International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
Multi Stage Fuzzy Damping Controller Using
Genetic Algorithms for the UPFC
H. Shayeghi
especially after a large or small disturbances. Sometimes the Power
System Stabilizer (PSS) installed on a specific generator cannot
provide effective damping for that kind of oscillations. In [5, 6], it is
shown that the addition of a conventional supplementary controller
to the UPFC is an effective solution to the problem. However, an
industrial process, such as a power system, contains different kinds of
uncertainties due to continuous load changes or parameters drift due
to power systems highly nonlinear and stochastic operating nature.
As a result, a fixed parameter controller based on the classical control
theory such as PI or lead-lag controller [5-8] is not certainly suitable
for the UPFC damping control methods. Thus, it is required that a
flexible controller be developed. Some authors suggested neural
networks method [9] and robust control methodologies [10-12] to
cope with system uncertainties to enhance the system damping
performance using the UPFC. However, the parameters adjustments
of these controllers need some trial and error. Also, although using
the robust control methods, the uncertainties are directly introduced
to the synthesis, but due to the large model order of power systems
the order resulting controller will be very large in general, which is
not feasible because of the computational economical difficulties in
implementing.
Recently, applications of the Fuzzy Logic (FL) theory to the
engineering issues have drawn tremendous attention from researchers
[13-14]. The fuzzy controller has a number of distinguish advantages
over the conventional one. It is not so sensitive to the variation of
system structure, parameters and operation points and can be easily
implemented in a large-scale nonlinear system. The most attractive
feature is its capability of incorporating human knowledge to the
controller with ease. This approach provides the FL systems better
functionality, performance, adaptability, reliability and robustness.
The most dynamic area of fuzzy systems research in the power
systems has been the stability enhancement and assessment. Some
authors used FL-based damping control strategy for TCSC, UPFC
and SVC in a multi-machine power system [15, 16]. The damping
control strategy employs non-optimal FL controllers that is why the
system’s response settling time is unbearable. Dash et al. presented a
fuzzy damping control system for series connected FACTS devices,
e.g. TCSC, UPFC and TCPST to enhance power system stability
[17]. The FL-based damping controller may exhibit lack of
robustness due to its simplicity and the system’s response for a wide
incursion in the operating condition is anticipated to deteriorate.
Limyingcharone et al. [18] applied fuzzy logic based UPFC for the
transient stability improvement. Khon and Lo [19] used a fuzzy
damping controller designed by micro Genetic Algorithm (GA) for
TCSC and UPFC to improve powers system low frequency
oscillations. The proposed method may have not enough robustness
due to its simplicity against the different kinds of uncertainties and
disturbances. Mak et al. [20] applied a GA-based ProportionalIntegral (PI) type fuzzy controller for UPFC to enhance power
Abstract—In this paper, a new Multi-Stage Fuzzy (MSF) DCvoltage regulator is proposed for the UPFC to damp power system
low frequency oscillations. In order for a fuzzy rule based control
system to perform well, the fuzzy sets must be carefully designed. A
major problem plaguing the effective use of this method is the
difficulty of accurately constructing the membership functions.
because it is a computationally expensive combinatorial optimization
problem. On the other hand, Genetic Algorithms (Gas) is a technique
that emulates biological evolutionary theories to solve complex
optimization problems by using directed random searches to derive a
set of optimal solutions. For this reason, in the proposed MSF type
PID controller, the membership functions are tuned automatically
using a modified GA’s based on the hill climbing method. The aim is
to reduce fuzzy system effort and take large parametric uncertainties
into account. This newly developed control strategy combines the
advantages of the GAs and fuzzy system control techniques and leads
to a flexible controller with simple stricture that is easy to implement.
The effectiveness of the new proposed control strategy is evaluated
under different operating conditions in comparison with the classical
controllers to demonstrate its robust performance through time
simulation studies and some performance indices.
Keywords--UPFC, Multi-Stage Fuzzy Controller, GAs, FACTS
devices, Power System Stability.
