[Paper Review] A Unified Residential Energy Cost Optimization Model for Smart Grid - Significance and Challenge

Muhammad Raisul Alam, Marc St‐Hilaire+1 more|arXiv (Cornell University)|May 4, 2015

Smart Grid Energy Management25 references3 citations

TL;DR

This paper proposes a unified non-convex Mixed Integer Nonlinear Programming (MINLP) model for residential energy cost optimization in smart grids, integrating diverse energy sources, storage, loads, and user preferences. It ensures Pareto optimality in microgrid energy trading and demonstrates that solution time grows exponentially with problem size, highlighting the need for heuristic trade-offs in real-time applications.

ABSTRACT

This article addresses the residential energy cost optimization problem in smart grid. To date, most of the previous research only consider a partial aspect of the cost optimization problem. As a result, they fail to analyze scenarios when the interconnected components along with their properties have to be considered simultaneously. The proposed model combines these partial models into a single unified cost optimization model. Therefore, it is able to analyze scenarios which are closer to practical implementation. Furthermore, it is useful to analyze the behavior of a population (e.g., smart buildings, smart cities, etc.) and properties of the components for specific scenarios (e.g., the impact of aggregate storage capacity, etc.). It allows energy trading in microgrid which introduces a cost fairness problem. It ensures Pareto optimality among the households which guarantees that no household will be worse off to improve the cost of others. Results show that it can maintain the user preferences and can react to a demand response program by rescheduling the household loads and sources. Finally, the paper addresses the challenge of the computational complexity of the proposed model, showing that solution time increases exponentially with the problem size and proposes possible approaches to solve this.

Motivation & Objective

• To address the gap in existing research that treats energy cost optimization in isolation, without considering the interplay of multiple components such as storage, renewables, and user preferences.
• To develop a unified optimization model that integrates partial models from prior work into a single framework capable of analyzing realistic, interconnected smart grid scenarios.
• To ensure cost fairness among households in microgrids by enforcing Pareto optimality, preventing any household from being worse off to benefit others.
• To analyze the impact of system-wide properties such as aggregate storage capacity and renewable generation on overall cost and individual household behavior.
• To investigate the computational complexity of the proposed model and identify practical approaches for real-time deployment despite exponential growth in solution time.

Proposed method

• Formulates a non-convex MINLP model that unifies energy sources (grid, renewables, storage), load types (shiftable, non-shiftable), and user preferences into a single optimization framework.
• Incorporates constraints for energy balance, storage dynamics (charging/discharging efficiency, self-discharge), and appliance operation windows to reflect real-world device behavior.
• Introduces multi-objective optimization to minimize individual household energy costs while ensuring Pareto optimality, avoiding unfair cost distribution in microgrid trading.
• Uses a transformation from MILP to MINLP to model nonlinear relationships in energy trading and storage, enabling more accurate representation of real microgrid operations.
• Employs numerical simulations with varying numbers of appliances, timeslots, and households to evaluate solution time and complexity, using the NEOS server with an 8-hour time limit.
• Analyzes time complexity by measuring median solution time across 29 random instances for different problem sizes, revealing exponential growth patterns.

Experimental results

Research questions

• RQ1 How can a unified optimization model integrate diverse components—such as renewable sources, storage, and user preferences—into a single framework for residential energy cost minimization?
• RQ2 What is the impact of energy trading in a microgrid on cost fairness among households, and how can Pareto optimality be enforced to ensure no household is worse off?
• RQ3 How does the computational complexity of the proposed MINLP model scale with increasing problem size in terms of appliances, timeslots, and households?
• RQ4 Can the model effectively reschedule household loads and energy sources in response to dynamic price signals and demand response programs while preserving user preferences?
• RQ5 What are the practical implications of exponential solution time growth for real-time deployment in smart grids, and what alternative approaches might mitigate this challenge?

Key findings

• The proposed unified MINLP model successfully integrates multiple components—grid, renewables, storage, and user preferences—into a single optimization framework, enabling analysis of complex, interconnected scenarios.
• The model ensures Pareto optimality in microgrid energy trading, guaranteeing that no household is made worse off to improve another’s cost, thus enhancing fairness and adoption potential.
• Solution time increases exponentially with the number of appliances, timeslots, and households, as demonstrated by simulations showing median solution times growing rapidly even for small problem instances.
• For the minimum configuration (2 households, 3 timeslots, 2 appliances), median solution time exceeds 8 hours for larger problem instances, indicating the model is NP-hard and impractical for exact solutions at scale.
• Despite exponential complexity, the model remains useful for analyzing system-level behavior in smart buildings, cities, and communities, including the impact of EVs and renewable energy integration.
• The model can be applied to predict user behavior and support cost-benefit analysis for net-zero energy communities, providing value to policymakers and utilities.