Economic Model Predictive Control Algorithm Research Articles

A Suboptimal Economic Model Predictive Control Algorithm for Large and Infrequent Disturbances

We present a suboptimal economic model predictive control (MPC) algorithm that combines the strengths of two common suboptimal MPC approaches, one based on a warm start and one based on an optimality gap. This algorithm is specifically designed to address a class of large and infrequent disturbances that are relevant when considering discrete actuators and production scheduling in control problems. We establish that this algorithm provides the same nominal performance guarantee as optimal economic MPC and is inherently robust, in an economic context, to large and infrequent disturbances. This inherent robustness guarantee is not attained by either individual algorithm. We conclude with a small production scheduling example to demonstrate the benefits of the proposed algorithm for a practical application.

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.

Approximate Dissipativity of Cost-Interconnected Systems in Distributed Economic MPC

We consider dissipativity properties of interconnected systems in the context of distributed economic model predictive control (MPC), with the subsystems being interconnected through their stage cost functions. The isolated subsystems, i.e., when neglecting the coupled portion of the individual stage costs, are assumed to be dissipative with respect to a specific supply rate related to their local stage cost function, which is commonly used in an economic MPC context. Based on these local dissipativity properties and the interconnection structure, a corresponding (approximate) dissipativity property for the overall system is inferred, which is structured and provides performance bounds for overall system operation. The resulting structured dissipativity property is exploited in the design and analysis of a distributed economic MPC algorithm. Numerical examples visualize the theoretical findings and the effectiveness of the proposed algorithm.

Adjoint optimisation for wind farm flow control with a free-vortex wake model

Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free-vortex methods can provide a computationally efficient way to model wind turbine wake dynamics for control optimisation. We present a control-oriented free-vortex wake model of a 2D and 3D actuator disc to represent wind turbine wakes. The novel derivation of the discrete adjoint equations allows efficient gradient evaluation for gradient-based optimisation in an economic model-predictive control algorithm. Initial results are presented for mean power maximisation in a two-turbine case study. An induction control signal is found using the 2D model that is roughly periodic and supports previous results on dynamic induction control to stimulate wake mixing. The 3D model formulation effectively models a curled wake under yaw misalignment. Under time-varying wind direction, the optimisation finds solutions demonstrating both wake steering and a smooth transition to greedy control. The free-vortex wake model with gradient information shows potential for efficient optimisation and provides a promising way to further explore dynamic wind farm flow control.

Fuel Economy-Oriented Vehicle Platoon Control Using Economic Model Predictive Control

Vehicle platoon control based on vehicle-to-vehicle (V2V) communication is one of the promising technologies to improve the performance of transportation systems. This paper presents a distributed controller to optimize a vehicle platoon’s fuel consumption by combining the switching feedback control and economic model predictive control (EMPC) methods. The closed-loop dynamics involving switching feedback gains with the constant time headway (CTH) policy are established firstly, and the multiple-predecessor following (MPF) communication topology is considered. In order to obtain the economy optimal feedback gain, we design a local optimal control problem for each vehicle, based on which the average dwell time is defined and the distributed EMPC algorithm is designed. Based on linear matrix inequalities (LMIs) and the Lyapunov theorem, the feedback gain selection method and the lower bound for average dwell time that guarantees asymptotic stability are analyzed rigorously. Then a modified algorithm that can ensure string stability is designed. Numerical simulations show a maximum of 6.84% fuel benefit compared with pure tracking-oriented methods.

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.

Periodically time-varying economic model predictive control with applications to nonlinear continuous stirred tank reactors

The economic cost functions can be periodically time-varying due to various economic factors such as the variations of product prices, energy consumptions, operating costs and customer demand changes. These time-varying parameters can lead to instability because the optimal steady state may not be asymptotically stable. In this paper, a periodically time-varying economic model predictive control algorithm is proposed. As the time-varying parameters in the economic cost functions vary, the average constraints are used to enforce the convergence without modifying the original economic cost functions so the transient economic performance can be improved. The time-varying terminal regions are included in the economic optimization problem in order to ensure recursive feasibility. The asymptotic convergence is proved by using the Lyapunov-like analysis. The developed predictive control algorithm is applied to the nonlinear continuous stirred tank reactors in order to gain the highest economic profits.

