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In the context of renewable energy systems, microgrids (MG) are a solution to enhance the reliability of power systems. In the last few years, there has been a growing use of energy storage systems (ESSs), such as hydrogen and battery storage systems, because of their environmentally-friendly nature as power converter devices. However, their short lifespan represents a major challenge to their commercialization on a large scale. To address this issue, the control strategy proposed in this paper includes cost functions that consider the degradation of both hydrogen devices and batteries. Moreover, the proposed controller uses scenarios to reflect the stochastic nature of renewable energy resources (RESs) and load demand. The objective of this paper is to integrate a stochastic model predictive control (SMPC) strategy for an economical/environmental MG coupled with hydrogen and battery ESSs, which interacts with the main grid and external consumers. The system's participation in the electricity market is also managed. Numerical analyses are conducted using RESs profiles, and spot prices of solar panels and wind farms in Abu Dhabi, UAE, to demonstrate the effectiveness of the proposed controller in the presence of uncertainties. Based on the results, the developed control has been proven to effectively manage the integrated system by meeting overall constraints and energy demands, while also reducing the operational cost of hydrogen devices and extending battery lifetime. • Implementation of an SMPC strategy based on a scenario-based approach. • Reduction of operation and maintenance costs and integration of uncertainties. • Minimization of the overall operational costs and maximization the profits. • Reduction of complexity and computational time. • Implementation of a unique control architecture to manage a microgrid in different modes. [ABSTRACT FROM AUTHOR]

With the release of the '2050 Net Zero Emissions from Shipping' by the International Maritime Organization (IMO) and China 'Carbon Neutrality' policy, it is imperative to develop renewable energy ships. River-sea going renewable energy ships have high economic benefits and low emissions. They can sail in both rivers and seas without other ships and barges. To realize the economical and low-carbon operation of river-sea going renewable energy ships, a variable time-scale power scheduling strategy is proposed. A new model of all-electric propulsion power is firstly proposed. The model focuses on the multi-variables coupling variations of a ship propulsion process, such as resistance, motion state, navigation speed, deadweight and so on. A voyage-power hierarchical framework which is based on a stochastic model predictive control (SMPC) method is developed to optimize the scheduling scheme. A novel variable time-scale control mechanism in view of uncertainty fluctuation quantization is proposed. Results show that the energy consumption of the proposed all-electric propulsion power computational model is reduced by 52.6%, compared with the traditional computational model. The operation cost and carbon emission which are determined by the proposed method is reduced by 21.6% and 35.9%, respectively. [Display omitted] • A new multi-variable coupling model of AEP power is proposed to improve the calculation accuracy of a river-sea going ship. • A voyage-power hierarchical scheduling framework is proposed by an improved stochastic model predictive control (SMPC) method. • A novel variable time-scale control mechanism in view of uncertainty fluctuation quantization is proposed. • Results show that the proposed AEP power model can improve the accuracy and economy of a ship power scheduling. [ABSTRACT FROM AUTHOR]

A recurrent neural network (RNN)-based approach is proposed in this paper to handle joint chance-constrained stochastic optimal control problems (SOCP) and stochastic model predictive control (SMPC) implementations. In the proposed approach, the joint chance constraint (JCC) in a SOCP is first reformulated as a quantile-based inequality. Then, the sample average approximation (SAA) method is used to build the RNN-based surrogate model for the quantile function. Afterwards, the RNN-based model is embedded into the probabilistic constraint of the SOCP. Subsequently, the SOCP involving the RNN-based model can be solved using a deterministic nonlinear optimization solver. Moreover, while applying the proposed approach to the SMPC, the SOCP involving the RNN-based model is solved repeatedly at different sampling instants, based on different initial system states. The proposed approach is applied to a numerical illustrating example and a chemical process case study to demonstrate its capability of handling the SOCP and the SMPC implementation. • Quantile reformulation of joint chance constraints and sample based empirical approximation. • Approximation of quantile function through recurrent neural network based surrogate model. • Stochastic optimal control problem is deterministically solvable though embedded RNN model. • Easy extension and implementation of the proposed approach to stochastic model predictive control problem. [ABSTRACT FROM AUTHOR]

