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A neuro-fuzzy controller for grid connected heavy duty gas turbine power plants
Mohamed Mustafa MOHAMED IQBAL
1,*
, Rayappan JOSEPH XAVIER
2
, Jagannathan
KANAKARAJ 3
1, 2
Department of Electrical & Electronics Engineering, Sri Ramakrishna Institute of
3
Technology, Coimbatore, Tamilnadu, India
Department of Electrical & Electronics Engineering, PSG College of Technology,
Coimbatore, Tamilnadu, India
*Correspondence: mohdiq_m@yahoo.co.in
9 Abstract: Frequent load fluctuation and set point variation may affect the stability of grid
10 connected Heavy Duty Gas Turbine power plants. To overcome such problems, a novel
11 neuro-fuzzy controller has been proposed in this paper for single-shaft heavy duty gas
12 turbines ranging from 18.2MW to 106.7MW. Neuro-fuzzy controller is developed using
13 hybrid learning algorithm and the effectiveness of the controller for all heavy duty gas
14 turbine plants (5, 6, 7 and 9 series) is demonstrated against the load disturbance and set
15 point variation in grid connected environment. Various time domain specifications and
16 performance index criteria of neuro-fuzzy controller are compared with that of fuzzy logic
17 controller and artificial neural network controller. The simulation results indicate that the
18 neuro-fuzzy controller yield optimal transient and steady state responses and tracks the
19 set point variation faster than fuzzy logic or artificial neural network controller. Hence
20 the neuro-fuzzy controller is identified as an optimal controller for the heavy duty gas
21 turbine plants. The neuro-fuzzy controller proposed in this paper is also applicable to the
22 latest derivative speedtronic control also.
23 Key words: Artificial neural network controller, Fuzzy logic controller, Heavy duty gas
24 turbine, Neuro-fuzzy controller, Simplified model, Speedtronic governor
1

1
2
3
1.
Introduction
Electrical power generation from biomass based gas turbine power plants has become attractive, because of the huge availability and the developments in gasifier technology
4
5
6
[1].
Heavy Duty Gas Turbine (HDGT) has numerous advantages such as less commissioning time, fast startup time, efficient energy conversion, flexibility for variety of fuels etc. [2]. The gas turbines are broadly classified as single-shaft and twin-shaft gas
7
8 turbine based on their construction and the governor used [3]. Since, renewable energy sources have also increased the system fluctuation, an effective control is required for the
9 renewable energy based systems [4-8]. Attempts were made to analyze the performance
10 of combined cycle gas turbine plants using Model predictive controller, robust controller
11 etc. [9, 10]. Further literature also reveals that the performance of grid connected gas
12 turbine plants in simple cycle operation need to be analyzed [11-14].
13 The authors had developed the fixed gain and self-tuning Proportional Integral
14 Derivative (PID) controller for the HDGT plants. On analyzing the results, Fuzzy self-
15 tuning PID controller was found to be more adaptive for the grid connected operation
16 [15]. The latest derivative of Mark V Speedtronic governor control system uses
17 Microprocessor for protection and control [16]. Since the Soft computing techniques
18 based controllers can be embedded with Microprocessor easily, it becomes a viable option
19 for the speedtronic governor controlled HDGT plants. Balamurugan et al. had developed
20 Artificial Neural Network (ANN) controller and Fuzzy Logic Controller (FLC) for only
21 7001E a model of HDGT [17]. But these controllers cannot be optimal until the response
22 of all the HDGT plants are analyzed. Also the input and output scaling gains of FLC had
23 not been adjusted by any optimization algorithm and hence this FLC cannot be an
24 adaptive controller. Therefore the authors have developed the ANN and FLC for all
2

