Economic Model Predictive Control Controller Research Articles

MPPT Strategy of Waterborne Bifacial Photovoltaic Power Generation System Based on Economic Model Predictive Control

At present, the new energy industry represented by photovoltaics has become the main force to realize the optimization of China’s energy structure and the goal of “double carbon”; with the absence of land resources, the waterborne bifacial photovoltaic has ushered in a new opportunity. Therefore, in order to address the problem that the maximum power point tracking (MPPT) of photovoltaics (PV) could not take into account, the dynamic economic performance in the control process, an economic model predictive control (EMPC), is proposed in this work to realize the MPPT of the waterborne bifacial PV power generation system. Firstly, the model of the bifacial PV module is constructed by combining the ray-tracing irradiance model and considering the effect of water surface albedo on the irradiance absorbed by the module. Secondly, the EMPC controller is designed based on the state-space model of the system to maximize the power generation as the economic performance index, and to solve the optimal input variables time by time to achieve a rolling optimization with the operational requirements of the system itself as the constraints. Thirdly, the MATLAB/Simulink (R2022a) simulation experimental results verify that the EMPC strategy could be utilized to achieve MPPT of the waterborne bifacial PV power generation system, according to the changes of environment. Finally, it is also demonstrated that the bifacial PV power generation system that employed the EMPC strategy outperformed the traditional MPPT algorithm, with respect to both output power tracking velocity and accuracy, and the power generation could be improved by about 6% to 14.5%, which significantly enhances the system’s dynamic process economics.

Energy-Optimal Control for Autonomous Underwater Vehicles Using Economic Model Predictive Control

Improving endurance is important for autonomous underwater vehicles (AUVs) as it affects the operational cost and application range of the vehicle. In this article, we propose an economic model predictive control (EMPC)-based controller to reduce the control energy of AUVs while performing waypoint tracking. The proposed EMPC controller optimizes stage costs capturing the control energy consumed within the prediction horizon and a terminal cost approximating the energy-to-go, the energy required to reach the desired waypoint from the end of the prediction horizon. To approximate the energy-to-go, we partition it into the dynamic and static segments based on the operational characteristics of the optimal vehicle maneuver obtained from off-line trajectory optimization using direct collocation (DC). To account for the disturbances caused by ocean currents, we adopt the energy-to-go to a virtual Earth-fixed frame that transforms the drift in the vehicle location to the drift in the desired waypoint. Theoretical and numerical analyses of the approximated energy-to-go reveal that the proposed controller can balance the tradeoffs among energy components spent for vehicle surge, heave, and yaw controls in consideration of vehicle dynamics. Simulations under different flow conditions are conducted to compare the proposed approach with DC and a line-of-sight (LOS) guidance-based approach that optimizes vehicle surge speed for energy minimization. Through simulations, it is shown that the proposed approach achieves near-optimal performance as DC and outperforms the LOS-based approach.

Economic Model-Predictive Control for Aircraft Forced Landing: Framework and Two-Level Implementation

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.

Economic model predictive control of nonlinear systems using a linear parameter varying approach

AbstractThis article proposes an economic model predictive control (EMPC) approach for linear parameter varying (LPV) systems. An efficient implementation of the associated MPC optimization problem is introduced based on transforming the LPV model into a linear time‐varying one by using an estimation of the scheduling variables along the prediction horizon. This estimation is based on the optimal states/inputs determined from the solution of the previous optimization problem while running the receding horizon strategy. Using this approach, the solution of the proposed LPV‐based EMPC scheme would be possible by solving a series of quadratic programming problems at each time instant. This approach allows reducing the computational burden compared with the solution of a nonlinear optimization problem that would result naturally from the LPV‐based formulation. The stability of the proposed approach is guaranteed by forcing the terminal state to converge towards the optimal equilibrium/working point of the system. Moreover, the terminal constraint is relaxed by using a constraint set around the terminal state instead of a constraint value and adding a penalty on the terminal state into the cost function. Besides, strict dissipativity is established as a sufficient condition to prove stability. Finally, the effectiveness of the LPV‐based EMPC strategy is shown by controlling a small‐scale pasteurization system in simulation. The comparison between the proposed control approach and standard MPC approaches is performed. Results show the advantages of the proposed LPV‐based EMPC controller in terms of economic cost minimization.

