04-07-2012, 03:34 PM
A Homogeneous Linear Programming Algorithm for the Security Constrained Economic Dispatch Problem
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Abstract
This paper presents a study of the simplified homogeneous
and self-dual (SHSD) linear programming (LP) interior
point algorithm applied to the security constrained economic dispatch
(SCED) problem. Unlike other interior point SCED applications
[1]–[3] that consider only the N security problem, this paper
considers both (N-1) and (N-2) network security conditions. An important
feature of the optimizing interior point LP algorithm is
that it can detect infeasibility of the SCED problem reliably.
INTRODUCTION
SECURITY dispatch refers to the case when the system is
dispatched such that it is in the normal secure state relative
to a pre-specified contingency list. In other words, for any contingency
belonging to this list, the redistribution of power flows
and voltages in the network, following a contingency, will result
in a normal system state [4]. In the event of a failure, security
dispatch ensures continuity of supply within the specified
voltage levels and frequency, and without violating rated limits
on any power equipment.
THE SHSD ALGORITHM
Two important aspects in the PCIP described in [3] have not
been solved satisfactorily from a practical point of view.
The first aspect is the choice of the initial solution. Although
the heuristic method presented in [3] works well in practice,
there is no guarantee that it presents a well-centered point.
The second aspect is the lack of a reliable method to detect solution
infeasibility or unboundedness of the LP problem. When
presented with an infeasible problem, the PCIP algorithm is not
able to reduce the residuals belowa certain nonzero level. Therefore,
the iterates diverge and their norm approaches infinity.
ITERATIVE CONSTRAINT SEARCH
Although the constraint set is reduced as indicated in Section
II-B-1, the number of constraints will still be large and only
a subset of them will be active. Therefore only critical cases
need to be included in the IP algorithm so as not to overburden
it by constraints. The method of iterative constraint search [15].
CONCLUSIONS
This paper proposes a SCED algorithm for preventive scheduling
used in scenario planning. The optimization is carried out
using the SHSD interior point method. As compared to the PCIP
algorithm, the SHSD algorithm was shown to have better computational
performance as well as superior computational properties:
i) it can always successfully start from a simple point and
ii) it can reliably detect solution infeasibility and unboundedness.