chapter 6 anfis based neuro-fuzzy...

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CHAPTER 6

ANFIS BASED NEURO-FUZZY CONTROLLER

6.1 INTRODUCTION

The quality of generated electricity in power system is dependent

on the system output, which has to be of constant frequency and must

maintain the scheduled power and voltage. The dynamic behaviour of the

system depends on disturbances and on changes in the operating point. The

unsteady nature of wind and frequent change in load demands may cause

large and severe oscillation of power for the considered wind-micro hydro-

diesel hybrid power system. In this Thesis, the supplementary controller for

LFC of the diesel generating unit takes care of sudden load changes and

maintains the system frequency, and the supplementary controller for BPC

takes care of the wind input variation and maintains the wind power

generation.

In the proposed work, Adaptive Neuro-Fuzzy Inference system

based Neuro-Fuzzy Controller (NFC) is designed individually for both

governor in diesel side and blade pitch control in wind side for performance

improvement of the wind-micro hydro-diesel hybrid system. This newly

developed control strategy combines the advantage of Neural Network and

Fuzzy Inference System and has simple structure that is easy to implement. In

order to keep system performance near its optimum, it is desirable to track the

operating conditions and use the updated parameters to control the system.

This work investigates the performance of wind-micro hydro-diesel hybrid

power system using ANFIS based NFC for LFC and BPC by simulation.

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This chapter is organized as follows. Section 2 describes the

introduction of Neuro-Fuzzy system. Section 3 demonstrates the Adaptive

Neuro-Fuzzy Inference System architecture. Section 4 describes the design of

ANFIS based Neuro-Fuzzy Controller for LFC and BPC of wind-micro

hydro-diesel hybrid power system. Section 5 demonstrates the simulation

results of the hybrid system with ANFIS based NFC. Section 6 shows the

analysis and performance comparison of the proposed controller. Summary of

the chapter is given in section 7.

6.2 NEURO-FUZZY SYSTEM

The techniques of fuzzy logic and neural networks suggest the

novel idea of transforming the burden of designing fuzzy logic systems to the

training and learning of connectionist neural networks and vice-versa. That is,

the neural networks provides connectionist structure and learning to the fuzzy

logic systems and the fuzzy logic systems provide the neural networks with a

structural framework with high–level fuzzy IF-THEN rule thinking and

reasoning. These benefits can be witnessed by the success in applying neuro-

fuzzy systems in areas like control of power system. Although the benefits of

combining fuzzy logic and neural networks are well known and have been

widely demonstrated, this work investigates its application in LFC and BPC

of an isolated wind-micro hydro-diesel hybrid power system, to improve the

system performance.

ANN have a massive parallel structure in the form of a directed

graph, composed of processing units( neurons) that are linked through

connections which may or may not have adjustable weights. Figure 6.1

shows a very simple structure of a Neural Network, composed of two layers

(input and output), each of them composed of three and two processing units

respectively.

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Figure 6.1 The general structure of a Neural Network

The advantages of neural networks over conventional systems are

their ability to perform non-linear input-output mapping, generalisation,

adaptability and fault tolerance (Lin and Lee 1996). On the other hand, the

main disadvantage of neural network is the broad lack of understanding of

how they actually solve a given problem. The main reason for this is that

neural networks do not break a problem down into its logical elements, but

rather solve it by a holistic approach, which can be hard to understand

logically. The main result of neural network learning process is reflected only

in a set of weights in which a full understanding of the functioning of the

neural network is an almost impossible task. To overcome this, hybrid Neuro-

Fuzzy system is proposed. Fuzzy logic which gives the benefit of enabling

systems more easily to make human-like decisions (Zadeh 1965), was

discussed in the previous chapters in detail.

The advantage gained from fuzzy logic approach is the ability to

express the amount of ambiguity in human thinking and subjectivity

(including natural language) in a comparatively undistorted manner. So, fuzzy

logic technique finds their applications in areas such as control (the most

widely applied area), pattern recognition, quantitative analysis etc.

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The main disadvantage of fuzzy systems, however, is that they do

not have much learning capability to tune their fuzzy rules and membership

functions. Normally, fuzzy rules are decided by experts or operators

according to their knowledge or experience. However, when the fuzzy system

model is designed, it is often too difficult (sometimes impossible) for human

beings to define all the fuzzy rules or membership functions.