1 HDGT plants in this paper overcoming these drawbacks. The literature survey on soft
2
3 computing techniques reveals that an excellent learning feature of ANN and the rule base feature of FLC can be combined to develop the adaptive controller [18, 19]. As the
4
5
6 frequent load fluctuation and set point variation may affect the stability, a novel Neuro-
Fuzzy Controller (NFC) has also been proposed in this paper for the grid connected
HDGT plants. Since the turbine speed of HDGT models developed by General Electric
7
8
Co., are limited between 95 to 107 percentage of rated speed [3], the effectiveness of the
NFC, FLC and ANN controllers are being demonstrated and an optimal controller
9 identified for the heavy duty gas turbine plants.
10 2.
Simplified Gas Turbine Model
11 Figure 1 shows the standard configuration of simple cycle gas turbine plant in grid
12 connected operation. The output power generated by the synchronous generator can be
13 controlled by the fuel input to the combustor. Rowen proposed the transfer function model
14 for analyzing a simple cycle operation of Speedtronic Governor based HDGT plants [3].
15 It includes three limiters namely speed, acceleration and temperature along with fuel
16 system and turbine dynamics. The acceleration limiter is useful only during startup time
17 and the temperature limiter takes the control action only when the exhaust temperature
18 exceeds the limit. Because of the less influence of these limiters during normal operation,
19 they have been eliminated. Speed control loop with speed governor and fuel system
20 dynamics has been identified as the predominant control loop [17]. The speed governor
21
22
23 as expressed in Equation (1) is a lag-lead compensator for deciding the fuel demand signal,
Wd
based on speed error, e
.
Wd(s) =
W(Xs+1)
Ys+Z
. e(s)
(1)
3

1 Droop governor mode was identified as a suitable mode for grid connected
2
3 operation [20]. Further the authors had optimized the speedtronic governor droop setting using Genetic Algorithm and it was found to be around 4 percent for all HDGT plants
4
5
6
[21]. For self-sustaining of gas turbine under no-load operation, fraction of rated fuel approximately 23 percentage is required [3].
Fuel system control includes valve positioner and fuel system actuator blocks, whose transfer function models are shown in
7
8
9
10
11
12
Equations (2) and (3) respectively.
Vp(s) = a bs+c
. Wd(s)
(2)
Wf2(s) =
1
1+s T
. Vp(s)
(3)
Based on fuel supply, Wf2 and the actual turbine speed, N, the turbine torque is
13 computed using a function, F2. The rotor time constant, T1 of HDGT models varies from
14 12.2 to 25.2. The simplified model of HDGT for simple cycle operation is shown in
15 Figure 2. Model parameters of various blocks in the simplified model are described in
16 [15, 17]. Because of the drooping nature of the speed governor, the steady state response
17 of HDGT models are found to be poor [17]. In order to improve the dynamic as well as
18 steady state responses, the controller has to be developed for maintaining stable operation
19 by controlling the fuel flow. Moreover the controller is required to be faster enough to
20 take control action during disturbances. The main purpose of this work is to identify an
21 optimal controller which can satisfy the controller requirement of the HDGT plants.
22 Therefore, ANN, FLC and NFC controllers are developed for the HDGT as presented in
23 Sections 3, 4 and 5 respectively and the responses are compared in Section-6 .
24 3.
Artificial Neural Network
25 McCulloch Pitts introduced the simplified neuron in the year 1943, since then the interest
26 on neural network has emerged and the ANN controller had been developed for many
4

1 applications [22-24]. ANN controller developed in this paper is a feed forward network
2
3 consisting of input layer, hidden layer and output layer as shown in Figure 3. Back propagation algorithm is used for learning while developing ANN controller for HDGT
4
5
6 plants. Two hidden layers namely hidden layer-1 and hidden layer-2 respectively have 28 and 15 no. of neurons with the bias values B
1
and B
2 as 1.0.
Totally 166 input-output patterns are collected based on the prior knowledge of
7
8 the plant with the conventional controller. Out of the total data patterns, 116 data patterns are selected randomly for training the neural network and the remaining 50 data patterns
9 are used for testing of neural network. The activation functions considered for the hidden
10 and output layers are Tansig and Purelin respectively. The network is trained upto 100
11 epochs with the learning rate of 0.5 for the goal of 0.005 by gradient descent method.
12 Then the ANN controller is implemented in the MATLAB/Simulink of HDGT plants and
13 the input and output signals of ANN controller are normalized by the scaling gains using
14 simplex search algorithm in order to maintain stable operation [25]. Then the step
15 response of HDGT models are analyzed as presented in Section 6.
16 4.
Fuzzy Logic Controller
17 Fuzzy logic is based on fuzzy set theory which was first introduced by Lotfi.A.Zadeh in
18 the year 1965. It gained widespread acceptance in various applications viz., modeling,
19 design and analysis of control and power system problems etc. [26-28]. Two inputs and
20
21
22
23 one output Sugeno fuzzy inference system have been used in this work to develop FLC for all the HDGT models [29]. The speed error, ‘ 𝐞 ’ and change in speed error, ‘ 𝐜𝐞 ’ are chosen as the input signals and control signal, ‘
𝐂 ’ is considered to be an output signal of
FLC as given in Figure 4. The scaling gains,
𝐆 𝐞
,
𝐆 𝐜𝐞
and
𝐆 𝐨
have been used to normalize
24 the input and output signals by simplex search algorithm [25].
5

