Economic Model Predictive Control Research Articles

Convex economic model predictive control for blade loads mitigation on wind turbines

AbstractEconomic model predictive control (EMPC) has received increasing attention in the wind energy community due to its ability to trade‐off economic objectives with ease. However, for wind turbine applications, inherent nonlinearities, such as from aerodynamics, pose difficulties in attaining a convex optimal control problem (OCP), by which real‐time deployment is not only possible but also a globally optimal solution is guaranteed. A variable transformation can be utilized to obtain a convex OCP, where nominal variables, such as rotational speed, pitch angle, and torque, are exchanged with an alternative set in terms of power and energy. The ensuing convex EMPC (CEMPC) possesses linear dynamics, convex constraints, and concave economic objectives and has been successfully employed to address power control and tower fatigue alleviation. This work focuses on extending the blade loads mitigation aspect of the CEMPC framework by exploiting its individual pitch control (IPC) capabilities, resulting in a novel CEMPC‐IPC technique. This extension is made possible by reformulating static blade and rotor moments in terms of individual blade aerodynamic powers and rotational kinetic energy of the drivetrain. The effectiveness of the proposed method is showcased in a mid‐fidelity wind turbine simulation environment in various wind cases, in which comparisons with a basic CEMPC without load mitigation capability and a baseline IPC are made.

Optimizing the switching operation in monoclonal antibody production: Economic MPC and reinforcement learning

Monoclonal antibodies (mAbs), crucial in medicine and biopharmaceuticals, require optimized large-scale production to meet high clinical dosage demands. Most of the processes for industrial mAb production rely on fed-batch operations, resulting in significant downtime. Transitioning to fully continuous and integrated processes holds the potential to boost product yield, enhance quality, and reduce storage costs for intermediate products. The integrated continuous mAb production process can be divided into the upstream and downstream processes. One crucial aspect that ensures the continuity of the integrated process is the switching of the capture columns, which are typically chromatography columns operated in a fed-batch manner downstream. Due to the discrete nature of the switching operation, advanced process control algorithms such as economic MPC (EMPC) are computationally difficult to implement. This is because an integer nonlinear program (INLP) needs to be solved online at each sampling time.This paper introduces two computationally-efficient approaches for EMPC implementation, namely, a sigmoid function approximation approach and a rectified linear unit (ReLU) approximation approach. It also explores the application of deep reinforcement learning (DRL). These three methods are compared to the traditional switching approach which is based on a 1 % product breakthrough rule and which involves no optimization.

Multi-flow optimization of a greenhouse system: A hierarchical control approach

Greenhouses are implemented all over the world to increase agricultural production thanks to controlled environmental conditions (inside temperature, moisture and CO2 contents). However, such systems are energy-intensive. The presented work focuses on controlling a greenhouse’ onsite multi-energy system (gas, heat and electricity), extended to a multi-flow system as the CO2 produced by the energy units is used as a plant fertilizers. In this view, a three levels hierarchical control has been developed: a steady state economic MPC is combined with a dynamic Multi-energy MPC and low-level PID controllers. This new controller aims at determining the best synergies for economic flows management, subject to compliance with the required climatic conditions in the greenhouse. The proposed controller is applied to a greenhouse which energy system is based on a thermal energy storage fueled by a gas boiler and a combined heat and power unit. The results are confronted to a usual ruled-based controller performed by greenhouses owners, showing a more efficient dynamic functioning of the energy system. Consequently, less gas is consumed (80.79 t to 76.03 t), heat is produced when needed, and electricity from the CHP is economically optimized allowing less importation from the grid (from 17.80 MWh to 15.88 MWh), and profitable selling.

An economic model predictive control-based flexible power point tracking strategy for photovoltaic power generation

In a high solar-power-penetration power grid, photovoltaic (PV) power generation requires to run in a flexible power point tracking (FPPT) mode. However, traditional hierarchical control-based FPPT strategy ignores the dynamic economic performance of PV power generation. To address this issue, an advanced FPPT strategy based on economic model predictive control (EMPC) is proposed to achieve higher dynamic economic performance. This strategy integrates the PV voltage reference calculation, PV voltage control, and pulse width modulation into one optimal control framework, utilizing the economic indices of the PV power generation system (PVPGS) as the cost function to achieve its economic optimization and power tracking. Due to the strong nonlinearity in the PVPGS, the EMPC optimization problem is non-convex, leading to a local optimum. A mixed integer nonlinear programming algorithm is developed, which utilizes a finite number of converter switching states for obtaining the global optimum. Simulations demonstrate that the EMPC-based FPPT strategy enhances the dynamic economic performance compared to the hierarchical control-based FPPT strategy.

