Applied mathematics in Engineering, Management and Technology 3(3) 2015:293-308
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Daming of local and inter-area oscillation for multi machine power
system with considered renewable energy
Homayon Ebrahimian1, Alireza Noruzi2, Mehdi Mirzaey1, Tohid Banki2
1- Department of Electrical Engineering, Ardabil Branch, Islamic Azad university, Ardabil, Iran
2- Department of Electrical Engineering, Bilesuvar Moghan Branch, Islamic Azad university, Bilesuvar Moghan, Iran
Abstract
In this paper a robust Power System Stabilizer (PSS) is proposed based on inverse
additive perturbation in a power system with wind farms. The proposed controller
designed by new modified Honey Bee Mating optimization namely Honey Bee
Mating Optimization (IHBMO) to achieve robustness of this strategy where the
optimization process is formulated based on an enhancement of system robust
stability margin. The designed optimal PSS is based on Fuzzy Logic Controller
(FLC). The effectiveness of the proposed technique is tested over ten macine 39
buses New England power system. Obtained results demonstrate the superiority of
proposed technique over conventional PSS.
Keywords: IHBMO, Fuzzy controller, PSS, Multi-machine.
NUMENCLUTURE
δ
ω
Pm
Pe
E'q
Efd
Te
T'do
KA
TA
vref
v
Rotor angle
Rotor speed
Mechanical input power
Electrical output power
Internal voltage behind x'd
Equivalent excitation voltage
Electic torque
Time constant of excitation circuit
Regulator gain
Regulator time constant
Reference voltage
Terminal voltage
I. INTRODUCTION
Some of the earliest power system stability problems included spontaneous power system oscillations at low
frequencies. These Low Frequency Oscillations (LFOs) are related to the small signal stability of a power
system and are detrimental to the goals of maximum power transfer and power system security. Once the
adjustment of using damper windings on the generator rotors and turbines to control these oscillations was
found to be satisfactory, the stability problem was thereby disregarded for some time [1]. But, as power systems
began to be operated closer to their consistency limits, the weakness of a synchronizing torque among the
generators was distinguished as a major cause of system instability [2]. Automatic Voltage Regulators (AVRs)
helped to improve the steady-state stability of the power systems, but transient stability started a concern for the
power system operators. With the development of large, interconnected power systems, another concern was the
transfer of large amounts of power across extremely long transmission lines. The addition of a supplementary
controller into the control loop, such as the introduction of Power System Stabilizers (PSSs) to the AVRs on the
generators, supplies the means to reduce the inhibiting effects of low frequency oscillations [3]. Most of the
time the PSSs and AVRs are locally controlled; which means that, the controller is designed to act on
measurements such as bus voltage, generator shaft speed, or rotor angle of the associated machine’s controls as
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presented in Fig. 1.
Figure 1.
Local Feedback Controller
In the recent years, renewable electrical energy such as wind power generations, have achieved a significant
level of penetration in the power systems due to infinite availability and low impact to environment. However,
wind power generation is staggering in nature. Matching the supply and the demand is often a problem. The
power output fluctuations from wind power generations cause a problem of low frequency oscillation,
deteriorate the system stability and make the power system operation more difficult. The power frequency and
the tie-line power deviations persist for a long term. In this status, the governor system may no longer be
capable to absorb the frequency fluctuations due to its slow response [4].
