ICMA2013-103-asli

Modeling, Identification and Control of a Heavy Duty
Industrial Gas Turbine
Iman Yousefi Mostafa Yari and Mahdi Aliyari Shoorehdeli
R&D Department Electrical Engineering Faculty
MAPNA Electric and Control Engineering and
Manufacturing Company - MECO
K. N. Toosi University of Technology
6th
Km Malard Road, Fardis, Karaj, Iran Tehran, Iran
imanyousefi@ieee.org mostafayari@ee.kntu.ac.ir , aliyari@eetd.kntu.ac.ir
Abstract – In this paper, modeling, identification and control
of a real 162MW heavy duty industrial gas turbine is taken into
account. This work is aimed to introduce a simple and
comprehensive model to test various controllers. Rowen's model
is used to present the mechanical behavior of the gas turbine,
while the identification of it is done using a feedforward neural
network. The control rules of the turbine are applied on both
models and a comparison of the results is also presented.
Index Terms – Governor, Heavy duty gas turbine, Neural
networks, Rowen's model, System identification.
I. INTRODUCTION
Gas turbines are used widely in industry. Gas turbine is a
system that provides torque with adjustable speeds that can be
used to rotate generators. There is always a need for modeling
the behavior of the gas turbine among the engineers to test the
performance of newly designed controllers. Therefore, our aim
in this paper is to create a comprehensive model using
operational data which is available in general. For it, two
reliable models constructed and their performance are
compared. Few studies on comparison between different
models of gas turbine have been done. From this point of view
this paper is distinguished from other modeling papers.
Rowen's model of a heavy duty gas turbine (HDGT) is
one of the most commonly used simplified ones [1]. A more
precise model of the gas turbine was also presented by Rowen
based on the previous study [2]. There is another frequently
cited model to describe the dynamic behavior of the gas
turbine which has deeper sight into internal processes, named
IEEE model [3]. There are several studies based on two
mentioned models [4]-[6]. A good review of various models
of the gas turbine is given in [7].
System identification is another way to analyze the
behavior of the systems besides the modeling. System
identification is the theory of finding the model using input-
output data [8]. Identified models can be classified into two
categories: predictor and simulator [9]. Predictor models use
system stored data to predict next steps of system outputs,
while simulative models use both system stored data and
model generated data. In order to compare the results of the
two controlled models, the simulative one is selected. Most
existing systems in industry have time-varying and non-linear
behavior; therefore nonlinear system identification is an
essential field of research. From a theoretical point of view,
general function approximators can model every behavior of
any system. Among the various types of such identifiers,
neural networks are more common. There are several studies
based on neural networks and training strategy [10]-[14].
The paper is organized as follows: in section II, the plant
model is taken into account. In section III Rowen’s model for
heavy duty gas turbines is described. Section IV is specified to
the description of the gas turbine output identification using
neural networks, while the control rules of the gas turbine and
the results of the simulations are presented in section V. The
evaluation of the models is done using the comparison of the
outputs with real data in the same section; and finally the
section VI concludes the paper.
II. PLANT MODEL DESCRIPTION
Industrial heavy duty gas turbines (HDGT) are specially
designed gas turbines for power generation which are
specified by their long life and higher availability compared to
other types of gas turbines [15].
The main parts of a gas turbine include the inlet duct, the
compressor, the combustion chamber, the turbine and the
nozzle or the gas-deflector. The operation of gas turbines is
basically the same. Multi stage compressor draws the air into
the engine through inlet duct, compresses it and then delivers
it to the combustion chamber. Each compressor stage
comprises a row of rotor blades and stator vanes. Of
importance is a row of stator vanes at the inlet (inlet guide
vanes, IGVs) whose angle may be changed by the control
system during operation [15]. Within the combustion chamber
the air is mixed with fuel and the mixture is ignited, producing
a rise in temperature and hence an expansion of the gases, at
relatively constant pressure. Roughly one third of the
compressor discharge air is mixed with the fuel to be burnt,
while the remaining air is mixed with combustion products to
become the turbine inlet flow which is now at turbine inlet
temperature [16]. These gases are guided through the exhaust
duct to a second environment, but first pass through the
turbine, which is designed to convert the energy of the gases
into the mechanical torque and to provide sufficient energy to
keep the compressor rotating and also to drive generator. The
second environment can be surrounding ambient conditions or
a heat recovery steam generator (HRSG) in a combined cycle
plant (CCP).
