Periodic economic model predictive control with nonlinear-constraint relaxation for water distribution networks

Non-linear economic model predictive control of water distribution networks

Space heating demand response potential of retrofitted residential apartment blocks

Cost-efficient measurement of room-level heat output from hydronic radiators is a major barrier to large-scale implementation of Economic Model Predictive Control (EMPC) in residential space heating for demand-side management. This paper therefore presents a novel EMPC strategy for hydronic radiators that relies on measurements of radiator pipe temperatures as a proxy for the radiator heat output, thus eliminating the need for costly flow-based meters at each radiator in a building. Simulation-based experiments indicate that the proposed proxy-based EMPC matches the performance of its heat-based counterpart. The proxy-based EMPC achieved a 16.6 % cost reduction compared to the heat-based EMPC's 16.8 %, with no comfort violations in both cases. Furthermore, the strategy shows resilience towards uncertainties in the user-estimated radiator exponent and maximum heating capacity. The proposed EMPC scheme also allows system operators to fine-tune the balance between cost savings and return temperatures using the proxy's upper limit. The findings presented in this paper suggest that the proposed proxy-based EMPC scheme provides a practical pathway for broader applications of EMPC in hydronic-based space heating with the prospect of unlocking significant load shifting potential, cost savings for end-users, and enhanced efficiency in individual and collective energy systems.

In microgrids, the volatility and uncertainty of renewable energy make it challenging to achieve optimal performance using hierarchical control strategies with time-scale separation for economic dispatch and real-time control. To address this issue and enhance transient optimization, a distributed economic model predictive control (EMPC) strategy based on the alternating direction method of multipliers (ADMM) is proposed in this paper. To reduce computational complexity and communication overhead in distributed control, the ADMM method is employed to solve the distributed EMPC problem in parallel. Using Lyapunov-based analysis, the study establishes the system's asymptotic stability. Moreover, it demonstrates that the EMPC strategy achieves an average performance equivalent to-or even exceeding-that of the optimal steady-state. Simulations validate the proposed algorithm's effectiveness in economic dispatch and frequency restoration, while demonstrating its advantages in minimizing computational load and communication requirements.

A reinforcement learning-based economic model predictive control framework for autonomous operation of chemical reactors

Economic Model Predictive Control for Optimal Operation of Home Microgrid with Photovoltaic-Combined Heat and Power Storage Systems

Cooperative economic model predictive control for linear systems with convex objectives

Application of economic MPC to the energy and demand minimization of a commercial building

This papers proposes new ways to enforce convergence to equilibria for Economic Model Predictive Control schemes. Economic Model Predictive Control is a control technique capable of optimizing an economic performance index while enforcing state and input constraints. For nonlinear systems and/or non-convex cost functionals, performance optimization may result in non converging behaviours. While this might be acceptable in some cases (i.e. operation of chemical reactors), it may be undesirable for other types of applications. In the present paper we discuss ways of enforcing convergence to equilibrium by trading it off with asymptotic performance. Indeed, while all trajectories converging to a given equilibrium yield the same asymptotic average cost, transient costs may differ and trade-offs are naturally highlighted between the latter and speed of convergence.

Multi-market demand response using economic model predictive control of space heating in residential buildings

This article proposes a two‐layer framework to maximize economic performance through dynamic process economics optimization while addressing fluctuating real‐world economics and enhancing cyberattack resilience via encryption in the feedback control layer for nonlinear processes. The upper layer employs a Lyapunov‐based economic model predictive control scheme, receiving updated economic information for each operating period, while the lower layer utilizes an encrypted linear feedback control system. Encrypted state information is decrypted in the upper layer to determine the economically optimal dynamic operating trajectory through nonlinear optimization. Conversely, the lower layer securely tracks this trajectory in an encrypted space without decryption. To mitigate the cyber vulnerability of the upper layer, we integrate a cyberattack detector that utilizes sensor‐derived data for attack detection. We quantify the errors stemming from quantization, disturbances, and sample‐and‐hold controller implementation. Simulation results of a nonlinear chemical process highlight the robustness and economic benefits of this new control architecture.