The rapid development of technology and economy has led to the development of chemical processes, large-scale manufacturing equipment, and transportation networks, with their increasing complexity. These large systems are usually composed of many interacting and coupling subsystems. Moreover, the propagation and perturbation of uncertainty make the control design of such systems to be a thorny problem. In this study, for a complex system composed of multiple subsystems suffering from multiplicative uncertainty, not only the individual constraints of each subsystem but also the coupling constraints among them are considered. All the constraints with the probabilistic form are used to characterize the stochastic natures of uncertainty. This paper first establishes a centralized model predictive control scheme by integrating overall system dynamics and chance constraints as a whole. To deal with the chance constraint, based on the concept of multi-step probabilistic invariant set, a condition formulated by a series of linear matrix inequality is designed to guarantee the chance constraint. Stochastic stability can also be guaranteed by the virtue of nonnegative supermartingale property. In this way, instead of solving a non-convex and intractable chance-constrained optimization problem at each moment, a semidefinite programming problem is established so as to be realized online in a rolling manner. Furthermore, to reduce the computational burdens and amount of communication under the centralized framework, a distributed stochastic model predictive control based on a sequential update scheme is designed, where only one subsystem is required to update its plan by executing optimization problem at each time instant. The closed-loop stability in stochastic sense and recursive feasibility are ensured. A numerical example is employed to illustrate the efficacy and validity of the presented algorithm in this study. • A distributed SMPC algorithm is developed for a class of stochastic systems. • Both individual and coupled probabilistic constraints are taken into account. • The intractable CCOP is converted into a tractable problem for online computation. • Computational complexity is reduced using the proposed distributed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, some data-based control design options that can be used to accommodate for the presence of uncertainties in continuous-state engineering systems are recalled and discussed. Focus is made on reinforcement learning, stochastic model predictive control and certification via randomized optimization. Some thoughts are also shared regarding the positioning of the control community in a data and AI-dominated period for which some suggestions and risks are highlighted. [ABSTRACT FROM AUTHOR]

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. • A novel unified spatial-temporal cooperative dispatching framework is proposed for the cross-regional IES. • A multi-time-scale rolling stochastic decision-making model is established to handle RES uncertainties. • The ADMM is implemented to achieve cross-regional rapid interactions iteration with only neighboring information. • The OCD is applied to decompose the complex spatial-temporal problem. [ABSTRACT FROM AUTHOR]

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. [Display omitted] • Integration of adaptive KDE and two-layer copula to model PV forecast uncertainty. • Proposal of a representative scenario generation method incorporating LH and CD. • Utilization of scenario-based SMPC to optimize ultra-short-term PV-ES HGS operation. • Identification of trade-off between load shifting performance and operational risks. [ABSTRACT FROM AUTHOR]

• Propose a SMPC based voltage regulation scheme to coordinate DG, OLTC, SVR and CBs considering uncertainty of DG outputs. • Use the time-correlated scenario generation method in the proposed SMPC framework. • Consider the single-phase regulation effect of OLTC, DGs and CBs. 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. [ABSTRACT FROM AUTHOR]

Highlights • A Monte Carlo ARIMAX forecasts is developed to predict the stochastic nature of crane demand. • SMPC utilising on DP is developed to increase cost saving and peak reduction for network of cranes. • SMPC and MPC with variable horizons are investigated to improve energy management performance of ESS compared to set-point controller. • A comparison analysis for different ESS location scenarios and the economic implications are conducted to evaluate the proposed models. Abstract An Energy Storage System (ESS) is a potential solution to increase the energy efficiency of low voltage distribution networks whilst reinforcing the power system. In this article, energy management systems have been developed for the control of an ESS connected to a network of electrified Rubber Tyre Gantry (RTG) cranes. Considering the highly volatile crane demand behaviour and uncertainty in the RTG crane demand prediction as a nonlinear optimisation problem, this paper presents and verifies an optimal energy control strategy based on a Stochastic Model Predictive Control (SMPC) algorithm. The SMPC controller aims to improve the reliability and economic performance of a network of RTG cranes, under a given ESS and network specification. A specific case, using different ESS locations, is presented and the results of the proposed SMPC and MPC control models are compared to a set-point controller using data collected from an instrumented electrified RTG cranes at the Port of Felixstowe, UK. The results indicate that the SMPC controller successfully reduce electrical energy costs, the peak demand and outperforms each of the presented control techniques. [ABSTRACT FROM AUTHOR]

Highlights • A novel data-driven approach is proposed for stochastic model predictive control. • Support vector clustering is adopted to learn an uncertainty set from scenarios. • A calibration procedure is developed to provide desirable probabilistic guarantees. • Finally, an uncertainty set-induced robust optimization problem is solved. • The proposed method requires less scenarios and can reduce conservatism. Abstract Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances. [ABSTRACT FROM AUTHOR]

