Adaptive Robust Optimization Research Articles

Improve operational flexibility of distribution systems using transportable resources

With the continuous progress of carbon neutrality, the accelerating integration of distributed renewable energy sources (RES) poses tremendous pressure on distribution systems' safe and stable operation. The distribution systems that cannot be upgraded in time, e.g., those in border areas, are hard to adapt to the large-scale integration of RES and the growing energy demand, facing a severe lack of operational flexibility. In light of this, the integrated mobile energy station (IMES), which consists of a battery system and photovoltaic cells, is used to improve operational flexibility and alleviate the need for upgrades. An adaptive robust allocation and dispatch model is introduced to coordinate the operation of the distribution system and IMES under multiple uncertainties. The first stage of the proposed model optimizes the locations of IMES using the forecast information of RES and loads, while the second stage optimizes the dispatch plan that is adaptive to the realization of uncertainties. Since the uncertain photovoltaic power in the IMES depends on its deployment location, the proposed model is an adaptive robust optimization with decision-dependent uncertainty, bringing great challenges to the solution. To solve it efficiently, a warmstart-enhanced column-and-constraint generation algorithm is introduced, in which the bi-level subproblem is solved by the dual method and outer approximation algorithm. Finally, case studies demonstrate the effectiveness of the proposed method. The participation of six IMESs can save 5.23 % on the system's total cost and avoid the load shedding caused by transmission congestion, indicating IMES's potential for economical and flexible operation of the system.

A comprehensive stochastic-based adaptive robust model for transmission expansion planning

To address various uncertainties appearing in the transmission expansion planning (TEP) problem, appropriate tools such as stochastic programming (SP) or robust optimization (RO) are required. On the other hand, both long-term (LT) and short-term (ST) uncertainties must be well captured to acquire the most reliable and robust solution. The current works model the LT uncertainty by RO and the ST uncertainty by SP, forming a two-stage adaptive robust optimization problem. In contrast, this paper presents a novel approach in which the SP and RO are simultaneously utilized to cope with each type of uncertainty, i.e., LT and ST uncertainty. Unlike the current methods with bilinear terms appearing in the subproblems, the trilinear terms appear in the objective function of the proposed approach, which are linearized accordingly. In addition, we propose a mixed-integer bilinear programming (MIBP) model to specify the rectangles used as uncertainty sets, which is further solved using Konno's algorithm. A standard column-and-constraint (CCG) generation solves the established tri-level structure. Two case studies are used to implement the formulation developed in this work. Results signify the effectiveness of the proposed method.

A machine learning approach to two-stage adaptive robust optimization

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train machine learning models that predict high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. The models can be applied to problems with varying dimensions. We also introduce novel methods to expedite training data generation and reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.

A robust approach to food aid supply chains

One of the great challenges in reaching zero hunger is to secure the availability of sufficient nourishment in the worst of times such as humanitarian emergencies. Food aid operations during a humanitarian emergency are typically subject to a high level of uncertainty. In this paper, we develop a novel robust optimization model for food aid operations during a humanitarian emergency, where we include uncertainty in the procurement prices, which is one of the primary sources of uncertainty in practice. Due to the multi-period and dynamic nature of food aid operations, we extend this robust optimization model to an adaptive robust optimization model, in which part of the decisions is taken after some of the uncertainty has been revealed. Moreover, we analyze a folding horizon approach for the nominal, robust, and adaptive robust optimization models in which decisions can be altered in later time periods. We compare the different approaches based on a food operations case in Syria. We show that the (adaptive) robust optimization approach outperforms the nominal approach in the non-folding horizon case, while the nominal approach performs best in the folding horizon case. Consequently, in case decisions have to be made early on, we show that applying robust optimization to food aid operations can make a difference. However, in case small adaptations can be made to the decisions taken in later time periods, then food aid operations can use a relatively simple approach in practice and apply a folding horizon approach each month to optimize decisions.

