Worst-case Realization Of Uncertainties Research Articles

Robust Emergency Preparedness Planning for Resilience Enhancement of Energy-Transportation Nexus Against Extreme Rainfalls

This paper proposes a robust emergency preparedness planning (EPP) scheme to optimally pre-position diverse mobile emergency resources (MERs) in staging locations and perform proactive network reconfiguration for resilience enhancement of energy-transportation nexus (ETN) against extreme rainfalls. Based on rainfall-runoff simulation with hydrodynamic partial differential equations, a risk identification approach for flood-prone transportation modeling is developed for vehicle travel time estimation and MER routing optimization. To handle uncertainties in line outages and flooded roads incurred by extreme rainfalls, a tri-level robust EPP model is proposed to determine the optimal emergency preparedness plan immunized against the worst-case realization of uncertainties. Furthermore, a tailored solution method combining nested column-and-constraint generation algorithm with multiple linearization techniques is devised to cope with the proposed nonlinear robust EPP model. Comparative studies have validated the effectiveness of the proposed scheme for resilience enhancement of the ETN confronted with extreme rainfall disasters.

Robust AC Transmission Expansion Planning Using a Novel Dual-Based Bi-Level Approach

The rapid integration of Renewable Energy Sources (RESs) strengthens the need for a power network that can robustly handle the system's uncertain scenarios. Thus, this paper proposes the first nonlinear novel dual based bi-level approach for robust AC Transmission Expansion Planning (TEP) plans with uncertainties in RES generations and loads. It utilizes a convex relaxation and is solved by Benders Decomposition (BD), where the master determines the robust AC TEP plan. The novel dual slave model for the second level of BD circumvents the issues in using the conventional conic dual theory and aids in the worst-case realization of uncertainties using additional novel constraints. The novel dual slave is solved using Interior Point Method (IPM), as it is not a mixed-integer problem. The proposed work also includes additional linear constraints to reduce the BD's slow convergence and direct the master towards optimality. The robustness of the AC TEP plans is verified by Monte-Carlo Simulation (MCS) of the actual nonlinear and non-convex AC Optimal Power Flow (OPF). The effect of the budget of uncertainty on the AC TEP plans is also investigated. A comparison with the results of a previous work reveals the superiority of the proposed work.

Optimal Demand Response Incorporating Distribution LMP With PV Generation Uncertainty

The utilization of aggregated demand-side flexibility via demand response (DR) has become a promising pathway for the integration of renewable energy resources in power systems. Nowadays, there are several management strategies for DR such as the price-based transactive control strategies. However, many of such existing price-based control strategies neglect the physics and operational constraints of the underlying distribution networks when computing the price, raising concerns regarding their theoretical and practical values. This paper studies this issue and investigates optimal DR (ODR) by incorporating the distribution locational marginal price (DLMP). In particular, we discuss DR in connection with DLMPs and propose a multi-period bilevel optimization problem to find the ODR strategy. The objective is to minimize the peak load, load fluctuation, and payments of load aggregators. In addition, a robust bilevel ODR model is formulated to provide a robust ODR strategy while minimizing operating costs under the worst-case realization of uncertainties; this mitigates the impact of forecasting errors on renewable energy resources. Then, we propose an efficient solution approach by employing the Karush-Kuhn-Tucker conditions and strong duality. Simulation results are presented to illustrate the mutual impacts of the interaction between DR and DLMP and the benefits of the robust ODR strategy.

Two-Stage Robust Sizing and Operation Co-Optimization for Residential PV–Battery Systems Considering the Uncertainty of PV Generation and Load

This article presents a two-stage adaptive robust optimization (ARO) for optimal sizing and operation of residential solar photovoltaic (PV) systems coupled with battery units. Uncertainties of PV generation and load are modeled by user-defined bounded intervals through polyhedral uncertainty sets. The proposed model determines the optimal size of PV–battery system while minimizing operating costs under the worst-case realization of uncertainties. The ARO model is proposed as a trilevel min–max–min optimization problem. The outer min problem characterizes sizing variables as “here-and-now” decisions to be obtained prior to uncertainty realization. The inner max–min problem, however, determines the operation variables in place of “wait-and-see” decisions to be obtained after uncertainty realization. An iterative decomposition methodology is developed by means of the column-and-constraint technique to recast the trilevel problem into a single-level master problem (the outer min problem) and a bilevel subproblem (the inner max–min problem). The duality theory and the Big-M linearization technique are used to transform the bilevel subproblem into a solvable single-level max problem. The immunization of the model against uncertainties is justified by testing the obtained solutions against 36 500 trial uncertainty scenarios in a postevent analysis. The proposed postevent analysis also determines the optimum robustness level of the ARO model to avoid over/under conservative solutions.

