Scenario-based Stochastic Approach Research Articles

Techno-economic modeling of a preventive-corrective strategy based on black-start services to resilience enhancement of distribution networks

High-impact with low-probability (HILP) events such as natural disasters or cyber-physical attacks severely affect power systems. The distribution networks experience significant challenges during HILP events. So, strategies need to be developed to enhance distribution networks' resilience. Hence, in this paper, a resilience enhancement strategy based on the potential of multi-microgrids is developed. The proposed strategy has a two-layered structure consisting of preventive and corrective measures within the hierarchical centralized energy management framework. The preventive measures are based on the black-start bilateral contract between the active distribution network operator and the multi-microgrids owner. The corrective measures are based on islanding microgrids during the event. The LP-Metric-based multi-objective optimization approach is employed for economic-resilient operational planning of the active distribution network. Moreover, a scenario-based stochastic approach is utilized to deal with renewable resources and load uncertainties. On the modified IEEE 33-bus active distribution network, the effectiveness of the proposed strategy is evaluated using the supplied load as a resilience index. The proposed black-start strategy has resulted in an increase of 181.57 % in the supplied load of the distribution network, while a reduction of 83.12 % in its curtailed load has been achieved. Consequently, the resilience index increased by 84 %. Additionally, the distribution system operation cost was reduced by 87.44 %, while the multi-microgrid owner's profit increased by 1004.68 %. The obtained results demonstrate that distribution system resilience has been enhanced within an economic framework, which validates the effectiveness of the proposed strategy.

A three-stage hybrid stochastic/IGDT framework for resilience-oriented distribution network planning

This article tackles the resilience-oriented distribution network planning (RODNP) problem utilizing a novel three-stage hybrid framework. The decision-making on the line hardening and DG placement is carried out in the first stage. In the second stage, emergency and normal operation optimization are conducted. The worst-case scenario is considered for evaluating the effect of a potential hurricane in post-event emergency operation conditions. In addition, a scenario-based stochastic approach is used to assess normal operation conditions. Finally, a risk-averse hardening re-plan is implemented in the third stage using the information gap decision theory (IGDT) notion as an effective non-deterministic optimization strategy under severe uncertainty. At this stage, distribution system planner (DSP) tries to develop a more resilient distribution network scheme against the most powerful hurricane possible while taking into account a predetermined parameter known as the resilience budget. The efficacy of the proposed approach is validated by conducting several case studies on the IEEE-33 bus test system. The results reveal that the proposed strategy may dramatically reduce the cost of both normal and emergency operations simultaneously.

Robust optimal scheduling of CHP-based microgrids in presence of wind and photovoltaic generation units: An IGDT approach

Application of combined heat and power (CHP) units beside the distributed energy resources (DERs) persuades the power systems via the formation of multi-carrier microgrids (MGs). This paper presents the day-ahead scheduling of multi-carrier MGs. Renewable distributed generators are known as undeniable parts of modern power systems, which may increase the chanciness of the system. Information gap decision theory (IGDT) is applied to address the uncertainties of renewable sources. Moreover, a scenario-based stochastic approach is used to model the uncertainty of electricity prices in this method. Indeed a hybrid stochastic-IGDT-based optimization problem is proposed for optimal energy management of multi-carrier MGs. According to this method, the operation of multi-carrier MGs would be robust against uncertainties and contain a minimum profit. The proposed problem has been formulated as mixed-integer linear programming (MILP). Finally, the proposed energy management has been implemented into a sample multi-carrier microgrid. The results showed that how the MG operator’s risk-averse character can change her/his decision-making. • Robust Optimal Scheduling of CHP-based Microgrids. • Proposing an IGDT-based approach to handle uncertainties of renewable generations. • Proposing a single level model for the IGDT method to obtain a global optimum. • Considering demand response programs for both thermal and electrical loads.

