Multiobjective Model Predictive Control for Residential Demand Response Management Under Uncertainty

TL;DR

The paper tackles residential demand response under uncertainty by introducing a multiobjective model predictive control (MOMPC) framework that minimizes both energy cost $F_{cost}$ and user dissatisfaction $F_{dissat}$. It leverages Laguerre function parameterization to reduce decision variables and transform the problem into linear inequalities, enabling efficient feasible search, and uses a convex-sampler enabled MOEA to handle constraints. Numerical analysis with real-world data demonstrates that the proposed method yields well-distributed Pareto fronts and outperforms existing MOMPC approaches, including in scenarios with forecast errors where the cost increase is only 0.52% versus at least 2.3% for competitors. The approach thus provides a robust, scalable tool for home energy management systems to balance cost savings and user comfort under uncertainty, by integrating energy storage, renewables, and appliance flexibility within a receding-horizon framework.

Abstract

Residential users in demand response programs must balance electricity costs and user dissatisfaction under real-time pricing. This study proposes a multiobjective model predictive control approach for home energy management systems with battery storage, aiming to minimize both objectives while mitigating uncertainties. Laguerre functions parameterize control signals, transforming the optimization problem into one with linear inequalities for efficient exploration. A constrained multiobjective evolutionary algorithm, incorporating convex sampler-based crossover and mutation, is developed to ensure feasible solutions. Simulations show that the proposed method outperforms existing approaches, limiting cost increases to 0.52\% under uncertainties, compared to at least 2.3\% with other methods.

Figures (5)

• Figure 1: The bound of three different forecasting error in the current time slot.
• Figure 2: Predicted and true values for (a) renewable power, (b) electricity price, and (c) power loads.
• Figure 3: Pareto fronts obtained by different methods for the minimization of energy costs (x-axis) and user dissatisfaction (y-axis). The proposed method (black circles) employs a model predictive control framework to mitigate uncertainty, resulting in superior tradeoff performance compared to other methods, including PDOR (red squares), NSGA-II with penalty (green diamonds), constrained NSGA-II (blue triangles), and MOIA (magenta inverted triangles).
• Figure 4: Normalized Manhattan distance of Pareto fronts to the ideal vector over function evaluations for various demand response management methods, illustrating the convergence behavior of each method.
• Figure 5: Power control by the proposed method for residential demand response management. The figure shows power values (left y-axis) and electricity market prices (right y-axis) over time, illustrating how the proposed method minimizes energy costs while maintaining user satisfaction. Negative total power consumption indicates excessive power sold back to the power grid with a feed-in tariff.