mathematical modelling and optimization of heat …
TRANSCRIPT
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