Information-Gap Decision Theory: Principles and Fundamentals

Rezaei, Navid; Ahmadi, Abdollah; Nezhad, Ali Esmaeel; Khazali, Amirhossein

doi:10.1007/978-3-030-04296-7_2

Cited by 5 publications

(5 citation statements)

References 44 publications

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“…In this section, a risk‐involved strategy is developed to handle severe uncertainties of price, demand and power generation of the CoMigs through the envelope‐bound IGDT 44 . The main advantage of this technique is that it does not depend on uncertainty structure; and hence, neither needs the fuzzy membership function nor the probability distribution function of uncertain variables 44 . In lieu of using these functions, the IGDT focuses on what is recognized and what is needed to be recognized.…”

Section: Mathematical Formulation Of the Three‐level Model For The Proposed Multi‐period Magep Problemmentioning

confidence: 99%

Reliability‐based risk‐involved macrogrid expansion planning considering community microgrids within a market environment

Shivaie

2021

Int Trans Electr Energ Syst

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In this paper, a new reliability-based risk-involved model is presented for multi-period macrogrid expansion planning (MAGEP) by amalgamating the notion of community microgrids (CoMigs) within a market environment. The main targets of the proposed model are not only to develop a holistic framework for the MAGEP problem, but also to scrutinize the impacts of the macrogrid-connected multi-CoMigs on power supply reliability enhancement.To that end, the mathematical formulation of the proposed model falls into a nonconvex mixed-integer nonlinear three-level optimization problem. The lower-level outlines a security-constrained bid-based-pool electricity market aimed at providing an efficient platform for different CoMigs and market participants-generation companies (GenCos) and distribution companies (DisCos)-to freely trade electrical power across the macrogrid. The intermediate-level represents an interactive decentralized multi-period twostage microgrid expansion planning (MIGEP) problem in which optimal expansion plans of the CoMigs obtained in the first stage will be examined against the reliability restrictions in the second stage. The upper-level, however, addresses a centralized multi-period techno-economic MAGEP problem, while handling the risks of planning arising from severe uncertainties in forecasted price, demand, and power generation of the CoMigs through a potent envelope-bound information-gap decision theory (IGDT). Due to its proper tackling of the non-convex mixed-integer nonlinear multi-level optimization problems, the symphony orchestra search algorithm (SOSA) is widely employed for solving the proposed model. Effectiveness and capability of the newly developed model are numerically analyzed and verified using its implementation on the IEEE 30-bus and IEEE 118-bus test systems. K E Y W O R D S community microgrids (CoMigs), envelope-bound information-gap decision theory (IGDT), macrogrid expansion planning (MAGEP), microgrid expansion planning (MIGEP), reliability

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Section: Mathematical Formulation Of the Three‐level Model For The Proposed Multi‐period Magep Problemmentioning

confidence: 99%

Reliability‐based risk‐involved macrogrid expansion planning considering community microgrids within a market environment

Shivaie

2021

Int Trans Electr Energ Syst

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“…IGDT is a robust optimization approach that is entirely independent of historical data. In this approach, a predicted value for each uncertain parameter is assumed and the sensitivity of the objective functions is analyzed regarding the variance of the uncertain parameters from the predicted value 28 . RN, RA, and risk‐taker (RT) are common IGDT strategies.…”

Section: Model Description and Problem Formulationmentioning

confidence: 99%

“…In recent years, different methods, such as stochastic programming, robust optimization, and fuzzy optimization, have been introduced to consider the uncertainties in the power system optimization problems, while each of them has its own pros and cons. The scenario‐based stochastic approaches rely on the historical data and the probability density function of uncertain parameters, which may not be always available or even have some difficulty to collect and evaluation 28 . The fuzzy optimization problem suffers from the same problem and must solve the optimization model for the different intervals of the parameters with uncertainties 28 and having enhanced computational complexity 29 .…”

Section: Introductionmentioning

confidence: 99%

“…The scenario‐based stochastic approaches rely on the historical data and the probability density function of uncertain parameters, which may not be always available or even have some difficulty to collect and evaluation 28 . The fuzzy optimization problem suffers from the same problem and must solve the optimization model for the different intervals of the parameters with uncertainties 28 and having enhanced computational complexity 29 . A robust or interval optimization is a bi‐level optimization problem, 28 which needs a careful determination of the uncertainty budgets of the uncertain parameters 29 .…”

Section: Introductionmentioning

confidence: 99%

“…The fuzzy optimization problem suffers from the same problem and must solve the optimization model for the different intervals of the parameters with uncertainties 28 and having enhanced computational complexity 29 . A robust or interval optimization is a bi‐level optimization problem, 28 which needs a careful determination of the uncertainty budgets of the uncertain parameters 29 . Another robust optimization method that is used to model uncertainties is the information gap decision theory (IGDT), which is suitable for solving optimization problems, especially in the absence of adequate information about the uncertainties.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An info‐gap risk‐averse optimization model for coordination of overcurrent protective relays considering power system uncertainty

Salahi

Rezaei

Moshtagh

2020

Int Trans Electr Energ Syst

Self Cite

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Summary The power system protection scheme must detect faults as soon as possible and isolate the faulty section from the rest of the network in the shortest possible time. Protection in medium voltage distribution networks is usually performed through applying coordinated protective overcurrent relays. Changes in the network topology and operational parameters may cause some uncertainties, which can have deteriorative impacts on the fault current measuring by overcurrent relays, hence lead to in‐coordinated operation of the overcurrent relays. In this paper, it is aimed to optimally solve the problem of the overcurrent relays coordination considering the fault current uncertainty. To this end, a new risk‐averse robust optimization portfolio is proposed based on information gap decision theory to derive the optimistic coordination scheme under severe uncertainties. The presented model is mathematically formulated and implemented effectively to some medium voltage test power systems. The illustrative numerical results demonstrate the effectiveness of the conducted optimization model in both risk‐neutral and risk‐averse strategies in procuring the robust coordination solution of the overcurrent relays.

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Scheduling of Energy Hub Resources Using Robust Chance-Constrained Optimization

et al. 2022

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This paper develops a robust chance-constrained model for handling the uncertainties of generation and consumption in multi-carrier energy hubs. The proposed model incorporates corresponding loading factors for each type of electrical, heating, and cooling loads. This is done to assess the maximum loadability of the whole system. In this respect, the chance-constrained approach is implemented for the feasibility assessment of the operation problem with uncertainties. The uncertainties which are assumed here include the forecast errors of electrical, heating, and cooling load demands, and the volatile solar power generation. The overall problem formulation is developed in the mixed-integer linear programming (MILP) framework. The standard chance-constrained approach is converted to a deterministic optimization model by utilizing the Big M method. The main objective of the proposed model is to maximize the loadability index with uncertainties while addressing the permissible risk index of the decision-maker. The studied energy hub comprises electrical, heating, and cooling loads, and the energy flow technique is adopted in this paper to model the load balance equations. The simulation results are presented for different scenarios while addressing features of the proposed model for the summer and winter seasons. Furthermore, the developed model is evaluated for different scenarios and a comparison is made with the information-gap decision theory

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Information-Gap Decision Theory: Principles and Fundamentals

Cited by 5 publications

References 44 publications

Reliability‐based risk‐involved macrogrid expansion planning considering community microgrids within a market environment

Reliability‐based risk‐involved macrogrid expansion planning considering community microgrids within a market environment

An info‐gap risk‐averse optimization model for coordination of overcurrent protective relays considering power system uncertainty

Scheduling of Energy Hub Resources Using Robust Chance-Constrained Optimization

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