Energy Demand Uncertainty Research Articles

Optimal design of distributed energy resource systems under large-scale uncertainties in energy demands based on decision-making theory

This study focuses on the optimal design of distributed energy resource systems with consideration of large-scale uncertainty of energy demands based on decision- making theory. Five integrated modeling and optimization frameworks are developed through the combined use of mixed integer linear programming and uncertainty decision-making criteria (including optimistic criterion, pessimistic criterion, Hurwicz criterion, Laplace criterion, and minimax regret criterion). Superstructure-based mixed integer linear programming models are used for the optimal design and optimal operation of the system where the objective function is to minimize the annual cost. The uncertainty of energy demands is represented by assuming a set of possible scenarios. The proposed methods are applied to the planning of a distributed energy resource system for a hotel in city of Guangzhou, China and their validity and effectiveness are verified. Results show that each method has its specific feature. Optimistic method is risky and recommends a relative small-scale system, while pessimistic method is conservative presenting a relative large-scale system. Hurwicz method is with great subjectivity, making different decisions at different values of optimism coefficient. Both Laplace method and minimax regret method identify a moderate-scale system as the best alternative. Sensitivity analyses on the energy demand scenarios are conducted and results show that the five methods have high sensitivity to the choice of scenarios.

Automated urban energy system modeling and thermal building simulation based on OpenStreetMap data sets

City districts have a large potential to reduce greenhouse gas emissions by usage of energy efficiency measures. Urban energy models (UEM) can be useful to analyze the impact of different energy efficiency actions on city districts. While simulation of demand data with high spatial and temporal resolution is often necessary to evaluate retrofit measures, the city's complex structure and lack of data often prevents a reliable application of such methods. This paper presents an urban energy modeling approach based on open-source geographical information system (GIS) datasets to reduce input data uncertainty and simplify city district modeling. We present a method to automatically extract basic city district data from OpenStreetMap (OSM) and enrich these datasets based on national building stock statistics. Building models with representative geometries and physical properties are automatically generated based on building archetype information. These models enable thermal simulation on urban scale. The approach is demonstrated for a use case in Germany, where a reference city district model has been generated with OSM data extraction and enrichment. The reference city district model has been used to perform a space heating net energy demand uncertainty analysis. The demand values simulated with the reference model show a sufficient fit with measured consumption values. The approach provides a fast and structured methodology to model city districts and simulate space heating energy demand on urban scale.

Development and validation of energy demand uncertainty model for electric city buses

The prediction of electric city bus energy demand is crucial in order to estimate operating costs and to size components such as the battery and charging systems. Unfortunately, there are unpredictable dynamic factors that can cause variation in the energy demand, particularly concerning driver choices and traffic levels. The impact of these factors on energy demand has been difficult to study since fast computing sufficiently accurate dynamic simulation models have been missing, properly quantified in terms of relevant inputs which contribute to energy demand. The objective is to develop and validate a novel electric city bus model for computing the energy demand, to study the nature and impact of various input factors. The developed equation-based model predicted real-world electric city bus energy consumption within 0.1% error. The most crucial unmeasurable input factors were the driven bus route, the number of stops, the elevation profile, the traffic level and the driving style. This understanding can be used to specify routes and stops for a given electric bus battery capacity. Worst-case scenarios are also necessary for electric bus sizing analysis. The best- and worst-case levels of the crucial factors were identified and with them synthetic best- and worst-case speed profiles were generated to demonstrate their effect to the energy demand. While the measured nominal consumption was 0.70 kWh/km, the computed range of variation was between 0.19 kWh/km and 1.34 kWh/km. For design sizing purposes, an electric city bus can have a broad range of possible energy consumption rates due to mission condition variations.

Robust optimal design of energy supply systems under uncertain energy demands based on a mixed-integer linear model

In designing energy supply systems, designers should consider the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method of energy supply systems under uncertain energy demands is proposed using a mixed-integer linear model so that it can consider discrete characteristics for selection and on/off status of operation and piecewise linear approximations for nonlinear performance characteristics of constituent equipment. First, a robust optimal design problem is formulated as a three-level min-max-min optimization one by expressing uncertain energy demands by intervals based on the interval programming, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering hierarchical relationships among design variables, uncertain energy demands, and operation variables. Then, a special solution method of the problem is proposed especially in consideration of the existence of integer operation variables. In a case study, the proposed method is applied to the robust optimal design of a cogeneration system with a simple configuration. Through the study, the validity and effectiveness of the method is ascertained, and some features of the obtained solutions are clarified.

