Stochastic Model Predictive Control Approach Research Articles

Optimal multi-layer economical schedule for coordinated multiple mode operation of wind–solar microgrids with hybrid energy storage systems

The aim of this paper is the design and implementation of an advanced model predictive control (MPC) strategy for the management of a wind–solar microgrid (MG) both in the islanded and grid-connected modes. The MG includes energy storage systems (ESSs) and interacts with external hydrogen and electricity consumers as an extra feature. The system participates in two different electricity markets, i.e., the daily and real-time markets, characterized by different time-scales. Thus, a high-layer control (HLC) and a low-layer control (LLC) are developed for the daily market and the real-time market, respectively. The sporadic characteristics of renewable energy sources and the variations in load demand are also briefly discussed by proposing a controller based on the stochastic MPC approach. Numerical simulations with real wind and solar generation profiles and spot prices show that the proposed controller optimally manages the ESSs, even when there is a deviation between the predicted scenario determined at the HLC and the real-time one managed by the LLC. Finally, the strategy is tested on a lab-scale MG set up at Khalifa University, Abu Dhabi, UAE.

Data-driven non-parametric chance-constrained model predictive control for microgrids energy management using small data batches

This paper presents a stochastic model predictive control approach combined with a time-series forecasting technique to tackle the problem of microgrid energy management in the face of uncertainty. The data-driven non-parametric chance constraint method is used to formulate chance constraints for stochastic model predictive control, while removing the dependency on probability density assumptions of uncertain variables and retaining the linear structure of the resulting optimization problem. The proposed approach is suitable for implementation on systems with limited computational power or limited memory storage, thanks to its simple linear structure and its ability to provide accurate results within pre-defined confidence levels, even when using small data batches. The proposed forecasting and stochastic model predictive control approaches are applied on a numerical example featuring a small grid-connected microgrid with PV generation, a battery storage system, and a non-controllable load, showing the ability to reduce costs by reducing the confidence level, and to satisfy pre-defined confidence levels.

Predictive Thermal Management for an Electric Vehicle Powertrain

The design of thermal management strategies for electric vehicle powertrains is an important task, since these strategies influence performance, energy consumption, safety and durability of the powertrain operation. In the present paper, a predictive thermal management strategy for the powertrain cooling system is developed. The aims are to minimize the energy consumption of the cooling system, to increase the efficiency of the electric motors and to operate them in a temperature area of safety and durability. The thermal management strategy is realized by a real-time capable nonlinear model predictive controller, incorporating a dynamical model for the powertrain of the battery electric vehicle under consideration. The usage of this model-based approach ensures a fast adaption of the control strategy to different vehicle architectures. Since predictions of the disturbances acting on the system are uncertain in general, the control strategy is extended by a stochastic model predictive control approach to handle uncertainties in the disturbance prediction. The effectiveness of the resulting strategies is demonstrated using an accurate simulation model. Special attention is given to the possible energy savings, the robustness with respect to uncertainties, as well as the computational effort of the algorithms.

Scenario-based model predictive control of water reservoir systems

The optimal operation of water reservoir systems is a challenging task involving multiple conflicting objectives. The main source of complexity is the presence of the water inflow, which acts as an exogenous, highly uncertain disturbance on the system. When model predictive control (MPC) is employed, the optimal water release is usually computed based on the (predicted) trajectory of the inflow. This choice may jeopardize the closed-loop performance when the actual inflow differs from its forecast. In this work, we consider - for the first time - a stochastic MPC approach for water reservoirs, in which the control is optimized based on a set of plausible future inflows directly generated from past data. Such a scenario-based MPC strategy allows the controller to be more cautious, counteracting droughty periods (e.g., the lake level going below the dry limit) while at the same time guaranteeing that the agricultural water demand is satisfied. The method's effectiveness is validated through extensive Monte Carlo tests using actual inflow data from Lake Como, Italy.

