Recourse-Cost Constrained Robust Optimization for Microgrid Dispatch With Correlated Uncertainties

To accomplish more practical scheduling of microgrids under source-load uncertainties, this paper proposes a novel recourse-cost constrained adaptive robust optimization (RC-ARO) model with integer recourse variables. Firstly, the dispatch plan in the nominal scenario is optimized in the first-stage of the proposed RC-ARO model to get the minimal operation cost, then the adjustment plan in the worst-case scenario is determined in the second-stage that minimizes the recourse-cost. It has overcome the defect that conventional ARO can only get the worst-cost scheduling plans. Besides, a new column-and-constraint generation (C& CG) algorithm with alternating optimization procedure (AOP) is developed to accelerate the solution of traditional nested-C& CG. Finally, case studies demonstrate the effectiveness and superiority of the proposed RC-ARO model and the novel solution algorithm.

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

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.

Deciphering Latent Uncertainty Sources with Principal Component Analysis for Adaptive Robust Optimization

For the optimal operation of building energy systems with uncertain energy consumption and renewable solar energy supply, the construction of uncertainty set is becoming especially important due to the conservatism of the solution in robust optimization. The general two-stage robust optimization with single-band uncertainty model considers the entire uncertain set for any uncertainty, which would result in too conservative solutions. In order to flexibly adapt the decision solutions for the robust optimal operation of building energy systems, the multiband uncertainty concept is introduced in adaptive robust optimization. An efficient method is defined to partitioning the single uncertainty band into multiple sub-bands on the basis of stochastic programming. And each individual uncertainty set is associated with a certain probability. The numerical study shows that the concept of multiband uncertainty set introduces great flexibility into the adaptive robust optimization model for the optimal operation of building energy systems.

Distribution system operators aim to improve hosting capacity (HC) of distribution networks (DNs) to accommodate more distributed rooftop photovoltaics (PVs). Although PV power generation delivers numerous benefits, power unbalance and voltage rise are two major obstacles that limit the network HC. To mitigate these issues, battery energy storage systems (BESSs) can be applied. Thus, this paper proposes a robustly optimal allocation method for BESSs, which aims to reduce the power unbalance and alleviate the voltage rise, and thus improve the HC of the unbalanced three-phase DNs. Considering that locations and capacities of distributed rooftop PVs are determined by customers, future PV installations are regarded as uncertainties. In addition, to deal with the uncertainties, the proposed BESS allocation problem is formulated as an adaptive robust optimization (ARO) model with integer recourse variables. Accordingly, a solution algorithm which integrates an alternating optimization procedure into a column-and-constraint generation algorithm is developed to efficiently solve the ARO model. With the proposed BESS allocation method, a new perspective on HC improvement is provided, which not only considers the worst power unbalance situation but also satisfies the allowed maximum PV capacity. The simulation results verify high efficiency and solution robustness of the proposed allocation method.

An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.

Considering the increasing penetration of renewable energy sources (RESs) into power grids, adopting efficient energy management strategies is vital to mitigate the uncertainty issues resulting from the intermittent nature of their output power. This paper aims to resolve the energy management problem by presenting an adaptive robust optimization (ARO) model in which uncertainties associated with solar and wind powers, consumer demand, and electricity prices are considered. The proposed model comprises three stages, one master and two subproblems, using both linearized and convexified power flow equations. Meanwhile, a new optimization-based bound tightening (OBBT) method is also presented to strengthen the relaxation. The proposed solution method solves the microgrid (MG) operation management problem with high accuracy due to considering the convexification method in a reasonable computational time and reducing operational costs compared to conventional models. The numerical results indicate the benefits of the proposed ARO and solution approach over traditional methods.

A robust approach to food aid supply chains

Robust Conic Satisficing

Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive RO (ARO) can exhibit too conservative solutions in terms of objective value degradation compared with the nominal case. One of the main reasons behind this conservatism is that, in many practical applications, uncertain constraints are directly designed as constraint-wise without taking into account couplings over multiple constraints. In this paper, we define a coupled uncertainty set as the intersection between a constraint-wise uncertainty set and a coupling set. We study the benefit of coupling in alleviating conservatism in RO and ARO. We provide theoretical tight and computable upper and lower bounds on the objective value improvement of RO and ARO problems under coupled uncertainty over constraint-wise uncertainty. In addition, we relate the power of adaptability over static solutions with the coupling of uncertainty set. Computational results demonstrate the benefit of coupling in applications. Funding: I. Wang was supported by the NSF CAREER Award [ECCS 2239771] and Wallace Memorial Honorific Fellowship from Princeton University. B. Stellato was supported by the NSF CAREER Award [ECCS 2239771].

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.

Distributed modeling considering uncertainties for robust operation of integrated energy system

A novel data‐driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M‐estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over‐conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data‐driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact robust counterpart in its general form for solving the resulting data‐driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short‐term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional robust optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017