Optimal Stochastic Operation of Integrated Low-Carbon Electric Power, Natural Gas, and Heat Delivery System

Integrated energy system is important for the high-efficient utilization of multitype energy systems. In this paper, the stochastic optimal operation is investigated for the micro integrated electric power, natural gas, and heat delivery system (IPGHS). First, a low-carbon micro-IPGHS is proposed with the comprehensive consideration of renewable generation, carbon-capture-based power-to-gas technology, and the combined power and heat units. Second, a scenario-based optimal operation model for micro-IPGHS is proposed to handle uncertainties in energy demand and renewable generation. In the proposed model, energy transactions between micro-IPGHS and upstream energy systems as well as constraints for battery storage, natural gas storage, and heat storage systems are considered. Finally, a case study is used for the proposed low-carbon micro-IPGHS to validate the optimal stochastic operation approach. The proposed integrated system can effectively utilize the variable clean energy for optimizing the delivery of the green operation in micro-IPGHS.

Optimal integrated sizing and operation of a CHP system with Monte Carlo risk analysis for long-term uncertainty in energy demands

In this study a probabilistic approach for optimal sizing of cogeneration systems under long-term uncertainty in energy demand is proposed. A dynamic simulation framework for detailed modeling of the energy system is defined, consisting in both traditional and optimal operational strategies evaluation. A two-stage stochastic optimization algorithm is developed, adopting Monte Carlo method for the definition of a multi-objective optimization problem. An Italian hospital facility has been used as a case study and a gas internal combustion engine is considered for the cogeneration unit. The results reveal that the influence of uncertainties on both optimal size and annual total cost is significant. Optimal size obtained with the traditional deterministic approach are found to be sub-optimal (up to 30% larger) and the predicted annual cost saving is always lower when accounting for uncertainties. Pareto frontiers of different CHP configurations are presented and show the effectiveness of the proposed method as a useful tool for risk management and focused decision-making, as tradeoffs between system efficiency and system robustness.

Optimal Design of Water Distribution Networks with Incorporation of Uncertainties and Energy Nexus

The reliability of water distribution networks is susceptible to large impacts resulting from uncertainties. Several factors may contribute to such uncertainties. These include nodal demands, reservoir/tank levels, and availability of system components. Additional sources of uncertainties arise when water-energy nexus is considered. For instance, when water desalination systems that are coupled with power plants are incorporated in the water distribution networks, uncertainties in energy demand influence the design of the water network system. In this work, a multi-objective optimization framework is developed for the design of water networks that involve dual-purpose power plants for simultaneous water desalination and power generation. The multi-objective model accounts for sustainability goals through environmental, economic, and societal metrics such as greenhouse gas emissions, net profit, and number of jobs created, respectively. Fossil fuels, as well as renewable biofuels and solar power, are considered as candidate sources of energy. Water resources include multiple systems such as dams, lakes, rivers, aquifers, and artificial storage lakes. Demands from agricultural, industrial as well as domestic needs in the region are considered. In order to incorporate uncertainty in the proposed approach, a stochastic optimization model is formulated with a probabilistic objective function and constraints. The network has multiple sources as well as demands with varied distributions. In order to find an overall distribution for probability density estimation, a decomposition scheme is applied where each scenario is solved separately as a sub-problem. The solution from sub-problem is used to find the probability using kernel density estimator. The modified model equations lead to a stochastic MINLP problem. The proposed framework and optimization formulations are applied to a case study in the Mexican state of Sonora. From the demand and natural resource distribution, 12 scenarios have been identified and the model is weighted by their probability of occurrence. The results are compared with the deterministic solution to obtain the cost associated with uncertainty.