Highlights • A predictive control model is proposed based on Pontryagin's Minimum Principle. • Power distribution over each moving horizon is solved using the shooting method. • Speed forecasting is realized via a Markov chain model. • Two typical model predictive controllers are compared. • The influence of moving horizon lengths is discussed. Abstract To improve computational efficiency of energy management strategies for plug-in hybrid electric vehicles (PHEVs), this paper proposes a stochastic model predictive controller (MPC) based on Pontryagin's Minimum Principle (PMP), which differs from widely used dynamic programming (DP)-based predictive methods. First, short-time speed forecasting is achieved using a Markov chain model, based on real-world driving cycles. The PMP- and DP-based MPCs are compared under four preview horizons (5 s, 10 s, 15 s and 20 s), and the results show that the computational time of the DP-MPC is almost four times of that in the PMP-MPC. Moreover, the influence of predication horizon length on computational time and energy consumption is examined. Given a preview horizon of 5 s, the PMP-MPC holds a total energy consumption cost of 7.80 USD and computational time per second of 0.0130 s. When the preview horizon increases to 20 s, the total cost is 7.77 USD with the computational time per second increasing to 0.0502 s. Finally, DP, PMP, and rule-based strategies are contrasted to the PMP-MPC method, further demonstrating the promising performance and computational efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

A wind energy producer participating in deregulated markets needs to make contracts on the energy it will supply in the next day. Deviations from the contracts, which could occur due to wind uncertainties, are compensated in real-time balancing markets at a considerable cost. Therefore, developing advanced day-ahead bidding and real-time operation strategies minimizing such imbalance costs constitutes an important problem. There are several works on finding optimal day-ahead bids but the real-time operation problem is not studied well. Motivated by this fact, we propose a new strategy in which the day-ahead bids are computed by solving a risk-averse stochastic program, and real-time operation is performed by a stochastic model predictive control-based algorithm with a risk control capability. The algorithm is applied to a realistic system composed of wind farms and a pumped hydro storage plant. Its performance is compared to a number of approaches appearing in the literature. Because the problem considered has two conflicting objectives of profit maximization and risk minimization, a Pareto optimality analysis is also conducted. Finally, the validity of a common practice followed in the literature, which is estimating the economic performance by bidding optimization, is investigated by comparing the estimate with the actual performance achieved by real-time operation methods. [ABSTRACT FROM AUTHOR]

We present an open-source solution for the operational control of drinking water distribution networks which accounts for the inherent uncertainty in water demand and electricity prices in the day-ahead market of a volatile deregulated economy. As increasingly more energy markets adopt this trading scheme, the operation of drinking water networks requires uncertainty-aware control approaches that mitigate the effect of volatility and result in an economic and safe operation of the network that meets the consumers’ need for uninterrupted water supply. We propose the use of scenario-based stochastic model predictive control: an advanced control methodology which comes at a considerable computation cost which is overcome by harnessing the parallelization capabilities of graphics processing units (GPUs) and using a massively parallelizable algorithm based on the accelerated proximal gradient method. [ABSTRACT FROM AUTHOR]

This paper provides a review of model predictive control (MPC) methods with active uncertainty learning. System uncertainty poses a key theoretical and practical challenge in MPC, which can be aggravated when system uncertainty increases due to the time-varying nature of system dynamics. For uncertain systems with stochastic uncertainty, this paper presents the stochastic MPC (SMPC) problem in the dual control paradigm, where the control inputs to an uncertain system have a probing effect for active uncertainty learning and a directing effect for controlling the system dynamics. The complexity of the SMPC problem with dual control effect is described in connection to stochastic dynamic programming as well as Bayesian estimation for its output feedback implementation. Further, implicit and explicit dual control methods for approximating the receding-horizon control problem with dual control effect are surveyed and analyzed with the intent to discuss the key challenges and opportunities in SMPC with dual control effect. [ABSTRACT FROM AUTHOR]

A multi-stage model predictive control approach is proposed to compensate the forecast error in a scenario-based two-stage stochastic dynamic economic dispatch problem through a feedback mechanism. Reformulating the problem as a finite moving-horizon optimal control problem, the proposed approach decelerates the growth of the number of scenarios by updating the system as uncertainties are gradually realized. Consequently, the computation time is reduced, and the problem is solved without the need for using scenario reduction techniques that compromise the accuracy of the solution. To exhibit the computational efficiency of the proposed approach, numerical experiments are conducted on the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

