Transcript - Bepress

Generalized Neuron and its
Applications
Dr. D.K. Chaturvedi
Department of Electrical Engineering
D.E.I. (Deemed University), Dayalbagh
Agra (U.P.), India
E-mail: [email protected]
Website: www.works.bepress.com/dk_chaturvedi
Organization
• Introduction to Artificial Neural Network
• Development of Generalized Neuron
• Validation and verification
• Applications of Generalized neuron
• Conclusions
How Do We Work?
INTERNAL
PROCESSES
INPUTS
Senses environment
See
Hear
Touch
Taste
Smell
Has knowledge
Has understanding/
intentionality
Can Reason
Exhibits behaviour
OUTPUTS
Human Brain
 A human brain is composed of neurons switching at speeds about a
million times slower than computers.
 Then also Humans are more efficient then computers due to massive
parallel processing in the brain.
 Moreover, not only humans, but even animals can process visual
information better than fastest computers.
 Unfortunately the understanding of Human brain is not complete.
 Human Brain Consisting of tiny processing cell (neuron)
Biological Neuron
• A typical neuron has three major regions:
cell body,
dendrites,
axon.
• Dendrite receives information from
neurons through axons- long fibers that
serve as transmission lines.
• The axon dendrite contact organ is called a
synapse. The signal reaching a synapse and
received by dendrites are electrical
impulses.
• The biological neuron functioning could be
exhibited with a simple electronics
(artificial neuron).
Artificial Neuron
Artificial Neural Network (ANN)
• ANN consists of many simple elements
called neurons.
Performance of ANN Depends
• Problem Complexity
• Complexity of Learning Algorithm
• Network Complexity
PROBLEM COMPLEXITY
Training data
- Number of data and their accuracy
- Range of Normalization
i.e. ±1.0, ±0.9, 0 to 1.0, 0.1 to 0.9 and so on.
- Noise in data (important for generalization)
- Sequence of presentation of training data
Type of functional mapping
like x-y, Dx-y, x-Dy, Dx-Dy.
Linear or Non-linear problem
Time variant or invariant Parametric Problem
Complexity of Learning Algorithm
 Weight Initialization
Random
Using Genetic Algorithm
 Initialization of Training Parameter
 Selection of Error Function
 Error calculation
 Batch mode (Cumulative error)
 Pattern mode (individual error)
 Selection of Training Algorithms
NETWORK COMPLEXITY
 Neuron Structure
- Aggregation - Activation fucntion
Weights

Input
 Number of hidden Layers
 Number of Neurons in the hidden layer
 Number and Type of Interconnections
(deterministic or stochastic)
T
Output
DEFERENT ANN MODELS
 - ANN
P - ANN
 -P -ANN
P - -ANN
Input
layer
 -hidden
layer
 -output
layer
Input
layer
P-hidden
layer
P -output
layer
Input
layer
 -hidden
layer
P -output
layer
Input
layer
P-hidden
layer
-output
layer
Effect of Neuron Aggregation Functions
on Modeling of Induction Motor
(Starting Characteristic)
Learning rate =0.4, Momentum =0.6, Gain Scale factor=1.0, Error Tolerance=0.005
Models
Training
Epochs
RMS Error
Min Error
Max Error
 - ANN
1150
0.02568
0.000376
0.888082
P - ANN
4090
0.14097
0.000632
0.287738
 -P -ANN
50
0.01661
0.000430
0.250279
P - -ANN
50
0.01358
0.000614
0.297254
Drawbacks of Conventional ANN
•
•
Large training time and
Complex ANN structure –
•
large number of neurons and
•
hidden layers
required to deal with complex problems.
•
To overcome these drawbacks, it is proposed to develop
a generalized neuron having more power, more
flexibility and improved level of accuracy by modifying
the conventional neuron architecture.
LIST OF COMPANSATORY OPERATORS
Generlaized Neuron Models based on the Compensatory
operators suggested by Muzumotto (1989)
A. Summation Type
Generalized Neuron model -0
O2 = O *W + Op *Wp
Generalized Neuron model -1 O1 = O *W + Op *(1-W)
Generalized Neuron model -3
O3 = O *W + (O - Op -OOp )*(1-W)
Generalized Neuron model -5
O5 = (OOp )*W + (O +Op )*(1-W)
B. Product Type
Generalized Neuron model -2
O2 = O W * O (1-W)
Generalized Neuron model -4
O4 = O W * (O - Op -OOp ) (1-W)
Generalized Neuron model -6
O6 = (O +Op )(1-W)* (OOp )W
where O =f1( (Xi*Wi+Xos)) and
Op = f2( P(Xi*Wi*Xop))
Structure of Generalized Neuron
Σ
Input
∏
f1
Σ
Output
f2
f1 - Sigmoid Function and f2 Gaussian function
BENCHMARK TESTING OF GENERALIZED
NEURON MODEL (GNM)
Benchmark problems-
•
•
•
•
•
•
Ex-or
4-bit parity
Mackey-glass time series
Character recognition
Sin(x1)*sin(x2)
Coding
Application of Generalized
Neuron model to Power Systems
• Electrical Load Forecasting
• Electrical Machines Modeling
– D.C. Machine
– Induction motor
– Synchronous Machine
• Load Frequency Control
Problem
• Power System Stabilizer
GN Based Power System Stabilizer
What is Power System
Stabilizer (PSS)?
• PSS aids in maintaining power system stability
and in improving dynamic performance by
providing supplementary signal to excitation
system.
• PSS has made a great contribution in enhancing
the operating quality of power system.
• The most commonly used PSS is a fixed
parameter type CPSS.
Conventional Power System Stabilizer
CPSS design is based on linearized model of
system around a certain operating point.

