An optimal power flow formulation including detailed modeling of generators

Abstract

This paper presents an optimal power flow (OPF) formulation including a detailed representation of synchronous machines and their control systems. The representation is accomplished by the inclusion of the algebrized differential equations representing the generators and their controllers, at an equilibrium point, to the set of algebraic load flow equations of the conventional OPF. The computational framework is structured with advanced concepts of object oriented modeling (OOM) using the C++ language. Automatic differentiation techniques are applied allowing users to define objective functions and operational constraints. An interior point method is used to obtain numerical solutions of the associated optimization problem. Numerical results are presented for a 45bus Southern Brazilian equivalent test system.

Capability Curve Modeling for Hydro-Power Generators in Optimal Power Flow Problems

“…The values of δ computed by Equation (5), which hereinafter will be denoted by δ st , together with the values of the internal and terminal voltage magnitudes, define the values of the active and reactive powers corresponding to the steady-state stability limit, i.e.,…”

“…In the technical literature, there are a few studies that incorporate the capability curve of generators in the formulation of the OPF, e.g., [5][6][7][8]. In these references, the representation of the capability curve is approximate in the sense that it does not include the limitations imposed by stability criteria.…”

Effect of Reactive Power Limit Modeling on Maximum System Loading and Active and Reactive Power Markets

“…to 1.5 p.u., in the generator's own base. Hence, it is assumed here that , which allows to readily obtain the required values of as follows: (12) where the subscripts refers to the system base values, and stands for the generator's base voltage, which is typically the same as . The maximum stator current of a generator is obtained by dividing its rated apparent power value by its rated terminal voltage [27], [28].…”

“…A variety of OPF models are widely used to dispatch generators and obtain pricing signals in electrical energy mar-0885-8950/$26.00 © 2010 IEEE kets [9]- [12]. More sophisticated market OPF models have been also proposed, where, for example, voltage stability and market clearance problems are jointly considered in the OPF formulation [6], [13], [14].…”