• A two-stage dispatch strategy for IPGS by using stochastic MPC is proposed. • Data-driven chance-constrained dispatch strategy is proposed to prevent adverse the effects of stochastic prediction errors. • A comprehensive evaluation index of the violation rate is proposed, evaluating the violation rate more reasonably. The optimal dispatch of the integrated power and natural gas systems can increase the utilization rate of renewable energy and energy efficiency while decreasing operation costs. The common prediction errors of wind power and electric load have the potential to negatively impact the normal operation of the integrated power and natural gas systems. A two-stage data-driven dispatch strategy is proposed to reduce this effect, consisting of the day-ahead dispatch stage and the intraday rolling dispatch stage using stochastic model predictive control (MPC). In the day-ahead dispatch stage, the data-driven chance constraints of tie-line power and reserve of gas-fired generators are built, and the day-ahead tie-line power is obtained and regarded as input parameters to the intraday dispatch stage. In the intraday dispatch stage, the data-driven chance constraints of tie-line power and reserve of gas-fired generators with the latest rolling prediction data are built, and the remaining control variables are obtained. The distribution characteristics of the stochastic prediction errors of wind power and electric load are captured and described by the variational Bayesian Gaussian mixture model with massive historical data. Then the original stochastic mixed-integer nonlinear programming problem is converted to a tractable deterministic one by the quantile-based analytical reformulation and convex relaxation technique. Finally, the proposed strategy is verified by the numerical experiments based on a modified IEEE 33-bus system integrated with a 10-node natural gas system and a micro hydrogen system. The numerical results demonstrate that the proposed strategy reduces the actual costs and decreases the violation rate caused by the stochastic prediction errors of wind power and electric load. [ABSTRACT FROM AUTHOR]

The performance of modern control methods, such as model predictive control, depends significantly on the accuracy of the system model. In practice, however, stochastic uncertainties are commonly present, resulting from inaccuracies in the modeling or external disturbances, which can have a negative impact on the control performance. This article reviews the literature on methods for predicting probabilistic uncertainties for nonlinear systems. Since a precise prediction of probability density functions comes along with a high computational effort in the nonlinear case, the focus of this article is on approximating methods, which are of particular relevance in control engineering practice. The methods are classified with respect to their approximation type and with respect to the assumptions about the input and output distribution. Furthermore, the application of these prediction methods to stochastic model predictive control is discussed including a literature review for nonlinear systems. Finally, the most important probabilistic prediction methods are evaluated numerically. For this purpose, the estimation accuracies of the methods are investigated first and the performance of a stochastic model predictive controller with different prediction methods is examined subsequently using multiple nonlinear systems, including the dynamics of an autonomous vehicle. [ABSTRACT FROM AUTHOR]

For discrete-time linear systems subject to multiplicative disturbance described by random variables, we develop a sampling-based Stochastic Model Predictive Control algorithm. Unlike earlier results employing a scenario approximation, we propose an offline sampling approach in the design phase instead of online scenario generation. The paper highlights the structural difference between online and offline sampling and provides rigorous bounds on the number of samples needed to guarantee chance constraint satisfaction. The approach does not only significantly speed up the online computation, but furthermore allows to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Under mild assumptions, asymptotic stability of the origin can be established. [ABSTRACT FROM AUTHOR]

Model predictive control (MPC) can effectively solve online optimization issues, even with various constraints, when maintained at high robustness. Considering the energy management issue of plug-in hybrid electric bus (PHEB) as a constrained nonlinear optimization problem, a strategy based on stochastic model predictive control (SMPC) is put forward and verified in this paper. Firstly, Markov Chain Monte Carlo Method (MCMC) is adopted to forecast velocity sequences at every current state, in the form of multi scale single step (MSSS), with post-processing algorithms to moderate fluctuations of the prediction results like average filtering, quadratic fitting, and the like. The offline simulation results show that the optimization can effectively improve the predictive accuracy, make the following energy management feasible and reduce the fuel consumption by 1.9%. Then the SMPC-based energy management strategy is proposed. In order to prevent the driving cycle state deficiencies from interrupting the prediction for practical application, a state reconstitution method is constructed accordingly. Besides, the predictive steps are made time-varying by an online accuracy estimation method and a corresponding threshold to maintain the accuracy of forecast. Finally, the hardware-in-the-loop (HIL) experiments are conducted and the results show that the SMPC-based strategy is reasonable and the fuel consumption decreases by 3.9% further with variable predictive steps than that of fixed ones. In summary, this paper illustrates an effective SMPC-based methodology for energy management for PHEB, and techniques like MSSS prediction with post-processing, state reconstitution method, online accuracy estimation can be adopted to solve similar problems. [ABSTRACT FROM AUTHOR]

