### Jorge Cortés

#### Professor

Decentralized Nash equilibrium seeking by strategic generators
for DC optimal power flow

A. Cherukuri,
J. Cortés

Annual
Conference on Information Systems and Sciences, Baltimore, Maryland, USA,
2017, electronic proceedings

### Abstract

This paper studies an electricity market consisting of
an independent system operator (ISO) and a group of generators. The
goal is to solve the DC optimal power flow (DC-OPF) problem: have
the generators collectively meet the power demand while minimizing
the aggregate generation cost and respecting line flow limits. The
ISO by itself cannot solve the DC-OPF problem as the generators are
strategic and do not share their cost functions. Instead, each
generator submits to the ISO a bid, consisting of the price per unit
of electricity at which it is willing to provide power. Based on
the bids, the ISO decides how much production to allocate to each
generator to minimize the total payment while meeting the load and
satisfying the line limits. We provide a provably correct,
decentralized iterative scheme, termed BID ADJUSTMENT ALGORITHM for
the resulting Bertrand competition game. The algorithm takes the
generators' bids to any desired neighborhood of the efficient Nash
equilibrium at a linear convergence rate. As a consequence, the
optimal production of the generators converges to the optimizer of
the DC-OPF problem. Our algorithm can be understood as "learning
via repeated play", where generators are "myopically selfish",
changing their bid at each iteration with the sole aim of maximizing
their payoff.

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Mechanical and Aerospace Engineering,
University of California, San Diego

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Ph: 1-858-822-7930

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