Actually, several plants prefer to employ conventional lead-lag structure PSSs, due to the ease of online tuning
and reliability [5]. However, the revenue of these controllers doesn’t have good behavior in different load
conditions. For this reason, a lot of intelligent algorithms have been introduced to optimal tuning of the PSSs
parameters such as Ant Colony (AC) [6], Genetic Algorithm (GA) [7], Particle Swarm Optimization [8],
Artificial Bee Colony [9] and etc.
The proposed algorithms are strong in optimization procedure but, they have some advantages and
disadvantages. For instance, GA is a powerful optimization technique, independent on the complexity of
problems where no prior knowledge is available. Also GA is very sufficient in finding global or near global
optimal solution of the problem, it requires a very long run time that may be several minutes or even several
hours depending on the size of the system under study [10-11].
The HBMO is a relatively new technique that has been empirically shown to perform well on many of these
optimization problems [5]-[7]. This optimization method has been widely applied to solve different problems
especially the locating problems in power system. Unfortunately, the standard HBMO algorithm often
converges to local optima, especially while handling problems with more local optima and heavier constraints.
This work presents the interactive strategy by considering the universal gravitation between queen and drone
bees for the standard HBMO algorithm to retrieve the disadvantages, which is called the IHBMO. In the other
word, the IHBMO introduces the concept of universal gravitation into the consideration of the affection
between drone bees and the queen bee within a honey bee colony. By assigning different values of the control
parameter, the universal gravitation should be involved for the IHBMO when there are various quantities of
drone bees and the single queen bee. The inverse additive perturbation is applied to represent unstructured
system uncertainties. For tuning the optimal rule base of fuzzy controller, the concept of enhancement of system
robust stability margin is formulated as the optimization problem. Also, the proposed IHBMO is considered as a
solution technique to problem. The obtained simulation results over ten machine-39 bus New England power
system demonstrate the robustness of the proposed strategy.
The remaining parts of the paper are organized as follows. In the second section, the formulation of power
system modeling is presented. The proposed controller structure is introduced in section three. The proposed
IHBMO and its application for the solution of the low oscillation problem with wind are presented in section
four. Obtained numerical results from New England power system are presented in section five and compared
with the other recently published methods. Section six concludes the paper.
II. PROBLEM STATEMENT
In this paper a multi-machine power system is considered as a test case where the third order model is presented
in [12]. Actually, the proposed power system consists of ten generators and the electrical and mechanical part of
ith generator is modeled as follow:
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.
 i (t )  w i (t )  w0
w0
D
( Pmi  Pei (t ))  i ( w i (t )  w0 )
Mi
Mi
.
1
E qi (t )  ' ( E fi (t )  Eqi (t ))
Tdoi
.
wi (t ) 
Eqi (t )  E 'qi (t )  ( xdi  xdi' ).I di (t )
Vti (t ) 
1 2 2
[ xsi Eqi  Vsi2 xqi2  2 xsi xdi xdsi Pei cot i ]1/2
xdsi
n
Pei (t )   Eqi' (t ) Eqj' (t )( B ij sin( ij (t ))  Gij cos( ij (t )))
j 1
n
Qei (t )   Eqi' (t ) Eqj' (t )(G ij sin( ij (t ))  Bij cos( ij (t )))
j 1
n
I di (t )   Eqj' (t )(G ij sin( ij (t ))  Bij cos( ij (t ))) 
j 1
n
I qi (t )   Eqj' (t )( B ij sin( ij (t ))  Gij cos( ij (t ))) 
j 1
Qei (t )
Eqi' (t )
Pei (t )
Eqi' (t )
Eqi (t )  xadi I fi (t )
Also, it can be presented after mathematical transformers where, ΔPe, Δw and ΔVt are quantities;
 S Ei  SVi
 .   T' S
  Pei   di Vi
 .   w0i
  wi    
Hi
 .  
  Vti   S  S
Vi

