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• This paper employs IGDT to model the uncertain factors in the day-ahead scheduling plan to reduce the large deviation between the day-ahead scheduling plan and the actual scheduling caused by source and load prediction errors. • To support IGDT in dealing with multiple uncertainties, this work implements a two-point estimation method and Cornish-Fisher series expansion to transform the multiple uncertainties (in terms of the source and the load) into a single power shortage uncertainty, thereby improving the solving efficiency of the IGDT model. • the Nataf inverse transformation and singular value decomposition techniques are introduced so that the 2PEM-Cornish-Fisher method could handle input variables that are correlated, thereby improving the applicability of the IGDT model. • This paper uses MPC rolling optimization within a day to correct the day-ahead scheduling deviation and compensate for the shortcomings of IGDT open-loop control. As the capacity of new energy sources connected to the regional integrated energy system increases, it is necessary to consider (i) the energy imbalance caused by multiple uncertainty factors and (ii) the correlation between the power output of those uncertainty sources in the overall system. This paper proposes a bi-level optimal energy scheduling strategy, which combines information gap decision theory (IGDT) with model predictive control (MPC). In order to reduce the large deviation between the day-ahead scheduling plan and the actual scheduling caused by prediction errors of source and load, the IGDT is adopted in the upper layer strategy to model the uncertain factors in the day-ahead scheduling plan. To support IGDT in dealing with multiple uncertainties, the two-point estimation method and Cornish-Fisher series expansion is used to transform the uncertainties of the sources and the loads into uncertainties of power unbalance. Moreover, the Nataf transformation and singular value decomposition (SVD) technique are introduced, so that the two-point estimation and Cornish-Fisher method could handle correlative variables, thereby the solving efficiency of the IGDT model can be improved much more. The MPC rolling optimization is adopted within a day to correct the day-ahead scheduling deviation and compensate for the shortcomings of IGDT open-loop control. Finally, the proposed method is applied to a numerical example to verify its effectiveness. [ABSTRACT FROM AUTHOR]

• Presenting a MILP framework to reduce computation time and achieve the optimal solution. • Using advanced technologies (EVs, BDGs, BESSs, and DRP) simultaneously to enhance SDN resilience. • Utilizing a hybrid stochastic-IGDT method to model uncertainties of RESs, electricity price, EVs, and load. • Providing RA and RT strategies to face the uncertainty of load. Due to climate changes, the occurrence of low-probability but high-impact disasters such as hurricanes, earthquakes, thunders and etc are increasing. So in the occurrence of these disasters, the resilient operation of smart distribution networks (SDNs) needs to be more investigated by researchers. To address this challenge, in this paper, the optimal resilient operation of the SDN in the presence of renewable energy resources (RERs) and intelligent parking lots (IPLs) is investigated. A hybrid stochastic-IGDT approach is developed to handle the uncertainties of the proposed model. So to do this, the stochastic method is used to modeling of RERs generation, electricity price, and EVs (arrival time, departure time, and initial energy) uncertainties. Also, due to the high impact of load uncertainties on the resilient operation of SDN, the information gap decision theory (IGDT) approach is applied to mitigate the uncertainties of load. In this paper, backup diesel generators (BDGs), battery energy storage systems (BESSs), and demand response programs (DRPs) are suggested to improve the resilient operation of SDN. In order to show the efficacy of the proposed model, four case studies are evaluated on a modified IEEE-33 bus test system. The numerical results indicate, in the risk-averse strategy, the SDN is robust against 7.2% increasing active load by having 10% more operation cost, and the resiliency of the system decrease 3.05% for the worst scenario. On the other side, in the risk-taker strategy, with decreasing 7.4% in active load, the operation cost decrease 10%, and the resiliency of the system increase 4.93%. [ABSTRACT FROM AUTHOR]

• Developing the flexibility metrics for the electrical and thermal networks; • Developing the flexibility and economic criteria as the objective functions; • Employing the NNC method to effectively solve the proposed multiobjective problem; • Utilizing a linear DR model to formulate the shiftable loads; • Employing the IGDT technique to model the uncertain parameters; This paper addressed the optimal operation of the microgrids (MGs) containing both the electrical and thermal loads. Combined Heat and Power (CHP) units, boilers, wind turbines, storage devices, Demand Response Resources (DRRs), as well as the power exchange possibility with the upstream wholesale market are the energy resources that have been considered as the portfolio of the decision maker. The aim of the MG operator is to provide the electrical and thermal loads of the network in the most economic and flexible way. Therefore, suitable metrics are developed in this paper in order to evaluate the flexibility of the system for both the electrical and thermal units. Then, considering both the flexibility and financial concerns, a multiobjective framework is proposed. The Information Gap Decision Theory (IGDT) method is employed to handle the uncertainties of the proposed problem. Since the objectives of the MG operator might be conflicting with each other, an efficient optimization approach should be employed to properly satisfy the operator's policies. The Normalized Normal Constraint (NNC) approach is employed here as an efficient method that is able to find the evenly distributed Pareto solutions. The IEEE 33-bus test system is utilized to simulate the proposed problem and analyze the results. The performance of the proposed problem is approved using different scenarios. The simulation results justify the advantages and necessities of the proposed problem. [ABSTRACT FROM AUTHOR]

