powerplant simulation

8/13/2019 Powerplant Simulation

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Presented by:Ashish Khetan

Indian Institute of Technology Guwahati

Tutors: Prof. Ulrich Rde, H. KstlerUniversity of Erlangen-Nuremberg

Germany

Indo-German Winter Academy 2007


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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

2Power Plant Simulation


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Schematic of a simplified fossil-fuel fired power plant


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4Power Plant Simulation Introduction

Schematic of simplified CCGT


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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

5Power Plant Simulation Introduction


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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



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Modular structure for heat exchanging system


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Vertical heated circular tubes, risers, ofevaporator

Homogeneous model Fundamental equations

Heat transfer calculations Flow patterns

Heat transfer regimes

Pressure loss calculation


9/369Power Plant Simulation Component models Boiler

Mass balance

Momentum balance



Energy balance

Heat balance of tube wall



Single phase liquid Bubbly flow

Slug flow

Annular flow Annular flow with entrainment

Drop flow

Single phase vapor



: additive friction factor for geometry elements

: tube wall friction


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14Power Plant Simulation Component models

Governing equations

h1 = h2 1 = 2 w = f ( p1, p2, h1, y )

Control valve model


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Governing equations po = pi+ pp pp = fI (, q)

h = fII (, q)

w(ho- hi) = H

Pump model


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Governing equations Flow equation, stodala law

Energy equation

hi ho = (hi hISO ) Power output

Pm = w (hi ho)

m = Pm /


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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 fewassumptions, maximum value of tangentialstress is



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Linear model, assuming thermal conductivity, density and thespecific heat are independent of temperature space and time

Radial heat conduction equation

Boundary condition

Large temperature excursions, non-linear model

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Courtesy: G.K. Lausterer

Power Plant Simulation Thermal stresses


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Condensate pump failure in a feedwater systemwithout buffers.

Where steam forms in the piping system andhow far pressure decreases upstream of thefeed pump ??

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Courtesy: A. Butterlin, Erlangen

Power Plant Simulation


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20Power Plant Simulation Fault event analysis

One dimensional heatable piping model Basic equations of the conservation laws for

mass, momentum & energy with heattransfer equations

Boundary points

Simulation over time


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21Power Plant Simulation Fault event analysis

Courtesy: A. Butterlin, Erlangen


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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



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A(h) be an approximation of A

Using Big O notation

Using h and h/t for some t

Solving the above two equations

23Power Plant Simulation Parallel ODE solvers


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Increases order of accuracy of the givennumerical approximation of true solution

Computing numerical approximations

, i = 1,,r, where representsRomberg sequence


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can all be computed in parallel The are determined such that is

more accurate than .

Taking = 1, order of the extrapolationformula equals Q = q+r-1

Equations for determining

,

,



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Given IVP,

Given generating method of order p Generating function with asymptotic

expansion in powers of hsy(to+H,h) , numerical approximationy(to+H) , true solution

y(to

+H,h) identifies u() identifies hs

Romberg sequence,



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Extrapolation formula

Explicit Richardson Euler method Generating method, forward euler method

Yo = yo, Yj= Yj-i + hf(Yj-i), j = 1,2,....my(to+H,h) = Ym, m = H/h



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System of equationsY = 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 Yjis calculatedindependent of the other set of d components byNewton iteration.



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For the IVP RK4 method is

Where

Slope is the weighted average

29Power Plant Simulation Parallel ODE solvers parallel iteration


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General form

Tabular form

31Power Plant Simulation Parallel ODE solvers parallel iteration


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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 differentstages.



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Taking G(Y) = hDf(Y), where D is a diagonalmatrix

Iterative form of implicit RK method

YjhDf(Yj) = yne + haf(yn) + h[A-D] f(Yj-1)

Initial approximationYo- hBf(Yo) = yne + hCf(yne)

B is an diagonal matrix and C is an arbitrary matrix



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Power plant can be simulated elegantly using themodelica script provided in the softwarepackages which use the basic equations involvingphysical variables to model its components.

These equations involve the partial derivatives,which are transformed into a much bigger set ofODEs.

Parallel ODE solvers facilitate a way of solving

these equations on parallel processors resultingin higher order of accuracy or reduced wall clocktime per step.



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Thermal power plant simulation and control, editedby Damian Flynn.

Transient simulation in power plant engineering,transparencies of Siemens Power generation.

Condensate pump failure in condensate preheaterstrings 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



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Thank you

powerplant simulation

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