Search

The flight environment of aerodynamically controlled missiles is full of complexity and uncertainty. To cope with the uncertainty more effectively and enhance the convergence performance in trajectory optimization problems for aerodynamically controlled missiles simultaneously, the chance-constrained sequential convex programming (CC-SCP) algorithm is proposed in this paper. The uncertainty is regarded as the chance constraint, and a smooth and differential approximation function is designed to transform this chance constraint into the constraint that the convex optimization method can handle. Subsequently, the originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems, in which an initial reference trajectory guess generation strategy is proposed, and a theoretical proof of the exact convex relaxation is given to enhance the algorithm's convergence performance and theoretical value, respectively. Numerical simulations are provided to verify the convergence and effectiveness of the CC-SCP algorithm, and the advantages of using the CC-SCP algorithm to cope with the uncertainty are illustrated. Furthermore, comparative simulation examples show that the proposed algorithm possesses a low conservatism, which means the proposed algorithm can obtain a bigger convergence region and a better solution than other current methods when handling the same chance constraints. Finally, the robustness of the algorithm is discussed. • The algorithm can handle the trajectory optimization problem with uncertainties. • The algorithm outperforms other current methods when handling the chance constraints. • A theoretical proof is given for the exact convex relaxation. [ABSTRACT FROM AUTHOR]

Forecast uncertainties pose a considerable challenge to the success of model predictive control (MPC) in buildings. Numerous possibilities for considering forecast uncertainties in MPCs are available, but an in-depth comparison is lacking. This paper compares two main approaches to consider uncertainties: robust and stochastic MPC. They are benchmarked against a deterministic MPC and an MPC with perfect forecast. The MPCs utilize a holistic building model to reflect modern smart homes that include photovoltaic power generation and storage, thermally controlled loads, and smart appliances. Real-world data are used to identify the thermal building model. The performance of the various controllers is investigated under three levels of uncertainty for two building models with different envelope performance. For the highly insulated building, the deterministic MPC achieves satisfactory thermal comfort when the forecast error is medium or low, but the thermal comfort is compromised for high forecast errors. In the poorly insulated building, thermal comfort is compromised at medium and high forecast errors. Compared to the deterministic MPC, the robust MPC increases the electricity cost by up to 4.5% and provides complete temperature constraint satisfaction while the stochastic MPC increases the electricity cost by less than 1% and fulfills the thermal comfort requirements. [ABSTRACT FROM AUTHOR]

The rapid development of microgrids (MGs) with various prosumers promotes the accommodation of renewable distributed generation (RDG) and provides platforms for local energy sharing among prosumers. However, the operational uncertainties pose enormous challenges to the day-ahead bidding of MGs in the wholesale electricity market and there is an urgent need for a local market to facilitate the local energy sharing. Thus, this paper proposes a risk-averse day-ahead bidding strategy for MGs with full consideration of the multiple uncertainties originating from the wholesale electricity market, RDG and loads. Based on the transactive energy (TE) sharing concept, the local market is formulated as a Stackelberg game (SG) to effectively capture the strategic interaction among the MG and prosumers, where a distributed iterative algorithm with a bisection approach that only requires exchanging TE-related information is adopted to achieve the SG equilibrium without compromising privacy concerns. To handle the uncertainties of RDG and loads, the power balances are formulated as chance constraints and a data-driven quantile forecasting method is developed for achieving the computational tractability of chance constraints without any prior knowledge or probability distribution assumptions. Furthermore, a risk criterion of the conditional value-at-risk is incorporated in the day-ahead bidding model of MGs for risk aversion towards uncertainties of the wholesale electricity market. The effectiveness of the proposed solution is extensively demonstrated through numerical simulation. • A risk-averse day-ahead bidding strategy of TE sharing MGs is presented. • A SG-based local TE market with privacy protection is developed. • The wholesale market uncertainties are addressed in a risk-averse manner via CVaR. • The power balance chance constraints are built to handle RDG and load uncertainties. • A data-driven quantile forecasting method is proposed to solve chance constraints. [ABSTRACT FROM AUTHOR]