• 1. To propose a quasi-quantum model, which can reasonably divide and guide the planning period to reduce uncertainty. • 2. To propose an evaluation model, which can analyze the uncertainty potential energy function before and after the planning to assist the quasi quantum model, so as to reasonably divide the planning cycle. • 3. To propose a three-layer planning framework, including planning cycle division, stochastic planning, and rolling planning. With the rapid development in social informatization, more and more factors, such as regional economy, technological development, and people's living needs, will affect the supply–demand relationship of regional integrated energy systems (RIES), which involve multiple energy forms. These factors turn the supply–demand relationship of an energy system into a nonlinear and time-varying chaotic system. This makes it difficult to predict and balance these relationships, which poses a huge challenge to the prediction, planning, operation, etc. Existing conventional methods attempt to quantify the prediction bias caused by various external environmental factors of energy systems and to weaken the uncertainty caused by multiple energy loads through random programming. However, uncertainty factors increase with the development of an energy system, thereby inreasing the requirements of such uncertainty quantification methods. Furthermore, in conventional methods, the prediction or planning decisions are often made by an observer while neglecting the impact of the observer's decision-making behavior on prediction and planning. Therefore, this paper proposes a three-layer planning framework for to solve the above problems. This architecture includes quasi-quantum uncertainty periodic evaluation, stochastic planning based on information gap decision theory, and rolling planning based on model predictive control. First, we establish a quasi-quantum model of multi-energy system prediction error based on the quasi-quantum wave function model to qualitatively analyze prediction errors affected by uncertainty before and after planning. Simultaneously, combined with the evaluation model of the quasi-quantum potential energy function, a quasi-quantum uncertainty period evaluation model is proposed. Based on the minimum equivalent planning entropy, the planning cycle of multistage rolling planning is divided to minimize uncertainty. Second, the information gap decision theory is used to quantify the influence range of source and load uncertainty in the planning process and the multistage planning cycle is randomly planned. Then, the model predictive control method is used to control the actual error, and the planning strategy is changed in time to reduce the planning deviation caused by the prediction error. Finally, adopting a Beichen demonstration area in Tianjin, China, as a case study, the effectiveness of the proposed method in uncertainty analysis and long-term planning improvement is verified. The three-layer planning framework can improve the adaptability of the regional integrated energy system in the long-term planning process, and can timely adjust the planning scheme to cope with the impact of unpredictable uncertainties in the planning process. © 2017 Elsevier Inc. All rights reserved. [ABSTRACT FROM AUTHOR]

• Studying a stochastic based model for CAESs in day-ahead energy and reserve markets. • Constraints formulation of CAES's reserve provision capability at every hour. • Modeling operation modes of CAESs in six different modes to provide reserve. • Introducing the CAESs reserve deliverability constraints during various hours. • Considering demand response program as curtailed demands. Regarding numerous benefits of the compressed air energy storage (CAES) in the utility level, these devices can be taken into account in energy and reserve markets. One of the most important features of CAES is its fast response ability, which makes it an attractive option to alleviate the uncertainties of renewable energy resources and demands. This paper proposes a two-stage mathematical optimization model for optimally day ahead operation of generation units as well as CAESs in energy and reserve markets in a stochastic way. The features of presented reserve model of CAESs are as follows: (a) considering two constraints in order to model the reserve of CAES for providing capability at each hour by six operation modes; (b) considering the limitations related to the state of charge in the CAESs. It is clear that there is an intrinsic deviation between predicted and actual uncertainty variables in a power system. This paper presents a stochastic optimal operation model on the basis of information gap decision theory together with risk averse strategy in order to overcome this information gap and to help independent system operator. As demand response program, the curtailed demand is considered for enhancing the market flexibility. The proposed model is formulated as a mixed-integer nonlinear problem, which is solved by CPLEX solver of the GAMS software. Employing the presented model in the 6-bus test system demonstrates the efficacy of the proposed model. Simulation results show that considering restrictions on reserve deliverability across multiple hours, lessens the total reserve by 22.75 MW and increases the operation cost by $438.26. [ABSTRACT FROM AUTHOR]