Performance comparison of energy supply systems under uncertain energy demands based on a mixed-integer linear model

In designing energy supply systems, several alternatives for design specifications are proposed, and their performances are evaluated and compared. In this paper, a method of comparing performances of two energy supply systems under uncertain energy demands is proposed based on a mixed-integer linear model. Uncertain energy demands are expressed by intervals. The minimum and maximum, and consequently their interval of the difference in the value of a performance criterion are evaluated for all the possible energy demands within their intervals. An optimization problem for this evaluation is formulated as a minimax mixed-integer linear programming one with integer and continuous operation variables. The problem is solved by evaluating upper and lower bounds for the optimal value of the difference in the value of the performance criterion repeatedly. In a case study, the minimum and maximum of the reduction in the annual total cost of a cogeneration system in comparison with a conventional energy supply system are evaluated, and the corresponding energy demands and operational strategies are identified. The influence of the uncertainty in energy demands on these results is also examined. Through the case study, the validity and effectiveness of the proposed method are clarified.

Quantification of the urban water-energy nexus in México City, México, with an assessment of water-system related carbon emissions

Global urbanisation will put considerable stress on both water and energy resources. While there is much research at the national and regional levels on the energy implications of water supply (the urban water-energy ‘nexus’), there is relatively little at the city scale. This literature is further diminished when attempting to account for the climate impact of urban water systems. A study of the urban water-energy-climate nexus is presented for México City. It is shown that 50% of México City water comes from a local aquifer with a further 30% deriving from energy-intensive surface sources which are pumped over considerable topography. The water supply system consumes 90% of the water system energy demand, and is responsible for the majority (90%) of the CO2e emissions. In the wastewater sector, 80–90% is discharged with no or little treatment, with correspondingly low energy demand. The small fraction that is treated accounts for the majority of energy use in the wastewater sector. This study shows the uncertainty in energy demand and CO2e emissions when reliant on secondary data which considerably over/under-estimate energy use compared with primary data. This has implications when assessing energy and carbon budgets. Three water savings options are assessed for their impact on energy and CO2e emissions reductions. Considerable reductions in water supply volumes and concomitant energy consumption and CO2e emissions are possible. However the extent of implementation, and the effectiveness of any implemented solutions depend on financing, institutional backing and public support. An additional measure to reduce the climate impact is to switch from traditional to renewable fuels. This work adds city-level quantification of the urban water-energy-climate nexus, allowing policy makers to discern which water-system elements are responsible for the greatest energy use and climate impact, and are better equipped to make targeted operational decisions.

Stochastic programming and market equilibrium analysis of microgrids energy management systems

Microgrids facilitate optimum utilization of distributed renewable energy, provides better local energy supply, and reduces transmission loss and greenhouse gas emission. Because the uncertainty in energy demand affects the energy demand and supply system, the aim of this research is to develop a stochastic optimization and its market equilibrium for microgrids in the electricity market. Therefore, a two-stage stochastic programming model for microgrids and the market competition model are derived in this paper. In the stochastic model, energy demand and supply uncertainties are considered. Furthermore, a case study of the stochastic model is conducted to simulate the uncertainties on the INER microgrids in Taiwanese market. The optimal investment of the generators and batteries installation and operating strategies are determined under energy demand and supply uncertainties for the INER microgrids. The results show optimal investment and operating strategies for the current INER microgrids are also determined by the proposed two-stage stochastic model in the market. In addition, trade-off between the battery capacity and microgrids performance is investigated. Battery usage and power trading between the microgrids and main grid systems are the functions of battery capacity.

Robust Optimal Operation of a Gas Turbine Cogeneration Plant Under Uncertain Energy Demands

Some optimal operation methods based on the mixed-integer linear programming (MILP) have been proposed to operate energy supply plants properly from the viewpoints of economics, energy saving, and CO2 emission reduction. However, most of the methods are effective only under certain energy demands. In operating an energy supply plant actually, it is necessary to determine the operational strategy properly based on predicted energy demands. In this case, realized energy demands may differ from the predicted ones. Therefore, it is necessary to determine the operational strategy so that it is robust against the uncertainty in energy demands. In this paper, an optimization method based on the MILP is proposed to conduct the robust optimal operation of energy supply plants under uncertain energy demands. The uncertainty in energy demands is expressed by their intervals. The operational strategy is determined to minimize the maximum regret in the operational cost under the uncertainty. In addition, a hierarchical relationship among operation modes and on/off states of equipment, energy demands, and energy flow rates of equipment is taken into account. First, a general formulation of a robust optimal operation problem is presented, which is followed by a general solution procedure. Then, in a numerical study, the proposed method is applied to a gas turbine cogeneration plant for district energy supply. Through the study, some features of the robust optimal operation are clarified, and the validity and effectiveness of the proposed method are ascertained.