Control of an isolated microgrid using hierarchical economic model predictive control

This article experimentally demonstrates a novel, microgrid control algorithm based on a two-layer economic model predictive control framework that was previously developed by the authors. This algorithm is applied to an isolated microgrid with a solar photovoltaic system, a battery bank and a gasoline-fuelled generator. The control system performance is experimentally compared to a baseline algorithm over 5 min and 10 h periods, while an experimentally validated model is used to compare performance over a full year. The results indicate that applying the proposed, two-layer economic model predictive control algorithm can reduce operating costs and CO2 emissions by 5%–10% relative to conventional, rule based methods, and by 10%–15% if improved solar and demand forecasts are available. Furthermore, the proposed two-level algorithm can achieve reductions of up to 5% compared with current state-of-the-art methods which only attempt to optimize performance in the energy management system.

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.

Homothetic tube-based robust offset-free economic Model Predictive Control

This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system’s state is augmented with disturbances and transformed into a new coordinate framework. Based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved. The proposed controller is demonstrated on a two-tanks system.

Efficient and Risk-Aware Control of Electricity Distribution Grids

This article presents an economic model predictive control (EMPC) algorithm for reducing losses and increasing the resilience of medium-voltage electricity distribution grids characterized by high penetration of renewable energy sources and possibly subject to natural or malicious adverse events. The proposed control system optimizes grid operations through network reconfiguration, control of distributed energy storage systems (ESSs), and on-load tap changers. The core of the EMPC algorithm is a nonconvex optimization problem integrating the ESSs dynamics, the topological and power technical constraints of the grid, and the modeling of the cascading effects of potential adverse events. An equivalent (i.e., having the same optimal solution) proxy of the nonconvex problem is proposed to make the solution more tractable. Simulations performed on a 16-bus test distribution network validate the proposed control strategy.

Optimal Strategy to Exploit the Flexibility of an Electric Vehicle Charging Station

The increasing use of electric vehicles connected to the power grid gives rise to challenges in the vehicle charging coordination, cost management, and provision of potential services to the grid. Scheduling of the power in an electric vehicle charging station is a quite challenging task, considering time-variant prices, customers with different charging time preferences, and the impact on the grid operations. The latter aspect can be addressed by exploiting the vehicle charging flexibility. In this article, a specific definition of flexibility to be used for an electric vehicle charging station is provided. Two optimal charging strategies are then proposed and evaluated, with the purpose of determining which strategy can offer spinning reserve services to the electrical grid, reducing at the same time the operation costs of the charging station. These strategies are based on a novel formulation of an economic model predictive control algorithm, aimed at minimising the charging station operation cost, and on a novel formulation of the flexibility capacity maximisation, while reducing the operation costs. These formulations incorporate the uncertainty in the arrival time and state of charge of the electric vehicles at their arrival. Both strategies lead to a considerable reduction of the costs with respect to a simple minimum time charging strategy, taken as the benchmark. In particular, the strategy that also accounts for flexibility maximisation emerges as a new tool for maintaining the grid balance giving cost savings to the charging stations.

Economic Model Predictive Control of Sampled-Data Linear Systems With Piecewise Constant Control

Abstract The paper studies an economic model predictive control (EMPC) problem for sampled-data linear systems with system constraints. The cost function consists of an economic part and a regulatory part, and a new EMPC algorithm with piecewise constant control is designed. Iterative feasibility of the designed optimization problem and input-to-state stability (ISS) of the closed-loop system are proved. In particular, we show that the closed-loop system is input-to-state stable with respect to the supremum norm of the economic cost, and the system state is ultimately bounded within a bound determined by the economic cost. Through thorough simulations, the effectiveness of the designed algorithm is verified and the tradeoff between control and economic performance is demonstrated.