• A novel DG hosting capacity evaluation method is proposed for multi-feeders system interconnected by external tie lines and SOPs. • An improved-IGDT model is presented to assess DG hosting capacity considering unpredictable integrated locations and uncertainty in outputs simultaneously. • A hybrid solution procedure integrated with genetic algorithm and model reformulation is developed to determine DG hosting capacity. Unknown integrated locations caused by unpredictable consumers' willingness and uncertainty in outputs induced by variable natural conditions are acknowledged challenges in the evaluation process of distributed generation (DG) hosting capacity (DGHC). For the former factor, this paper first proposes a novel assessment model to obtain the maximum feasible capacity no matter consumers in which locations have the possibility to stall DG. The decision variables of max operator and min operator are DG capacities and integrated locations respectively. Notably, unlike the previous works for one radial feeder, the interplay of DGHC in multi-feeders interconnected by tie lines and soft open points is also taken into consideration. After that, to combine uncertainties in integrated locations and outputs simultaneously, the above DGHC assessment model is further transformed into an improved information gap decision theory (IGDT) model with worst-case constraints for DG integrated locations. The specific solution procedure is also developed to solve this nonlinear IGDT model effectively. Case studies demonstrate that the evaluation results of DGHC based on this method always have the applicability and feasibility for any nodes in distribution system. [ABSTRACT FROM AUTHOR]

• A novel generator start-up sequence optimization strategy is proposed in this work, taking the integration time of wind-solar hybrid systems into account. • The proposed model requires fewer variables compared with other models, therefore the computational efficiency can be greatly improved. • The confidence gap decision theory based generator start-up sequence strategy is proposed to address the generation uncertainty of wind-solar hybrid systems. • Better generator start-up sequence solutions with higher computational efficiency and less conservatism can be attained by employing the proposed strategy. A reasonable start-up sequence of generators considering renewable energy generation integration can effectively improve the restoration efficiency of the power system concerned. The restoration strategy of generators is time-sensitive, however, the computation procedure of existing methods is not fast enough to meet the requirements of practical applications. In this paper, the generator start-up sequence optimization (GSSO) problem is addressed with the integration of wind-solar hybrid systems (WSSs) considered in bulk power systems. Specifically, a deterministic model for GSSO is formulated to maximize the total generation capability during the restoration procedure, in which fewer auxiliary variables are required to promote the computational efficiency. On this basis, in order to deal with the inherent and significant uncertainties of WSSs, a confidence gap decision theory (CGDT) based approach is proposed combining the advantages of stochastic optimization and the information gap decision theory based method while considering the worst-case realization of unknown probability distributions, so that a chance-constrained robust generator start-up solution is thereby attained. Moreover, the formulated CGDT based model is transformed into a mixed integer linear programming problem. Finally, the IEEE 39-bus power system and a modified version of an actual power system in China are employed to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• Coordinating conventional Volt-VAr devices with distributed energy resources. • Incorporating demand response program into the Volt-VAr control problem. • Utilizing ε-constraint approach to generate Pareto optimal solutions. • Using IGDT to develop a robust decision-making approach. • Developing a mixed-integer linear programing framework. Distributed energy resources (DERs), such as renewable energy sources (RESs) and energy storage systems (ESSs), are inevitable parts of future power grids. However, the high penetration of RESs may cause voltage violation issues in distribution levels. To this end, the application of the Volt-VAr management (VVM) scheme is highlighted. This paper aims to maintain voltage levels within standard ranges with optimal coordination of different resources at minimum operational costs and voltage deviation. In more detail, this article develops a new VVM in distribution networks to effectively coordinate novel smart grid technologies such as PV inverters, time of use demand response program (TOU-DRP), energy storage systems (ESSs) with traditional devices, including on-line tap changer transformer (OLTC) and switchable capacitor banks (SCBs). Because the coordinated VVM is a bi-objective model that minimizes both operating cost and voltage deviation, it is proposed to use the ε-constraint technique to identify optimal Pareto solutions. To handle the uncertainty related to RESs and load demands, a robust technique based on information gap decision theory (IGDT) is also utilized. The formulation is configured as a mixed-integer linear program (MILP) and solved by CPLEX. It was implemented on the 118-bus distribution network under various conditions. The simulation results clearly show that the coordination of DERs and traditional devices has a significant impact on maintaining voltage levels within permissible ranges while minimizing operational costs. A higher degree of uncertainty radius can also be obtained if DRP participates in the VVM scheme. [ABSTRACT FROM AUTHOR]

