Download - Power Plant Simulation
![Page 1: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/1.jpg)
Power Plant Simulation
Presented by: Ashish Khetan
Indian Institute of Technology Guwahati
Tutors: Prof. Ulrich Rüde, H. Köstler University of Erlangen-Nuremberg
Germany
Indo-German Winter Academy 2007
![Page 2: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/2.jpg)
Techniques of modeling ◦ Introduction ◦ Object oriented modeling ◦ Component models◦ Thermal stresses◦ Analysis of fault events
Parallel ODE solvers for simulation◦ Introduction ◦ Richardson extrapolation method◦ Parallel iteration method
Summary & conclusions
2
Outline
Power Plant Simulation
![Page 3: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/3.jpg)
3
Introduction
Power Plant Simulation
Schematic of a simplified fossil-fuel fired power plant
![Page 4: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/4.jpg)
4
Combined Cycle Gas Turbine
Power Plant Simulation Introduction
Schematic of simplified CCGT
![Page 5: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/5.jpg)
Steady state simulation◦ Thermodynamic design of water&steam cycle ◦ Design of components◦ Part load behavior ◦ Pressure loss calculation
Transient Simulation ◦ Start up, shutdown behavior◦ Thermal stress◦ Massflow oscillations◦ Design and study of control concepts◦ Analysis of fault events
5
Steady state and Transient simulation
Power Plant Simulation Introduction
![Page 6: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/6.jpg)
Model structuring approach based on ◦ Representation of plant components◦ Interconnections between them
Physical ports◦ THT : Thermo-hydraulic terminal◦ DHT : Distributed heat transfer terminal◦ THHT : Thermo-hydraulic & heat transfer terminal◦ HT : Heat transfer terminal◦ MT : Mechanical terminal
Internal model description Software packages: APROS, LEGO, DYMOLA
6
Object Oriented modeling
Power Plant Simulation
![Page 7: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/7.jpg)
7
Object Oriented modeling-contd.
Power Plant Simulation
Modular structure for heat exchanging system
![Page 8: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/8.jpg)
8
Component models: Boiler
Power Plant Simulation
Vertical heated circular tubes, risers, of evaporator
Homogeneous model ◦ Fundamental equations
Heat transfer calculations◦ Flow patterns ◦ Heat transfer regimes
Pressure loss calculation
![Page 9: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/9.jpg)
9
Fundamental equations
Power Plant Simulation Component models Boiler
Mass balance
Momentum balance
![Page 10: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/10.jpg)
10
Fundamental equations-contd.
Power Plant Simulation Component models Boiler
Energy balance
Heat balance of tube wall
![Page 11: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/11.jpg)
11
Flow patterns
Power Plant Simulation Component models Boiler
Single phase liquid Bubbly flow Slug flow Annular flow Annular flow with entrainment Drop flow Single phase vapor
![Page 12: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/12.jpg)
12
Heat transfer regimes
Power Plant Simulation Component models Boiler
![Page 13: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/13.jpg)
13
Pressure loss calculation
Power Plant Simulation Component models Boiler
: additive friction factor for geometry elements
: tube wall friction
![Page 14: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/14.jpg)
14
Control Valve
Power Plant Simulation Component models
Governing equations
◦h1 = h2
◦ρ1 = ρ2
◦w = f ( p1, p2, h1, y )
Control valve model
![Page 15: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/15.jpg)
15
Pump
Power Plant Simulation Component models
Governing equations ◦po = pi + pp
◦pp = fI (Ω, q)
◦τh = fII (Ω, q)
◦
◦w(ho- hi) = τH Ω
Pump model
![Page 16: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/16.jpg)
16
Steam turbine
Power Plant Simulation Component models
Governing equations◦ Flow equation, stodala law ◦ Energy equation
hi – ho = ( hi – hISO )η◦ Power output
Pm = w (hi – ho)
τm = Pm / Ω
![Page 17: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/17.jpg)
Need of analysis◦ Thick walled components of steam generator and
turbine are the limiting factors◦ Spatial non-stationary temperature distribution◦ Extreme positions ◦ Optimization of start up, shut-down or load
changes ◦ Rapid operation implies more temperature
excursions Calculation of thermal stress values, with
few assumptions, maximum value of tangential stress is
17
Thermal stresses
Power Plant Simulation
![Page 18: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/18.jpg)
Linear model, assuming thermal conductivity, density and the specific heat are independent of temperature space and time
Radial heat conduction equation
Boundary condition
Large temperature excursions, non-linear model
18
Mathematical model
Courtesy: G.K. Lausterer
Power Plant Simulation Thermal stresses
![Page 19: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/19.jpg)
Condensate pump failure in a feedwater system without buffers.
Where steam forms in the piping system and how far pressure decreases upstream of the feed pump ??
