Stochastic Model Predictive Control Research Articles

Hierarchical-stochastic model predictive control for a grid-interactive multi-zone residential building with distributed energy resources

Using Model Predictive Control (MPC) is a promising method for enabling grid-interactive efficient buildings. Since MPC relies on a building model and the forecasts of external disturbances to derive optimal inputs, the uncertainties due to forecast errors and model inaccuracies can deteriorate the control performance. Most existing MPC studies for the built environment are deterministic MPC without consideration of uncertainties even though several different methods (e.g., stochastic MPC) are available in the literature to deal with them. Even studies that consider forecast uncertainties often neglect model inaccuracies. Hence, in the present paper, a novel hierarchical-stochastic MPC is proposed considering forecast uncertainties and model inaccuracies, and its performance is compared with deterministic, stochastic, and hierarchical MPC for power management in a residential building with distributed energy resources. The control objective is the cost-optimal scheduling of a heat pump, a battery for energy storage, and a rooftop photovoltaic system. Measurement data is used to identify the building model. The results for one-week simulation in winter show that (1) the deterministic MPC results in an unacceptable level of temperature constraint violations in two out of five rooms; (2) the hierarchical MPC can reduce the temperature constraint violations to an acceptable level at the expense of increased cost; (3) the stochastic MPC achieves the same reduction in temperature constraint violations as the hierarchical MPC but at slightly lower costs; and (4) the new proposed hierarchical-stochastic MPC results in both lower temperature constraint violations and lower financial expenses than the use of stochastic or hierarchical MPC individually.

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 dispatch of the storage 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.

Distributed Stochastic Model Predictive Control for Heterogeneous Vehicle Platooning Under Uncertainty

Distributed Stochastic Model Predictive Control for Heterogeneous Vehicle Platooning Under Uncertainty

Output Feedback Stochastic Model Predictive Control for Linear Systems with Convex Optimization Approach

Output Feedback Stochastic Model Predictive Control for Linear Systems with Convex Optimization Approach

Event-Triggered Stochastic Model Predictive Control for Constrained Queueing Networks

Event-Triggered Stochastic Model Predictive Control for Constrained Queueing Networks

A Stochastic MPC-Based Flexibility Scheduling Strategy for Community Integrated Energy System Considering Multi-Temporal-Spatial-Scale and Inertia Components

The network trend of isolated communities adds urgency to accelerate the deployment of community integrated energy systems (CIES). CIES effectively combines and optimizes multiple energy systems, leveraging their complementarity for efficient utilization and economical energy supply. However, the escalating intricacies of coupling multiple energy sources and the rising system uncertainties both pose challenges to flexibility scheduling of energy supply and demand. Additionally, the potential flexibility of building thermal inertia and pipeline gas linepack in diverse CIES, encompassing residential, commercial, and industrial communities, remains unexplored. To tackle these issues, a stochastic model predictive control (SMPC) based multi-temporal-spatial-scale flexibility scheduling strategy considering multiple uncertainty sources and system inertia components is proposed. First, the optimization model of CIES is formulated to improve operational flexibility and efficiency, resolve energy discrepancies and expand the capacity for renewable energy utilization. Then, the SMPC-based framework embedding an auto-regressive model and scenario generation method are established to make real-time corrections to the day-ahead scheduling stage and offset the prediction errors of uncertainty sources economically. Furthermore, thermal inertia of the aggregated buildings with different envelopes and linepack in gas pipelines are both leveraged to enhance the flexibility and synergy of CIES. Finally, a case study is executed to verify the effectiveness and applicability of the proposed strategy. The simulation results unequivocally demonstrate that this strategy successfully coordinates and harnesses complementary advantages from various energy sources, fostering a balanced energy supply-demand equilibrium across multiple temporal and spatial scales.

On the Inherent Distributional Robustness of Stochastic and Nominal Model Predictive Control

We define a notion of distributional robustness, via the Wasserstein metric, for closed-loop systems subject to errors in the disturbance distribution used to construct the controller. We then establish sufficient conditions for stochastic model predictive control (SMPC) to satisfy this definition of distributional robustness and establish a similar notion of distributional robustness for economic applications of SMPC. These results address incorrectly or unmodeled disturbances, demonstrate the efficacy of scenario optimization as a means to approximate and solve the SMPC problem, and unify the descriptions of robustness for stochastic and nominal model predictive control. This definition of distributional robustness for closed-loop systems is general and can be applied to other stochastic optimal control algorithms and, potentially, the developing field of distributionally robust control.

