Power Plant Simulation

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I presented this document in 6th Indo-German Winter Academy 2007.

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    I am an Engineer in Thermal Power plant and interested in programming .. I wanna develop simlulation package.. Please guide me
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Power Plant Simulation

  1. 1. Power Plant Simulation<br />Presented by: <br />Ashish Khetan<br />Indian Institute of Technology Guwahati<br />Tutors: Prof. Ulrich Rüde, H. Köstler <br />University of Erlangen-Nuremberg<br />Germany<br />Indo-German Winter Academy 2007 <br />
  2. 2. <ul><li>Techniques of modeling
  3. 3. Introduction
  4. 4. Object oriented modeling
  5. 5. Component models
  6. 6. Thermal stresses
  7. 7. Analysis of fault events
  8. 8. Parallel ODE solvers for simulation
  9. 9. Introduction
  10. 10. Richardson extrapolation method
  11. 11. Parallel iteration method
  12. 12. Summary & conclusions</li></ul>2<br />Outline<br />Power Plant Simulation <br />
  13. 13. 3<br />Introduction <br />Schematic of a simplified fossil-fuel fired power plant<br />Power Plant Simulation <br />
  14. 14. 4<br />Combined Cycle Gas Turbine<br />Schematic of simplified CCGT<br />Power Plant Simulation Introduction <br />
  15. 15. Steady state simulation<br />Thermodynamic design of water&steam cycle <br />Design of components<br />Part load behavior <br />Pressure loss calculation <br />Transient Simulation <br />Start up, shutdown behavior<br />Thermal stress<br />Massflow oscillations<br />Design and study of control concepts<br />Analysis of fault events<br />5<br />Steady state and Transient simulation<br />Power Plant Simulation Introduction <br />
  16. 16. Model structuring approach based on <br />Representation of plant components<br />Interconnections between them <br />Physical ports<br />THT : Thermo-hydraulic terminal<br />DHT : Distributed heat transfer terminal<br />THHT : Thermo-hydraulic & heat transfer terminal<br />HT : Heat transfer terminal<br />MT : Mechanical terminal<br />Internal model description<br />Software packages: APROS, LEGO, DYMOLA<br />6<br />Object Oriented modeling<br />Power Plant Simulation <br />
  17. 17. 7<br />Object Oriented modeling-contd.<br />Modular structure for heat exchanging system<br />Power Plant Simulation <br />
  18. 18. 8<br />Component models: Boiler<br />Power Plant Simulation <br />Vertical heated circular tubes, risers, of evaporator <br />Homogeneous model <br />Fundamental equations<br />Heat transfer calculations<br />Flow patterns <br />Heat transfer regimes <br />Pressure loss calculation<br />
  19. 19. 9<br />Fundamental equations<br /><ul><li>Mass balance
  20. 20. Momentum balance</li></ul>Power Plant Simulation Component models Boiler <br />
  21. 21. 10<br />Fundamental equations-contd.<br /><ul><li>Energy balance
  22. 22. Heat balance of tube wall </li></ul>Power Plant Simulation Component models Boiler <br />
  23. 23. 11<br />Flow patterns<br />Power Plant Simulation Component models Boiler <br />Single phase liquid<br />Bubbly flow<br />Slug flow <br />Annular flow<br />Annular flow with entrainment<br />Drop flow<br />Single phase vapor <br />
  24. 24. 12<br />Heat transfer regimes<br />Power Plant Simulation Component models Boiler <br />
  25. 25. 13<br />Pressure loss calculation <br /> : additive friction factor for geometry elements<br /> : tube wall friction <br />Power Plant Simulation Component models Boiler <br />
  26. 26. 14<br />Control Valve<br />Governing equations <br />h1 = h2<br />ρ1 = ρ2<br />w = f ( p1, p2, h1, y )<br />Control valve model<br />Power Plant Simulation Component models<br />
  27. 27. 15<br />Pump<br />Pump model<br />Power Plant Simulation Component models<br />Governing equations <br />po = pi + pp<br />pp = fI (Ω, q)<br />τh = fII (Ω, q)<br />w(ho- hi) = τH Ω<br />
  28. 28. 16<br />Steam turbine<br />Power Plant Simulation Component models<br />Governing equations<br />Flow equation, stodala law<br />Energy equation <br />hi – ho = (hi – hISO )η<br />Power output <br /> Pm = w (hi – ho)<br />τm = Pm / Ω<br />
  29. 29. Need of analysis<br />Thick walled components of steam generator and turbine are the limiting factors<br />Spatial non-stationary temperature distribution<br />Extreme positions <br />Optimization of start up, shut-down or load changes <br />Rapid operation implies more temperature excursions<br />Calculation of thermal stress values, with few assumptions, maximum value of tangential stress is <br />17<br />Thermal stresses<br />Power Plant Simulation<br />
  30. 30. Linear model, assuming thermal conductivity, density and the specific heat are independent of temperature space and time<br />Radial heat conduction equation <br />Boundary condition <br />Large temperature excursions, non-linear model <br />18<br />Mathematical model <br />Courtesy: G.K. Lausterer<br />Power Plant Simulation Thermal stresses<br />
  31. 31. <ul><li>Condensate pump failure in a feedwater system without buffers.
  32. 32. Where steam forms in the piping system and how far pressure decreases upstream of the feed pump ??</li></ul>19<br />Fault event analysis<br />Courtesy: A. Butterlin, Erlangen<br />Power Plant Simulation<br />
  33. 33. 20<br />Modeling <br />Power Plant Simulation Fault event analysis<br />One dimensional heatable piping model<br />Basic equations of the conservation laws for mass, momentum & energy with heat transfer equations<br />Boundary points<br />Simulation over time <br />