I. INTRODUCTION
I
N the recent years, the fast progress in the field of power
electronics had opened new opportunities for the application of the
FACTS devices as one of the most effective ways to improve
power system operation controllability and power transfer limits [1–
2]. The Unified Power Flow Controller (UPFC) is regarded as one of
the most versatile devices in the FACTS device family [3-4] which
has the ability to control power flow in the transmission line, improve
the transient stability, mitigate system oscillation and provide voltage
support. It performs this through the control of the in-phase voltage,
quadrate voltage and shunts compensation due to its mains control
strategy [1,4]. Investigations on the UPFC main control effects show
that the UPFC can improve system transient stability and enhance the
system transfer limit as well. The application of the UPFC to the
modern power system can therefore lead to the more flexible, secure
and economic operation [10]. When the UPFC is applied to the
interconnected power systems, it can also provide significant
damping effect on tie line power oscillation through its
supplementary control. The modern power system tends to be
interconnected to yield the most economic benefits. However, low
frequency oscillation will occur on the heavily loaded tie lines
H. Shayeghi is with the Department of Technical Eng., University of
Mohaghegh Ardabili, Ardabil, Iran (corresponding author to provide phone:
98-551-2910; fax: 98-551-2904; e-mail: hshayeghi@ gmail.com).
145
International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
system damping. Although, the fuzzy PI controller is simpler and
more applicable to remove the steady state error, it is known to give
poor performance in the system transient response.
In order to overcome the above drawbacks and focus on the
separation PD part from the integral part, this paper presents a new
Multi Stage Fuzzy (MSF) PID controller with fuzzy switch for the
UPFC DC-voltage controller to enhance the dynamic stability. This is
a form of behavior based control, where the PD controller becomes
active when certain conditions are met. The resulting structure is a
controller using two-dimensional inference engines (rule base) to
reasonably perform the task of a three-dimensional controller. The
proposed method requires fewer resources to operate and its role in
the system response is more apparent, i.e. it is easier to understand the
effect of a two-dimensional controller than a three-dimensional one
[21]. One of the importance and essential step toward the design of
any successful fuzzy controllers is accurately constructing the
membership functions. On the other hand, extraction of an
appropriate set of membership functions from the expert may be
tedious, time consuming and process specific. Thus, in order to
reduce fuzzy system effort a modified GAs is used for the optimum
tuning of the membership functions in the proposed MSF controller,
automatically. GAs, are a heuristic search; optimization technique
inspired by natural evolution and has attractive features such as
robustness, simplicity, etc. However, it cannot guarantee that the best
solution will be found. In fact, sometimes it converges to local, rather
than global optima. To overcome this drawback, a modified GA
based on the hill climbing method is proposed to improve
optimization synthesis such that the global optima are guaranteed and
the speed of algorithms convergence is extremely improved, too. The
effectiveness of the developed controller is demonstrated through
time simulation studies and some performance indices. Results
evaluation show that the proposed MSF controller achieves good
robust performance for a wide range of operating conditions and is
superior to the classical controller. Moreover, the proposed control
strategy has simple structure and does not require an accurate model
of the plant and fairly easy to implement which can be useful for the
real world complex power system.
vt
It
⎡vBtd ⎤ ⎡ 0
⎢v ⎥ = ⎢
⎣ Btq ⎦ ⎣ xB
⎡ mB cos δ B vdc ⎤
− xB ⎤ ⎡iBd ⎤ ⎢
⎥
2
⎥
⎢ ⎥+⎢
0 ⎥⎦ ⎣iBq ⎦ ⎢ mB sin δ B vdc ⎥
2
⎣
⎦
(2)
vdc =
3mE
[cos δ E
4Cdc
⎡iEd ⎤ 3mB
sin δ E ]⎢ ⎥ +
[cos δ B
⎣iEq ⎦ 4Cdc
⎡iBd ⎤
sin δ B ]⎢ ⎥
⎣iBq ⎦
vb
iB
vB
x BV
xB
VSC-E
Vdc
Infinite
bus
VSC-B
xE
UPFC
mE δ E mB δ B
Fig. 1. SMIB power system equipped with UPFC.
