Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Analysis, Modelling and Simulation of Energy Systems 1999 (June): Master of. Science in Mechanical Engineering at Aalborg University, IET (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) (October): Employed and enrolled as Ph.D. student at Aalborg University working with the project “Modelling of Thermodynamic Fuel Cell Systems”. Brief CV, Mads Pagh Nielsen:

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Course outline (m.m. 1-3) 1.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. 2.Mini-module: “Introduction to Engineering Equation Solver part II”. Further work with EES. Working with tables, plots, using array variables and using array operators. 3.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.

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Course outline (m.m. 4-6) 4.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. 5.Mini-module: “Modelling of system components”. Developing stationary models of thermodynamic components such as heat exchangers, wind turbines, pumps etc. 6.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!)

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Course outline (m.m. 7-10) 7.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. 8.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. 9.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). 10.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!

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Formal definition of modelling: “The activity of translating a real problem into mathematics for subsequent analysis” (Some might disagree?)

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen People interpret things differently

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen 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?

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen What is modelling? The process: 1. Identify the real problem 2. List the factors and assumptions 3. Formulate and solve the mathematical problem 4. Interpret the mathematical solution 5. Compare with the real world ? Did assumptions hold?

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen 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!

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen 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 to be the correct answer nor a correct input variable. Always keep models as simple as possible!

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen 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.

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Thermodynamics is strongly non-linear! Where f i is either linear or non-linear functions depending on the unknown x’s

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen 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.

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen »Taylorisation« of functions

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Iterative algorithm (Newton): 1. Choose initial values and set (‘0’ denote initial values). 2. Substitute the x’s into (*). 3. Solve for the  x’s (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. (*)

Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Sir Isaac Newton!