Analysis, Modelling and Simulation of Energy Systems, SEE-T9

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Analysis, Modelling and Simulation of Energy
Systems
Brief CV, Mads Pagh Nielsen

• 1999 (June) Master of. Science in Mechanical
  Engineering at Aalborg University, IET.
• 1999 (August) Hired at Intecon A/S in Aalborg,
  Denmark, as advisory engineer.
• Among other things being in charge of
  following larger projects
• Design and operational optimization of an
  industrial combined heat and power plant.
• - Design optimization of an
  efficient wood-chip removal plant (information-
  and
• research project done in
  collaboration with the Danish Energy Ministry and
  the Wood-
• Industry).
• - Energy efficient air-filters
  (demonstration-project done for the Danish Energy
  Ministry).
• 2000 (October) Employed and enrolled as Ph.D.
  student at Aalborg University working with the
  project Modelling of Thermodynamic Fuel
  Cell Systems.

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Course outline (m.m. 1-3)

• Mini-module Introduction to Engineering
  Equation Solver (EES) part I. Introduction to
  the modelling software EES basic purpose,
  functionality and examples. Solution of the
  general non-linear problem of multiple equations
  using the general multi dimension Newton Raphson
  method. Usage of guesses and limiting of variable
  values.
• Mini-module Introduction to Engineering
  Equation Solver part II. Further work with EES.
  Working with tables, plots, using array variables
  and using array operators.
• Mini-module Introduction to Engineering
  Equation Solver part III. Introduction to
  procedures, sub programs and modules advantages
  and drawbacks.
• Literature Lecture notes about EES Reference
  Manual.

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Course outline (m.m. 4-6)

• Mini-module Basic conservation equations.
  Derivation of the stationary forms of 1st law of
  thermodynamics for open- and closed systems and
  definition of basic thermodynamic relations
  useful in modelling of energy systems. The
  continuity equation (conservation of mass). How
  to use the 1st law of thermodynamics and the
  continuity equation on a system control volume?
  Calculation of thermodynamic- and calorimetric
  properties i.e. use of diagrams, tables and use
  of EES to attain these properties and the
  importance of choosing appropriate unit system.
• Mini-module Modelling of system components.
  Developing stationary models of thermodynamic
  components such as heat exchangers, wind
  turbines, pumps etc.
• Mini-module Advanced conservation laws and
  structured modelling. Use of multi-gate methods
  in the modelling of energy systems. Conservation
  of energy in the presence of chemical reaction
  (in particular combustion) and calculation of
  properties of ideal gas mixtures.
• Literature Lecture notes about modelling of
  energy systems written by the lecturer (me!)

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Course outline (m.m. 7-10)

• Mini-module Modelling of part load conditions
  part I. Part-load characteristics for components
  (i.e. pumps, turbines, compressors etc.). Usage
  of characteristics in computer modelling
  introducing numerical techniques such as
  interpolation in ordered tables and multi
  dimension non-linear regression using the method
  of least squares.
• Mini-module Modelling of part load conditions
  part II. An example on an advanced utilisation
  of part load modelling. Usage of models in
  optimisation. Sensitivity- and uncertainty
  analysis in evaluating sensitive parameters.
• Mini-module Advanced cycles. Combined-cycle
  co-production plants, chemical plants
  (exemplified by a fuel cell system). Discussion
  of the term complexity and the necessity of
  detailed- contra lumped modelling. Briefly about
  classification of losses (exergy or 2nd law
  analysis).
• Mini-module A primer on optimisation of energy
  systems. Choice of objective function (for
  example economy, volume, effectiveness
  operational conditions etc.) and usage of
  parameter analysis in determining free
  parameters.
• Literature Additional lecture notes made by the
  lecturer still due to be written!

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Formal definition of modelling
The activity of translating a real problem into
mathematics for subsequent analysis
(Some might disagree?)
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People interpret things differently ?
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Motivation Why model?

• Design and Optimization
• How do we make our system optimal from scratch or
  how can we improve the existing system?
• Validation
• Will the proposed system we have designed work
  correctly subjected to the environment it
  operates in, is it feasible to construct it
  compared to other alternatives and does it
  fulfill its purpose?
• Interpolation
• Usage for filling in missing data for instance
  parameters we can not measure from experiments.
• Extrapolation
• Predictions into the future How is our plant
  economy in 20 years?

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What is modelling? The process
?
1. Identify the real problem
2. List the factors and assumptions
Did assumptions hold?
3. Formulate and solve the mathematical problem
5. Compare with the real world
4. Interpret the mathematical solution
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Problem identification
Design is within a scientific context the art of
describing predictable systems. MPN, 2002
Should we attempt to re-design this pencil
sharpener??!
Junk in equals junk out! Be critical!
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Assumptions
Simplicity is beautiful but it is extremely
complicated to attain it. MPN, 2002
Parameter estimation and choice of the phenomena
we would like to model is difficult! The model
should reflect this. A complicated model with
inaccurate input is not making us any smarter
rather often more confused! Uncertainty of
models and inputs have to be analyses And
compared accordingly! Do not expect 1.9823673467
to be the correct answer nor a correct input
variable. Always keep models as simple as
possible!
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Solution of the problem

• When we have formulated our problem we use our
  theoretical
• skills to develop a solvable mathematical
  model.
• In almost any case his turns out to be a number
  simultaneously
• coherent mathematical expressions we need to
  solve. This is the
• (relatively) easy part of modelling!
• Subsequently, we need to be able to interpret
  and validate the
• result critically against empirical knowledge
  or experiments.

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Thermodynamics is strongly non-linear!
Where fi is either linear or non-linear functions
depending on the unknown xs
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A few notable points

• There is hardly any real thermodynamic process
  that can be modelled without solution of
  non-linear equations!
• In order to have a consistent system the number
  of equations and variables has to be similar. If
  not, the system will be either over- or under
  determined and we cannot find a general
  solution.
• If the system consists of n linear functions
  and the system is said to be numerically
  consistent we can always find a unique solution.
  However, if we CANNOT check this generally for
  non-linear equations nor guarantee one unique
  solution! We can often have several feasible
  solutions, which make solution of the system
  anything but trivial. The numerical complexity
  mentioned above is due to the non-linearity.
• In general, systems of non-linear equations have
  to be solved iteratively using numerical
  methods. Analytical solution is rarely possible.

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Taylorisation of functions
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Iterative algorithm (Newton)
()
1.       Choose initial values and set (0
denote initial values). 2.       Substitute the
xs into (). 3.       Solve for the ?xs (linear
algebra). 4.       Is convergence reached? If
yes, output result. If not, continue. 5.      
Set all 6.       Set all and go
back to point 2.
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Sir Isaac Newton!