Driven by the global energy transition and the urgent“dual carbon”goals,regional integrated energy system(RIES)planning is undergoing a paradigm shift from carbon reduction to negative carbon emissions.This paper pr...Driven by the global energy transition and the urgent“dual carbon”goals,regional integrated energy system(RIES)planning is undergoing a paradigm shift from carbon reduction to negative carbon emissions.This paper provides a comprehensive review of the theoretical frameworks and technical pathways for RIES planning from a carbon-centric perspective.A key contribution is the proposed Carbon-Energy-Economy(CEE)triple-dimensional governance framework,which endogenizes carbon factors into planning decisions through emission constraints,trading mechanisms,and capture technologies.We first analyze the fundamental characteristics of RIES and their critical role in achieving carbon neutrality,detailing advancements in multi-energy coupling models,energy router concepts,and standardized energy hub modeling.The paper further explores multi-energy flow analysis methods,and systematically compares the applicability and limitations of various planning algorithms,with emphasis on addressing uncertainties from renewable integration.Finally,we highlight the integration of artificial intelligence with traditional optimization methods,offering new pathways for intelligent,adaptive,and low-carbon RIES planning.This review underscores the transition towards data-physical fusion models,cooperative uncertainty optimization,multi-market planning,and innovative zero/negative-carbon technological routes.展开更多
In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants ...In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants in energy trading.Firstly,the energy trading process is analyzed between each subject based on the establishment of the operation framework of multi-agent participation in energy trading.Secondly,the optimal operation model of each energy trading agent is established to develop a bi-level game model including each energy participant.Finally,a combination algorithm of improved robust optimization over time(ROOT)and CPLEX is proposed to solve the established game model.The experimental results indicate that under different fitness thresholds,the robust optimization results of the proposed algorithm are increased by 56.91%and 68.54%,respectively.The established bi-level game model effectively balances the benefits of different energy trading entities.The proposed algorithm proposed can increase the income of each participant in the game by an average of 8.59%.展开更多
Integrated-energy systems(IESs)are key to advancing renewable-energy utilization and addressing environmental challenges.Key components of IESs include low-carbon,economic dispatch and demand response,for maximizing r...Integrated-energy systems(IESs)are key to advancing renewable-energy utilization and addressing environmental challenges.Key components of IESs include low-carbon,economic dispatch and demand response,for maximizing renewable-energy consumption and supporting sustainable-energy systems.User participation is central to demand response;however,many users are not inclined to engage actively;therefore,the full potential of demand response remains unrealized.User satisfaction must be prioritized in demand-response assessments.This study proposed a two-stage,capacity-optimization configuration method for user-level energy systems con-sidering thermal inertia and user satisfaction.This method addresses load coordination and complementary issues within the IES and seeks to minimize the annual,total cost for determining equipment capacity configurations while introducing models for system thermal inertia and user satisfaction.Indoor heating is adjusted,for optimizing device output and load profiles,with a focus on typical,daily,economic,and environmental objectives.The studyfindings indicate that the system thermal inertia optimizes energy-system scheduling considering user satisfaction.This optimization mitigates environmental concerns and enhances clean-energy integration.展开更多
In order to promote the utilization level of new energy resources for local and efficient consumption,this paper introduces the biogas(BG)fermentation technology into the integrated energy system(IES).This initiative ...In order to promote the utilization level of new energy resources for local and efficient consumption,this paper introduces the biogas(BG)fermentation technology into the integrated energy system(IES).This initiative is to study the collaborative and optimal scheduling of IES with wind power(WP),photovoltaic(PV),and BG,while integrating carbon capture system(CCS)and power-to-gas(P2G)system.Firstly,the framework of collaborative operation of IES for BG-CCS-P2G is constructed.Secondly,the flexible scheduling resources of the source and load sides are fully exploited,and the collaborative operation mode of CCS-P2G is proposed to establish a model of IES with WP,PV,and BG multi-energy flow coupling.Then,with the objective of minimizing the intra-day operating cost and the constraints of system energy balance and equipment operating limits,the IES withWP,PV,and BG collaborative optimal scheduling model is established.Finally,taking into account the uncertainty of the output of WP and PV generation,the proposed optimal scheduling model is solved by CPLEX,and its validity is verified by setting several scenarios.The results show that the proposed collaborative operation mode and optimal scheduling model can realize the efficient,low-carbon,and economic operation of the IES with WP,PV,and BG and significantly enhance the utilization of new energy for local consumption.展开更多
Against the backdrop of China’s“dual-carbon”target,clean energy generation currently accounts for about 3.8 trillion kilowatt-hours,or 39.7 percent of total power generation,establishing a reasonable market trading...Against the backdrop of China’s“dual-carbon”target,clean energy generation currently accounts for about 3.8 trillion kilowatt-hours,or 39.7 percent of total power generation,establishing a reasonable market trading mechanism while enhancing the low-carbon economic benefits of the integrated energy system(IES)and optimizing the interests of various entities within the distribution system has become a significant challenge.Consequently,this paper proposes an optimization strategy for a low-carbon economy within a multi-agent IES that considers carbon capture systems(CCS)and power-to-gas(P2G).In this framework,the integrated energy system operator(IESO)acts as the primary leader,while energy suppliers(ES),energy storage operators(ESO),and load aggregators(LA)follow.At the level of low-carbon technology,a coupling model of P2G and CCS is developed,leading to the establishment of an IES that incorporates energy conversion and storage equipment.Economically,effective control of system carbon emissions in market trading is progressively established.Lastly,the trading decision model of the system is integrated within a master-slave game framework,utilizing an improved differential evolution algorithm in conjunction with the distributed equilibrium method of quadratic programming for solution.The calculation example demonstrates that the strategy safeguards the benefits for both parties in the game and achieves energy savings and carbon reduction for the system.展开更多
Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems(HIES),which enhance energy sustainabili...Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems(HIES),which enhance energy sustainability through coordinated electricity,thermal,natural gas,and hydrogen utilization.This study proposes a two-stage distributionally robust optimization(DRO)-based scheduling method to improve the economic efficiency and reduce carbon emissions of HIES.The framework incorporates a ladder-type carbon trading mechanism to regulate emissions and implements a demand response(DR)program to adjustflexible multi-energy loads,thereby prioritizing RES consumption.Uncertainties from RES generation and load demand are addressed through an ambiguity set,enabling robust decision-making.The column-and-constraint generation(C&CG)algorithm efficiently solves the two-stage DRO model.Case studies demonstrate that the proposed method reduces operational costs by 3.56%,increases photovoltaic consumption rates by 5.44%,and significantly lowers carbon emissions compared to conventional approaches.Furthermore,the DRO framework achieves a superior balance between conservativeness and robustness over conventional stochastic and robust optimization methods,highlighting its potential to advance cost-effective,low-carbon energy systems while ensuring grid stability under uncertainty.展开更多
The integrated energy systems(IESs)offer a practical solution for achieving low-carbon targets in residential buildings.However,IES encounters several challenges related to increased energy consumption and costs due t...The integrated energy systems(IESs)offer a practical solution for achieving low-carbon targets in residential buildings.However,IES encounters several challenges related to increased energy consumption and costs due to fluctuations in renewable energy generation.Leveraging building flexibility to address these power fluctuations within IES is a promising strategy,which requires coordinated control between air-conditioning systems and other IES components.This study proposes a cross-time-scale control framework that contains optimal scheduling and on-the-fly flexible control to reduce the cost impacts of a residential IES system equipped with photovoltaic(PV)panels,batteries,a heat pump,and a domestic hot water tank.The method involves three key steps:solar irradiance prediction,day-ahead optimal scheduling of energy storage,and intra-day flexible control of the heat pump.The method is validated through a high-fidelity residential building model with actual weather and energy usage data in Frankfurt,Germany.Results reveal that the proposed method limits the cost increase to just 2.67% compared to the day-ahead schedule,whereas the cost could increase by 7.39% without the flexible control.Additionally,computational efficiency is enhanced by transforming the mixed-integer programming(MIP)into nonlinear programming(NLP)problem via introducing action-exclusive constraints.This approach offers valuable support for residential IES operations.展开更多
With the intensification of the energy crisis and the worsening greenhouse effect,the development of sustainable integrated energy systems(IES)has become a crucial direction for energy transition.In this context,this ...With the intensification of the energy crisis and the worsening greenhouse effect,the development of sustainable integrated energy systems(IES)has become a crucial direction for energy transition.In this context,this paper proposes a low-carbon economic dispatch strategy under the green hydrogen certificate trading(GHCT)and the ladder-type carbon emission trading(CET)mechanism,enabling the coordinated utilization of green and blue hydrogen.Specifically,a proton exchange membrane electrolyzer(PEME)model that accounts for dynamic efficiency characteristics,and a steam methane reforming(SMR)model incorporating waste heat recovery,are developed.Based on these models,a hydrogen production–storage–utilization framework is established to enable the coordinated deployment of green and blue hydrogen.Furthermore,the gas turbine(GT)unit are retrofitted using oxygenenriched combustion carbon capture(OCC)technology,wherein the oxygen produced by PEME is employed to create an oxygen-enriched combustion environment.This approach reduces energy waste and facilitates low-carbon power generation.In addition,the GHCT mechanism is integrated into the system alongside the ladder-type CET mechanism,and their complementary effects are investigated.A comprehensive optimization model is then formulated to simultaneously achieve carbon reduction and economic efficiency across the system.Case study results show that the proposed strategy reduces wind curtailment by 7.77%,carbon emissions by 65.98%,and total cost by 12.57%.This study offers theoretical reference for the low-carbon,economic,and efficient operation of future energy systems.展开更多
To address the issues of unclear carbon responsibility attribution,insufficient renewable energy absorption,and simplistic carbon trading mechanisms in integrated energy systems,this paper proposes an electricheat-hyd...To address the issues of unclear carbon responsibility attribution,insufficient renewable energy absorption,and simplistic carbon trading mechanisms in integrated energy systems,this paper proposes an electricheat-hydrogen integrated energy system(EHH-IES)optimal scheduling model considering carbon emission stream(CES)and wind-solar accommodation.First,the CES theory is introduced to quantify the carbon emission intensity of each energy conversion device and transmission branch by defining carbon emission rate,branch carbon intensity,and node carbon potential,realizing accurate tracking of carbon flow in the process of multi-energy coupling.Second,a stepped carbon pricing mechanism is established to dynamically adjust carbon trading costs based on the deviation between actual carbon emissions and initial quotas,strengthening the emission reduction incentive.Finally,a lowcarbon economic dispatch model is constructed with the objectives of minimizing operation cost,carbon trading cost,wind-solar curtailment penalty cost,and energy loss.Simulation results show that compared with the traditional economic dispatch scheme 3,the proposed schemel reduces carbon emissions by 53.97%and wind-solar curtailment by 68.89%with a 16.10%increase in total cost.This verifies that the model can effectively improve clean energy utilization and reduce carbon emissions,achieving low-carbon economic operation of EHH-IES,with CES theory ensuring precise carbon flow tracking across multi-energy links.展开更多