• Renewable energy community consisting of residential customers with photovoltaic power plant and energy storage system. • Stochastic model predictive control to maximize renewable energy community economic savings. • Control algorithm for reversible solid oxide cells and hydrogen storage optimal management. • Physically based local model to predict reversible solid oxide cell performance. • Effective management of uncertainties correlated to users' demand and renewable energy production. The use of reversible solid oxide cells within a renewable energy community results a promising application which permits to balance the temporal mismatch between renewable energy production and users' demand through hydrogen as energy vector. Differently from batteries and supercapacitors, this technology is characterized by a high stored energy density and a negligible daily self-discharge. Nevertheless, the system management is more complex requiring cell behaviour optimization and hydrogen storage control. Here this work proposes a control algorithm for reversible solid oxide cell operation coupled to renewable energy sources within a renewable energy community formed by an aggregation of fifteen residential customers. Based on forecasts of loads and renewable energy production, the proposed algorithm, a stochastic model predictive control, can optimize system operation aiming at economic benefit maximization. The transition between the fuel cell mode for power generation and the electrolysis mode for energy storage through hydrogen production was set considering the available renewable energy, the power demand of community members and the energy sell-back price in order to increase the auto-consumed amount as well as to favour the electricity exchange within the renewable energy community. Since the reversible solid oxide cell is the key-point in such a system, SIMFC-SIMEC (SIMulation of Fuel Cells and Electrolysis Cells), a physically based 2D model, allowed an effective prediction of cell behaviour deriving the efficiency of electricity and hydrogen production from local physicochemical feature and working parameter gradients on each stacked cell plane. [ABSTRACT FROM AUTHOR]

Dynamic wireless charging can strengthen the connection between in-motion electric vehicles and microgrids. To ensure the coordination between electric vehicles with the dynamic wireless charging mode (DWCEVs) and hybrid power system in the microgrid, this paper proposes a collaborative strategy consisting of the two-layer control structure. The objective of the upper layer controller is to minimize the power exchange between the main grid and microgrid, while calculating the reference power of the lower layer controller. Then, the lower layer controller allocates charging power to individual DWCEVs according to the reference value optimized by the upper layer controller, while taking into account the charging requirements of different DWCEVs. In addition, we consider the uncertainties of photovoltaic arrays power generation, traffic flow, electric vehicle battery capacity, and consumed state of charge as well as the corresponding processing methods. According to the number of control variables, the upper controller adopts the regular optimal control, and the lower controller adopts the stochastic model predictive control. Finally, the case studies demonstrate the effectiveness of the proposed collaborative strategy. • A two-layer control strategy is proposed for coordination between DWCEVs and HPS. • A PCS is designed to meet charging demands of individual DWCEVs. • Uncertainties of the DWCEVs-HPS model are investigated. • Results demonstrate the effectiveness of the proposed collaborative strategy. [ABSTRACT FROM AUTHOR]

The propagation and accumulation of uncertainty within the water supply, power generation, and environment (WPE) nexus may induce unexpected failures. Effective control strategies are needed to reduce the failure risks. Optimal control of the WPE nexus is challenging because of the complex interconnections and the multiple stakeholders. This study employs stochastic dynamical systems to simulate interconnected WPE systems and compares the performance of centralized, decentralized, and hybrid control strategies. The WPE nexus within the Hehuang region of China is selected as a case study. The results show that all controllable agents are either selfish or generous, protecting or sacrificing their own security, respectively. Hybrid control is the most suitable strategy for realistic cases, because it balances the risks of selfish and generous agents. The manager's role is to balance or hedge the risks and costs across agents by adjusting their decision preferences. This involves changing the risks of generous agents and the control costs of selfish agents. The three control strategies have little impact on system bottlenecks, despite obvious changes in the trajectories of the highest and lowest risk contribution ratios. Overall, this study advances the understanding of different control strategies for the WPE nexus, helping to mitigate the failure risk and improve the management of real systems. • Comparison of centralized, decentralized, and hybrid control strategies. • All controllable agents can be categorized as selfish or generous. • Hybrid control is considered the most suitable strategy for realistic cases. • The manager balances or hedges risks and costs by adjusting agents' preferences. [ABSTRACT FROM AUTHOR]

