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

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

Stochastic linear Model Predictive Control with chance constraints – A review

The simulation-based design and development of various vehicle active safety systems necessitate an enhanced understanding of the driver-vehicle-road system, and particular attention is paid to the improved modelling of the driver driving control characteristics. In this paper, a novel driver steering control model based on stochastic model predictive control (SMPC) is proposed to effectively incorporate the random variation characteristics of road friction. A multi-point driver preview approach is employed to represent the driver's perception of the desired path. An internal vehicle dynamic model with parameter uncertainty in the friction coefficient is formulated to represent the knowledge and adaptation of the driver to the variations in road conditions. A transport delay is applied to reflect the driver's physiological constraints. The SMPC method is then used to minimise a weighted cost function. Simulation and experimental validations are presented to demonstrate the effectiveness and practicability of the proposed modelling framework.

This paper proposes a stochastic model predictive control (MPC) approach to optimize the fuel consumption in a vehicle following context. The practical solution of that problem requires solving a constrained moving horizon optimal control problem using a short-term prediction of the preceding vehicle’s velocity. In a deterministic framework, the prediction errors lead to constraint violations and to harsh control reactions. Instead, the suggested method considers errors, and limits the probability of a constraint violation. A conditional linear Gauss model is developed and trained with real measurements to estimate the probability distribution of the future velocity of the preceding vehicle. The prediction model is used to evaluate two different stochastic MPC approaches. On the one hand, an MPC with individual chance constraints is applied. On the other hand, samples are drawn from the conditional Gaussian model and used for a scenario-based optimization approach. Finally, both developed control strategies are evaluated and compared against a standard deterministic MPC. The evaluation of the controllers shows a significant reduction of the fuel consumption compared with standard adaptive cruise control algorithms.

Wind energy has been drawing considerable attention in recent years. However, due to the random nature of wind and high failure rate of wind energy conversion systems (WECSs), how to implement fault-tolerant WECS control is becoming a significant issue. This paper addresses the fault-tolerant control problem of a WECS with a probable actuator fault. A new stochastic model predictive control (SMPC) fault-tolerant controller with the Conditional Value at Risk (CVaR) objective function is proposed in this paper. First, the Markov jump linear model is used to describe the WECS dynamics, which are affected by many stochastic factors, like the wind. The Markov jump linear model can precisely model the random WECS properties. Second, the scenario-based SMPC is used as the controller to address the control problem of the WECS. With this controller, all the possible realizations of the disturbance in prediction horizon are enumerated by scenario trees so that an uncertain SMPC problem can be transformed into a deterministic model predictive control (MPC) problem. Finally, the CVaR object function is adopted to improve the fault-tolerant control performance of the SMPC controller. CVaR can provide a balance between the performance and random failure risks of the system. The Min-Max performance index is introduced to compare the fault-tolerant control performance with the proposed controller. The comparison results show that the proposed method has better fault-tolerant control performance.

The efficacy of control systems for distribution grids can be influenced by different sources of uncertainty. Stochastic Model Predictive Control (SMPC) can be employed to compensate for such uncertainties by integrating their probability distribution into the control problem. An efficient SMPC algorithm for online control applications is the stochastic tube SMPC, which is able to treat the evaluation of the chance constraints analytically. However, this approach is efficient only when the calculation of the constraint back-off is applied to a linear model. To address this issue, this work employs Gaussian Processes to approximate the nonlinear part of the power flow equations based on offline training, which is integrated into the SMPC formulation. The resulting SMPC is first validated and then tested on a benchmark system, comparing the results with Deterministic MPC and SMPC that excludes Gaussian Processes. The proposed SMPC proves to be more efficient in terms of cost minimization, reference tracking and voltage violation reduction.

The domain of attraction is central to stability and recursive feasibility of model predictive control (MPC). For stochastic linear systems, this paper addresses the problem of enlarging the domain of attraction of stochastic MPC (SMPC) for offset-free tracking. The proposed SMPC strategy relies on using an artificial steady-state target to enlarge the domain of attraction while ensuring recursive feasibility. The key advantage of the proposed strategy is that it alleviates the computation of an additional robust control invariant set to greatly simplify the SMPC design. Furthermore, the proposed SMPC strategy for offset-free tracking circumvents feasibility loss due to target changes since the feasible region is independent of the desired steady-state target. The SMPC strategy is demonstrated on a benchmark DC-DC converter case study, where its performance is compared to that of standard SMPC for regulation based on tighter constraints and a recently proposed SMPC strategy with a first-step constraint.

ABSTRACTThis article proposes a parallel algorithm of stochastic model predictive control (SMPC) for linear discrete‐time systems. The proposed algorithm uses multiple threads to solve respective optimization problems at different time steps in parallel, without inter‐thread communication during each optimization. Each thread sequentially solves a stochastic optimal control problem (SOCP) for optimizing closed‐loop performance against future disturbances and a partial minimization problem for optimizing a subset of decision variables of the SOCP. The partial minimization problem computes the control input according to the last measured state to satisfy chance constraints and can be solved much faster than the original SOCP. Consequently, the proposed algorithm can reduce the implementable minimum sampling period compared to the original SMPC. A numerical example of controlling room temperature showed that the proposed algorithm achieves control performance almost identical to that of closed‐loop SMPC, which optimizes closed‐loop performance. However, the implementable minimum sampling period of the proposed algorithm is much shorter than that of the closed‐loop SMPC, even with parallelization overhead.

