Chance-constrained Optimization Research Articles

Sample-Based Optimal Dispatch of Shared Energy Storage in Community Microgrids Considering Uncertainty

Shared energy storage (SES) in communities equipped with renewable energy sources (RESs) can effectively maintain power supply reliability. However, the dispatch of SES is highly influenced by the uncertainty of RES output. Traditional optimization approaches, such as chance-constrained optimization (CC) and robust optimization (RO), have limitations. The former relies heavily on distribution information, while the latter tends to be overly conservative. The above problems are prominent when the size of available samples is limited. To address this, we introduce the concept of statistical feasibility and propose a sample-based robust optimization approach. This approach constructs the uncertainty set through shape learning and size calibration based solely on the sample set and further reconstructs it by introducing constraint information. Our numerical studies show that the proposed approach can obtain feasible optimal results with a 10.82% cost increase compared to deterministic optimization, and the reconstruction of the uncertainty set can increase the level of utilization of the stability requirement to around 0.05. Comparisons with several traditional optimization approaches demonstrate the effectiveness of the proposed approach.

A bi-objective data-driven chance-constrained optimization for sustainable urban medical waste management

A bi-objective data-driven chance-constrained optimization for sustainable urban medical waste management

Finding search directions in quasi-Newton methods for minimizing a quadratic function subject to uncertainty

We investigate quasi-Newton methods for minimizing a strongly convex quadratic function which is subject to errors in the evaluation of the gradients. In particular, we focus on computing search directions for quasi-Newton methods that all give identical behavior in exact arithmetic, generating minimizers of Krylov subspaces of increasing dimensions, thereby having finite termination. The BFGS quasi-Newton method may be seen as an ideal method in exact arithmetic and is empirically known to behave very well on a quadratic problem subject to small errors. We investigate large-error scenarios, in which the expected behavior is not so clear. We consider memoryless methods that are less expensive than the BFGS method, in that they generate low-rank quasi-Newton matrices that differ from the identity by a symmetric matrix of rank two. In addition, a more advanced model for generating the search directions is proposed, based on solving a chance-constrained optimization problem. Our numerical results indicate that for large errors, such a low-rank memoryless quasi-Newton method may perform better than a BFGS method. In addition, the results indicate a potential edge by including the chance-constrained model in the memoryless quasi-Newton method.

Stochastic Operation of Multi-Terminal Soft Open Points in Distribution Networks With Distributionally Robust Chance-Constrained Optimization

Stochastic Operation of Multi-Terminal Soft Open Points in Distribution Networks With Distributionally Robust Chance-Constrained Optimization

Enhancing supply chain resilience with recovery strategies under electricity shortages

Electricity shortages triggered by extreme events have profoundly disrupted supply chains (SCs) in recent years. As SC operations heavily depend on electricity, simultaneous uncertainties may occur in supply and production capacities, demand, and transportation capacity if electric trucks are used. To enhance SC resilience, it is imperative to combine new recovery strategies (i.e. alternative energy sources and alternative transportation vehicles (ATVs)) with traditional ones to restore SC performance. However, these strategies have not been investigated quantitatively. Besides, only partial probability distribution information of uncertainties may be available under electricity shortages. Thus, this work improves SC resilience from a worst-case perspective, where the moment information is known. For the problem, a bi-objective distributionally robust chance-constrained optimisation model is constructed to balance the total cost and the service level. Then, an effective ϵ-model-based constructive heuristic (ϵ-MBCH) is developed. Compared with the ϵ-constraint method, the efficiency of ϵ-MBCH is improved by 99.81%. Based on stress tests and sensitivity analyses on a real case, key managerial insights include: (i) the ATV strategy is indispensable under varying severities of electricity shortages; (ii) the inventory management strategy helps reduce reliance on power generators and diesel trucks; and (iii) mitigating demand variability is essential for reducing costs.

Distributionally robust chance-constrained optimization of MEPS considering hydrogen-containing and phased carbon trading mechanisms

Distributionally robust chance-constrained optimization of MEPS considering hydrogen-containing and phased carbon trading mechanisms

Aggregation Modeling for Integrated Energy Systems Based on Chance-Constrained Optimization

Integrated energy systems (IESs) strengthen electricity–gas–heat multi-energy coupling and reduce wind and light abandonment. For grids with superior distribution, IESs are similar to virtual energy storage systems and are able to realize efficient interaction with the grid by synergizing the operating status of the internal equipment and improving the security, economy, and flexibility of the grid’s operation. However, the internal equipment coupling of an IES is complex, and determining how to evaluate its adjustable capacity range (that is, the upper and lower boundaries of its external energy demand) considering the uncertainty and volatility of wind power and photovoltaic output is a problem to be solved. To solve this problem, this paper presents a chance-constrained evaluation method for the adjustable capacity of IESs. Firstly, mathematical models and operational constraints of each device within the IES are established. Secondly, based on the mathematical model of chance-constrained planning, an adjustable capacity range assessment model considering the uncertainty of wind and photovoltaic output is established. Finally, the MATLAB/Yalmip/Gurobi solver is used for the optimization solution, and the adjustable capacity range interval of the constructed IES model is solved using an arithmetic example to analyze and verify the correctness and validity of the method and to study the influencing factors of its adjustable range.