Microgrids are subsystems of the distribution grid which comprises generation capacities, storage devices and flexible loads, operating as a single controllable system either connected or isolated from the utility grid. In this work, microgrid management system is developed in a stochastic framework. It is seen as a constraint-based system that employs forecasts and stochastic techniques to manage microgrid operations. Uncertainties due to fluctuating demand and generation from renewable energy sources are taken into account and a two-stage stochastic programming approach is applied to efficiently optimize microgrid operations while satisfying a time-varying request and operation constraints. At the first stage, before the realizations of the random variables are known, a decision on the microgrid operations has to be made. At the second stage, after random variables outcomes become known, correction actions must be taken, which have a cost. The proposed approach aims at minimizing the expected cost of correction actions. Mathematically, the stochastic optimization problem is stated as a mixed-integer linear programming problem, which is solved in an efficient way by using commercial solvers. The stochastic problem is incorporated in a model predictive control scheme to further compensate the uncertainty through the feedback mechanism. A case study of a microgrid is employed to assess the performance of the on-line optimization-based control strategy and the simulation results are discussed. The method is applied to an experimental microgrid: experimental results show the feasibility and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

As renewable energy penetrations increase, wind farms may be required to provide ancillary services such as frequency regulation. For wind farms, two issues complicate frequency regulation: turbine-wake interactions alter the available wind power, and the future power reference signal is uncertain. This paper presents a stochastic model predictive controller (MPC) for wind farms to track an uncertain frequency regulation signal while accounting for wakes. The controller uses a simplified Park model with wake propagation delay to predict turbine-wake interactions. The controller operates without any knowledge of the future power regulation signal or wind speed. The controller solves a nonconvex stochastic optimization program using scenario optimization. Our stochastic MPC tracks with 7%–10% less error than our deterministic MPC controllers. • A novel model-predictive control (MPC) approach for wind farm frequency regulation. • The controller does not know the future regulation signal and accounts for waking. • We use an estimate of the future regulation signal within each MPC horizon. • We formulate a stochastic MPC approach that accounts for the forecast uncertainty. • Our approach tracks the signal while minimizing power loss from wake deficits. [ABSTRACT FROM AUTHOR]

The “scenario approach” provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly’s dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly’s dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. [ABSTRACT FROM AUTHOR]

In this paper a rolling horizon approach is applied for simultaneous optimization of the rail freight car fleet size and allocation problem. Developed dynamic model of loaded and empty rail freight car flows explicitly treats state, control and station capacity constraints in presence of various freight car types under the partial substitutability among them. Demands and traveling times are considered as random variables. Proposed approach is applied to a set of test cases and it shown to be successful, ultimately providing a new managerial tool for more effective and efficient planning and analyzing rail freight car fleets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system. [ABSTRACT FROM AUTHOR]

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization. [ABSTRACT FROM AUTHOR]

We propose an energy management algorithm for isolated industrial power systems that integrate uncertain renewable generation and energy storage. The proposed strategy is designed to ensure sustainable and cost-effective operations by managing the energy flows in the grid, and is structured so to cope with: (1) high levels of renewable power penetration, and (2) load profiles characterized by non-smooth patterns and irregular events (i.e., events such as those occurring from connections/disconnections of large scale equipment, or from large wind speed ramps). The proposed algorithm leverages a stochastic economic model predictive control (MPC) scheme capable of dealing simultaneously with the dispatch and scheduling of the local generation units. More precisely, the scheme embeds a mixed-integer linear programming (MILP) optimal control policy formulation together with a stochastic programming approach. Moreover, the optimization problem accounts for multiple techno-economical objectives, such as minimization of operational costs, battery degradation, and non-utilized energy. We test the algorithm on a case study of an isolated offshore Oil & Gas platform producing energy onsite with conventional gas turbines and a local wind farm, while integrating a battery energy storage system. The results show that the proposed approach can issue ensemble predictions that successfully capture the potential irregular variations just by using recent past information of the associated random variable, even when no particular sudden events are anticipated in the near-future (i.e., step changes/trend reversals). In this way, the approach provides useful future information for the optimal management of the grid. This effect is numerically quantified via simulations that compare the performance of the proposed stochastic optimization approach against its deterministic MPC version in several realistic operating conditions. The empirical results suggest that the stochastic version leads to better scheduling of the conventional generators, with up to 12.86% reductions of the operating cost, 2.56% reduction in fuel consumption and emissions, and 35.29% reduction in status transitions (on/off) of the gas turbines, while keeping dumped energy and battery degradation as low as possible. • Stochastic model predictive control for energy management of isolated power systems. • Auto-regressive Quantile Regression Forests for irregular events prediction. • Optimal system operation under load steps variations and wind power trend reversals. • Minimization of battery degradation, gas turbines ON/OFF commands and dumped energy. [Display omitted] [ABSTRACT FROM AUTHOR]