Fuzzy Logic (Zadeh 1965) and Artificial Neural Networks (Haykin

1998) are complementary technologies in the design of intelligent systems.

The combination of these two technologies into an integrated system appears

to be a promising path toward the development of the intelligent systems

capable of capturing qualities characterising the human brain. The neural

network can improve the transparency, making them closer to fuzzy systems,

while fuzzy systems can self adapt, making them closer to neural networks

(Lin and Lee 1996).

Neural fuzzy systems (Jang et al. 2005 and Lin and Lee 1996) have

attracted the growing interest of researchers in various scientific and

engineering areas, especially in the area of control; hybrid Neuro-Fuzzy

systems seem to be attracting increasing interest.

6.3 ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM (ANFIS)

Adaptive Neuro-Fuzzy Inference System (ANFIS) is an Artificial

Intelligence technique which creates a fuzzy inference system based on the

input-output model data pairs of the system. ANFIS combines neural network

and fuzzy system together. ANFIS can be employed in a wide variety of

applications of modelling, decision making, signal processing and control.

ANFIS is a class of adaptive network that is functionally equivalent to Fuzzy

Inference System. Since ANFIS design starts with the pre-structured system,

the membership function of input and output variables contain more

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information that Neural Network has to drive from sampled data sets.

Knowledge regarding the systems under design can be used right from the

start. Hence, the proposed ANFIS controller is more efficient. The rules are in

the linguistic forms and so intermediate results can be analyzed and

interpreted easily (Ashok Kusagur et al. 2010).

ANFIS is a multi layer adaptive neural network based Fuzzy

Inference System. ANFIS algorithm is composed of fuzzy logic and neural

networks with 5 layers to implement different node functions to learn and

tune parameters in a Fuzzy Inference System (FIS) structure using a hybrid

learning mode. In the forward pass of learning, with fixed premise

parameters, the least squared error estimate approach is employed to update

the consequent parameters and to pass the errors to the backward pass. In the

backward pass of learning, the consequent parameters are fixed and the

gradient descent method is applied to update the premise parameters. Premise

and consequent parameters will be identified for membership function (MF)

and FIS by repeating the forward and backward passes. ANFIS is fuzzy

Sugeno model put in the framework of adaptive systems to facilitate learning

and adaption (Jang 1993). Such framework makes Fuzzy Logic Controller

more systematic and less relying on expert knowledge.

To present the ANFIS architecture, let us consider two fuzzy rules

based on a first order sugeno model:

Rule 1 : IF (x is A1) and (y is B1) THEN (f1=p1x+ q1y +r1)

Rule 2 : IF (x is A2) and (y is B2) THEN (f2=p2x + q2y +r2)

where x and y are the inputs , Ai and Bi are the fuzzy sets, fi are the outputs

within the fuzzy region specified by the fuzzy rule, pi, qi and ri are the design

parameters that are determined during the training process.

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Figure 6.2 illustrates the equivalent ANFIS architecture for this

sugeno model (Jang et al. 2005), where nodes of the same layer have similar

functions.

Figure 6.2 ANFIS architecture

Out of the five layers, the first and fourth layers consist of adaptive

nodes while the second, third and fifth layers consist of fixed nodes. The

adaptive nodes are associated with their respective parameters, get duly

updated with each subsequent iteration while the fixed nodes are devoid of

any parameters.

Layer 1: Fuzzification layer:

Every node i in this layer 1 is an adaptive node. The outputs of

layer 1 are the fuzzy membership grade of the inputs, which are given by:

O i1 = Ai (x), For i= 1,2 (6.1)

O i1 = Bi-2 (y), For i= 3,4 (6.2)

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where x and y is the inputs to node i, where A is a linguistic label (small,

large) associated with this node. Where Ai(x), Bi-2(y) can adapt any fuzzy

membership function. The membership function for A can be any appropriate

parameterized membership function such as the generalised bell function.

A(x) 2b

i

i

1

x c1a

(6.3)

where { ai, bi., ci } is the parameter set. In fact, any continuous and piecewise

differentiable functions, such as commonly used trapezoidal (or)

triangular-shaped membership functions, are also qualified candidates for

node functions in this layer. Parameters in this layer are referred to as premise

parameters.