The gas turbine which is studied in this paper is a single-
shaft machine with a 200MVA compressor-side generator. It
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Proceedings of 2013 IEEE
International Conference on Mechatronics and Automation
August 4 - 7, Takamatsu, Japan

uses natural gas as fuel and can service in both simple cycle
and combined cycle. The rated speed is 3000RPM that can
maintain the frequency of 50Hz. The compressor is a sixteen
staged one with the pressure ratio of 1:11.75. The other main
parts are two vertical combustors and a four staged power
turbine. Output power of this gas turbine at ISO conditions
with fuel’s lower heating value (LHV) of 50035kj/kg and with
excluding the inlet-outlet pressure loss is 162MW.
III. ROWEN’S MODEL FOR HDGT
The mathematical representation of a HDGT in dynamic
studies is shown in Fig. 1. This model was introduced by
Rowen in [1] and completed in [2]. The sequence of model
blocks is: fuel demand limitation, no load consumption, valve
positioner and fuel system dynamic, volume discharge delays,
output torque and temperature models, temperature
measurement system and Inlet guide vanes (IGV) system.
There are three major controls which are shown in this figure.
These are load/speed controller (also known as load/frequency
controller), temperature controller and IGV controller.
IGV are to regulate the air mass flow drawn into the
compressor. The duty of them is to keep the output
temperature at a more or less constant value namely design
point, so the maximum performance of the gas turbine is
reached.
The functions of the model depicted in Fig.1, are as
follow:
1 660 365.2 311.34(1 )R ff T m N= + − + − (1)
2 0.22 1.22 0.5(1 )ff m N= − + + − (2)
0.257
3
519
460a
f Ligv N
T
= × ×
+
(3)
where RT is exhaust gas rated temperature (o
C), fm is per unit
fuel flow, N is per unit speed, Ligv is output of the IGV
and aT is the ambient temperature (o
C).
The parameters of the Rowen's model for the gas turbine
can be calculated using practical data of the gas turbine. [15]
suggests a set of equations to extract these parameters.
The mentioned equations are based on the thermodynamic
rules of the gas turbine. The parameter estimation scheme is
the same. First of all, using gathered data, the compressor and
turbine irreversible adiabatic efficiencies are calculated.
Applying the mentioned efficiencies and also the hot end and
cold end characteristics, the parameters of (1) and (2) can also
be calculated. The other measurements and gathered data like
minimum fuel flow to maintain flame, fuel piping
approximate volume, average temperature of the fuel, etc. can
lead to extraction of the other parameters such as no load
consumption, fuel system lag time and compressor discharge
lag time. It is worth mentioning that the goal of [15] is to
calculate the parameters of the model at full load operation.
Although the calculated parameters are still usable in loading
and unloading conditions, but the effect of the IGV on the
model has to be taken into account. The related values are
considered equal to the corresponding values in [2]. The IGV
actuator parameters and limits are also set to be equal to
corresponding values of the under-study industrial gas turbine.
The inertia of the gas turbine-generator set can be
calculated using the following equation [17]:
2
2HS
J
ω
= (4)
where S is rated generator power (KVA), ω is rotating
frequency (rad/s) and H is inertia constant (s). Note that
calculations of all the parameters are valid only in the linear
area of the turbine response with respect to speed deviations.
There are three major controls which are shown in Fig. 1,
IGV control, load/frequency control and temperature control.
The IGV controller is affected by exhaust gas temperature,
while the minimum value of temperature and load/frequency
control leads to the generating the fuel demand signal.
IV. IDENTIFICATION USING NEURAL NETWORKS
The identification of gas turbine is studied in this section.
There are three methods to identify an output of a system:
• White-box method: using system equations to
describe the model behavior.
• Black-box method: this method that use input-output
data for identification purpose, usually used when the
equations of the system are too complicated. The
mentioned technique is studied in this paper.
• Grey-box method: in this method the system
equations are known but the parameters of the
equations are unknown.
The first step of identification process is pre-processing.
Normalization and noise filtering are used. It is worth noting
that the process noise is assumed to be white noise. For
normalization and filtering, (5) and (6) are used respectively:
( )max
x
x
x
′ = (5)
1
( ) ( ) 1,2, , ( 1)
1
( ) ( ) , ,
m n
i m
m
i m n
x m x i m N n
n
x m x i m N n N
n
+
=
= −
⎧
′′ = = − +⎪
⎪
⎨
⎪ ′′ = = −
⎪⎩
∑
∑
(6)
where x is the data vector, x′ is the normalized data vector,
x′′ is the filtered data, m is the window number, n is the
window length and N is the data number.
