coefficients forms a region, which is defined as ATC region (ATCR) in this paper. According to the messages of ATCs of each single-contract, the boundary of ATCR is approximated by a set of quadratic functions via a patching technology. The approximation of the ATCR and the visualization take a novelly practical approach called offline-online calculation. IEEE 30-bus system is chosen to test the method with respect to point-to-point transfers and area-to-area transfers. The computing results are visualized through a class of graphs. The virtue of ATCR is that it can provide the global message of possible increasing transfer in the system. The characteristic of the proposed method in this paper is its behave of online calculation. Numerical tests show the effect of the new approach.

Keywords: semismooth equations, security region, Available Transfer Capability Region (ATCR), quadratic approximation..

Mathematics Subject Classification: Primary: 65H10, 65K05; Secondary: 37N4.

Citation: Xiaojiao Tong, Felix F. Wu, Jifeng Su. Quadratic approximation and visualization of online contract-based available transfer capability region of power systems. Journal of Industrial & Management Optimization, 2008, 4 (3) : 553-563. doi: 10.3934/jimo.2008.4.553

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