Risk-constrained bidding and offering strategy for sector-coupled electricity-hydrogen systems incorporating accessibility level of mobility sector

To enhance the economic viability of integrated energy systems, it is important to balance risk and reward while ensuring operational flexibility and compliance with regulatory constraints. Developing an integrated risk measurement method for energy trading in energy markets that complies with regulatory constraints adds another layer of complexity, especially when dealing with large-scale heterogeneous energy systems, such as those dominated by green hydrogen. Ensuring adherence to market regulations, grid codes, and flexible requirements requires a thorough understanding of legal frameworks and policy considerations, as well as integrating regulatory constraints into the bidding/offering strategies. To address these challenges and enable the profitable development of integrated electricity-hydrogen energy systems (IEHSs), this paper develops a risk-constrained bidding/offering self-scheduling strategy for IEHSs that allows for simultaneous trading in day-ahead energy and reserve electricity markets. The developed self-scheduling strategy regulates hydrogen and power flow in a centralized manner, taking into account the operational limits of the power sector, hydrogen fueling stations (HFSs), electric vehicle parking lots, fuel cell vehicle parking lots, and renewable energy sources. As a salient feature, the important human-related factors in the mobility sector are included in the proposed strategy to motivate private owners to collaborate with IEHSs and to accommodate the charging demand of vehicles with electricity market signals. To obtain the robust day-ahead schedule, economic risks associated with renewable power generation, calls for reserve deployment, and electricity market prices are taken into consideration. Towards this end, a stochastic adaptive robust optimization approach is proposed to control the risk of profit variability, which is solved by a nested column-and-constraint generation algorithm. The effectiveness and feasibility of the proposed strategy are verified using the modified IEEE 14-bus test system, as a standard scale of local IEHSs. The numerical results highlight the synergies impact between HFSs and the power sector, resulting in an increase in the profit of the IEHS from $101.654k to $275.078k. Furthermore, the IEHS can improve its profit margin and competitiveness by employing the tri-level stochastic adaptive robust optimization approach. This approach ensures that the IEHS is resistant to sudden changes in real-time interactions, even with an 8.14% increase in the imbalance cost.

Smart landscaping design for sustainable net-zero energy smart cities: Modeling energy hub in digital twin

In our study, we introduce an innovative energy management system optimized for energy hubs in net-zero energy smart cities, emphasizing sustainability as a core objective. Our approach intricately integrates distributed generation systems and storage facilities within a digital twin framework, incorporating landscape considerations to promote environmental harmony. By prioritizing sustainability, our strategy aims to minimize operational costs while maximizing energy efficiency and reducing carbon emissions. We employ specialized energy flow algorithms for each grid, designing energy hubs that leverage renewable resources and mobile storage to enhance sustainability. To address complexity, our model utilizes a non-convex mixed-integer nonlinear programming structure and robust adaptive optimization techniques, combining the Gray Wolf and Krill Herd algorithms. Through simulations, we demonstrate significant improvements in power system efficiency, including notable reductions in power loss, peak voltage fluctuations, and temperature variations. Our research underscores the critical role of smart landscaping in advancing sustainable energy management for net-zero energy smart cities, facilitating seamless integration of energy hubs with the surrounding landscape within a digital twin paradigm.

Incorporating local uncertainty management into distribution system planning: An adaptive robust optimization approach

As the penetration of renewable energy sources (RES) significantly increases, their inherent uncertainty has brought about a paradigm shift in distribution system planning and operation. The existing planning methodologies usually consider the uncertainty during the investment and day-ahead stages while neglecting the interactive power fluctuations during the intraday stage, resulting in planning schemes with a risk of inadequate regional stability. In light of this, this paper proposes a novel adaptive robust distribution system planning approach that integrates local uncertainty management (LUM) to provide a comprehensive and refined consideration of uncertainty. First, we introduce the concept of LUM that can effectively address the deviations between predicted and actual power of RES and load. Second, we propose the adaptive robust planning model for the distribution system, in which the investment and day-ahead operation are considered in the first stage, while LUM is considered in the second stage to maintain the local stability of interactive power. The proposed model can actively manage uncertainties of RES and load demand, reaching the optimal balance between the investment cost, operational cost, and LUM cost. Finally, by employing the column-and-constraint generation (C&CG), the adaptive robust planning model is decoupled into a master min problem and a slaver max-min problem, after which the max-min problem is converted into a single mixed-integer linear programming (MILP) problem through the strong duality theory and big-M method. The effectiveness of the proposed model is demonstrated using a real-world distribution system located in Fujian Province, China. The simulation results indicate that the proposed model achieves a quantitative decrease of approximately 10% in total cost compared to deterministic planning. Sensitivity analysis is also conducted to reveal the trade-off between economic cost and robustness level.