Water Distribution Networks (WDNs) are crucial for meeting current and future urban water demands. Knowledge of future water demand at different time scales is fundamental for optimal WDN design and operations. Various predictive models of water demand have been proposed in the literature, ranging from traditional time series analysis to cutting-edge machine learning and deep learning techniques. However, the task of forecasting urban water demand remains mostly decoupled from the design of the optimal control of the related WDN. Current performance assessment of demand predictive models focuses predominantly on forecast accuracy, overlooking their practical implications on WDN operations. Meanwhile, the existing research on WDN management often assumes either perfect knowledge of future water demands or employs empirical approximations and aggregate statistics to estimate future water needs. This study bridges this gap by scrutinizing the actual operational value of water demand forecasts in designing optimal operations of WDNs.Here, we develop a forecast-informed optimal WDN control framework to evaluate the operational value of water demand forecasts for WDN operations. Our framework comprises two main modules. The first module computes water demand forecasts. We comparatively evaluate a suite of different forecasting models —including Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors, Multilayer Perceptron, Convolutional Neural Network, and Long Short-Term Memory (a network augmented with an attention mechanism) —across various forecast horizons (1/6/12 hours and 1/3/7/14 days ahead). The most accurate forecasts are integrated into the second module, an economic nonlinear Model Predictive Control (MPC) algorithm designed to optimize WDN operations. Within this module, an Artificial Neural Network (ANN) – based surrogate model encapsulates the hydraulics of the physical WDN, enhancing the optimization process while reducing complexity.We demonstrate our forecast-informed optimal WDN control framework on a real WDN of a rural town with approximately 10,000 inhabitants. Water demand data collected in the Netherlands for a period of 10 years (2007-2017) at 5-minute resolution and corresponding meteorological data are used to train the water demand forecasting models. The MPC module computes the optimal control sequence for 7 pumps and 1 valve in the WDN to minimize pump energy costs while meeting water demands and ensuring safety storage in 5 tanks. Initial findings reveal that the ANN-based surrogate model can accurately incorporate the WDN characteristics (R2 > 0.85), facilitating its integration into the MPC for an efficient and simplified representation of a real-world WDN. Further, MPC fed by 24-hour ahead water demand forecasts achieves potential energy savings of approximately 18% compared to a benchmark rule-based control strategy. Our framework yields a versatile simulation-based optimization tool for evaluating the impact of demand forecasts on WDN management. Future research efforts will aim at refining and comparing deterministic and stochastic water demand forecasts within the MPC framework, under diverse operational objectives.

In this work, we consider economic model predictive control (EMPC) for scheduled switching operations. The proposed EMPC scheme takes advantage of a set of auxiliary controllers that locally stabilizes the optimal steady state of each operating mode. In the proposed approach, EMPC operations are divided into two phases - an infinite-time operation phase and a mode transition phase, depending on the current sampling time and the scheduled mode switching time. The proposed EMPC design is computationally efficient and enjoys enlarged feasibility regions than the auxiliary controllers. Sufficient conditions to ensure recursive feasibility of the proposed EMPC design are established. Simulation results of a chemical process example demonstrate the applicability and effectiveness of our approach.

Lyapunov-based economic model predictive control for nonlinear descriptor systems

This article presents an optimization-based control framework for the autonomous forced landing of a fixed-wing unmanned aircraft (UA). A two-level model-predictive control (MPC) scheme is proposed to realize this framework, where an economic model-predictive control (EMPC) in a long piecewise constant fashion is proposed at the high level, while a short fixed-horizon linear time-varying MPC at the low level responds to fast dynamics of UA and tracks the optimal path provided by the high-level controller, alleviating computational burden compared to the high-frequency single-layer MPC scheme. Compared with a single EMPC setup with high sampling frequency, this hierarchical EMPC controller can significantly reduce the computational complexity and make it feasible to be implemented in real time. In addition, it also responds to disturbances (e.g., wind) and aircraft fast dynamics in a timely manner. The recursive feasibility and stability of the high- and low-level MPC schemes are established. The performance of the proposed EMPC forced landing function is illustrated by simulation case studies on both Aerosonde and Skywalker X8, compared favorably with competing schemes.