This paper presents a scenario-based method to solve the chance-constrained optimization for the nonconvex program. The sample complexity is first developed to guarantee the probabilistic feasibility. Then through the sampling on uncertain parameters, many scenarios are generated to form a large-scale deterministic approximation for the original chance-constrained program. Solving the resulting scenario-based nonconvex optimization is usually time-consuming. To overcome this challenge, we propose a sequential approach to find the global optimum more efficiently. Moreover, two novel schemes: branching-and-sampling and branching-and-discarding are developed for the chance-constrained 0–1 program by refining the scenario set in order to find a less conservative solution. Finally, model predictive control and process scheduling problem are taken as examples to evaluate the effectiveness of proposed optimization approaches. • A scenario-based approach is presented for nonconvex chance-constrained programs. • A sequential method is proposed to solve nonconvex programs to a global optimum. • A branching-and-sampling method is proposed for 0–1 chance-constrained programs. • The branching-and-discarding method is proposed for 0–1 chance-constrained programs. [ABSTRACT FROM AUTHOR]

• Techno-economic analysis of battery storage systems providing frequency control. • A stochastic, data-driven optimisation algorithm to optimise the battery controller. • Use of frequency data and detailed, yet computationally efficient battery models. • Case study of Germany shows the highest margins for a battery rated at 1.6 MW/1.6 MWh. • Calendar ageing drives battery degradation, while cycle ageing has less impact. Optimal investment in battery energy storage systems, taking into account degradation, sizing and control, is crucial for the deployment of battery storage, of which providing frequency control is one of the major applications. In this paper, we present a holistic, data-driven framework to determine the optimal investment, size and controller of a battery storage system providing frequency control. We optimised the controller towards minimum degradation and electricity costs over its lifetime, while ensuring the delivery of frequency control services compliant with regulatory requirements. We adopted a detailed battery model, considering the dynamics and degradation when exposed to actual frequency data. Further, we used a stochastic optimisation objective while constraining the probability on unavailability to deliver the frequency control service. Through a thorough analysis, we were able to decrease the amount of data needed and thereby decrease the execution time while keeping the approximation error within limits. Using the proposed framework, we performed a techno-economic analysis of a battery providing 1 MW capacity in the German primary frequency control market. Results showed that a battery rated at 1.6 MW, 1.6 MWh has the highest net present value, yet this configuration is only profitable if costs are low enough or in case future frequency control prices do not decline too much. It transpires that calendar ageing drives battery degradation, whereas cycle ageing has less impact. [ABSTRACT FROM AUTHOR]