• A distributed solar hybrid CCHP system is constructed by using PV/T panels. • A bi-level sizing optimization model of the PV/T-CCHP system is established. • The economic, energy, and environmental objectives are considered. • The impacts of solar energy and energy storage equipment are quantitatively evaluated. In this paper, a distributed solar hybrid combined cooling, heating, and power (CCHP) system is constructed by installing photovoltaic/thermal (PV/T) panels in the CCHP (PV/T-CCHP) system. A bi-level optimization model is established to obtain the optimal sizing of the equipment in the PV/T-CCHP. The upper-level optimization model is formulated as a multi-objective optimization problem, which considers the economic, energy, and environmental performance of the PV/T-CCHP system compared with the conventional separated production system. The equipment sizing results obtained by the upper-level optimization model can achieve the trading off in terms of cost, primary energy consumption, and carbon emission reduction. The lower-level optimization model, which is formulated as a mixed-integer linear programming, determines the operating strategy of the PV/T-CCHP system. Non-dominated sorting genetic algorithm-II is employed to solve the upper-level optimization model. The final optimal sizing results are obtained from the Pareto solution set leveraging fuzzy decision theory. The optimal sizing results demonstrate that PV/T-CCHP saves 5.82% in annual total cost, 22.63% in annual primary energy, and 37.51% in annual carbon emissions reduction, which verifies the effectiveness of the proposed optimization model. In addition, the impacts of solar energy and energy storage equipment on the system performance are quantitatively evaluated. [ABSTRACT FROM AUTHOR]

• A new model is proposed for the day-ahead self-scheduling problem of microgrids. • In this model the microgrid provide ancillary services for system operators. • Microgrid reschedules its resources to provide services to distribution operator. • Uncertainties on the reserve and flexibility ramping product deployment are modeled. • Capacity of provided ancillary services decreases with increasing risk parameter. In this paper, a new decision-making framework is proposed for the day-ahead self-scheduling problem of microgrids, in which the microgrid operator (MGO) can provide ancillary services for both the independent system operator (ISO) and the distribution system operator (DSO). The MGO provides the reserve and flexible ramping product (FRP) services for the ISO through participating in the corresponding markets. Also, the MGO reschedules its resources to provide the requested services for the DSO. To model the uncertain behavior of the renewable energy resource, demand, and real-time energy price, the MGO problem is modeled as a two-stage stochastic model. Then, the uncertainties of the reserve and the FRP deployment in real-time operation are modeled using the information gap decision theory approach. The results show the effects of the different strategies in scheduling the local resources adopted by the MGO to participate in the energy and ancillary service markets. In the risk-based model proposed for the MGO, increasing the risk parameter decreases the capacity of the provided reserve and ramp-up FRP while it increases the energy sold to the day-ahead energy market. [ABSTRACT FROM AUTHOR]

• Proposing a multiple-radius OPF model for the power systems under the penetration of off-shore WFs. • Introducing a weighted IGDT technique which considers the geographical location of WFs. • Considering VSC-HVDC to connect off-shore WFs to the grid. Increasing the penetration of renewable energies creates various operational and even security challenges for power systems, due to the variability of their output power and inability to provide system inertia. These issues are even more inevitable in power systems which are connected to off-shore wind farms (WFs) in different locations, creating more complexity in decision making process. This paper, proposes a decision making model to increase the robustness of optimal power flow in presence of off-shore WFs. Information gap decision theory (IGDT) is used as a decision making tool for dealing with the uncertainty radius of multiple WFs, by definition of weighting factors for the uncertainty of each WF. Voltage source converter (VSC)-based high voltage DC (HVDC) transmission links are considered to connect the off-shore WFs to the main AC grid. The proposed optimization model, which includes both AC transmission and HVDC systems constraints, is implemented on the IEEE 118-bus standard test system and solved by general algebraic modeling system (GAMS) optimization software. The simulation results show the economic effect of location factor in definition of uncertainty for WFs. [ABSTRACT FROM AUTHOR]

