Stochastic Model Predictive Control Scheme Research Articles

Stochastic Model Predictive Control Based on Polynomial Chaos Expansion With Application to Wind Energy Conversion Systems

The wind energy conversion system (WECS) has a complex structure, and its state space model is highly nonlinear. Due to the random uncertainty of wind speed, it poses a huge challenge to achieve optimal control tasks and ensure the safe and stable operation of the system. Therefore, this article proposes a stochastic model predictive control strategy based on Polynomial Chaotic Expansion (PCE), which achieves the control tasks of MPPT and constant power regions in wind energy conversion systems. Firstly, a simple algorithm is proposed to obtain a set of basis functions that are suitable for the stochastic variable wind speed. Then, the obtained basis functions are used to propagate the uncertainty of the original uncertain differential equation of the wind energy conversion system through polynomial chaotic expansion. Combining the operating region and constraint conditions of the wind energy conversion system, the original stochastic uncertainty problem is transformed into a deterministic convex optimization problem. Using NREL 5MW wind turbine as the research object for simulation, the task of capturing maximum wind energy in MPPT area and tracking rated power points in constant power area was achieved. The experimental results show that the proposed control method can effectively improve the wind energy capture capability and achieve accurate tracking of output power to rated power.

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.

Stochastic model predictive control-based countermeasure methodology for satellites against indirect kinetic cyber-attacks

The objective of this paper is to provide a stochastic framework to optimally avoid collision between a maneuverable spacecraft and a space object or debris. The satellite collision can be caused through a cyber-attack on a satellite by colliding it with a considered strategic satellite. Consequently, it is highly imperative that critical operational space assets be provided with autonomous collision avoidance systems. The collision avoidance methodology proposed in this paper will reduce the collision probability to an acceptable level and protect the satellite against indirect kinetic cyber-attacks initiated by designing optimal collision avoidance maneuvers using a stochastic model predictive control strategy. The collision probability is estimated using the available historical Two-Line Elements of determined objects, and the model predictive control scheme guarantees the safety of the space close approaches. The proposed and developed collision-avoidance countermeasure methodology is numerically simulated for the collision case study between the Iridium-33 and the Cosmos-2251 satellites. The results demonstrate and illustrate the effectiveness, capabilities, and advantages of our proposed methodology in avoiding probable collisions due to indirect kinetic cyber-attacks.

Efficient and Simple Gaussian Process Supported Stochastic Model Predictive Control for Bioreactors using HILO-MPC

Model-based control of biotechnological processes is, in general, challenging. Often the processes are complex, nonlinear, and uncertain. Hence modeling tends to be complex and is often inaccurate. For this reason, non-model-based control strategies developed via fask, bench-scale, or pilot plant experiments are often applied in the biotechnology industry. Model-based control and optimization techniques can increase processes’ performance and automation level, thereby decreasing costs and guaranteeing the desired specifications. These rely on a model of the process to make predictions and optimize the inputs to the plant. To improve the quality of the models, it is often helpful to use combined first principle and data-driven models together in a hybrid modeling approach which increases the model prediction capabilities. The residual uncertainty of the hybrid model should be taken into account in the control level to satisfy the process specifications and constraints. This paper proposes to use a stochastic model predictive control scheme that exploits a hybrid, Gaussian processes-based model. We outline the effectiveness of the stochastic model-based approach in combination with a suitable Kalman filter for state estimation considering an example biotechnological process. Furthermore, we underline that appropriate tools exist that allow the simple application of such methods even for the novice user. To do so, we use an open-source Python package — HILO-MPC, which allows the simple yet efficient formulation and solution of machine learning-supported optimal control and estimation problems.

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.

Comparative assessment of alternative MPC strategies using real meteorological data and their enhancement for optimal utilization of flexibility-resources in buildings

Model predictive control (MPC) method shows superiority in enhancing system performance. But its actual performance in operation is hampered by forecast uncertainties. Different methods have been proposed to mitigate the impacts of these uncertainties, such as shrinking horizon MPC (SHMPC) and stochastic MPC (SMPC). However, the year-round performance of these methods has rarely been investigated, and little is known about their relative performance, particularly in utilization of building flexibility-resources. In this study, the year-round performance of conventional MPC (CMPC), SHMPC and SMPC strategies when used to optimize utilization of flexibility-resources in buildings with PV power generation and battery storage systems are compared using real-time optimal control (RTC) as the benchmark, and their enhancement is ultimately proposed. Forecast uncertainties are quantified based on real meteorological data. Different optimization horizon start times and shrinking intervals are tested. Results show that there is no one control strategy which is superior to the other strategies under all operating conditions. The SMPC strategy has a higher probability of achieving daily cost saving than CMPC and SHMPC strategies, but still has higher daily costs than the RTC strategy in the winter. Hybrid control strategies with proper control schemes implemented under different operating conditions are therefore recommended.

