Case 1: Let load variation only appear randomly in the most

important generating station (area 5) as shown in Figure 4.11(a). In

this case, the step-load will increase at instants of 0(sec), 5(sec) and

10(sec) with the corresponding magnitudes of 0.005(p.u.), 0.01(p.u.)

and 0.02(p.u.). Such step-load will decrease at instants of 15(sec) and

20(sec) to the amplitudes of 0.01(p.u.) and 0.05(p.u.), respectively. It

would be consistent with an actual condition of daily load in a power

plant.

- Case 2: Let load variations occur at all generating areas in the

power system model built earlier as shown in Figure 4.11(b). Load in

the area #5 is the same of the first case, meanwhile loads in the other

areas are embedded at different instants and amplitudes

28 trang |

Chia sẻ: honganh20 | Ngày: 08/03/2022 | Lượt xem: 104 | Lượt tải: 0
Bạn đang xem trước 20 trang tài liệu **Study on stabilization and optimization of a large - Scale system applying for power systems**, để xem tài liệu hoàn chỉnh bạn click vào nút DOWNLOAD ở trên

traints. The author applied analytical methods to
propose a novel control strategy using modified Riccati equations in
dealing with the transient stability problem of the three-machine
electric power system. The author also suggested a hybrid control
scheme applying a PD-like fuzzy logic controller and
superconducting magnetic energy storage devices to tackle the load-
frequency control of a five-machine interconnected power network.
Although the research results are obtained by numerical simulation
demonstrations, this study is completely significant in practical
applications.
c, Research methods
- Theoretical research: Analyze the theory, build theoretical basis
for control problems under uncertainties with a number of given laws
3
and constraints. The goal is to maintain the system frequency at the
nominal value and bring the stability back to the power grid.
- Tools: Lyapunov’s stability theory, Riccati equation, linear
algebra, fuzzy logic control, etc.
- Based on the above tools, this thesis presented a control
strategy applying modified Riccati equations to find an optimal
feedback control law with a state gain vector. The goal of this control
scheme is to damp instantaneous fluctuations caused by noises,
thereby ensuring the stability of the system. The next part of the
study focuses on designing an intelligent control strategy applying a
PD-type fuzzy logic controller and superconducting magnetic energy
storage (SMES) to maintain the network frequency at the nominal
value. The control performances obtained in this study are verified
through numerical simulations using MATLAB/Simulink package. It
is supposed that these research achievements are able to be a
fundamental study for the further studies of large-scale systems
under uncertainties, then they can be applied for the reality.
3. Scientific and practical significances
- Reaffirm the correctness of several theories which have been
applied for studies on the control engineering of optimization and
fuzzy logic.
- Propose a simplest and best method for calculation to obtain
good control performances satisfying acceptable tolerances. Then,
this method has been applied for two typical control problems of the
large-scale power system: transient stabilization and load-frequency
control problems.
4
- Practical significances: There is no doubt that the power system
plays an extremely important role for a nation, thus the stability and
reliability of power transmission need to be seriously considered.
The control strategies proposed in this study are able to enhance the
control performances and ensure the stability and economy of the
power network.
The main contents of the thesis
The thesis includes four chapters:
Chapter I. Overview of large-scale systems: generally analyze
large-scale systems with domestic and foreign studies which were
reported in the past.
Chapter II. The theory of distributed systems and decentralized
