Decentralized-distributed robust electric power scheduling for multi-microgrid systems

Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty

Adaptive robust scheduling optimization of a smart commercial building considering joint energy and reserve markets

There are different uncertainties in microgrids’ (MG) operation such as output power of renewable energy sources (RESs), electricity price and load demand. Ignoring these existing uncertainties in the optimization problem imposes high cost to the system and the lack of reliability. This paper presents a general linear framework for microgrid optimization problem using robust optimization method. Adaptive robust optimization (ARO) model is a min-max-min problem in which the first level targets to determine the on/off status of dispatchable units, the second one aims find the worst case of uncertain parameters and eventually in third level the operational costs are minimized. This model is converted to a min-max one by using Karush-Kuhn-Tucker (KKT) conditions and then the ensuing model is linearized. A control parameter named budget of uncertainty is considered to determine the level of robustness and being conservative. The more budget of uncertainty we consider, the more robust model we obtain. An optimum point in which the expected cost is minimal and a compromise between the level of robustness and operational cost is reached. A modified IEEE-33 bus system is considered to evaluate the adequacy of proposed linear ARO model. Simulation results prove that the proposed ARO model is appropriately able to deal with the existing uncertainties and results in lower expected cost compared to deterministic model.

The rapid growth of microgrids with various distributed energy resources (DERs) brings new opportunities for local energy sharing in the microgrids. However, the uncertainties of renewable distributed generation and loads pose a great technical challenge for a microgrid operator (MGO). Thus, this paper proposes a transactive energy sharing (TES) approach for the MGO and DER aggregators to minimize the total social cost, considering network operating constraints. Accordingly, a two-settlement transactive energy (TE) market with an incentive energy pricing scheme is developed to encourage the participation in the energy sharing. Besides, the real-time energy transactions of the aggregators are considered in a day-ahead optimization stage to address their negative impacts on microgrid operation. To solve the proposed TES problem, an alternating direction method of multipliers (ADMM) is applied. The uncertainties in each ADMM local problem are further addressed by an adaptive robust optimization (ARO) method solved by a column-and-constraint generation (C&CG) algorithm. The updated dual and coupling variables at each ADMM iteration could interact with the C&CG algorithm, impairing ADMM convergence. To solve this issue, an alternating uncertainty-update procedure is developed. The simulation results verify the high efficiency and solution robustness of the proposed TES method.

The disordered nature of electric vehicle (EV) charging and user electricity consumption behaviors has intensified the strain on the grid. Meanwhile, energy storage technologies and microgrid interconnections still lack effective supply–consumption regulations and cost–benefit optimization mechanisms. Therefore, the system’s operational efficiency holds significant potential for improvement. This paper proposes hierarchical optimization strategies for the multi-microgrid system to address these issues. In the lower layer, for the charging states of EVs in a single microgrid, an improved simulation method to enhance accuracy and a recursion mechanism of an energy storage margin band to facilitate intelligent EV-to-grid interaction are proposed. Additionally, in conjunction with demand management, an adaptive optimization method and a Pareto decision method are proposed to achieve optimal peak shaving and valley filling for both the EVs and load, yielding a 38.5% reduction in the total electricity procurement costs. The upper layer is built upon the EV–load management strategies of microgrids in the lower layers and evolves into a distributed interconnection structure. Furthermore, a dynamic optimization mechanism based on state mapping and a collaborative optimization method are proposed to improve storage benefits and energy synergies, achieving a 22.1% reduction in the total operating cost. The results provided demonstrate that the proposed strategy optimizes the operation of the multi-microgrid system, effectively enhancing the overall operational efficiency and economic performance.

