Economic Model Predictive Control Research Articles

Economic model predictive control for energy management of a microgrid connected to the main electrical grid

Electric microgrids have become an interesting tool to facilitate the inclusion of renewable energies. Its architecture and control system plays a fundamental role in the implementation of these systems. This paper proposes a control strategy for the management of energy resources in a residential microgrid. The system is made up of a set of solar panels as renewable resource, a storage system formed by a lithium-ion battery bank and a consumption profile according to a residence. The microgrid will be connected to the main electrical grid and the proposed management strategy consists in the implementation of a suitable Economic Model Predictive Control, where it considers the costs of use for the different components of the microgrid, thus contemplating the participation of the system as an active agent in the electricity market. Simulations were carried out with different scenarios of available resources and prediction times. In all cases, the objectives fulfilling by satisfying the restrictions operational and technical imposed on the system.

Efficiency-Oriented MPC: Using Nested Structure to Realize Optimal Operation and Control

Optimal operation and control, which can result in the global optimal operation performance of industrial processes, has been a hot topic in recent control strategy designs. However, existing control strategies, such as real-time optimization (RTO), dynamic real-time optimization (DRTO), and economic model predictive control (EMPC), have their own limitations, and they can only generate sub-optimal operation performance. In order to further improve online global operation performance, a new kind of control strategy named efficiency-oriented model predictive control (EfiMPC) is proposed in this paper. The aim of the EfiMPC is discussed first, and then, the ideal EfiMPC strategy with a nested structure is proposed, where the inner layer is the offline construction of an efficiency-oriented terminal region, and the outer layer is the direct optimization of the transient operation performance. This efficiency-oriented terminal region can guarantee a dynamic operation performance in the closed-loop perspective, and a better global operation performance can thus be obtained. A practical EfiMPC strategy, which replaces the offline construction of the efficiency-oriented terminal region with the online optimization of the average dynamic operation performance in the inner layer, is also proposed, and the recursive feasibility as well as the closed-loop stability of practical EfiMPC are discussed. Finally, a CSTR application was used to test the superiority of the proposed EfiMPC strategy, and the simulation results show that EfiMPC can obtain the best global operation performance compared with the other three control strategies; thus, the effectiveness of EfiMPC is demonstrated.

Hierarchical Economic Model Predictive Control Approach for a Building Energy Management System With Scenario-Driven EV Charging

To handle the increasing number of electric vehicles (EVs) and their effect on the infrastructure, intelligent and coordinated charge management is necessary. In this paper, this problem is considered in the context of a commercial building energy management system (EMS) with vehicle-to-grid capable employee EV charging stations (EVCSs). We propose a hierarchical economic model predictive control (EMPC) scheme for the operation of the EMS with EV charge management. An aggregator plans the operation of the EMS and an aggregated perspective of the EVCSs. A distributor then allots the aggregated charge power to the individual EVCSs. Both layers employ EMPC to jointly consider the objectives of monetary costs, building temperature comfort, EV charge satisfaction and battery degradation. For the predictions of EV usage behavior, scenario generation based on usage data and user input is employed. The main contributions of this paper are the symmetric consideration of EV charging objectives using EMPC in both levels of the hierarchy, as well as the introduction of a scalable and adaptable averaged scenario generation approach.

Distributed economic model predictive control for an industrial fluid catalytic cracking unit ensuring safe operation

The economic performance of a fluid catalytic cracking (FCC) unit plays an important role in the refinery factory. In order to improve the dynamic economic performance as well as ensure safe operation, cooperative distributed economic model predictive controls (DL-EMPCs) that optimize the product yields of the FCC unit are proposed. Discrete-time Lyapunov constraints in the MPC are designed to guarantee stability and limit the MPC output such that the decrease ratio of Lyapunov function of the closed-loop system is no less than those obtained by the designed distributed auxiliary controller. The auxiliary controller is structural and designed based on a multi-model approximation of the plant due to the strong non-linearity of the FCC unit, which can keep the system’s convergence despite the unmeasurable disturbance and the model mismatch. The feasibility and stability of the proposed DL-EMPCs are discussed as well. The proposed algorithm was applied to an industrial FCC unit model based on a refinery factory in Jiujiang, China. The results show that better economic benefits are achieved compared to the set-point regulating MPC when no disturbance occurs. Additionally, the robust performance is verified that the unit with the controller can be manipulated in a safe region even if the disturbances exist.