Distributed Adaptive Robust Restoration Scheme of Cyber-Physical Active Distribution System With Voltage Control

The increasing penetration of distributed generators (DGs) and the advancement of information and communication technologies (ICTs) will facilitate the transformation of the traditional passive distribution network towards a cyber-physical active distribution system (CPADS). With the increasing risks of extreme events, such as natural disasters (e.g., flooding) and cyber-physical attacks, it is critical for CPADS to formulate a restoration scheme to improve its resilience. Therefore, in this paper, a distributed adaptive robust restoration scheme with voltage/var control is presented to cope with the high-impact but low-frequency events. First, a detailed cyber-physical system model is established, including the dynamic routing and the quality-of-services (QoS) in both optical fiber networks and 5G wireless networks. Then, the interactions between the cyber system and the physical system are analyzed. Based on the cyber-physical system model, a two-stage restoration scheme with voltage/var control is proposed by coordinately scheduling different network assets in day-ahead and in real-time. The formulated problem is solved by adaptive robust optimization (ARO). To further enhance the resilience of the CPADS, a distributed restoration framework is proposed. The distributed problem is solved by the alternating direction method of multipliers (ADMM) algorithm, and the convergence of the discrete problem is ensured by introducing the alternating optimization procedure (AOP). Considering the cyber faults, a boundary variable compensation and residual relaxation mechanism is proposed in ADMM. The proposed framework and methodology are verified in the case study. The convergence and the efficiency of the proposed algorithm are verified. Compared with the state-of-art works, the advantages in load restoration capability of the proposed method are shown.

Aggregator-Network Coordinated Peer-to-Peer Multi-Energy Trading via Adaptive Robust Stochastic Optimization

Aggregator-Network Coordinated Peer-to-Peer Multi-Energy Trading via Adaptive Robust Stochastic Optimization

Achieving Emission-Reduction Goals: Multi-Period Power-System Expansion Under Short-Term Operational Uncertainty

Stochastic adaptive robust optimization is capable of handling short-term uncertainties in demand and variable renewable-energy sources that affect investment in generation and transmission capacity. We build on this setting by considering a multi-year investment horizon for finding the optimal plan for generation and transmission capacity expansion while reducing greenhouse gas emissions. In addition, we incorporate multiple hours in power-system operations to capture hydropower operations and flexibility requirements for utilizing variable renewable-energy sources such as wind and solar power. To improve the computational performance of existing exact methods for this problem, we employ Benders decomposition and solve a mixed-integer quadratic programming problem to avoid computationally expensive big-M linearizations. The results for a realistic case study for the Nordic and Baltic region indicate which investments in transmission, wind power, and flexible generation capacity are required for reducing greenhouse gas emissions. Through out-of-sample experiments, we show that the stochastic adaptive robust model leads to lower expected costs than a stochastic programming model under increasingly stringent environmental considerations.

An adaptive robust service composition and optimal selection method for cloud manufacturing based on the enhanced multi-objective artificial hummingbird algorithm

The smooth execution of tasks in the cloud manufacturing (CMfg) process can be significantly affected by various real-world uncertainties, resulting in inefficiencies or even failures of the composite manufacturing service (CMS). Nevertheless, current research primarily concentrates on post-exception emergency handling methods, heavily dependent on the planned CMS and real-time status of manufacturing resources, often leading to suboptimal temporary adjustments or even the inability to find a viable solution. Hence, there is an urgent necessity to enhance the robustness of the planned CMS during the service composition and optimal selection (SCOS) phase. In pursuit of this goal, the paper initially presents an adaptive robust service composition and optimization selection (ARSCOS) model. This model dynamically determines whether to await exception resolution or invoke an alternative service, considering the circumstances when a service exception arises and employing task delay time to characterize the robustness of a specific CMS. Subsequently, an enhanced multi-objective artificial hummingbird algorithm (EMOAHA) is devised for this model. Finally, the efficacy of EMOAHA is demonstrated by applying it to nine different scales of civilian unmanned aerial vehicle manufacturing SCOS problems and 17 benchmark functions. The results illustrate that the proposed EMOAHA exhibits superior convergence and diversity in comparison to the other 11 classical intelligent optimization algorithms.

