Measuring the validity and performance of energy models

This paper is concerned with approaches to validating and judging the performance of energy models. There has been a proliferation of models of all sorts. These models not only attempt to deal with many different aspects of industry and market behaviour but also involve widely different modelling methodologies. Several attempts have been made to classify and to evaluate these methodological approaches; they are not repeated here. Rather this paper focuses on criteria for determining the validity of a model that are quantitative and hopefully rigorous. Different validation criteria are suggested for econometric time-series models, models, and mathematical programming models. Finally, an appeal is made for including validation measures in future energy modelling studies.     

Novel model reduction techniques for refinery-wide energy optimisation

The oil refining industry mainly uses linear programming (LP) modelling tools for refinery optimisation and planning purposes, on a daily basis. LPs are attractive from the computational time point of view; however these models have limitations such as the nonlinearity of the refinery processes is not taken into account. In addition, building the LP model can be an arduous task that requires collecting large amounts of data. The main aim of this work is to develop approximate models to replace the rigorous ones providing a good accuracy without compromising the computational time, for refinery optimisation. The data for deriving approximate models has been generated from rigorous process models from a commercial software, which is extensively used in the refining industry. In this work we present novel model reduction techniques based upon optimal configuration of artificial neural networks to derive approximate models and demonstrate how these models can be used for refinery-wide energy optimisation.     

Energy import resilience with input–output linear programming models

In this work we develop a new approach to study the energy import resilience of an economy using linear programming and economic input–output analysis. In particular, we propose an energy import resilience index by examining the maximum level of energy import reduction that the economy can endure without sacrificing domestic demands. A mixed integer programming model is then developed to compute the resilience index efficiently. The methodology is applied to a case study using China input–output data to study the energy import resilience under different power generation portfolio assumptions. We demonstrate how our models can be used to uncover important inter-sectoral dependencies, and to guide decision-makers in improving the energy resilience in a systematic manner.     

Assessing and optimizing the economic and environmental impacts of cogeneration/district energy systems using an energy equilibrium model

Energy equilibrium models can be valuable aids in energy planning and decision-making. In such models, supply is represented by a cost-minimizing linear submodel and demand by a smooth vector-valued function of prices. In this paper, we use the energy equilibrium model to study conventional systems and cogeneration-based district energy (DE) systems for providing heating, cooling and electrical services, not only to assess the potential economic and environmental benefits of cogeneration-based DE systems, but also to develop optimal configurations while accounting for such factors as economics and environmental impact. The energy equilibrium model is formulated and solved with software called WATEMS, which uses sequential non-linear programming to calculate the intertemporal equilibrium of energy supplies and demands. The methods of analysis and evaluation for the economic and environmental impacts are carefully explored. An illustrative energy equilibrium model of conventional and cogeneration-based DE systems is developed within WATEMS to compare quantitatively the economic and environmental impacts of those systems for various scenarios.     

Mathematical algorithms to locate factories to transform biomass in bioenergy focused on logistic network construction

Many linear programming models have been developed to study the logistics and determine the best setup for bioenergy chains. Most use network structures built from nodes with one or more depots and arcs connecting these depots. Each depot is a source of a certain biomass type. Nodes can also represent a biomass storage point or a production facility (e.g., power plant) where the biomass is used. Arcs represent transport routes between depots. To combine GIS spatial studies with linear programming models, it is necessary to design a network from a digital map. In this research a mathematical calculation method is developed to select the actual points on the map for the locations of a bioenergy plant that will then be considered as biomass destinations in a network model. The base data for this model is city's locations and the bioenergy they required, given in GIS maps (shape files), although also it can be the points where the biomass is produced. The limits of the studied area should be defined in advance, for example, a country, a province or a region. Criteria selection for plant location is two: all the energy produced by the plant should be used; the cost to transport the energy produced should be minimal. With these criteria, the cities are grouped in sets, which should be supplied by a power energy plant. Each plant supplying a given subset of cities will be located in the center of gravity specified by the coordinates and the energy required by each city in the subset. The algorithm provides the locations of points where plants that transform biomass into bioenergy for a group of cities are placed. The points to locate plants are then taken as destination nodes in the network when the logistics models are implemented. In the next step, the network is analyzed by linear programming techniques to supply the optimal location for the power plants or factories depending on the available biomass sources. In this paper a practical example applied to Spanish rural regions is discussed.     