In reality the actual power system has nonlinear characteristics and operates over a wide
range of operating conditions.

CPSS tuning to cope with most of the
operating conditions is quite difficult.

In last decade, ANNs and fuzzy set theoretic
approach have been proposed for PSS.

Why ANN as PSS?
• It can easily accommodate the non-linearities
and time dependencies.
• Intelligent : It could work for wide operating
range and handle unforeseen situation in a
better way.
• On-Line learning: Performance can be
improved from the past experiences.
• Adaptive PSS: No need to change PSS
parameter, if system changes.
COMPARISON OF NETWORK COMPLEXITY
INVOLVED IN ANN AND GN BASED PSS
COMPONENTS
ANN
(7-7-1)
GNM
(1)
Number of neurons used
08
01
Number of layers containing processing
neurons
02
01
Number of interconnections
56
15
Number of biases used
08
02
Number of aggregation/ activation functions
08
02
6,47,000
8,700
Training epochs required to reach error level
of 0.001
Generalized Neuron Based Adaptive Power
System Stabilizer
• Adaptive PSSs use self-tuning adaptive control scheme. The
structure of a self-tuning adaptive PSS has two parts:
i. an on-line parameter identification and
ii. control strategy.
• At each sampling period, mathematical model is obtained by on-line
identification method to track the dynamic behavior of the plant.
Then control strategy calculates the control signal based on on-line
identified parameters.
• Adaptive PSS can adjust its parameters on-line according to the
changes in environment, and maintain desired control ability over a
wide operating range of the power system.
• The main limitation of adaptive control is that it takes large amount
of computing time for on-line parameter identification. To overcome
this problem, a GN is used to develop an adaptive PSS.
GN identifier

A GN identifier is placed in parallel with the system and has the
following inputs:
Xi (t) = [ω_vector, u_vector]
where ω_vector=[ω(t), ω(t-*T), ω(t-2*T), ω(t-3*T)]
u_vector=[u(t-T), u(t-2*T), u(t-3*T)]
T is the sampling period, and w is angular speed, rad/s.

The dynamics of the change in angular speed of the synchronous
generator can be viewed as a non-linear mapping as below:
ω(t+T) = fi (Xi(t))

The GN-identifier for the plant can be represented by a non-linear
function Fi.
ωi(t+T) = Fi (Xi (t), Wi (t))
where, Wi(t) is the matrix of GN identifier weights at time instant t.