Robust model-predictive thermal control of lithium-ion batteries under drive cycle uncertainty

The exposure of electric vehicle batteries to rapid charging and discharging profiles, particularly under uncertainty in the drive schedules, requires effective strategies to forecast and avoid thermal excursions during operation. In this work, we present a light gradient boosting-based machine learning model to create probabilistic forecasts of the discharge current over a forecast horizon in real time. A surrogate of a physics-based computational model provides the functional relationship for the battery temperature, using which a stochastic model-predictive control strategy is developed to derive the optimal cooling schedule based on the probabilistic forecast. The effectiveness of the stochastic model-predictive control approach is assessed on the US06 driving cycle, in comparison to a constant coolant flow and persistence forecast-based control. It is shown that the total number of temperature excursion instances using the stochastic model-predictive control is reduced by about 69% compared to the constant coolant flow case and by over 51% compared to persistence-forecast-based control. Further, the total coolant usage is reduced by about 73% compared to persistence forecast-based control. The stochastic model-predictive control approach provides more flexibility by allowing a wider range of control and battery pack design parameters to obtain optimal performance with minimum coolant use.

A hybrid stochastic model predictive design approach for cooperative adaptive cruise control in connected vehicle applications

Wireless communication among connected and automated vehicles (CAVs) enables cooperative driving, particularly using cooperative adaptive cruise control, hence allowing CAVs to safely move closer to each other and improving traffic flow. However, reducing the gap between vehicles may cause collision, especially when a sudden deceleration in the vehicle platoon occurs. Furthermore, if some of the CAVs in the platoon lose communication, even for a short period, they may detect sudden changes in traffic with delay, and their reaction to avoid collision could be unsuccessful. Hence, an efficient emergency braking system can help preserve safety. This becomes even more important in high-speed driving, where a crash can put human lives in danger. This paper presents a discrete hybrid stochastic model predictive control approach to achieve a safe and efficient traffic system through CAV platooning. Three operational modes for vehicles are considered: free following, warning, and emergency braking. Each CAV in the free-following mode basically follows its preceding vehicle while enforcing maximum allowable deceleration in the emergency-braking mode. In the warning mode, the vehicle aims to slightly increase its headway and velocity difference from its predecessor to avoid possible danger. The warning/emergency-braking mode may be activated when the speed difference between a CAV and its preceding vehicle drops below a threshold. It is further assumed that vehicle distance sensing is subject to error. Each vehicle shares its current location, velocity, and future acceleration profile, calculated by solving a mixed-integer programming problem, with its follower vehicles. Simulation studies demonstrate the efficacy of the proposed control design approach compared to existing controllers in the literature in the presence of intermittent communication.

Long-term stochastic model predictive control for the energy management of hybrid electric vehicles using Pontryagin’s minimum principle and scenario-based optimization

This paper presents a new approach to efficiently integrate long prediction horizons subject to uncertainty into a stochastic model predictive control (MPC) framework for the energy management of hybrid electric vehicles. By exploiting Pontryagin’s minimum principle, we show that the energy supply required to obtain a certain change in the state of charge (SOC) of the battery can be approximated using a quadratic equation. The parameters of these mappings depend on the power request imposed by the driving mission and thus allow to compress the time-resolved power profile into only three scalar variables. Having a driving mission divided into several segments of arbitrary length, the corresponding sequence of quadratic approximations allows to reformulate the original energy management problem as a quadratic program, which offers an efficient way to include a large number of future scenarios. The resulting scenario-based stochastic MPC approach prevents SOC boundary violations with a certain probability, which can be controlled by the number of scenarios considered. To validate the quadratic approximation, we study two numerical examples using two different vehicles, a series hybrid electric passenger car and a battery-assisted trolley bus. Finally, a case study based on the operation of the latter is provided, which demonstrates the expected behavior and the real-time capability of the stochastic MPC approach. While the SOC is maintained in predefined boundaries with high probability, the required energy supply is only increased by 1.41% compared to the non-causal optimum.

