Michael R. von Spakovsky

An environomic approach for the modeling and optimization of a district heating network based on centralized and decentralized heat pumps, cogeneration and/or gas furnace. Part I: Methodology

Although heat pump based district heating is often an obvious solution from an energy standpoint, adapting the delivery temperature to the most exigent users is detrimental to overall system performance. This pitfall can be avoided with a centralized plant of heat pumps, cogeneration units and an auxiliary furnace, supplemented by decentralized heat pumps. However, the problem of mixed energy production and delivery which this poses is complex and presents for the engineer the daunting if not impossible task of adequately, much less optimally, determining the best system for the job. In this first of a series of two articles, an environomic methodology for aiding in this task is described and the details of the environomic model for a district heating network based on centralized and decentralized heat pumps presented. This methodology is used to model the thermodynamic, economic, and environmental characteristics of such a system in order that its final configuration and corresponding component designs can be optimized. In the accompanying article [1], a complete set of results for the optimal synthesis, design and operation of the network is given and discussed. The resulting solution space is highly nonlinear, non-contiguous and is effectively searched using a genetic algorithm. The system’s environmental characteristics are introduced into the model through pollution damage cost terms and pollution penalty functions which adapt to the system’s changing emissions and to local and global pollutant conditions. Results are shown for various district heating user distributions and fuel and electricity prices. The approach presented is an attempt to respond at the synthesis, design and operational level of an energy system to the concept of sustainablility.

Finite time generalization of thermal exergy

Abstract An extended exergy allowing some inevitable dissipative properties (e.g. those occurring in boundary layers) can be formulated for finite rate transitions, which lead a system not in equilibrium with the environment (or “dead state”) to equilibrium with it in a finite time. This exergy is a function of the end states and the process duration or a process intensity index. This exergy simplifies to classical thermal exergy in the limiting case of infinite duration, when the property of reversibility is recovered due to the vanishing rates. The functional of the extended exergy can be derived either as a finite time extension of the classical thermodynamic work extracted from a system and its environment or by evaluating a functional of the dissipated classical exergy. With finite time exergy, one can effectively optimize various continuous and multistage processes encountered in the theory of energy conversion and energy exchange in systems with a finite exchange area or with a finite contact time. However, the most important application of the dissipative exergy is the enhanced bounds predicted for the work delivery (consumption) in finite rate processes. These bounds are stronger than classical thermostatic bounds. In our formulation, nonlinear thermodynamic models are linked with ideas and methods of variational calculus. The variational formalism, with certain energy like and momentum like quantities strongly analogous to those known from analytical mechanics and optimal control theory, is an effective tool in the optimization of work. In this theoretical framework, one can easily discuss the role of finite process intensity and finite duration. The optimality of a specific irreversible process for the finite time transition of a fluid from one thermodynamic state to another is pointed out as well as a connection between the process duration, optimal dissipation and the optimal process intensity measured in terms of a Hamiltonian function. Our analysis proves that finite time exergy is different for processes approaching equilibrium with the environment, in which work is released (engine mode) and for processes departing equilibrium in which work is supplied (heat pump mode). However, the coincidence between the dissipative exergies and classical exergy is shown for the quasistatic case. The hysteretic properties of the finite time exergy cause a decrease in the maximum work received from a system in engine mode and an increase of work added to a system in heat pump mode, features which are particularly important in high rate regimes or for short duration thermodynamic processes. These results prove that the limits implied by the classical exergy theory should be replaced by the more realistic, stronger limits which are obtained for finite time processes.

