A least squares solution for optimal power flow sensitivity calculation

A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By app...

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Bibliographic Details
Published in:IEEE transactions on power systems 1992-08, Vol.7 (3), p.1394-1401
Main Authors: Venkatesh, S.V., Liu, W.-H.E., Papalexopoulos, A.D.
Format: Article
Language:English
Subjects:
240200 - Power System Networks, Transmission & Distribution- (1990-)
990200 - Mathematics & Computers
ALGORITHMS
COMPUTER CODES
Control systems
Costs
ELECTRIC UTILITIES
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
LEAST SQUARE FIT
Least squares approximation
Least squares methods
Linear programming
Load flow
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
Medical services
NUMERICAL SOLUTION
OPTIMIZATION
POWER
Power generation
POWER TRANSMISSION AND DISTRIBUTION
Power transmission lines
Production
PUBLIC UTILITIES
SENSITIVITY
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Summary:A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By applying the Kuhn-Tucker conditions, the derivatives of the Lagrangian at the solution with respect to free variables provide a set of over-determined equations for the Lagrange multipliers. A least-squares estimation of the Lagrange multipliers with the over-determined set of equations is used. The mathematical formulation of the least-squares problem for the sensitivity calculation is presented. A computationally efficient method of solving the normal equation is derived. Special care has been taken to accurately model all controls and all operating and security constraints. The algorithm has been tested on a reasonably large system. The results indicate the validity of the approach.< >
ISSN:0885-8950
1558-0679
DOI:10.1109/59.207359