A Demand Response-Based Solution to Overloading in Underdeveloped Distribution Networks

This paper addresses the problem of overloading in power distribution networks, which stems from the transmission systems being incapable of delivering power from source to consumers during peak hours. This causes frequent power-outages (or blackouts), requiring the consumers to rely on alternative energy sources, e.g., Uninterrupted Power Supply (UPS) systems with batteries to meet their essential needs. This paper proposes a demand response (DR) framework to eliminate the problem of network overloading. The flexibility in the consumption of batteries and air conditioners (ACs) is exploited in the proposed framework. The operation of ACs is manipulated while maintaining occupant comfort, and the power flow from mains and batteries is scheduled based on an ensemble of demand forecast avoiding network overloading and consequent power-outages. The problem is modeled in an optimal control setting and solved using a stochastic model predictive control strategy, and a computationally effective method is also proposed to efficiently solve the underlying optimization problems. Towards the end, simulation results show the efficacy of the proposed framework to avoid overloading.

Comparative Assessment of Alternative Mpc Strategies Using Real Meteorological Data and Their Enhancement for Optimal Utilization of Flexibility-Resources in Buildings

Model predictive control (MPC) method shows superiority in enhancing system performance. But its actual performance in operation is hampered by forecast uncertainties. Different methods have been proposed to mitigate the impacts of these uncertainties, such as shrinking horizon MPC (SHMPC) and stochastic MPC (SMPC). However, the year-round performance of these methods has rarely been investigated, and there is little knowledge on their relative performance, particularly in optimal utilization of flexibility-resources in buildings. In this study, the year-round performance of conventional MPC (CMPC), SHMPC and SMPC strategies when used to optimize utilization of flexibility-resources in buildings are compared using real-time optimal control (RTC) as the benchmark, and their enhancement is ultimately proposed. Forecast uncertainties are quantified based on real meteorological data. Different optimization horizon start times and shrinking intervals are tested. Results show that there is no one control strategy which is superior to the other strategies under all operating conditions. The SMPC strategy has a higher probability of achieving daily cost saving than CMPC and SHMPC strategies, but still has higher daily costs than the RTC strategy in the winter. Hybrid control strategies with proper control schemes implemented under different operating conditions are therefore recommended.

An improved stochastic model predictive control operation strategy of integrated energy system based on a single-layer multi-timescale framework

Economy, robustness and computational efficiency are of paramount metrics for an operation strategy of an integrated energy system (IES). To achieve the trade-off of the three metrics, a multi-layer framework is extensively exploited in existing operation strategies. This work, however, proposes a single-layer multi-timescale framework which can coordinate different operation performances associated with various timescales simultaneously. Based on the framework, an improved stochastic model predictive control (SMPC) operation strategy is further developed by embedding the proposed framework into its prediction horizon. To solve the multi-timescale optimization of the improved SMPC, the constraints and cost function are presented in the multi-timescale form, and the supplied and demands are forecast by the least square support vector machine. A simulator of an IES is thereafter constructed to mimic real system and used to evaluate the performance of the proposed strategy by operation cost, accumulative error and computation time with respect to economy, robustness and computational efficiency, respectively. Finally, the improved SMPC strategy is compared with a traditional single-layer and a hierarchical strategy by a case study. The results show that the improved strategy has the best tradeoff performance aforementioned. The multi-timescale framework can be also integrated into other operation strategies.

Stochastic Model Predictive Control Based Reference Planning for Automated Open-Water Channels

A stochastic model predictive control scheme is developed within the context of planning water-level references for an automated channel. The references are provided as inputs to decentralized feedback controllers that regulate the capacity for gravity-fed supply of flow at points along the channel. An operational challenge is to comply with constraints on channel-flow and water-level transients in the automatic response to changes in the off-take flow load and water-level references. The proposed approach is to determine the reference inputs using a model of the channel dynamics that includes a forecast of off-take demand. Specifically, a structured probabilistic representation of the forecast is used to formualte a chance-constrained optimal control problem that is solved in a receding horizon fashion. A scenario-based approximation of this difficult optimal control problem is considered. The size of the approximating quadratic program scales with the prediction horizon and the number of water-level regulation points. But importantly, the size does not ultimately depend on the number of scenarios used to construct the approximation. Simulations and experimental results from an operational channel are presented to demonstrate the method.