An interval-prediction based robust optimization approach for energy-hub operation scheduling considering flexible ramping products

The energy-hub (EH) technique provides a new-type conceptual framework for the interaction, coupling, conversion of different forms of energies to achieve the improvement of energy usage efficiency. In this paper, an optimal economic dispatching model for a residential-level EH in the energy market considering the flexible ramping product (FRP) is proposed. As distinct from existing studies, in this work, we assume that the EH not only involves bidding in the energy market but may also get profits by providing the FRP to the grid. The discussed problem is formulated as a two-stage robust optimization (RO) model, wherein the first-stage is dedicated to minimizing the operation cost of the EH by optimizing its bidding strategy (energy and flexible ramping trading quantities) in the DA market, while the second-stage aims to determine the optimal re-dispatch/corrective schedule of the EH (including adjusted output of EH components, bidding and flexible ramping amount) in the RT market to achieve the energy balancing with the least cost, considering the worst-case realization of uncertainties. In practice, since the selection of uncertainty interval has an important impact on the efficacy of the RO solution, we propose an interval prediction-based approach combining the long short-term memory (LSTM) recurrent neural network and bootstrapping technique to determine the uncertainty interval used in our RO formulation. Compared with the conventional empirical-based interval-setting, the proposed prediction-based technique is useful to reduce the conservative level of RO solutions by deep learning the value of historical data and reflecting the real error distribution of point forecast results in its estimation. The effectiveness of the proposed methodology is examined based on a residential EH case, and the obtained results confirm the validity of the proposed approach in actual implementations.

A hybrid robust distributed model for short-term operation of multi-microgrid distribution networks

In a multi-microgrid active distribution network (MADN), every microgrid (MG) or distribution company (DISCO) is operated as a distinct entity with a different risk level in dealing with uncertainties. Hence, a centralized management for these types of networks is not possible. Moreover, in a centralized formulation, it is very difficult to model different risk levels of uncertainties appropriate to each entity. This paper presents a hybrid robust optimization framework for distributed operation of a MADN. In the first stage, the risk-averse information gap decision theory (IGDT) approach is applied to the model of renewable generation and load uncertainties. To maintain the convex structure of the problem, a robust optimization approach with the worst case realization of uncertainty is used to model day-ahead market price uncertainty. Then, based on a heuristic approach and augmented Lagrangian relaxation (ALR) methods, the centralized problem is decomposed into a DISCO problem and several MG problems with a desired risk level. The proposed method is applied to a modified IEEE 33-bus system, and the numerical results are presented for different case studies. The efficiency of the proposed model is shown by comparing the results with those of centralized and traditional distributed robust optimization models.

Semi-infinite programming for global guarantees of robust fault detection and isolation in safety-critical systems

The increasing uncertainty due to advances in modern systems has negatively impacted system health and safety. System health and safety problems associated with uncertainty can be attributed to (1) inadequate system design, (2) ill-suited controller and operating envelope, and (3) lack of robustness in system diagnostics. The latter issue (3) is the main focus of this paper. This work presents an algorithm for the design of active fault detection and isolation (FDI) tests that provide rigorous guarantees of robustness in safety-critical systems. A semi-infinite program with implicit functions embedded is formulated with the objective of maximizing FDI effectiveness at the worst-case realization of uncertainty by manipulating admissible system inputs, while taking into account system safety constraints. This problem is solved locally and globally illustrating deficiencies in the performance of FDI tests designed for the mean values of anticipated uncertainty. The resulting solution is an optimally performing fault diagnostic test that guarantees system safety over the entire domain of uncertainty. This is illustrated using a benchmark three-tank system and further analyzed through Monte Carlo simulation and k-NN classification.