1 Triangular membership function and constant membership function are chosen for
2
3 the input signals and the output control signal respectively. Seven fuzzy sets namely,
Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive
4
5
Small (PS), Positive Medium (PM) and Positive Big (PB) are used for both the input and
6 output membership functions [17]. From the expert knowledge about HDGT performance, the range of membership functions for ‘ e ’, ‘ ce ’ and ‘ C ’ are selected as [0,
7
8
1], [-1, 0] and [-1, 1] respectively. Table 1 shows totally 49 fuzzy rules for developing the
9
FLC. Fuzzy IF-THEN rules are characterized by an appropriate fuzzy set and membership function in the form: IF e
is NB AND ce
is NB, THEN
C
is NB.
10
11
12
The output signal has been obtained by fuzzification, rule evaluation and defuzzification procedures [29]. Initially the speed error ( e
) and change in speed error
( ce
) signals have been fuzzified and the antecedent of each fuzzy rule is evaluated using
13 fuzzy operator (PROD). Then the consequent part of each fuzzy rule has been arrived by
14 using the implication operator (MIN). Further, all the output fuzzy sets are combined
15 using aggregation operator (MAX). The output control signal of FLC has been obtained
16 by defuzzifying the aggregated output fuzzy set by using weighted average (WTAVER)
17 method. By the same procedure, FLC for all the HDGT are developed and the step
18 responses are compared as presented in Section 6.
19 5.
Neuro-Fuzzy Controller
20 Neuro-Fuzzy System based control logic has gained an advantage by combining the rule
21 base feature of fuzzy logic and an efficient learning ability of neural networks [30]. Since
22 the Neuro-Fuzzy Controller (NFC) is developed from the input-output data patterns and
23 rule base of the HDGT plants, a predetermined model structure is not required.
24 Application of learning algorithm in Neuro-Fuzzy system through neural network also
6

1 helps to visualize the changes in error signal which are useful in updating the parameter
2
3
[31]. Takagi, Sugeno, Kang (TSK) network has been found superior than Mamdani network in terms of network size and the learning accuracy. The gradient method based
4
5 learning rule has the tendency to get trapped into local minima. Therefore, TSK network based NFC has been developed for HDGT plants by hybrid learning algorithm.
6
7
5.1.
Architecture of Neuro-Fuzzy System
8
9
Neuro-Fuzzy based controller can be designed by properly selecting the input and output signals to represent the dynamic behavior of the system [30]. Speed error ‘ 𝐞 ’ and change in speed error ‘ 𝐜𝐞 ’ have been used as the input signals and ‘ 𝐂 ’ as the output signal for
10 NFC in this work. The basic architecture of Type-3 Neuro-Fuzzy for the following two
11
12
13
14
IF-THEN rules of TSK type are shown in Figure 5 [19].
Rule 1: IF ( 𝐞
is X
1
) and ( 𝐜𝐞
is Y
1
) THEN
(𝐟
𝟏
= 𝐚
𝟏 𝐞 + 𝐛
𝟏 𝐜𝐞 + 𝐫
𝟏
)
Rule 2: IF ( 𝐞
is X
2
) and ( 𝐜𝐞
is Y
2
) THEN
(𝐟
𝟐
= 𝐚
𝟐 𝐞 + 𝐛
𝟐 𝐜𝐞 + 𝐫
𝟐
)
The neuro-fuzzy architecture has five layers out of which the square nodes (Layers
15 1 and 4) are the adaptive nodes and circle nodes (Layers 2, 3 and 5) are the fixed nodes.
16 The nodes of layer 1 has modifiable parameters (premise parameters) pertaining to the
17
18
19
20 input membership functions and calculate the degree of membership functions for the inputs, ‘ e ’ and ‘ 𝐜e ’. Here, X i
, Y i
are the linguistic variables of ‘ e ’ and ‘ ce ’ respectively and the output control signal of i th node of j th
layer in the neuro-fuzzy model is denoted by
O
Lj.i
. The i th
node output of Layer-1 are the membership functions,
μ
X i
(e)
and
μ
Y i
(ce)
21
22
23 as represented in Equations (4) and (5) [19].
O
L1,i
= μ
X i
(e)
; i=1 and 2
O
L1,i
= μ
Y i
(ce)
; i=3 and 4
(4)
(5)
7