Combinatorial chance-constrained economic optimization of distributed energy resources

The transformation of the energy system towards sustainable energy sources is characterized by an increase in weather dependent distributed energy resources (DER). This adds a layer of uncertainty in energy generation on top of already uncertain load distribution. At the same time, many households are fitted with renewable generation units and storage systems. The increased intermittent generation in the distribution grid leads to new challenges for the commitment and economic dispatch of DER. The main challenge addressed in this work is to decide which available resources to select for a given task. To solve this, we introduce Stochastic Resource Optimization (SRO), a general purpose, combinatorial, chance-constrained optimization model for the short-term economic selection of stochastic DER. It incorporates correlations between stochastic resources are using copula theory. The contributions of this paper are twofold: First, we validate the applicability of the SRO formulation on a simplified congestion management use-case in a small neighbourhood grid comprised of prosumer households. Second, we provide an analysis of the performance of different solving algorithms for SRO problems and their run-times. Our results show that a fast metaheuristic algorithm can provide high quality solutions in acceptable time on the evaluated problem sets.

The Value of Drilling—A Chance-Constrained Optimization Approach

Managing uncertainty is a core challenge in mine planning. Mine planners often represent various planning variables, such as equipment performance and geological parameters, as random variables due to inherent uncertainties. This paper looks at geological uncertainty and its impact on mine planning. Some traditional approaches to manage this uncertainty include using conditional simulations or mathematical programming in the planning process. Drilling additional holes, despite its cost, is a common method to reduce uncertainty using additional samples to reduce deposit variance. In this paper, we first outline an ore blending optimization model which uses chance-constrained programming to manage property limit risk when selecting the order of ore feed into a processing facility. In coal mining, in tactical planning horizons, the order of coal seam removal is usually predetermined, allowing a blending model to ensure optimal feed properties. Using chance-constrained programming allows us to blend the uncertainties from geological models to maximize plant output while adhering to property constraints. We use the chance-constrained blending model to determine the value of additional information from infill drilling. The model prioritizes drilling locations that reduce uncertainty and improve blending outcomes. A case study on a coking coal mine in Queensland, Australia, demonstrates the model’s application, highlighting significant improvements in blending by reducing the variance of high-quality blocks. The study concludes that targeting high-quality blocks for variance reduction can better accommodate lower-quality material, offering a more valuable approach than the traditional focus of reducing uncertainty in low-quality blocks. This approach provides insights for improving mine planning strategies and showcases the potential of chance constraints in optimizing ore blending under uncertainty.

Closed-loop supply chain network design with price-greenness-sensitive demand: A distributionally robust chance-constrained optimization approach

Closed-loop supply chain network design with price-greenness-sensitive demand: A distributionally robust chance-constrained optimization approach

Scenario-based robust reachability analysis for networked airport delay dynamics

This work introduces a novel scheme to represent delay dynamics in airport networks. A key feature of the proposed scheme is that uncertainty affecting network operation is accounted for via a robust reachability analysis approach. In particular, the dynamical system is adopted to describe the propagation of outbound and inbound delays between airport nodes. A probabilistic reach set for this networked system is formulated as a chance-constrained optimization program. Then, we resort to a data-driven randomized computation method called scenariooptimization , where the chance constraint is replaced by a set of scenario-based deterministic constraints. Besides, the robustness of the reach set is explicitly derived through a posterior algorithm. Moreover, we conduct the extensive experiments on a dataset of real-world airport delays in China and provide some interesting results. Additionally, the case study at a refined scenario level shows the potential of the proposed approach in application.

Optimizing quasi-dynamic wireless charging for urban electric buses: A two-scenario mathematical framework with grid and PV-battery systems

Optimizing quasi-dynamic wireless charging for urban electric buses: A two-scenario mathematical framework with grid and PV-battery systems

Sample-Based Continuous Approximate Method for Constructing Interval Neural Network.