Where, v Et , i E , v Bt and i B are the excitation voltage, excitation
current, boosting voltage, and boosting current, respectively; C dc and
vdc are the DC link capacitance and voltage, respectively. The
nonlinear model of the SMIB system as shown in Fig. 1 is described
by:
.
(4)
ω = ( Pm − Pe − DΔω ) / M
.
δ = ω 0 (ω − 1)
(5)
(6)
.
Eq′ = (− Eq + E fd ) / Tdo′
(7)
.
E fd = (− E fd + K a (Vref − Vt )) / Ta
Where,
′ + ( X d − X d′ )I td
Pe = Vtd I td + Vtq I tq ; E q = E qe
Vt = Vtd + jVtq ;Vtd = X q I tq ; Vtq = E q′ − X d′ I td
I td = I tld + I Ed + I Bd ; I tq = I tlq + I Eq + I Bq
I tld =
xE
1 meVdc
1
I Ed +
Vb cos δ
cos δ E −
XT
XT 2
XT
I tlq =
xE
1 meVdc
1
I Eq −
sin δ E +
Vb sin δ
XT
XT 2
XT
( x dt − x BB x b 3 )
x m V
Vb cos δ − dt B dc cos δ B
2
x dE
x dE
I Ed =
( x + x BB x b 2 ) m eV dc
x BB
cos δ E
E ′ − dt
2
x dE
x dE
( xqt + xBB xa 2 ) meVdc
xqt mBVdc
( x + xBB xa 3 )
sin δ E
= dt
sin δ B −
Vb sin δ −
2
xqE
xqE 2
xqE
+
I Bd =
Figure 1 shows a SMIB system equipped with a UPFC. The
UPFC consists of an Excitation Transformer, a Boosting
Transformer, two three-phase GTO based Voltage Source Converters
(VSCs), and a DC link capacitors. The four input control signals to
the UPFC are mE, mB, δE, and δB. Where, mE is the excitation
amplitude modulation ratio, mB is the boosting amplitude modulation
ratio, δE is the excitation phase angle and δB is the boosting phase
angle. By applying Park’s transformation and neglecting the
resistance and transients of the ET and BT transformers, the UPFC
can be modeled as [22-23]:
(1)
xT
iE
I Eq
⎡ m E cos δ E v dc ⎤
⎥
− x E ⎤ ⎡i Ed ⎤ ⎢
2
+
⎥
⎢ ⎥ ⎢
0 ⎥⎦ ⎣i Eq ⎦ ⎢ m E sin δ E v dc ⎥
⎣
2
⎦
itl
xtE
II. POWER SYSTEM MODEL WITH UPFC
⎡v Etd ⎤ ⎡ 0
⎢v ⎥ = ⎢
⎣ Etq ⎦ ⎣ x E
vo
( xb 3 x E − xb1 )
x m V
Vb cos δ + b1 B dc cos δ B
x dE
x dE 2
+
I Bq = −
x − x E xb 2 meVdc
xE
cos δ E
E q′ + b1
x dE
2
x dE
( xa 3 xE + xb1 )
( x − xE xa 2 ) meVdc
x mV
Vb sin δ + a1 B dc sin δ B + a1
sin δ E
xqE
2
xqE 2
xqE
x dT = X tE + X d′ ; x qT = X q + X tE ; x ds = X E + x dT ; x qs = X E + x qT
xa1 =
xb1 =
( xqs X T + xqT X E )
XT
; xa 2 = 1 +
xqT
XT
; xa 3 = −
xqT
XT
;
x
x
( xds X T + xdT X E )
; xb 2 = 1 + dT ; xb 3 = dT
XT
XT
XT
xqE = −(
xBB xqT xE
XT
+ xE xqT + xBB xqs ); xdE = (
xBB xdT xE
+ xE xdT + xBB xds )
XT
The equation for real power balance between the series and shunt
converters is given by:
(8)
Re(V B I B∗ − V E I E∗ ) = 0
A. Power system linearised model
A linear dynamic model is obtained by linearizing the nonlinear
model around an operating condition. The linearized model of the
(3)
146
International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
III. GA-BASED HYBRID FUZZY AGC
power system as shown in Fig. 1 is given as follows:
(9)
•
Δ δ = ω 0 Δω
Because of the complexity and multi-variable conditions of the
power system, conventional control methods may not give
satisfactory solutions. On the other hand, their robustness and
reliability make fuzzy controllers useful for solving a wide range of
the control problems in power systems. In this paper, a modified GAbased MSF (GAMSF) controller is proposed to the UPFC DCvoltage regulator for damping of the power systems low frequency
oscillations. The motivation of using the proposed GAMSF
controller is to take large uncertainties in power system operation
conditions into account. This control strategy combines fuzzy PD
