Neural Network Approach for

Predicting Drum Pressure and Level

in a Coal-fired Subcritical Power Plant

Eni OKO and Meihong Wang Process and Energy Systems Research Group, School of Engineering

University of Hull HU6 7RX, United Kingdom

10th European Conference on Coal Research and its Applications Sept 15-17, 2014, University of Hull, UK

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

Background

Layout of Coal-fired Subcritical Power Plant1

Background

Boiler Drum is a critical component of a coal-fired subcritical

power plant:

acts as energy reservoir in the plant enabling it to cope

with short term load changes

dictates overall plant dynamics due to the slower

dynamics compared to the steam turbine dynamics

Due to tightening regulations, deserves study of the

dynamics for operation and control purposes

Data-based approach such as neural networks less

laborious than physical modelling

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

Boiler Drum Process

Represented by a detailed first principle model

according to Åström and Bell [3] using gPROMS tool.

Inputs: Feedwater flowrate, Steam flowrate and heat

energy input

Outputs: Drum pressure and drum water level

Thermodynamic properties of water/steam were

obtained using IAPWS-95 formulation in Aspen Properties

via COThermo interface.

Thermodynamic property derivatives were obtained using

polynomial approximations of steam table calculations from NIST REFPROP V9.1.

Boiler Drum Process

Global Conservation Equations Downcomer-Riser Dynamics

Drum Dynamics

stfwwtwsts mmVVdt

d ][

stsfwfwsatpttwtwwstss mhmhQTCMpVVhVhdt

d ][

rdcrvwrvs mmVVdt

d ])1([

rwwsrwdc

satprrrvwwrvss

mhhhhmQ

TCMpVVhVhdt

d

))((

])1([

)]1()ρ(ρα

ρ[1

ρρ

ρα

swr

s

sw

wv

s

swrIn

VVV wtst

k

VAgm swrdcvw

dc

)(2

cdsdrrsds mmmVdt

d

])([1

dt

dTCm

dt

dpVV

dt

dhV

dt

dhV

hhhh

hhmm sat

pdwdsdw

wdws

sds

wsws

fww

fwcd

)()( 0

rdcrdcrsdsd

d

ssd mmmVV

Tm

d

sdwdd

A

VVL

rvdcwtwd VVVV )1(

Boiler Drum Data

Data obtained at open loop conditions using the developed

model

The system is excited by perturbing the inputs in

succession with a series of step changes in no particular

order

Perturbation in each input is sustained for an hour resulting

to a total test period of 3 hours (10800 seconds).

Other inputs are maintained at their equilibrium value while

perturbing the other.

Boiler Drum Data

40

50

60

70

80

90

100

110

120

130

140

0 500 1000 1500 2000 2500 3000 3500

Fee

dw

ate

r Fl

ow

(kg

/s)

Time (s)

40

50

60

70

80

90

100

110

120

130

140

3500 4500 5500 6500

Ste

am F

low

(kg

/s)

Time (s)

1.20E+08

1.30E+08

1.40E+08

1.50E+08

1.60E+08

1.70E+08

1.80E+08

1.90E+08

2.00E+08

2.10E+08

7100 8100 9100 10100

He

at In

pu

t (W

)

Time (s)

Boiler Drum Data

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 2000 4000 6000 8000 10000

Dru

m w

ate

r le

vel (

m)

Time (s)

8.5E+06

9.0E+06

9.5E+06

1.0E+07

1.1E+07

1.1E+07

1.2E+07

1.2E+07

1.3E+07

0 2000 4000 6000 8000 10000

Dru

m P

ress

ure

(P

a)

Time (s)

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

Neural Networks (NNs)

Computational paradigm inspired from the structure of

biological neural networks and their way of encoding and

solving problems.

Able to identify underlying highly complex relationships

based on input-output data only.

Neural Networks (NNs)

NN model capable of reproducing time-dependent

(dynamic) data takes into account the time variable by

means of a memory process.

This is done using NN architectures with feedback

connections among neurones and time delay lines (TDL)

NARX NN is a typical NN with feedback connections

enclosing several layers of the network and a TDL.

NARX Model

NARX Model is defined by the Equation:

y(t) = f[y(t-1),y(t-2),...,y(t-ny),u(t-1),u(t-2),...,u(t-nu)]

Where:

(y(t))=Current value of predicted output signal expressed

(y(t-1),y(t-2),...,y(t-ny))= Previous values of the output signal

(u(t-1),u(t-2),...,u(t-nu)) = Previous values of an independent

(exogenous) input signal.

For NARX NN, the previous values are recorded using the

TDL and the nonlinear polynomial function (f)

approximated using a feedforward NN

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

NARX Model Training

Training complicated due to the feedback loop; ideally

dynamic training algorithm which is complex is needed

y(t)

Feedforward

Network

T

D

L

T

D

L ŷ(t)

u(t)

ŷ(t)

Feedforward

Network

T

D

L

T

D

L

u(t)

(a) Parallel Architecture

(Standard NARX Architecture)

(b) Series-Parallel Architecture

With (b), less complex static training algorithm is used for

training.