Layer 2: Rule layer:

Every node in this layer is a fixed node labelled M, whose output is

the product of all the incoming signals. The outputs of this layer can be

represented as:

O i2 = wi = Ai (x) . Bi (y), i=1,2 (6.4)

Each node output represents the firing strength of a rule.

Layer 3: Normalization layer:

Every node in this layer is a fixed node labeled N. The ith node

calculates the ratio of the ith rule’s firing strength to the sum of all rule’s firing

strength.

3 ii

1 2

wOi w i 1,2(w w )

(6.5)

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For convenience, outputs of this layer are called normalized firing strengths.

Layer 4: De-fuzzification layer:

Every node i in this layer is an adaptive node. The output of each

node in this layer is simply the product of the normalized firing strength and a

first order polynomial.

O i4 = iw fi = iw (pi x+ qi y +ri ) i=1, 2 (6.6)

where iw is a normalized firing strength from layer 3 and { pi , qi , ri } is the

parameter set of this node. Parameters in this layer are referred to as

consequent parameters.

Layer5: Summation neuron:

This single node in this layer is a fixed node labelled , which

computes the overall output as the summation of all incoming signals.

i i5 ii i i

i 1 2

w fO w f

(w w ) (6.7)

Thus we have constructed an adaptive network that is functionally

equivalent to a Sugeno fuzzy model.

From the ANFIS architecture shown in Figure 6.2, it is observed

that when the values of the premise parameters are fixed, the overall output

can be expressed as a linear combination of the consequent parameters. More

precisely, the output f in Figure 6.2 can be rewritten as

1 2i 2 1 1 2 2

1 2 1 2

w wf . f .f w .f w .fw w w w

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1 1 1 1 1 1 2 2 2 2 2 2(w .x)p (w .y)q (w )r (w .x)p (w .y)q (w )r (6.8)

which is linear in the consequent parameters p1, q1, r1, p2, q2 and r2.

The ANFIS structure is tuned automatically by least square

estimation and the back propagation algorithm (hybrid learning).

6.4 DESIGN OF ANFIS BAESD NEURO-FUZZY

CONTROLLER

The development of the control strategy to control the frequency

deviation of the wind-micro hydro-diesel hybrid power system using the

concept of ANFIS control scheme is presented here. The proposed

neuro-fuzzy method combines the advantages of neural networks and fuzzy

system to design a model that uses a fuzzy theory to represent knowledge in

an interpretable manner and the learning ability of a neural network to

optimize its parameters. ANFIS is a specific approach in Neuro-fuzzy

development which was first introduced by Jang (1993). To start with, we

design the controller using ANFIS scheme. The model considered here is

based on Takagi- Sugeno fuzzy inference model. The block diagram of the

proposed ANFIS based NFC for LFC and BPC of wind-micro hydro- diesel

hybrid power system is shown in Figure 6.3.

Figure 6.3 Block diagram of ANFIS based Neuro-Fuzzy Controller

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The inputs to the ANFIS based Neuro-Fuzzy controller for LFC of

the hybrid system on diesel side are error E( Fs) and change in error E

Fs)’.

The fuzzification unit converts the crisp data into linguistic

variables, which is given as input to the rule based block. The set of 49 rules

are written on the basis of previous knowledge/experiences in the rule based

block. Hybrid learning algorithm is used to train the neural network to select

the proper set of rule base. For developing the control signal, the training is

very important step in the selection of the proper rule base. Once the proper

rules are selected and fired, the control signal required to obtain the optimal

output is generated. The output of NN unit is given as input to the

de-fuzzification unit and the linguistic variables are converted back into the

crisp form.

This chapter proposes a systematic approach for establishing a

concise ANFIS that is capable of online self-organizing and self-adapting its

internal structure for learning the required control knowledge that satisfies the

desired system performance. The proposed ANFIS based NFC uses a hybrid

learning algorithm to identify consequent parameters of Sugeno type fuzzy

inference system. This algorithm applies a combination of least square

method and back propagation gradient descent method for training fuzzy

inference system membership function parameters to emulate a given training

data set.

Steps to design the ANFIS based NFC are given below.