controller and integral controller with a fuzzy switches. The fuzzy PD
stage is employed to penalize fast change and large overshoots in the
control input due to corresponding practical constraints. The integral
stage is also used to get disturbance rejection and zero steady state
error. In order for a fuzzy rule based control system to perform well,
the fuzzy sets must be carefully designed. A major problem plaguing
the effective use of this method is the difficulty of accurately and
automatically tuning of the membership functions. Because, it is a
computationally expensive combinatorial optimization problem and
also extraction of an appropriate set of the membership function from
the expert may be tedious, time consuming and process specific. On
the other hand, the GA is more suitable to deal with the problem of
lacking experience or knowledge than other searching methods in
particular [24], when the phenomena being analyzed are describeble
in terms of rules for action and learning processes. Thus, in order to
reduce fuzzy system effort and cost, a modified GA based on the hill
climbing method is used to optimally tune of the membership
functions in the proposed MSF controller. Fig. 3 shows the structure
of the proposed strategy for the UPFC DC-voltage regulator. In this
structure, the input values are converted to truth-value vectors and
applied to their respective rule bases. The output truth-value vectors
are not defuzzified to crisp value as with a single stage fuzzy logic
controller, but are passed onto the next stage as a truth value vector
input. The darkened lines in Fig. 3 indicate truth value vectors. To
improve the controller performance under very heavy loading of
power systems (δ>70o) a static switch is used in the controller output
to increase the applied control signal. In this effort, all membership
functions are defined as triangular partitions with seven segments
from -1 to 1. Zero is the center membership function which is
centered at zero. The partitions are also symmetric about the ZO
membership function as shown in Fig. 4.
(10)
Δω = (−ΔPe − DΔω ) / M
(11)
•
Δ E q/ = (−ΔE q + ΔE fd ) / Tdo/
•
(12)
•
(13)
Δ E fd = −ΔE fd / T A − K A ΔV / T A
Δ v dc = K 7 Δδ + K 8 ΔE q/ − K 9 Δv dc + K ce Δm E
+ K cδe Δδ E + K cb Δm B + K cδb Δδ B
Where,
Δ Pe = K 1 Δ δ + K 2 Δ E q/ + K
pd
Δ v dc + K
pe
Δm E + K
p δe
Δδ E + K
pb
Δm B + K
pδb
Δδ B
Δ E q/ = K 4 Δ δ + K 3 Δ E q/ + K qd Δ vdc + K qe Δ m E + K qδe Δ δ E + K qb Δ m B + K qδb Δ δ B
Δ V t = K 5 Δ δ + K 6 Δ E q/ + K vd Δ v dc + K ve Δ m + K v δ e Δ δ E + K vb Δ m B + K v δ b Δ δ B
K1, K2, K9, Kpu ,Kqu and Kvu are the linearization constants. The
state-space model of power system is given by:
(14)
x = Ax + Bu
Where, the state vector x , control vector u , A and B are:
Δδ
Δm Δδ ]
x = [ Δδ Δω ΔE q′ ΔE fd Δv dc ] , u = [ Δm
T
E
⎡ 0
⎢
K
⎢ − 1
M
⎢
K
⎢
A = ⎢ − /4
Tdo
⎢
⎢− K A K 5
⎢ TA
⎢ K
7
⎣
w0
0
0
0
0
0
K2
M
K
− /3
Tdo
K K
− A 6
TA
K8
0
⎤
K pd ⎥
⎥
M ⎥
K
− qd/ ⎥⎥ , B =
Tdo
⎥
K K
− A vd ⎥
TA ⎥
− K 9 ⎥⎦
0
−
−
0
1
Tdo/
1
−
TA
0
0
⎡
⎢ K pe
⎢ − M
⎢ K
⎢ − qe
⎢
Tdo/
⎢ K K
⎢− A vc
TA
⎢
⎣⎢ K ce
E
−
−
B
0
K pδe
−
M
K qδe
−
Tdo/
K K
− A vδe
TA
K cδe
−
B
0
K pb
0
⎤
K pδb ⎥
M ⎥⎥
K
− q/δb ⎥
Tdo ⎥
K K ⎥
− A vδb ⎥
TA ⎥
K cδb ⎦⎥
−
M
K qb
Tdo/
K A K vb
TA
K cb
The block diagram of the linearized dynamic model of the SMIB
power system with UPFC is shown in Fig. 2.
