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Model Predictive Building Climate Control for Mitigating Heat Pump Noise Pollution (Extended Version)

Yun Li, Jicheng Shi, Colin N. Jones, Neil Yorke-Smith, Tamas Keviczky

TL;DR

The paper addresses heat pump noise pollution, a barrier to widespread HP adoption in dense environments, by extending model predictive control (MPC) for building climate management to explicitly mitigate acoustic nuisance. It introduces a MILP-friendly framework that uses a piecewise affine approximation of the HP noise pattern $L^{hp}=f(P)$ and relies on a linearized indoor-thermal model to predict outcomes under different control inputs. Two noise-cost designs are proposed: Option 1 uses $J_n=\sum_t \frac{L^{hp}_t}{L^{amb}_t}$ and Option 2 imposes $L^{hp}_t \le L^{amb}_t + \delta_t$ (equivalently $J_n=\sum_t (L^{hp}_t-L^{amb}_t)^+$), both enabling tractable optimization. Numerical experiments with a high-fidelity building simulator demonstrate that HP noise can be significantly reduced with only a small increase in energy cost, validating the approach and its potential for real-world deployment.

Abstract

Noise pollution from heat pumps (HPs) has been an emerging concern to their broader adoption, especially in densely populated areas. This paper explores a model predictive control (MPC) approach for building climate control, aimed at minimizing the noise nuisance generated by HPs. By exploiting a piecewise linear approximation of HP noise patterns and assuming linear building thermal dynamics, the proposed design can be generalized to handle various HP acoustic patterns with mixed-integer linear programming (MILP). Additionally, two computationally efficient options for defining the noise cost function in the proposed MPC design are discussed. Numerical experiments on a high-fidelity building simulator are performed to demonstrate the viability and effectiveness of the proposed design. Simulation results show that the proposed approach can effectively reduce the noise pollution caused by HPs with negligible energy cost increase.

Model Predictive Building Climate Control for Mitigating Heat Pump Noise Pollution (Extended Version)

TL;DR

The paper addresses heat pump noise pollution, a barrier to widespread HP adoption in dense environments, by extending model predictive control (MPC) for building climate management to explicitly mitigate acoustic nuisance. It introduces a MILP-friendly framework that uses a piecewise affine approximation of the HP noise pattern and relies on a linearized indoor-thermal model to predict outcomes under different control inputs. Two noise-cost designs are proposed: Option 1 uses and Option 2 imposes (equivalently ), both enabling tractable optimization. Numerical experiments with a high-fidelity building simulator demonstrate that HP noise can be significantly reduced with only a small increase in energy cost, validating the approach and its potential for real-world deployment.

Abstract

Noise pollution from heat pumps (HPs) has been an emerging concern to their broader adoption, especially in densely populated areas. This paper explores a model predictive control (MPC) approach for building climate control, aimed at minimizing the noise nuisance generated by HPs. By exploiting a piecewise linear approximation of HP noise patterns and assuming linear building thermal dynamics, the proposed design can be generalized to handle various HP acoustic patterns with mixed-integer linear programming (MILP). Additionally, two computationally efficient options for defining the noise cost function in the proposed MPC design are discussed. Numerical experiments on a high-fidelity building simulator are performed to demonstrate the viability and effectiveness of the proposed design. Simulation results show that the proposed approach can effectively reduce the noise pollution caused by HPs with negligible energy cost increase.

Paper Structure

This paper contains 13 sections, 12 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Building Thermal Dynamics
  4. Heat Pump and Ambient Noises
  5. Control Design Objective
  6. Model Predictive Control Design
  7. MPC Formulation
  8. Piecewise Affine Approximation of HP Noise Pattern
  9. Noise Cost Function Design
  10. Option 1
  11. Option 2
  12. Simmulation Results
  13. Conclusions

Figures (6)

  • Figure 1: Nonlinear heat pump noise pattern and its piecewise affine approximation.
  • Figure 2: Simulation diagram.
  • Figure 3: Open-loop prediction performance of ARX model: (a) training set (MAE = 0.16$^\circ$C), (b) test set (MAE = 0.14$^\circ$C).
  • Figure 4: Ambient noise profile used in simulation.
  • Figure 5: Simulation results for noise cost in \ref{['eq:inverse_penalty']}: (a) Pareto curves of energy cost and noise cost, (b) $L_{\text{den}}$, (c) $L_{\text{quiet}}$ and domination time.
  • ...and 1 more figures