Stochastic Predictive Energy Management of Multi-Microgrid Systems

Next-generation power systems will require innovative control strategies to exploit existing and potential capabilities of developing renewable-based microgrids. Cooperation of interconnected microgrids has been introduced recently as a promising solution to improve the operational and economic performance of distribution networks. In this paper, a hierarchical control structure is proposed for the integrated operation management of a multi-microgrid system. A central energy management entity at the highest control level is responsible for designing a reference trajectory for exchanging power between the multi-microgrid system and the main grid. At the second level, the local energy management system of individual microgrids adopts a two-stage stochastic model predictive control strategy to manage the local operation by following the scheduled power trajectories. An optimal solution strategy is then applied to the local controllers as operating set-points to be implemented in the system. To distribute the penalty costs resulted from any real-time power deviation systematically and fairly, a novel methodology based on the line flow sensitivity factors is proposed. Simulation and experimental analyses are carried out to evaluate the effectiveness of the proposed approach. According to the simulation results, by adopting the proposed operation management strategy, a reduction of about 47% in the average unplanned daily power exchange of the multi-microgrid system with the main grid can be achieved.

A stochastic optimal energy management strategy considering battery health for hybrid electric bus

The problem of battery health coupled with energy management brings a considerable challenge to the hybrid electric bus. To address this challenge, three contributions are made to realize optimal energy management control while prolonging battery life. First, a semi-empirical aging model of lithium iron phosphate battery is built and identified by the data fitting method, based on the battery cycling test. Besides, a severity factor map is constructed by employing the proposed aging model to characterize the relative aging of the battery under different operating conditions. Second, to make the driver demand torque more appropriate for statistical prediction, a Markov chain is formulated to predict driving behavior and also a stochastic vehicle mass estimation method is proposed to assist the prediction of required torque. Then, a stochastic multi-objective optimization problem is formulated by taking the severity factor map as a battery degradation criterion, where minimized battery degradation and fuel consumption can be simultaneously realized. Finally, a stochastic model predictive control strategy that considers battery health is established. Both simulation and hardware-in-loop tests are performed. The results demonstrate that fuel economy and battery degradation can be improved by 16.73% and 13.8% compared with rule-based strategy, respectively.

An Adaptive Stochastic Model Predictive Control Strategy for Plug-in Hybrid Electric Bus During Vehicle-Following Scenario

Vehicle-following operation is a typical scenario in the future intelligent transportation environment. Keeping a safe distance is the most important goal in the vehicle-following scenario. For a plug-in hybrid electric bus (PHEB) running in a specific urban route, the challenge will become how to realize the optimal power split in hybrid powertrain under the premise of maintaining driving safety. Considering the above issues, this paper proposes a stochastic model predictive control (SMPC) strategy for PHEBs during vehicle-following scenario. Firstly, Markov chain-based stochastic driving model is built using real-world bus driving condition data, which is applied to predict future demand torque over a finite receding horizon. And then, a sequential quadratic programming (SQP) algorithm is adopted to solve the rolling optimization problem. Meanwhile, brake specific fuel consumption and electric motor efficiency are fitted offline to match the SMPC strategy. Furthermore, a piecewise function is given to adjust the adaptive factor that balancing fuel economy and vehicle-following in the pre-set cost function. Finally, to verify the control performance of the proposed strategy, a nonlinear model predictive control strategy with dynamic programming optimization (DP-MPC) and a rule-based (RB) strategy are employed for comparison study. Results indicate that the proposed strategy is effectiveness to the given driving condition with excellent fuel economy and vehicle-following performance. Under the driving condition of Chongqing 303 bus line in China and China typical, the fuel consumption is reduced by 20.58% and 37.89% compared with RB strategy, respectively. It is closer to the fuel consumption reduction of 16.77% and 13.11 optimized by DP-MPC. Driving safety during vehicle-following also be demonstrated in the driving condition of Chongqing 303 bus line and China typical.

Model predictive control with traffic information-based driver’s torque demand prediction for diesel engines

This article addresses a real-time optimal control problem of diesel engines. A stochastic model predictive control scheme is presented for the torque control problem of diesel engines where the driver’s demand torque is predicted using traffic information, and the probability distribution is exploited to represent the stochastic characteristics in the driver’s behavior. It will be shown by the simulation validation that the proposed scheme achieves much better performance of emission and energy consumption.

A Two-Layer Stochastic Model Predictive Control Scheme for Microgrids

A two-layer control scheme based on model predictive control (MPC) operating at two different timescales is proposed for the energy management of a grid-connected microgrid (MG), including a battery, a microturbine, a photovoltaic (PV) system, a partially non predictable load, and the input from the electrical network. The high-level optimizer runs at a slow timescale, relies on a simplified model of the system, and is in charge of computing the nominal operating conditions for each MG component over a long time horizon, typically one day, with sampling period of 15 min, so as to optimize an economic performance index on the basis of available predictions for the PV generation and load request. The low-level controller runs at higher frequency, typically 1 min, relies on a stochastic MPC (sMPC) algorithm, and adjusts the MG operation to minimize the difference, over each interval of 15 min, between the planned energy exchange and the real one, so avoiding penalties. The sMPC method is implemented according to a shrinking horizon strategy and ensures probabilistic constraints satisfaction. Detailed models and simulations of the overall control system are presented.

