Determination of multiple solutions of load flow equations

This paper is concerned with the problem of finding all the real solutions (all components of the solution vector must be real values) of load flow equations. Solutions in which some of the components are complex values are of no interest as they have no physical significance as a load flow solution...

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Bibliographic Details
Published in:	Sadhana (Bangalore) Vol. 41; no. 8; pp. 855 - 867
Main Authors:	Mahata, Pankaj, Rao, P S Nagendra
Format:	Journal Article
Language:	English
Published:	New Delhi Springer India 01-08-2016 Springer Nature B.V
Subjects:	Engineering zero load solution critical point zero load condition manifold multiple solutions voltage stability continuation Load flow
Online Access:	Get full text
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Summary:	This paper is concerned with the problem of finding all the real solutions (all components of the solution vector must be real values) of load flow equations. Solutions in which some of the components are complex values are of no interest as they have no physical significance as a load flow solution. This problem is significant not only because of its theoretical challenge but also, its relationship with several system behavior related issues. Approaches suggested so far for solving this problem are rather ad hoc, computationally demanding and have been demonstrated only on very small systems. Further, it has been subsequently shown by others that many of these methods are not capable of finding all solutions. In this work a new approach is proposed which is more systematic and seems to have the potential to handle even large problems. We show that for any system it is possible to find the multiple load flow solutions (MLFS) corresponding to a given operating point extremely easily, starting from a set of points that are referred to as zero load solutions (ZLS) in this paper. It is shown that the complete set of ZLS is unique for a system and MLFS for any other operating point can be obtained starting from these ZLS using only the Newton’s load flow method. The set of procedures for implementing the proposed scheme are illustrated and their features are highlighted by considering several sample systems.
ISSN:	0256-2499 0973-7677
DOI:	10.1007/s12046-016-0524-5