• Optimal Bayesian experiment design for parameter inference in constrained nonlinear systems. • Using surrogate models based on arbitrary polynomial chaos for efficient sample-based computation of the expected utility function. • Chance constrained handling in Bayesian experiment design. The optimal design of experiments is crucial for maximizing the information content of data across a wide-range of experimental goals. This paper presents a Bayesian approach to optimal experiment design (OED) for parameter inference in constrained, dynamic, and nonlinear systems under noisy, incomplete, and indirect measurements. Bayesian OED maximizes an expected utility objective, which accounts for prior and posterior uncertainty in the model parameters from an information-theoretic standpoint. Due to the complicated form of the expected utility, it must be estimated using sample-based methods and, in particular, a nested Monte Carlo estimator that is expensive to evaluate using the full dynamic model. We propose a novel surrogate model based on arbitrary polynomial chaos (aPC), which readily applies to any type of prior distribution. The aPC expansions are constructed locally at each design visited during the iterative optimization procedure. The main cost in aPC, which is the determination of the expansion coefficients, is minimized by estimating these coefficients from only a minimal set of dynamic model evaluations. Although sample-based estimators can also be applied to the chance constraints, this leads to a potentially large number of binary variables, such that a smooth moment-based approximation is preferred in this work. Numerical simulations indicate that the proposed surrogate can significantly lower the computational cost of the Bayesian OED, while guaranteeing the original chance constraints are satisfied without noticeably increasing the average time to find a solution. As such, this methodology appears to have the potential to pave the way for real-time or sequential dynamic experiment design in a fully Bayesian setting. [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 • The study proposes an advanced control structure in 3 layers aiming the optimal efficiency energy management for Grid-Connected Hybrid Power Plant. • The control structure is based on a Stochastic Model Predictive Control and an optimal finite-state machine to take into account disturbances variations. • Disturbance estimation techniques based on of NAR Neural Networks are applied to have prediction of renewable sources. • The studied control method is compared, through simulation, to a deterministic MPC approach to illustrate an improved performance. Abstract This study presents a complete advanced control structure aimed at the optimal and most efficient energy management for a Grid-Connected Hybrid Power plant. This control scheme is composed of process supervision and process control layers, and it is a possible technology to enable improvements in the energy consumption of industrial systems subject to constraints and process demands. The proposed structure consists of the combination of a Model-Based Predictive Controller, formulated within the Chance Constraints framework to deal with stochastic disturbances (renewable sources, as solar irradiance), an optimal finite-state machine decision system and the use of disturbance estimation techniques for the prediction of renewable sources. The predictive controller uses feedforward compensation of estimated future disturbances, obtained by the use of Nonlinear Auto-Regressive Neural Networks with time delays. The proposed controller aims to perform the management of which energy system to use and to decide where to store energy between multiple storage options. This has to be done while always maximizing the use of renewable energy and optimizing energy generation due to contract rules (maintain maximal economic profit). The proposed method is applied to a case study of energy generation in a sugar cane power plant, with non-dispatchable renewable sources (such as photovoltaic and wind power generation), as well as dispatchable sources (as biomass and biogas). This hybrid power system is subject to operational constraints, as to produce steam in different pressures, sustain internal demands and, imperiously, produce and maintain an amount of electric power throughout each month, defined by strict contract rules with a local Distribution Network Operator (DNO). This paper aims to justify the use of this novel approach to optimal energy generation in hybrid microgrids through simulation, illustrating the performance improvement for different cases. [ABSTRACT FROM AUTHOR]

At present, electricity generation is responsible for more than a quarter of the greenhouse gas emissions in the US. Integrating significant amounts of renewable energy sources into a power grid is probably the most accessible way to reduce carbon emissions from power grids and slow down climate change. Unfortunately, the most accessible renewable power sources, such as wind and solar, are highly intermittent and thus bring a lot of uncertainty to power grid operation and challenge existing optimization and control policies. The chance-constrained (CC) alternating current optimal power flow (AC-OPF) framework finds the minimum cost of generation dispatch, maintaining the power grid operation within security limits with a prescribed probability. Unfortunately, the AC-OPF problem's chance-constrained extension is non-convex, computationally challenging, and requires knowledge of system parameters and also needs additional assumptions to be made about the behavior of renewable generation probability distribution. Known linear and convex approximations to the above problems, though tractable, are too conservative for operational practice and do not consider uncertainty in system parameters. This paper presents an alternative data-driven approach for solving the stochastic AC-OPF problem, based on Gaussian process regression (GPR) to close this gap. The Gaussian process (GP) approach learns a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The latter is then used to determine the solution of CC-OPF efficiently, by accounting for both input and parameter uncertainty. The practical efficiency of the proposed approach using different approximations for GP-uncertainty propagation is validated and illustrated using a number of standard IEEE test cases. • Chance constrained optimal power flow based on data-driven approach. • Gaussian process regression for solving stochastic optimal power flow. • Gaussian processes for handling uncertainties in power systems. • Machine learning for power system optimization. [ABSTRACT FROM AUTHOR]