A Stochastic Model Predictive Control Strategy for Extended Range Electric Vehicle

The Energy Management Strategy(EMS) of the Extended-Range Electric Bus (E_REB) plays an important role in the fuel economy and emission performance. This paper presents a Stochastic Model Predictive Control (SMPC) strategy based on Stochastic Dynamic Programming (SDP) and Model Predictive Control (MPC) for E_REB. SMPC applies Markov stochastic prediction model to predict the power demand of driving cycles, converts the SDP algorithm into the local optimization algorithm within the finite horizon, then the global suboptimal strategy can be obtained by solving a finite horizon optimization problem. SMPC can greatly save the online computation and operation time, achieve the goal of real-time online control. Simulation results of E_EVB are presented to demonstrate the effectiveness of the SMPC.

Exploitation of uncertain weather forecast data in power network management

Abstract: In power network management, the heat capacity of transmission lines originally arises from the line temperature constraint. The line temperatures are affected not only by the Joule heat but also by the thermal environment. This motivates us to exploit weather forecast data to improve the power management performance. The goal of this paper is to propose a stochastic model predictive control scheme for this purpose. In particular, we compensate for the probabilistic uncertainty by means of chance constraint optimization. The effectiveness of the proposed control scheme is examined through numerical simulation of power grids under the area dependent uncertainty and transmission line failure.

Modelling of coal trade process for the logistics enterprise and its optimisation with stochastic predictive control

In the paper, a typical coal trade process is described and modelled, where one logistics enterprise with blending equipments lies in the core and two types of common contracts are elucidated to define constraints. A mixed-integer model is built and featured by addressing contract violation, blending operation, real-time price information and arbitrarily distributed stochastic demands. To deal with the stochastic demands, probabilistic constraints are formed. Accordingly, stochastic model predictive control strategy with both receding horizon and decreasing horizon formulations is developed to handle the probabilistic constraints and exploit the value of newest price information. By solving a series of mixed-integer linear programmes, optimal coal trade decisions for the logistics enterprise can be obtained, including procurement decision, selling decision and operational decision of the blending equipments. Thorough simulation experiments are carried out and compared with three different strategies, which interpret the effectiveness of the proposed strategy.

A Stochastic Model Predictive Control Strategy for Energy Management of Series PHEV

Splitting power is a tricky problem for series plug-in hybrid electric vehicles (SPHEVs) for the multi-working modes of powertrain and the hard prediction of future power request of the vehicle. In this work, we present a methodology for splitting power for a battery pack and an auxiliary power unit (APU) in SPHEVs. The key steps in this methodology are (a) developing a hybrid automaton (HA) model to capture the power flows among the battery pack, the APU and a drive motor (b) forecasting a power request sequence through a Markov prediction model and the maximum likeli-hood estimation approach (c) formulating a constraint stochastic optimal control problem to minimize fuel consumption and at the same time guarantee the dynamic performance of the vehicle (d) solving the optimal control problem using the model predictive control technique and the YALMIP toolbox. Our simulation experimental results show that with our stochastic model predictive control strategy a series plug-in hybrid electric vehicle can save 1.544 L gasoline per 100 kilometers compared to another existing power splitting strategy.

Stochastic predictive control of battery energy storage for wind farm dispatching: Using probabilistic wind power forecasts

The limited dispatchability of wind energy poses a challenge to its increased penetration. One technically feasible solution to this challenge is to integrate a battery energy storage system (BESS) with a wind farm. This highlights the importance of a BESS control strategy. In view of this, a stochastic model predictive control scheme is proposed in this paper. Based on the forecasted wind power distributions, the proposed scheme ensures the optimal operation of BESS in the presence of practical system constraints, thus bringing the wind-battery combined power output to the desired dispatch levels. The salient feature of the proposed scheme is that it takes into account the non-Gaussian wind power uncertainties. In this scheme, a probabilistic wind power forecasting model is employed as the prediction model, which quantifies the non-Gaussian uncertainties in wind power forecasts. Using chance constraints, the quantified uncertainties are incorporated into the controller design, thus forming a chance constrained stochastic programming problem. Using warping function, this problem is recast as a convex quadratic optimization problem, which is tractable both theoretically and practically. This way, the proposed control scheme handles the non-Gaussian uncertainties in wind power forecasts. The simulation results on actual data demonstrate the effectiveness of the proposed scheme. The data used in the simulation are obtained in the real operation of a wind farm in China.