Integrated energy systems(IES)are widely regarded as a key enabler of carbon neutrality,enabling the coordinated use of electricity,heat,and gas to support large-scale renewable integration.Yet their practical deploym...Integrated energy systems(IES)are widely regarded as a key enabler of carbon neutrality,enabling the coordinated use of electricity,heat,and gas to support large-scale renewable integration.Yet their practical deployment still faces major challenges,including rigid thermoelectric coupling,insufficient operational flexibility,and fragmented carbon and certificate market mechanisms.To address these issues,this study proposes a low-carbon economic dispatch model for integrated energy systems(IES)that reduces emissions and costs while improving renewable energy utilization.A coordinated framework integrating carbon capture,utilization,and storage,two-stage power-to-gas,combined heat and power,and ground-source heat pump technologies enhances multi-energy complementarity and overcomes the heat-led constraints of traditional combined heat and power systems.A unified carbon emission trading and green certificate trading mechanism is designed to balance economic and environmental goals through cross-market synergy.To address uncertainty,a distributionally robust chance-constrained model based on Kullback-Leibler divergence is introduced in Scenario 8.The model is solved using the GUROBI solver under multiple scenarios.Simulation results show a cost reduction from$56,166.66 to$25,840.32,carbon emission cuts from 801.38to 440.90 t,and wind/photovoltaic utilization rates reaching 98%,which fully demonstrates the effectiveness of the proposed framework in achieving cost-efficient low-carbon operation of IES.展开更多
Under the“dual carbon”goals,this paper constructs an optimization model of the comprehensive energy system in the park.A stepwise carbon excess rate mechanism and an electric vehicle coupling strategy are proposed:A...Under the“dual carbon”goals,this paper constructs an optimization model of the comprehensive energy system in the park.A stepwise carbon excess rate mechanism and an electric vehicle coupling strategy are proposed:A carbon quota trading system is established based on the baseline method,and the stepwise function is adopted to quantify the cost of excess carbon emissions;Introduce the price demand response and the two-way interaction mechanism of electric Vehicle vehicle-to-grid(V2G)to enhance the flexible regulation ability.Aiming at the uncertainty of wind and solar output,a typical scene set is generated by combining Latin hypercube sampling with the scene reduction method.The goal is to minimize the operating cost and maximize the consumption of renewable energy,and it is solved through the CPLEX solver in the MATLAB platform.Through simulation verification of the proposed models and methods in various scenarios,the simulation results show that under the coupling of the carbon excess rate trading mechanism,the demand response mechanism,and the vehicle-to-grid interaction of electric vehicles,the total daily operating cost of the system decreases by 25.3%,reduce the dual pressure of energy consumption costs and the economic environment,and achieve the coordinated optimization of economic and ecological benefits.展开更多
The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in futu...The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in future low carbon societies.However,uncertainties from renewable energy and load variability threaten system safety and economy.Conventional chance-constrained programming(CCP)ensures reliable operation by limiting risk.However,increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks.To address this,this paper proposes a risk-adjustable chance-constrained goal programming(RACCGP)model,integrating CCP and goal programming to balance risk and cost based on system risk assessment.An intelligent nonlinear goal programming method based on the state transition algorithm(STA)is developed,along with an improved discretized step transformation,to handle model nonlinearity and enhance computational efficiency.Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP,and the solution method outperforms average sample sampling in efficiency and solution quality.展开更多
In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
Owing to increasing environmental concerns and resource scarcity, integrated energy system shave become widely used in communities. Rural energy systems, as one of the important links of the energy network in China, s...Owing to increasing environmental concerns and resource scarcity, integrated energy system shave become widely used in communities. Rural energy systems, as one of the important links of the energy network in China, suffer from low energy efficiency and weak infrastructure. Therefore, it is particularly important to increase the proportion of electricity consumption and build an integrated energy system for rural electrification in China(IESREIC) with a rural distribution network as the core, in line with national conditions. In this study, by analyzing the Chinese regional differences and natural resource endowments, the development characteristics of the IESREIC are summarized. Then, according to the existing rural energy problems, key technologies are proposed for the IESREIC, such as those for planning and operation, value sharing, infrastructure, and a management and control platform. Finally, IESREIC demonstration projects and business models are introduced for agricultural production, rural industrial systems, and rural life. The purpose is to propose research concepts for the IESREIC, provide suggestions for the development of rural energy, and provide a reference for the construction of rural energy systems in countries with characteristics similar to those of China.展开更多
The integrated energy system(IES)is an important energy supply method for mitigating the energy crisis.A station-and-network–coordinated planning method for the IES,which considers the integrated demand responses(IDR...The integrated energy system(IES)is an important energy supply method for mitigating the energy crisis.A station-and-network–coordinated planning method for the IES,which considers the integrated demand responses(IDRs)of flexible loads,electric vehicles,and energy storage is proposed in this work.First,based on load substitution at the user side,an energy-station model considering the IDR is established.Then,based on the characteristics of the energy network,a collaborative planning model is established for the energy station and energy network of the IES,considering the comprehensive system investment,operation and maintenance,and clean energy shortage penalty costs,to minimize the total cost.This can help optimize the locations of the power lines and natural gas pipelines and the capacities of the equipment in an energy station.Finally,simulations are performed to demonstrate that the proposed planning method can help delay or reduce the construction of new lines and energy-station equipment,thereby reducing the investment required and improving the planning economics of the IES.展开更多
Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainti...Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.展开更多
The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high co...The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high cost of communication and complex modeling.Meanwhile,the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency,which is difficult to apply online.For the coordinated optimization problem of the electricity-gas-heat IES in this study,we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient.Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization,dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy.Compared with centralized optimization,the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication.The proposed method considers the dual uncertainty of renewable energy and load in the training.Compared with the traditional iterative solution method,it can better cope with uncertainty and realize real-time decision making of the system,which is conducive to the online application.Finally,we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.展开更多
In an integrated energy system(IES) composed of multiple subsystems, energy coupling causes an energy supply blockage or shutdown in one subsystem, thereby affecting the energy flow distribution optimization of other ...In an integrated energy system(IES) composed of multiple subsystems, energy coupling causes an energy supply blockage or shutdown in one subsystem, thereby affecting the energy flow distribution optimization of other subsystems.The energy supply should be globally optimized during the IES energy supply restoration process to produce the highest restoration net income. Mobile emergency sources can be quickly and flexibly connected to supply energy after an energy outage to ensure a reliable supply to the system, which adds complexity to the decision. This study focuses on a powergas IES with mobile emergency sources and analyzes the coupling relationship between the gas distribution system and the power distribution system in terms of sources, networks, and loads, and the influence of mobile emergency source transportation. The influence of the transient process caused by the restoration operation of the gas distribution system on the power distribution system is also discussed. An optimization model for power-gas IES restoration was established with the objective of maximizing the net income. The coordinated restoration optimization decision-making process was also built to realize the decoupling iteration of the power-gas IES, including system status recognition, mobile emergency source dispatching optimization, gas-to-power gas flow optimization, and parallel intra-partition restoration scheme optimization for both the power and gas distribution systems. A simulation test power-gas IES consisting of an 81-node medium-voltage power distribution network, an 89-node medium-pressure gas distribution network, and four mobile emergency sources was constructed. The simulation analysis verified the efficiency of the proposed coordinated restoration optimization method.展开更多
With increasing reforms related to integrated energy systems(IESs),each energy subsystem,as a participant based on bounded rationality,significantly influences the optimal scheduling of the entire IES through mutual l...With increasing reforms related to integrated energy systems(IESs),each energy subsystem,as a participant based on bounded rationality,significantly influences the optimal scheduling of the entire IES through mutual learning and imitation.A reasonable multiagent joint operation strategy can help this system meet its low-carbon objectives.This paper proposes a bilayer low-carbon optimal operational strategy for an IES based on the Stackelberg master-slave game and multiagent joint operation.The studied IES includes cogeneration,power-to-gas,and carbon capture systems.Based on the Stackelberg master-slave game theory,sellers are used as leaders in the upper layer to set the prices of electricity and heat,while energy producers,energy storage providers,and load aggregators are used as followers in the lower layer to adjust the operational strategy of the system.An IES bilayer optimization model based on the Stackelberg master-slave game was developed.Finally,the Karush-Kuhn-Tucker(KKT)condition and linear relaxation technology are used to convert the bilayer game model to a single layer.CPLEX,which is a mathematical program solver,is used to solve the equilibrium problem and the carbon emission trading cost of the system when the benefits of each subject reach maximum and to analyze the impact of different carbon emission trading prices and growth rates on the operational strategy of the system.As an experimental demonstration,we simulated an IES coupled with an IEEE 39-node electrical grid system,a six-node heat network system,and a six-node gas network system.The simulation results confirm the effectiveness and feasibility of the proposed model.展开更多
Integrated energy systems(lESs)represent a promising energy supply model within the energy internet.However,multi-energy flow coupling in the optimal configuration of IES results in a series of simplifications in the ...Integrated energy systems(lESs)represent a promising energy supply model within the energy internet.However,multi-energy flow coupling in the optimal configuration of IES results in a series of simplifications in the preliminary planning,affecting the cost,efficiency,and environmental performance of IES.A novel optimal planning method that considers the part-load characteristics and spatio-temporal synergistic effects of IES components is proposed to enable a rational design of the structure and size of IES.An extended energy hub model is introduced based on the“node of energy hub”concept by decomposing the IES into different types of energy equipment.Subsequently,a planning method is applied as a two-level optimization framework-the upper level is used to identify the type and size of the component,while the bottom level is used to optimize the operation strategy based on a typical day analysis method.The planning problem is solved using a two-stage evolutionary algorithm,combing the multiple-mutations adaptive genetic algorithm with an interior point optimization solver,to minimize the lifetime cost of the IES.Finally,the feasibility of the proposed planning method is demonstrated using a case study.The life cycle costs of the IES with and without consideration of the part-load characteristics of the components were$4.26 million and$4.15 million,respectively,in the case study.Moreover,ignoring the variation in component characteristics in the design stage resulted in an additional 11.57%expenditure due to an energy efficiency reduction under the off-design conditions.展开更多
基金supported by the Natural Science Foundation of China(Grants U2166211)Zhejiang Provincial Natural Science Foundation of China(Grants LY24E070006 and LMS25E070002).