Energy and environmental systems planning under uncertainty—An inexact fuzzy-stochastic programming approach

In this study, an inexact fuzzy-stochastic energy model (IFS-EM) is developed for planning energy and environmental systems (EES) management under multiple uncertainties. In the IFS-EM, methods of interval parameter fuzzy linear programming (IFLP) and multistage stochastic programming with recourse (MSP) are introduced into a mixed-integer linear programming (MILP) framework, such that the developed model can tackle uncertainties described in terms of interval values, fuzzy sets and probability distributions. Moreover, it can reflect dynamic decisions for facility-capacity expansion and energy supply over a multistage context. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability, where three cases are considered based on different energy and environmental management policies. The results indicate that reasonable solutions have been generated. They are helpful for supporting: (a) adjustment or justification of allocation patterns of regional energy resources and services, (b) formulation of local policies regarding energy consumption, economic development and environmental protection, and (c) in-depth analysis of tradeoffs among system cost, satisfaction degree and environmental requirement under multiple uncertainties.     

Community-scale renewable energy systems planning under uncertainty—An interval chance-constrained programming approach

In this study, an inexact community-scale energy model (ICS-EM) has been developed for planning renewable energy management (REM) systems under uncertainty. This method is based on an integration of the existing interval linear programming (ILP), chance-constrained programming (CCP) and mixed integer linear programming (MILP) techniques. ICS-EM allows uncertainties presented as both probability distributions and interval values to be incorporated within a general optimization framework. It can also facilitate capacity-expansion planning for energy-production facilities within a multi-period and multi-option context. Complexities in energy management systems can be systematically reflected, thus applicability of the modeling process can be highly enhanced. The developed method has then been applied to a case of long-term renewable energy management planning for three communities. Useful solutions for the planning of energy management systems have been generated. Interval solutions associated with different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help decision makers identify desired policies under various economic and system-reliability constraints. The generated solutions can also provide desired energy resource/service allocation and capacity-expansion plans with a minimized system cost, a maximized system reliability and a maximized energy security. Tradeoffs between system costs and constraint-violation risks can also be tackled. Higher costs will increase system stability, while a desire for lower system costs will run into a risk of potential instability of the management system. They are helpful for supporting (a) adjustment or justification of allocation patterns of energy resources and services, (b) formulation of local policies regarding energy consumption, economic development and energy structure, and (c) analysis of interactions among economic cost, system reliability and energy-supply security.     

Modelling renewable supply chain for electricity generation with forest, fossil, and wood-waste fuels

In this paper, a multiple objective model to large-scale and long-term industrial energy supply chain scheduling problems is considered. The problems include the allocation of a number of fossil, peat, and wood-waste fuel procurement chains to an energy plant during different periods. This decision environment is further complicated by sequence-dependent procurement chains for forest fuels. A dynamic linear programming model can be efficiently used for modelling energy flows in fuel procurement planning. However, due to the complex nature of the problem, the resulting model cannot be directly used to solve the combined heat and electricity production problem in a manner that is relevant to the energy industry. Therefore, this approach was used with a multiple objective programming model to better describe the combinatorial complexity of the scheduling task. The properties of this methodology are discussed and four examples of how the model works based on real-world data and optional peat fuel tax, feed-in tariff of electricity and energy efficiency constraints are presented. The energy industry as a whole is subject to policy decisions regarding renewable energy production and energy efficiency regulation. These decisions should be made on the basis of comprehensive techno-economic analysis using local energy supply chain models.     

An interval full-infinite mixed-integer programming method for planning municipal energy systems – A case study of Beijing

In this study, an interval full-infinite mixed-integer municipal-scale energy model (IFMI-MEM) is developed for planning energy systems of Beijing. IFMI-MEM is based on an integration of existing interval-parameter programming (IPP), mixed-integer linear programming (MILP) and full-infinite programming (FIP) techniques. IFMI-MEM allows uncertainties expressed as determinates, crisp interval values and functional intervals to be incorporated within a general optimization framework. It can also facilitate capacity-expansion planning for energy-production facilities within a multi-period and multi-option context. Then, IFMI-MEM is applied to a real case study of energy systems planning in Beijing. The results indicate that reasonable solutions have been generated. They are helpful for supporting (a) adjustment of the existing demand and supply patterns of energy resources, (b) facilitation of dynamic analysis for decisions of capacity expansion and/or development planning, and (c) coordination of the conflict interactions among economic cost, system efficiency, pollutant mitigation and energy-supply security.     

An efficient linear programming model and optimization algorithm for trigeneration

Trigeneration is a booming technology for efficient and clean provision of energy. It has potential for reducing pollution emissions dramatically. Similar to combined heat and power (CHP) production, cost-efficient operation of a trigeneration system can be planned using an optimization model based on hourly load forecasts. A long-term planning model decomposes into thousands of hourly models, which can be solved separately. In this paper, we model the hourly trigeneration problem as a linear programming (LP) model with a joint characteristic for three energy components to minimize simultaneously the production and purchase costs of three energy components, as well as CO₂ emissions costs. Then we explore the structure of the problem and propose the specialized Tri-Commodity Simplex (TCS) algorithm that employs this structure efficiently. The speed of TCS is based on extremely fast basis inverse operations and reuse of old basic solutions from previously solved hourly models. We compare the performance of TCS with realistic models against an efficient sparse Simplex code using the product form of inverse. In test runs, TCS is from 36 to 58 times faster when starting from the initial basis and from 43 to 179 times faster when reusing the old basis.     