control. This chapter mainly focused on building a mathematical
model for the large-scale power networks and evaluating the stability
of the systems. The author proposed two control problems, i.e.
transient stability and load-frequency control for whole the multi-
machine electric power plant.
Chapter III. Study on an effective decentralized control
strategy to stabilize a large-scale power grid. The proposed control
method using improved Riccati equations has been applied for a
three-machine power system. Simulation results implemented in
MATLAB/Simulink environment were presented to demonstrate
control quality of the proposed strategy.
Chapter IV. Study on load-frequency control of an
interconnected power system. In this chapter, the author presented a
novel control scheme to maintain the network frequency at a nominal
value (50Hz). The proposed control method is a hybrid integration of
5
PD-like fuzzy logic controllers and SMES devices. Good simulation
achievements clarified the feasibility of the control strategy studied
in this chapter.
Conclusion and discussion: Conclude studied results and
present discussions for future work.
CHAPTER 1: OVERVIEW
1.1 Characteristics of large-scale systems
1.2. Related work
1.2.1. Domestic studies
1.2.2. Foreign studies
1.3. Brief conclusions relating to the thesis
1.4. Conclusion for chapter I
- Study on stability of the large-scale systems under uncertainties
is a new research in Vietnam and in the world. In fact, the electric
power grid in Vietnam is considered to be a typical example of the
large-scale systems, so that this study plays an important role in
reality.
- There have been a number of studies on the large-scale
systems, especially the interconnected power networks. In dealing
with the stability of a multi-machine electric power grid, there exist a
lot of control strategies, such as PID, fuzzy logic, neural network,
optimal and adaptive control methods. However, each control
strategy still needs to be further improved to design the best control
method in dealing with the stability of a large-scale power system.
6
CHAPTER 2: DISTRIBUTED SYSTEMS AND
DECENTRALIZED CONTROL FOR LARGE-SCALE
POWER SYSTEMS
2.1. Introduction
A multi-machine power grid is considered to be a typical
example of large-scale systems. Such a power system normally
consists of several generation areas; each area is considered to be a
control area which includes three basic components: a governor, a
turbine and a synchronous machine with electrical load.
Figure 2.1. A large-scale power system model consists of N
interconnected areas
In this study, the author proposes two stability control problems
for a multi-machine power system. The first one is a transient
stability problem, and the second one is load-frequency control
problem which is the key for automatic generation control (AGC) of
a power grid.
2.2. Mathematical model of a multi-machine power system
Consider a n-machine electric power system with an equation
describing rotor motion of the ith generator as follows:
i i i i mi eiM D P P
, i = 1, 2,, n (2.1)
7
Where: ij ij1 cos( )
n
ei i j i jj
P E E Y
In (2.1), ,i miM P và iE are constant for each synchronous
generator. Let:
i
i
D
M
, i = 1, 2,, n (2.2)
Let a vector 2( 1)nx R be:
0 0
1 2 1, 1 1 1, 1,( , ,..., , ,..., )
T
n n n n n n n n n nx (2.3)
where in in n , ,in i n i i
and 0ij are solved from
the power balance:
0
ij( )ei miP P với i = 1, 2,, n – 1 (2.4)
The Lur’e-Postnikov function as:
( )
T
x Ax Bf y
y C x
(2.5)
Equation (2.5) can be rewritten as:
0 1
( ) h ( )
1 0 0
0 1
i i i i i
i i
x x y x
y x
, i = 1, 2,, n – 1
(2.10)
The system given by (2.10) presenting interconnected Lur’e –
Postnikov subsystems. These subsystems are given by:
1
( ) ; , 1, 2,...,
s
T
i i i i i i ij ij i i i
j
x A x b e h c x i s
2.2.2. Analysis of subsystems
Each subsystem can be modelled by the following equation:
8
1
0 1
( )
1 0 0
[0 1]
i i i
i i
x x y
y x
(2.13)
