MATHEMATICAL MODELLING AND OPTIMIZATION

OF HEAT RATE OF A THERMAL POWER PLANT

by

VINOD KRISHNA

Submitted

in fulfilment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

INDIAN INSTITUTE OF TECHNOLOGY, DELHI

July, 1986

CERTIFICATE

This is to certify that the thesis entitled

'MATHEMATICAL MODELLING AND OPTIMIZATION OF HEAT RATE

OF A TuRNAL POWER PLANT' being submitted by

Mr. Vinod Krishna to the Indian Institute of Technology,

New Delhi for the award of the degree of Doctor of

Philosophy in Mechanical Engineering is a record of the

candidate's• own bonafide research work.

Mr. Vinod Krishna has worked under our guidance

and supervision and has fulfilled the requirements for

the submission of this thesis, which to our knowledge,

has reached the requisite standard.

The results contained in this work have not been

submitted, in part or in full to any other University

or Institute for the award of any degree.

(Dr. S,K. Gupta) Assistant Professor Mechanical Engg. Department Indian Institute of Techno-logy, Delhi New Delhi-110016

01-.0-"Y o rE(6 (Dr. P.B. Sharma) Assistant Professor Mechanical Engineering Department Indian Institute of Technology, New Delhi-110016

ACKNOWLEDGEMENT.

I feel great pleasure to express my deepest sense of

gratitude towards Dr. P.B. Sharma and Dr. S.K. Gupta for

their supervision, valuable guidance, kind help and

encouragement throughout this work.

I am grateful to the Central Electricity Authority

and Power Engineers Training Society for sponsoring my

candidature for undertaking the work reported in the present

thesis. I am also indebted to the Mechanical Engineering

Dept. I.I.T., Delhi for providing the necessary facilities

for carrying out the present investigation.

I wish to acknowledge the support and co-operation

of the authorities of Badarpur Thermal Power Station,

Indraprastha Thermal Power Station and Singrauli Super Thermal

Power Station in carrying out the experimental investigations

reported in the present thesis.

I am also indebted to Mr. B. Sinha former Director

General P.E.T.S. and Mr. Ramlikhani former Chief Engineer,

M.P.E.U. for encouragements and useful discussions.

I sincerely acknowledge the powerful inspiration and

moral support by my extremely cooperative wife, Kiran.

Last but not the least the support of Mr. Ashok

Vashistha for typing the thesis and Mr. B.B. Arora and

N.C. Saraswat in the graphical assistance is gratefully

acknowledged.

. 1C;A\JA:A"

It • 7. SC. (VINOD KRISHNA)

ABSTRACT.

The work reported in the thesis is concerned with

modelling and optimization of heat rate of a thermal

power plant. Realistic models for the three prime

efficiency functions namely; Turbine Heat Rate, Boiler

Efficiency and Plant Heat Rate are developed in terms of

controllable operating parameters of the plant. Experimental

investigations have been carried out on 60MW and 210MW

units for validation of the models developed in the

present work. These efficiency functions are then

optimized with respect to operating parameters of the

power cycle and the boiler using a paramety is optimization

technique.

The work of present investigation is presented

under four major heads viz. a steady state model of heat

rate, a transient model for turbine heat rate, experimental

investigations and heat rate optimization.

The steady state model for turbine heat rate

developed in the present work incorporates real time

effect of auxiliary heat inputs and leak-offs to and from

the turbine system. Penalty on heat rate due to deterio-

ration in condenser back pressure has been modelled using

a linear model which predicts effect of individual

condenser performance factors on heat rate and the

results of this model are comparable with heat balance

model at near MCR conditions of the plant. The steady

(1)

state model also incorporates cross effects of boiler

excess air on turbine heat rate through two-way coupling.

Boiler efficiency and combustion losses have been modelled

directly in terms of operating parameters like excess air,

particle size and flue gas exit temperature. The effect

of these boiler parameters on plant heat rate has been

studied using the models for boiler efficiency and turbine

heat rate, utilizing a concept of two-way coupling.

The present work also reports on the development

of a model of turbine heat rate under load transients.

In development of this model a lumped reheater time

constant approach has been used for comprehending the

transient response of various flows.and unit outputs and

hence the turbine heat rate. The basic reheater time

constant has been determined using an in-situ experiment

on a 210MW unit. In the present work a governor test

rig was designed,developed and commissioned for determining

the governor time constant. The lumped reheater time

constant was determined from the knowledge of the governor

time constant and the basic time constant of the reheater.