A Novel Stochastic Model Predictive Control Considering Predictable Disturbance With Application to Personalized Adaptive Cruise Control

A Novel Stochastic Model Predictive Control Considering Predictable Disturbance With Application to Personalized Adaptive Cruise Control

Optimal dispatch for cross-regional integrated energy system with renewable energy uncertainties: A unified spatial-temporal cooperative framework

Cross-regional energy sharing is a promising way to alleviate the imbalance in energy distribution. However, there is a risk that the uncertain fluctuations of intermittent renewable energy sources (RES) could be transmitted across regional transmissions, resulting in large-scale system economic inefficiency and security concerns. To this end, a unified spatial-temporal cooperative framework for the integrated energy system, which considers the coordination between intra-regional multi-energy coupling and cross-regional multi-agent-system energy sharing, is proposed in this paper. First, in the temporal dimension, a multi-time-scale stochastic decision-making model is established based on stochastic model predictive control (SMPC). Thus, slow-response units are arranged to gain economic goals in day-ahead stage and the closed-loop rolling adjustment is implemented on fast-response units to achieve accuracy supply-demand balance in real-time stage. Second, in the spatial dimension, a fully distributed dispatch approach is adopted to address the information sharing barriers, which only requires neighboring information and considers consistency of boundary control variables on border lines. Finally, to improve the computational efficiency, the established complex time sequential model is decomposed into a set of time-discrete parallel sub-problems, using the optimal condition decomposition (OCD) technique. Simulation results on a cross-regional test system demonstrate that proposed framework can increase the wind power consumption capacity and reduce operation cost through cross-regional cooperation, while the parallel decomposition can save 67.25 % of the computation time relative to the serial computation.

Control strategy for biopharmaceutical production by model predictive control.

The biopharmaceutical industry is rapidly advancing, driven by the need for cutting-edge technologies to meet the growing demand for life-saving treatments. In this context, Model Predictive Control (MPC) has emerged as a promising solution to address the complexity of modern biopharmaceutical production processes. Its ability to optimize operations and ensure consistent product yields has made it an attractive option for manufacturers in this sector. Furthermore, MPC's alignment with the Process Analytical Technology (PAT) initiative provides an additional layer of assurance, facilitating real-time monitoring and enabling swift adjustments to maintain process integrity. This comprehensive review delves into the various applications of MPC, ranging from robust control to stochastic model predictive control, thereby equipping biotechnologists and process engineers with a powerful toolset. By harnessing the capabilities of MPC, as elucidated in this review, manufacturers can confidently navigate the intricate bioprocessing landscape and unlock this approach's full potential in their production processes.

Chance-constrained stochastic MPC of greenhouse production systems with parametric uncertainty

Greenhouse climate control is important to provide sufficient fresh food for the growing population in an economical and sustainable manner. However, the developed crop-climate models are generally complex with parametric uncertainties and far from describing the real system accurately, which affects adversely the control system’s performance. To improve optimality and guarantee robustness during the control process, we develop and implement a stochastic model predictive control (MPC) scheme for greenhouse production systems considering parametric uncertainties. By leveraging the advantages of model linearization, the proposed chance-constrained MPC method enables a more straightforward formulation of uncertainty constraints and computationally cheaper optimization in comparison to directly using the nonlinear model. Finally, the efficacy of the proposed approach is demonstrated on a greenhouse climate control case study.

A Distributionally Robust Optimization Approach to Two-Sided Chance-Constrained Stochastic Model Predictive Control With Unknown Noise Distribution

In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of multiple two-sided chance constrained discrete-time linear systems corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying Bool's inequality. In this proposed DR-SMPC framework, an exact second-order cone approach is adopted to abstract the multiple two-sided chance constraints by considering the first and second moments of the noise. With the proposed DR-SMPC algorithm, the worst-case probability of violating safety constraints is guaranteed to be within a pre-specified maximum value. By flexibly adjusting this pre-specified maximum probability, the feasible region of the initial state can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are rigorously established by introducing a binary initialization strategy for the nominal state. A simulation study of a single spring and double mass system was conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm.