Robust planning for distributed energy storage systems considering location marginal prices of distribution networks

Energy storage plays an important role in integrating renewable energy sources and power systems, thus how to deploy growing distributed energy storage systems (DESSs) while meeting technical requirements of distribution networks is a challenging problem. This paper proposes an area-to-bus planning path with network constraints for DESSs under uncertainty. First, a distribution location marginal price (DLMP) formulation with maximum fluctuation boundaries of uncertainties is designed to select vulnerable areas exceeding voltage limits and higher line losses that occur in distribution networks. Different from simple multi-scenario power flow calculation and sensitivity analysis, DLMP with time and regional characteristics could be more intuitive to reflect line losses and voltage limits of distribution networks through price signals. After that, a two-stage stochastic robust optimization based planning method is developed to determine locations and capacities of DESSs in vulnerable areas. To make the uncertainty problem more tractable, stochastic scenarios are used to portray upper and lower boundaries of uncertainties, which avoids too-conservative decisions for robust optimization. Finally, numerical tests are implemented to testify the reasonability and validity of the proposed area-to-bus planning path under uncertainty. Compared with the DESSs planning framework without DLMP, the costs of DESSs are observably reduced with DLMP. With same budgets of uncertainty, investment costs of DESSs for the stochastic robust optimization with 30 and 50 scenarios are 3.91% and 4.45% lower than classical adaptive robust optimization (ARO).

Reactive power management considering Transmission System Operator and Distribution System Operator coordination

The increasing integration of Distribution Energy Resources (DER) in the distribution system has brought the necessity of a change in grid management and also for better coordination between the Transmission System Operator (TSO) and the Distribution System Operator (DSO). This work proposes a reactive power management model to be used by DSOs, in which reactive power flexibility from DER, and also from On-Load Tap Changer (OLTC) transformers and capacitor banks are used to handle voltage problems that may arise in both transmission and distribution grids due to the uncertain production of Renewable Energy Sources (RES). Besides, it is proposed that the DSO may provide a service to the TSO, in which the latter requests a reactive power setpoint from the first one, in the TSO-DSO boundary. Adaptive robust optimization on an Alternating Current Optimal Power Flow (AC-OPF) is modelled, ensuring that the DSO receives a feasible solution and is able to manage congestion and voltage problems. The proposed model is compared with its stochastic equivalent to assess its strengths and drawbacks. To test and validate the proposed models, a 37-bus Medium Voltage (MV) distribution grid with high RES penetration is used. An important conclusion is that, though the robust model presents a safer solution than the stochastic model, the operator must be aware of the trade-off between the desired level of robustness and the expected operating cost.

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

With the increase in renewable energy penetration and the widespread use of electric vehicles, the uncertainty of controllable resources adversely affects the economic scheduling of smart buildings. Meanwhile, the smart building can take advantage of its flexibility through multiple markets mechanism. Therefore, this paper proposes an optimal scheduling model for the smart commercial building, including electric vehicle charging, which partakes in the day-ahead energy reserve markets. Firstly, the behavior of electric vehicles is obtained through Monte Carlo simulation. This paper categorizes electric vehicles according to their behavioral characteristics and proposes corresponding scheduling strategies. Then, the joint energy and reserve markets mechanism is introduced, and the robust adaptive optimization (ARO) method is employed to deal with uncertainties. The proposed model is a three-level and two-stage model, which can be solved by the column and constraints generation algorithm. Finally, the economy and feasibility of the proposed model are validated through a case study. Results show that the ARO method saves 3%–4% of expenses more than the pure robust optimization method, and the proposed joint markets mechanism can increase profits by 1%–4%.

Multistage Adaptive Robust Binary Optimization: Uncertainty Set Lifting versus Partitioning through Breakpoints 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.

An Adaptive Robust Optimization Model for Microgrids Operation Using Convexified AC Power Flow Equations

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.