Nonpharmaceutical Stochastic Optimal Control Strategies to Mitigate the COVID-19 Spread

This article proposes a stochastic nonlinear model predictive controller to support policymakers in determining robust optimal nonpharmaceutical strategies to tackle the COVID-19 pandemic waves. First, a time-varying SIRCQTHE epidemiological model is defined to get predictions on the pandemic dynamics. A stochastic model predictive control problem is then formulated to select the necessary control actions (i.e., restrictions on the mobility for different socioeconomic categories) to minimize the socioeconomic costs. In particular, considering the uncertainty characterizing this decision-making process, we ensure that the capacity of the healthcare system is not violated in accordance with a chance constraint approach. The effectiveness of the presented method in properly supporting the definition of diversified nonpharmaceutical strategies for tackling the COVID-19 spread is tested on the network of Italian regions using real data. The proposed approach can be easily extended to cope with other countries’ characteristics and different levels of the spatial scale. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the emerging need for developing effective methods to support policymakers in mitigating the effects of the COVID-19 pandemic. The proposed feedback control strategy—combining a multiregion epidemiological model with a nonlinear stochastic model predictive control approach—allows the robust identification of the most effective restrictive measures considering the corresponding effects on the healthcare and socioeconomic systems. The proposed framework is a general and flexible method that can be applied to various real scenarios, leveraging mobility data, available from the Google mobility service, to recognize patterns and predict future behaviors of individuals.

Control of Jump Markov Uncertain Linear Systems With General Probability Distributions

This paper introduces a method to control a class of jump Markov linear systems with uncertain initialization of the continuous state and affected by disturbances. Both types of uncertainties are modeled as stochastic processes with arbitrarily chosen probability distributions, for which however, the expected values and (co-)variances are known. The paper elaborates on the control task of steering the uncertain system into a target set by use of continuous controls, while chance constraints have to be satisfied for all possible state sequences of the Markov chain. The proposed approach uses a stochastic model predictive control approach on moving finite-time horizons with tailored constraints to achieve the control goal with prescribed confidence. Key steps of the procedure are (i) to over-approximate probabilistic reachable sets by use of the Chebyshev inequality, and (ii) to embed a tightened version of the original constraints into the optimization problem, in order to obtain a control strategy satisfying the specifications. Convergence of the probabilistic reachable sets is attained by suitable bounding of the state covariance matrices for arbitrary Markov chain sequences. The paper presents the main steps of the solution approach, discusses its properties, and illustrates the principle for a numeric example.

Online optimal dispatch based on combined robust and stochastic model predictive control for a microgrid including EV charging station

To achieve carbon neutrality and meet the increased charging demand of electric vehicles, microgrids incorporating renewable energy and charging stations are considered one of the potential solutions. However, the inevitable uncertainties of renewable energy and load demand become a challenge for the online charging dispatch of the microgrid. Considering these uncertainties, this paper proposes a two-stage optimal framework for the online dispatch of a grid-connected DC microgrid. The first stage presents a power coordination model to obtain the schedule plans of the main grid, the energy storage unit and the charging station, where the combined robust and stochastic model predictive control approach with different granular models is developed to solve this problem and effectively deal with these uncertainties. In the second stage, the charging station allocation model is designed to determine the charging power for every EV, which takes into account the max-min fairness of the charging power. Numerical cases in the presence of uncertainties are studied to evaluate the proposed dispatch framework and the solving approaches. The simulation results show its superiority in both computational efficiency and operating cost.

Stochastic model predictive control for driver assistance control of intelligent vehicles considering uncertain driving environment

Advanced driver assistance control faces great challenges in cooperating with the nearby vehicles. The assistance controller of an intelligent vehicle has to provide control efforts properly to prevent possible collisions without interfering with the drivers. This paper proposes a novel driver assistance control method for intelligent ground vehicles to cooperate with the nearby vehicles, using the stochastic model predictive control algorithm. The assistance controller is designed to correct the drivers’ steering maneuvers when there is a risk of possible collisions, so that the drivers are not interfered. To enhance the cooperation between the vehicles, the nearby vehicle motion is predicted and included in the assistance controller design. The position uncertainties of the nearby vehicle are considered by the stochastic model predictive control approach via chance constraints. Simulation studies are conducted to validate the proposed control method. The results show that the assistance controller can help the drivers avoid possible collisions with the nearby vehicles and the driving safety can be guaranteed.