Thermoeconomic Modeling and Parametric Study of Hybrid Solid Oxide Fuel Cell-Gas Turbine-Steam Turbine Power Plants Ranging From 1.5MWeto10MWe

Detailed thermodynamic, kinetic, geometric, and cost models are developed, implemented, and validated for the synthesis/design and operational analysis of hybrid solid oxide fuel cell (SOFC)-gas turbine-steam turbine systems ranging in size from 1.5 MWe to 10 MWe. The fuel cell model used in this research work is based on a tubular Siemens-Westinghouse-type SOFC, which is integrated with a gas turbine and a heat recovery steam generator (HRSG) integrated in turn with a steam turbine cycle. The current work considers the possible benefits of using the exhaust gases in a HRSG in order to produce steam, which drives a steam turbine for additional power output. Four different steam turbine cycles are considered in this research work: a single-pressure, a dual-pressure, a triple-pressure, and a triple-pressure with reheat. The models have been developed to function both at design (full load) and off-design (partial load) conditions. In addition, different solid oxide fuel cell sizes are examined to assure a proper selection of SOFC size based on efficiency or cost. The thermoeconomic analysis includes cost functions developed specifically for the different system and component sizes (capacities) analyzed. A parametric study is used to determine the most viable system/component syntheses/designs based on maximizing the total system efficiency or minimizing the total system life cycle cost.

Investigation of the Effects of Various Energy and Exergy-Based Figures of Merit on the Optimal Design of a High Performance Aircraft System

This paper shows the advantages of applying exergy-based analysis and optimization methods to the synthesis/design and operation of aircraft systems. In particular, an Advanced Aircraft Fighter (AAF) with three subsystems: a Propulsion Subsystem (PS), an Environmental Control Subsystem (ECS), and an Airframe Subsystem - Aerodynamics (AFS-A) is used to illustrate these advantages. Thermodynamic (both energy and exergy based), aerodynamic, geometric, and physical models of the components comprising the subsystems are developed and their interactions defined. Off-design performance is considered as well and is used in the analysis and optimization of system synthesis/design and operation as the aircraft is flown over an entire mission. An exergy-based parametric study of the PS and its components is first presented in order to show the type of detailed information on internal system losses which an exergy analysis can provide and an energy analysis by its very nature is unable to provide. This is followed by a series of constrained, system synthesis/design optimizations based on five different objective functions, which define energy-based and exergy-based measures of performance. The former involve minimizing the gross takeoff weight or maximizing the thrust efficiency while the latter involve minimizing the rates of exergy destruction plus the rate of exergy fuel loss (with and without AFS-A losses) or maximizing the thermodynamic effectiveness. A first set of optimizations involving four of the objecttives (two energy-based and two exergy-based) are performed with only PS and ECS degrees of freedom. Losses for the AFS-A are not incorporated into the two exergy-based objectives. The results show that as expected all four objectives globally produce the same optimum vehicle. A second set of optimizations is then performed with AFS-A degrees of freedom and again with two energy- and exergy-based objectives. However, this time one of the exergy-based objectives incorporates AFS-A losses directly into the objective. The results are that with this latter objective, a significantly better optimum vehicle is produced. Thus, an exergy-based approach is not only able to pinpoint where the greatest inefficiencies in the system occur but appears at least in this case to produce a superior optimum vehicle as well by accounting for irreversibility losses in subsystems (e.g., the AFS-A) only indirectly tied to fuel usage.Copyright

A Decomposition Strategy Applied to the Optimal Synthesis/Design and Operation of an Advanced Fighter Aircraft System: A Comparison With and Without Airframe Degrees of Freedom