The next steps are model structure selection and model
training. There is no presented theoretical solution for optimal
model selection up to now [10] and usually every designer
uses some specific models. This becomes the soft point of the
model design. Despite, there are some methods to select the
model structure. One of them is to start with the simple
models. The complexity of the model increases until the
enough precision is reached.
612

⊗ ○
0.6824
0.06 1s +
1
1 0.398s+
0.005s
e−
1
1 0.1s+
0.04s
e−
÷
○
○
○
1 0.8533
0.8533
1 12.256s
−
+
+
1
1 1.7s+
3f
1
1 3.1s+
fm
fm
N
N
N
excT
○
N
Ligv
1f
2f
RAT
mechτ
○
lossτ
○
loadτ
1
20.3s
N
○
Fig. 1 Rowen's model for HDGT for dynamic studies [1]-[2]
In this study, a feedforward neural network with one
hidden layer is used as a nonlinear identifier. The reason is
described in the other paper of the writers [11].
Relations in a neural network are not clearly given, but
they are stored in the network and its parameters. Neural
networks are formed of several layers of simple processing
units, called neurons. Communication between neurons is
done by weights. Necessary information for mapping input to
output store by the weights in the network [11].
A multilayer feedforward neural network has one input
layer, one output layer, and a number of hidden layers. A
single layer feedforward neural network is shown in Fig. 2.
The input layer neurons do not perform any computations; but
to distribute the inputs from input layer to hidden layer
through weights. In the hidden layer, first the weighted sum of
the inputs is computed as follows:
( )
1
1,2, ,
p
Th h
j ij i j
i
z W x W x j m
=
= = =∑ (7)
Then the result of (7) passes through a nonlinear
activation function in hidden layer. In this paper tansig
function with the following equation is used as activation
function in hidden layer.
( ) 2
2
1
1 x
Tansig x
e−
= −
+
(8)
The activation functions of neurons in the output layer are
linear; only compute the weighted sum of their inputs such as
shown in (9):
( )
1
1,2, ,
h
Tl o o
jl i l
j
y W v W v l n
=
= = =∑ (9)
1x
2x
px
1Y
nY
1V
mV
11
h
W
h
pmW
11
o
W
o
mnW
Fig. 2 Feedforward neural network with one hidden layer [12]
Training means the adaptation of weights in a network
such that the error between the desired output and the network
output is minimized [12]. In this paper Levenberg-Marquardt
method is used to find the weights of the network. The
following equations are used in the mentioned method:
( ) ( ) ( )1ij ij ijw k w k w k+ = + Δ (10)
( )
1
( ) ( ) ( ) ( )T T
ijw k J w J w I J w E wμ
−
⎡ ⎤Δ = +⎣ ⎦ (11)
Where J is the Jacobian matrix, µ is a constant, I is an identity
matrix and ( )E w is an error function [13].
Levenberg-Marquardt learning algorithm gives a good
exchange between the speed of the Newton algorithm and the
stability of the steepest descent method [14].
After selecting the model structure and training, the model
has to be evaluated. For this purpose new data namely test
data is needed. In this paper the evaluation is done using the
mean square of errors (MSE) as performance criterion. The
model that produces smallest MSE can be introduced as the
613

best model. The relation of MSE performance criterion is
shown in (12).
[ ]
2
1
1
( ) ( )
N
i
MSE T i O i
N =
= −∑ (12)
which N is the data number, T is the real output of the
system, O is the output of the model.
Fitness, which is defined for tangible measures of the
accuracy of the model, is another performance criterion used
to evaluate the results. The relation of Fitness is also shown in
(13).
2
2
100 1
O T
Fitness
T T
⎛ ⎞−
⎜ ⎟= × −
⎜ ⎟−⎝ ⎠
(13)
whereT is the mean of the vectorT .
V. SIMULATIONS
The simulation results are taken into account in this part.
At the beginning, the results of the identification are analyzed.
For the pre-processing stage, residual - that is the
difference between filtered and real data - analysis is studied.
White noise values are mutually uncorrelated with zero mean.
This characteristic can be used to evaluate data filtering. As an
example the results of autocorrelation analysis and histogram
of the residual data of fuel demand input is depicted in Fig. 3.
For identification part, the input data are the normalized
fuel and the normalized IGV demands; and the output data are
normalized power and exhaust temperature. Identification of
the gas turbine leads to two multi-input single-output models.