Cooperative Distributed GPU Power Capping for Deep Learning Clusters

The recent GPU-based clusters that handle deep learning (DL) tasks have the features of GPU device heterogeneity, a variety of deep neural network (DNN) models, and high computational complexity. Thus, the traditional power capping methods for CPU-based clusters or small-scale GPU devices cannot be applied to the GPU-based clusters handling DL tasks. This article develops a cooperative distributed GPU power capping (CD-GPC) system for GPU-based clusters, aiming to minimize the training completion time of invoked DL tasks without exceeding the limited power budget. Specifically, we first design the frequency scaling approach using the online model estimation based on the recursive least square method. This approach achieves the accurate tuning for DL task training time and power usage of GPU devices without needing offline profiling. Then, we formulate the proposed FS problem as a Lagrangian dual decomposition-based economic model predictive control problem for large-scale heterogeneous GPU clusters. We conduct both the NVIDIA GPU-based lab-scale real experiments and real job trace-based simulation experiments for performance evaluation. Experimental results validate that the proposed system improves the power capping accuracy to have a mean absolute error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt; \!1\%$</tex-math></inline-formula> , and reduces the deadline violation ratio of invoked DL tasks by 21.5% compared with other recent counterparts.

Multi-market demand response from pump-controlled open canal systems: an economic MPC approach to pump-scheduling

Abstract Participation in demand response (DR) has been explored for many large energy-using assets based on day ahead electricity markets. In this manuscript, we propose the use of multiple electricity spot markets to enable price-based DR for open canal systems in the Netherlands, where many large pumping stations are used for flood mitigation and control of groundwater levels. In the new strategy for pump-scheduling, we combine the day ahead and intraday electricity markets to be used in a hierarchical receding horizon economic Model Predictive Control (MPC). We formulate the decision problem as a Mixed-Integer Quadratic Problem (MIQP), to be solved to near global optimality. A cost-potential analysis was performed for multiple market strategies and the automatic Frequency Restoration Reserves (aFRRs), using actual market and water system data. We show new insights into the trade-off between CO2 emissions and operating cost, the difference between the German and Dutch markets, and temporal changes in market conditions due to renewable energy integration. We observe that the German energy market is rewarding DR more than the Dutch equivalent, due to the higher renewable energy market penetration. The proposed multi-market strategy leads to a cost decrease of 10 and 16% in the Netherlands in 2017 and 2019, respectively. When applying German market scenarios, we found a cost-saving potential of 56 and 50% in 2017 and 2019, respectively. The cost-saving potential for the aFRR market was found to be up to 12% in the Netherlands and 28% in Germany, through a conservative analysis. The results suggest that the proposed control system, optimising costs over the day ahead, intraday and possibly the aFRR markets, is profitable compared to the current strategy in both the current and future electricity market.

Valorizing Steelworks Gases by Coupling Novel Methane and Methanol Synthesis Reactors with an Economic Hybrid Model Predictive Controller

To achieve the greenhouse gas reduction targets formulated in the European Green Deal, energy- and resource-intensive industries such as the steel industry will have to adapt or convert their production. In the long term, new technologies are promising. However, carbon capture storage and utilization solutions could be considered as short-term retrofitting solutions for existing steelworks. In this context, this paper presents a first experimental demonstration of an approach to the utilization of process off-gases generated in a steelworks by producing methane and methanol in hydrogen-intensified syntheses. Specifically, the integration of two methane synthesis reactors and one methanol synthesis reactor into a steel plant is experimentally simulated. An innovative monitoring and control tool, namely, a dispatch controller, simulates the process off-gas production using a digital twin of the steel plant and optimizes its distribution to existing and new consumers. The operating states/modes of the three reactors resulting from the optimization problem to be solved by the dispatch controller are distributed in real time via an online OPC UA connection to the corresponding experimental plants or their operators and applied there in a decentralized manner. The live coupling test showed that operating values for the different systems can be distributed in parallel from the dispatch controller to the test rigs via the established communication structure without loss. The calculation of a suitable control strategy is performed with a time resolution of one minute, taking into account the three reactors and the relevant steelworks components. Two of each of the methane/methanol synthesis reactors were operated error-free at one time for 10 and 7 h, respectively, with datasets provided by the dispatch controller. All three reactor systems were able to react quickly and stably to dynamic changes in the load or feed gas composition. Consistently high conversions and yields were achieved with low by-product formation.

