Some deficiencies in optimal power flow

Curtailed number and reduced controller movement optimization algorithms for real time voltage/reactive power control

“…Without loss of generality, we assume that the vector bk can be partitioned into two sub-vectors b: and bt corresponding to the constraint sets 7 1~ and /I respectively. Linearizing (1) at the E-th iteration, we have…”

Introduction to Electric Power Systems

“…The development of the OPF algorithm by Newton ' s method [55,57,58] , is based on the success of the Newton ' s method for the power fl ow calculations. Sparse matrix techniques applied to the Newton power fl ow calculations are directly applicable to the Newton OPF calculations.…”

A new heuristic approach to deal with discrete variables in optimal power flow computations

“…In this approach at each iteration only a subset of discrete variables which are sufficiently close to a discrete value are rounded-off, the remaining variables (treated as continuous) being then reoptimized. It is largely agreed that the round-off technique is generally suitable for discrete variables with small steps (e.g., load tap changer (LTC) transformer ratio and phase shifter angle) but requires some caution for discrete variables with larger steps (e.g., shunt compensation banks, network switching) [12], [14], [16]. However, the round-off approaches act "blindly" since they do not look at the discretization effect on either the objective or the inequality constraints, suffering in consequence from two drawbacks: (i) the solution feasibility is not guaranteed while no method to restore feasibility is proposed, and (ii) the objective value may be unacceptably deteriorated.…”

“…The simplest approach for handling discrete variables is based on the rounding-off strategy [12]. In this technique, the OPF relaxation is first solved by treating all variables as continuous.…”

“…Meanwhile a large spectrum of approaches have been proposed to deal with discrete variables, e.g. simple heuristics [12], [15], penalty functions within NLP of LP solvers [16]- [18], ordinal optimization [19], recursive mixed-integer linear programming [20], interior point cutting plane [21], global optimization methods [22]- [25], etc.…”