[Paper Review] A Dynamical Systems Approach to Energy Disaggregation

Roy Dong, Lillian J. Ratliff+2 more|arXiv (Cornell University)|Apr 2, 2013

Smart Grid Energy Management17 references3 citations

TL;DR

This paper proposes a dynamical systems framework for energy disaggregation that models each appliance as a single-input, single-output system, estimating device-level power consumption from aggregate measurements using optimal control and system identification. The method achieves accurate disaggregation on simulated and real experimental data, with minor errors corrected via physical priors like maximum power limits.

ABSTRACT

Energy disaggregation, also known as non-intrusive load monitoring (NILM), is the task of separating aggregate energy data for a whole building into the energy data for individual appliances. Studies have shown that simply providing disaggregated data to the consumer improves energy consumption behavior. However, placing individual sensors on every device in a home is not presently a practical solution. Disaggregation provides a feasible method for providing energy usage behavior data to the consumer which utilizes currently existing infrastructure. In this paper, we present a novel framework to perform the energy disaggregation task. We model each individual device as a single-input, single-output system, where the output is the power consumed by the device and the input is the device usage. In this framework, the task of disaggregation translates into finding inputs for each device that generates our observed power consumption. We describe an implementation of this framework, and show its results on simulated data as well as data from a small-scale experiment.

Motivation & Objective

• To develop a data-driven, dynamical systems-based framework for non-intrusive load monitoring (NILM) that avoids per-device sensors.
• To improve energy disaggregation accuracy by modeling device power consumption as dynamic systems with identifiable inputs.
• To enable integration with real-time control and demand response systems in smart buildings.
• To reduce reliance on large unsupervised training datasets by leveraging device-specific system models.
• To address limitations of existing unsupervised methods like HMMs and sparse coding in low-data regimes.

Proposed method

• Each appliance is modeled as a single-input, single-output (SISO) dynamical system, with power consumption as output and device usage as input.
• The disaggregation problem is formulated as an optimal control inverse problem: recover the input (device usage) that generates the observed aggregate power signal.
• System identification techniques are used to estimate device dynamics from limited training data, including autoregressive models with exogenous inputs (ARX).
• A change detection algorithm is applied to generate input signals for device activation patterns in the experimental setup.
• Physical priors—such as maximum current draw (e.g., 10 A for monitors)—are used to correct misclassification errors in the estimation.
• The framework is validated on both simulated data and a small-scale experiment with real appliances (microwave, toaster, kettle).

Experimental results

Research questions

• RQ1 Can a dynamical systems framework improve energy disaggregation accuracy compared to unsupervised methods?
• RQ2 How well can device-specific system models be estimated from limited training data?
• RQ3 Can optimal control-based inversion of aggregate signals recover individual device power consumption?
• RQ4 How do physical constraints (e.g., max power) improve disaggregation robustness?
• RQ5 To what extent do device dynamics and transient behaviors (e.g., microwave startup) affect model accuracy?

Key findings

• The method achieved complete recovery of simulated energy disaggregation data, demonstrating theoretical accuracy under ideal conditions.
• On real experimental data, the estimated power signals closely matched ground truth measurements, with only minor deviations.
• The microwave was initially misclassified as a monitor due to similar power dynamics, but correction using a maximum current prior (10 A) restored correct identification.
• The framework outperformed unsupervised methods like HMMs and sparse coding in low-data regimes, as it leverages device-specific dynamics rather than relying on large dictionaries.
• Transitions like the microwave’s two-step power rise were poorly captured by standard over-damped models, indicating a need for hybrid system modeling in future work.
• The method successfully decoupled device dynamics from user behavior, enabling independent learning of device profiles and usage patterns.