  34. 34. 21<br />Results <br />Courtesy: A. Butterlin, Erlangen<br />Power Plant Simulation Fault event analysis<br />
  35. 35. <ul><li>Parallel processors
  36. 36. Parallel methods for solving Initial-value problems for ordinary differential equations.
  37. 37. Explicit IVP methods (parallelism across the problem)
  38. 38. Implicit IVP solvers (Linear algebra problem)
  39. 39. Parallelism across the ODE method
  40. 40. Methods with improved quality of the numerical solution
  41. 41. Methods with reduced ‘wall clock time’ per step
  42. 42. Richardson extrapolation method
  43. 43. Parallel iteration method</li></ul>22<br />Parallel ODE solvers- Introduction <br />Power Plant Simulation<br />
  44. 44. A(h) be an approximation of A <br />Using Big O notation <br />Using h and h/t for some t<br />Solving the above two equations <br />23<br />Richardson extrapolation<br />Power Plant Simulation Parallel ODE solvers <br />
  45. 45. 24<br />Richardson extrapolation-contd. <br /><ul><li>Increases order of accuracy of the given numerical approximation of true solution
  46. 46. Computing numerical approximations</li></ul> , i = 1,…,r, where represents Romberg sequence <br />Power Plant Simulation Parallel ODE solvers <br />
  47. 47. can all be computed in parallel<br />The are determined such that is more accurate than .<br />Taking = 1, order of the extrapolation formula equals Q = q+r-1<br />Equations for determining <br /> ,<br /> , <br />25<br />Richardson extrapolation- contd.<br />Power Plant Simulation Parallel ODE solvers <br />
  48. 48. <ul><li>Given IVP,
  49. 49. Given generating method of order p
  50. 50. Generating function with asymptotic</li></ul> expansion in powers of hs<br />y(to+H,h) , numerical approximation<br />y(to+H) , true solution <br /><ul><li>y(to+H,h) identifies u(Δ)
  51. 51. Δ identifies hs
  52. 52. Romberg sequence,</li></ul>26<br />Richardson extrapolation-application to IVP solvers<br />Power Plant Simulation Parallel ODE solvers <br />
  53. 53. <ul><li>Extrapolation formula
  54. 54. Explicit Richardson Euler method
  55. 55. Generating method, forward euler method</li></ul>Yo = yo, Yj = Yj-i + hf(Yj-i), j = 1,2,....m<br />y(to+H,h) = Ym , m = H/h<br />27<br />Richardson extrapolation-application to IVP solvers-contd.<br />Power Plant Simulation Parallel ODE solvers <br />
  56. 56. System of equations<br />Y = F(Y), F: Rdk-> Rdk<br />Y is the unknown function<br />F is a nonlinear function<br /> Iteration method <br />Yj - G(Yj) = F(Yj-1) - G(Yj-1), j= 1,2....<br />G is a free function with block diagonal jacobian matrix, the blocks of which are of dimension d<br />Each set of d components of Yj is calculated independent of the other set of d components by Newton iteration.<br />28<br />Parallel iteration <br />Power Plant Simulation Parallel ODE solvers <br />
  57. 57. For the IVP<br />RK4 method is<br />Where<br />Slope is the weighted average <br />29<br />Rungekutta method-fourth order<br />Power Plant Simulation Parallel ODE solvers parallel iteration <br />
  58. 58. Family of explicit RK method<br />Where <br />30<br />Explicit RK methods <br />Power Plant Simulation Parallel ODE solvers parallel iteration <br />
  59. 59. General form<br />Tabular form <br />31<br />Implicit RK methods<br />Power Plant Simulation Parallel ODE solvers parallel iteration <br />
  60. 60. <ul><li>Given IVP,
  61. 61. General form of implicit RK methods, with k stages</li></ul> yn+1 = yn + hbof(yn) + hbTf(Y) ,<br />Y = yne + haf(yn) + hAf(Y)<br /><ul><li>e : column vector with dimension k with unit entries
  62. 62. a, b : k dimensional vectors
  63. 63. A : k by k matrix
  64. 64. It uses the average value of the slope at the different stages. </li></ul>32<br />Parallel iteration-application to implicit RK methods<br />Power Plant Simulation Parallel ODE solvers <br />
  65. 65. <ul><li>Taking G(Y) = hDf(Y), where D is a diagonal matrix
  66. 66. Iterative form of implicit RK method</li></ul>Yj – hDf(Yj) = yne + haf(yn) + h[A-D] f(Yj-1)<br /><ul><li>Initial approximation</li></ul>Yo - hBf(Yo) = yne + hCf(yne)<br /><ul><li>B is an diagonal matrix and C is an arbitrary matrix</li></ul>33<br />Parallel iteration-application to implicit RK methods- contd.<br />Power Plant Simulation Parallel ODE solvers <br />
  67. 67. <ul><li>Power plant can be simulated elegantly using the modelica script provided in the software packages which use the basic equations involving physical variables to model its components.
  68. 68. These equations involve the partial derivatives, which are transformed into a much bigger set of ODEs.
  69. 69. Parallel ODE solvers facilitate a way of solving these equations on parallel processors resulting in higher order of accuracy or reduced wall clock time per step. </li></ul>34<br />Summary & conclusions<br />Power Plant Simulation <br />
  70. 70. Thermal power plant simulation and control, edited by Damian Flynn.<br />Transient simulation in power plant engineering, transparencies of Siemens Power generation.<br />Condensate pump failure in condensate preheater strings without a feedwater tank Dipl –physics, A. Butterlin, Erlangen<br />On-line thermal stress monitoring using mathematical models – G. K. Lausterer <br />Parallel ODE solvers – P. J. van der Houwen & B. P. Sommeijer <br />References<br />35<br />Power Plant Simulation <br />
  71. 71. Thank you<br />36<br />

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