1. Draw the simulink model for LFC and BPC of an isolated

wind-micro hydro-diesel hybrid power system with Takagi-

Sugeno inference model Fuzzy Logic Controller.

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2. Simulate it with seven membership functions for the two

inputs, error ( Fs) and change in error ( Fs)’ and with rule

base shown in Figure 6.5. Simulation steps are same as

explained in previous chapters for FLC.

3. Collect the training data while simulating the system with

Fuzzy Logic Controller to design the ANFIS based NFC.

4. The two inputs, i.e. error ( Fs on diesel side and PGW on

wind side) and change in error ( Fs’, PGW ’) and the output

signal gives the training data.

5. Use ANFIS edit to create the FIS file (lfcanfi23.fis).

6. Load the training data collected from step2 and load the

lfcanfi23.fis file.

7. Choose the hybrid learning algorithm.

8. Train the collected data with generated FIS up to particular

number of Epochs.

Figure 6.4 shows the FIS editor of Sugeno type Fuzzy Inference

System with two inputs (error and change in error) and one output. Each input

is having seven linguistic variables with triangular membership functions. 49

rules are framed and it is shown in Figure 6.5. The rules are viewed by rule

viewer as shown in Figure 6.6.

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Figure 6.4 FIS editor (Sugeno model) with two inputs and one output

Figure 6.5 Rule editor of Fuzzy Sugeno model

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Figure 6.6 Rule viewer of Fuzzy Sugeno model

After running this FIS file with simulink model, the training dataare collected and loaded by the ANFIS editor. The ANFIS editor windowshown in Figure 6.7 has all the provisions for loading the data and FIS filefrom the workspace and also for training and testing the data for better controlperformance.

Figure 6.7 ANFIS editor window

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Figure 6.8 shows the loading and training of data to ANFIS

structure. The ANFIS structure is trained with hybrid learning up to 50

epochs, with error tolerance of zero.

Figure 6.8 Training of data with hybrid learning method

The ANFIS information obtained after simulation is as follows.

ANFIS info:

Number of nodes: 131

Number of linear parameters: 49

Number of nonlinear parameters: 42

Total number of parameters: 91

Number of training data pairs: 101

Number of checking data pairs: 0

Number of fuzzy rules: 49

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Start training ANFIS...

1 3.32714e-006

2 0.000173762

Figure 6.9 shows the ANFIS structure for the designed NFC for

LFC and BPC of wind-micro hydro-diesel hybrid power system.

Figure 6.9 ANFIS architecture of Neuro-Fuzzy Controller for LFC and

BPC of wind-micro hydro-diesel hybrid power system

6.5 SIMULATION RESULTS

Simulations are performed with the proposed ANFIS based NFC

for LFC and BPC of the hybrid power system with system parameters given

in Appendix 1. The ANFIS based NFC, improves the performance of the

hybrid system by the learning and training approach. For the same system

parameters, simulink model of the hybrid power system is simulated with

FLC (Mamdani model) and conventional PIC for performance comparison.

All the responses such as change in frequency, change in wind power, change

in diesel power and change in hydro power during various load disturbances

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are observed and investigated in terms of settling time, overshoot and steady

state error value to get the optimum performance of the wind-micro hydro-

diesel hybrid power system.

Simulation is carried out for 1%, 2%, 3%, 4% and 5% step load

change ( PL=0.01 p.u., 0.02 p.u., 0.03 p.u., 0.04 p.u. and 0.05 p.u.) at

t = 0 sec. The change in frequency of the system, change in wind power

generation, change in diesel power generation and change in hydro power

generation for 4% (0.04 p.u.) step load change is shown in Figures 6.10, 6.11,

6.12 and 6.13 respectively.

Figure 6.10 Change in frequency of the hybrid system with ANFIS

based NFC, FLC and PIC for a step load change of 4%

0 1 2 3 4 5-0.02

-0.01

0

0.01

Time in secs.s)

PICFLCANFIS

159

Figure 6.11 Change in wind power generation of the hybrid system with

ANFIS based NFC, FLC and PIC for a step load change of

4%

Figure 6.12 Change in diesel power generation of the hybrid system with

ANFIS based NFC, FLC and PIC for a step load change of

4%

0 1 2 3 4 5 6 7 8-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time in secs.