Comparison of economic model predictive control and rule‐based control for residential energy storage systems

This study quantifies the benefits of implementing model predictive control on residential solar PV and energy storage systems considering a time-of-use demand tariff, feed-in tariff and varying PV system sizes and battery life-cycle costs. The control system analysed makes use of economic model predictive control (EMPC) whereby the objective function is directly tied to the economics of the system. Using residential load and PV data from an Australian distribution network service provider, the EMPC controller is compared to a rule-based controller, highlighting the benefits of EMPC in regards to annual economic performance and battery energy throughput. The EMPC algorithm is then tested using 10 residential customers at the low voltage feeder level showing the capacity for the EMPC controller to shift peak demand and flatten the aggregated load profile of 30 residential customers.

Economic model predictive control for demand flexibility of a residential building

Future building energy management systems will have to be capable of adapting to variation in the rate of production of energy from renewable sources. Controllers employing a model predictive control (MPC) framework can optimise and schedule energy usage based on the availability of renewably generated energy. In this paper, an MPC using artificial neural networks (ANNs) was implemented in a residential building. The ANN-MPC was successfully tested and demonstrated good performance predicting the building's energy consumption. The controller was then modified to function as an economic MPC (EMPC) to optimise demand flexibility (i.e., the ability to adapt energy demands to fluctuations in supply). The operational costs of energy usage were associated with this demand flexibility, which was represented by three flexibility indicators: flexibility factor, supply cover factor, and load cover factor. The results from a day-long test showed that these flexibility indicators were maximised (flexibility factor ranged from −0.88 to 0.67, supply cover factor from 0.04 to 0.13, and load cover factor from 0.07 to 0.16) when the EMPC controller's demand flexibility was compared to that of a conventional proportional-integral (PI) controller. The EMPC framework for demand flexibility can be used to regulate on-site energy generation, grid consumption, and grid feed-in and can thus serve as a basis for overall optimisation of the operation of heating systems to achieve greater demand flexibility.

Price-responsive model predictive control of floor heating systems for demand response using building thermal mass

Floor heating (FH) system is a widely-used thermally active building system, which can take advantage of building thermal mass to shift energy demands to off-peak hours. Its ability of effective utilization of low-temperature energy resources also helps to increase energy efficiency and reduce greenhouse gas emissions. However, control of FH systems remains a challenge due to the large thermal inertia of the pipe-embedded concrete floor. In the context of smart grids, the control issue becomes more complicated because the dynamic electricity prices need to be taken into consideration to achieve economic benefits and encourage demand response participation. In this study, an advanced optimal control method, i.e., model predictive control (MPC), is developed for FH systems, which can simultaneously consider all the influential variables including weather conditions, occupancy and dynamic electricity prices. Considering the on-line computational efficiency, a control-oriented dynamic thermal model for a room integrated with FH system is developed and represented in a stochastic state-space form. An economic MPC controller, formulated as a mixed integer linear programming problem, is designed for FH systems. A TRNSYS-MATLAB co-simulation testbed is developed to test and compare different control methods under various operating conditions in terms of energy consumption, thermal comfort and operating costs. Test results show that, compared to the conventional on-off controller, the MPC controller is able to use building thermal mass to optimally shift energy consumption to low-price periods, improve thermal comfort at the beginning of occupancy, reduce energy demand during peak periods, and save electricity costs for residential end-users. The weather conditions and electricity prices have influences on the start-up time and duration of preheating, energy flexibility potential and electricity cost savings of FH systems.

Distributed economic model predictive control of wastewater treatment plants

In this work, we consider the distributed economic model predictive control (EMPC) of a wastewater treatment plant described by Benchmark Simulation Model No. 1 and compare its performance with two commonly used control methods. The plant is decomposed into two subsystems based on the topology of the process, the requirement in our distributed control system design and the computational considerations. A local EMPC controller is designed for each subsystem. Two different designs are considered. In the first design, the centralized model is used in each subsystem EMPC controller design; and in the second design, a subsystem model is used in each subsystem EMPC design. The performance of these two distributed EMPC designs are compared with a centralized model predictive control (MPC) scheme and a centralized EMPC scheme from different aspects including effluent quality, operating cost, and computational efficiency. The simulation results demonstrate that the distributed EMPC with each subsystem EMPC controller designed based on the entire system model is more favourable in terms of control performance.