Stochastic model predictive control (SMPC) provides a probabilistic framework for MPC of systems with stochastic uncertainty. A key feature of SMPC is the inclusion of chance constraints, which enables a systematic trade-off between attainable control performance and probability of state constraint violations in a stochastic setting. This paper presents an overview of core concepts in SMPC in relation to MPC and stochastic optimal control, with numerical illustrations on a typical chemical process. Estimation of stochastic disturbances as well as the impact of estimation quality of stochastic disturbances on the SMPC performance are discussed. Some avenues for future research in SMPC are suggested. [ABSTRACT FROM AUTHOR]

Electric energy generation from renewable energy sources is generally non-dispatchable due to its intrinsic volatility. Therefore, its integration into electricity markets and in power system operation is often based on volatility-compensating energy storage systems. Scheduling and control of this kind of coupled systems is usually based on hierarchical control and optimization. On the upper level, one solves an optimization problem to compute a dispatch schedule and a coherent allocation of energy reserves. On the lower level, one performs online adjustments of the dispatch schedule using, for example, model predictive control. In the present paper, we propose a formulation of the upper level optimization based on data-driven probabilistic forecasts of the power and energy output of the uncontrollable loads and generators dependent on renewable energy sources. Specifically, relying on probabilistic forecasts of both power and energy profiles of the uncertain demand/generation, we propose a novel framework to ensure the online feasibility of the dispatch schedule with a given security level. The efficacy of the proposed scheme is illustrated by simulations based on real household production and consumption data. [ABSTRACT FROM AUTHOR]

Uncertainties in oil demands have significant effects on the routing and scheduling of oil tankers and inevitably influence the pertinent fleet operational expenses, shortage and excess inventory penalties, and chartering costs. In this paper, we study a stochastic maritime scheduling transportation-inventory problem to transport crude oil from a source using a set of fully loaded heterogeneous vessels to be fully unloaded at a destination over a finite time horizon. Daily demands at the destination are normally distributed random variables and different penalties are imposed on the shortages/excesses in daily storage levels at the destination. The expected total cost of such a fleet operation, consists of the total vessels’ operational expenses, expected total penalties resulting from violating specified lower and upper bounds at the destination storage facility, and chartering expenses. We aim to simultaneously optimize the fleet schedules and maintain desirable daily storage levels to meet the stochastic demand requirements at the destination with acceptable reliability levels. We formulate the problem as a stochastic optimization model and then use chance constrained programming to convert it to an exact mixed-integer nonlinear program with a convex objective function and linear constraints. Solutions obtained via the proposed stochastic model and its deterministic counterpart are compared and analyzed to gain insights into the impact of the variations in demands and the probabilities of meeting demands on the overall operation and cost structure. [ABSTRACT FROM AUTHOR]

• A novel data-driven surrogate is developed for chance constraint reformulation. • Wind curtailment dispatch is explicitly modeled in chance constraints. • A correction strategy is proposed to ensure modeling accuracy. • The proposed approach is effective under arbitrary distribution assumptions. Chance-constrained optimization (CCO) has been widely used for uncertainty management in power system operation. With the prevalence of wind energy, it becomes necessary to consider wind curtailment as a dispatch variable in CCO. However, the wind curtailment will cause an impulse for the uncertainty distribution, yielding challenges for explicit modeling of chance constraint. In this paper, a novel data-driven framework is developed to handle this issue. By modeling the wind curtailment as a cap enforced on the wind power output, the proposed framework constructs a data-driven surrogate to describe the relationship between wind curtailment and the tightening boundary of chance constraints. This allows us to reformulate the CCO with wind curtailment as a mixed-integer second-order cone programming (MI-SOCP) problem. An error correction strategy is developed by solving a convex linear programming (LP) to improve the modeling accuracy. The notable characteristic of the proposed method is that the chance constraints with wind curtailment can be explicitly and accurately handled without any distribution assumptions, which provides great convenience for the power dispatch under a high percentage of renewables. Case studies performed on the PJM 5-bus and IEEE 118-bus systems demonstrate that the proposed method is capable of accurately accounting the influence of wind curtailment dispatch in CCO. It shows that the proposed method outperforms existing methods by producing more economic and secure solutions for the chance-constrained energy and reserve scheduling problem under uncertainties. [ABSTRACT FROM AUTHOR]