PICFLCANFIS

0 1 2 3 4 5 6 70

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Time in secs.

PICFLCANFIS

160

Figure 6.13 Change in hydro power generation of the hybrid system

with ANFIS based NFC, FLC and PIC for a step load

change of 4%

From the simulation results, settling time for change in frequency,

change in wind, diesel and hydro power generation of the hybrid power

system for the proposed ANFIS based NFC, conventional PIC and FLC for a

step load change of 1%, 2%, 3%, 4% and 5% are observed and tabulated in

Table 6.1.

0 1 2 3 4 5

-2

-1

0

1

2

3

4

x 10-3

Time in secs.

PICFLCANFIS

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On analysing the performance from the Table 6.1, it is observed

that the proposed ANFIS based NFC damps out the deviations in frequency,

wind, diesel and hydro power with less settling time for various load

disturbances (from 0.01 p.u. to 0.05 p.u.). The proposed ANFIS based NFC

maintains steady response and is more reliable than the fixed parameter PIC

and FLC, regardless of changes in load power variations. The proposed

controller generates a control signal to the governor, which in turn controls

the diesel power generation to maintain the system frequency and power

generation of the renewable hybrid system.

The amplitude of the second oscillation for dynamic responses

(deviations in frequency, wind, diesel and hydro power) of the hybrid system

for various load disturbances are observed and tabulated in Tables 6.2 and 6.3

for ANFIS based NFC, FLC and PIC.

Table 6.2 Amplitude of oscillations for deviations in frequency and

wind power for NFC, FLC and PIC against various load

disturbances

Loadchange

(p.u.)

Change in frequency(Hz) Change in wind power(p.u. KW)

ANFIS based

NFCFLC PIC

ANFIS based

NFCFLC PIC

0.01 -0.0004056 -0.001114 -0.0009308 -0.0004831 -0.0005421 -0.0009607

0.02 -0.001202 -0.001821 -0.001993 -0.0009222 -0.001189 -0.001897

0.03 -0.001664 -0.002252 -0.002824 -0.001265 -0.001632 -0.002857

0.04 -0.002 -0.00328 -0.0037 -0.001519 -0.001874 -0.003847

0.05 -0.002716 -0.004 -0.004499 -0.0002019 -0.002214 -0.004804

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Table 6.3 Amplitude of oscillations for deviations in diesel and hydro

power for NFC, FLC and PIC against various load

disturbances

Loadchange(p.u.)

Change in diesel power(p.u. KW) Change in hydro power(p.u.KW)

ANFIS basedNFC

FLC PIC ANFIS basedNFC

FLC PIC

0.01 0.01091 0.01156 0.01165 0.0000911 0.0002187 0.0001843

0.02 0.02145 0.02249 0.02334 0.0002214 0.0003901 0.000354

0.03 0.03107 0.03384 0.03502 0.0003842 0.0004734 0.0005562

0.04 0.04302 0.04474 0.04658 0.0004944 0.0006289 0.0007336

0.05 0.05334 0.0556 0.05816 0.0005382 0.0007826 0.0008961

On analysing the performance from the Tables 6.2 and 6.3, the

amplitude of oscillations of the proposed ANFIS based NFC is less

compared to FLC and PIC. Simulation of the hybrid power system with the

proposed ANFIS based NFC shows improved system performance when

compared to conventional PIC and FLC.

6.6 ANALYSIS AND PERFORMANCE COMPARISON

An investigation on the dynamic responses of frequency change

and change in wind, diesel and hydro power generation have been carried out

for LFC and BPC of the hybrid power system using the proposed ANFIS

based NFC for different load changes and compared with FLC and

conventional PI Controller. Figure 6.14 shows the comparison of responses

(frequency response, change in wind, diesel and hydro power) in terms of

settling time for ANFIS based NFC, FLC and PIC against a step load change

of 4%(0.04 p.u.).

164

Figure 6.14 Comparison of dynamic responses of the hybrid system forNFC, FLC and PIC in terms of settling time (seconds)against a step load change of 4%

The bar chart in Figures 6.15, 6.16, 6.17 and 6.18 illustrates the

performance comparison of the hybrid system for change in frequency,change in wind power, change in diesel power and change in hydro power

respectively for three controllers (ANFIS based NFC, FLC and PIC) in termsof settling time against various load disturbances.