A study of risk free and risky portfolio investment optimisation strategies under multi-objective constraints

The purpose of portfolio investment is to maximise returns while minimizing risks. For investors with different risk attitudes, this research uses Economic Model Predictive Control (EMPC) to study the multi-objective securities portfolio problem and obtains a multi-objective securities strategy that guarantees the maximum return and the minimum risk under different risk attitudes through the tracking method, considering the return, risk, and other factors of the securities portfolio. Finally, the effectiveness of the strategy is verified by simulation, and an analytical method for selecting the optimal portfolio of securities is proposed.

Model Predictive Control With Wind Preview for Aircraft Forced Landing

Autonomous emergency landing capability of fixed-wing aircraft is essential for opening airspace for civil unmanned aviation. This paper proposes a goal-oriented control scheme to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exploit</i> wind information for the benefit of forced landing. Different from general disturbances in a classic control system, a favorable wind would help aircraft to glide to a selected landing site more easily so increase the level of safety, while an adverse wind may render a selected landing site infeasible. We formulate the forced landing problem with wind preview information in the framework of Economic Model Predictive Control (EMPC) which aims to maximize the aircraft's final altitude when reaching a target region. A double-layer MPC scheme is adopted to lessen the computational burden and to increase the prediction time window for practical implementation, where a piecewise-constant disturbance preview based EMPC (DP-EMPC) maximizes the altitude at the upper-level, and a linear MPC is employed at the lower-level to track the reference signal optimized by the upper-level planner. Moreover, the effectiveness of the goal-oriented optimal control scheme is illustrated by several case studies, where an unmanned aircraft is gliding towards potential landing sites under various conditions.

Distributed economic predictive control of integrated energy systems for enhanced synergy and grid response: A decomposition and cooperation strategy

The close integration of increasing operating units into an integrated energy system (IES) results in complex interconnections between these units. The strong dynamic interactions create barriers to designing a successful distributed coordinated controller to achieve synergy between all the units and unlock the potential for grid response. To address these challenges, we introduce a directed graph representation of IESs using an augmented Jacobian matrix to depict their underlying dynamics topology. By utilizing this representation, a generic subsystem decomposition method is proposed to partition the entire IES vertically based on the dynamic time scale and horizontally based on the closeness of interconnections between the operating units. Exploiting the decomposed subsystems, we develop a cooperative distributed economic model predictive control (DEMPC) with multiple global objectives that regulate the generated power at the grid’s requests and satisfy the customers cooling and system economic requirements. In the DEMPC, multiple local decision-making agents cooperate sequentially and iteratively to leverage the potential across all the units for system-wide dynamic synergy. Furthermore, we discuss how subsystem decomposition impacts the design of distributed cooperation schemes for IESs and provide a control-oriented basic guideline on the optimal decomposition of complex energy systems. Extensive simulations demonstrate that the control strategies with different levels of decomposition and collaboration will lead to marked differences in the overall performance of the IES. The standard control scheme based on the proposed subsystem configuration outperforms the empirical decomposition-based control benchmark by about 20%. The DEMPC architecture further improves the overall performance of the IES by about 55% compared to the benchmark.

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

Self-stabilizing economic model predictive control without pre-calculated steady-state optima: Stability and robustness

We propose a new economic nonlinear model predictive control (eNMPC) formulation that tracks the optimality conditions of the real-time optimization problem rather than any specific steady states. The proposed formulation maintains its nature of optimizing economic performance and assured stability properties with the Lyapunov inequality constraint for the closed-loop control. Under general assumptions, we prove that the proposed controller is asymptotically stable without process disturbances and is input-to-state stable when there is a process disturbance. The proposed eNMPC is demonstrated on two case studies and compared against setpoint-tracking NMPC with setpoints determined by the steady-state real-time optimizer to show improved dynamic performance. We also highlight the capability of self-stabilization of the new eNMPC with parameter updates in the process model.