Urban activity allocation under criteria of transportation energy efficiency

A linear programming optimization technique is applied to the problem of allocating new land using activities in an existing urban area. While it is recognized that energy is not yet as decisive a factor in the determination of household and firm locational patterns as other factors such as accessibility and time costs, the model attempts to resolve land allocation problems by means of minimizing total transportation energy costs alone. Such an analysis may serve as a benchmark against which other policies and their energy repercussions could and should be measured.     

Goal programming model for sustainable electricity production from biomass

In this paper, we present a goal programming model for block level energy planning in order to make a block self‐sufficient in electricity consumption, which includes the commercial energy consumption goal, the goal of generating electricity from biomass and food production goals with linear constraints on the available sources such as human power, animal power, tractor power, land area and on the requirement of the block such as cooking energy, lighting energy and energy for other operations, such as fodder for animal population. We try to achieve these goals through proper allocation of land for different crops. After reformulating the developed goal programming model into a linear programming format, we use the HYPER LINDO software package to solve it in a Pentium‐based IBM‐PC compatible computer system. The developed model is solved for a typical Indian block, namely Nilakkottai Block in Tamil Nadu, India. The model solution shows that the goal of generating electricity from biomass is achieved, the commercial energy consumption goal and pulses requirement goal are under‐achieved and the sugar requirement goal is over‐achieved. Furthermore, the cereal, vegetable and oilseed production goals are achieved. Copyright © 2000 John Wiley & Sons, Ltd.     

An inexact optimization model for regional energy systems planning in the mixed stochastic and fuzzy environment

In this study, an interval‐parameter superiority–inferiority‐based regional energy management model has been developed for supporting regional energy management (REM) systems planning under uncertainty. This method is based on an integration of the existing interval mathematical programming, superiority–inferiority‐based fuzzy–stochastic programming and mixed integer linear programming techniques. It can explicitly address the system uncertainties that can be expressed as fuzzy‐random variables and/or interval numbers. In addition, dynamic interrelationships among system parameters can be successfully reflected through the introduction of fuzzy‐random variables and the associated transition probabilities. The developed method has then been applied to a case of long‐term REM planning. Useful solutions for the planning of energy management systems have been generated, which can be used for generating decision alternatives and thus help resource managers identify desired policies under various economic and system‐reliability constraints. The generated solutions can also provide desired plans for energy resource/service allocation and facility capacity expansion with a minimized system cost, maximized system reliability and maximized energy security. Tradeoffs between system costs and constraint‐violation risk levels can also be tackled. Higher costs will increase system stability, while a desire for lower system costs will run into a risk of potential instability of the management system. The results also suggest that the proposed methodology is applicable to practical problems that are associated with uncertain information. Copyright © 2008 John Wiley & Sons, Ltd.     

Planning of community-scale renewable energy management systems in a mixed stochastic and fuzzy environment

In this study, an interval-parameter superiority–inferiority-based two-stage programming model has been developed for supporting community-scale renewable energy management (ISITSP-CREM). This method is based on an integration of the existing interval linear programming (ILP), two-stage programming (TSP) and superiority–inferiority-based fuzzy-stochastic programming (SI-FSP). It allows uncertainties presented as both probability/possibilistic distributions and interval values to be incorporated within a general optimization framework, facilitating the reflection of multiple uncertainties and complexities during the process of renewable energy management systems planning. ISITSP-CREM can also be used for effectively addressing dynamic interrelationships between renewable energy availabilities, economic penalties and electricity-generation deficiencies within a community scale. Thus, complexities in renewable energy management systems can be systematically reflected, highly enhancing applicability of the modeling process. The developed method has then been applied to a case of long-term renewable energy management planning for three communities. Useful solutions for the planning of renewable energy management systems have been generated. Interval solutions associated with different energy availabilities and economic penalties have been obtained. They can be used for generating decision alternatives and thus help decision makers identify desired policies under various economic and system-reliability constraints. The generated solutions can also provide desired energy resource/service allocation plans with a minimized system cost (or economic penalties), a maximized system reliability level and a maximized energy security. Tradeoffs between system costs and energy security can also be tackled. Higher costs will increase potential energy generation amount, while a desire for lower system costs will run into a risk of energy deficiency. They are helpful for supporting: (a) adjustment or justification of allocation patterns of renewable energy resources and services, (b) formulation of local policies regarding energy utilization, economic development and energy structure under various energy availabilities and policy interventions, and (c) analysis of interactions among economic cost, system reliability and energy-supply shortage.     