  Ei'
 Tdi RVi SVi

RVi S Ei 
 REi'


Tdi' SVi    Pei  

Td 0i 

 
 E fdi Where,
0    wi   0

  R' 
 Ei 
S    Vti  
  Td 0i RVi 
 ' Ei  
Tdi SVi 

S Ei'
Di
Hi
S Ei'  SVi
RVi
ΔPei is the state deviation in generator electromagnetic power for the ith subsystem
Δωi is the state deviation in rotor angular velocity for the ith subsystem,
ΔVti is the state deviation in the terminal voltage of the generator for the ith subsystem
S Ei 
S ' Ei 
EqiU si
X d i
cos  i  U si2
E 'qiU si
X 'd  i
X d i  X q i
cos  i  U si2
REi 
U si
sin  i
X d i
REi' 
U si
sin  i
X 'd  i
SVi  S Ei  RVi
X d i X q i
cos 2 i
X 'd  i  X q  i
X 'd  i X q  i
cos 2 i
U ti
V
, RVi  S Ei / ti
 i
Eqi
A. Mechanical Oscillation Frequency
The linearized rotor motion equation for synchronous generator can be described as:
TJ
d w
 Tm  Te  TD
dt
Where,
ΔTm is the mechanical input torque
ΔTe is the electromagnetic torque and ΔTe =K1Δδ+ K2Δδ,
By neglecting the K2ΔE’q the formulation can be described as; ΔTe =K1Δδ+ ΔTD
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D is the natural damping constant
Accordingly the above equation after Laplace transformer and Δw=sΔδ/w0 can be described as;
TJ
s 2 
s
  K1  D
w0
w0
Which can be described as;
TJ s 2  Ds  w0 K1  0
OR
s 2  2 n wn s  wn2  0
Accordingly, we can achieve the following equation from above equations;
 n  D / 2 w0TJ K1
wn  w0 K1 / TJ
Where,
ξn is the damping factor
wn is the undamped mechanical oscillation frequency
Usually the value of D is small, so the system damping is low. In order to enhance the system damping for
suppressing the low frequency oscillation, the positive damping term is added by PSS.
B. Power System Model
A 10-machine 39-bus power system with wind farms is considered as a test case for this paper which is
presented in Fig. 2. To assess the effectiveness and robustness of the proposed method over a wide range of
loading conditions, different operation conditions are considered. Details of the system data and operating
condition are given in Ref. [13]. The proposed power system is divided to four area with connected wind farm
as shown in Fig. 2.
Zone 1
Zone 3
G8
G10
28
8
29
10
PW3
26
25
9
31
G9
27
39
18
24
32
16
17
G6
G1
15
33
21
12
34
1
6
14
35
22
23
36
11
2
37
13
19
20
30
G2
7
38
3
PW1
4
5
G7
G4
G3
G5
Zone 2
PW2
PW4
Zone 4
Figure 2.
Structure of power system with wind farms
C. Wind power model
It is clear that the output power of wind generator depends on wind velocity. The wind speed model chosen in
this study consists of four-component model [14], that is defined as;
VW  VWB  VWG  VWR  VWN
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Where
WB V = Base wind velocity
WG V = Gust wind component
WR V = Ramp wind component
WN V = Noise wind component
The base wind velocity component is represented in literature as:
VWB  K B
Where KB is a constant and assumed to presenting the wind power. The gust wind velocity can be defined as;
VWG
0
t  T1G


 Vcos T1G  t  T1G  TG

t  T1G  TG
0
Where,
Vcos  (MAXG / 2) 1  cos 2 (t / TG )  (T1G / TG )
MAXG is the gust peak
TG is the gust period
T1G is the gust starting time
(1-cosine) gust is an essential component of wind velocity for dynamic studies
The ramp wind velocity component is described as:
VWG
0
t  T1R


 Vramp T1R  t  T2 R

t  T2 R
0
Where,
Vramp  MAXR[1  (t  T2G ) / (T1R  T2 R )]
MAXR is the ramp peak
T1R is the ramp start time
T2R is the ramp maximum time
This component may be used to approximate a step change with T2R >T1R. Also, the random noise component
can be described as:
N
VWN  2[ SV (i ) ]1/2 cos(i t  i )t  0
i 1
Where,
i  (i  1/ 2)
i is a random variable with uniform probability density on the interval 0 to 2π and the spectral density function
can be defined as:
2 K N F 2 [i ]
SV (i )  2
 [1  ( Fi /  )2 ]4/3
Where KN is the surface drag coefficient which is considered 0.004 and F is turbulence scale which is
considered 2000, and μ is the mean speed of wind at reference height. Various study have shown that values of
N=50, and Δω = 0.5-2.0 rad/s provide results of excellent accuracy.
D. Characteristic of wind generator output power
The output power of studied wind generator is expressed by a nonlinear function of the power coefficient Cp as
function of blade pitch angle, β, and tip speed ratio, γ. The tip speed ratio is presented as follow:
R