Development and experimental validation of hierarchical energy management system based on stochastic model predictive control for Off-grid Microgrids

Abstract In this study, a hierarchical energy management system (EMS) is proposed, to coordinate different energy sources in an islanded multi-good microgrid. The first layer deals with the daily scheduling problem, while the second layer balances the generation in real-time. A novel second layer formulation, relying on model predictive control under a scenario-based stochastic approach (sMPC), is introduced and it is compared to a reference formulation, based on a central proportional-integral controller following the indications set by the first layer. The proposed sMPC explicitly accounts for uncertainty considering several scenarios of very-short term forecast errors, that act as disturbances for the system. The sMPC evaluates the control actions and the correction rules required to guarantee optimal operations through disturbance-feedback. The EMS is implemented in an experimental setup and tested for daily operations under a rolling horizon approach. The accuracy of the numerical system simulation is evaluated, resulting in an average discrepancy of 1.7%, in terms of operation cost, with respect to the experimental operations. Then, a test case comparing the proposed EMS with the reference approach shows that the adoption of sMPC allows to approach the lowest possible operation cost achievable by a second layer with an advantage of 2.7 % against the reference case. Finally, the developed sMPC leads to only 0.5% additional costs than an ideal controller working on the same control layer.

Thermodynamic modeling of compressed air energy storage for energy and reserve markets

Compressed air energy storage (CAES) system is one of the highly efficient and low capital cost energy storage technologies, which is used on a large scale. However, due to multiple operational and technical limitations, the CAES operation should be incorporated with thermodynamic characteristics. Therefore, in this paper, novel thermodynamic modeling of CAES facility integrated with the hybrid thermal, wind, and photovoltaic (PV) farms to participate in energy and reserve markets is investigated. Considering the thermodynamic characteristics makes the proposed scheduling more realistic, while imposes multiple constraints on the optimal operation of the hybrid system. The operation of the CAES facility during charging and discharging modes, considering thermodynamic characteristics are analyzed simultaneously, and the state of charge of the cavern is calculated for both modes. In addition to taking into account the thermodynamic characteristics, the recovery cycle capability is embedded for the CAES facility to recover heat from the turbine in the preheater results in increased turbine efficiency. The proposed scheduling of the hybrid system is exposed by high-level uncertainty caused by energy and reserve market prices, as well as wind and PV farms power fluctuation. Hence, the scenario-based stochastic approach is applied based on real historical data of the KHAF station in IRAN to handle existing uncertainties. Numerical results are provided for different cases. The major conclusions of the numerical results show the effectiveness of the recovery cycle from profit improvement and burned fuel reduction up to 11.36% and 11.33%, respectively, while the thermodynamical constraints in the CAES performance make the realistic model, compared with the conventional CAES.

Economic-environmental analysis of combined heat and power-based reconfigurable microgrid integrated with multiple energy storage and demand response program

Microgrids (MGs) are solutions to integrate high shares of variable renewable energy which can contribute to more economical and environmental benefits, as well as improving the energy supply efficiency. One significant potential of MGs is an expanded opportunity to use the waste heating energy from the conversion of the primary fuel (such as natural gas) to generate electricity. The use of waste heat in combined heat and power (CHP)-based MG is more efficient to meet local load and decrease the emission pollution. Hence, this paper elaborates on optimal multi-objective scheduling of CHP-based MG coupled with compressed air energy storage (CAES), renewable energy, thermal energy storage (TES), and demand response programs through shiftable loads, which considers a reconfiguration capability. The embedded CAES, in addition to the charging/discharging scheme, can operate in a simple cycling mode and serve as a generation resource to supply local load in an emergency condition. The daily reconfiguration of MG will introduce a new generation of MG named reconfigurable microgrid (RMG) that offers more flexibility and enhances system reliability. The RMG is coupled with TES to facilitate the integration of the CHP unit that enables the operator to participate in the thermal market, in addition to the power market. The main intents of the proposed multi-objective problem are to minimize the operation cost along with a reduction in carbon emission. The epsilon-constraint technique is used to solve the multi-objective problem while fuzzy decision making is implemented to select an optimal solution among all the Pareto solutions. The electricity prices and wind power generation variation are captured as random variables in the model and the scenario-based stochastic approach is used to handle them. Simulation results prove that the simultaneous integration of multiple technologies in CHP-based RMG decreases the operation cost and emission up to 3 % and 10.28 %, respectively.