The random fluctuations in inlet flow represent a common uncertainty in aero-engine compressors, necessitating the control of its effects through blade optimization design. To account for the impact of inlet flow fluctuations on performance in blade design optimization, an efficient multi-objective adaptive robust aerodynamic design optimization (ARADO) method is proposed. The optimization method employs a novel sparse polynomial chaos expansion (PCE) and the advanced noisy Gaussian process regression (NGPR) technique is used to establish an initial stochastic surrogate model (SSM) containing statistical moments of aerodynamic performance. By introducing advanced sparse signal processing concepts, the sparce PCE significantly enhances the efficiency of acquiring each training sample for SSM. During the optimization process, the initial SSM autonomously updates based on historical optimization data, without requiring high precision across the entire design space. Compared to traditional model-based aerodynamic robust optimizations, the proposed ARADO method exhibits a faster convergence speed and achieves a superior average level of the optimal solution set. It also better balances various optimization objectives, concentrating the space distribution of optimal solutions closer to the average level. Ultimately, the ARADO is applied to the aerodynamic robust design of a high-load compressor airfoil across all operating incidences. The optimization results enhance aerodynamic performance while reducing performance diversity, thus aligning more closely with practical engineering requirements. Through data analysis of the optimal solutions, robust design guidelines for blade aerodynamic shapes are obtained, along with insights into the flow mechanisms that enhance aerodynamic robustness.

This paper compares risk-averse optimization methods to address the self-scheduling and market involvement of a virtual power plant (VPP). The decision-making problem of the VPP involves uncertainty in the wind speed and electricity price forecast. We focus on two methods: risk-averse two-stage stochastic programming (SP) and two-stage adaptive robust optimization (ARO). We investigate both methods concerning formulations, uncertainty and risk, decomposition algorithms, and their computational performance. To quantify the risk in SP, we use the conditional value at risk (CVaR) because it can resemble a worst-case measure, which naturally links to ARO. We use two efficient implementations of the decomposition algorithms for SP and ARO; we assess (1) the operational results regarding first-stage decision variables, estimate of expected profit, and estimate of the CVaR of the profit and (2) their performance taking into consideration different sample sizes and risk management parameters. The results show that similar first-stage solutions are obtained depending on the risk parameterizations used in each formulation. Computationally, we identified three cases: (1) SP with a sample of 500 elements is competitive with ARO; (2) SP performance degrades comparing to the first case and ARO fails to converge in four out of five risk parameters; (3) SP fails to converge, whereas ARO converges in three out of five risk parameters. Overall, these performance cases depend on the combined effect of deterministic and uncertain data and risk parameters. Summary of Contribution: The work presented in this manuscript is at the intersection of operations research and computer science, which are intrinsically related with the scope and mission of IJOC. From the operations research perspective, two methodologies for optimization under uncertainty are studied: risk-averse stochastic programming and adaptive robust optimization. These methodologies are illustrated using an energy scheduling problem. The study includes a comparison from the point of view of uncertainty modeling, formulations, decomposition methods, and analysis of solutions. From the computer science perspective, a careful implementation of decomposition methods using parallelization techniques and a sample average approximation methodology was done . A detailed comparison of the computational performance of both methods is performed. Finally, the conclusions allow establishing links between two alternative methodologies in operations research: stochastic programming and robust optimization.

This paper addresses the planning problem of residential micro combined heat and power (micro-CHP) systems (including micro-generation units, auxiliary boilers, and thermal storage tanks) considering the associated technical and economic factors. Since the accurate values of the thermal and electrical loads of this system cannot be exactly predicted for the planning horizon, the thermal and electrical load uncertainties are modeled using a two-stage adaptive robust optimization method based on a polyhedral uncertainty set. A solution method, which is composed of column-and-constraint generation (C&CG) algorithm and block coordinate descent (BCD) method, is proposed to efficiently solve this adaptive robust optimization model. Numerical results from a practical case study show the effective performance of the proposed adaptive robust model for residential micro-CHP planning and its solution method.