Figure 6.15 Comparison of frequency response for NFC, FLC and PICin terms of settling time (seconds) against various loaddisturbances

0

0.01

0.02

0.03

0.04

0.05

Change infrequency

(Hz)

Change inwind

power(p.u.KW)

Change indieselpower

(p.u.KW)

Change inhydropower

(p.u.KW)

Sett

ling

tim

e in

sec

onds

ANFIS based NFC

FLC

PIC

0

1

2

3

4

1% 2% 3% 4% 5%

Sett

ling

time

in s

econ

ds

Load disturbance in percentage

ANFIS based NFC

FLC

PIC

165

Figure 6.16 Comparison of change in wind power response for NFC,

FLC and PIC in terms of settling time (seconds) against

various load disturbances

Figure 6.17 Comparison of change in diesel power response for NFC,



0

2

4

6

8

10

1% 2% 3% 4% 5%

Sett

ling

time

in s

econ

ds


ANFIS based NFC

FLC

PIC

0

1

2

3

4

1% 2% 3% 4% 5%

Sett

ling

time

in s

econ

ds


ANFIS based NFC

FLC

PIC

166

Figure 6.18 Comparison of change in hydro power response for NFC,



The bar chart in Figures 6.19, 6.20, 6.21 and 6.22 illustrates the

performance comparison of three controllers (ANFIS based NFC, FLC and

PIC) in terms of amplitude of oscillations against various load disturbances.

Figure 6.19 Comparison of change in frequency response of the hybrid

system for NFC, FLC and PIC in terms of oscillations (Hz)

against various load disturbances

0

0.5

1

1.5

2

2.5

3

3.5

1% 2% 3% 4% 5%

Sett

ling

time

in s

econ

ds


ANFIS based NFC

FLC

PIC

0

0.001

0.002

0.003

0.004

0.005

1% 2% 3% 4% 5%

Am

plitu

de o

f osc

illat

ion

in H

z


ANFIS based NFC

FLC

PIC

167

Figure 6.20 Comparison of change in wind power response of the hybrid

system for NFC, FLC and PIC in terms of oscillations

(p.u. KW) against various load disturbances

Figure 6.21 Comparison of change in diesel power response of the

hybrid system for NFC, FLC and PIC in terms of

oscillations (p.u. KW) against various load disturbances

0

0.001

0.002

0.003

0.004

0.005

1% 2% 3% 4% 5%

Am

plitu

de o

f osc

illat

ion

in p

.u.K

W


ANFIS based NFC

FLC

PIC

0

0.01

0.02

0.03

0.04

0.05

0.06

1% 2% 3% 4% 5%

Am

plitu

de o

f osc

illat

ion

in p

.u.K

W


ANFIS based NFC

FLC

PIC

168

Figure 6.22 Comparison of change in hydro power response of the

hybrid system for NFC, FLC and PIC in terms of

oscillations (p.u. KW) against various load disturbances

From the performance comparison, it is observed that the overshoot

and settling time of the ANFIS based NFC is lower than those of FLC and

conventional PIC. The results obtained using ANFIS based NFC proposed in

this work outperform both conventional PIC and FLC by its hybrid learning

algorithm.

6.7 SUMMARY

An attempt is made in this work to develop a control strategy that

combines the advantages of neural networks and fuzzy inference system for

LFC and BPC of an isolated wind-micro hydro-diesel hybrid power system.

The hybrid learning algorithm applied by the proposed ANFIS structure trains

the Fuzzy Inference System membership function parameters for better

dynamic performance of the hybrid system. The designed ANFIS based NFC

for LFC and BPC of the hybrid system is investigated for various load

disturbances by simulation. It is observed from the simulation results that the

proposed controller is effective and provides significant improvement in

0

0.0002

0.0004

0.0006

0.0008

0.001

1% 2% 3% 4% 5%

Am

plitu

de o

f osc

illat

ion

in p

.u.K

W


ANFIS based NFC

FLC

PIC

169

system performance by combining the benefits of fuzzy logic and neural

networks. The proposed ANFIS based Neuro-Fuzzy Controller maintains the

system reliable for sudden load changes and proves its superiority.

chapter 6 anfis based neuro-fuzzy...

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