Adaptive robust optimization for lot-sizing under yield uncertainty

In manufacturing environments, uncertain production yield directly impacts the quality and feasibility of the production planning decisions. This paper investigates the use of adaptive robust optimization to hedge against uncertain yield when determining a production plan, and to react properly when updated information unfolds. We first derive a myopic adaptive robust policy for the inventory management problem, a special case of the lot-sizing problem where the setup and the production costs are omitted. We show that the policy is optimal under mild assumptions. Second, we address a multi-period single-item lot-sizing problem with a backorder and uncertain yield via adaptive robust optimization. We formulate an adaptive robust model based on the budgeted uncertainty set, where we exploit a linear approximation to transform the quadratic constraints into a mixed-integer linear program. We also propose a column and constraint generation algorithm to solve the adaptive model exactly. Finally, we demonstrate the performances of the proposed approaches and the value of the adaptive robust solutions through extensive numerical experiments.

A two‐stage adaptive‐robust optimization model for active distribution network with high penetration wind power generation

AbstractHigh penetration of uncertain wind power generation brings challenges to power system operational security and economy. Here, an adjustable box uncertainty set is first presented to characterize the spatiotemporal correlation of multiple wind power generations. Afterward, a two‐stage risk‐adjusted robust energy dispatching model is established as a min‐max‐min optimization problem for active distribution networks operating with high penetration wind power generation. Then a three‐layer Nest Column and Constraint Generation (NCCG) decomposition approach is designed to efficiently solve the proposed model. Finally, the proposed two‐stage adaptive robust optimization model and NCCG approach are validated by a distribution network with uncertain wind power generations, and the simulation results indicate the distribution network operation economy could be compromised with robustness by adjusting the conservative regulation parameter.

Optimal Scheduling of Virtual Power Plant Considering Reconfiguration of District Heating Network

A combined heat and power virtual power plant (CHP-VPP) can effectively control the distributed resources in an electric–thermal coupling system and solve the problem of lack of flexibility caused by large-scale renewable energy grid connection. Similar to the optimal reconfiguration of distribution network topology by operating switches, the district heating system is also equipped with tie and sectionalizing valves to realize the optimal adjustment of district heating network (DHN) topology, which provides an economical and effective method for improving the power system’s flexibility. Based on this, this paper proposes a CHP-VPP economic scheduling model considering reconfigurable DHN. Firstly, the energy flow model is introduced to reduce the computational complexity. Secondly, adaptive robust optimization solved by the column-and-constraint generation algorithm is used to settle the randomness of wind power to ensure that the results are feasible in all worst scenarios. Finally, the feasibility of the proposed model is illustrated by case studies based on an actual CHP-VPP. The results show that compared with the reference case, considering the reconfigurability of DHN in the CHP-VPP optimization scheduling process can reduce the cost by about 2.78%.

Expansion planning of the transmission network with high penetration of renewable generation: A multi-year two-stage adaptive robust optimization approach

This paper addresses the multi-year two-stage expansion planning of the transmission network of a power system with high penetration of renewable generation modeling long-term uncertainty by using adaptive robust optimization. The multi-year nature of the problem is modeled by considering a comprehensive view of the planning horizon. A cardinality-constrained uncertainty set is used to model the future worst-case uncertainty realization of the peak power consumption of loads, along with the capacity and marginal production cost of generating units. Unlike previous works, we model certain features of the operation that are typically ignored in multi-year robust transmission network expansion planning problems, namely, the operational variability of renewable generating units, the operational flexibility of conventional generating units, and the non-convex operational feasibility sets of storage facilities. The solution procedure employed for this multi-year two-stage robust problem, which is formulated as a three-level problem, is based on the combination of the nested column-and-constraint generation algorithm with two exact acceleration techniques. We analyze the performance of the proposed model through the use of the IEEE 24-bus Reliability Test System and the IEEE 118-bus Test System. Numerical results show that the use of the multi-year approach leads to reductions in the total worst-case cost of up to 7% in comparison with the static and sequential static procedures. Moreover, an underestimation of the total worst-case cost of more than 8% is attained when ignoring certain operational constraints of conventional generating units and storage facilities. Lastly, a sensitivity analysis is presented in order to illustrate the impact of the maximum deviations of the uncertain parameters on the total worst-case cost.