This paper presents the open-source stochastic model predictive control framework GRAMPC-S for nonlinear uncertain systems with chance constraints. It provides several uncertainty propagation methods to predict stochastic moments of the system state and can consider unknown parts of the system dynamics using Gaussian process regression. These methods are used to reformulate a stochastic MPC formulation as a deterministic one that is solved with GRAMPC. The performance of the presented framework is evaluated using examples from a wide range of technical areas. The experimental evaluation shows that GRAMPC-S can be used in practice for the control of nonlinear uncertain systems with sampling times in the millisecond range.

Stochastic Nonlinear Model Predictive Control with Active Model Discrimination: A Closed-Loop Fault Diagnosis Application

Stochastic Model Predictive Control (SMPC) has attracted increasing attention for autonomous driving in recent years, since it enables collision-free maneuvers and trajectory planning and can deal with uncertainties in a non-conservative way. Many promising strategies have been proposed on how to use SMPC to select appropriate maneuvers and plan safe trajectories in uncertain environments. The limitation of these approaches is that they focus on scenarios where only one vehicle is controlled by SMPC and is, thus, reacting to the surrounding vehicles; however, the surrounding vehicles do not react to the SMPC-controlled vehicle, which means there is no mutual interaction. However, when multiple autonomous vehicles are driving on the road, each individual vehicle will take the behavior of the other surrounding vehicles into account and adjust its individual decisions accordingly in trajectory planning. This paper, therefore, examines in simulations how the interactive control system of multiple SMPC-controlled vehicles behave based on a Distributed SMPC (DSMPC) framework. For a three-lane highway scenario, we first investigate the effects of the risk parameter of the collision avoidance probabilistic constraint on non-interactive and interactive vehicle systems and provide insights into how to parameterize the controllers in interactive vehicle systems.

A stochastic model predictive control (SMPC) method is proposed for trajectory tracking of quadrotor helicopters with stochastic disturbances. The stochastic disturbances are assumed to be Gaussian white noises. The existing robust control methods generally guarantee that the tracking performances under the worst-case disturbances satisfying given conditions. However, the worst-case disturbances may have a vanishingly small probability of occurrence in practice, so these methods show great conservative. In this paper, the tracking errors caused by the disturbances are limited in the acceptable range with the given probability. The hierarchical control structure is used. In the outer loop, the position loop, SMPC controllers are designed for position tracking. In the inner loop, the attitude loop, the nonlinear dynamics are linearized by the feedback linearization strategy, and an SMPC controller is designed for attitude tracking. Finally, simulation results verify the effectiveness of the proposed method.

A methodology has been developed for optimizing building supervisory control strategies, employing building models that incorporate stochastic models of occupant behaviour and serve as the objective function evaluator in a stochastic model predictive control (SMPC) architecture. The SMPC architecture accounts for variability in building performance due to occupant behaviour and is shown to generate a sequence of automatic window opening decisions for a mixed mode building which lead to more robust building performance in the face of occupant window use than a heuristic controller. A set of receding optimization time horizons are described which enable the use of complex building models in simulated SMPC. Results of a case study show that deterministic optimization predicts a 50% increase in building performance, while stochastic optimization leads to a more conservative and more reliable 33% performance improvement, which takes into consideration the impact of occupant behaviour.

In this chapter, a multi-time scale stochastic model predictive control (MPC) approach is applied to solve the cooperative distributed energy scheduling problem of smart homes. In this problem, a variety of energy resources are considered for each smart home, and every smart home has a capability of power transaction with the retailer through the electrical grid as well as with the other connected smart homes. The challenges of the problem include modeling the technical and economic constraints of the energy resources and addressing the variability and uncertainty issues of renewables’ power that change the optimization problem to a stochastic, dynamic (time-varying), and mixed-integer nonlinear programming (MINLP) problem. To deal with the variability and uncertainty issues, a multi-time scale stochastic MPC is applied. Applying the multi-time scale approach in the stochastic MPC is able to simultaneously consider the precise resolution for the problem variables and the vast vision for the optimization time horizon. In addition, linear programming (LP) and genetic algorithm (GA) are combined (GA-LP) and applied in the problem as an effective and fast optimization technique. The numerical studies about the small and large systems demonstrate the competences of the proposed approach.KeywordsCooperative distributed energy schedulingMulti-time scale model predictive control (MPC)Photovoltaic (PV) panelsSmart homesStochastic optimization

The charging management of plug-in electric vehicles (PEVs) in San Francisco considering the effect of drag force on the vehicles, the real driving routes of vehicles, the social aspects of drivers' behaviour, the type of PEVs and the PEV penetration level is presented in this study. In this study, the drivers' responsiveness probability, to provide vehicle-to-grid service at the parking lot, is modelled with respect to the value of the incentive, drivers' social class and the real driving routes in San Francisco. Herein, the Monte Carlo Markov Chain is applied to estimate the hourly probability distribution function of the state of charge (SOC) of the PEV fleet in the day. The main data set applied in this study includes the real longitude and latitude of driving routes of vehicles in San Francisco, recorded in every four-minute interval of the day. In this study, a stochastic model predictive control is applied in the optimisation problem to address the variability and uncertainty issues of PEVs' SOC and renewables' power. Herein, quantum-inspired simulated annealing algorithm is applied as the optimisation technique. It is demonstrated that the type of PEVs, the PEV penetration level and even the social class of drivers can affect the problem results.