Strategic Bidding in Distribution Network Electricity Market Focusing on Competition Modeling and Uncertainties

Developing the electricity market at the distribution level can facilitate the energy transactions in distribution networks with a high penetration level of distributed energy resources (DERs) and microgrids (MGs). However, the lack of comprehensive information about the marginal production cost of competitors leads to uncertainties in the optimal bidding strategy of participants. The electricity demand within the network and the price in the wholesale electricity market are two other sources of the uncertainties. In this paper, a day-ahead-market-based framework for managing the energy transactions among MGs and other participants in distribution networks is introduced. A game-theory-based method is presented to model the competition and determine the optimal bidding strategy of participants in the market. Robust optimization technique is employed to capture the uncertainties in the marginal cost of competitors. Additionally, the uncertainties in demand are modeled using a scenario-based stochastic approach. The results obtained from case studies reveal the merit of considering competition modeling and uncertainties.

Fostering long-term care planning in practice: extending objectives and advancing stochastic treatment within location-allocation modelling

Many countries are currently concerned with the planning of networks of Long-Term Care (LTC), which requires considering a multiplicity of policy objectives and anticipating the impact of key uncertainties. Nevertheless, location-allocation literature has not been modelling key health policy objectives, and the use of stochastic planning models entails low practical usability due to prohibitive computational times. This study tackles these issues by proposing an approach that supports the reorganization of LTC networks (in terms of services location, capacity planning and patients allocation) while exploring different health policy objectives and considering uncertainty within a reasonable computational time, leading to the development of a stochastic multi-objective mathematical programming model – the LTCNetPlanner. The LTCNetPlanner builds upon health economics and policy concepts to model the maximization of health and wellbeing together with cost- and equity-related objectives within location-allocation literature. Concerning uncertainty, a scenario-based stochastic approach is developed and alternative scenario reduction methods enabling a faster model resolution are explored within the LTCNetPlanner. Specifically, it is proposed a novel Morphol-KMG method able to reduce the number of scenarios while accounting for experts’ knowledge. A case study in the Great Lisbon region is explored, showing the usefulness of the proposed scenario reduction method to reduce computational times, and how planning decisions change when health and wellbeing benefits are considered.

RETRACTED: Probabilistic scheduling of power-to-gas storage system in renewable energy hub integrated with demand response program

• Power-to-gas storage is integrated with energy system based on energy hub concept. • Proposing an incentive-based demand response program via load shifting capability. • Proposing a stochastic approach to handle the system uncertainties. • The introduced stochastic approach is modeled as a mixed-integer linear problem. Reliable energy supply is a significant challenge for the power system operators. The increase of emerging resources, as well as multi-carrier consumers in energy systems, lead to the integration of multi-carrier energy systems. The energy hub (EH) is one of the central infrastructures which smooths the combination and interdependency of various energy carriers to increase the efficiency and reliability. A novel technology, such as power-to-gas (P2G) storage, is a great option for achieving a renewable resources-based integrated energy system with high efficiency. The P2G storage is regarded as a viable energy storage approach to cover ever-increasing renewable energy resources variability in power system operations. The contribution of this paper is to present an optimal stochastic scheduling problem of EH integrated with P2G storage, combined heat and power (CHP) unit, wind power, boiler, electrical storage, and thermal storage to meet electrical, heat, and gas demands considering demand response program (DRP). The load shifting based DRP is applied on the electrical loads to reduce the operation cost of the EH. Also, the P2G storage system is used as a new resource that makes a connection between electrical and natural gas networks by converting the power to hydrogen and after that to natural gas through two processes including electrolysis and mechanization, respectively. A scenario-based stochastic approach is applied to handle the uncertainties related to the electrical loads, wind power, and electricity price. The objective of the proposed problem is to minimize the total operation cost of EH, which is modeled as a mixed-integer linear programming (MILP) problem model. The numerical results are implemented for different cases which demonstrate the effectiveness of the integration of the P2G based multi-carrier energy storage and DRPs on the operation cost of EH. The achieved results confirm the proposed approach by demonstrating the considerable reduction in operating cost of the EHS by approximately 7%.

