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Energy Management for Prepaid Customers: A Linear Optimization Approach

Maitreyee Marathe, Line A. Roald

TL;DR

This paper addresses energy management for prepaid electricity customers who risk disconnection when wallet balance runs low. It introduces a linear threshold-based approach, the Average Forecast Greedy (AFG) model, which uses only daily average load demands and can be solved by a greedy algorithm, avoiding heavy MILP solvers. Through comparisons with two MILP benchmarks (DFM and OBM) on real load data, AFG achieves similar or better performance with substantially reduced forecast granularity and communication requirements, enabling practical, privacy-friendly, local hardware implementations. The work demonstrates the method’s robustness across perfect, limited, and imperfect forecast scenarios and highlights its potential for real-world deployment in prepaid energy systems.

Abstract

With increasing energy prices, low income households are known to forego or minimize the use of electricity to save on energy costs. If a household is on a prepaid electricity program, it can be automatically and immediately disconnected from service if there is no balance in its prepaid account. Such households need to actively ration the amount of energy they use by deciding which appliances to use and for how long. We present a tool that helps households extend the availability of their critical appliances by limiting the use of discretionary ones, and prevent disconnections. The proposed method is based on a linear optimization problem that only uses average power demand as an input and can be solved to optimality using a simple greedy approach. We compare the model with two mixed-integer linear programming models that require more detailed demand forecasts and optimization solvers for implementation. In a numerical case study based on real household data, we assess the performance of the different models under different accuracy and granularity of demand forecasts. Our results show that our proposed linear model is much simpler to implement, while providing similar performance under realistic circumstances.

Energy Management for Prepaid Customers: A Linear Optimization Approach

TL;DR

This paper addresses energy management for prepaid electricity customers who risk disconnection when wallet balance runs low. It introduces a linear threshold-based approach, the Average Forecast Greedy (AFG) model, which uses only daily average load demands and can be solved by a greedy algorithm, avoiding heavy MILP solvers. Through comparisons with two MILP benchmarks (DFM and OBM) on real load data, AFG achieves similar or better performance with substantially reduced forecast granularity and communication requirements, enabling practical, privacy-friendly, local hardware implementations. The work demonstrates the method’s robustness across perfect, limited, and imperfect forecast scenarios and highlights its potential for real-world deployment in prepaid energy systems.

Abstract

With increasing energy prices, low income households are known to forego or minimize the use of electricity to save on energy costs. If a household is on a prepaid electricity program, it can be automatically and immediately disconnected from service if there is no balance in its prepaid account. Such households need to actively ration the amount of energy they use by deciding which appliances to use and for how long. We present a tool that helps households extend the availability of their critical appliances by limiting the use of discretionary ones, and prevent disconnections. The proposed method is based on a linear optimization problem that only uses average power demand as an input and can be solved to optimality using a simple greedy approach. We compare the model with two mixed-integer linear programming models that require more detailed demand forecasts and optimization solvers for implementation. In a numerical case study based on real household data, we assess the performance of the different models under different accuracy and granularity of demand forecasts. Our results show that our proposed linear model is much simpler to implement, while providing similar performance under realistic circumstances.
Paper Structure (26 sections, 6 equations, 4 figures, 4 tables, 2 algorithms)

This paper contains 26 sections, 6 equations, 4 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Threshold-based energy management
  3. Contributions
  4. Paper organization
  5. Model Formulations
  6. Detailed Forecast MILP (DFM) model
  7. Modeling considerations
  8. Mathematical formulation
  9. Average Forecast Greedy (AFG) model
  10. Solving the AFG model
  11. Computing virtual wallet recharge
  12. Computing thresholds
  13. Optimal Benchmark MILP (OBM) model
  14. Qualitative Comparison - Computation, Communication, and Information Requirements
  15. Computational requirements
  16. ...and 11 more sections

Figures (4)

  • Figure 1: Illustration of threshold-based energy management with wallet balance and load thresholds (top figure) and load demand (bottom figure). Load demand is served when the wallet balance is greater than the corresponding threshold. Note that load 1 is served only partially, while load 2 is served fully.
  • Figure 2: Illustration of virtual wallet recharge
  • Figure 3: Perfect forecast: Percentage point (%pt.) improvement in priority service factor (PSF) over baseline for the proposed AFG model (blue) and the benchmark models DFM (red) and OBM (green)
  • Figure 4: Imperfect forecast: Priority service factor (PSF) and customer disconnections (indicated by 'x' mark) for the proposed model AFG (blue), the benchmark models DFM (red), OBM (green), and the baseline BSL model (purple)