### Jorge Cortés

#### Professor

Iterative bidding in electricity markets: rationality and robustness

A. Cherukuri, J. Cortés

IEEE Transactions on Network Science and Engineering 7 (3) (2020), 1265-1281

### 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 in the
network. The ISO by itself cannot solve the DC-OPF
problem as 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. Regarding
convergence, we show that 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. Regarding robustness, we show that the
algorithm is robust to affine perturbations in the bid
adjustment scheme and that there is no incentive for any
individual generator to deviate from the algorithm by
using an alternative bid update scheme. We also
establish the algorithm robustness to collusion, i.e.,
we show that, as long as each bus with generation has a
generator following the strategy, there is no incentive
for any group of generators to share information with
the intent of tricking the system to obtain a higher
payoff. Simulations illustrate our results.

pdf

Mechanical and Aerospace Engineering,
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