Cooperation-Based Distributed Economic MPC for Economic Load Dispatch and Load Frequency Control of Interconnected Power Systems

In this letter, a distributed economic model predictive control (EMPC) strategy is proposed for economic load dispatch and load frequency control of interconnected power systems. A general economic cost function is used in the EMPC to calculate the control sequence directly optimizes the economic performance of the system without using a hierarchical control structure, thus achieving both the real-time optimization and transient optimization. A cooperation-based distributed EMPC algorithm is proposed and the asymptotic stability is proven. Simulation results reveal the advantages of the proposed method.

Mode‐based energy storage control approach for residential photovoltaic systems

This study presents a novel mode-based energy storage control approach. Assuming that an energy storage device (ESD) is equipped with a set of predetermined real-time control modes, the dispatch objective is to select an optimal mode instead of a continuous charging or discharging power value. A two-stage algorithm is developed for mode selection. In the first stage, a sliding 24 h economic model predictive control algorithm is used to determine the power outputs of the ESD for the next 24 h. In the second stage, the output sign for the next time step determines the class of modes to be elected (charging or discharging). The information from the first stage is used to compute the total cost for each selected mode. The mode with the lowest day-ahead cost is chosen. The residential electricity consumption data collected in the PECAN Street Project is used in the simulation to validate the performance of the proposed algorithm. Simulation results show that using a mode-based approach reduces the sensitivity to forecasting errors along with load and solar variability. The algorithm performance is consistent across different load patterns.

Implementation of an economic MPC with robustly optimal steady-state behavior

Designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance in presence of plant-model mismatch is still an open problem. Starting from previous work, we elaborate an EMPC algorithm using the offset-free formulation from tracking MPC algorithms in combination with modifier-adaptation technique from the real-time optimization (RTO) field. The augmented state used for offset-free design is estimated using a Moving Horizon Estimator formulation, and we also propose a method to estimate the required plant steady-state gradients using a subspace identification algorithm. Then, we show how the proposed formulation behaves on a simple illustrative example.

Economic model predictive control of chemical processes with parameter uncertainty

Abstract This work proposes an EMPC (Economic Model Predictive Control) algorithm that integrates RTO (Real Time Optimization) and EMPC objectives within a single optimization calculation. Robust stability conditions are enforced on line through a set of constraints within the optimization problem. A particular feature of this algorithm is that it constantly calculates a set point with respect to which stability is ensured by the aforementioned constraints while searching for economic optimality over the horizon. In contrast to other algorithms reported in the literature, the proposed algorithm does not require terminal constraints or penalty terms on deviations from fixed set points that may lead to conservatism. Changes in model parameters over time are also compensated for through parameter updating. The latter is accomplished by including the parameters’ values as additional decision variables within the optimization problem. Several case studies are presented to demonstrate the algorithm’s performance.

Economic MPC with Terminal Cost and Application to Oilsand Separation

In this work, a novel approach to construct the terminal cost for economic model predictive control (EMPC) is developed. In the proposed approach, an auxiliary nonlinear controller which renders the desired optimal steady state asymptotically stable is taken advantage of. The proposed terminal cost is constructed such that it reflects the economic performance of the auxiliary controller over sufficiently large but finite steps. The proposed EMPC design provides guaranteed closed-loop economic performance which does not depend on the length of the prediction horizon. This means that the proposed EMPC algorithm could be very computationally efficient. The proposed EMPC algorithm is applied to an oilsand primary separation vessel. The simulation results demonstrate the effectiveness of the proposed approach.

Transient average constraints in economic model predictive control

In this paper, an economic model predictive control algorithm is proposed which ensures satisfaction of transient average constraints, i.e., constraints on input and state variables averaged over some finite time period. We believe that this stricter form of average constraints (compared to previously proposed asymptotic average constraints) is of independent interest in various applications such as the operation of a chemical reactor, where e.g. the amount of inflow or the heat flux during some fixed period of time must not exceed a certain value. Besides guaranteeing fulfillment of transient average constraints for the closed-loop system, we show that closed-loop average performance bounds and convergence results established in the setting of asymptotic average constraints also hold in case of transient average constraints. Furthermore, we illustrate our results with a chemical reactor example.