Based on Walker and McClamroch (1967), we select a
Lyapunov candidate as:
0
( ) ( )
T
i ic x
T
i i i i i i i i iV x x H x y dy (2.18)
Where Hi is a constant matrix, and i is a scalar number.
According to [20], the Popov constraint as:
1 1Re (1 j )c (A j I) 0Ti i i ib (2.19)
. 21/2
(7.15)( ) ( ) g
T
i i i i i i i iV x y x (2.20)
Now we carry out stable area as * 0.ix Based on a procedure
proposed by Walker and McClamroch, let 1 0i
and consider
the following condition:
2
22 2 2
( 1)
0 0i i
i
(2.22)
An approximation i of the stable region i ( )i i . We get:
0: ( ) , 1,2,..., -1i i i i ix V x V i n (2.36)
where 0
iV is determined from (2.35).
2.2.3. Stable region
With each given value i , we can select a positive number
0
ij(0 os )i i c given in (2.30)
' ' 0 0sin( ) sin , k = 1, 2ik ik in iny y
1i i i (2.52)
Where, ( )m i i iG is combined with (2.51), one can be
obtained below:
9
1
1 1 0 1 0 0
1
( )
2 cos sin sin( )
( )
n
i M i
i n i in in in i ij ij ij
ji m i
j i
H
M M A M A
H
i = 1, 2,, n – 1 (2.53)
From (2.53) it is possible to recognize that the smaller Aịj is, the
easier the value of εi can be selected. This means that the
decomposition of the power system model should be performed in
such a way that the resulting subsystems are weakly coupled. This is
also the general principle to analyze a large-scale electric power
system.
2.3. Control strategies to stabilize a power system
2.3.1. Introduction
2.3.2. Transient stability problem
Recall a N-machine electric power system with the following
mathematical [18-20]:
0
0 0
( ) ( ) ( ) ( , ( )),
( ) , 1,2,3,...,
i i i i i i
i i
x t A x t B u t f t x t t t
x t x i N
(2.60)
In dealing with the nonlinearities of the system, the author
suggested using a two-step method based on Riccati equations to
establish the linear decentralized control law as follows.
Step 1: Establish the modified algebraic Riccati equations in a
form as follows:
10
1
1,
1,
0
N
T T T
i i i i i ij ij ij i i i i i i
j j i
N
T T
ij i i ji ji i
j j i
A P PA P p G G P PB R B P
p W W W W Q
(2.64)
where Ri > 0 and Qi(ni x ni) and Pi(ni x ni) are defined matrices.
Step 2: Solve the above Riccati equations to find the control law
as follows:
1
( ) ( )i i i
T
i i i i
u t K x t
K R B P
(2.65)
The feedback control law mentioned in (2.65) is capable of
recovering the stability of a large-scale system after presence of
disturbances. Hence, it is also applied to an interconnected electric
power system, particularly the three-machine network. In this
perspective, the corresponding control law can be given below:
0
0 0
1
( ) ( )
( ) ( )
( ) ( )
i i i
i i i i i
Pi mi mi Xi ei ei
T
i i i i
u t K x t
K t K t
K P t P K X t X
K R B P
(2.66)
The effectiveness of this control law will be specifically
demonstrated in the following section through a number of numerical
simulations using MATLAB/Simulink package.
11
2.3.3. Fuzzy logic applied for load-frequency control
2.3.3.1 Definition of fuzzy logic control
2.3.3.2. Principles and steps to design a fuzzy logic controller
2.3.4. Fuzzy logic controllers
2.4. Conclusions for Chapter 2
The main objective of this study is to analyze the large-scale
nonlinear and uncertain systems with a typical example of
interconnected power networks. The author also presented an
approach to evaluate the stability region for such a power system in a
case of considering it as a set of weakly interconnected subsystems
by applying Lyapunov theory.
For the stability issue of a large-scale power system, the author
proposed two problems: transient stability and load-frequency
control. To each control problem, the author presented a particular
control strategy which will be discussed in the following chapters.
Chapter 3: Decentralized control strategy to stabilize a
power system
3.1. Introduction
3.2. Structure of a multi-machine electric power system
Figure 3.1: Typical structure of a power system
12
3.3. Mathematical model of a power system
Figure 3.2. Three-machine electric power system model