NARX Model Training

lD

pD mFW NARX NN

mST

Q

Training with simulated data from the detailed physical model.

Early stopping technique used to avoid overfitting: Data

divided into training (70%), validation (15%) and testing

(15%) data.

Levenberg-Marquardt training algorithm used (trainlm) with

mean squared error (MSE) performance function.

100 neurones in the hidden layer each with a sigmoid

transfer function

NARX Model Training

0 50 100 150 200 250 300

10-6

10-4

10-2

100

102

Best Validation Performance is 4.8725e-07 at epoch 300M

ea

n S

qu

are

d E

rro

r (

ms

e)

306 Epochs

Train

Validation

Test

Best

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

Results

-20 -15 -10 -5 0 5 10 15 20

0

0.5

1

1.5

2

2.5

3

x 10 6

Lag

Correlations

Zero Correlation

Confidence Limit

Co

rrela

tio

n

-20 -15 -10 -5 0 5 10 15 20

0

1

2

3

4

5

6

7

x 10 -11

Lag

Correlations

Zero Correlation

Confidence Limit

Error Autocorrelation Plot

Drum Pressure Prediction Error

Autocorrelation Plot

Drum Level Prediction Error

Autocorrelation Plot

The plots show reliable estimate of the network

parameters, weights and biases

Results

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25x 10

7

Dru

m P

res

su

re (

Pa

)

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000-4

-2

0

2

4x 10

4

Err

or

Time (s)

Training Targets

Training Outputs

Validation Targets

Validation Outputs

Test Targets

Test Outputs

Errors

Response

Targets - Outputs

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Dru

m L

ev

el (m

)

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000-2

0

2

4x 10

-4

Err

or

Time (s)

Training Targets

Training Outputs

Validation Targets

Validation Outputs

Test Targets

Test Outputs

Errors

Response

Targets - Outputs

Output/Target Comparison (Drum Pressure) Output/Target Comparison (Drum Level)

Results

Step Change Test: Performed on one input at a time

while other inputs remain unchanged

+30 kg/s step change in feedwater flowrate

0.035

0.036

0.037

0.038

0.039

0.04

0.041

0.042

0 50 100 150 200

Dru

m L

eve

l (m

)

Time (s)

Actual NARX

9.80000E+06

9.90000E+06

1.00000E+07

1.01000E+07

1.02000E+07

1.03000E+07

1.04000E+07

1.05000E+07

1.06000E+07

1.07000E+07

0 50 100 150 200

Dru

m P

ress

ure

(P

a)

Time (s)

Actual NARX

Results

+10 MW step change in Heat Input

0.0325

0.033

0.0335

0.034

0.0345

0.035

0.0355

0.036

0.0365

0 50 100 150 200 250

Dru

m L

eve

l (m

)

Time (s)

Actual NARX

1.04000E+07

1.06000E+07

1.08000E+07

1.10000E+07

1.12000E+07

1.14000E+07

1.16000E+07

0 50 100 150 200 250

Dru

m P

ress

ure

(P

a)

Time (s)

Actual NARX

Results

0.035

0.036

0.037

0.038

0.039

0.04

0.041

0.042

0.043

0 50 100 150 200 250

Dru

m L

eve

l (m

)

Time (s)

Actual NARX

+10 kg/s step change in Steam Flowrate

9.20000E+06

9.40000E+06

9.60000E+06

9.80000E+06

1.00000E+07

1.02000E+07

1.04000E+07

1.06000E+07

1.08000E+07

0 50 100 150 200 250D

rum

Pre

ssu

re (

Pa)

Time (s)

Actual NARX

Outline

Background

Boiler Drum Data

NARX Model

NARX Model Training

Results

Conclusion and Future Work

Conclusion and Future Work NARX NN can be used to obtain reliable dynamic model

of a boiler drum from the plant input-output operating

data only.

Use of NARX NN avoids the rigours of reliable parameter

estimation often needed in modelling from first principle.

As it is the case with all empirical models, NARX NN

models are only reliable when they are used within the

conditions that they were trained.

The NARX NN model developed in this study is subject to

the inherent deficiencies in Åström and Bell [3] model

which was used to obtain the training data.

Development of model predictive control (MPC) of the

boiler drum based on the NARX NN model is on-going.

References

1) Illustrations and text are taken from the Spirax Sarco website 'Steam Engineering Tutorials' at

http://www.spiraxsarco.com/resources/steam-engineering-tutorials.asp. Illustrations and text are

copyright, remains

the intellectual property of Spirax Sarco, and have been used with their full permission

2) Åström, K.J. and Bell, R.D. Drum-boiler dynamics. Automatica 2000; 36: 363-378.

Acknowledgement

Natural Environment Research Council (NERC), UK

EU FP7 Marie Curie

Multiphase Flow Measurement Research Group,

South East University, Nanjing, China

Questions???

Contact:

Dr Meihong Wang

Process and Energy Systems Engineering Group,

School of Engineering, University of Hull HU6 7RX

Tel.: +44 1482 466688. E-mail address: Meihong.Wang@hull.ac.uk

Thank you for your Attention!