A Prudent Framework for Understanding Risk-Awareness in Demand Response

TL;DR

This paper develops a theoretical framework to understand how risk-aware behaviors in demand response are driven by superquadratic cost functions and skewed price uncertainties, highlighting the role of prudent demand in risk aversion.

Contribution

It introduces the concept of prudent demand based on third-order derivatives, linking risk-averse behavior to superquadratic cost functions and skewed price distributions in demand response.

Findings

Future price uncertainty influences immediate consumption decisions.

The response magnitude scales with the skewness of price distribution.

Numerical simulations and a real-world case study validate the theoretical insights.

Abstract

We show that risk-aware behaviors in demand response originate from superquadratic state-dependent cost functions and price uncertainty with skewed distributions. We obtain such results through developing a novel theoretical demand response framework that combines non-anticipatory multi-stage decision-making with superquadratic cost functions. We introduce the concept of prudent demand, defined by a positive third-order derivative of the cost function, which is the first principle for risk-averse behavior despite a risk-neutral objective. Our analysis establishes that future price uncertainty affects immediate consumption decisions, and the extent of this response scales proportionally with the skewness of the price distribution. We visualize our theoretical findings through numerical simulations and illustrate their practical implications using a real-world case study.