Mathematical model for energy planning of rural India

This paper describes an integrated energy system planning approach for Wardha District in Maharashtra State, India, for the year AD 2000 and gives an optimal mix of new/conventional energy technologies using a computer-based mixed integer linear programming model. The district level planning is accomplished by successively applying in two stages a new statistical extrapolation technique for moving first from the village level energy scenarios based on surveys to the corresponding energy scenarios at the block level and then for moving next from the block level scenarios to the desired district level planning profile. The model is suitably scaled for obtaining the optimal results at the district level owing to limitations on the available memory on the PC-AT system in use. Energy options for seasonal crops have been considered explicitly in the model. Post-optimal analysis based on a linear programming model to study the effect of the variations in parameters on the optimal solution has been performed.     

Sustainable cities – modelling urban energy supply and demand

A model of urban energy consumption has been developed using energy supply data and post-code information. The model simulates spatial and diurnal variations in energy demand, and also models the effect of energy-management measures and associated reductions in CO₂ emissions. A linear programming optimisation module is used to identify the most cost-effective measures to achieve specified CO₂ or energy reduction-targets. When combined with data from an associated attitudinal survey, the model can be used to assess the potential for CO₂ reduction in the urban environment.     

Multi-criteria evaluation for the optimal adoption of distributed residential energy systems in Japan

Evaluation of sustainable residential energy system is complex process, in which not only the economic aspect, but also the energetic and environmental effects should be taken into consideration. In this paper, an integrated design and evaluation model has been developed, by combing linear programming and multi-criteria evaluation method, in order to determine the optimal residential energy system while considering different types of information. As an illustrative example, an investigation is conducted for a typical residential building in Kitakyushu, Japan. A set of residential energy alternatives, including both conventional energy and renewable energy applications, are assumed for adoption. Based on the optimal design results from the linear programming, the various alternatives have been assessed against economic, energetic and environmental criteria. According to the evaluation results, currently, renewable energy systems are not competitive unless strong attention is paid to the environmental benefits. All electric system may be a transitional consideration before reaching an actual low carbon residential energy system. Furthermore, the evaluation result is greatly influenced by the criteria priority, as well as the evaluation method.     

The effect of circumsolar radiation on a solar concentrating system

Empirical models for the energy distribution of the sun, as seen after atmospheric scattering, show a strong correlation on an annual or month-by-month basis to observed data. When applied to cases where the requirement is for a real-time solar energy distribution, such as in the optimisation of the flux distributions in imaging concentrators, these models prove insufficient. In this paper we present results illustrating trends in observed solar profiles that are invariant to changes in location that lay the framework to a definitive solar model. We show how using this information, a more complete understanding of the effect of a change in the spatial energy distributions of the sun can have on the size of the spatial energy distribution in the absorber plane of a (linear Fresnel) concentrating collector.     

A superstructure model of an isolated power supply system using renewable energy: Development and application to Jeju Island,Korea

In this study, we aim to develop a superstructure-based optimization model using mixed integer linear programming (MILP) to determine the optimal combination and sizing for a hybrid renewable energy system to be used in an isolated area. The developed model has a three-layered energy structure to reflect the current reality in which energy production and consumption sites are generally separate. A variety of economic factors, including distance between facilities and an installation area, are considered for a more accurate estimation of the total annualized cost. Two types of optimization models, i.e., with and without a battery, are proposed to evaluate the economic and technical effects of a storage device to resolve operation issues caused by intermittent resources. An application case study on Jeju Island, Korea, confirms that the proposed model is suitable for decision making at the planning stage of a renewable energy system.     

Modelling of hybrid energy system—Part I: Problem formulation and model development

A well designed hybrid energy system can be cost effective, has a high reliability and can improve the quality of life in remote rural areas. The economic constraints can be met, if these systems are fundamentally well designed, use appropriate technology and make use effective dispatch control techniques. The first paper of this tri-series paper, presents the analysis and design of a mixed integer linear mathematical programming model (time series) to determine the optimal operation and cost optimization for a hybrid energy generation system consisting of a photovoltaic array, biomass (fuelwood), biogas, small/micro-hydro, a battery bank and a fossil fuel generator. The optimization is aimed at minimizing the cost function based on demand and potential constraints. Further, mathematical models of all other components of hybrid energy system are also developed. This is the generation mix of the remote rural of India; it may be applied to other rural areas also.