Economic versus energetic model predictive control of a cold production plant with thermal energy storage

Economic model predictive control has been proposed as a means for solving the unit loading and unit allocation problem in multi-chiller cooling plants. The adjective economic stems from the use of financial cost due to electricity consumption in a time horizon, such is the loss function minimized at each sampling period. The energetic approach is rarely encountered. This article presents for the first time a comparison between the energetic optimization objective and the economic one. The comparison is made on a cooling plant using air-cooled water chillers and a cold storage system. Models developed have been integrated into Simscape , and non-convex mixed optimization methods used to achieve optimal control trajectories for both energetic and economic goals considered separately. The results over several scenarios, and in different seasons, support the consideration of the energetic approach despite the current prevalence of the economic one. The results are dependent on the electric season and the available tariffs. In particular, for the high electric season and considering a representative tariff, the results show that an increment of about 2.15% in energy consumption takes place when using the economic approach instead of the energetic one. On the other hand, a reduction in cost of 2.94% is achieved. • Simscape models with real data are used in a non-convex mixed optimization problem. • A modified real coded genetic algorithm has been deployed for control use. • Economic control partially loses the ‘green’ properties associated with TES usage. • Energetic control yields 2% energy savings over economic, with a 3% cost increase.

Economic Model Predictive Control of Enhanced Operation Performance for Industrial Hierarchical Systems

Economic operation performance has been a primary consideration in recent control strategy designs for industrial processes. This performance refers to the accumulated economic cost corresponding to dynamic evolution and final steady-state phase. Incorporating an economic model predictive controller (EMPC) to the industrial hierarchy, i.e., the real-time optimizer followed by the advanced controller EMPC, is a well-reasoned approach for performance improvement. However, model mismatch among layers may lead to infeasibility issue and final static operation error/offset. This article presents a novel offset-free EMPC scheme, which admits algorithm feasibility in the presence of process constraints and model mismatch. The convergence and offset-free properties w.r.t. the best attainable steady state are guaranteed. Specifically, this scheme contains a dynamic target optimization stage and an EMPC stage. The stabilization formulations are designed, respectively, for dissipative and nondissipative systems, to maximum possible performance improvement. Finally, the method is illustrated by the typical chemical plant examples. The results show that the offset-free EMPC scheme aligns well in the hierarchically controlled system with emphasis on performance improvement.

Distributed Economic MPC for Dynamically Coupled Linear Systems With Uncertainties.

In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.

Performance of predictive control for a continuous horizontal fluidized bed dryer

Advanced process control can benefit to the operation efficiency and quality of tablets produced by wet granulation lines. Following the development of a new fully continuous fluidized bed reactor as a potential substitute for the current batch dryer design, this paper examines the energy and product quality performances of two predictive control strategies using an experimentally validated simulator. The first one proposes an economic model predictive controller explicitly minimizing the dryer energy consumption. The second one follows the same objective, but uses a simpler classical predictive control framework implementing targets on manipulated variables to drive them toward low energy consumption operating points. Both controllers lead to similar performances, and consume about 20% less energy than a reference feedback scheme without manipulated variable setpoints. Results also show that tracking the product quality attribute significantly benefits from a feedforward action because of the long residence time. This article addresses a subject little explored by the literature, the control of continuous fluidized bed dryers, and clearly demonstrates that a standard linear strategy can reduce the operating costs with an appropriate design.

Economic model predictive control for multi-energy system considering hydrogen-thermal-electric dynamics and waste heat recovery of MW-level alkaline electrolyzer

A large-scale alkaline electrolyzer (AE), can convert renewable electricity into green hydrogen and recoverable heat, and consequently unlock great flexibility to accommodate renewable power variability. This paper proposes an economic model predictive control (EMPC) based daily optimal operation strategy for a multi-energy system (MES) which unleashes the cross-sectoral operational flexibility of AE. A dynamic power-to-hydrogen&heat (P2H2) model for AE is presented, considering heat recovery and efficiency variation under different loading conditions. Instead of incorporating the nonlinear P2H2 model into the operating optimization model of MES, this paper has developed a more computationally efficient algorithm that uses the P2H2 model for post-evaluation of optimal scheduling derived from a mixed-integer linear programming (MILP)-based EMPC. Comparative cases based on real data of a Danish energy island Bornholm, demonstrate the effectiveness, robustness of the proposed method and the potential value of AE’s operational flexibility in the MESs. The results reveal that the proposed method contributes to additional operation cost savings of 59% and 38% compared to a traditional rule-based strategy and an economic strategy without P2H2 model.

