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Modelling Irrational Behaviour of Residential End Users using Non-Stationary Gaussian Processes

Nam Trong Dinh, Sahand Karimi-Arpanahi, Rui Yuan, S. Ali Pourmousavi, Mingyu Guo, Jon A. R. Liisberg, Julian Lemos-Vinasco

TL;DR

The authors' simulations using real-world data show that the proposed DR model provides a more realistic estimate of price-responsive behaviour considering irrationality, and a chance-constrained optimisation model for CBS operation that deals with the unpredictability of the end-user irrationality.

Abstract

Demand response (DR) plays a critical role in ensuring efficient electricity consumption and optimal use of network assets. Yet, existing DR models often overlook a crucial element, the irrational behaviour of electricity end users. In this work, we propose a price-responsive model that incorporates key aspects of end-user irrationality, specifically loss aversion, time inconsistency, and bounded rationality. To this end, we first develop a framework that uses Multiple Seasonal-Trend decomposition using Loess (MSTL) and non-stationary Gaussian processes to model the randomness in the electricity consumption by residential consumers. The impact of this model is then evaluated through a community battery storage (CBS) business model. Additionally, we apply a chance-constrained optimisation model for CBS operation that deals with the unpredictability of the end-user irrationality. Our simulations using real-world data show that the proposed DR model provides a more realistic estimate of end-user price-responsive behaviour when considering irrationality. Compared to a deterministic model that cannot fully take into account the irrational behaviour of end users, the chance-constrained CBS operation model yields an additional 19% revenue. Lastly, the business model reduces the electricity costs of solar end users by 11%.

Modelling Irrational Behaviour of Residential End Users using Non-Stationary Gaussian Processes

TL;DR

The authors' simulations using real-world data show that the proposed DR model provides a more realistic estimate of price-responsive behaviour considering irrationality, and a chance-constrained optimisation model for CBS operation that deals with the unpredictability of the end-user irrationality.

Abstract

Demand response (DR) plays a critical role in ensuring efficient electricity consumption and optimal use of network assets. Yet, existing DR models often overlook a crucial element, the irrational behaviour of electricity end users. In this work, we propose a price-responsive model that incorporates key aspects of end-user irrationality, specifically loss aversion, time inconsistency, and bounded rationality. To this end, we first develop a framework that uses Multiple Seasonal-Trend decomposition using Loess (MSTL) and non-stationary Gaussian processes to model the randomness in the electricity consumption by residential consumers. The impact of this model is then evaluated through a community battery storage (CBS) business model. Additionally, we apply a chance-constrained optimisation model for CBS operation that deals with the unpredictability of the end-user irrationality. Our simulations using real-world data show that the proposed DR model provides a more realistic estimate of end-user price-responsive behaviour when considering irrationality. Compared to a deterministic model that cannot fully take into account the irrational behaviour of end users, the chance-constrained CBS operation model yields an additional 19% revenue. Lastly, the business model reduces the electricity costs of solar end users by 11%.
Paper Structure (28 sections, 1 theorem, 34 equations, 10 figures, 4 tables)

This paper contains 28 sections, 1 theorem, 34 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related works
  4. Objectives and contributions
  5. Local energy community with CBS
  6. Problem formulation for local end users
  7. Utility model of local end users with loss aversion
  8. Time inconsistency
  9. Consumption randomness as bounded rationality
  10. MSTL decomposition on consumption data
  11. Normality check of the randomness component
  12. Autocorrelation of the randomness component
  13. Non-stationary Gaussian processes
  14. Problem formulation for the CBS operator
  15. Considering loss aversion and time inconsistency via a deterministic model
  16. ...and 13 more sections

Key Result

Theorem 1

Let $\mathbf{\Lambda}$ be a square diagonal matrix and $\mathbf{K}$ be a positive semi-definite matrix, then $\mathbf{\Lambda}^\top \mathbf{K} \mathbf{\Lambda}$ is symmetric and positive semi-definite.

Figures (10)

  • Figure 1: Local energy community structure with RHO setting
  • Figure 2: A flowchart summarising end-user consumption randomness modelling
  • Figure 3: Comparison of local consumption of a winter weekday. The top figure depicts consumption considering only loss aversion (LA), while the bottom figure includes both loss aversion and time inconsistency properties (LA+TI)
  • Figure 4: The ACF plot of an end user's randomness time series
  • Figure 5: Randomness covariance matrix of an end user generated from the proposed non-stationary kernel
  • ...and 5 more figures

Theorems & Definitions (1)

  • Theorem 1