A decomposition methodology based on the concept of “thermoeconomic isolation” applied to the synthesis/design and operational optimization of an advanced tactical fighter aircraft is the focus of this research. Conceptual, time, and physical decomposition were used to solve the system-level as well as unit-level optimization problems. The total system was decomposed into five sub-systems as follows: propulsion sub-system (PS), environmental control sub-system (ECS), fuel loop sub-system (FLS), vapor compression and PAO loops sub-system (VC/PAOS), and airframe sub-system (AFS) of which the AFS is a non-energy based sub-system. A number of different configurations for each sub-system were considered. The most promising set of candidate configurations, based on both an energy integration analysis and aerodynamic performance, were developed and detailed thermodynamic, geometric, physical, and aerodynamic models at both design and off-design were formulated and implemented. A decomposition strategy called Iterative Local-Global Optimization (ILGO) developed by Munoz and von Spakovsky (2000b,c) was then applied to the synthesis/design and operational optimization of the advanced tactical fighter aircraft. This decomposition strategy is the first to successfully closely approach the theoretical condition of “thermoeconomic isolation” when applied to highly complex, highly dynamic non-liner systems. This contrasts with past attempts to approach this condition, all of which were applied to very simple systems under very special and restricted conditions such as those requiring linearity in the models and strictly local decision variables. This is a significant advance in decomposition and has now been successfully applied to a number of highly complex and dynamic transportation and stationary systems. This paper presents the detailed results from one such application, which additionally considers a non-energy based sub-system (AFS).© 2003 ASME

Development of Thermodynamic, Geometric, and Economic Models for Use in the Optimal Synthesis/Design of a PEM Fuel Cell Cogeneration System for Multi-Unit Residential Applications

Thermodynamic, geometric, and economic models are developed for a proton exchange membrane (PEM) fuel cell system for use in cogeneration applications in multi-unit residential buildings. The models describe the operation and cost of the fuel processing sub-system and the fuel cell stack sub-system. The thermodynamic model reflects the operation of the chemical reactors, heat exchangers, mixers, compressors, expanders, and stack that comprise the PEMFC system. Geometric models describe the performance of a system component based on its size (e.g., heat exchanger surface area), and, thus, relate the performance at off-design conditions to the component sizes chosen at the design condition. Economic models are based on data from the literature and address the cost of system components including the fuel processor, the fuel cell materials, the stack assembly cost, the fuel cost, etc. As demonstrated in a forthcoming paper, these models can be used in conjunction with optimization techniques based on decomposition to determine the optimal synthesis and design of a fuel cell system. Results obtained using the models show that a PEMFC cogeneration system is most economical for a relatively large cluster of residences (i.e. 50) and for manufacturing volumes in excess of 1500 units per year. The analysis also determines the various system performance parameters including an electrical efficiency of 39% and a cogeneration efficiency of 72% at the synthesis/design point.

Optimal Synthesis/Design of a Pem Fuel Cell Cogeneration System for Multi-Unit Residential Applications–Application of a Decomposition Strategy

The application of a decomposition methodology to the synthesis/design optimization of a stationary cogeneration proton exchange membrane (PEM) fuel cell system for residential applications is the focus of this paper. Detailed thermodynamic, economic, and geometric models were developed to describe the operation and cost of the fuel processing subsystem and the fuel cell stack sub-system. Details of these models are given in an accompanying paper by the authors. In the present paper, the case is made for the usefulness and need of decomposition in large-scale optimization. The types of decomposition strategies considered are conceptual, time, and physical decomposition. Specific solution approaches to the latter, namely Local-Global Optimization (LGO) are outlined in the paper Conceptual/time decomposition and physical decomposition using the LGO approach are applied to the fuel cell system. These techniques prove to be useful tools for simplifying the overall synthesis/design optimization problem of the fuel cell system. The results of the decomposed synthesis/design optimization indicate that this system is more economical for a relatively large cluster of residences (i.e. 50). Results also show that a unit cost of power production of less than 10 cents/kWh on an exergy basis requires the manufacture of more than 1500 fuel cell sub-system units per year. Finally, based on the off-design optimization results, the fuel cell system is unable by itself to satisfy the winter heat demands. Thus, the case is made for integrating the fuel cell system with another system, namely, a heat pump, to form what is called a total energy system.