文摘Driven by the global energy transition and the urgent“dual carbon”goals,regional integrated energy system(RIES)planning is undergoing a paradigm shift from carbon reduction to negative carbon emissions.This paper provides a comprehensive review of the theoretical frameworks and technical pathways for RIES planning from a carbon-centric perspective.A key contribution is the proposed Carbon-Energy-Economy(CEE)triple-dimensional governance framework,which endogenizes carbon factors into planning decisions through emission constraints,trading mechanisms,and capture technologies.We first analyze the fundamental characteristics of RIES and their critical role in achieving carbon neutrality,detailing advancements in multi-energy coupling models,energy router concepts,and standardized energy hub modeling.The paper further explores multi-energy flow analysis methods,and systematically compares the applicability and limitations of various planning algorithms,with emphasis on addressing uncertainties from renewable integration.Finally,we highlight the integration of artificial intelligence with traditional optimization methods,offering new pathways for intelligent,adaptive,and low-carbon RIES planning.This review underscores the transition towards data-physical fusion models,cooperative uncertainty optimization,multi-market planning,and innovative zero/negative-carbon technological routes.
基金supported by the National Nature Science Foundation of China(Nos.62063019)Natural Science Foundation of Gansu Province(22JR5RA241,2023CXZX-465).
文摘In this study,we construct a bi-level optimization model based on the Stackelberg game and propose a robust optimization algorithm for solving the bi-level model,assuming an actual situation with several participants in energy trading.Firstly,the energy trading process is analyzed between each subject based on the establishment of the operation framework of multi-agent participation in energy trading.Secondly,the optimal operation model of each energy trading agent is established to develop a bi-level game model including each energy participant.Finally,a combination algorithm of improved robust optimization over time(ROOT)and CPLEX is proposed to solve the established game model.The experimental results indicate that under different fitness thresholds,the robust optimization results of the proposed algorithm are increased by 56.91%and 68.54%,respectively.The established bi-level game model effectively balances the benefits of different energy trading entities.The proposed algorithm proposed can increase the income of each participant in the game by an average of 8.59%.
基金supported by the science and technology foundation of Guizhou province[2022]general 013the science and technology foundation of Guizhou province[2022]general 014+1 种基金the science and technology foundation of Guizhou province GCC[2022]016-1the educational technology foundation of Guizhou province[2022]043.
文摘Integrated-energy systems(IESs)are key to advancing renewable-energy utilization and addressing environmental challenges.Key components of IESs include low-carbon,economic dispatch and demand response,for maximizing renewable-energy consumption and supporting sustainable-energy systems.User participation is central to demand response;however,many users are not inclined to engage actively;therefore,the full potential of demand response remains unrealized.User satisfaction must be prioritized in demand-response assessments.This study proposed a two-stage,capacity-optimization configuration method for user-level energy systems con-sidering thermal inertia and user satisfaction.This method addresses load coordination and complementary issues within the IES and seeks to minimize the annual,total cost for determining equipment capacity configurations while introducing models for system thermal inertia and user satisfaction.Indoor heating is adjusted,for optimizing device output and load profiles,with a focus on typical,daily,economic,and environmental objectives.The studyfindings indicate that the system thermal inertia optimizes energy-system scheduling considering user satisfaction.This optimization mitigates environmental concerns and enhances clean-energy integration.
文摘In order to promote the utilization level of new energy resources for local and efficient consumption,this paper introduces the biogas(BG)fermentation technology into the integrated energy system(IES).This initiative is to study the collaborative and optimal scheduling of IES with wind power(WP),photovoltaic(PV),and BG,while integrating carbon capture system(CCS)and power-to-gas(P2G)system.Firstly,the framework of collaborative operation of IES for BG-CCS-P2G is constructed.Secondly,the flexible scheduling resources of the source and load sides are fully exploited,and the collaborative operation mode of CCS-P2G is proposed to establish a model of IES with WP,PV,and BG multi-energy flow coupling.Then,with the objective of minimizing the intra-day operating cost and the constraints of system energy balance and equipment operating limits,the IES withWP,PV,and BG collaborative optimal scheduling model is established.Finally,taking into account the uncertainty of the output of WP and PV generation,the proposed optimal scheduling model is solved by CPLEX,and its validity is verified by setting several scenarios.The results show that the proposed collaborative operation mode and optimal scheduling model can realize the efficient,low-carbon,and economic operation of the IES with WP,PV,and BG and significantly enhance the utilization of new energy for local consumption.
基金supported by the National Natural Science Foundation of China(No.52077137).