• Stochastic model predictive yaw control strategy based on intelligent scenarios generation. • New quasi-PID optimization problem for generating optimal scenarios. • Novel co-evolution bonobo optimizer to solve the quasi-PID problem. • Improving the energy capture efficiency by 0.26%–0.43% while reducing the yaw time ratio by 0.35%–1.58%. Wind direction is random and time-varying, which is arduous to be accurately predicted. The yaw control based on the predicted wind direction is limited by the accuracy of the wind direction prediction, which leads to narrow improvement in the energy capture efficiency of the wind turbine (WT). For this issue, a Stochastic Model Predictive Yaw Control (SMPYC) strategy based on Intelligent Scenarios Generation (ISG) is proposed. Herein, in view of the uncertainty of wind direction prediction, the ISG method is proposed to generate scenarios that characterize it, then the yaw action optimized through the proposed scenario-based SMPYC is performed to improve the energy capture efficiency of WTs. Specifically, ISG creates an optimization problem from scenarios generation in each control period, and the co-evolution bonobo optimizer is improved to solve the optimal scenarios in real time for this high-dimensional multimodal problem. The proposed SMPYC based on ISG is tested using historical wind direction data, and its effectiveness and advantages under different accuracy of wind direction prediction are validated by the test results. The proposed SMPYC reduces the yaw time ratio by 0.35%-1.58% and improves the energy capture efficiency by 0.26%-0.43% in comparison with the baseline MPYC. For a 5 MW WT, the gained energy production could reach 1.14–1.88 × 105 kWh in a year, which corresponds to an additional annual profit of 68,000–110,000 yuan. Consequently, the proposed method is promising to enhance the energy capture efficiency and has important application value for reducing the cost of wind power. [ABSTRACT FROM AUTHOR]

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. • Year-round performance of alternative MPC strategies is investigated and compared. • Their enhancement for optimal use of building flexibility-resources is proposed. • Forecast uncertainties are quantified based on real meteorological data. • No one MPC strategy is superior to other MPC strategies under all conditions. • Hybrid control method is recommended for optimal building flexibility-resource use. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an investigation of how Model Predictive Control (MPC) and weather predictions can increase the energy efficiency in Integrated Room Automation (IRA) while respecting occupant comfort. IRA deals with the simultaneous control of heating, ventilation and air conditioning (HVAC) as well as blind positioning and electric lighting of a building zone such that the room temperature as well as CO2 and luminance levels stay within given comfort ranges. MPC is an advanced control technique which, when applied to buildings, employs a model of the building dynamics and solves an optimization problem to determine the optimal control inputs. In this paper it is reported on the development and analysis of a Stochastic Model Predictive Control (SMPC) strategy for building climate control that takes into account the uncertainty due to the use of weather predictions. As first step the potential of MPC was assessed by means of a large-scale factorial simulation study that considered different types of buildings and HVAC systems at four representative European sites. Then for selected representative cases the control performance of SMPC, the impact of the accuracy of weather predictions, as well as the tunability of SMPC were investigated. The findings suggest that SMPC outperforms current control practice. [Copyright &y& Elsevier]

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. [Display omitted] • A single-layer multi-timescale framework is proposed. • An improved stochastic model predictive control operation strategy is developed. • Renewables and demands are forecast by least square support vector machine. • Comparisons of the improved strategy with a traditional single-layer and a hierarchical strategy are performed. [ABSTRACT FROM AUTHOR]