K1
+ + ΔP
e
−
+
K pu
ΔPm
+
w0
S
1
MS + D
+
K5
K4
K2
K pd
K6
K qu
K8
U
K cu
+
−
−
1
K 3 + STdo/
ΔE q/
+
+
1
S + K9
+
−
ka
1 + STa
K qd
− ΔVref
−
+
−
K vu
−
K vd
ΔVdc
K7
Fig. 2. Modified Heffron–Phillips transfer function model.
Modified GA
Fuzzyfy D
ΔVdc
Fuzzyfy P
Ki/s
PID Switch
Rule Base
PD
Rule Base
Fuzzyfy I
K-1
Defuzzify
MSF Controller
GAMSF Controller
+
δE
K-2
delta
If delta <70o then pass up path
else down path
1/s
Fig. 3. Structure of the proposed GAMSF control strategy
147
International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
NM
-1
NS
-b
ZO PS
-a 0
NB: Negative Big
NS: Negative Small
PM: Positive Medium
PM
a
PB
b
1
∫e
NB
NM: Negative Medium
PS: Positive Small
PB: Positive Big
Fig. 4. Symmetric fuzzy partition.
NB
NM
NS
ZO
PS
PM
PB
NB
NB
NB
NB
NB
NM
NS
ZO
TABLE I
PD RULE BASE
∆e
NM
NS
ZO
NB
NB
NB
NB
NB
NM
NB
NM
NS
NM
NS
ZO
NS
ZO
PS
ZO
PS
PM
PS
PM
PB
NB
NM
NM
NM
NM
NM
NM
NM
PM
PB
PB
PB
PB
PB
PB
PB
∫
0
PS
NM
NS
ZO
PS
PM
PB
PB
PM
NS
ZO
PS
PM
PB
PB
PB
PB
ZO
PS
PM
PB
PB
PB
PB
For acquiring better performance, number of generation, population
size, crossover rate and mutation rate is chosen 100, 20, 0.97 and 0.08,
respectively. Here, the modified GA evolution procedure is applied to
exact tune of membership functions of the proposed MSF controller for
design of the proposed MSF DC-voltage regulator. The Results of
membership function set values are listed in Table 3.
Start
X(0) (Initial condition)
sst (Step), Prec (Accurate), st= sst
Generate initial population
randomly
∆f=f(x0+sst)-f(x0)
NO
-sst st =
Change the mutation
probability
Calculate the fitness value of each Individual
∆f ≥ 0
Selection
Yes
Crossover
x=x0, ∆f=-1
Mutation
∆f=f(x+st)-f(x), x=x+st
NO
∆f ≥ Prec
NO
∆f < 0
Elitism to createnew generation
Yes
Print optimal value of membership
functions parameters
Yes
Hill Climbing Method
Yes
Algorithm
convergence
Yes
No
Is fitness value
improve
Classical GA
End
Fig. 5. Flowchart of the proposed GA based on the hill climbing method.
