# Continuous Time Multi-stage Stochastic Reserve and Unit Commitment

## TL;DR

This paper presents a continuous time multi-stage stochastic optimization model for scheduling power units, improving accuracy in ramping constraints and enhancing system reliability in electricity markets.

## Contribution

It introduces a novel continuous time variational approach for unit commitment and reserve scheduling, capturing ramping events more accurately than traditional methods.

## Key findings

- Improved system reliability due to better ramping constraint modeling.
- Lower real-time costs achieved through more accurate scheduling.
- Enhanced scheduling precision in day-ahead electricity markets.

## Abstract

In this paper we introduce a continuous time multi stage stochastic optimization for scheduling generating units, their commitment, reserve capacities and their continuous time generation profiles in the day-ahead wholesale electricity market. Our formulation approximates the solution of a variational problem, in which the balance, generation capacity and ramping constraints are in continuous time. Due to the greater accuracy of our representation of ramping events this approach improves the system reliability and lowers the real-time cost.