The high penetration of renewable energy into distribution networks poses increasing challenges on voltage control. To address this issue, this paper presents a double-layer stochastic model predictive control algorithm to regulate voltage profile in active distribution networks. In the proposed algorithm, voltage regulation is achieved by coordination of an upper layer controller and a lower layer controller. In the upper layer, the number of operation of mechanical voltage regulation devices, including transformer with on-load tap changer and capacitor banks, is minimized in an hourly timescale. In the lower layer, the controller minimizes the active power curtailments and power losses with a control period of 5 min. The proposed double-layer stochastic model predictive voltage control utilizes not only the reactive power control, but also the active power curtailment to regulate bus voltages. In addition, mechanical voltage regulation devices and distributed generations are controlled in two different timescales. Case studies on a modified IEEE-33 bus system demonstrate that compared with traditional control and two-stage stochastic voltage control, the proposed algorithm can achieve an improvement of 8.05% and 7.43%, respectively. • Double-layer stochastic model predictive voltage control method is proposed. • The future status and uncertainties of distribution networks are considered. • Reactive power control is further compensated by active power curtailment. • Mechanical devices and distributed generations controlled in different timescales. [ABSTRACT FROM AUTHOR]

Virtual Power Plants (VPPs) comprising renewables and hydrogen production through power-to-gas technologies can help to increase renewable penetration and to improve operational flexibility and economic performance. However, the uncertainty inherent to forecasts of renewable generation and energy prices renders cost effective operation difficult. The present paper approaches the issue by means of receding-horizon stochastic optimization (i.e. by stochastic Model Predictive Control (MPC)). Differently from previous works, we do not tackle computational tractability with a sampling-based approach, but by mapping quantile forecasts of virtual energy profiles to the mode of operation that has the highest probability of being optimal. This way, we reduce the computational load and the forecasting burden. Furthermore, simulation studies show that the proposed algorithm can attain a significant percentage of the revenue of optimal control with perfect forecasts. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of designing data-driven stochastic Model Predictive Control (MPC) for linear time-invariant systems under additive stochastic disturbance, whose probability distribution is unknown but can be partially inferred from data. We propose a novel online learning based risk-averse stochastic MPC framework in which Conditional Value-at-Risk (CVaR) constraints on system states are required to hold for a family of distributions called an ambiguity set. The ambiguity set is constructed from disturbance data by leveraging a Dirichlet process mixture model that is self-adaptive to the underlying data structure and complexity. Specifically, the structural property of multimodality is exploited, so that the first- and second-order moment information of each mixture component is incorporated into the ambiguity set. A novel constraint tightening strategy is then developed based on an equivalent reformulation of distributionally robust CVaR constraints over the proposed ambiguity set. As more data are gathered during the runtime of the controller, the ambiguity set is updated online using real-time disturbance data, which enables the risk-averse stochastic MPC to cope with time-varying disturbance distributions. The online variational inference algorithm employed does not require all collected data be learned from scratch, and therefore the proposed MPC is endowed with the guaranteed computational complexity of online learning. The guarantees on recursive feasibility and closed-loop stability of the proposed MPC are established via a safe update scheme. Numerical examples are used to illustrate the effectiveness and advantages of the proposed MPC. [ABSTRACT FROM AUTHOR]

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to generate autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power. • We reformulate the scenario-based stochastic model predictive control algorithm. • We add a constraint that forces the control strategy to be equal across scenarios. • The reformulation is tested on a system with a battery, load and PV system. • The probabilistic forecasts and multivariate forecasts are thoroughly evaluated. • The reformulation results in increased profit, self-consumption and self-sufficiency. [ABSTRACT FROM AUTHOR]

This paper develops a tractable approximation for stochastic model predictive control (SMPC). Under the proposed approach, we solve multiple deterministic MPC (DMPC) problems over individual scenarios of the uncertain variables to obtain a set of control policies and select from this candidate set a control input that yields the best approximation of the SMPC solution (i.e., yields the smallest statistical measure of the objective function (e.g., expected value) and of the constraints). This approach is a scenario decomposition scheme that overcomes tractability issues of SMPC (which solves problems that incorporate multiple scenarios all-at-once). Moreover, the approach enables flexible handling of complex statistical measures (e.g., medians, quantiles, and chance constraints) and enables prioritization of objectives and constraints (this is difficult to do with off-the-shelf optimization solvers). An application to a nonlinear mechanical pulping process demonstrates that the approach provides high quality solutions. We hypothesize that this is because the optimal SMPC policy lives in a space that is spanned by the control policies for the individual scenarios. Moreover, we note that a traditional DMPC policy corresponds to the policy of an individual scenario (the mean scenario is typically chosen). Consequently, the proposed approach can do no worse than DMPC and can be interpreted as an approach that seeks to find a DMPC policy that best approximates the SMPC policy. [ABSTRACT FROM AUTHOR]