# Iterative bidding in electricity markets: rationality and robustness

## TL;DR

This paper introduces a decentralized iterative bidding algorithm for electricity markets that guarantees convergence to an efficient equilibrium, demonstrating robustness against perturbations and collusion, thus ensuring reliable market operation.

## Contribution

It proposes the BID ADJUSTMENT ALGORITHM, a provably correct, linear-converging, decentralized scheme for strategic bidding in electricity markets, with robustness to perturbations and collusion.

## Key findings

- Algorithm converges linearly to the efficient Nash equilibrium.
- The scheme is robust to affine bid perturbations.
- No incentive for deviation or collusion among generators.

## 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.