### Jorge Cortés

#### Professor

Distributed coordination of power generators for a linearized
optimal power flow problem

A. Cherukuri, A. D. Domínguez-García,
J. Cortés

Proceedings of the American Control Conference, Seattle, Washington, USA, 2017, pp. 3962-3967

### Abstract

This paper considers the problem of optimally dispatching a set of
generators in a power system; these generators are interconnected to
some loads via a network of buses. We consider scenarios when the
power network is operating at steady state, and a small change in
the load occurs at some of the load buses. Upon occurrence of this
event, the network seeks to find the change in generator injections
and voltage phase angles that makes the new steady state meet the
modified load with minimum total generation cost (corresponding to
the summation of the individual convex cost functions of the
generating units). The resulting optimization problem is nonconvex
due to the nonconvex power balance constraints at the buses. We
consider a convex approximation of the problem where the power
balance constraints are linearized around the initial steady-state
operating point. Assuming that each bus can communicate with buses
connected to it in the physical power network, we provide two
provably correct continuous-time distributed strategies that allow
the generators to find the optimal power set points. Both designs
build on the saddle-point dynamics of the Lagrangian of the
optimization problem. Various simulations illustrate our results.

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