# Day-Ahead Energy Market as Adjustable Robust Optimization: Spatio-Temporal Pricing of Dispatchable Generators, Storage Batteries, and Uncertain Renewable Resources

## TL;DR

This paper models day-ahead energy markets using adjustable robust convex programming, incorporating renewable uncertainty and dispatchable resources, to analyze market behavior and optimal resource management.

## Contribution

It introduces a novel market model with a multi-variable prosumption cost function based on a parameterized max-min program, enabling unified evaluation of dispatchability and renewable uncertainty.

## Key findings

- Renewable generators do not always have priority over conventional generators due to uncertainty.
- Market merit order can reverse depending on renewable penetration levels.
- Optimal battery penetration maximizes individual profits in long-term market evolution.

## Abstract

We present modeling and analysis of day-ahead spatio-temporal energy markets in which each competitive aggregator aims at making the highest profit by managing a complex mixture of different energy resources, such as conventional generators, storage batteries, and uncertain renewable resources. First, we develop an energy market model in terms of an adjustable robust convex program. This market modeling is novel in the sense that the prosumption cost function of each aggregator, which evaluates the cost to realize an amount of spatio-temporal energy prosumption, is a multi-variable function resulting from a "parameterized" max-min program, in which the variable of the prosumption cost function is involved as a continuous parameter and the variable of dispatchable resources is involved as an adjustable variable for energy balance. This formulation enables to reasonably evaluate a reward for intertemporal dispatchability enhancement and a penalty for renewable energy uncertainty in a unified way. In addition, it enables to enforce a market regulation in which every aggregator is responsible for absorbing his renewable energy uncertainty by managing his own dispatchable energy resources. Second, in view of social economy as well as personal economy, we conduct a numerical analysis on the premise of several photovoltaic penetration levels. In this numerical analysis, we demonstrate that renewable generators do not always have priority of energy supply higher than conventional generators due to their uncertainty and limited dispatchability, meaning that the merit order of conventional and renewable generators can reverse. Furthermore, we analyze long-term evolution of competitive energy markets demonstrating that there can be found a social equilibrium of battery penetration levels, at which maximum personal profit with respect to battery system enhancement is attained.