文摘Against the backdrop of China’s“dual-carbon”target,clean energy generation currently accounts for about 3.8 trillion kilowatt-hours,or 39.7 percent of total power generation,establishing a reasonable market trading mechanism while enhancing the low-carbon economic benefits of the integrated energy system(IES)and optimizing the interests of various entities within the distribution system has become a significant challenge.Consequently,this paper proposes an optimization strategy for a low-carbon economy within a multi-agent IES that considers carbon capture systems(CCS)and power-to-gas(P2G).In this framework,the integrated energy system operator(IESO)acts as the primary leader,while energy suppliers(ES),energy storage operators(ESO),and load aggregators(LA)follow.At the level of low-carbon technology,a coupling model of P2G and CCS is developed,leading to the establishment of an IES that incorporates energy conversion and storage equipment.Economically,effective control of system carbon emissions in market trading is progressively established.Lastly,the trading decision model of the system is integrated within a master-slave game framework,utilizing an improved differential evolution algorithm in conjunction with the distributed equilibrium method of quadratic programming for solution.The calculation example demonstrates that the strategy safeguards the benefits for both parties in the game and achieves energy savings and carbon reduction for the system.
基金supported by National Key Research and Development Program(2024YFE0115600).
文摘Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems(HIES),which enhance energy sustainability through coordinated electricity,thermal,natural gas,and hydrogen utilization.This study proposes a two-stage distributionally robust optimization(DRO)-based scheduling method to improve the economic efficiency and reduce carbon emissions of HIES.The framework incorporates a ladder-type carbon trading mechanism to regulate emissions and implements a demand response(DR)program to adjustflexible multi-energy loads,thereby prioritizing RES consumption.Uncertainties from RES generation and load demand are addressed through an ambiguity set,enabling robust decision-making.The column-and-constraint generation(C&CG)algorithm efficiently solves the two-stage DRO model.Case studies demonstrate that the proposed method reduces operational costs by 3.56%,increases photovoltaic consumption rates by 5.44%,and significantly lowers carbon emissions compared to conventional approaches.Furthermore,the DRO framework achieves a superior balance between conservativeness and robustness over conventional stochastic and robust optimization methods,highlighting its potential to advance cost-effective,low-carbon energy systems while ensuring grid stability under uncertainty.
基金supported by the National Key Research and Development Program of China(2022YFB4200902)。
文摘The integrated energy systems(IESs)offer a practical solution for achieving low-carbon targets in residential buildings.However,IES encounters several challenges related to increased energy consumption and costs due to fluctuations in renewable energy generation.Leveraging building flexibility to address these power fluctuations within IES is a promising strategy,which requires coordinated control between air-conditioning systems and other IES components.This study proposes a cross-time-scale control framework that contains optimal scheduling and on-the-fly flexible control to reduce the cost impacts of a residential IES system equipped with photovoltaic(PV)panels,batteries,a heat pump,and a domestic hot water tank.The method involves three key steps:solar irradiance prediction,day-ahead optimal scheduling of energy storage,and intra-day flexible control of the heat pump.The method is validated through a high-fidelity residential building model with actual weather and energy usage data in Frankfurt,Germany.Results reveal that the proposed method limits the cost increase to just 2.67% compared to the day-ahead schedule,whereas the cost could increase by 7.39% without the flexible control.Additionally,computational efficiency is enhanced by transforming the mixed-integer programming(MIP)into nonlinear programming(NLP)problem via introducing action-exclusive constraints.This approach offers valuable support for residential IES operations.
基金supported by National Natural Science Foundation of China(52477101)Natural Science Foundation of Jiangsu Province(BK20210932).
文摘With the intensification of the energy crisis and the worsening greenhouse effect,the development of sustainable integrated energy systems(IES)has become a crucial direction for energy transition.In this context,this paper proposes a low-carbon economic dispatch strategy under the green hydrogen certificate trading(GHCT)and the ladder-type carbon emission trading(CET)mechanism,enabling the coordinated utilization of green and blue hydrogen.Specifically,a proton exchange membrane electrolyzer(PEME)model that accounts for dynamic efficiency characteristics,and a steam methane reforming(SMR)model incorporating waste heat recovery,are developed.Based on these models,a hydrogen production–storage–utilization framework is established to enable the coordinated deployment of green and blue hydrogen.Furthermore,the gas turbine(GT)unit are retrofitted using oxygenenriched combustion carbon capture(OCC)technology,wherein the oxygen produced by PEME is employed to create an oxygen-enriched combustion environment.This approach reduces energy waste and facilitates low-carbon power generation.In addition,the GHCT mechanism is integrated into the system alongside the ladder-type CET mechanism,and their complementary effects are investigated.A comprehensive optimization model is then formulated to simultaneously achieve carbon reduction and economic efficiency across the system.Case study results show that the proposed strategy reduces wind curtailment by 7.77%,carbon emissions by 65.98%,and total cost by 12.57%.This study offers theoretical reference for the low-carbon,economic,and efficient operation of future energy systems.
文摘To address the issues of unclear carbon responsibility attribution,insufficient renewable energy absorption,and simplistic carbon trading mechanisms in integrated energy systems,this paper proposes an electricheat-hydrogen integrated energy system(EHH-IES)optimal scheduling model considering carbon emission stream(CES)and wind-solar accommodation.First,the CES theory is introduced to quantify the carbon emission intensity of each energy conversion device and transmission branch by defining carbon emission rate,branch carbon intensity,and node carbon potential,realizing accurate tracking of carbon flow in the process of multi-energy coupling.Second,a stepped carbon pricing mechanism is established to dynamically adjust carbon trading costs based on the deviation between actual carbon emissions and initial quotas,strengthening the emission reduction incentive.Finally,a lowcarbon economic dispatch model is constructed with the objectives of minimizing operation cost,carbon trading cost,wind-solar curtailment penalty cost,and energy loss.Simulation results show that compared with the traditional economic dispatch scheme 3,the proposed schemel reduces carbon emissions by 53.97%and wind-solar curtailment by 68.89%with a 16.10%increase in total cost.This verifies that the model can effectively improve clean energy utilization and reduce carbon emissions,achieving low-carbon economic operation of EHH-IES,with CES theory ensuring precise carbon flow tracking across multi-energy links.