  blade Blade
VW
The power coefficient can be presented as:
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  (  3) 
CP  (0.44  0.0167  )sin 
  0.0184(  3) 
15  0.3 
At the end, the output of mechanical power for wind generator is:
PW 
1
 Ar CPVW3
2
Where, ρ (=1.25 kg/m3) is the air density and Ar (=1735 m2) is the swept area of blade.
III. FUZZY LOGIC CONTROLLER
In classical control, the value of control is determined in relation to a number of data inputs using a set of
equations to express the entire control process. Expressing human experience in the form of a mathematical
formula is a very difficult task, if not an impossible one. Accordingly, Fuzzy Logic Controller (FLC) provides a
simple tool to interpret this experience into reality [15]. FLCs are rule-based controllers with resembles
structure with a knowledge based controller except that the FLC utilizes the principles of the fuzzy set theory in
its data representation and its logic. The classic structure of FLC can be simply presented in Fig. 3.
Knowledge
Base
Decision
Making Logic
Slip
Figure 3.
Defuzzificatio
n Interference
Actual Control
Non Fuzzy
Process Output and
State
Fuzzification
Interference
Multi-machine Power
System Model
The conventional fuzzy controller structure
A set of fuzzy rules represents the FLC mechanism for adjusting the effect of certain system stimuli. Thus, the
aim of fuzzy control systems is to replace a skilled human operator with a fuzzy rules-based system. The FLC
also provides an algorithm which can convert the linguistic control strategy, based on expert knowledge, to
automatic control strategies.
Thus, to reduce fuzzy system effort cost, in this paper proposed an intelligent technique for optimal tuning of
fuzzy controller. Fig. 4, shows the structure of the proposed IHBMO-FPSS to improve power system stability.
IV. THE IHBMO TECHNIQUE
This section the standard HBMO briefly reviewed. For better illustration see ref [16]. At the start of the flight,
the queen is initialized with some energy content and returns to her nest when her energy is within some
threshold from zero or when her spermatheca is full. In developing the algorithm, the functionality of workers is
restricted to brood care, and therefore, each worker may be represented as a heuristic which acts to improve
and/or take care of a set of broods. A drone mates with a queen probabilistically using an annealing function as:
prob (Q , D )  e
 ( f )
S (t )
(7)
Where Prob (Q, D) is the probability of adding the sperm of drone D to the spermatheca of queen Q (that is, the
probability of a successful mating); ∆( f ) is the absolute difference between the fitness of D (i.e., f (D)) and the
fitness of Q (i.e., f (Q)); and S(t) is the speed of the queen at time t. It is apparent that this function acts as an
annealing function, where the probability of mating is high when both the queen is still in the start of her
mating–flight and therefore her speed is high, or when the fitness of the drone is as good as the queen’s [17].
After each transition in space, the queen’s speed, S(t), and energy, E(t), decay using the following equations:
S  t  1   HBMO  S  t 
(8)
E  t  1  E  t   γHBMO
(9)
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Where αHBMO(t) is speed reduction factor and γHBMO is the amount of energy reduction after each transition (α, γ
ϵ [0,1]).
Thus, HBMO algorithm may be constructed with the following five main stages:
Step 1: The algorithm starts with the mating flight, where a queen (best solution) selects drones probabilistically
to form the spermatheca (list of drones). A drone is then selected from the list at random for the creation of
broods.
Step 2: Creation of new broods by crossoverring the drones’ genotypes with the queen’s (Breeding process).
The breeding process can transfer the genes of drones and the queen to the jth individual based on the Equation
(10).
child  parent i  HBMO ( parent k  parent i ) (10)
Where βHBMO is the decreasing factor (βHBMO ~U (0, 1)).
Step 3: Use of workers (heuristics) to conduct local search on broods (trial solutions).
Step 4: Adaptation of workers’ fitness based on the amount of improvement achieved on broods as follows:
Brood ik  Brood ik  ( HBMO   HBMO )Brood ik
 HBMO  [0,1],0   HBMO  1
(11)
Step 5: Replacement of weaker queens by fitter broods.
The standard HBMO technique has a flexible and well-balanced mechanism to enhance the global and local
exploration abilities. The main disadvantage of the HBMO algorithm is the fact that it may miss the optimum,
not strong enough to maximize the exploitation capacity and provide a near optimum solution in a limited
runtime period. Nonetheless, the standard HBMO method is prosperous for finding best answer in optimization
problem. However, the algorithm makes use of an independent random, βHBMO ~U (0, 1). This factor used to
affect the stochastic nature of the standard HBMO algorithm, as shown in equation (14). In the other word, the
original Breeding process design of the drone bee’s movement only considers the relation between the queen