Purpose:Accuracy of dose calculation models and robustness under various uncertainties are key factors influencing the quality of intensity modulated proton therapy (IMPT) plans. In this work, a robust IMPT optimization based on accurate Monte Carlo (MC) dose calculation is developed.Methods:We used an in‐house developed and graphics processing unit (GPU) accelerated MC for dose calculation. For robust optimization, dose volume histograms (DVHs) were computed for each uncertainty scenario at each optimization iteration. A gradient based adaptive method was used to improve the DVHs with adjustable scenario weights. GPUs were employed to accelerate the optimization process. Uncertainties in patient setup and proton range were considered in all cases studied. Additionally, the uncertainty of intra‐fraction relative shift between fields was considered for craniospinal irradiation cases. The adaptive robust optimization method was compared with for clinical cases at several different disease sites.Results:Comparing with the traditional optimization target volume (OTV) based method, the adaptive robust optimization spared critical structures better while maintain the target coverage in clinical cases. For example, the right parotid hot spot dose was reduced from 78.5Gy to 74.5Gy as shown in Fig. 1. For craniospinal irradiation, the adaptive method found the robust solution at field junctions without manual feathering of the match lines. Even for relatively large head‐and‐neck cases and craniospinal cases, the whole process of MC dose calculation and robust optimization can be done within 30 minutes on a system of 100 Nvidia GeForce GTX Titan cards.Conclusion:A robust IMPT treatment planning system is developed utilizing an adaptive method. The treatment planning optimization is based on MC dose calculation and is accelerated by GPU to be clinically viable.This work is supported in part by Varian Medical Systems.

Proactive and reactive scheduling of the steelmaking and continuous casting process through adaptive robust optimization

Two methods for multistage adaptive robust binary optimization are investigated in this work. These methods referred to as binary decision rule and finite adaptability inherently share similarities in dividing the uncertainty set into subsets. In the binary decision rule method, the uncertainty is lifted using indicator functions which result in a nonconvex lifted uncertainty set. The linear decision rule is further applied to a convexified version of the lifted uncertainty set. In the finite adaptability method, the uncertainty set is divided into partitions and a constant decision is applied for each partition. In both methods, breakpoints are utilized either to define the indicator functions in the lifting method or to partition the uncertainty set in the finite adaptability method. In this work, we propose variable breakpoint location optimization for both methods. Extensive computational study on an illustrating example and a larger size case study is conducted. The performance of binary decision rule and finite adaptability methods under fixed and variable breakpoint approaches is compared.

Multimicrogrid (MMG) systems play an increasingly important role in the smart grid. They come with various potential cyberattacks, which may cause power supply interruption or even human casualties. Therefore, decision-making for timely mitigation of cyberattack risks is highly desirable in the security protection of power systems. However, there is a lack of effective decentralized decision-making strategies that are able to deal with MMG scenarios through distributed consensus. To address this issue, a decentralized consensus decision-making (DCDM) approach is proposed in this article for the security of MMG systems. It achieves decentralized consensus without the need of a trusted authority or central server, making it distinct from existing consensus methods. Meanwhile, it guarantees the consistency and nonrepudiability of consensus results, which are stored on the blockchain in sequence. In each of the distributed agents, the approach consists of a fuzzy static Bayesian game model (FSB-GM) to determine the optimal security strategy and a hybrid consensus algorithm to achieve consensus. The FSB-GM considers the fuzzy preferences of different types of attackers and defenders. The hybrid consensus algorithm is implemented by the fusion improvement of two consensus mechanisms in the blockchain. The effectiveness of the presented approach is demonstrated through a case study on an MMG system.

A chance-constrained energy management in multi-microgrid systems considering degradation cost of energy storage elements

Adaptive Optimization in Non-Stationary Environments with Hierarchical Learning

This article proposes a novel data-driven adaptive robust optimization (ARO) framework based on principal component analysis (PCA). By performing PCA on uncertainty data, the correlations among uncertain parameters are effectively captured, and principal components are identified. Uncertainty data are then projected onto each principal component, and distributional information is extracted from the projected uncertainty data using kernel density estimation. To explicitly account for asymmetric uncertainties, we introduce forward and backward deviations into uncertainty sets. The proposed data-driven ARO approach enjoys a less conservative solution compared with conventional robust optimization methods. A numerical example and an application in process network planning are presented to demonstrate the effectiveness of the proposed approach. Some promising extensions are also made within the proposed framework. Specifically, we investigate a data-driven uncertainty set in a low-dimensional subspace, and derive a theoretical bound on the performance gap between ARO solutions due to the dimension reduction of uncertainties.