Real-time adaptive sparse-identification-based predictive control of nonlinear processes

This study introduces a sparse identification-based model predictive control (MPC) framework that incorporates on-line updates of the sparse-identified model to account for nonlinear dynamics and model uncertainty in process systems. The methodology involves obtaining a nonlinear first-order ordinary differential equation model using sparse identification for nonlinear dynamics (SINDy), which is integrated into two control schemes: Lyapunov-based MPC (LMPC) for achieving steady-state operation and Lyapunov-based economic MPC (LEMPC) for achieving both closed-loop stability and optimal economic performance. To improve prediction accuracy, an on-line model update scheme is proposed for the SINDy models. Specifically, an error-trigger mechanism that utilizes prediction errors and then uses the most recent process data to update the parameters of the SINDy model in real-time is designed. By incorporating the error-triggered on-line model updates in the SINDy-based LMPC and LEMPC, the dynamic performance of the process is enhanced, ensuring closed-loop stability, optimality, and smooth control actions. Following theoretical results on the boundedness of the closed-loop states and detailed discussions on the selection criteria for parameters of the error-triggered SINDy update scheme, the effectiveness of the proposed methodology is demonstrated through a chemical process example with time-varying disturbances under the LEMPC framework.

Terminal weight and constraint design for wave energy converter economic model predictive control problems

Terminal weight and constraint design for wave energy converter economic model predictive control problems

Offshore wind power generation system control using robust economic MPC scheme

With the increasing penetration of wind power in the modern power system, the economic model predictive control (EMPC) has been widely employed in the control of the offshore wind power generation system for promoting the dynamic economy. A robust EMPC strategy, aiming to minimizing damage to the turbine while maximizing the electric power output, is developed in this paper to enhance the dynamic economic performance under uncertain wind speed variation. A linear model is utilized to approximate the original nonlinear behavior of the wind power generation system, while the consequent linearization error is taken as the external disturbance of the control system. A linear feedback controller with a robust control invariant set is designed to restrict the deviation between the nominal linear system and the actual nonlinear wind power generation system. Plant simulations, as well as NREL FAST code testing, are given to demonstrate the proposed controller's effectiveness throughout the overall operating region.

VALIDATION OF PHOTOVOLTAIC MODEL FOR APPLICATION IN A DISTRIBUTED ENERGY SOURCE USING WEATHER DATA

This work presents a photovoltaic model for a simulation of the electric energy production of a distributed energy system. The model will be validated through measured weather data and energy produced by an 88.04 kWp power plant installed on the Federal University of Espírito Santo (UFES) in Vitória. The validation consists of comparing the real power data acquired by the photovoltaic plant and the power data calculated from the model using weather data, specifications of the panels and inverters and the constructive characteristics of the system. The proposed model is based on the paper “Management of an island and grid-connected microgrid using hybrid economic model predictive control with weather data”, Applied Energy, v. 278, 2020, https://doi.org/10.1016/j.apenergy.2020.115581. In addition, the model has been improved with the inclusion of new intrinsic parameters of the material, the calculation of losses and the adjustments for different tilt angles and azimuth orientations. Results of this method reveal that the model was able to reproduce the behavior of the real photovoltaic plant, presenting a mean absolute percentage error of 8.8% between real and simulated data.

Enhanced reinforcement learning in two-layer economic model predictive control for operation optimization in dynamic environment

Economic model predictive control (EMPC) has attracted an abundance of interest in both academic and industrial communities in recent years because it is able to increase the economic profits of dynamic systems. For greater computational efficiency, two-layer EMPC schemes are applied in some complex process control. However, the performance of two-layer EMPC is significantly influenced by the accuracy of the chosen process model. Reinforcement learning (RL) has been studied as a model-free strategy of model-based control approaches, but its safety and stability remain a concern. In order to estimate the model parameters of nonlinear dynamic systems in real time, this work introduces a unique scheme for merging two-layer EMPC and RL. In this scheme, the two-layer EMPC technique maintains closed-loop stability and recursive feasibility while operating the closed-loop dynamic system optimally. And the RL agent continually compares the observed states to the predictions made by the EMPC and modifies the time-varying parameters as necessary. The usability of the proposed scheme is shown on a chemical process of ethylene oxide production in dynamic environment. This work enables online and continuous control, optimization, and model correction, and makes process production optimization more feasible and profitable.