Multi-Scenario Model Predictive Control for Greenhouse Crop Production Considering Market Price Uncertainty

This paper presents a stochastic model predictive control (SMPC) strategy to maximize the economic profit of a greenhouse crop production. The strategy consists of an optimization problem that is solved with a multi-scenario MPC formulation (MS-MPC). It considers the uncertainty of market price by using its historical evolution per year as multiple price scenarios in the cost function. MS-MPC calculates a single set of dates to harvest and sell the crop production that optimizes profits for all the considered scenarios. In addition, MS-MPC determines the optimal temperature references that should be achieved inside the greenhouse for the growth of the crop. A case study for a Mediterranean tomato crop is simulated to analyze the performance of the developed MS-MPC strategy using a hierarchical control architecture with two layers. In the upper layer, MS-MPC calculations are executed following a receding horizon implementation. In the lower layer, regulatory control techniques are applied to reach the optimal temperature references by using natural ventilation and a heating system. Results show that MS-MPC can improve economic profits compared to the use of an average price scenario for the MPC calculations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the need of greenhouse farmers for strategies that maximize profit considering market prices and crop production dynamics. It is not easy for them to make decisions to achieve such long-term objectives while minimizing economic risks, because market prices are very difficult to predict. As a solution, this work presents a novel control strategy to maximize profits by means of automatic selection of the best possible dates to harvest and sell the crop production. This selection is made thanks to considering the uncertainty of market prices in the control strategy by evaluating different scenarios, which are recorded evolutions of the prices from previous years. Although the strategy was tested in simulation, results suggest that using multiple scenarios of historical prices is better for the optimization of profits than just considering an average yearly trend of prices. The more scenarios are considered, the more protection against possible evolution of market prices is obtained. In future research, this control strategy could be extended to include other uncertainties of factors affecting decision making, such as weather forecasts.

Distributed Stochastic Model Predictive Control for Scheduling Deterministic Peer-to-Peer Energy Transactions Among Networked Microgrids With Hybrid Energy Storage Systems

Distributed Stochastic Model Predictive Control for Scheduling Deterministic Peer-to-Peer Energy Transactions Among Networked Microgrids With Hybrid Energy Storage Systems

Stochastic Model Predictive Control based Fast-Slow Coordination Automatic Generation Control

Stochastic Model Predictive Control based Fast-Slow Coordination Automatic Generation Control

Scenario-based ultra-short-term rolling optimal operation of a photovoltaic-energy storage system under forecast uncertainty

The rapid development of renewable energy sources (RESs) facilitates the coordinated operation of different energy sources to hedge against the uncertain and non-dispatchable nature of RESs. In this paper, we propose an effective approach for ultra-short-term optimal operation of a photovoltaic-energy storage hybrid generation system (PV-ES HGS) under forecast uncertainty. First, a generic approach for modelling forecast uncertainty is designed to capture PV output characteristics in the form of scenarios. Then, stochastic model predictive control (SMPC) is utilized in the coordinated operation of PV-ES HGS for load shifting under forecast uncertainty. Finally, a PV-ES power station located in Northeast China is selected as a case study to validate the feasibility and effectiveness of the proposed method in detail. The results show that: (1) The forecast uncertainty modelling method, which incorporates adaptive kernel density estimation (KDE) and two-layer nested copula, could capture the characteristics of PV output effectively. (2) The proposed sampling procedure ensures the representativeness and temporal dependence of scenarios extracted from the joint predictive density, leading to stability and efficiency in solving the stochastic optimization problems. (3) The SMPC-based coordinated operation strategy exhibits significant superiority in load shifting performance and resistance to risks. The standard deviation of residual load (SDORL) is reduced by 17.5% on average compared to the conventional scheme. Thus, this work provides operators with guidance in the ultra-short-term optimal operation of a PV-ES HGS under forecast uncertainty.

Distributed non‐linear model predictive control with Gaussian process dynamics for two‐dimensional motion of vehicle platoon

AbstractThe platoon control of connected and automated vehicles is an important topic in transportation research. The characteristics of non‐linearities, external disturbances, and strong coupling are non‐negligible in two‐dimensional motion control. An integrated longitudinal and lateral vehicle dynamics is required. A Gaussian Process‐based Distributed Stochastic Model Predictive Control (GP‐DSMPC) for two‐dimensional motion is proposed. It achieves global longitudinal stability and lateral error suppression. Gaussian process (GP) regression is employed to approximate the unknown model error. For the two‐norm chance constraints, over‐approximating the confidence ellipse to an outer polyhedron is an effective way to reduce the conservativeness and coupling effect in longitudinal and lateral motion. A neighbour‐average target trajectory is designed with an upper‐level optimization for adjustable target coefficients. The sum of the local cost functions is used as a Lyapunov candidate to achieve the global stability of the longitudinal motion. Some conditions on penalty weights and target coefficients among subsystems, and terminal outputs are derived. Simulation results reveal that the proposed method is effective for disturbance attenuation and performs better than distributed non‐linear model predictive control without GP estimation under low‐friction road conditions.