The result of the identification of output power and exhaust
temperature are depicted in Fig. 4 and Fig. 5 respectively.
TABLE I shows the evaluation results of the identification.
In Rowen’s model a linear model is assumed with respect
to speed by applying the speed constraint of 95% to 107% of
nominal speed [15].
-50 -40 -30 -20 -10 0 10 20 30 40 50
-0.005
0
0.005
0.01
0.015
0.02
0.025
Autocorrelation of filtred fuel demand residual
lag
-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01
0
500
1000
1500
2000
2500
Histogram of filtred fuel demand residual
lag
Fig. 3 Autocorrelation result and histogram of fuel demand residual
0 1000 2000 3000 4000 5000
0
50
100
150
Time (s)
Power(MW)
Real Output
Estimated Output
0 1000 2000 3000 4000 5000
-5
0
5
Time (s)
IdentificationError(MW)
Identification Error
Fig. 4 Identification results of output power using test data
0 1000 2000 3000 4000 5000
200
300
400
500
600
Time (s)
Exhausttemperature(°C)
Real Output
Estimated Output
0 1000 2000 3000 4000 5000
-20
-10
0
10
20
Time (s)
IdentificationError(°C)
Identification Error
Fig. 5 Identification results of exhaust temperature using test data
TABLE I
PERFORMANCE CRITERIA OF IDENTIFIED OUTPUTS USING TEST
DATA
Output
Number of
neurons
MSE
criterion
Fitness
criterion
Power 10 2.869e-6 99.39
Exhaust temperature 10 8.468e-6 97.56
Selection of the proper controller is done by the Low
Value Selector (LVS) that depends on various conditions; so
the LVS has an inner logic. The control rule of the system is
as follows: The speed controller is activated at the 95% to
100% of nominal speed. After that the load controller will be
activated. If the exhaust temperature goes further of a certain
value, the output temperature controller is activated. It is
worth noting that load/speed controller includes two separate
controllers which are speed controller and load controller.
After meeting the nominal speed and synchronizing to the
614

network, a signal named synchronizing signal will be sent to
the controller that activates the load controller.
In order to compare the results, the operation of Rowen’s
model and neural network simulative model is studied here.
The mentioned control rule leads to generating the control
system of gas turbine. This control system is called governor.
The various controllers in the governor are proportional
(P) and proportional-integrator (PI) type. The coefficients of
the simulated governor is the same as the real governor, so a
comparison between them can be made.
MSE and Fitness performance criteria are also applied.
The results are shown in Fig. 6. TABLE II shows the
evaluation results. As illustrated in TABLE II, output power
can better be described by Rowen’s model; while neural
simulator is better in the exhaust temperature modeling.
Regarding to the high value for MSE criterion of the
Rowen’s model in modeling the exhaust temperature, and also
the small difference between performance criterion values for
the other output; it can be said that neural simulator can gain
more attention in modeling the behavior of the gas turbine.
VI. CONCLUSION
In this paper modeling, identification and control of a
HDGT was studied in order to build a model that is suitable
for controller testing. Rowen’s model was under focus in
modeling part, while neural networks used for identification
purposes. The stored data from a 162MW HDGT was used to
derive the parameters of Rowen’s model and also to train the
neural simulator.
MSE and Fitness performance criteria were used to
evaluate the results. According to both of them, the results of
pre-processing and identification were satisfactory.
A brief explanation of control logic was also stated and
the simulation results of controlled outputs of the two models
were compared with the stored data.
0 100 200 300 400 500 600 700 800 900
0
50
100
150
200
Time (Sec.)
Electricalpower(MW)
Real output
Output of the Rowens model
Output of the neural simulator
0 100 200 300 400 500 600 700 800 900
200
300
400
500
600
Time (Sec.)
Exhausttemperature(oC)
Real output
Output of the Rowens model
Output of the neural simulator
Fig. 6 Controlled outputs of the two models in comparison with the real
output
TABLE II
PERFORMANCE CRITERIA OF THE TWO MODELS OUTPUTS
Model Output MSE criterion Fitness criterion
Rowen
Power 0.149 99.09
Exhaust temperature 47.125 90.09
Neural
Simulator
Power 0.452 98.43
Exhaust temperature 1.323 98.33
It is shown that both Rowen’s model and neural simulator
have acceptable performance in modeling the output power,
while neural simulator has better performance in modeling the
exhaust temperature.
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