Robust multi-objective optimization for energy production scheduling in microgrids

ABSTRACTIn order to achieve better economic and environmental benefits of microgrids (MGs) under multiple uncertainties in renewable energy resources and loads, a novel energy production scheduling method is proposed based on robust multi-objective optimization with minimax criterion. Firstly, a mixed integer minimax multi-objective formulation is developed to capture uncertainties as well as minimize economic and environmental objectives. Secondly, the primal problem is decomposed into a bi-level optimization problem, which attempts to seek robust scheduling scheme set under the worst-case realization of uncertainties in a multi-objective framework. Finally, a hierarchical meta-heuristic solution strategy, including multi-objective cross entropy algorithm and δ+ indicator, is designed to solve the reconstructed problem. Numerical results demonstrate that the proposed scheduling method can effectively attenuate the disturbance of uncertainties as well as reduce energy costs and emissions, as compared with single-objective robust optimization and multi-objective optimization scheduling approaches. This study could offer useful insights which help decision-makers balance robustness and comprehensive benefits in the operation of MGs.

A two-stage robust investment model for a risk-averse price-maker power producer

Generation investors face uncertainties that can have a considerable effect on the profitability and, thus, on the generation investment plan. To hedge the risks associated with uncertainties in generation investment decision-making, this paper proposes a two-stage bi-level robust model for application in risk-averse price-making generation investment considering participation in the spot electricity market. The investor is immunized in the model against worst-case realization of uncertainties, such as future demand and power produced by non-dispatchable generation units. The level of risk-aversion in the proposed model is controlled using an uncertainty budget. The resulting mixed-integer linear programming model is solved using Benders decomposition algorithm. The performance of the proposed model is demonstrated using the Garver and IEEE reliability test systems (IEEE-RTS) and the results are compared with those obtained in deterministic cases. As the results show, the proposed model is linearized to be globally optimized by existing branch-and-bound solvers with a good accuracy. A 10% uncertainty in forecasted values of demand/non-dispatchable power generation can lead to a decrease of 16.16% and 26.56% in profit in comparison with deterministic cases in the Garver and IEEE-RTS test systems, respectively. Moreover, the more the risk-averse is investor, the less profit is obtained from generation investment.

Integrated scheduling of energy supply and demand in microgrids under uncertainty: A robust multi-objective optimization approach

As a Demand Response (DR) based working mode, the integrated scheduling of energy supply and demand provides an effective approach to improve economic and environmental benefits for Microgrids (MGs). However, it is still a challenging issue to cover uncertainties caused by intermittent renewable energy and random loads while optimizing multiple objectives in economy and environment. To tackle this issue, an integrated scheduling approach for MGs is proposed based on robust multi-objective optimization. Firstly, load shifting in a finite time is introduced to express an acceptable DR program for industrial customers. A minimax multi-objective optimization model is formulated to seek the minimum operation costs and emissions under the worst-case realization of uncertainties, which are captured by the robust sets with budgets of uncertainty. Secondly, a strong duality based model transformation method is implemented to cope with the strong coupling and nonlinearity in the proposed formulation. Also, Multi-Objective Cross Entropy (MOCE) algorithm is adopted to solve the reconstructed model for simultaneously optimizing all the objectives. Finally, detailed comparative experiments are conducted in problem level, model level and algorithm level. The simulation results show that the proposed scheduling approach can effectively attenuate the disturbances of uncertainties as well as achieve optimal economic and environmental benefits, compared with single-objective robust optimization scheduling approaches and deterministic multi-objective optimization scheduling approaches. Meanwhile, the validity and effectiveness of the robust multi-objective optimization approach for the MG integrated scheduling problem under uncertainty are confirmed.

A risk-averse signal setting policy for regulating hazardous material transportation under uncertain travel demand

To effectively regulate risk associated with hazmat transportation and minimize travel cost over road network under uncertain travel demand, a min-max bi-level programming problem (MMBLPP) is proposed to determine traffic signal settings. A risk-averse signal setting policy using budget of uncertainty (BOU) is presented against the worst-case realization of uncertainty in travel demand. A risk-averse model determining system optimum routes for hazmat carriers is presented where travel delay incurred by regular traffic at downstream junctions has been taken into account. A min-max single-level model (MMX) and a bundle-like solution method are proposed to determine risk-averse signal settings under BOU-based travel demand. To investigate the effectiveness of proposed model, numerical evaluations using real-world road network are empirically made with various scenarios of transport policies. These results reported obviously indicate that the proposed model achieved relatively better results than did traditional one against high-consequence scenarios of uncertain travel demand while substantially mitigating risk in the worst cases.