bee, which is selected by the mating wheel selection, and the one selected randomly. Hence, it is not strong
enough to maximize the exploitation capacity. In order to overcome this drawback, the Interactive Honey Bee
Mating Optimization (IHBMO) algorithm is proposed based on the structure of original HBMO algorithm. In
the other word, by employing the Newtonian law of universal gravitation described in the equation (12), the
universal gravitations between the queen bee and the selected drone bees are exploited. The gravitational force
between two particles (F12) with the mass of the first and second particles (m1 and m2), and the distance between
them (r12) can be expressed as:
F12  G
m1 m 2 ^
r21
r212
(12)
Where, G is gravitational constant. ˆr21 denotes the unit vector in the equation (13):
^
r21 
r2  r1
| r2  r1 |
(13)
In the optimization procedure with IHBMO algorithm, the mass 𝑚1 is replaced by the symbol, F(parenti), which
is the fitness value of the queen bee that picked by applying the mating wheel selection. The mass, 𝑚2, is
replaced by the fitness value of the randomly selected drone bee and is denoted by the parameter, F(parentk).
The universal gravitation in the equation (12) is formed in the vector format. Therefore, the quantities of it on
different dimensions can be considered separately. Hence, 𝑟21 is calculated by taking the difference between the
objects only on the concerned dimension currently and the universal gravitation on each dimension is calculated
separately. In other words, the intensity of the gravitation on different dimensions is calculated one by one.
Therefore, the gravitation on the jth dimensions between parenti and parentk can be expressed in the equation
(14). Finally, the equation (14) can be modified in iteration interval t with the equation (15):
Fik j  G
F ( parent i )  F ( parent k ) parent kj  parent ij
.
( parent kj  parent ij )2 | parent kj  parent ij |
(14)
child ij (t  1)  parent ij (t )  Fik j .[ parent ij (t )  parent kj (t )]
(15)
Extending the consideration of the universal gravitation between the drone bees, which is picked by the queen
bee, and more than one drone bees is achievable by adding different Fik.[ parentk – parenti] into the equation
(15). Thus, the gravitation Fik plays the role of a weight factor controlling the specific weight of [parentk –
parenti]. The normalization process is taken in order to ensure that Fik ~U (0, 1). Through the normalization of
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Fik the gravitational constant (G) can be deleted.
In general, the whole process of IHBMO algorithm can be summarized at the five main steps as follows:
1. Generate an initial population: In this step, an initial population based on state variable is generated,
randomly. That is formulated as:
D  [D1 , D 2 , D3 ,..., D n ]
Di  (d i1 , d i2 ,..., d im )
(16)
Where, dij is the jth state variable value of ith drone bee. For each individual (Di) the objective function values
are evaluated. The queen was chosen according to the best solution (minimum objective function value). The
other solutions which were generated during this phase became the drones to be used during the mating flight
(trial solutions). The speed of queen at the start and the end of a mating flight is generated in this step.
2. Flight matting: At the start of the flight mating, the queen flies with her maximum speed and energy. A
drone is selected from the population of drones with the largest prob(Q, D). The mating probability is calculated
based on the objective function values of the queen and the selected drone. If the mating is successful (i.e., the
drone passes the probabilistic decision rule), the drone's sperm is stored in the queen's spermatheca and the
queen’s speed and energy decay is reduced by Eqs. (12)-(13). Otherwise, the flight matting is continues until
the speed S(t) is less than a threshold d or the queen's spermatheca gets full.
3. Breeding process: In this step, a population of broods is generated based on mating between the queen bee
and the drone bees stored in the queen's spermatheca. The generation of new broods is occurred by
crossoverring the drones’ genotypes with the queen’s. The jth brood is generated by using the equation (15).
4. Adaptation of worker‘s fitness: In this step, after new broods are generated, an attempt is made to improve
both the new solutions and the best solution by using of a mutation procedure as equation (10):
5. Replacement of weaker queens by fitter broods and Check the termination criteria: If the new brood is
better than the current queen, it takes the place of the queen. If the brood fails to replace the queen, then this
brood will be one of the drones in the next flight mating of the queen. Meanwhile, if the termination criterion is
satisfied then finish the algorithm. Otherwise, it discards all of the previous trial solutions (brood set) then the
generation of new drones is set and goes to stage 2.
FIX
FIX
Rule base
Slipi
Membership
functions
+

