14-11-2012, 03:08 PM
Optimal Power Flow
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An Optimal Power Flow (OPF) function schedules the power system controls to optimize an objective
function while satisfying a set of nonlinear equality and inequality constraints. The equality constraints
are the conventional power flow equations; the inequality constraints are the limits on the control and
operating variables of the system. Mathematically, the OPF can be formulated as a constrained nonlinear
optimization problem. This section reviews features of the problem and some of its variants as well as
requirements for online implementation.
Optimal scheduling of the operations of electric power systems is a major activity, which turns out to
be a large-scale problem when the constraints of the electric network are taken into account. This
document deals with recent developments in the area emphasizing optimal power flow formulation and
deals with conventional optimal power flow (OPF), accounting for the dependence of the power
demand on voltages in the system, and requirements for online implementation.
The OPF problem was defined in the early 1960s (Burchett et al., Feb. 1982) as an extension of
conventional economic dispatch to determine the optimal settings for control variables in a power
network respecting various constraints. OPF is a static constrained nonlinear optimization problem,
whose development has closely followed advances in numerical optimization techniques and computer
technology. It has since been generalized to include many other problems. Optimization of the electric
system with losses represented by the power flow equations was introduced in the 1960s (Carpentier,
1962; Dommel and Tinney, Oct. 1968). Since then, significant effort has been spent on achieving faster
and robust solution methods that are suited for online implementation, operating practice, and security
requirements.
Conventional Optimal Economic Scheduling
Conventional optimal economic scheduling minimizes the total fuel cost of thermal generation, which
may be approximated by a variety of expressions such as linear or quadratic functions of the active
power generation of the unit. The total active power generation in the system must equal the load plus
the active transmission losses, which can be expressed by the celebrated Kron’s loss formula. Reserve
constraints may be modeled depending on system requirements. Area and system spinning, supplemental,
emergency, or other types of reserve requirements involve functional inequality constraints. The
forms of the functions used depend on the type of reserve modeled. A linear form is evidently most
attractive from a solution method point of view. However, for thermal units, the spinning reserve model
is nonlinear due to the limit on a unit’s maximum reserve contribution. Additional constraints may be
modeled, such as area interchange constraints used to model network transmission capacity limitations.
This is usually represented as a constraint on the net interchange of each area with the rest of the system
(i.e., in terms of limits on the difference between area total generation and load).