20
Optimal Power Flow
Mohamed E. ElHawary
Dalhousie University
20.1
Conventional Optimal Economic Scheduling
..............
20
2
20.2
Conventional OPF Formulation
....................................
20
3
Application of Optimization Methods to OPF
20.3
OPF Incorporating Load Models
...................................
20
7
Load Modeling
.
Static Load Models
.
Conventional OPF
Studies Including Load Models
.
Security Constrained OPF
Including Load Models
.
Inaccuracies of Standard
OPF Solutions
20.4
SCOPF Including Load Modeling
.................................
20
9
Influence of Fixed Tap Transformer Fed Loads
20.5
Operational Requirements for Online
Implementation
.............................................................
20
10
Speed Requirements
.
Robustness of OPF Solutions with
Respect to Initial Guess Point
.
Discrete Modeling
.
Detecting
and Handling Infeasibility
.
Consistency of OPF Solutions
with Other Online Functions
.
Ineffective ‘‘Optimal’’
Rescheduling
.
OPFBased Transmission Service Pricing
20.6
Conclusions
....................................................................
20
14
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 largescale 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.
OPF seeks to optimize a certain objective, subject to the network power flow constraints and
system and equipment operating limits. Today, any problem that involves the determination of the
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2006 by Taylor & Francis Group, LLC.
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instantaneous ‘‘optimal’’ steady state of an electric power system is referred to as an Optimal Power Flow
problem. The optimal steady state is attained by adjusting the available controls to minimize an objective
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 Spring '10
 DR
 Optimization, The Land, ........., optimal power flow, OPF

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