3.4. A control strategy to stabilize an interconnected power
system
Assuming that this model consists of N subsystems, its
corresponding mathematical representation is as follows1:
0
0 0
( ) ( ) ( ) ( , ( )),
( ) , 1,2,3,...,
i i i i i i
i i
x t A x t B u t f t x t t t
x t x i N
(3.23)
where, fi(t, x(t)) = fi(x) denotes the interconnected components which
represent all nonlinear characteristics of the ith subsystem. Such terms
should satisfy the Lipshitz conditions as:
( )
,
( ) ( )
i n
i i
f x c x
x y
f x f y h x y
(3.24)
13
1,
( ) ( , ), 1,2,3,..., .
N
i ij ij i j
j j i
f x G g x x i N
(3.25)
Where gij(xi, xj) is a nonlinear function, which must satisfy the
following constraint:
( , ) W (t) (t) , , ji
nn
ij i j i i ij j i jg x x x W x x x (3.26)
( )ix t
( ) . ( )i i iu t K x t *( ) 0ix t
Figure 3.3. Feedback control model for the control area #i
3.5. Simulation and discussion
In this chapter, the author presents three simulation cases to
demonstrate the effectiveness of the proposed control strategy. First,
three steps need to be implemented as follows :
Step 1: Design of the control plant, a typical example of an
interconnected electric power grid.
Using the simulation parameters given in the two reports, the
following equations can be obtained for the first and second
machines:
1,
( ) ( ) ( ) ( , ), 1,2,3,..., .
N
i i i i i ij ij ij i j
j j i
x t A x t B u t p G g x x i N
(3.30)
14
Step 2: Find the solution of the algebraic Riccati equations given
in (3.23).
Using MATLAB environment, solving the Riccati equations
presented in (2.64) with the given simulation parameters, the control
law, especially the following two gain vectors (computed from
(3.26)), can be obtained:
1 1 1 1
2 2 2 2
1
2
[ ]
[ 174.7398 42.2510 10.7218 5.2562]
.
[ ]
[ 174.2508 29.2102 10.7003 5.4231]
P X
P X
K K K K K
K K K K K
(3.31)
Step 3: Carry out the necessary numerical simulations to demonstrate the
feasibility of the proposed control method.
In this step, we give two simulation cases with the initial conditions
indicated in Table.
Figure 3.4: Dynamic responses of the first and second machines in the
simulation case #1
0 1 2
0
0.5
1
1
,2
(
ra
d
)
time (s)
(a)
Machine 1
Machine 2
0 1 2
-2
0
2
4
1
,2
(
ra
d
/s
)
time (s)
(b)
Machine 1
Machine 2
0 1 2
-0.5
0
0.5
P
m
1
,2
(
p
.u
.)
time (s)
(c)
Machine 1
Machine 2
0 1 2
-0.5
0
0.5
1
X
e 1
,2
(
p
.u
.)
time (s)
(d)
Machine 1
Machine 2
15
Figure 3.5: Dynamic responses of the first and second machines in the
simulation case #2
Figure 5: Comparative results of settling times for four state parameters
0 1 2
0
0.5
1
time (s)
(a)
1
,2
(
ra
d
)
Machine 1
Machine 2
0 1 2
-2
0
2
4
1
,2
(
ra
d
/s
)
time (s)
(b)
Machine 1
Machine 2
0 1 2
-0.5
0
0.5
P
m
1
,2
(
p
.u
.)
time (s)
(c)
Machine 1
Machine 2
0 1 2
-1
0
1
2
X
e 1
,2
(
p
.u
.)
time (s)
(d)
Machine 1
Machine 2
Machine 1 Machine 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(a)
S
e
tt
lin
g
t
im
e
(s
)
P
m
X
e
Machine 1 Machine 2
0
0.1
0.2
0.3
0.4
0.5
(b)
S
e
tt
lin
g
t
im
e
(s
)
P
m
X
e
16
3.6. Conclusions for Chapter 3
This Chapter has studied an effective linear decentralized control
strategy to find an optimal solution for the stabilization issue of the
large-scale system. A three-machine electric interconnection model
representing a typical case study of the large-scale systems has also
been taken into account. First, this model is mathematically
formulated then the linear decentralized control scheme is applied to
recover the stability of the network after the presence of the
disturbances. Numerical simulation results obtained have
demonstrated the feasibility and superiority of the proposed control
method. For future work, with the diversity and complexity of the
practical electric power systems, modern control techniques, such as
fuzzy logic and neural network should be considered to further
improve the effectiveness of the studied regulation strategy. In this
aspect, a robust control scheme can be built in an efficient