Scheduling Energy Cogeneration Units under Energy Demand Uncertainty

This work presents a methodology for the scheduling of networks that consist of various energy cogeneration units (i.e., generate both electrical energy and heat) under high energy demand uncertainties of bounded form. First, a mathematical framework for the problem in question is developed, and then we present a reactive scheduling approach that relays on multiparametric programming and a receding horizon. In brief, the original mathematical scheduling model is reformulated into a multiparametric programming problem, wherein we consider as uncertain parameters: the energy demands as well as the initial and the final state of the overall system. The resulting parametric optimization problem is solved once and off-line, and afterwards a receding horizon-like approach is applied for the reactive scheduling –that acts on the fly in the energy demand realizations– by performing just function evaluations and avoiding the on-line optimization of such systems. A couple of problem instances are solved to shed light on the potential benefits of the suggested method. The proposed concept has highly practical interest and is very promising since could find application in several other optimization problems that can involve: large-scale optimization problems and process scheduling problems under uncertainty.

Real time operation of μCHP systems using fuzzy logic

Micro Combined Heat and Power (μCHP) technologies are usually operated according to a predetermined conventional heat or electricity led operation strategy (HLOS, ELOS) [1]. μCHP systems can contribute to the transition to a low carbon economy through their relative efficient operation, their ability to use renewable fuels and reduce electrical distribution network losses. Previously, an online linear programming optimiser (LPO) for operating a μCHP system has been developed with the ability to significantly reduce operation costs when compared with HLOS and ELOS [2]. However, the online LPO depends on historical demands. In order to deal with the complexities inherent in the operation of μCHP systems, such as uncertainties in energy demands and performance, a fuzzy logic (FL) approach is required.In this paper, a real time fuzzy logic operation strategy (FLOS) has been developed and evaluated, which aims to minimise operation costs and CO2 emissions of a μCHP system. Three simulation scenarios have been investigated for the real time FLOS: the feed-in tariff (FIT) scheme; the trade of electricity; the introduction of a carbon tax. In all three scenarios investigated. Results show that the real time FLOS significantly reduces operation costs and CO2 emissions when compared with HLOS and ELOS.

Uncertain programming of building cooling heating and power (BCHP) system based on Monte-Carlo method

Uncertainty of building energy demands has large influence on accuracy of building cooling heating and power (BCHP) programming model. Uncertain programming model is proposed to optimize BCHP system with consideration of uncertainty of energy demands. Monte-Carlo method (MCM) and mixed-integer nonlinear programming (MINLP) are integrated in the model (M–M model for short). MCM can be used to simulate the uncertainty of energy demands avoiding dimension disaster and complex calculation. Correlation between different energy demands can also be considered in the model. And facility scheme and operation strategy can be optimized simultaneously in MINLP model. A numerical example is calculated with the M–M model. Convergence rate of expected values of the variables optimized in the model is high. Influence of energy demand uncertainty is studied with investigation of expected values, standard deviations of evaluation indicators and facility capacities. Sensitivity of the parameters to energy demand uncertainty is much different. It is unnecessary to consider uncertainty of energy demands when evaluating system feasibility with indicators of annual cost saving rate and annual natural gas saving rate, for they are influenced only a little by uncertainty of energy demands. While uncertainty of energy demands must be considered when studying parameters related to assistant facilities, which are very sensitive to the uncertainty. The result is valuable for designing strategy of facility scheme.

Robust Optimal Design in Multistage Expansion of a Gas Turbine Cogeneration Plant Under Uncertain Energy Demands

In designing cogeneration plants, the estimation of energy demands is an important work. However, many conditions under which energy demands are estimated have some uncertainty at the design stage. Therefore, designers should consider that energy demands have some uncertainty, evaluate the robustness in the performance under uncertain energy demands, and design plants rationally in consideration of the robustness. The authors have developed a robust optimal design method based on the minimax regret criterion for the single-stage planning of energy supply plants. In this paper, the method is extended for the multistage expansion planning. Under uncertain energy demands increasing stepwise, equipment capacities and utility contract demands as well as energy flow rates for each expansion period are determined in consideration of their sequential relationships to minimize the maximum regret in the annual total cost and satisfy all the possible energy demands for all the expansion periods. Through a case study on a gas turbine cogeneration plant for district energy supply, features of the economic robustness and the robust optimal design are clarified in relation to the uncertainty in energy demands and the numbers of years for the expansion periods.