In safety-critical engineering applications, such as robust prediction against adversarial noise, it is necessary to quantify neural networks' uncertainty. Interval neural networks (INNs) are effective models for uncertainty quantification, giving an interval of predictions instead of a single value for a corresponding input. This article formulates the problem of training an INN as a chance-constrained optimization problem. The optimal solution of the formulated chance-constrained optimization naturally forms an INN that gives the tightest interval of predictions with a required confidence level. Since the chance-constrained optimization problem is intractable, a sample-based continuous approximate method is used to obtain approximate solutions to the chance-constrained optimization problem. We prove the uniform convergence of the approximation, showing that it gives the optimal INN consistently with the original ones. Additionally, we investigate the reliability of the approximation with finite samples, giving the probability bound for violation with finite samples. Through a numerical example and an application case study of anomaly detection in wind power data, we evaluate the effectiveness of the proposed INN against existing approaches, including Bayesian neural networks, highlighting its capability to significantly improve the performance of applying INNs for regression and unsupervised anomaly detection.

Bridging chance-constrained and stochastic optimization for risk estimation of virtual energy hubs dominated by hybrid vehicles under diverse uncertainties: To improve economic sustainability

Bridging chance-constrained and stochastic optimization for risk estimation of virtual energy hubs dominated by hybrid vehicles under diverse uncertainties: To improve economic sustainability

Stochastic home care transportation with dynamically prioritized patients: An integrated facility location, fleet sizing, and routing approach

Stochastic home care transportation with dynamically prioritized patients: An integrated facility location, fleet sizing, and routing approach

Distributionally robust chance-constrained optimization with Gaussian mixture ambiguity set

Distributionally robust chance-constrained optimization with Gaussian mixture ambiguity set

Chance-Constrained Optimal Design of PV-Based Microgrids under Grid Blackout Uncertainties

A grid blackout is an intractable problem with serious economic consequences in many developing countries. Although it has been proven that microgrids (MGs) are capable of solving this problem, the uncertainties regarding when and for how long blackouts occur lead to extreme difficulties in the design and operation of the related MGs. This paper addresses the optimal design problem of the MGs considering the uncertainties of the blackout starting time and duration utilizing the kernel density estimator method. Additionally, uncertainties in solar irradiance and ambient temperature are also considered. For that, chance-constrained optimization is employed to design residential and industrial PV-based MGs. The proposed approach aims to minimize the expected value of the levelized cost of energy (LCOE), where the restriction of the annual total loss of power supply (TLPS) is addressed as a chance constraint. The results show that blackout uncertainties have a considerable effect on calculating the size of the MG’s components, especially the battery bank size. Additionally, it is proven that considering the uncertainties of the input parameters leads to an accurate estimation for the LCOE and increases the MG reliability level.

Reliability-based sizing of islanded multi-energy microgrid: a conic chance-constrained optimization approach

AbstractThis paper presents a methodology to optimally design a multi-energy microgrid with thermal and electric loads considering $$N-1$$ N - 1 and probabilistic regulation reserves. This methodology consists of a chance-constrained optimization that determines the optimal sizing of the microgrid. Microgrid operations are rigorously considered by modelling hourly thermal and electric demand patterns as well as technology production schedules over a year. Such schedules include both electric and thermal power balances, ramp constraints, $$N-1$$ N - 1 and regulation reserves, among others. To ensure a reliable microgrid design and operation, reserve constraints have been proposed to deal with both $$N-1$$ N - 1 generation contingencies, and forecast errors. $$N-1$$ N - 1 reserves guarantee that a sudden outage of any of the electric generators is strategically covered by the remaining generators in order to avoid load shedding. Additionally, nonzero-mean random forecast errors of electric load and solar production are addressed by a set of chance constraints able to schedule asymmetric up and down regulation reserves. Their levels are high enough to cover hourly random forecast errors (or intermittencies) with a high threshold probability. The proposed methodology results in a mixed integer second-order cone program. Results of microgrid designs with and without reliability reserves are carefully analysed and compared. Neglecting reliability constraints leads to a lower-cost design at the expense of exposing the microgrid to unsafe operation. Finally, sensitivity analysis to study the optimal portfolio sizing with respect to electric BESS investment cost, solar production forecast mean error, and random intermittency threshold probability are performed.

Distributionally robust chance-constrained optimization for the integrated berth allocation and quay crane assignment problem

Distributionally robust chance-constrained optimization for the integrated berth allocation and quay crane assignment problem

A chance-constrained optimization approach integrating project scheduling and material ordering to manage the uncertain material supply

A chance-constrained optimization approach integrating project scheduling and material ordering to manage the uncertain material supply