Developments in Optimal Power Flow

The Minimum Cost Optimal Power Flow Problem Solved via the Restart Homotopy Continuation Method

“…Hence one can make the re-asonable assumption that" such an occurrence is generally rare. This is further justified by the fact that, results of commerc~al algorithms report.ed by Burchett et al, [1982a, b, 19841, EI-Kady et al, [1986 do not concern themselves with line-flow limit violations. Thé following sections will present these heuristics, after the basic ideas underlying the rules are presented.…”

Fuel-cost minimisation for both real-and reactive-power dispatches

“…To handle the large-scale problems of this nature, the idea of P-Q decomposition was applied to the optimal power flow [5][6][7], where the problem is decomposed into the real-power optimisation problem (P-problem) and the reactive-power optimisation problem (Q-problem). The Pproblem is to minimise the production cost under the assumption that system voltages are held constant, and the Q-problem is to minimise the transmission loss under the assumption that real-power generation is held constant.…”

“…A typical approach is to augment the constraints into an objective function by using the Lagrange multipliers [11] and/or penalty functions, and to minimise the augmented objective function by using one of the optimisation schemes, such as the steepest descent algorithm Paper 3096C (P9), first received 20th July and in revised form 14th December 1983 The authors are with the Department of Electrical Engineering, Cullen College of Engineering, University of Houston, Central Campus, Houston, Texas 77004, USA [1,7], or the sequential unconstrained minimisation technique (SUMT) [6]. Other approaches are the use of linearprogramming approximation to the nonlinear problem [8,10], or the use of the quadratic approximation to the objective function in order to apply the quadraticprogramming technique [12].…”

“…(a) Unlike the usual approach of minimising the transmission loss [6,7,10,14], the total production cost (or fuel cost) is the objective function to be minimised by both Pand Q-optimisation modules. This approach unifies two decoupled optimisation problems into one reference framework and avoids the switching of objective functions from one to another.…”

“…This method avoids the use of penalty functions and/or calculation of Lagrange multipliers [1,6,7]; additionally, the step length is calculated without the need of a linear-search algorithm as in other methods.…”