integration with the decentralized control methodology proposed in
the present paper.
17
CHAPTER 4: LOAD-FREQUENCY CONTROL OF A
LARGE-SCALE POWER SYSTEM
4.1. Introduction
4.2. Mathematical model of a large-scale power system in LFC
4.2.1. Introduction to large-scale power systems
4.2.2. Mathematical model of a large-scale power system
,D iP
,tie iP
( )iF s
, ( )T iG s, ( )G iG s , ( )P iG s
, ( )G iP s , ( )Tnr iP s( )iU s
Figure 4.2. A typical model of a generation area
From Figure 4.2, a mathematical model of the above system can
be described as follows:
, , , ,( ) ( ) ( ) ( ) ( ) ,i P i Tnr i D i tie iF s G s P s P s P s (4.1)
, , ,( ) ( ). ( ),Tnr i Tnr i G iP s G s P s (4.2)
, ,
1
( ) ( ) ( ) ( ) .G i G i i i
i
P s G s U s F s
R
(4.3)
1,,
2
( ) ( ) ,areas # & # are connected directly
( ) .
0, otherwise
n
ij i j
j j itie i
T F s F s i j
sP s
(4.4)
18
4.2.3. A model of superconducting magnetic energy storage - SMES
Figurer 4.3. A model of SMES unit
The output voltage of the converter is:
, 1 2 0 0.cos ' .cos 'd i d d d dE U U V V (4.11)
where Vd0 and V’d0 , α and α’ denote the ideal no-load DC
voltages and firing angles of converter R1 and R2, respectively.
Assuming that such two 6-pulse AC/DC thyristor – based converters
are completely symmetrical, the DC output of the 12-pulse converter
can be calculated as follows
,
, 0,
,
0 if rectifying mode
2
2 .cos with
0 if inverting mode
2
d i
d i d i
d i
E
E V
E
(4.12)
In terms of using the SMES as an efficient part of the LFC
strategy, it is necessary to mathematically model such an SMES
device. According to the tie-line bias control idea, ACE signals must
be collected, and then they are taken to both the LFC regulator and
the SMES. It means that each generating power should be equipped
with an LFC controller and an SMES. The control idea is that the
load changes can be compensated by charging or discharging of the
inductor, thus the DC current Id,i should become a controlled
19
quantity.
(a)
,D iP
( )iF s
( )jF s
,tie iP
1
iR
, ( )G iP s , ( )T iP s
, ( )
Calculation
tie iP s
SMES
Model
( )iF s
,SM iP
,D mP ,D n
P
Tie-line mn
Figure 4.7. SMES model in MATLAB/Simulink
4.3. LFC controllers
4.3.1 Conventional controllers
4.3.2. PD-like fuzzy logic controllers
Control system using a PD-like fuzzy logic controller is shown
in Figure 4.8.
20
( )iF siU
UK
iuDefuzzi-
fication
Evaluation
of control
rules
Fuzzifi-
cation
eK
deK
iace
idace
iACE
idACE
,
Calculate
( )tie iP s
Compute
ACE &i idACE
Rule base PD-BASED FUZZY LOGIC
CONTROLLER
Database
, ( )L iP s
( )kF s
( )iF s
CONTROL-AREA MODELi
, ( )tie iP s
, ( )tie iP s
( )iF s
Figure 4.8. Structure of a PD-based FL controller for the area i.
4.4. Numerical simulation results and discussion
- Case 1: Let load variation only appear randomly in the most
important generating station (area 5) as shown in Figure 4.11(a). In
this case, the step-load will increase at instants of 0(sec), 5(sec) and
10(sec) with the corresponding magnitudes of 0.005(p.u.), 0.01(p.u.)
and 0.02(p.u.). Such step-load will decrease at instants of 15(sec) and
20(sec) to the amplitudes of 0.01(p.u.) and 0.05(p.u.), respectively. It
would be consistent with an actual condition of daily load in a power
plant.
- Case 2: Let load variations occur at all generating areas in the
power system model built earlier as shown in Figure 4.11(b). Load in
the area #5 is the same of the first case, meanwhile loads in the other
areas are embedded at different instants and amplitudes.
4.4.1. Capability of PD-based fuzzy logic controllers
The maximum overshoots as well as the settling times of PD-
based fuzzy logic controllers are much smaller than PI regulators. As
a result, the control performances of the proposed controllers are
much better than those of the conventional PI regulators for
21
conducting the maintenance of the network frequency against the
load disturbances.
Since load change only appears in the fifth area, the frequency of