Chance constraints are suitable for industrial process modeling under uncertain conditions, where constraints cannot be strictly satisfied or do not need to be fully satisfied. In this paper, a single machine scheduling problem involving flexible maintenance, production, and uncertainty is modeled as a chance constrained dynamic optimization problem (CCDOP). A novel method is proposed for transforming the CCDOP into an equivalent deterministic dynamic optimization problem (DOP) with fixed state jump times. Furthermore, by using the idea of l 1 penalty function and a smooth approximation technique, the resulting deterministic DOP becomes a smoothing penalty problem, which is a non-convex nonlinear parameter optimization problem (NNPOP) with simple bounds on the variables. To solve the NNPOP, a gradient-based stochastic search algorithm (GSSA) is developed based on a gradient-based adaptive search algorithm (GASA) and a novel stochastic search algorithm (NSSA). The convergence analysis result shows that the GSSA is a globally convergent algorithm. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method. Numerical results show that the GSSA has excellent convergence behavior with robust computation feature, providing better results compared with the other typical methods. • A CCDOA is developed for the single machine scheduling problem. • Propose a novel technique to transform the CCDOP into an equivalent CDPOP. • Design a GASA, which is effective for ill-conditioned problems. • Design a NSSA, in which no parameters tuning is required. • Propose a GSSA for the NNPOP and comparison results imply its superiority. [ABSTRACT FROM AUTHOR]

• Novel constrained grey-box optimization framework using Gaussian process models. • New almost everywhere differentiable acquisition function for composite functions. • Efficient moment-based approximation of chance constraints. • Tailored algorithm for enrichment sub-problem that exploits model structure. • Performance comparison with Bayesian optimization on diverse set of test problems. [Display omitted] Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space. BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure. In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers. COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data. Overall, COBALT shows very promising performance on both unconstrained and constrained test problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses super-efficiency issue based on input relaxation model in stochastic data envelopment analysis. The proposed model is not limited to using the input amounts of evaluating DMU, and one can obtain a total ordering of units by using this method. The input relaxation super-efficiency model is developed in stochastic data envelopment analysis, and its deterministic equivalent, also, is derived which is a nonlinear program. Moreover, it is shown that the deterministic equivalent of the stochastic super-efficiency model can be converted to a quadratic program. As an empirical example, the proposed method is applied to the data of textile industry of China to rank efficient units. Finally, when allowable limits of data variations for evaluating DMU are permitted, the sensitivity analysis of the proposed model is discussed. [Copyright &y& Elsevier]

Abstract: In this paper, additive model is used to provide an alternative approach for estimating returns to scale in data envelopment analysis. The proposed model is developed in both stochastic and fuzzy data envelopment analysis. Deterministic (crisp) equivalents are obtained which correspond to the stochastic and fuzzy models. Numerical examples are, also, used to illustrate the proposed approaches. [Copyright &y& Elsevier]

Deterministic optimization approaches have been well developed and widely used in the process industry to accomplish off-line and on-line process optimization. The challenging task for the academic research currently is to address large-scale, complex optimization problems under various uncertainties. Therefore, investigations on the development of stochastic optimization approaches are needed. In the last few years we proposed and utilized a new solution concept to deal with optimization problems under uncertain operating conditions as well as uncertain model parameters. Stochastic optimization problems are solved with the methodology of chance constrained programming. The problem is to be relaxed into an equivalent nonlinear optimization problem such that it can be solved by a nonlinear programming (NLP) solver. The major challenge towards solving chance constrained optimization problems lies in the computation of the probability and its derivatives of satisfying inequality constraints. Approaches to addressing linear, nonlinear, steady-state as well as dynamic optimization problems under uncertainty have been developed and applied to various optimization tasks with uncertainties such as optimal design and operation, optimal production planning as well as optimal control of industrial processes under uncertainty. In this paper, a comprehensive summary of our recent work on the theoretical development and practical applications is presented. [Copyright &y& Elsevier]