yrefi
d/dt
KI
Membership
functions
Inference
engine
Membership
functions

1/S

Defuzzier

_
Fuzzification
Rule base
Membership
functions
d/dt
Membership
functions

S
Defuzzier
Rule base
Fuzzification
Membership
functions

KD
Membership
functions
Inference
engine
Inference
engine
Fuzzification

Membership
functions
IHBMO
KP
Defuzzier
Fuzzy PID Controller
Figure 4.
Proposed Fuzzy Controller Structure
300
Efd
PSS

Excitation
∆
Generator
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V. SIMULATION RESULTS
In this paper, an IHBMO-FPSS is proposed, which combines the advantage of the IHBMO and fuzzy control
techniques to achieve good robust performance. It should be mentioned that obtaining the optimal decisionmaking logic for the proposed IHBMO fuzzy control strategy is very important to achieve the desired level of
robust performance [9], because it is a computationally expensive combinatorial optimization problem. Usually,
the rule-base sets are determined by experience and control knowledge of a human expert. However, experts
may not always be available and even when available it is a trial-and-error process that takes much time and
cost [9]. The results of the fuzzy rule-base sets are listed in Tables 1-3. In the proposed rule-base optimization
problem, the membership function sets for the KPi, KIi and Kdi are defined as triangular partitions with five
segments from 0 to 1 [18]. In this study the controllers are connected to G2 – G10 in the test system. Evaluation
of the Integral of the Time multiplied Absolute value of the Error (ITAE) and Figure of Demerit (FD) based on
the system performance characteristics are defined as [19]:
FD  (500 OS )2  (8000 US )2  0.01T s2
ITAE  100 
t sim
 t (|  |).dt
0
Where, Overshoot (OS), Undershoot (US) and settling time of the rotor angle deviation of the machine is
considered for evaluation of the FD. “Fig. 5”, shows the plot of obtained fitness function value.
OPTIMAL RULE-BASE FOR KII
NB
NS
PS
PB
NB
NM
PB
ZO
PB
NS
NM
NB
ZO
ZO
Z
PM
NM
PM
PM
PS
NS
PM
NS
NM
PB
PM
NB
NS
NS
TABLE II.
OPTIMAL RULE-BASE FOR KDI
NB
NS
PS
PB
NB
NS
NS
PB
NM
NS
PM
ZO
NB
ZO
Z
NM
NB
ZO
ZO
PS
NS
PM
PM
NB
PB
NM
NB
PM
NS
TABLE III.
OPTIMAL RULE-BASE FOR KPI
NB
NS
PS
PB
NB
NS
NS
PB
NM
NS
PM
ZO
NB
ZO
Z
NM
NB
ZO
ZO
PS
NS
PM
PM
NB
PB
NM
NB
PM
NS
TABLE I.
Fitness
0.7
0
Iteration
Figure 5.
100
Variations of the fitness functions
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The wind velocity in four area is presented in Fig. 6. Also, wind power generations are presented in Fig. 7, and
Fig. 8-10 shows tie-line power deviation in nominal load condition.
7.2
PW1
PW2
PW3
PW4
7
PW1
Wind Velocity (m/s)
6.7
6.3
6
5.7
5.5
5.2
5
50
100
200
Figure 6.
300
400
Time (sec)
500
600
700
Wind velocity
5.2
PW1
PW2
PW3
PW4
Wind power generation (pu)
4.6
PW1
4
3.2
2.6
2
1.4
0.8
0.2
50
100
Figure 7.
200
300
400
Time (sec)
500
600
700
Wind power generations
Scenario 1
In this paper two scenarios are presented to test the proposed control strategy in New England power system.
For the first scenario, it is very important that, the performance of the proposed controller is tested under
transient conditions by applying a 6-cycle three-phase fault or increasing the mechanical torque. So, in this
scenario a 6-cycle three-phase fault is applied in line 26-29 and bus 29. The responses of generators 1, 3, 7 and
9 are presented in Fig. 11. Also the numerical results of FD and ITAE are presented in Table 4.
Tie-line power deviation (pu) 1-2
0.07
0
-0.06
Figure 8.
50
100
200
400
300
Time (sec)
500
600
700
System response in first scenario under nominal load condition (Solid: Proposed, Dashed: CPSS,
Doted: No-PSS)
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Tie-line power deviation (pu) 1-3
0.07
0
-0.06
Figure 9.
50
100
200
400
300
Time (sec)
500
600
700
