Economic Model Predictive Control Research Articles

Data-driven economic MPC with asymptotic stability and strong duality verification using Hankel matrix

We consider the problem of dynamic regulation with an economic cost function to control unknown linear systems, in which improving the economic performance and guaranteeing the stability of economical optimal equilibrium point are control objectives. A data-driven economic MPC scheme is presented using measured input-output trajectories without a prior system identification step. Our method uses Hankel matrices which include one input-output data trajectory for prediction in economic MPC, while persistently exciting of the input generating the data is needed. One of the novelties of the presented framework is directly verifying the strong duality property from input-output trajectory with the general cost function, considered as the supply rate. This is used to find a Lyapunov function for data-driven economic MPC. Under the strong duality assumption, asymptotic stability of the economical optimal equilibrium point for the closed-loop system with terminal equality constraint is guaranteed. The proposed data-driven economic MPC approach needs only persistently exciting data trajectory along with an upper bound on the system order and need no model description and no online parameter estimation. The proposed scheme applicability compared to the existing model-based economic MPC and data-driven MPC is illustrated for continuous stirred tank reactor (CSTR) and a numerical example and the robustness of the proposed scheme is evaluated in the case of measurement noise, as well as nonlinear model for CSTR system.

A novel two-stage multi-objective dispatch model for a distributed hybrid CCHP system considering source-load fluctuations mitigation

Small-scale distributed energy systems with combined cooling, heating, and power (DES-CCHP) production have attracted international interest. However, fluctuating loads and renewable energies continuously disturb the real-time operation of DES-CCHP and even the connected grid, hindering the broad application of grid-connected DES-CCHP. In this paper, a novel model predictive control (MPC) based two-stage strategy is developed for DES-CCHP, with multiple timescales consideration. In the first stage, a multi-objective MPC is built with inheritance and fusion mechanisms of multi-step scheduling instructions, simultaneously minimizing operation costs and power fluctuations. The second stage performs intelligent decision-making on the results of the first stage, which allows appropriate state-switching instructions to ensure economy. Meanwhile, the decision-making rejects the unnecessary one and triggers a second-round flexibility-based interventional optimization to revise scheduling planning. The case studies show that compared to dispatch without MPC, the economic single-objective MPC, single-stage multi-objective MPC (only applies the first-stage models), and two-stage multi-objective MPC save costs by 5.31 %, 4.80 %, and 4.57 %, respectively. As for fluctuations mitigation, the single-stage and two-stage models significantly smooth power fluctuations by 51.66 % and 69.93 %, respectively. The proposed strategy operates DES-CCHP economically, stably, and grid-friendly under a rugged operating environment.

Two‐layer dynamic economic nonlinear model predictive control for a Lithium‐ion battery charge process with random disturbances

AbstractThe charging process of lithium‐ion batteries is necessary for normal operation, and improper lithium‐ion battery charging strategy can cause side reactions, significant temperature rise, performance degradation, and safety concerns. This paper proposes a two‐layer dynamic economic nonlinear model predictive control economic model predictive control (EMPC) method for lithium‐ion battery charge management in which the non‐Gaussian random noise of voltage and current signal are taken into account. In the two‐layer EMPC, the upper layer finds the optimal reference trajectory, and the power in the future prediction horizon is chosen as an economic indicator to optimize the upper layer. The lower layer tracks the optimal trajectory, and model predictive control based on generalized correntropy is used. The economic cost of the system and the dynamic changes of the process are considered to greatly reduce the computational complexity and realize rapid battery charge management. Finally, the simulation results show that the tracking error of the two‐layer EMPC method based on generalized correntropy is stable around 0, while the tracking error of the two‐layer EMPC method based on MSE is stable around 0.003. The average control action times of the proposed two‐layer EMPC and single‐layer EMPC are 0.0052 and 0.0267 s, respectively. It is verified that the proposed method performs better for the lithium‐ion battery charging process with random disturbances.

Modeling and economic model predictive control of constrained cutterhead system with disturbance in tunnel boring machines

Tunnel boring machines (TBMs) are usually the first choice for tunneling construction with its advantages on high safety, time saving, and less operators. Cutterhead system is an important component for TBMs since it is used to excavate rocks and soil. It is difficult to guarantee both the boring efficiency and energy saving under the excavating rock disturbances and the constraints on the driving motors in TBMs by manual operation. To deal with this problem, it is necessary to develop advanced control algorithms for the cutterhead system. Thus, we investigate an economic model predictive control (EMPC) structure for cutterhead system in TBMs. A generalized nonlinear dynamic model of TBM cutterhead system is built based on the first principle method. An economic cost is constructed with the boring efficiency and energy cost to evaluate the tunnel construction quality. EMPC algorithms are designed to optimize the constructed economic cost for a cutterhead system to guarantee good economic performance. It is shown that EMPC can improve the economic performance of the cutterhead system.

Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition

Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC problems requires the computationally efficient online solution of mixed integer optimization problems, which are generally difficult to solve. In this paper, we propose a machine learning-based branch and check Generalized Benders Decomposition algorithm for the efficient solution of such problems. We use machine learning to approximate the effect of the complicating variables on the subproblem by approximating the Benders cuts without solving the subproblem, therefore, alleviating the need to solve the subproblem multiple times. The proposed approach is applied to a mixed integer economic MPC case study on the operation of chemical processes. We show that the proposed algorithm always finds feasible solutions to the optimization problem, given that the mixed integer MPC problem is feasible, and leads to a significant reduction in solution time (up to 97% or 50×) while incurring small error (in the order of 1%) compared to the application of standard and accelerated Generalized Benders Decomposition.

Stochastic economic model predictive control for renewable energy and ancillary services trading with storage

The provision of renewable-based ancillary services (AS) is paramount for the stable operation of power systems featuring high renewable penetration. The combined operation of storage with renewables enables aggregators to increase the reliability of their energy and frequency control AS offers. Existing dispatch strategies for the supply of both energy and AS are usually rule-based or involve tracking a technical reference signal, hence economically suboptimal for aggregators. This study proposes a comprehensive decision framework in which first a stochastic optimization derives bids on energy and AS markets, then stochastic economic model predictive control (SEMPC) optimizes the storage dispatch in order to maximize the profit and minimize the storage degradation, as a function of the predicted renewable production and the expected AS activation. The framework is applied to a real-world case study where storage combined with wind power participates in the energy market, the frequency containment market and the frequency restoration reserve market. The SEMPC-based approach increases market revenue by 15% compared to a standard reference-tracking MPC, and reduces storage degradation by 23%. The stochastic formulation lowers the sensitivity of the economic objectives to renewable energy forecast errors, compared to deterministic approaches.

Economically optimal operation of recirculating aquaculture systems under uncertainty

This study presents a novel economical operation scheme for recirculating aquaculture systems (RASs). The proposed approach is comprised of a moving horizon estimator and an economic model predictive controller (EMPC), which, respectively, provide the necessary feedback for the EMPC and make economically optimal decisions for the RAS. The scheme is enabled by a mechanistic RAS model, which is coupled with an objective function that jointly optimizes the economics of aquatic biomass growth and utility expenditure. The proposed scheme is tested on a rainbow trout case study, whereby it is compared against the previous state-of-the-art control approach in aerator failure and temperature disturbance scenarios. In both test scenarios, EMPC scheme outperforms the previous state state-of-the-art controller in terms of process economics (up to 41% improvement) as well as shorter batch times (up to 22% shortening). Furthermore, the scheme is shown to be capable of estimating uncertain parameters with little error (generally in the order of 5%) and negligible effect on economic performance when compared to cases with full measurement access and no uncertainty. The proposed scheme provides a new and automated way to ensure RASs operate with maximal productivity, thus further incentivizing sustainability and the uptake of this technology.

Dynamic wind farm flow control using free-vortex wake models

Abstract. A novel dynamic economic model-predictive control strategy is presented that improves wind farm power production and reduces the additional demands of wake steering on yaw actuation when compared to an industry state-of-the-art reference controller. The novel controller takes a distributed approach to yaw control optimisation using a free-vortex wake model. An actuator-disc representation of the wind turbine is employed and adapted to the wind farm scale by modelling secondary effects of wake steering and connecting individual turbines through a directed graph network. The economic model-predictive control problem is solved on a receding horizon using gradient-based optimisation, demonstrating sufficient performance for realising real-time control. The novel controller is tested in a large-eddy simulation environment and compared against a state-of-the-art look-up table approach based on steady-state model optimisation and an extension with wind direction preview. Under realistic variations in wind direction and wind speed, the preview-enabled look-up table controller yielded the largest gains in power production. The novel controller based on the free-vortex wake produced smaller gains in these conditions while yielding more power under large changes in wind direction. Additionally, the novel controller demonstrated potential for a substantial reduction in yaw actuator usage.