Strategic Implicit Balancing With Energy Storage Systems via Stochastic Model Predictive Control

Battery Energy Storage Systems (BESS) may exploit the increasing price volatility in imbalance settlement mechanisms via inter-temporal arbitrage. However, participating in these markets requires a careful trade-off between expected profits, accounting for the impact of BESS actions on prevailing imbalance prices, the financial risks and the incurred battery degradation costs. This paper introduces a novel forecast-informed Model Predictive Control (MPC) methodology in which a strategic and potentially risk-averse BESS performs implicit balancing by taking out-of-balance positions in near-real time. Thereby it anticipates expected imbalance prices in a European-style balancing market, and takes into account state of charge-dependent battery degradation costs. To this end, an attention-based recurrent neural network forecasting technique is leveraged to predict the System Imbalance. The proposed methodology is tested on a real-life case study of the Belgian balancing market. Expected profits of a 2 MW/2 MWh BESS (21,784 MW/month) are shown to exceed those of different benchmarks available in the literature, including the profit associated with participating in the day-ahead energy market with perfect price foresight (7,082 /MW/month). From a system perspective, these implicit balancing actions performed by the BESS owner reduce the system imbalance in 75% of all cases, thus improving the cost-efficiency of power systems.

Stochastic MPC based double-time-scale voltage regulation for unbalanced distribution networks with distributed generators

With the increasing penetration of renewable energy resources, the uncertainty of renewable energy resources output introduces challenges to voltage control in distribution networks (DNs). To solve these problems, this paper proposes a double-time-scale voltage control scheme for unbalanced DNs based on stochastic model predictive control (SMPC) to coordinate multiple voltage control devices. In fast-time-scale control, the active and reactive power outputs of distributed generators (DGs) are optimized to minimize voltage deviation, active power curtailment and reactive power fluctuation. In the slow-time-scale control, optimal tap changes of on-load tap changers (OLTC), step voltage regulators (SVR), and switched capacitor banks (CBs) are calculated to reduce voltage deviation and tap operations. Additionally, in the fast-time-scale control, the SMPC-based scheme adopts a scenario generation approach to represent the uncertainty of DG output. Considering the temporal correlation of the DG output, different prediction scenarios and scenario probabilities are obtained by the empirical cumulative distribution function fitted by the historical measurement data. In this paper, the effectiveness of the proposed double-time-scale voltage control scheme is verified by the unbalanced IEEE123 node system. The case study demonstrates that the proposed voltage scheme can effectively keep the three-phase voltages in unbalanced DN within the secure operation range and achieve better voltage profiles.

Contraction-Based Stochastic Model Predictive Control for Nonlinear Systems With Input Delay Using Multidimensional Taylor Network

For nonlinear systems with stochastic uncertainties and input delay, the existing control approaches based on the robust mechanism are generally conservative in most practical scenarios. Within this context, a stochastic model predictive control (MPC) scheme based on uncertainty contraction is proposed here to reduce conservativeness and improve real-time performance. In terms of the Lyapunov-Razumikhin theorem, a robust variational controller (RVC) is deduced as the primary controller for the variational dynamic with input delay. A variational vector field in Wasserstein metric space is constructed to detect the minimum geodesic between the uncertainty distribution and the desired one. Integrating RVC along the minimum geodesic, the modified auxiliary controller is developed for tracking the nominal trajectory with less conservatism. Subsequently, the chance constraints of stochastic states are transformed into the deterministic quantile constraints of nominal states. The sparse multi-dimensional Taylor network based on Bayesian compressive sensing is designed to parameterize the ambiguity set in Wasserstein metric space for higher computational efficiency.A tractable MPC scheme is then formulated to achieve the reference index with an improved trade-off between robustness and real-time performance.The stochastic input-to-state stability of the considered system is verified theoretically by the Lyapunov-Krasovskii theorem. The effectiveness of the proposed scheme is confirmed by a numerical simulation derived from a practical industrial process.