The frequence response test of the governor model has

further been used for the validation of the results of the

transient study.

Experiments have been conducted on 60MW and 210MW

boiler and turbine units for validation of various

formulations developed in the present investigation:

These include experiments on 210MW and 60MW boilers for

validation of statistical model for unburnt carbon loss

developed in the present investigation. Turbine heat

run tests were also carried out to compare the results of

the present study with those obtained from ASME:PTC-6,

acceptance test code.

Using the above validated formulations, the turbine

heat rate is optimized subject to variations in cycle

parameters viz. steam inlet conditions, extraction pressures

and temperatures and condenser back pressure. Boiler

efficiency is optimized subject to variation in excess air

and particle size at various flue gas exit temperatures.

Finally an integral objective function of plant heat rate

is formulated in terms of operating 'terminal conditions. The

plant heat rate is then optimized subject to variations

in above turbine cycle and boiler parameters.

The results of the present study provide a

realistic assessment of both the steady state and transient

behaviour of turbine heat rate of a thermal power plant.

The results of the optimization study further reveal that

the extractions before reheater play a significant role

in deciding the optimum values of plant heat rate.

CONTENTS

Page

CERTIFICATE

ACKNOWLEDGEMENTS

ABSTRACT (1)

NOMENCLATURE (iv)

INTRODUCTION CHAPTER-1 1

1.1 Introduction

1.2 Aims and Objectives 2

4 1.3 Scope

1.3.1 Steady state models 4

1.3.2 Transient models 6

1.3.3 Optimization 7

1.3.4 Experimental investigations 8

1.4 Importance of the problem and

main thrust 8

1.5 Order of presentation 11

CHAPTER-2 LITERATURE SURVEY

2.1 Review of relevant literature and

problem formulation

2.1.1 The performance measures under

steady state condition

2.1.2 The plant performance under

load transients

2.1.3 Optimization

2.2 Need for present work

12

12

19

20

21

2.3 Methodology of present work 23

Page

2.3.1 The modelling techniques 23

2.3.2 The optimization techniques 23

2.3.3 Experimental investigations 24

CHAPTER-3 MODELLING OF HEAT RATE UNDER STEADY-STATE

CONDITION

3.1 Introduction 25

3.2 The system 26

3.3 A model for turbine heat rate under

steady state condition 27

3.3.1 Formulations for steam flows 28

J, Main, reheat and extraction

steam flows 28

.2 Auxiliary steam flows 36

3.3.2 Steam property formulations 38

3.4 Effect of terminal conditions on 39

turbine heat rate

3.4.1 Effect of load, auxiliary steam

consumption and main steam

properties 40

3.4.2 Effect of final feed

temperature 41

3.4.3 Effect of reheat spray on turbine heat rate

41

3.5 Effect of condenser performance on

turbine heat rate 43

3.5.1 Condenser performance parameters 43

3.5.2 Condenser back pressure correc-tions factor on turbine heat

rate-a nonlinear model 45

,1 Evaluation of condenser

correction factor 49

3.5.3 A reduced order model for deter-mination of effect of condenser

performance on heat rate 51

Effect of individual conden-

ser performance parameters

on it's back pressures 51

2 Evaluation of condenser

correction factor 54

3.6 Plant heat rate as affected by

combustion parameters 59

3.6.1 Two way coupling between boiler

and turbine 59

3.6.2 A model for two way coupling 60

.1. Effect of excess air and

particle size on boiler

efficiency 60

.2 Effect of excess air on THR 61

3.6.3 A statistical model for combus-

tion losses and formulation

of boiler efficiency 63

COmbustion and residence

time of a pulverized fuel

particle 64

.2. A probability density function

for unburnt carbon loss 70

.3 An empirical model for

unburnt carbon loss 72

.4 Boiler efficiency formula-

tions and unaccountable

losses 74

3.6.4 An integrated model for plant

heat rate as affected by

boiler parameters-excess air

and particle size

.1 Plant heat rate as affected

by flue gas outlet tempera-'