1
2
3
4
5
6
7
8
9
The nodes in layer 2 denoted as ‘P’ multiplies their input in order to compute the firing strength of the rule,
W i
as expressed in Equation (6) [19].
O
L2,i
= W i
= μ
X i
(e) × μ
Y i
(ce)
; i=1 and 2 (6)
The layer 3 node denoted as ‘N’ normalizes the firing strength calculated by layer
2 nodes. The normalized firing strength,
W i is the ratio between the i th
rule firing strength,
W i
and the sum of
W
1
and
W
2 as given in Equation (7) [19].
O
L3,i
= W i
=
W i
W
1
+ W
2
; i=1 and 2 (7)
The normalized firing strength and first order polynomial ( f i ) of the consequent parameters ( a i , b i and r i ) are multiplied as in Equation (8) to obtain the output of layer 4
10 nodes [19].
11
O
L4,i
= W i
f i
= W i
(a i e + b i ce + r i
)
; i=1 and 2 (8)
12 At the layer 5, the layer 4 outputs are summed up and the overall output (C) of the
13 NFC is obtained as shown in Equation (9). The overall output of NFC can be represented
14 in expanded form and generalized form as Equation (10) and (11) respectively [19].
15
16
17
O
L5
= C = ∑ W i
f i
= (w
1 1
+ w
2 2
)
C = [
W
1
W
1
+W
2
] (a
1 e + b
1 ce + r
1
) + [
W
1
W
2
+W
2
] (a
2 e + b
2 ce + r
2
)
C =
∑ W i f i
; i=1 and 2
(9)
(10)
(11)
18 5.2.
Design Procedure
19 ANFIS editor in MATLAB has been used to develop NFC in three stages namely ‘load
20 data’, ‘generate Fuzzy Inference System (FIS)’ and ‘train FIS’ [31, 32]. Initially, the
21 input-output data patterns, 145 in total are identified based on prior knowledge of the
22 HDGT models. From the data patterns, 70 percent (102 data pairs) are chosen randomly
23 for training and loaded in Editor Window. The remaining 30 percent (43 data pairs) are
8