• Proposing an EH based on CCHP-ORC equipped by SWD, hydrogen electrolyser and EVs. • Assessing the effects of installation of WST on optimal operation of EH and other storage devices. • Modeling EVs uncertainties using scenario generation. • Presenting a Robust stochastic optimization using IGDT. • Considering two objective functions simultaneously as operational costs and emission. With the development of human societies, new industries and needs are being formed which supplying their power and energy consumption, requires the development of equipment and infrastructure in the field of power generation and transmission. An example of these industries are seawater desalination (SWD) units. In addition, increasing attention to air pollution has led to the proliferation of electric vehicles (EVs) or the use of hydrogen as a zero emission fuel. Energy hubs (EHs) can benefit from advantages such as optimal use of installation capacity and environmental potential by accepting to provide other needs along with common requirements such as electricity, cooling, and heating. In this case, EH is able to increase its flexibility by converting energy into the desired product and storing it in a different form as of electrical or thermal energy. In this paper, EH utilizes a SWD with Reverse Osmosis (RO) technology as a flexible load and an Organic Rankine Cycle (ORC) as a new technology for generating electrical power by means of thermal power. In addition, for better interact with available EVs, one parking lot and a Battery Swapping Station (BSS) are introduced. The Electrolyser uses the electrical power to supply the required amount of hydrogen, and the hydrogen tank in addition to fuel cell (FC) help to balance the production and consumption of hydrogen. In order to model the existing uncertainties, scenario generation method as well as information gap decision theory (IGDT) method have been used. The efficacy of the proposed model is evaluated on a smart commercial building in Qeshm Island, which is located a few kilometers off the southern coast of Iran. [ABSTRACT FROM AUTHOR]

• A framework of multi-energy system integrating with a liquid air energy storage system was proposed. • The LAES system could interact with the converter components of the combine cooling, heating and power system, such as combined heating and power, auxiliary boiler and chillers, to realize the complementary utilization of power, thermal energy and cold energy. • The information gap decision theory method was used to study power dispatching strategies of the LAES integrated systems, including risk-neutral, risk-averse and risk-taker strategy. In this paper, a framework of multi-energy system (MES) integrating with a liquid air energy storage (LAES) system was proposed. LAES, where liquid air works as an energy storage media, is a powerful and eco-friendly technology for storing renewable energy resources and reducing grid curtailment. Considering the characteristics of LAES (i.e. cold and heat circulation), the incorporation of LAES system into the Combined Cooling, Heating and Power system can achieve integrated use of energy and effectively save energy. Moreover, the prices of electricity will affect the overall cost of the MES. In other words, the decision-makers of the MES need to consider the uncertainty of electricity prices when making power dispatching decisions. To model the uncertainty of electricity prices, the information gap decision theory method was used to study power dispatching strategies of the MES. Three different strategies were proposed, including risk-neutral, risk-averse and risk-taker. In addition, demand response algorithms were used to study load transfer strategies. The results show that the demand responses of the three strategies are effective in terms of load transfer and cost saving. The total operation cost in the risk-neutral strategy with demand response can be 6.82% less than that without demand response; In the risk-taker strategy with demand response, the allowable grid electricity price is reduced by 25.24% when the opportunity cost drops by $8,000, and 23.32% without demand response. With additional robustness cost, the acceptable price change ratio using demand response is 21.91% in the risk-averse strategy, and 20.04% without demand response. [ABSTRACT FROM AUTHOR]

[Display omitted] • Modeling a CCHP-based EH optimal operation involving a SPCASE and ISC; • Making use of the RA-IGDT as an approach in combination with the AUGMECON method; • Propounding a bi-level optimization problem based on RA-IGDT; and. • Minimizing the operational and environmental costs of the whole system. Energy Hub (EH) is known as a complex system capable of transferring, conversion, and saving various energies in a Microgrid (MG). An important issue for investors is taking the advantage of EH for optimal management of all energy carriers, particularly in anticipating energy price. In this paper, a model for EH is considered for the purpose of the optimal operation of MG with multiple energy carrier infrastructures for day-ahead. The goal of optimization is to minimize operational and environmental costs subject to numerous technical constraints. The proposed EH manages dispatchable generation, i.e. Combined Cooling, Heat and Power (CCHP) as well as non-dispatchable generations, i.e., Wind Turbine (WT) and Photovoltaic (PV). It considers an Ice Storage Conditioner (ISC) along with a Thermal Energy Storage System (TESS) as the Energy Storage System (ESS). In particular, the effects of Solar-Powered Compressed Air Energy Storage (SPCAES) as a novel ESS are studied on the performance and efficiency of the EH operational and environmental costs. A bi-level stochastic optimization problem based on information gap decision theory (IGDT) with risk averse (RA) strategy is considered to save the Microgrid operator (MGO) from the risks of information gap between the predicted and actual uncertainty variables. The bi-level stochastic optimization problem is reorganized into a single level problem obtained by Karush-Kuhn-Tucker method. As uncertainty variables compete to expand their enveloped-bounds, the augmented ε-constraint method is employed to address the multifaceted RA-IGDT-based stochastic optimization problem proposed in the study. Implementation of the proposed framework on the typical EH shows the efficacy of the ESSs to reduce the operation costs as well as the emissions in the day-ahead energy management. [ABSTRACT FROM AUTHOR]