Stochastic Model Predictive Control of Hybrid Energy Storage for Improving AGC Performance of Thermal Generators

In order to improve the automatic generation control (AGC) performance of thermal generators, this paper presents a stochastic model predictive control (SMPC) approach for a battery/flywheel hybrid energy storage system (HESS) to distribute power. The approach combines an adaptive Markov chain for power demand prediction of HESS, a scenario tree generation and model predictive control strategy. To develop an effective prediction model to deal with the randomness of a thermal generator in response to AGC command, a Markov chain is used to describe the randomness of the HESS power demand, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> information is used to adapt to the fluctuation of the AGC command. A scenario tree generation approach is proposed to make better use of the Markov probability matrix. Based on these efforts, an SMPC approach is proposed for HESS energy management. Simulation results show that the regulation performance of the proposed approach outperforms conventional approaches, and that its performance is close to the model predictive control strategy with prescient information of the future power demand. In addition, compared with other approaches such as rule-based strategies, it does less damage to the battery and yields higher annual average net benefits in the whole life cycle.

Fast Stochastic MPC Implementation via Policy Learning

Stochastic Model Predictive Control (MPC) gained popularity thanks to its capability of overcoming the conservativeness of robust approaches, at the expense of a higher computational demand. This represents a critical issue especially for sampling-based methods. In this work we propose a policy learning MPC approach, which aims at reducing the cost of solving stochastic optimization problems. The presented scheme relies upon the use of neural networks for identifying a mapping between the current state of the system and the probabilistic constraints. This allows to reduce the sample complexity to be less than or equal to the dimension of the decision variable, significantly scaling down the computational burden of stochastic MPC approaches, while preserving the same probabilistic guarantees. The efficacy of the proposed policy-learning MPC is proved by means of a numerical example.

Recursively Feasible Stochastic Predictive Control Using an Interpolating Initial State Constraint

We present a stochastic model predictive control (SMPC) framework for linear systems subject to possibly unbounded disturbances. State of the art SMPC approaches with closed-loop chance constraint satisfaction recursively initialize the nominal state based on the previously predicted nominal state or possibly the measured state under some case distinction. We improve these initialization strategies by allowing for a continuous optimization over the nominal initial state in an interpolation of these two extremes. The resulting SMPC scheme can be implemented as one standard quadratic program and is more flexible compared to state-of-the-art initialization strategies. As the main technical contribution, we show that the proposed SMPC framework also ensures closed-loop satisfaction of chance constraints and suitable performance bounds.

Two-Stage Energy Management for Energy Storage System by Using Stochastic Model Predictive Control Approach

There is a growing tendency for industrial consumers to invest in both photovoltaic (PV) and energy storage systems (ESSs) to meet their electricity requirements. However, the uncertainty of load demand and PV output brings great challenges for ESS operation. In this paper, a stochastic model predictive control (MPC) approach-based energy management strategy for ESSs is proposed. A non-parametric probabilistic prediction method embedded in time series correlation is adopted to describe the uncertainty of load demand and PV output. Then, a two-stage energy management model is proposed aiming at minimizing the total operation cost. The upper stage can generate an hourly operation strategy for ESSs, while the lower stage focuses on a more detailed minute-level operation strategy. The hourly operation strategy is also used as a basis to guide the ESS operation in the lower stage. Besides, a chance constraint was introduced to achieve a win–win solution between PV power consumption and electricity tariff, while the terminal value constraint of the capacity of ESSs to better cope with the uncertainty beyond the prediction time window. Finally, the numerical results showed that the proposed method can achieve an effective ESS energy management strategy.

