Cooperative economic model predictive control for linear systems with convex objectives

Space heating demand response potential of retrofitted residential apartment blocks

Non-linear economic model predictive control of water distribution networks

In this paper, a periodic economic model predictive control (EMPC) strategy with nonlinear algebraic constraint relaxations for water distribution networks (WDNs) is presented. A WDN is usually modeled by a series of differential-algebraic equations. When the hydraulic pressure/head and flow relations in the interconnected pipes are considered, the nonlinear algebraic equations will appear in the control-oriented model of WDNs. Specifically, two types of nonlinear algebraic equations are studied in terms of unidirectional and bidirectional flows in pipes. These nonlinear algebraic constraints are iteratively relaxed by a series of linear constraints. Therefore, the proposed EMPC strategy can be implemented by solving an optimization problem using the linear programming technique. Finally, the EMPC strategy with nonlinear algebraic constraint relaxations is verified in the Richmond water network. The comparison results of applying nonlinear EMPC strategy are also provided. The proposed nonlinear-constraint relaxation technique turns out to be much faster than the one obtained by a standard nonlinear optimization solver.

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.

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

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

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.

This paper investigates the self-triggered model predictive control for networked linear systems. The self-triggered mechanism is designed based on switched cost functions, which can be used to enhance systems performance and are more appropriate for complex industrial requirements in contrast with a single cost function approach. The model predictive controller is designed by solving an optimization problem and the self-triggered condition is designed. With the proposed self-triggered mechanism, much network computation and communication burden are reduced and Zeno behavior can be excluded. Moreover, asymptotic stability of the networked systems with model predictive control strategy is shown via average dwell-time technique. Finally, the numerical simulation example is given to illustrate the effectiveness of the proposed methods.

A tracking MPC formulation that is locally equivalent to economic MPC

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.

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

Economic Model Predictive Control: Designs and Implementation

ABSTRACTIn order to dynamically operate the gold cyanidation leaching process (GCLP) under uncertainty, a multi‐stage economic model predictive control (EMPC) is proposed for GCLP for the transient and steady‐state economic optimization. The proposed multi‐stage EMPC is composed of two steps. In the first step, the unmeasurable uncertain parameters are estimated by using Tikhonov regularization based method, so as to avoid amplification and propagation of the noise measurements into the estimation. Based on the estimated results, the scenario tree for multi‐stage EMPC is generated from the historical data using a data‐driven approach, and the control inputs are obtained from solving the resulting large nonlinear programming problem (NLP) at each sampling point. The resulting uncertainty model and the probability of each scenario are more consistent with the actual industrial GCLP, and the solutions are less conservative. The efficiency of the proposed multi‐stage EMPC is verified through a simulated industrial GCLP. Compared with other EMPC methods, including classic EMPC and multi‐stage EMPC with box uncertainty region, the proposed method can reduce the economic cost while accounting for the constraints at the same time.