Risk evaluation and retail electricity pricing using downside risk constraints method

Electricity in the retail market has a different value for different types of consumers. Therefore, different retail prices are usually determined for various consumers in the retail market. However, imposed risks from uncertain parameters are a big challenge in the real-time retail market pricing process. This paper proposed a real-time pricing (RTP) framework for various users including residential, commercial, and industrial consumers by the electricity retailer. In addition, uncertainties of various input parameters such as output power of renewable energy resources, electricity demand, and pool market price are modeled using scenario-based stochastic approach while downside risk constraints method is proposed to model risk associated with uncertainties. By implementing this method, electricity retailer will be able to select various risk-based strategies. Furthermore, numerical results illustrate the various risks versus various profits by the occurring of each scenario which helps the retailer for decisions-making in different scenarios. According to obtained results, retailer by choosing of zero risk strategy can reduce its risk by 100% while expected profit is reduced by 2.07%. In addition, offered RTP by the retailer is higher for industrial, commercial, and residential customers, respectively. Finally, risk-averse and risk-neutral strategies of electricity retailer are determined in the power procurement problem.

RETRACTED: Risk-averse stochastic operation of a power system integrated with hydrogen storage system and wind generation in the presence of demand response program

Wind generation (WG) units as renewable energy sources (RESs) are increasing in the world due to environmental functions and lack of conventional energy sources. Also, hydrogen storage system (HSS) as an energy storage system (ESS) is used to cope with variable nature of RESs in which the concepts of power to hydrogen (P2H) and hydrogen to power (H2P) are defined. In this work, a risk-averse stochastic operation of HSS and WG is modeled using a scenario-based stochastic approach by considering price-responsive demand response (DR) program. All uncertainties are modeled via a scenario-based stochastic approach while the risk related uncertainties are modeled via the downside risk constraints (DRC) to capture the risk-averse operation of the HSS and WG. In order to investigate the impact of DRC implementation, a risk-averse strategy is compared versus risk-neutral strategy. Compared results show that the risk-in-cost (RIC) is reduced while the expected operation cost (EOC) is raised to deal with the risk of the uncertainty.

Enabling Demand Response Potentials for Resilient Microgrid Design

The future microgrids (MGs) hosting a great deal of uncertain and intermittent local renewable generations are envisioned to need for fast and flexible units in the generation side. Demand response, however, as a load shaping tool can alleviate the needs. This paper proposes a model to consider demand response potentials activated by time-varying prices in MG design studies. The model aims at maximizing MG owner’s profit while technical limits and constraints are adhered. The model also ensures that the designed MG is resilient against islanding events. To handle complexity of the model, Benders decomposition is used to decompose the model into a master problem and two types of sub-problems. The master problem optimizes binary variables indicating installing status of generating units and batteries. The first type of sub-problems optimizes continuous variables, and the second ensures the resilient operation of the MG against islanding events. In the model, the uncertainties associated with load and intermittent generation resources are captured via a scenario-based stochastic approach. The demand behavior in response to time-varying prices is modeled via price elasticity coefficients. The effectiveness of the proposed model is demonstrated through extensive numerical studies and sensitivity analyses.

A Two Stage Stochastic Programming Model of the Price Decision Problem in the Dual-channel Closed-loop Supply Chain

In this paper, we propose a new model for designing integrated forward/reverse logistics based on pricing policy in direct and indirect sales channel. The proposed model includes producers, disposal center, distributers and final customers. We assumed that the location of final customers is fixed. First, a deterministic mixed integer linear programming model is developed for integrated logistics network design. Then the stochastic counterpart of the proposed mixed integer linear programming model is developed by using scenario-based stochastic approach. We use the value of the stochastic solution (VSS) as a measure to evaluate the accuracy of stochastic programming approach. VSS value showed that using stochastic approach for solving the proposed model is sufficient. Moreover, we could obtain optimal values of sale prices in direct and indirect sale channel and service level by considering forward and reverse flow together.

A stochastic optimization model for integrated forward/reverse logistics network design

In this paper, we develop a stochastic programming model for an integrated forward/reverse logistics network design under uncertainty. First, an efficient deterministic mixed integer linear programming model is developed for integrated logistics network design to avoid the sub-optimality caused by the separate design of the forward and reverse networks. Then the stochastic counterpart of the proposed MILP model is developed by using scenario-based stochastic approach. Numerical results show the power of the proposed stochastic model in handling data uncertainty.