1 used for testing of the network. Then a grid partitioning scheme is selected for generating
2
3
FIS and constant MF is chosen for the output signal. Seven fuzzy sets namely, Negative
Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS),
4
5
6
Positive Medium (PM) and Positive Big (PB) as shown in Figures 6 and 7 are chosen for the input and output signals respectively. The range of MF for the ‘e’, ‘ce’ and ‘C’ signals are considered to be [0, 1], [-1, 0] and [-1, 1] respectively. Then the hybrid learning
7
8 algorithm is selected as the optimization method and the FIS is trained upto 100 epochs with the error tolerance of zero.
9 Because of the simplest approach, computational efficiency and easy
10 implementation, Triangular Membership Function (MF) was preferred for the motor
11 control application [33]. In this paper, both the Triangular and Trapezoidal MFs are
12 considered for the input signals and the training and testing error values for 5001M,
13 7001Ea and 9001Ea models are compared as shown in Table 2. It reveals that both the
14 training and testing error values are less for the triangular input MF than trapezoidal MF.
15 Therefore the FIS is created for the HDGT models by considering the triangular MF for
16 the input signals. Then the trained FIS is used in the MATLAB/Simulink and the step
17 response of the HDGT models with NFC are compared with that of FLC and ANN
18 controllers as illustrated in Section 6.
19 6.
Simulation Results and Discussion
20 ANN, FLC and NFC as described in Section 3, 4 and 5 respectively are developed for the
21 HDGT models. The step response with an optimal droop setting of 4 percentage is
22 obtained against the load disturbance and set point variation. Since the performance of all
23 the HDGT models are nearly similar with these controllers, 5001M, 7001E a and 9001E a
24 HDGT alone are considered for the analysis. The simulation results are compared based
9

1
2 on maximum peak overshoot (
𝐌𝐩
), rise time (
𝐓𝐫
), settling time (
𝐓𝐬
) and steady state error (
𝐄𝐬𝐬
). Integral of Squared error (ISE) and Integral of Time multiplied with Squared
3
4
7
8
9
Error (ITSE) as shown in Equations (12) and (13) are also being used as the performance
5
6 evaluation indices to analyze the response of the HDGT models.
𝐐
𝐈𝐒𝐄
= ∫ 𝐞 𝟐 𝐝𝐭
𝐐
𝐈𝐓𝐒𝐄
= ∫(𝐞 𝟐 ) 𝐭 𝐝𝐭
(12)
(13)
Initially the MATLAB/Simulink model of 5001M, 7001E a
and 9001E a
models are simulated upto 10 seconds for a unit step load disturbance applied at time, t=1.0 second and the step responses are shown in Figures 8, 9 and 10 respectively. The respective time
10 domain specifications and performance indices are shown in Table 3. It is found that the
11 steady state offset is almost zero by using all these controllers. ANN controller requires
12 more time to reach the steady state value. However, the FLC improves both the dynamic
13 and steady state response than ANN controller. The settling time of the models using FLC
14 are found to be less than 1 second. The simulation results also convey that the NFC
15
16 proposed in this paper improves the dynamic and steady state response. It is also found that the NFC reduces the offset and overshoot (
𝐌𝐩
). The values of ‘
𝐓𝐫 ’ and ' 𝐓𝐬 ’ have
17 decreased very much by using NFC and hence the steady state response is reached faster
18 than FLC and ANN controllers. The performance evaluation indices of the HDGT models
19 with NFC are also found to be lesser than that of FLC and ANN controllers. It confirms
20 that the proposed NFC yield an optimal transient and steady state response.
21 The responses of NFC, FLC and ANN controllers are obtained against the set point
22 variation and the effectiveness demonstrated.
Four set points with the magnitudes 1.0 p.u.,
23 1.05 p.u., 1.0 p.u. and 0.95 p.u. are set at 0, 10, 20 and 30 seconds respectively and the
24 MATLAB/Simulink model of HDGT plants are simulated upto 40 seconds. Figures 11,
10

1 12 and 13 respectively show the peak step response of 5001M, 7001E a
and 9001E a
models
4
5
6
2
3 against these set point variation. It reveals that the NFC tracks the set point variation and reaches the steady state response faster than FLC and ANN controllers. The performance indices of 5001M, 7001E a
and 9001E a
models at these set points are shown in Table 4. It indicates that the NFC performs better than that of FLC and ANN controllers for all set point variation. Even though the latest derivative Mark-VI and Mark-VIe system has an
7
8 additional feature viz., backup protection and Ethernet based I/O communication respectively, all these versions use microprocessor based logic for the turbine control [34,
9 35]. Therefore, the NFC algorithm proposed in this paper can also be applied to the newer
10 versions of speedtronic control system, in order to avoid inevitable shutdown in grid
11 connected environment.
12 7.
Conclusions
13 The dynamic simulation model has been derived for the grid connected HDGT plants.
14 The soft computing controllers have been implemented with MATLAB/Simulink model
15 of HDGT plants and analyzed their behavior against the load disturbance. Triangular
16 membership function has been identified as an effective membership function type for
17 the NFC. Eventhough the transient and steady state responses are improved by ANN,
18 FLC and NFC controllers, the comparative results witness that the NFC impart greater
19 improvement than FLC and ANN controllers.
20 Further, the effectiveness of the controllers have been tested against the setpoint
21 variations at different intervals. The time domain specifications and performance
22 evaluation indices convey that the NFC responds faster for all setpoint variations and
23 helps to reach the steady state equilibrium faster. The performance indices confirm that
24 the NFC yield optimal transient and steady state response. Since the set point in grid
11

