Design and simulation of a steam turbine generator using observer based and lqr controllers

17
Design and Simulation of a Steam Turbine Generator using Observer Based and LQR Controllers
Mustefa Jibril 1
, Messay Tadese 2
, Eliyas Alemayehu Tadese 3
1.
School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia
2.
School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia
3.
Faculty of Electrical & Computer Engineering, Jimma Institute of Technology, Jimma, Ethiopia
mustefazinet1981@gmail.com
Abstract: Steam turbine generator is an electromechanical system which converts heat energy to electrical energy.
In this paper, the modeling, design and analysis of a simple steam turbine generator have done using
Matlab/Simulink Toolbox. The open loop system have been analyzed to have an efficiency of 76.92 %. Observer
based & linear quadratic regulator (LQR) controllers have been designed to improve the generating voltage.
Comparison of this two proposed controllers have been done for increasing the performance improvement to
generate a 220 Dc volt. The simulation result shows that the steam turbine generator with observer based controller
has a small percentage overshoot with minimum settling time than the steam turbine generator with LQR controller
and the open loop system. Finally, the steam turbine generator with observer based controller shows better
improvement in performance than the steam turbine generator with LQR controller.
[Mustefa Jibril, Messay Tadese, Eliyas Alemayehu Tadese. Design and Simulation of a Steam Turbine
Generator using Observer Based and LQR Controllers. Researcher 2020;12(6):17-21]. ISSN 1553-9865 (print);
ISSN 2163-8950 (online). http://www.sciencepub.net/researcher. 3. doi:10.7537/marsrsj120620.03.
Keywords: Steam turbine, Generator, Observer based controller, linear quadratic regulator
1. Introduction
A Steam Turbine is a mechanical system that
takes thermal energy from pressurized steam and
converted it into mechanical output. Because the
turbine generates rotational speed motion, it is
particularly used to drive electrical generators. a steam
turbine gain power from a steam. As hot, steam passes
through the turbine ' the blades will spinning. Steam
expands and cools, convert most of the energy it
contains. This steam continuously spins the blades.
The blades converts the potential energy of the steam
into kinetic energy. Steam turbines is used to drive a
generator in order to produce electricity. In this paper,
a steam turbine is designed to run a series wound DC
generator. The shaft of the turbine is connected to the
shaft of the generator with two gears at each side with
a gear ratio between them.
2. Mathematical Modeling
Figure 1 shows the diagram of the steam turbine
with a DC generator interconnection unit.
The mechanical power developed by the steam
turbine expressed by the equation:
     1in out
dW d
V F t F t
dt dt

  
Figure 1. Steam turbine generator
Where:
W weight of steam in the steam turbine [g];
V – Volume of steam turbine [m3];
 – Density of steam [g/cm3];
F – Steam mass flow rate [g/s];
t – Time [sec.].
Assuming that the output mass flow rate of the
steam turbine is proportional to the pressure in the
turbine system:
 0
0
2out
F
F P
P

Where:
P – Steam pressure in the system [kPa];
P0 – rated pressure;

Researcher 2020;12(6) http://www.sciencepub.net/researcher RSJ
18
F0 – rated output mass flow of the system
Assuming constant temperature in the system:
 3
d dP
dt dt P
 
 

From equations (1) to (3), it results:
    out out
in out T
dF dFdP
F t F t V V
dt P P dt dt
 

 
      
 
Where
T V
P



 
 - Time constant
Then Equation (1) become
 
     4out
T out in
dF t
F t F t
dt
  
The steam mass flow rate is
     in outF t F t F t 
The turbine speed is integrally related to the
steam flow rate:
          1 5in outt F t F t F t dt    
Substituting Equation (5) for
 outF t
into
Equation (4) yields the transfer function between the
input steam mass flow and the output turbine torque.
 
 
 1
6
1
T
in T
s
F s s
 



2.1 Modeling of DC Generator
The generated voltage is directly proportional to
the generator input speed
 1 2 7ge k 
Where: k1 is a speed proportional constant.
The generator input speed is the product of the
gear ratio and the steam turbine output speed
 2 1 8n 
Therefore Equation (7) becomes
 1 1 9ge k n
Then the transfer function between
 inF s
and
 ge s
become
 
 
1
1
g T
in T
e s k n
F s s




The equation of the generator is
     
     10a
g f a f a L a
di t
e t L L R R R i t
dt
    
Now substituting Equation (9) in to Equation
(10) yields
     
     1 1 11a
f a f a L a
di t
k n t L L R R R i t
dt
     
Taking the Laplace transform and obtaining the
transfer function the input speed and the output
current yields
 
     
 1
1
12a
f a f a L
I s nk
s s L L R R R

   
The output voltage is simply the product of load
resistance times the armature current
     13L aV s R I s
Now substituting Equation (13) in to Equation
(12) yields
 
     
 1
1
14L
f a f a L
V s nR k
s s L L R R R

   
Finally combining Equation (6) to Equation (14)
yields to the transfer function between the input steam
mass flows to the output generated voltage
 
        
1
1
L T
in T f a f a L
V s nR k
F s s s L L R R R



    
The parameters of the system is shown in Table
1 below
Table 1 System parameters
No Parameters Symbol Value
1 Time constant T 2 second
2 Speed proportional constant. 1k 4 Vs/rad
3 Gear ratio n 4
4 Field winding inductance fL 3 H
5 Field winding resistance fR 2 ohm
6 Armature winding inductance aL 4 H
7 Armature winding resistance aR 4 ohm
8 Load resistance LR 8 ohm
Numerically the transfer function become
 
