Model Predictive Control for Stabilizing District Heating Grids with Renewable Energy Sources

Core Concepts

The core message of this article is to develop a model predictive control (MPC) approach with terminal ingredients to stabilize the temperatures and storage masses in district heating grids (DHGs) that are transitioning to renewable energy sources (RES).

Abstract

The article presents a thermo-hydraulic model of a general DHG that includes multiple producers, consumers, and thermal energy storages (TESs). The model is formulated as an ordinary differential equation-based state-space representation that can be used for MPC design. The key highlights are: The authors derive a sufficient condition for the stabilizability of the DHG model by exploiting its structural properties. This is a crucial requirement for applying MPC with terminal ingredients. The authors calculate suitable terminal ingredients, including a terminal cost and a terminal region, for an exemplary DHG case study. This allows the MPC to guarantee asymptotic stability of the closed-loop system. The case study demonstrates the practicability of the MPC approach with terminal ingredients. It shows that the MPC can effectively stabilize the system states, including the temperatures and storage masses, while satisfying operational constraints. The authors also investigate an extended MPC formulation that incorporates a piece-wise constant stage cost, terminal cost, and terminal region. This allows the MPC to exhibit a predictive behavior and achieve smoother control input trajectories during transitions between different steady-state set points. Overall, the article presents a comprehensive approach to design a stabilizing MPC for RES-based DHGs, which is an important step towards the decarbonization of the heat sector.

Stats

The total masses of the TESs are set to mtes,1 = 50 · 103kg and mtes,2 = 30 · 103kg. The heat loss coefficient is set to (κv)v = (κe)e = 0.2 kJ/(K·s) for v ∈ V, e ∈ E. The density of water, the ambient temperature, the specific heat capacity of water and the pipe friction coefficient are set to ρ = 988.05 kg/m3, Ta = 10.0°C, cp = 4.18 kJ/(kg·K), λ = 0.02, respectively.

Quotes

None.

Key Insights Distilled From

Model Predictive Control of District Heating Grids Using Stabilizing Terminal Ingredients

by Max Rose,Han... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01820.pdf

Deeper Inquiries

How can the MPC approach be extended to handle uncertainties in the heat demand and supply forecasts?

To handle uncertainties in heat demand and supply forecasts within the MPC approach, several strategies can be implemented. One common method is to incorporate scenario-based optimization, where multiple scenarios of possible heat demand and supply variations are considered. By optimizing the control inputs for each scenario and selecting the best course of action based on the predicted outcomes, the MPC controller can adapt to uncertainties effectively. Another approach is to utilize robust optimization techniques, which involve optimizing the control inputs while considering a range of possible variations in the forecasts. This ensures that the controller's performance remains satisfactory even under the worst-case scenarios. Additionally, stochastic MPC can be employed, where probabilistic forecasts of heat demand and supply are used to generate control policies that account for the uncertainty distribution. By integrating these methods, the MPC framework can effectively handle uncertainties in heat demand and supply forecasts.

What are the potential challenges and limitations of applying the proposed MPC approach to large-scale, complex district heating networks?

When applying the proposed MPC approach to large-scale, complex district heating networks, several challenges and limitations may arise. One significant challenge is the computational complexity associated with optimizing control inputs for a vast network with numerous interconnected components. As the size of the network increases, the optimization problem becomes more computationally demanding, requiring efficient algorithms and computational resources. Another challenge is the need for accurate and real-time data acquisition and communication systems to provide the necessary information for the MPC controller to make informed decisions. Additionally, the dynamic nature of district heating networks, with varying heat demand and supply patterns, can pose challenges in developing accurate models and forecasts for the MPC framework. Furthermore, the integration of multiple energy sources, storage systems, and consumer demands in a large-scale network can introduce complexities in designing control strategies that optimize overall system performance while ensuring stability and reliability.

How can the MPC framework be integrated with other optimization-based energy management strategies to further improve the overall efficiency and flexibility of RES-based district heating systems?

Integrating the MPC framework with other optimization-based energy management strategies can enhance the efficiency and flexibility of RES-based district heating systems. One approach is to combine MPC with model predictive EMS, where the EMS optimizes the overall system operation over longer time horizons, while the MPC controller focuses on real-time control actions to address immediate deviations from the desired state. By coordinating these two strategies, the system can achieve both long-term optimization and short-term responsiveness. Additionally, integrating MPC with machine learning algorithms can improve the accuracy of heat demand and supply forecasts, enabling the controller to make more informed decisions. Furthermore, coupling MPC with demand response programs can allow the system to dynamically adjust heat supply based on consumer preferences and grid conditions, enhancing flexibility and grid stability. By leveraging the strengths of different optimization-based strategies in a coordinated manner, RES-based district heating systems can achieve higher efficiency, reliability, and sustainability.