A Decomposition Strategy Based on Thermoeconomic Isolation Applied to the Optimal Synthesis/Design and Operation of a Fuel Cell Based Total Energy System

A decomposition methodology based on the concept of “thermoeconomic isolation” applied to the synthesis/design and operational optimization of a stationary cogeneration proton exchange membrane fuel cell (PEMFC) based total energy system (TES) for residential/commercial applications is the focus of this paper. A number of different configurations for the FC based TES were considered. The most promising set based on an energy integration analysis of candidate configurations was developed and detailed thermodynamic, kinetic, geometric, and economic models at both design and off-design were formulated and implemented. An original decomposition strategy called Iterative Local-Global Optimization (ILGO) developed in earlier work by two of the authors was then applied to the synthesis/design and operational optimization of the FC based TES. This decomposition strategy is the first to successfully closely approach the theoretical condition of “thermoeconomic isolation” when applied to highly complex, nonlinear systems. This contrasts with past attempts to approach this condition, all of which were applied to very simple systems under very special and restricted conditions such as those requiring linearity in the models and strictly local decision variables. This is a major advance in decomposition and has now been successfully applied to a number of highly complex, highly non-linear, and dynamic transportation and stationary systems. This paper presents the detailed results from one such application.Copyright

Multi-Objective Optimization for the Sustainable-Resilient Synthesis/Design/Operation of a Power Network Coupled to Distributed Power Producers via Microgrids

In this paper, a multiobjective optimization approach is proposed for evaluating the sustainable synthesis/design and operation of sets of small renewable and non-renewable energy production technologies coupled to power production/transmission/distribution networks via microgrids. The optimization is conducted over a quasi-stationary twenty four-hour, winter period. Partial load behavior of the generators is included by introducing non-linear functions for efficiency, costs and emissions as a function of the electricity generated by every technology. A new index for resiliency is included in the multiobjective optimization model in order to account for the capacity of the power network system to self-recover to a new normal state after experiencing an unanticipated catastrophic event. Since, sustainability/resiliency indices are typically not expressed in the same units, a set of weighting factors are employed to calculate the value of a composite sustainabilityresiliency index, applying fuzzy logic to minimize the effects of the subjectivity created in the selection of weights. Results indicate that the inclusion of microgrids into the network leads to a better overall network efficiency, a reduction in life cycle costs, and an improved network resiliency. On the other hand, total life SO 2 emissions and network reliability are not improved when microgrids are included.

Advanced Fighter Aircraft Sub-Systems Optimal Synthesis/Design and Operation: Airframe Integration Using a Thermoeconomic Approach

A decomposition methodology based on the concept of “thermoeconomic isolation” and applied to the synthesis/design and operational optimization of an advanced tactical fighter aircraft is presented in this paper. Conceptual, time, and physical decomposition are used. The physical decomposition strategy employed, called Iterative Local-Global Optimization (ILGO), was developed by Munoz and von Spakovsky and has been applied to a number of complex stationary and transportation applications. This decomposition strategy is the first to successfully closely approach the theoretical condition of “thermoeconomic isolation” when applied to highly complex, highly dynamic, non-linear systems. The total system is decomposed into eight sub-systems, five of which have degrees of freedom (a total of 493). These five are the airframe sub-system (AFS), the propulsion sub-system (PS), the environmental control sub-system (ECS), the fuel loop subsystem (FLS), and the vapor compression and PAO loops subsystem (VC/PAOS). The three without degrees of freedom are the equipment group (EGS), the permanent payload (PPS) and the expendable payload (EPS). For the ones with degrees of freedom, detailed aerodynamic, geometric, thermodynamic, and physical models at both design and off-design were formulated and implemented. The highly complex problem of integrating the synthesis/design of the airframe sub-system with the PS and the thermal driven sub-systems (ECS, FLS, and VC/PAOS) is solved using the novel decomposition approach mentioned above. The most promising set of aircraft sub-system configurations based on both aerodynamic performance and energy integration analysis are evaluated for all mission stages including the transients segments. The optimal configuration (synthesis) and geometry (design) of the airframe sub-system is determined simultaneously with that for the total aircraft system, i.e. with that for all of the other sub-systems. Results for this system and its sub-systems are presented below.