Self-tuning kernel Gaussian method for predictive control systems

This paper introduces a novel Gaussian process approach for systems with unknown disturbances with quasi-periodic patterns to enhance the performance of a robust economic model predictive controller. A self-tuning kernel is proposed to substitute the periodic kernel used in the hybrid Gaussian process models in order to predict forthcoming disturbances more accurately while demanding a shorter training horizon. The proposed method is applied to a domestic solar thermal system, in which the hot water demand has a recurrent pattern, yet there is a slight variation daily. The simulation results demonstrate that the proposed controller has a reliable and precise prediction of future demand, and therefore it is able to manage the solar thermal system properly under various hot water load scenarios. Specifically, the proposed controller yields more than 5% improvement over a proportional–integral–derivative controller in terms of energy saving associated with the electricity usage for an auxiliary heat source.

Microgrid Optimal Dispatch Based on Distributed Economic Model Predictive Control Algorithm

A microgrid cluster is composed of multiple interconnected microgrids and operates in the form of cluster, which can realize energy complementation between microgrids and significantly improve their renewable energy consumption capacity and system operation reliability. A microgrid optimal dispatch based on a distributed economic model predictive control algorithm is proposed in this paper. Firstly, the control task of the microgrid power generation system is defined, which is required to meet the load demand while reducing the economic loss of the system and realize dynamic economic optimization. The global objective function is designed based on the control task, and the detailed design method of the distributed economic model predictive controller is given. The control law is obtained by an iterative calculation using the Nash optimal method, which can effectively reduce the amount of data in the communication network. Finally, a microgrid group composed of four microgrids is used as an example for simulation verification. The simulation results show that the distributed economic model predictive control algorithm proposed in this paper has good economic benefits for microgrid dispatching.

Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control (MPC) algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems. Economic MPC can be used in a power system to ensure frequency stability, real-time economic optimization, control of the system and optimal load dispatch from it. A generalized terminal penalty term was used, and the finite-time convergence of the system was guaranteed. The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system, which had two areas connected by an AC tie line. The simulation results demonstrated the effectiveness of the algorithm.

Stable nonlinear model predictive control with a changing economic criterion

This paper proposes a novel stable economic model predictive control (EMPC) strategy for constrained nonlinear systems with changing economic criteria. The traditional EMPC may lead to infeasibility and even instability of the closed-loop system when the criterion has been changed. Firstly, a generalised terminal constraint is introduced to ensure the recursive feasibility of the economic optimisation problem, which enforces the terminal states to converge to an arbitrary equilibrium state rather than a predetermined fixed one at the initial time. Then the stability constraint is constructed by solving an auxiliary optimisation problem online, which is the key to guaranteeing the asymptotic stability of the closed-loop system. Finally, sufficient conditions for feasibility and asymptotic stability are derived in the context of changing economic criteria. The main feature of the proposed strategy is that it does not need to know the changes of economic criterion in advance, and its properties and effectiveness are exemplified by simulations on a nonlinear chemical process example.

Event-triggered economic MPC with relaxed contractive constraints

This paper proposes a novel event-triggered economic model predictive control (EMPC) scheme of constrained nonlinear systems. Some auxiliary positive-definite functions at economic optimal equilibrium points are defined for economic performance functions that are generally non-convex and non-positive-definite. The optimal value function of the auxiliary function is used to design an adjustable stability constraint which is imposed on the original EMPC optimization problem. The design of the contractive constraint can avoid Zeno behaviors during the triggered process. Especially, the event-triggered condition is designed by relaxed contractive constraint and the updated control laws. Sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the obtained results is illustrated by a simulation example of a continuously stirred tank reactor.

A simplified economic model predictive control for a gas lifted oil production network based on modifier adaptation

We propose a novel simplified economic model predictive controller (EMPC) for supervisory control of an offshore petroleum production network composed of two wells, a riser, and a separator. The proposed controller uses a gradient-and-modifier-based methodology to mimic a nonlinear EMPC (it considers a nonlinear process model and cost function), while only solving quadratic programming. We alter the modifier adaptation to depend on an estimator and employ slack variables to improve feasibility. Tips for appropriate design, to improve stability and robustness, are presented. Since the tested facility is subject to multiple disturbances, we also use a regulatory controller to stabilize the system. Finally, we compare our method to a linear EMPC and self-optimizing control in various scenarios considering disturbances, noise, and model inconsistencies. The proposed controller always tends towards the economic optimal point, presenting similar nominal performance as the others advanced controllers and better robustness.