Health-Aware Economic MPC for Operational Management of Flow-Based Networks Using Bayesian Networks

This paper presents a health-aware economic Model Predictive Control (EMPC) approach for the Prognostics and Health Management (PHM) of generalized flow-based networks. The proposed approach consists of the integration of the network reliability model obtained from a Bayesian network in the control model. The controller is then able to optimally manage the supply taking into consideration the distribution of the control effort, to extend the life of the actuators by delaying the network reliability decay as much as possible. It also considers an optimal inventory replenishment policy based on a desired risk acceptability level, leading to the availability of safety stocks for unexpected excess demand in networks. The proposed implementation is illustrated with a real case study corresponding to an aggregate model of the Drinking Water transport Network (DWN) of Barcelona.

Economic nonlinear model predictive control of fatigue for a hybrid wind-battery generation system

An economic nonlinear model predictive controller (ENMPC) is formulated for a wind turbine-battery hybrid generation system. The controller aims to maximize the operational profit of the generator by balancing between generated wind power and turbine tower fatigue as well as battery cyclic fatigue. Other than the tower fore-aft fatigue, tower side-side fatigue is also considered to assess impact on overall economic performance. A moving horizon estimator (MHE) is formulated to provide meaningful initialization to the ENMPC in presence of plant model mismatch.The formulated controller utilizes the parametric online rainflow counting (PORFC) approach for direct cyclic fatigue cost minimization within ENMPC. The closed-loop simulation shows significantly higher profit compared to a realistic base-case scenario and relatively higher profit compared to another economic controller.

A novel Nonlinear Model Predictive Controller for Power Maximization on Floating Offshore Wind Turbines

Reducing the Levelized Cost of Energy is the main objective of wind turbine industry, in particular for the emerging sector of floating offshore turbines. In this work, a novel Economic Nonlinear Model Predictive Control (ENMPC) strategy is developed to maximize the power production of floating offshore wind turbines. The control problem is solved through an indirect method, which achieves the computational efficiency required to apply it in real world cases. A non-linear Reduced Order Model of the floating turbine predicts aerodynamic power, generator temperature and platform motions inside the controller. A set of constraints, including a bound on the generator temperature, the thrust and platform velocities are imposed. Simulations using the open-source engineering tool OpenFAST on the 5MW NREL wind turbine supported by the OC3 spar buoy platform [1] are performed to validate the turbine model and then to assess the controller performances in realistic wind and sea state conditions. With respect to the standard controller, a 4.3% increase of generated power in rated conditions is achieved with a more stable generator temperature.

Individual pitch control by convex economic model predictive control for wind turbine side-side tower load alleviation

The wind turbine side-side tower motion is known to be lightly damped. One viable active damping solution is realized by deploying individual pitch control (IPC) such that counteracting blade forces are created to alleviate the tower fatigue loading caused by this motion. Existing IPC methods for side-side tower damping in the literature, such as linear quadratic regulator and lead-lag controller, cannot accommodate direct optimization and tradeoff tunings of the wind turbine economic performance. In this work, a novel side-side tower damping IPC strategy under a convex economic model predictive control (CEMPC) framework is therefore developed to address these challenges. The main idea of the framework lies in the variable transformation in power and energy terms to obtain linear dynamics and convex constraints, over which the economic performance of the wind turbine is maximized with a globally optimal solution in a receding horizon manner. The effectiveness of the proposed method is showcased in a high-fidelity simulation environment under both steady and turbulent wind cases. Lower fatigue damage on the side-side tower bending moment is attained with an acceptable level of pitch activities, negligible impact on the blade loads, and minor improvement on the power production.