文摘Integrated energy systems(IES)are widely regarded as a key enabler of carbon neutrality,enabling the coordinated use of electricity,heat,and gas to support large-scale renewable integration.Yet their practical deployment still faces major challenges,including rigid thermoelectric coupling,insufficient operational flexibility,and fragmented carbon and certificate market mechanisms.To address these issues,this study proposes a low-carbon economic dispatch model for integrated energy systems(IES)that reduces emissions and costs while improving renewable energy utilization.A coordinated framework integrating carbon capture,utilization,and storage,two-stage power-to-gas,combined heat and power,and ground-source heat pump technologies enhances multi-energy complementarity and overcomes the heat-led constraints of traditional combined heat and power systems.A unified carbon emission trading and green certificate trading mechanism is designed to balance economic and environmental goals through cross-market synergy.To address uncertainty,a distributionally robust chance-constrained model based on Kullback-Leibler divergence is introduced in Scenario 8.The model is solved using the GUROBI solver under multiple scenarios.Simulation results show a cost reduction from$56,166.66 to$25,840.32,carbon emission cuts from 801.38to 440.90 t,and wind/photovoltaic utilization rates reaching 98%,which fully demonstrates the effectiveness of the proposed framework in achieving cost-efficient low-carbon operation of IES.
基金sponsored by National Natural Science Foundation of China(52077137).
文摘Under the“dual carbon”goals,this paper constructs an optimization model of the comprehensive energy system in the park.A stepwise carbon excess rate mechanism and an electric vehicle coupling strategy are proposed:A carbon quota trading system is established based on the baseline method,and the stepwise function is adopted to quantify the cost of excess carbon emissions;Introduce the price demand response and the two-way interaction mechanism of electric Vehicle vehicle-to-grid(V2G)to enhance the flexible regulation ability.Aiming at the uncertainty of wind and solar output,a typical scene set is generated by combining Latin hypercube sampling with the scene reduction method.The goal is to minimize the operating cost and maximize the consumption of renewable energy,and it is solved through the CPLEX solver in the MATLAB platform.Through simulation verification of the proposed models and methods in various scenarios,the simulation results show that under the coupling of the carbon excess rate trading mechanism,the demand response mechanism,and the vehicle-to-grid interaction of electric vehicles,the total daily operating cost of the system decreases by 25.3%,reduce the dual pressure of energy consumption costs and the economic environment,and achieve the coordinated optimization of economic and ecological benefits.
基金Project(2022YFC2904502)supported by the National Key Research and Development Program of ChinaProject(62273357)supported by the National Natural Science Foundation of China。
文摘The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in future low carbon societies.However,uncertainties from renewable energy and load variability threaten system safety and economy.Conventional chance-constrained programming(CCP)ensures reliable operation by limiting risk.However,increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks.To address this,this paper proposes a risk-adjustable chance-constrained goal programming(RACCGP)model,integrating CCP and goal programming to balance risk and cost based on system risk assessment.An intelligent nonlinear goal programming method based on the state transition algorithm(STA)is developed,along with an improved discretized step transformation,to handle model nonlinearity and enhance computational efficiency.Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP,and the solution method outperforms average sample sampling in efficiency and solution quality.
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金supported by the National Natural Science Foundation of China(No.51977141)headquarters technology project of State Grid Corporation of China(No.5400-202025208A-0-0-00)
文摘Owing to increasing environmental concerns and resource scarcity, integrated energy system shave become widely used in communities. Rural energy systems, as one of the important links of the energy network in China, suffer from low energy efficiency and weak infrastructure. Therefore, it is particularly important to increase the proportion of electricity consumption and build an integrated energy system for rural electrification in China(IESREIC) with a rural distribution network as the core, in line with national conditions. In this study, by analyzing the Chinese regional differences and natural resource endowments, the development characteristics of the IESREIC are summarized. Then, according to the existing rural energy problems, key technologies are proposed for the IESREIC, such as those for planning and operation, value sharing, infrastructure, and a management and control platform. Finally, IESREIC demonstration projects and business models are introduced for agricultural production, rural industrial systems, and rural life. The purpose is to propose research concepts for the IESREIC, provide suggestions for the development of rural energy, and provide a reference for the construction of rural energy systems in countries with characteristics similar to those of China.
基金supported in part by the National Key R&D Program of China(2018YFB0905000)the Science and Technology Project of the State Grid Corporation of China(SGTJDK00DWJS1800232)
文摘The integrated energy system(IES)is an important energy supply method for mitigating the energy crisis.A station-and-network–coordinated planning method for the IES,which considers the integrated demand responses(IDRs)of flexible loads,electric vehicles,and energy storage is proposed in this work.First,based on load substitution at the user side,an energy-station model considering the IDR is established.Then,based on the characteristics of the energy network,a collaborative planning model is established for the energy station and energy network of the IES,considering the comprehensive system investment,operation and maintenance,and clean energy shortage penalty costs,to minimize the total cost.This can help optimize the locations of the power lines and natural gas pipelines and the capacities of the equipment in an energy station.Finally,simulations are performed to demonstrate that the proposed planning method can help delay or reduce the construction of new lines and energy-station equipment,thereby reducing the investment required and improving the planning economics of the IES.