Stochastic Model Predictive Control Approach to Autonomous Vehicle Lane Keeping

Stochastic Model Predictive Control Approach to Autonomous Vehicle Lane Keeping

Stochastic model predictive control for remanufacturing system management

Uncertainties in the quality, quantity, and operational time of used products pose a challenge to the management of remanufacturing systems. In addition, it becomes a necessity to optimize the operation of the remanufacturing system to balance the quality of products, remanufacturing efficiency, and service level. In this study, a stochastic discrete-time dynamical model is proposed to represent a remanufacturing system, where the relationship between the market satisfaction, inventory status, and operational actions is explicitly modeled. This includes production and inventory planning, resource allocation and acquisition. To handle uncertainties, a stochastic model predictive control approach is proposed to plan the actions that optimize the remanufacturing efficiency. Our results in the simulation examples show that: (a) without supplies, the remanufacturing system has better stability and robustness than a conventional manufacturing system with the same initial stocks; and (b) with insufficient initial stocks, the remanufacturing system demands fewer and more gradual supplies, thereby keeping the system stable. Finally, a sensitivity analysis is conducted for testing the performance of the remanufacturing system. By changing the operational action capacity, different state equilibria are discovered, which correspond to distinct system response characteristics. The study reveals notable managerial insights and effects of product commonality, demand patterns, and operational actions scheduling on the efficiency of the remanufacturing system.

Wind Power Smoothing With Energy Storage System: A Stochastic Model Predictive Control Approach

The utilization of energy storage system (ESS) is an effective method for dealing with the randomness and variability of wind power. Therefore, improving the coordination between ESS and wind power is a direction worthy of research. This study develops a two-layer stochastic model predictive control (SMPC) method for wind power smoothing on different time-scales. The proposed optimization framework smooths wind energy by adjusting the charge and discharge power of hybrid ESSs; moreover, it combines the SMPC approach and the chance constraints to address the uncertainties of wind energy. Furthermore, the previous states are taken into account, in addition to states within the rolling time horizon, to obtain optimal control of the hybrid ESSs, and capacity planning for hybrid ESSs is conducted simultaneously. The numerical results obtained through amplitude-frequency simulation comparison prove that the proposed method is superior to the conventional method in terms of minimizing the frequency fluctuation of wind power and the size of the ESS.

Scenario-Based Probabilistic Reachable Sets for Recursively Feasible Stochastic Model Predictive Control

This letter presents a stochastic model predictive control approach (MPC) for linear discrete-time systems subject to unbounded and correlated additive disturbance sequences, which makes use of the scenario approach for offline computation of probabilistic reachable sets. These sets are used in a tube-based MPC formulation, resulting in low computational requirements. Using a recently proposed MPC initialization scheme and nonlinear tube controllers, we provide recursive feasibility and closed-loop chance constraint satisfaction, as well as hard input constraint guarantees, which are typically challenging in tube-based formulations with unbounded noise. The approach is demonstrated in simulation for the control of an overhead crane system.

Uncertainty-resistant stochastic MPC approach for optimal operation of CHP microgrid

The combined heat and power (CHP) microgrid can work both effectively and efficiently to provide electric and thermal power when an appropriate schedule and control strategy is provided. This study proposes a stochastic model predictive control (MPC) framework to optimally schedule and control the CHP microgrid with large scale renewable energy sources. This CHP microgrid consists of fuel cell based CHP, wind turbines, PV generators, battery/thermal energy storage system (BESS/TESS), gas fired boilers and various types of electrical and thermal loads scheduled according to the demand response policy. A mixed integer linear programming based energy management model with uncertainty variables represented by typical scenarios is developed to coordinate the operation of the electrical subsystem and thermal subsystem. This energy management model is integrated into an MPC framework so that it can effectively utilize both forecasts and newly updated information with a rolling up mechanism to reduce the negative impacts introduced by uncertainties. Simulation results show that the approach proposed in this paper is more efficient when compared with an open loop based stochastic day-ahead programming (S-DA) strategy and a MPC strategy. In addition, the impacts of fuel cell capacity and TESS capacity on microgrid operations are investigated and discussed.