Hierarchical economic MPC for systems with storage states

Economic model predictive control (EMPC) differs from conventional tracking model predictive control by explicitly incorporating the plant economic cost into the stage cost. One particular class of systems of interest in the deployment of economic MPC are those containing storage devices such as microgrids and hybrid electric vehicles. Such systems may benefit from a two layer control architecture due to the wide range of time-scales that can be exhibited, with the first and second layers comprising a scheduling controller and the EMPC controller respectively. This, in turn, requires an alternative control system formulation since its structure differs from standard economic MPC.This paper proposes an EMPC control algorithm that is suitable for this particular two-layer problem. The proposed control algorithm ensures that feasibility is always maintained, even in the presence of a changing cost function. Existing EMPC theory is extended in order to prove stability of a set of economically optimal steady states, in a finite time setting. The proposed controller is then used in a simulation of a network connected, hybrid solar photovoltaic (PV) / battery system, and demonstrated to provide superior performance to standard EMPC.

Dynamic Modeling and Economic Model Predictive Control with Production Mode Switching for an Industrial Catalytic Naphtha Reforming Process

Catalytic naphtha reforming is a crucial process in producing gasoline or aromatic compounds. The characteristic of two production modes gives rise to different economic optimization and control objectives. In the present work, we design an economic model predictive control (EMPC) with a production mode switching strategy to cope with these problems. First, a rigorous dynamic process model is established to simulate the naphtha reforming process. Then, we formulate different economic objective functions and simplify the process model for each production mode, and also enable the EMPC controller to switch the production mode automatically according to empirical equations. Three case studies are presented to test the performance of our proposed control strategy. The results show that the designed EMPC controller with production mode switching can successfully overcome the economic disturbances and improve the production profits in different production modes. In addition, it also has a fast response time to ...

Robust Periodic Economic Predictive Control based on Interval Arithmetic for Water Distribution Networks

This paper addresses a robust periodic economic model predictive control (EMPC) based on interval arithmetic with unknown-but-bounded additive disturbances for the management of water distribution networks (WDNs). The system constraints in presence of system disturbances are tightened along the prediction horizon by means of the proposed interval arithmetic and considering that system variables in the WDN model are also subject to some algebraic equations. These algebraic equations should be satisfied when the disturbances have effects on those system variables. The EMPC controller is designed with adding the terminal state constraint. The periodically optimal steady states are obtained by employing a periodic EMPC planner with the nominal model. This periodic steady states are subsequently used to be terminal states. The on-line robust constraint satisfactions are implemented into the robust periodic EMPC controller. Finally, the proposed control strategy is verified using a case study.

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

This paper presents an application case study of an economic model predictive control (EMPC) method for optimizing the building demand and energy cost under the time-of-use price policy. The control strategy is comprised of an economic objective function that accounts for the combination of energy and demand costs with a time-of-use rate structure, a dynamic thermal process and power model of the building thermal mass dynamics, and a set of constraints to ensure the building is operated properly. The optimization is a min–max optimization problem and is converted to a linear program. The EMPC method is implemented in a commercial office building located in Milwaukee, Wisconsin, USA. An internet-based control architecture is developed to carry out tests with the EMPC controller at a remote location. The test results show that the EMPC strategy is capable of shifting the peak demand to off-peak hours and reducing energy costs compared to a baseline case for the building.

IGCC Power Plant Dispatch Using Infinite-Horizon Economic Model Predictive Control

The Integrated Gasification Combined Cycle (IGCC) possesses many benefits over traditional power generation plants, ranging from increased efficiency to flex-fuel and carbon capture opportunities. A lesser-known benefit of the IGCC configuration is the ability to load track electricity market demands. The idea being that process modifications to enable dispatch capabilities will allow for a time-shift of power production away from periods of low energy value to periods of high value. The work begins with an illustration of Economic Model Predictive Control (EMPC) as a vehicle to exploit dispatch capabilities by pursuing the objective of maximizing revenue directly. However, implementation of EMPC can result in unexpected and, at times, pathological closed-loop behavior, including inventory creep and bang–bang actuation. To address these issues, an infinite-horizon version of EMPC is developed and shown to avoid many of the performance issues observed in the finite-horizon version. The paper concludes with an in-depth discussion of energy value forecasting and how the quality of forecasts can be incorporated into the design of the infinite-horizon EMPC controller.