Guidelines to develop software for thermoeconomic analysis of energy systems

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Guidelines to develop software for thermoeconomic
analysis of energy systems

• César Torres, Antonio Valero and Erika Perez
• Centro de Investigación de Recursos y Consumos
  Energéticos
• University of Zaragoza (SPAIN)

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Objectives

• The main objective of this paper is to show the
  guidelines to develop a software for the
  thermoeconomic analysis of energy systems, making
  special emphasis on
• The thermoeconomic data model
• The cost formation process of products and
  residues
• The application to thermoeconomic diagnosis

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Thermoeconomic Model
1..m
1..n
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Productive and Dissipative Components

• An energy system has two types of components
• Productive components
• Dissipative components
• Productive components provide
• Functional Products
• Resources (Fuel) to other process
• Residues and waste disposals
• Dissipative components are required to
• Reduce or eliminate the environment impact of
  residues and wastes
• Maintain the operation conditions of the system,
  from a physical and/or a legal point of view
• Improve the efficiency of the system

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Productive Structure
Nr Device Fuel Product Type
1 Combustor E5 E2E1 P
2 Compressor E6 E1E0 P
3 Turbine E2E3 E6E7 P
4 HRSG E3E4 E8 P
5 Stack E4 E9 D
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The Fuel-Product Table

• The productive diagram is a graphic
  representation of the thermoeconomic model of the
  plant.
• The inputs of a component are its resources
• The outputs of a component are its products
• The Fuel Product table is the adjacency matrix of
  the productive graph

Represents the external resources
F0 F1 Fj Fn
P0 E01 E0j E0n
P1 E10 E11 E1j E1n

Pi Ei0 Ei1 Eij Ein

Pn En0 En1 Enj Enn
Represents the system outputs
Represents the production of the i-th component
becomes fuel of the j-th component
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The Fuel Product Table (II)

• The productive graph and its Fuel Product table
  can be applied to
• Thermoeconomic Optimization (TFA)
• Thermoeconomic Diagnosis
• Identify the cost formation process of product
  and residues
• Analyze different aggregation level of a system
• The FP table can be built automatically from the
  information provided by the productive structure
  of the system. Valero and Torres proposed in
  1988 an algorithm based on the Exergy Cost
  Theory.

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FP Table Builder
Build Incidence Matrices
Compute
Productive Structure
Compute
FP Table
Compute
Build Incidence Matrices
Compute
Flow Exergy Values
Compute
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TAESS Intro Pannel
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TAESS Data Input
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TAESS General data 1
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TAESS FP Table
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TAESS FP Diagram
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Objectives

• The main objective of this paper is to show the
  guidelines to develop a software for the
  thermoeconomic analysis of energy systems, making
  special emphasis on
• The thermoeconomic data model
• The cost formation process of products and
  residues
• The application to thermoeconomic diagnosis

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The Cost Model

• The exergy costing rules can be written as
• The cost of product is equal to the cost of the
  resources required to obtain it, plus the cost of
  the residues generated

• The cost of the external resources is known

exergy cost (kW)
exergoeconomic cost (/h)

• The cost of each flow making up the product is
  proportional to its exergy

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Residue Cost Distribution

• The cost of a residue must be allocated to one or
  several productive components

The Residue Cost Distribution ratios represent
the portion of the cost of the residue dissipated
in the r-th component which has been generated in
the i-th productive component.

• To determine the values of Cri we must define
  the distribution cost ratios (RCD) as

• Therefore, the cost of the residues allocated to
  each productive unit, is given by

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Costing Equations

• The unit production cost could be obtained by
  solving the following system of lineal equations

is a (n x n) matrix whose elements are the unit
consumption values, defined as
is a (n x n) matrix whose elements are the ratios
of the residues generated per production unit
is a (n x 1) vector whose elements are the cost
of the external resources consumed in each
component per production unit
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Cost Decomposition

• The unit exergy cost of the product could be
  decomposed into two parts

represents the unit production cost due to
irreversibilities of the components
represents the unit production cost due to the
residues
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Cost Decomposition Activity Diagram
Build
Compute
FP Table
Compute
Compute
Residue Cost Distribution Ratios
Build
Compute
Compute
Compute
Compute
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Themoeconomic Analysis Sequence Diagram
Thermoeconomic Analysis
FPR model
FP Builder
Productive Structure
Thermodynamic Model
Economic Model
buildFP(state)
getStructure()
productive structure
FP table
getExergies(state)
exergies
getResourcesCost()
resource cost
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TAESS Matrix RP
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TAESS Cost Analysis Report
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TAESS Cost Formation Graph
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Objectives

• The main objective of this paper is to show the
  guidelines to develop a software for the
  thermoeconomic analysis of energy systems, making
  special emphasis on
• The thermoeconomic data model
• The cost formation process of products and
  residues
• The application to thermoeconomic diagnosis

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Thermoeconomic Diagnosis

• The objective of the thermoeconomic diagnosis is
  the location and quantification of the anomalies
  causing the reduction of the system efficiency.

• It is based on the comparison of two
  thermodynamic states
• Obtains a set of common indexes for every
  component of the system, whose could be used in
  combination with other parameters to provide
  useful information for the plant operation.
• Relates the variation of the irreversibilities
  and resources consumption to the variation of the
  efficiency of each component.

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Malfunction and Dysfunction

• The irreversibility increase of a component could
  be decomposed into two contributions
• The irreversibility increase due to a variation
  of the efficiency of the component itself
  (MALFUNCTION).
• The variation of the production objective of the
  component due to the malfunctions of others
  components (DYSFUNCTION)

DFk0 represents the irreversibility increase of
the component k-th caused by a variation of the
outputs (final products or residues)

• The sum of the malfunctions caused by a component
  is called MALFUNCTION COST

DFji represents the irreversibility increase of
the component j-th caused by a malfunction in the
i-th component
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The Fuel Impact Formula

• There are two approaches to allocate the fuel
  impact of a system

• The costs of the internal malfunctions are
  valuated by the production cost due only to
  irreversibilities. The cost of the residues
  variation is considered as another contribution
  to the fuel impact.

• The cost of the internal malfunctions are
  valuated by the production cost and they include
  the residues variation effect.

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Thermoeconomic Diagnosis Activity Diagram
FPR Model for Reference State
Compute
Build
Compute
Compute
FPR Model for Current State
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TAESS Diagnosis
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TAESS Diagnosis Report
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TAESS Irreversibility Analysis Graph
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TAESS Fuel Impact Analysis Graph
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Productive and Dissipative Structures

• It has been shown there is not only a productive
  structure but a dissipative structure
• The dissipative structure describes how the
  process of residues and wastes formation is. It
  could be as complex as the productive one.
• The productive and dissipative structures are not
  independent but they are interrelated. A
  malfunction in a component cause both an increase
  of the irreversibilities of the components and an
  increase of the residues.
• Therefore, to make a correct thermoeconomic
  diagnosis we must define both good productive and
  dissipative structures.

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Conclusions

• This paper should be understood as a functional
  description for developing software for
  thermoeconomic analysis of energy systems.
• It includes the following new contributions
• A FP table builder algorithm.
• A cost decomposition methodology.
• Fuel Impact analysis of residues and wastes
• From now on the problem of thermoeconomic
  diagnosis should not be to compute cost indexes
  but analyzing the results.
• A demo program, called TAESS, is available from
  the authors at http//www.exergoecology.com to
  illustrate the ideas presented in the paper.

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Exergoeconomics web page
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Thank you very much for your attention