1 connected operation is a frequently varying parameter and the NFC satisfy the control
2
3 requirement, the NFC proposed in this work is identified as an optimal controller for the grid connected HDGT plants.
4
5
6
The overall analysis of HDGT plants with soft computing controllers indicates that the NFC is able to maintain stable operation for all HDGT models irrespective of the rotor time constants. NFC proposed in this paper can also be applied to the latest
7
8 derivative speedtronic governor control system of HDGT plants in grid connected operation.
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[34] Barker W, Cronin M. SPEEDTRONIC™ Mark VI Turbine Control System. GE
Power Systems GER-4193A. Oct. 2000, 1-14.
[35] Dey N. Managing an Effective Centralized Control Room for Brown Field Projects in Gas Plant. In: International Petroleum Technology Conference; 6-9 December
2015; Doha, Qatar.
Fuel
Compressor
Inlet Air
Figure 1.
Combustor
Gas Turbine
Exhaust gas
Synchronous
Generator
3φ Mains
Gear Box
Gas turbine power plant in grid connected mode
Reference
Speed
+
_ e
Actual
Speed
Speed
Controller
N
Speed Governor
𝑊(𝑋𝑠 + 1)
(𝑌𝑠 + 𝑍)
0.23
0.77
Load torque
+
+
Rotor
Dynamics
_
1
𝑇1𝑠
Figure 2.
Td
Turbine torque
F2
Wf2
N
Simplified model of HDGT plant for simple cycle operation
+
Valve Positioner
Wd 𝑎
(𝑏𝑠 + 𝑐)
Vp
Fuel System
1
(1 + 𝑠 𝑇)
Wf2
16

15
16
17
1
2
3
10
11
12
13
14
6
7
8
9
4
5
B
1
Hidden
Layer-1
1
Hidden
W i,j
Layer-2
1
Speed error, e
Input
Layer
W
1,i
2 p
2 q
B
2
W j,1
Control output
Output
Layer
Figure 3.
Architecture of ANN controller for HDGT plants
Actual
Speed
Reference
Speed
+
_
G e e e 𝑑𝑢 𝑑𝑡 G ce ce
Fuzzy
Logic
G
Controller o
C
To Speed
Governor
Figure 4. Simulink model of FLC for HDGT plants
Error (e)
NB NM NS Z PS PM PB
NB NB NB NB NM NM NS
NM NB NB NM NM NS Z
NS NB NM NS NS Z
Z
PS
PS PM
Z NM NM NS Z
PS NM NS Z PS
PS PM PM
PS PM PB
PM NS Z PS PM PM PB PB
PB Z PS PM PM PB PB PB
Table 1.
Fuzzy rule base of FLC for HDGT plants
17

3
4
5
6
7
1
2
Speed error, e
Change in
Speed error, c e
X
1
P
W
1
N
𝑊
1 e ce 𝑓
1
X
2 e ce
Y
1
Y
2
P
W
2
N
𝑊
2 𝑓
2
Layer-1 Layer-2 Layer-3 Layer-4
Figure 5. Architecture of neuro-fuzzy model
𝑊
1 1
𝑊
2 2
∑
C
To Speed
Governor
Layer-5
Model
Code
Training Error Testing Error
Triangular MF Trapezoidal MF Triangular MF Trapezoidal MF
8
9
10
11
12
13
14
15
16
17
18
19
20
5001M
7001E a
9001E a
0.00048264
0.00038364
0.00041512
0.013713
0.011343
0.014281
0.03249
0.028938
0.032519
0.73341
0.57125
Table 2. Training and testing error of NFC by triangular and trapezoidal MFs
1
NB NM NS Z PS PM PB
0.5
0
0.5
0
Universe of Discourse
1
NB
Figure 6. Input membership functions of NFC
NM NS Z PS PM
Universe of Discourse
Figure 7. Output membership functions of NFC
0.76533
PB
18