ΔVDC
PB
NM
NM
NM
NM
NM
NM
NM
According to Fig. 4, for the exact tuning of the used membership
functions in the proposed method we must find the optimal value for a
and b parameters. Where 0<a<b<1. To acquire an optimal combination,
we adopt the modified GA’s as the search method. Fig. 5 shows the
flowchart of the modified GA approach for optimization. In this
algorithm, the classical GA is used to find near optimal global value and
then the proposed hill climbing method is used to find global optimum
value. In order to guarantee global optima and improve the convergence
speed, results of the GA is being used as initial conditions for the hill
climbing method.
Before proceeding with the GA approach, the suitable coding and
fitness function should be chosen. In this study, a and b parameters for
the ΔVDC, ∆(ΔVDC), ∫ΔVDC and output membership functions are
expressed in term of string consisting of 0 and 1 as shown in Fig. 6 by
binary coding. It can be seen that the length of the chromosome is 40
genes (bit). For our optimization, the following fitness function is
proposed:
t
(15)
fitness = 1 / 10 × ITAE , ITAE = t ΔVDC dt
P=P+0.1
e=∆VDC
There are two rule bases used in the GAMSF controller. The
first is called the PD rule bases as it operates on the truth vectors
form the error (e) and change in error (∆e) inputs. A typical PD
rule base for the fuzzy logic controller is given in Table 1. This
rule base responds on a negative input from either error (e) or
change in error (∆e) with a negative value. Thus, driving the
system toward the commanded value. Table 2 shows a PID switch
rule base. This rule base is designed to pass through the PD input
if the PD input is not in zero fuzzy set. If the PD input is in the
zero fuzzy set, then the PID switch rule base passes the integral
error values (∫e). This rule base operates as the behavior switch,
giving the control to PD feedback when the system is in motion
and reverting to integral feedback to remove steady state error
when the system is no longer moving.
NB
NM
NS
ZO
PS
PM
PB
TABLE II
PID SWITCH RULE BASE
PD Values
NM
NS
ZO
PS
NS
NB
PS
PM
NS
NM
PS
PM
NS
NS
PS
PM
NS
ZO
PS
PM
NS
PS
PS
PM
NS
PM
PS
PM
NS
PB
PS
PM
∫ΔVDC
∆ (ΔVDC)
Output
1 0 1 0 0 0 1 1 0 0 1 11 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0
Fig. 6. String encoding membership function
148
No
International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
TABLE III
OPTIMAL VALUES OF PARAMETERS a AND b
Membership
function
Δω
∆( Δω)
∫Δω
output
Pe 2
Classical GA
Modified GA
a
b
a
b
0.87
0.035
0.25
0.2
0.95
0.06
0.62
0.6
0.9
0.03
0.2
0.2
1
0.09
0.6
0.6
Pe 2 ref
k pp +
k pi
mB
s
Δω
Fig. 7. PI- type power flow controller with damping controller
Vdc
IV. SIMULATION RESULT
In this section different comparative cases are examined to
show the effectiveness of the proposed GAMSF controller in
comparison with the conventional UPFC controllers. In this study,
the conventional PI type controllers as shown in Figs. 7 and 8 are
considered for power-flow and DC-voltage regulator. The
Conventional Damping Controller (CDC) is designed to
produce an electrical torque in phase with the speed
deviation according to phase compensation method. The
four control parameters of the UPFC (mB, mE, δB and δB)
can be modulated in order to produce the damping torque.
In this study, mB is modulated in order to damping
controller design. The speed deviation Δω is considered as
the input to the damping controller. The structure of the
UPFC based damping controller is shown in Fig.9. It
consists of gain, signal washout and phase compensator
blocks. The parameters of the CDC are obtained using the
phase compensation technique [25] for the nominal
operating condition with damping ratio of 0.5 as follows:
1+sT1
1+sT2
sTw
1+sTw
KDC
mB
Fig. 9. Block diagram of UPFC based conventional damping controller.