Optimal unit sizing of cogeneration systems in consideration of uncertain energy demands as continuous random variables

An optimal unit sizing method for cogeneration systems is proposed using energy demands as continuous random variables. In this method, design variables such as equipment capacities and maximum contract utility demands are determined together with the systems' operational strategies so as to minimize an expected value of the annual total cost subject to the satisfaction of all the possible energy demands. In evaluating the expected value, decision variables and the objective function are considered as piece-wise linear functions of energy demands by applying a sensitivity analysis in linear programming and an enumeration method in mixed-integer programming. This optimization problem is formulated and solved based on a hierarchical optimization algorithm. A numerical study is carried out on a fuel cell cogeneration system installed in an office building. Through the study, the influence of uncertainties in energy demands on a system's economics and optimal equipment capacities are clarified.

105 エネルギー供給システムの多段階拡張におけるロバスト最適設計 : 相対ロバスト性基準による検討

A robust optimal design method for multistage expansion of energy supply systems based on the relative robustness criterion is proposed so that they are robust economically against the uncertainty in energy demands which increase stepwise with construction of buildings. Equipment capacities and utility contract demands as well as energy flow rates for each expansion period are determined to minimize the maximum normalized regret or the maximum regret rate in the levelized annual total cost and satisfy all the possible energy demands for the overall planning period. This optimization problem is formulated as a kind of multilevel linear programming problem, and its solution is obtained by repeatedly evaluating upper and lower bounds for the optimal value of the maximum regret rate by means of the fractional, the bilevel, and the linear programming. Through a numerical case study on a cogeneration system, the relationship between the optimal equipment capacities and the uncertainty in energy demands or the number of years for expansion periods is clarified.

Robust Optimal Design in Multistage Expansion of Energy Supply Systems.

A robust optimal design method based on the minimax regret criterion is proposed for multistage expansion planning of energy supply systems. Under uncertain energy demands increasing stepwise, equipment capacities and utility contract demands as well as energy flow rates for each expansion period are determined in consideration of their hierarchical relationships to minimize the maximum regret in the annual total cost and satisfy all the possible energy demands for the whole planning period. This optimization problem is formulated as a kind of multilevel linear programming problem, and its solution is derived by repeatedly evaluating upper and lower bounds for the optimal value of the maximum regret. Through a numerical case study on a cogeneration system for district energy supply, features of the economic robustness and multistage expansion planning are clarified in relation to the uncertainty in energy demands and the number of years for expansion periods.

A Reappraisal of Energy Supply and Demand in 2050

In this paper dealing with the medium term (2020) and long term (2050) world energy mix the author has attempted to present a single most likely scenario, contrary to the usual multiple scenario approach. A second main characteristic is that the emphasis is not on the uncertainties of energy demand but on the potential limitations on the offer of fossil fuels and mainly of oil and gas. The main conclusions are that by 2050 we will need a large increase of the world nuclear industry, not only for the production of electricity but also to complement the oil industry, by providing it with necessary CO2 emissions freeheat and hydrogen. This nuclear- based hydrogen would allow to give a sustainable future to the oil industry, and to the automobile industry, by providing synthesis fuels on an economically and ecologically sound basis.

Multiobjective Robust Optimal Design of Energy Supply Systems Based on Minimax Regret Criterion.

A multiobjective robust optimal design method based on the minimax regret criterion is proposed to determine equipment capacities of energy supply systems so that they are robust in economic and energy saving characteristics against the uncertainty in energy demands. Equipment capacities and utility contract demands as well as energy flow rates are determined to minimize a weighted sum of maximum regrets in the annual total cost and primary energy consumption and to satisfy all the possible energy demands. This optimization problem is formulated as a kind of multilevel linear programming problem, and its solution is obtained by repeatedly evaluating lower and upper bounds for the optimal value of the weighted sum of the maximum regrets. Through a numerical case study on a cogeneration system, the trade-off relationship between the robustness of economic and energy saving characteristics is charified.