基金supported by the National Key Research and Development Project of China(2018YFE0122200).
文摘Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.
基金supported by The National Key R&D Program of China(2020YFB0905900):Research on artificial intelligence application of power internet of things.
文摘The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high cost of communication and complex modeling.Meanwhile,the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency,which is difficult to apply online.For the coordinated optimization problem of the electricity-gas-heat IES in this study,we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient.Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization,dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy.Compared with centralized optimization,the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication.The proposed method considers the dual uncertainty of renewable energy and load in the training.Compared with the traditional iterative solution method,it can better cope with uncertainty and realize real-time decision making of the system,which is conducive to the online application.Finally,we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.
基金supported by the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network (XTCX202001)National Natural Science Foundation of China (52077061)。
文摘In an integrated energy system(IES) composed of multiple subsystems, energy coupling causes an energy supply blockage or shutdown in one subsystem, thereby affecting the energy flow distribution optimization of other subsystems.The energy supply should be globally optimized during the IES energy supply restoration process to produce the highest restoration net income. Mobile emergency sources can be quickly and flexibly connected to supply energy after an energy outage to ensure a reliable supply to the system, which adds complexity to the decision. This study focuses on a powergas IES with mobile emergency sources and analyzes the coupling relationship between the gas distribution system and the power distribution system in terms of sources, networks, and loads, and the influence of mobile emergency source transportation. The influence of the transient process caused by the restoration operation of the gas distribution system on the power distribution system is also discussed. An optimization model for power-gas IES restoration was established with the objective of maximizing the net income. The coordinated restoration optimization decision-making process was also built to realize the decoupling iteration of the power-gas IES, including system status recognition, mobile emergency source dispatching optimization, gas-to-power gas flow optimization, and parallel intra-partition restoration scheme optimization for both the power and gas distribution systems. A simulation test power-gas IES consisting of an 81-node medium-voltage power distribution network, an 89-node medium-pressure gas distribution network, and four mobile emergency sources was constructed. The simulation analysis verified the efficiency of the proposed coordinated restoration optimization method.
基金supported by the National Natural Science Foundation of China(Grant No.62063016)。
文摘With increasing reforms related to integrated energy systems(IESs),each energy subsystem,as a participant based on bounded rationality,significantly influences the optimal scheduling of the entire IES through mutual learning and imitation.A reasonable multiagent joint operation strategy can help this system meet its low-carbon objectives.This paper proposes a bilayer low-carbon optimal operational strategy for an IES based on the Stackelberg master-slave game and multiagent joint operation.The studied IES includes cogeneration,power-to-gas,and carbon capture systems.Based on the Stackelberg master-slave game theory,sellers are used as leaders in the upper layer to set the prices of electricity and heat,while energy producers,energy storage providers,and load aggregators are used as followers in the lower layer to adjust the operational strategy of the system.An IES bilayer optimization model based on the Stackelberg master-slave game was developed.Finally,the Karush-Kuhn-Tucker(KKT)condition and linear relaxation technology are used to convert the bilayer game model to a single layer.CPLEX,which is a mathematical program solver,is used to solve the equilibrium problem and the carbon emission trading cost of the system when the benefits of each subject reach maximum and to analyze the impact of different carbon emission trading prices and growth rates on the operational strategy of the system.As an experimental demonstration,we simulated an IES coupled with an IEEE 39-node electrical grid system,a six-node heat network system,and a six-node gas network system.The simulation results confirm the effectiveness and feasibility of the proposed model.
基金the National Natural Science Foundation of China(Grant No.51821004)supported by the Major Program of the National Natural Science Foundation of China(Grant No.52090062)The author Chengzhou Li also thank the China Scholarship Council(CSC)for the financial support.
文摘Integrated energy systems(lESs)represent a promising energy supply model within the energy internet.However,multi-energy flow coupling in the optimal configuration of IES results in a series of simplifications in the preliminary planning,affecting the cost,efficiency,and environmental performance of IES.A novel optimal planning method that considers the part-load characteristics and spatio-temporal synergistic effects of IES components is proposed to enable a rational design of the structure and size of IES.An extended energy hub model is introduced based on the“node of energy hub”concept by decomposing the IES into different types of energy equipment.Subsequently,a planning method is applied as a two-level optimization framework-the upper level is used to identify the type and size of the component,while the bottom level is used to optimize the operation strategy based on a typical day analysis method.The planning problem is solved using a two-stage evolutionary algorithm,combing the multiple-mutations adaptive genetic algorithm with an interior point optimization solver,to minimize the lifetime cost of the IES.Finally,the feasibility of the proposed planning method is demonstrated using a case study.The life cycle costs of the IES with and without consideration of the part-load characteristics of the components were$4.26 million and$4.15 million,respectively,in the case study.Moreover,ignoring the variation in component characteristics in the design stage resulted in an additional 11.57%expenditure due to an energy efficiency reduction under the off-design conditions.