Using the above designed CDC controller optimal parameters of the
conventional power-flow controller (kpp and kpi) and DC-voltage
regulator (kdp and kdi) are obtained using genetic algorithm [24] for
operating condition 1 as given in Appendix. Optimum values of the
power-flow controller are obtained as kpp=0.5385 and kpi=1.8259. When
the parameter of power-flow controller are set at their optimum values,
the parameters of DC-voltage regulator are now optimized and obtained
as kdp=0.398 and kdi=0.5778.
The performance of the proposed UPFC based GAMSF DCvoltage regulator and CDC damping controllers for 10% step
sudden change in reference power on transmission line 2 and
mechanical power are shown in Figs. 10 to 12 for different load
conditions. The loading condition and system parameters are
given in Appendix. .
1
0.12
0.5
0.1
0
ΔVdc
-0.5
-1
-0.5
-1.5
0.04
-1.5
-2
0.02
-2
5
Time
10
-2.5
0
15
0.08
0.06
-1
-2.5
0
δe
x 10-3
x 10-4
0
Δw
Δω
536.0145s( s + 3.656)
( s + 0.1)(s + 4.5)
0.5
k di
s
Fig. 8. PI-type DC-voltage regulator
ΔPe
CDC =
k dp +
Vdcfef
5
Time
10
0
15
0
5
Time
10
15
Fig. 10. Power system response for operation point 1 (Nominal loading) under ΔPe2fer=0.1 pu; Solid (GAMSF) and Dashed (Conventional)
x 10-4
1.5
8
0.1
6
0.08
ΔVdc
0.5
0
-0.5
-1
-1.5 0
5
Time
10
15
0.12
ΔPe
10
1
Δw
x10-3
2
4
0.06
2
0.04
0
0.02
-2 0
5
Time
10
15
00
5
Time
10
Fig. 11. Power system response for operation point 5 (Heavy loading) under ΔPe2fer=0.1 pu; Solid GAMSF) and Dashed (Conventional)
149
15
International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
0.015
0.15
2
0.1
1.5
0.01
0
0.1
0
ΔPe
ΔVdc
Δw
1
0.05
0.005
-0.05
-0.005
-0.5
-0.1
-0.01
-1
-0.15
-0.015 0
5
Time
10
-1.5
-0.2 0
15
0
5
Time
10
15
-2 0
5
Time
10
15
Fig. 12. Power system response for operation point 7 (Very heavy loading) under ΔTm =0.1 pu; Solid (GAMSF) and Dashed (Conventional)
It can be seen that the proposed GAMSF controller is very
effective, achieve good robust performance and compared to CDC
have the best ability to reduce power system low frequency
oscillations.
To demonstrate the performance robustness of the proposed
control strategy, the Integral of the Time multiplied Absolute value of
the Error (ITAE) and Figure of Demerit (FD) based on the system
performance characteristics are being used as:
ITAE =
∫
20
0
( w1 Δ Pe 2 + w 2 Δ V dc + w 3 Δ ω ) ⋅ tdt
FD = ( OS Δ w × 2500 ) + (US Δ w × 2500 ) + T
2
2
V. CONCLUSIONS
In this paper, a new multi stage fuzzy PID type controller based on
GAs is proposed for the UPFC DC-voltage regulator for damping
power systems low frequency oscillations. In order for a fuzzy rule
based control system to perform well, the fuzzy sets must be carefully
designed. A major problem plaguing the effective use of rule based
fuzzy control system is the difficulty of accurately constructing the
membership functions. Because it is a computationally expensive
combinatorial optimization problem. For this reason, a modified GA
based on the hill climbing method is used to optimally tune of the
membership functions automatically to reduce the fuzzy system
effort and cost. The proposed control strategy combines advantage of
fuzzy PD and integral controllers with a fuzzy switch and leads to a
flexible controller with simple structure which requires fewer
resources to operate and its role in the system response is more
apparent. Thus, its construction and implementation are fairly easy,
which can be useful in real world power system. The effectiveness of
the proposed controller has been tested on a SMIB power system in
comparison with the conventional UPFC controllers under different
operating conditions. The following conclusions can be drawn about
the proposed method.