  2
18
2.5 1in
V s
F s s s

 
The state space form of the transfer function is
 
2.5 1 1
1 0 0
0 18
x x u
y x
    
    
   



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3. The Proposed Controllers Design
3.1 Observer-Based Controller Design
The deal with the general case where only a
subset of the states, or linear combinations of them,
are obtained from measurements and are available to
our controller. Such a guidelines is referred to as the
output feedback problem.
The output is of the form
 15y Cx Du 
We shall examine a class of output feedback
controllers constructed in two stages:
1. Contracting an observer | a system dynamics
that is driven by the inputs and the outputs of the
system, and yield an deliberation of its state variables;
2. Using the estimated state instead of the actual
state in a estate response scheme.
The block diagram of the steam turbine
generator system with the observer-based controller is
shown in Figure 2 bellow.
Figure 2 Block diagram of the steam turbine generator
system with the observer-based controller
The controller Gc (s) can be further derived in
the following form:
     
1
16cG s I K sI A BK HC B

    
With its state space realization
   17c
A BK HC B
G s
K I
  
   
The controller Gc (s) in Equation (17) is called
the observer-based controller, since the structural idiot
of the observer is implicitly reflected within the
controller.
Where the state space model of the plant, G, the
state feedback gain vector K, and the observer gain
vector H are then returned, respectively.
We select the weighting matrix Q and R as
8 0
1
0 8
Q and R
 
  
 
And we select the observer gain vector as
2
0.5
H
 
  
 
And we obtain the state feedback gain vector K
as
 1.7720 2K 
The observer-based controller state space
representation become
 
4.272 39 2
1 9 0.5
1.772 2
o o
o o
x x u
y x
    
    
   


3.2 LQR Controller Design
LQR is a controller that gives the best possible
achievement with respect to some given measure of
performance. The realization measure is a quadratic
function composed of state vector and manipulated
input. The block diagram of the steam turbine
generator with LQR controller is shown in Figure 2
below.
Figure 3 Block diagram of the steam turbine generator
with LQR controller
Here we choose Q and R matrixes as
3 0
5
0 3
Q and R
 
  
 
The value of obtained feedback gain matrix K of
LQR is given by
 0.2166 0.2649K 
4. Result and Discussion
In this section, the open loop simulation of the
generated voltage and power, the simulation of the
performance comparison of the proposed controllers
for generating a desired voltage is discussed below.
Figure 4. Open loop generated voltage

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4.1 Simulation of the open loop steam turbine
generator voltage and power
The open loop voltage and power generated for a
steam mass flow of 5 g/s input is shown in Figure 4
and Figure 5 respectively.
Figure 5. Open loop output power
As Figure 4 and Figure 5, in the first 10 seconds,
the voltage increases from 0 to 90 volts and it reaches
is steady state value of 90 volt and the output power is
1000 W. The induced voltage in the armature circuit
and the input power to the generator simulation result
is shown in Figure 6 and Figure 7 respectively.
Figure 6. The induced voltage in the armature circuit
Figure 7. Input power
The efficiency of the system become
1000
100% 100% 76.92%
1300
Output power W
Input power W
   
4.2 Comparison of the Steam Turbine
Generator with Observer Based & LQR
Controllers for Generating a Desired Voltage
The simulation result of the performance of the
steam turbine generator with observer based & LQR
controllers for generating a desired voltage of 220 Dc
volt is shown in Figure 8 below.
Figure 8. Performance of the steam turbine generator
with observer based & LQR controllers for generating
a desired voltage of 220 Dc volt
As seen from Figure 8, the steam turbine
generator with observer based controller has a small
percentage overshoot and a settling time of 7 second
which is better than the steam turbine generator with
LQR controller and the open loop system.
5. Conclusion
In this paper, a simple steam turbine generator is
modeled and designed using a series wound Dc
generator. The open loop system is simulated for
generated voltage, input and output power. For a
steam mass flow of 5 g/s the steam turbine generator
generates a 90 volt with an output power of 1000 W.
The generator induced armature circuit voltage is
simulated with an input power of 1300 W. The
efficiency of the simple steam turbine generator is
76.92 %. Comparison of the steam turbine generator
with observer based & LQR controllers for generating
a desired voltage of 220 Dc volt have been simulated
and the simulation result shows that the steam turbine
generator with observer based controller has a small
percentage overshoot and less settling time than the
steam turbine generator with LQR controller and the
open loop system. Finally the comparison and analysis
result prove the effectiveness of the proposed steam
turbine generator with observer based controller.
Reference
1. K. Dinesh “Design and Structural Analysis of
Steam Turbine” Journal of Engineering and
Applied Sciences, Vol. 13, Issue 1, pp. 162-164,
2018.
2. P. I. Onwuamaeze “Improving Steam Turbine
Efficiency: An Appraisal” Research Journal of

21
Mechanical Operations, Vol. 1, No. 1, pp. 24-30,
2018.
3. Hosham S. et al. “Enhancement of Performance
for Steam Turbine in Thermal Power Plants
using Artificial Neural Network and Electric
Circuit Design” Applied Computational
Intelligence and Soft Computing, Vol. 2018,
Article ID. 8042498, 9 pages, 2018.
4. V I Brezgin et al. “Improvement of Steam
Turbine Operational Performance and Reliability
with using Modern Information Technologies”
Journal of Physics: Conference Series, Vol. 891,
2017.
5. A. Sinan “Performance Analysis of a Steam
Turbine Power Plant at Part Load Conditions”
Journal of Thermal Engineering, Vol. 3, Issue 2,
pp. 1121-1128, 2017.
6. Li Sun et al. “Performance Modeling of New and
Existing Steam Turbines” Ind. Eng. Chem. Res,
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6/20/2020

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