Direct learning of improved control policies from historical plant data

The continuous optimization of the operational performance of chemical plants is of fundamental importance. This research proposes a method that utilizes policy-constrained offline reinforcement learning to learn improved control policies from abundant historical plant data available in industrial settings. As a case study, historical data is generated from a nonlinear chemical system controlled by an economic model predictive controller (EMPC). However, the method’s principles are broadly applicable. Theoretically, it is demonstrated that the learning-based controller inherits stability guarantees from the baseline EMPC. Experimentally, we validate that our method enhances the optimality of the baseline controller while preserving stability, improving the baseline policy by 1% to 20%. The results of this study offer a promising direction for the general improvement of advanced control systems, both data-informed and stability-guaranteed.

Effects on district heating networks by introducing demand side economic model predictive control

Using economic model predictive control in space heating systems, the heat demand can flexibly be adapted to varying scenarios of conflicting objectives such as thermal comfort, energy consumption, and peak demand. With a controller that minimizes the heating costs subject to thermal comfort constraints within occupancy hours, the resulting heat demand will depend on the cost mechanism. In the context of Swedish district heating networks, optimal demand side control is a multi-objective problem due to variable costs based on both energy consumption and peak demand. By simulating heat demand control using a gray-box model estimated from a Swedish space heating system, we investigate how the established price structures influence the heat load of a population of buildings with economic model predictive control. Our results suggest that by adjusting the incentives from the type of price structures commonly used today, the peak demand can often be reduced by 10-20% with a minor increase in consumption of 1-2%. We also show that by charging the peak demand for multiple buildings collectively, it is financially beneficial to cooperatively control buildings which can reduce the combined consumption and peak demand even further.

Economic model predictive control for packed bed chemical looping combustion

This study presents an economic model predictive control (EMPC) scheme for the packed-bed reactor (PBR) design of a chemical looping combustion (CLC) system. This scheme is enabled by a pseudo-homogeneous process model, which accurately represents the macroscopic process behaviour, and enables economics to be optimized online. Both CLC stages are optimized whereby the oxidation stage considers energy generation and inert gas use, while the reduction stage economizes CO2 production and fuel use. To understand the behaviour of the EMPC, the scheme is tested on a CLC plant represented by a multi-scale process model. Both stages are tested under varying initial inlets, energy prices, carbon prices, and fuel prices. The optimal policy for the oxidation stage is found to be that of maximal peak temperature, where the EMPC results in revenue while a standard NMPC controller may result in losses. The optimal reduction stage behaviour is highly dependent on carbon and fuel prices whereby a trade-off between CO2 selectivity and throughput are observed. The EMPC approach is found to be economically superior to advanced regulatory control with up to an order-of-magnitude and ∼33% economic improvements in the oxidation and reduction stages, respectively. This study represents a step forward towards the adoption of the intensified PBR CLC process as an emerging and viable technology for heat generation with inherent CO2 capture.

Improving Efficiency Under Safety Constraints for Drilling Process Optimization Using Economic Model Predictive Control With Zone Tracking

Improving Efficiency Under Safety Constraints for Drilling Process Optimization Using Economic Model Predictive Control With Zone Tracking

Distributed Economic MPC for Synergetic Regulation of the Voltage of an Island DC Micro-Grid

Distributed Economic MPC for Synergetic Regulation of the Voltage of an Island DC Micro-Grid

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.

A two-level MPC method for the operation of a gas pipeline system under demand variation

A gas pipeline system is in an almost continual state of transition due to changing gas demand. A control method is required to keep a gas pipeline operating in an energy-saving status and provide reliable transmission service for the customers. Model predictive control (MPC) predicts the future states of a system, making it suitable for following gas demand changes. However, to avoid computation time challenges associated with formulating the MPC problem as a large-scale MINLP, an online two-level MPC system is proposed, comprising an upper-level economic MPC (EMPC) and a lower-level tracking MPC (TMPC). EMPC adopts energy cost as the objective function and utilizes a simplified nonlinear model to address long-horizon optimization, while TMPC tracks the status optimized in EMPC, to find the optimal output pressure and the on-off status of the compressors and compressor stations. The performance of the method is demonstrated through application to case studies.

Efficient management of HVAC systems through coordinated operation of parallel chiller units: An economic predictive control approach

In developed countries, air conditioning systems have become major contributors to energy consumption in buildings. Cooling installations made up of independent chiller units connected in parallel pose a challenge in finding the most energy-efficient management strategy. This article proposes a novel economic model predictive control strategy to optimize the operation of multiple-chiller HVAC systems according to an economic cost comprising energy consumption as well as a thermal comfort index. Provided that the gradient of the economic cost function can be calculated or estimated, the proposed controller only entails the solution of a single quadratic programming (QP) problem at each sampling period, reducing computational requirements and thus facilitating the deployment on commercial embedded HVAC management platforms. The proposed controller improves economic performance. As our numerical analysis shows, optimal sequencing is achieved for the case of dual-chiller plants. Moreover, the controller adapts to possible variations in the economic criteria, enabling the system to respond to changes in electricity price and user preferences. A realistic case study, using a high fidelity model of a building simulated in TRNSYS, demonstrates the effectiveness of the proposed methodology. In particular, the proposed controller demonstrates to be more efficient than state-of-the-art QP-based economic predictive controllers in achieving a reduction of the energy consumption up to 5.19%, which is in line with the targeted reduction of 7.9% by 2030 in the EU Green Deal's ‘Fit for 55’ package.