1
2
3
4
5
6
7
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5
Time in Second
6 7 8 9
Figure 8. Step response of 5001M model with NFC, FLC and ANN
NFC
FLC
ANN
10
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5
Time in Second
6 7 8 9
Figure 9. Step response of 7001E a
model with NFC, FLC and ANN
NFC
FLC
ANN
10
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5
Time in Second
6 7 8 9
Figure 10. Step response of 9001E a model with NFC, FLC and ANN
NFC
FLC
ANN
10
19

3
4
1
2
Time Domain Specifications
Model
Controller
Code
Mp Tr Ts Ess
(p.u.) (Sec) (Sec) (p.u.)
5001M
Q
Performance
Indices
ISE
Q
ITSE
NFC 0.0003 0.3829 0.6856 0.005 0.2566 0.0397
FLC 0.0007 0.4001 0.7359 0.0052 0.2743 0.0455
7001E
9001E a a
ANN 0.016 1.361 2.281 0.0002 0.7444 0.3429
NFC 0.0018 0.4055 0.7366 0.0064 0.2867 0.05
FLC 0.0067 0.4317 0.8099 0.0062 0.2939 0.0526
ANN 0.0191 1.4083 2.3605 0.0007 0.7467 0.3480
NFC 0.002 0.4322 0.7349 0.0019 0.2741 0.0442
FLC 0.0016 0.4321 0.7828 0.0026 0.2942 0.0512
ANN 0.0174 1.3783 2.2545 0.0005 0.7524 0.3508
Table 3.
Time domain specifications and performance indices of HDGT models
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8
0 5 10 15 20
Time in Second
25 30 35
Figure 11.
Response of 5001M model with controllers for various set points
NFC
FLC
ANN
40
20

6
7
8
3
4
5
9
10
11
12
1
2
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8
0
NFC
FLC
ANN
5 10 15 20
Time in Second
25 30 35
Figure 12.
Response of 7001E a
Model with Controllers for various set points
40
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8
0 5 10 15 20
Time in Second
25 30 35
Figure 13.
Response of 9001E a
model with controllers for various set points
NFC
FLC
ANN
40
21

Performance Indices at different Setpoints
Model
Code
For Set point-1.0 For Set point-1.05 For Set point-1.0 For Set point-0.95 p.u. p.u. p.u. p.u.
Q
ISE
Q
ITSE
Q
ISE
Q
ITSE
Q
ISE
Q
ITSE
Q
ISE
Q
ITSE
NFC 0.2566 0.0397 0.2577 0.0520 0.2588 0.0760 0.2600 0.1111
5001M FLC 0.2743 0.0455 0.2755 0.0583 0.277 0.0909 0.2785 0.1392
ANN 0.7444 0.3429 0.7488 0.3916 0.7512 0.4421 0.7536 0.5190
NFC 0.2867 0.05 0.2881 0.0662 0.2894 0.0943 0.2907 0.1347
7001E a
FLC 0.2939 0.0526 0.2953 0.0682 0.2968 0.1004 0.2982 0.1474
ANN 0.7467 0.3480 0.7497 0.3806 0.7519 0.4261 0.7542 0.4996
NFC 0.2741 0.0442 0.2748 0.0516 0.2760 0.0764 0.2772 0.1140
9001E a FLC 0.2942 0.0512 0.295 0.0601 0.2965 0.0921 0.2981 0.1402
ANN 0.7524 0.3508 0.7581 0.4153 0.7606 0.4671 0.7630 0.5446
1
2 Table 4. Performance indices of HDGT models for different set point variation
22