ture

77

78

3.7 Results and discussions 80

CHAPTER-4 TURBINE HEAT RATE UNDER LOAD-TRANSIENTS

4.1 Introduction 101

4.2 The system and it's transfer function

representation 103

4.3 Modelling of system parameters for

sudden load changes 104

4.4 Transients in turbine heat rate neglecting variations in feed enthalpy-

a case study 107

4.5 Transient variation in turbine heat rate considering variation in feed

enthalpy 111

4.6 Determination of reheater time constant 112

4.6.1 Governor test rig for determi-nation of governor time constant 113

1 Design aspects of governor

test rig 114

.2 Steady state load test 116

.3 Load transient test 117

.4 Estimation of governor time

constant 119

4.6.2 Determination of basic time constant of reheater and lumped

reheater time constant 120

4.7 Results and discussions 122

CHAPTER-5 EXPERIMENTAL INVESTIGATIONS

5.1 Field measurements on 210MW/60MW

boilers

5.1.1 Coal sampling and particle size

analysis

131

131

5.1.2 Determination of unburnt

carbon loss 135

5.1.3 Experiments to establish inter-relation between boiler and turbine side parameters due to

two-way coupling 138

,L Determination of values of reheat spray flow rates corresponding to different excess air values and burner

tilt at various loads

2 To determine constants in the relationship between final feed temperature and reheat

spray

5.1.4 Boiler losses-a comparative study of the proposed efficiency

model with boiler test code 146

5.2 Turbine heat run-a comparative study

with ASME: PTC-6 code 148

5.3 Results and discussions 156

5.3.1 Boiler performance tests 156

5.3.2 Turbine heat run tests 157

CHAPTER-6 OPTIMIZATION OF HEAT RATE

6.1 Introduction

6.2 The objective function and various

constraints 161

6.2.1 The objective function for

turbine heat rate 161

.1 The variables and constraints 165

6.2.2 The objective function, variables and constraints for boiler

efficiency 166

6.2.3 Objective function for plena

heat rate 168

139

142

158

6.3 Optimization of turbine heat rate subject to variation in extraction

parameters

6.3.1 Optimization of 'THR' at constant condenser back pressure

condition

6.3.2 Optimization of 'THR' accounting for variations in condenser

back pressure

6.4 Optimization of plant heat rate

6.4.1 Optimizing boiler efficiency 172

6.4.2 Integral optimization of turbine heat rate and boiler efficiency 173

6.5 An analytical approach of turbine heat

rate optimization 174

6.5.1 Optimizing number of feed

heaters. 177

6.6 Results and discussions 180

CHAPTER-7 DISCUSSION OF RESULTS

7.1 Heat rate under steady state condition 191

7.2 Turbine heat rate under load

transients 199

7.3 Experimental investigations 202

7.3.1 Field tests on 210MW and 60MW

boilers 202

7.3.2 Turbine, heat run tests 204

7.4 Heat rate optimization 205

7.4.1 Optimization of THR subject to variation in extraction

parameters 206

7.4.2 Optimization of THR subject to variation in extraction parame-ters and condenser performance 208

169

169

170

7.4.3 Boiler efficiency optimization 209

7.4.4 Optimization of plant heat rate 210

CHAPTER-8 MAIN CONCLUSIONS 213

REFERENCES 224

APPENDIX-B

APPENDIX-C

APP ENDI X-D

Flow measurements using'annubar'flow

sensors and determination of flow constants in various formulations of

mass flow rates

A-1 Main steam, reheat steam and extraction steam flow rates and

flow constants 232

A-2 Leak-off flows and flow constants 236

A-3 Mass balance of HP & LP turbines 241

A-4 Mass flows as functions of

pressures 242

Some important design and operating

parameters of boiler turbine and

auxiliaries for a 210 MW unit

B-1 Boiler design and operating

parameters 245

B-2 Fuel ,furnace and combustion data 250

B-3 Turbine cycle: design and

operating parameters 253

Salient features of a 210MW power

plant simulator 257

Power cycle heat balance diagrams

and control volume approach

D-1 Power cycle heat balance diagram 260

0-2 Control volume approach for

boiler testing 262

APPENDICES

APPENDIX-A

APPENDIX-E Algorithms and flow diagrams of computer programs 271

APPENDIX-F Notes on some formulations

F-1 Leak-off flow formulations-value of 6 277

F-2 Determination of effect of individual factorsinfluencing back pressure 278