Power Plant Simulation

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

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


3

Introduction


Schematic of a simplified fossil-fuel fired power plant

4

Combined Cycle Gas Turbine

Power Plant Simulation Introduction

Schematic of simplified CCGT

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

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


7

Object Oriented modeling-contd.


Modular structure for heat exchanging system

8

Component models: Boiler


Vertical heated circular tubes, risers, of evaporator

Homogeneous model ◦ Fundamental equations

Heat transfer calculations◦ Flow patterns ◦ Heat transfer regimes

Pressure loss calculation

9

Fundamental equations

Power Plant Simulation Component models Boiler

Mass balance

Momentum balance

10

Fundamental equations-contd.


Energy balance

Heat balance of tube wall

11

Flow patterns


Single phase liquid Bubbly flow Slug flow Annular flow Annular flow with entrainment Drop flow Single phase vapor

12

Heat transfer regimes


13

Pressure loss calculation


: additive friction factor for geometry elements

: tube wall friction

14

Control Valve

Power Plant Simulation Component models

Governing equations

◦h1 = h2

◦ρ1 = ρ2

◦w = f ( p1, p2, h1, y )

Control valve model

15

Pump


Governing equations ◦po = pi + pp

◦pp = fI (Ω, q)

◦τh = fII (Ω, q)

◦

◦w(ho- hi) = τH Ω

Pump model

16

Steam turbine


Governing equations◦ Flow equation, stodala law ◦ Energy equation

hi – ho = ( hi – hISO )η◦ Power output

Pm = w (hi – ho)

τm = Pm / Ω

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


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

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


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

21

Results

Power Plant Simulation Fault event analysis

Courtesy: A. Butterlin, Erlangen

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


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

24

Richardson extrapolation-contd.


Increases order of accuracy of the given numerical approximation of true solution

Computing numerical approximations , i = 1,…,r, where represents

Romberg sequence

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.


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


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.


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


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

Family of explicit RK method

Where

30

Explicit RK methods


General form

Tabular form

31

Implicit RK methods


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


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 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


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

Thank you

36