System response in first scenario under heavy load condition (Solid: Proposed, Dashed: CPSS, Doted:
No-PSS)
Tie-line power deviation (pu) 1-4
0.07
0
-0.06
Figure 10.
50
100
200
400
300
Time (sec)
500
600
700
System response in first scenario under light load condition (Solid: Proposed, Dashed: CPSS, Doted:
No-PSS)
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-3
x 10
1
Speed Division G1
0
-2
0
2
4
6
8
10
6
8
10
Time (sec)
-3
x 10
Speed Division G3
2
0
-2
0
2
x 10
2
Speed Division G7
4
Time (sec)
-3
0
-2
0
2
4
Time (sec)
6
8
10
2
4
Time (sec)
6
8
10
-3
x 10
Speed Division G9
1
0
-1
0
Figure 11.
Generators response at first scenario under nominal load condition (Solid: Proposed, Dashed: CPSS)
 Scenario 2
In the second scenario a 0.1 step is applied over the torque of generators. The tie-line response of power system
is presented in Fig. 13-15. Also, the responses of 1, 3, 7 and 9 generators are presented in Fig. 12-15. The
numerical results of FD and ITAE are presented in Table 5.
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Tie-line power deviation (pu) 1-2
0.07
0
-0.06
Figure 12.
50
100
200
400
300
Time (sec)
500
600
700
System response in second scenario under nominal load condition (Solid: Proposed, Dashed: CPSS,
Doted: No-PSS)
Tie-line power deviation (pu) 1-3
0.07
0
-0.06
Figure 13.
50
100
200
400
300
Time (sec)
500
600
700
System response in second scenario under heavy load condition (Solid: Proposed, Dashed: CPSS,
Doted: No-PSS)
Tie-line power deviation (pu) 1-4
0.07
0
-0.06
Figure 14.
50
100
200
400
300
Time (sec)
500
600
700
System response in second scenario under light load condition (Solid: Proposed, Dashed: CPSS, Doted:
No-PSS)
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x 10 -4
Speed Division G1
2
0
-
0
2
x 10
4
6
8
10
6
8
10
6
8
10
6
8
10
Time (sec)
-4
Speed Division G3
5
0
-
0
2
4
Time (sec)
x 10
-4
Speed Division G7
5
0
-5
0
x 10
2
4
2
4
-3
Time (sec)
Speed Division G9
1
0
-1
0
Time (sec)
Figure 15.
Generators response at first scenario under nominal load condition (Solid: Proposed, Dashed: CPSS)
TABLE. 4. CALCULATE OF FD AND ITAE FOR DIFFERENT LOAD CHANGES.
IHBMO
CPSS
Change load
ITAE
FD
ITAE
FD
25%
2.8293 1.6251 9.656 8.455
20%
1.1093 1.2543 8. 856 8.490
15%
1.1110 1.0137 8.890 8.466
10%
1.0123 1.0225 8.265 8.349
5%
1.0313 1.0129 8.853 8.763
Nominal
1.0113 1.2421 8.876 8.223
-5%
1.2413 1.2663 8.243 8.324
-10%
1.1542 1.2514 8.866 8.365
-15%
1.1652 1.2665 8.234 8.387
-20%
1.1334 1.1322 8.734 8.376
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-25%
2.1542 1.1652 9.029 8.376
TABLE. 5. CALCULATE OF FD AND ITAE FOR DIFFERENT LOAD CHANGES.
IHBMO
CPSS
Change load
ITAE
FD
ITAE
FD
25%
2.3411 1.0321 9.6947 8.3109
20%
1.0193 1.0302 8. 4771 8.0382
15%
1.0232 1.0203 8.4571 8. 6898
10%
1.0133 1.0243 8.4539 8.0117
5%
1.0322 1.0421 8. 5404 8.0446
Nominal
1.0244 1.0321 8.5069 8.0488
-5%
1.1093 1.0445 8.5294 8.0551
-10%
1.1034 1.0421 8.4432 8.0621
-15%
1.1033 1.1342 8.5570 8.0726
-20%
1.1045 1.1034 8.7436 8.1157
-25%
1.1135 1.1211 12.6553 8. 0117
IV. CONCLUSION
In this paper, a design scheme of robust PSS ten-machine New England power system using by considering
inverse additive perturbation in a power system with wind farms is presented through hybrid technique of fuzzy
controller and improved HBMO. By proposed IHBMO, the rule based of fuzzy controller is optimized to damp
power system oscillation where. The proposed technique is tested in various load condition for the solution of
the low frequency oscillation problem in power system. The proposed test case is compared with Classic PSS
through different load conditions and numerical results of ITAE and FD. Obtained numerical results and
simulation results demonstrate that the proposed strategy satisfied the stability of multi-machine power system.
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