Optimization of stochastic lossy transport networks and applications to power grids

TL;DR

This paper models stochastic power transport networks to analyze how controllable resources can reduce power losses, revealing the interplay between flexibility, load uncertainty, and network design.

Contribution

It introduces a mathematical model for stochastic transport networks with controllable resources, providing explicit insights into their performance trade-offs.

Findings

Explicit relationships between control flexibility and power loss reduction

Interaction effects of load uncertainty and network structure

Guidelines for optimizing controllable resources in power grids

Abstract

Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of controllable resources in a lossy transport network and the performance gain they yield in terms of expected power losses. Our results are explicit and reveal the interaction between the level of flexibility, the intrinsic load uncertainty and the network structure.