19
Fault event analysis
Courtesy: A. Butterlin, Erlangen
Power Plant Simulation
![Page 20: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/20.jpg)
20
Modeling
Power Plant Simulation Fault event analysis
One dimensional heatable piping model Basic equations of the conservation laws
for mass, momentum & energy with heat transfer equations
Boundary points Simulation over time
![Page 21: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/21.jpg)
21
Results
Power Plant Simulation Fault event analysis
Courtesy: A. Butterlin, Erlangen
![Page 22: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/22.jpg)
Parallel processors Parallel methods for solving Initial-value
problems for ordinary differential equations.◦ Explicit IVP methods (parallelism across the
problem)◦ Implicit IVP solvers (Linear algebra problem)
Parallelism across the ODE method◦ Methods with improved quality of the numerical
solution ◦ Methods with reduced ‘wall clock time’ per step
Richardson extrapolation method Parallel iteration method
22
Parallel ODE solvers- Introduction
Power Plant Simulation
![Page 23: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/23.jpg)
A(h) be an approximation of A
Using Big O notation
Using h and h/t for some t
Solving the above two equations
23
Richardson extrapolation
Power Plant Simulation Parallel ODE solvers
![Page 24: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/24.jpg)
24
Richardson extrapolation-contd.
Power Plant Simulation Parallel ODE solvers
Increases order of accuracy of the given numerical approximation of true solution
Computing numerical approximations , i = 1,…,r, where represents
Romberg sequence
![Page 25: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/25.jpg)
can all be computed in parallel The are determined such that is
more accurate than . Taking = 1, order of the extrapolation
formula equals Q = q+r-1 Equations for determining , ,
25
Richardson extrapolation- contd.
Power Plant Simulation Parallel ODE solvers
![Page 26: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/26.jpg)
Given IVP,
Given generating method of order p Generating function with asymptotic expansion in powers of hs y(to+H,h) , numerical approximation
y(to+H) , true solution y(to+H,h) identifies u(Δ) Δ identifies hs
Romberg sequence,
26
Richardson extrapolation-application to IVP solvers
Power Plant Simulation Parallel ODE solvers
![Page 27: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/27.jpg)
Extrapolation formula
Explicit Richardson Euler method◦ Generating method, forward euler method
Yo = yo, Yj = Yj-i + hf(Yj-i), j = 1,2,....m
y(to+H,h) = Ym , m = H/h
27
Richardson extrapolation-application to IVP solvers-contd.
Power Plant Simulation Parallel ODE solvers
![Page 28: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/28.jpg)
System of equations Y = F(Y), F: Rdk→ Rdk
◦ Y is the unknown function◦ F is a nonlinear function
Iteration method Yj - G(Yj) = F(Yj-1) - G(Yj-1), j= 1,2....
◦ G is a free function with block diagonal jacobian matrix, the blocks of which are of dimension d
◦ Each set of d components of Yj is calculated independent of the other set of d components by Newton iteration.
28
Parallel iteration
Power Plant Simulation Parallel ODE solvers
![Page 29: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/29.jpg)
For the IVP RK4 method is
Where
Slope is the weighted average
29
Runge kutta method-fourth order
Power Plant Simulation Parallel ODE solvers parallel iteration
![Page 30: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/30.jpg)
Family of explicit RK method
Where
30
Explicit RK methods
Power Plant Simulation Parallel ODE solvers parallel iteration
![Page 31: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/31.jpg)
General form
Tabular form
31
Implicit RK methods
Power Plant Simulation Parallel ODE solvers parallel iteration
![Page 32: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/32.jpg)
Given IVP,
General form of implicit RK methods, with k stages
yn+1 = yn + hbof(yn) + hbTf(Y) ,
Y = yne + haf(yn) + hAf(Y)
◦ e : column vector with dimension k with unit entries◦ a, b : k dimensional vectors◦ A : k by k matrix
It uses the average value of the slope at the different stages.
32
Parallel iteration-application to implicit RK methods
Power Plant Simulation Parallel ODE solvers
![Page 33: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/33.jpg)
Taking G(Y) = hDf(Y), where D is a diagonal matrix
Iterative form of implicit RK method
Yj – hDf(Yj) = yne + haf(yn) + h[A-D] f(Yj-1)
◦ Initial approximation Yo - hBf(Yo) = yne + hCf(yne)
◦ B is an diagonal matrix and C is an arbitrary matrix
33
Parallel iteration-application to implicit RK methods- contd.
Power Plant Simulation Parallel ODE solvers
![Page 34: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/34.jpg)
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.
These equations involve the partial derivatives, which are transformed into a much bigger set of ODEs.
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.
34
Summary & conclusions
Power Plant Simulation
![Page 35: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/35.jpg)
Thermal power plant simulation and control, edited by Damian Flynn.
Transient simulation in power plant engineering, transparencies of Siemens Power generation.
Condensate pump failure in condensate preheater strings without a feedwater tank Dipl –physics, A. Butterlin, Erlangen
On-line thermal stress monitoring using mathematical models – G. K. Lausterer
Parallel ODE solvers – P. J. van der Houwen & B. P. Sommeijer
References
35Power Plant Simulation
![Page 36: Power Plant Simulation](https://reader035.vdocuments.us/reader035/viewer/2022062219/554a2a78b4c90520578b4cf7/html5/thumbnails/36.jpg)
Thank you
36