Integrated inventory and transportation management with stochastic demands: A scenario-based economic model predictive control approach

The integration of inventory and transportation operations is a challenging task in multi-echelon supply chain management. Uncertainties in customer demands can have serious consequences, such as inventory fluctuations and transportation changes. Policies of integrated inventory and transportation management aim to find a balance between supply and demand and can minimize the total operating cost for the entire supply chain. In this study, we propose a scenario-based economic model predictive control (EMPC) framework for integrated inventory and transportation management of multi-echelon supply chains with stochastic demands. The proposed scenario-based EMPC framework can provide real-time optimal operations for automated inventory and transportation management with a minimum operating cost and a guaranteed risk probability. As the number of scenarios is linked with the risk probability, we develop a design condition to choose the number of scenarios and ensure that optimal operations from the proposed framework can guarantee the desired risk probability. Finally, we present a case study of a three-echelon supply chain benchmark to demonstrate the effectiveness of the proposed EMPC framework and provide several comparison results to show its performance.

A new dissipativity condition for asymptotic stability of discounted economic MPC

Economic Model Predictive Control has recently gained popularity due to its ability to directly optimize a given performance criterion, while enforcing constraint satisfaction for nonlinear systems. Recent research has developed both numerical algorithms and stability analysis for the undiscounted case. The introduction of a discount factor in the cost, however, can be desirable in some cases of interest, e.g., economics, stochastically terminating processes, Markov decision processes, etc. Unfortunately, the stability theory in this case is still not fully developed. In this paper we propose a new dissipativity condition to prove asymptotic stability in the infinite horizon case and we connect our results with existing ones in the literature on discounted economic optimal control. Numerical examples are provided to illustrate the theoretical results.

Multi-Objective-Based Tuning of Economic Model Predictive Control of Drinking Water Transport Networks

In this paper, the tuning of economic model predictive control (EMPC) applied to drinking water transport networks (DWTNs) is addressed using multi-objective optimization approaches. The tuning strategies are based on Pareto front calculations of the underlying multi-objective problem. This feature represents an improvement with respect to the standard EMPC approach for weight tuning based on trial and error. Different multi-objective optimization methods with corresponding normalization approaches of the controller objectives are first studied to explore the dynamic nature of the Pareto fronts. An automated decision-making strategy is proposed to select the preferred controller parameters as a function of different disturbance values. The tuning requires an offline training phase and an online application phase. During the offline phase, the controller parameters are selected for different disturbances using the decision-making strategy. During the online phase, two approaches are evaluated: (i) exploiting the controller parameters with the highest frequency in the resulting histogram or (ii) using a regression model between the controller parameters and the disturbances. The proposed tuning strategies are applied to a real-life simulation case study based on the Barcelona DWTN. The simulation results show that the proposed tuning strategies outperform the baseline results by exploiting the periodicity of the water demands profile.

A high-fidelity building performance simulation test bed for the development and evaluation of advanced controls

We present an open-source building performance simulation test bed, the Advanced Controls Test Bed (ACTB), that interfaces high-fidelity Spawn of EnergyPlus building models, with advanced controllers implemented in Python. The ACTB leverages the Building Optimization Testing and Alfalfa platforms for managing simulations, providing an external clock, a representational state transfer (REST) application programming interface (API), and key performance indicators for evaluating the effectiveness of control strategies. The REST API allows the development of external controllers programmed in languages such as Python, which provides flexibility and a rich choice of scientific libraries for designing control sequences. We present three test cases based on the U.S. Department of Energy's Reference Small Office Building to demonstrate the ACTB's capabilities: (a) rule-based controls compliant with ASHRAE Guideline 36 control sequences; (b) an economic model predictive control implemented using do-mpc; and (c) a deep Q-network reinforcement learning agent implemented using OpenAI Gym. Abbreviations: ACTB: Advanced Controller Test Bed; AHU: Air Handling Unit; AI:Artificial Intelligence; API: Application Programming Interface; BEM: Building EnergyModeling; BSS: Best Subset Selection; DOE: Department of Energy; DQN: Deep-QNetwork; EKF: Extended Kalman Filter; FMI: Functional Mock-up Interface; FMU:Functional Mock-up Unit; FSS: Forward Stepwise Selection; HVAC: Heating; Ventilationand Air Conditioning; KPI: Key Performance Indicator; LTI: Linear Time-Invariant; MBL: Modelica Buildings Library; MHE: Moving Horizon Estimator; MPC: ModelPredictive Control; N4SID: Numerical Subspace State-Space System Identification; REST: Representational State Transfer; RL: Reinforcement Learning; ROM: Reducedorder model