Economic Model Predictive Control in Buildings Based on Piecewise Linear Approximation of Predicted Mean Vote Index

Energy shortage is a challenge for many countries, and building energy consumption accounts for a considerable proportion of global energy consumption. The main work of this paper is to optimize the energy consumption of heating, ventilating, and air conditioning (HVAC) systems in buildings based on economic model predictive control (EMPC). The cost in EMPC design includes energy consumption and predicted mean vote (PMV), which is an index that evaluates the thermal comfort of indoor occupants. In order to model the nonlinearity of the PMV index, we propose a lattice piecewise linear (PWL) approximation, which has high approximation precision and facilitates the resulting optimization problem, which is basically a piecewise quadratic programming problem. For the piecewise quadratic programming, we propose a descent algorithm that converges quickly and scales well with the length of the prediction horizon in the EMPC problem. The experimental results demonstrate that the proposed method saves 19.78% of the electricity cost compared to the conventional control strategy and significantly increases indoor comfort. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> — The motivation of this article is to provide a control strategy to reduce building energy consumption and ensure indoor thermal comfort. In most of the existing methods for air conditioning temperature control, the occupants’ comfort hasn’t been considered. In this paper, thermal comfort is described by the PMV index, which is basically nonlinear. In order to model the thermal comfort more accurately, in this paper, the PMV index is approximated piecewise linearly in order to meet the requirements of accuracy and computational efficiency. The resulting optimization problem is not hard to solve, and we provide an efficient algorithm for solving this optimization problem. Preliminary simulation experiments demonstrate that this approach is practical, i.e., it achieves energy reduction and ensures thermal comfort. Our strategy, however, has not yet been deployed in real buildings. In future research, we will propose similar techniques for large-scale systems in order to solve energy optimization problems containing multiple thermal zones and realize the proposed technique in real buildings.

Economic Model Predictive Control for Microgrid Optimization: A Review

Microgrids have emerged as a promising solution to integrate distributed energy resources (DERs) and supply reliable and efficient electricity. The operation of a microgrid involves the coordination of different DERs and loads. To date, various control methods have been developed to maximize the overall benefit while satisfying various constraints. Now it is urgently needed to understand and comprehend these approaches to further stimulate the deployment of microgrids. This paper presents an overview for researchers on economic model predictive control (EMPC) methods of microgrids to achieve a variety of objectives such as cost minimization and benefit maximization. The fundamental principle of the EMPC theory is explained in detail. The most popular and important strategies applied to stand-alone microgrids, grid-connected microgrids, residential smart homes, as well as networked microgrids are discussed. Future trends are also highlighted.

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.

PV/Hydrogen DC microgrid control using distributed economic model predictive control

The integration of hydrogen energy into a photovoltaic-dominated microgrid is now becoming a promising approach to improve the photoconversion efficiency and enhance the operating reliability. However, the energy management and power regulation of the Photovoltaic/Hydrogen DC microgrid face challenges due to the intermittency of photovoltaic (PV) power generation and the randomness of load. In this paper, a distributed economic model predictive control (DEMPC) scheme is developed for a PV/Hydrogen DC microgrid, which integrates the energy management, economic optimization, and power regulation into one optimal control framework. Based on the developed distributed converter-based mathematical model, three local controllers are designed to achieve the economic targets of PV subsystem, alkaline electrolyzer subsystem, and proton exchange membrane fuel cell subsystem respectively, which cooperate with each other through the communication network to realize the power supply–demand balance, DC bus voltage stability, and economic optimization. A mixed integer nonlinear programming algorithm utilizing the finite converter switching states is embedded into the DEMPC to solve the non-convex local optimization problems efficiently. The effectiveness and superiority of the proposed DEMPC scheme are verified by simulations under varying irradiance and load conditions, indicating that the DEMPC can achieve a comparable overall dynamic economic performance with a significantly reduced computation burden and power oscillation, compared to the centralized economic model predictive control (CEMPC).