this station will be affected with the biggest deviation (the highest
overshoot and the longest settling time). It means that the control
indexes in this area are at the worst.
4.4.2. Effectiveness of the SMES devices
Figure 4.11. Two load changes applied for simulation purpose
0 5 101520 30 40 50
0
0.005
0.01
0.015
0.02
0.025
Time (sec)
(a)
Lo
ad
v
ar
ia
tio
n
(p
.u
.)
A#5
0 5 101520 30 40 50
0
0.005
0.01
0.015
0.02
0.025
Time (sec)
(b)
Lo
ad
v
ar
ia
tio
n
(p
.u
.)
A#1
A#2
A#3
A#4
A#5
22
Figure 4.12. Frequency deviations in the areas #1, #4 and #5 in
the first simulation case
Figure 4.13. A comparison of maximum overshoots
(absolute values) and settling times for all areas in the first
simulation case.
0 10 20 30 40 50
-0.03
-0.02
-0.01
0
0.01
Time (sec)
(a)
F
re
q
B
ia
s
(
p
.u
.)
A#5-PI
A#5-FLC
0 10 20 30 40 50
-15
-10
-5
0
5
x 10
-3
Time (sec)
(b)
F
re
q
B
ia
s
(
p
.u
.)
A#1-PI
A#4-PI
A#1-FLC
A#4-FLC
PI FLC
0
0.005
0.01
0.015
0.02
0.025
Type of Controller
(a)
M
a
x
im
u
m
o
v
e
rs
h
o
o
ts
(
p
.u
.)
A#1
A#2
A#3
A#4
A#5
PI FLC
0
5
10
15
20
25
30
35
40
Type of Controller
(b)
S
e
tt
lin
g
t
im
e
s
(
s
e
c
)
A#1
A#2
A#3
A#4
A#5
23
4.5. Conclusion for Chapter 4
From this Chapter, it is well known the following conclusions
can be drawn.
- LFC is the core of an automatic generation control, playing an
important role to ensure the stability and economy of a
practical large-scale interconnected power plant.
- PD-based fuzzy logic controllers can solve efficiently the issue
of LFC, achieving the better control performances compared
with conventional regulators, such as PI.
- SMES units can be used in combination with efficient
controllers to obtain the optimal control properties, such as
the lowest overshoots and the smallest settling times.
- Due to the complexity of a large and modern power system in
practice, it is necessary to model more exactly such electric
grid to deal with LFC problem by applying the improved
control strategies as mentioned in this study.
Finally, since loads of a power system, which depend only on
customers, can vary randomly and continually over time, they should
be measured to create the fully practical database for necessary
control schemes. This might be of interest for our work in the future.
CHAPTER 5: CONCLUSION AND DISCUSSION
5.1. Evaluation of research findings
Study on large-scale systems under nonlinearities and
uncertainties is a difficult task. Because of the high complexity and
high order of the large-scale system, the calculation for analysis of
the system rapidly increases. Moreover, the increasing effect of
24
uncertain and random disturbances make the design of control
strategies more challenging.
In this thesis, based on the existed research results for the large-
scale systems, the author proposed a study focusing on stability
solution for a multi-machine electric power grid, which is considered
to be a typical example of the large-scale systems. To deal with this
problem, the following tasks have been conducted:
a) Modeling an interconnected power system under
uncertainties.
b) Proposed and designed a decentralized control using
modified Riccati equations to stabilize the network, thereby the
control method is able to quickly extinguish transient
fluctuations caused by disturbances in the electric power grid.
c) Presented a procedure to design a hybrid control scheme as an
effective integration of PD-type fuzzy logic controllers and
SMES devices for the load-frequency control. The random and
continuous load variations in a power network strongly affect on
the system frequency as well as the tie-line power flow.
Applying the proposed control method in this study both the
system frequency and the tie-line power flow can be maintained
at the nominal and scheduled values, thus the stability and
reliability of the grid can be guaranteed.
With the proposed control s

Các file đính kèm theo tài liệu này:

- study_on_stabilization_and_optimization_of_a_large_scale_sys.pdf