(16)
2
s
Where, w1=1 and w2=w3=1000, Overshoot (OS), Undershoot
(US) and settling time of frequency deviation is considered for
evaluation of the FD. The values of ITAE and FD are calculated for
the different loading conditions as given in Appendix. Tables 4 and 5
show the damping performance of the GAMSF and classical
controllers. Examination of these Tables reveals that in comparison
with the PI controller, the system performance is significantly
improved by the GAMSF controller designed for UPFC DC-voltage
regulator in this paper against the loading conditions changes.
TABLE IV
PERFORMANCE INDEX OF ITAE
Operating
Pe=0.1
conditions MFPID
1
2
3
4
5
6
7
17.9
13.1
17.1
16.5
18.8
12.8
13.4
PI
158.1
41.3
122.3
118.3
198.3
41.2
Unstable
1. Due to non-model base, it can be used to control a wide range of
complex and nonlinear systems.
2. It is effective and ensures robust performance for a wide range
operating conditions.
3. It dose not require an accurate model of the power system, has
simple structure and easy to implement.
4. The system performance characteristics in terms of ‘ITAE’ and
‘FD’ indices reveal that this control strategy is a promising
control scheme for damping power system low frequency
oscillations.
Tm=0.1
MFPID
PI
12.5
16.6
18.4
17.4
27.5
16.1
43.2
276
314.2
678.3
934.2
3539.9
284.6
Unstable
TABLE V
PERFORMANCE INDEX OF FD
Operating
Pe=0.1
conditions MFPID
1
2
3
4
5
6
7
0.21
0.17
0.08
0.08
0.02
0.21
0.0230
PI
1.37
1.04
0.24
0.28
0.29
1.34
Unstable
APPENDIX: POWER SYSTEM DATA
Tm=0.1
MFPID
PI
5.6
7.5
17.5
17.9
61.1
5.9
88.3
The operating conditions and nominal parameters of the
system are listed in Tables 6 and 7. The uncertainty area for
active and reactive power ranges as: 0.7 ≤ P ≤ 1.15 and
84.6
106.7
273.9
361.2
374.9
76.5
Unstable
0 . 1 ≤ Q ≤ 0 .3 .
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International Journal of Electrical Power and Energy Systems Engineering 1;3 © www.waset.org Summer 2008
TABLE VI
OPERATING CONDITIONS
1) Nominal load
P=0.80
Q=0.15
2
P=0.90
Q=0.17
3
P=1.00
Q=0.20
4
P=1.10
Q=0.28
Vt=1.032
Vt=1.032
Vt=1.032
Vt=1.032
5) Heavy load
P=1.125
Q=0.285
Vt=1.032
6
7) Very heavy load
P=0.70
P=1.15
Q=0.10
Q=0.30
Vt=1.032
Vt=1.032
Generator
TABLE VII
SYSTEM PARAMETERS
′ = 5.044 s
M = 8 MJ/MVA Tdo
X q = 0.6p.u
Excitation system
Transformers
Transmission line
X d = 1pu
X d′ = 0.3pu
D=0
K a = 10
Ta = 0.05s
X = 0.1 pu
X E = 0.1 pu
T
X B = 0.1 pu
X = 1pu
L
P = 0.8 pu
V = 1.0 pu
V = 1.0 pu
DC link parameter
V DC = 2 pu
C
δ = -78.21
UPFC parameter
m = 0.08
δ = -85.35
Ks = 1
Operating condition
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b
t
B
D
E
DC
= 1 pu
D
B
m = 0.4
E
Ts = 0.05
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H. Shayeghi received the B.S. and M.S.E. degrees in Electrical Engineering from KNT
and Amirkabir Universities of Technology in 1996 and 1998, respectively and the PhD
degree in Electrical Engineering from Iran University of Science and Technology
(IUST), Tehran, Iran, in 2006. Currently, He is an Assistant Professor at Technical
Engineering Department of University of Mohaghegh Ardabili, Ardabil, Iran. His
research interests are in the application of Robust Control, Artificial Intelligence to load
forecasting, power system control design and power system restructuring. He is a
member of Iranian Association of Electrical and Electronic Engineers (IAEEE) and
IEEE and WASET.
151