After Training
w(t+T) = fi (Xi(t)) ≈ wi(t+T) = Fi (Xi (t), Wi (t)),
Disturbance
w(t)
Plant
u-vector
GN
Identifier
+
Unit
Delay
-
Σ
ω_ vector
Fig. 1 Schematic diagram of proposed GN Identifier
Results of GN identification for a
3-Phase to Ground fault at
generator bus for 100 ms
at P=0.7, Q=0.3 (lag).
Results of GN identification
when one line is removed and
reenergized from double line
circuit at P=0.2, Q=0.2 (lag).
Experimental Results of GN identifier at 23% step change in Torque reference.
GN based Controller
u_vector
GN
Controller
PLANT
ω_vector
Learning
Algorithm
GN-identifier
Output ωi(t+nT)
w
Performance of GNAPSS under different operating conditions and disturbances
(b) Removal of one line at 0.5s and re-energization at
5s, P=0.9 pu, Q=0.4 pu, lead
(a) 100ms 3-phase to ground fault, P= 0.7 pu, Q= 0.3 pu lead
(c) Step change in torque, P=0.2 pu and Q=0.2pu, lag
EXPERIMENTAL SETUP
 The physical model consists of a three-phase 400MW reduced
scale micro- synchronous generator connected to a constant
voltage bus through a double circuit transmission line model.
 The transmission lines are modeled by six Π sections, each section
is equivalent of 50 km length. The transmission line parameters
are the equivalent of 1000 MVA, 300 km and 500 kV.
 The governor turbine characteristics are simulated using the micromachine prime mover. It can be achieved by dc motor which is
controlled as a linear voltage to torque converter.

The Laboratory model mainly consists of the turbine M, the
generator G, the transmission line model, the AVR, DSP board and
Man-machine interface.
DC motor
M
AC generator
Transmission Line
G
B1
Timing Circuit
for B1, B2, B3
AVR
Vref
PSS
B2
B3
Exciter
Tref
Infinite
busbar
Δω and Δώ
Experimental setup for Laboratory Power System model
IMPLEMENTATION of GNPSS
The GNPSS control algorithm is implemented on a single board computer, which uses
a Texas Instruments TMS320C31 digital signal processor (DSP) to provide the
necessary computational power.
The DSP board is installed in a personal computer with the corresponding
development software and debugging application program.
The analog to digital input channel of DSP board receives the input signal and control
signal output is converted by the digital to analog converter. The IEEE type PSS1A
CPSS is also implemented on the same DSP, with a 1ms sampling period. The following
tests have been performed on the experimental set up to study the performance of the
GNPSS and CPSS.
1. Three phase to ground fault
2. Two phase to ground fault
3. Single phase to ground fault
4. One line removed and re-energized from a double line circuit.
5. Change in governor Mechanical power reference.
Experimental Results of GN based adaptive PSS
at P=0.8 pu and Power Factor = 0.9 leading for a step change in Pref.
Experimental results of Two-Phase to ground fault at P=0.8 pu and
power factor 0.9 leading
1and 2 step change in voltage reference
3 and 4 step change in torque reference
5 three phase to ground fault
6 and 7 removal of one transmission line from double line system
and re-energized.
Fig. 4 Performance of GNPSS and GN based adaptive PSS
under different operating conditions and disturbances at
p=0.2 pu and q=0.2 pu (lead).
Comparison of GNPSS and Adaptive
GNPSS
Fig. 6 Performance of GNPSS and GN based adaptive PSS when one line is
removed at 0.5 sec. and re-energized at 5.5 sec and then again same line is
removed at 10.5 sec. and re-energized at 15.5 sec. at P=0.8 pu and Q=0.4 pu
(leading).
MULTIMACHINE SYSTEM
• The previously trained GNPSS also tested on a fivemachine power system without infinite bus system with
multi-mode oscillations.
• In this system, generators #1, #2 and #4 are much larger
than generators #3 and #5. All five generators are equipped
with governors, AVRs and exciters.
• The whole system can be viewed as a combination of two
areas connected through a tie transmission line between
bus #6 and bus #7. Generators #1 and #4 form one area
and generators #2, #3 and #5 form another area.
• Under normal operating condition, each area serves its
local load and is almost fully loaded with a small load flow
over the tie line.
Bus #3
Bus #6
G#3
Load #2
Bus #7
G#1
G#2
Bus #8
G#4
G#5
Load #1
Bus #4
Load #3
Schematic diagram of a five-machine power
system.
____ GNPSS
-.-.CPSS
____ GNPSS
-.-.CPSS
____ GNPSS
-.-.CPSS
System Response with GNPSS installed on Generator #3 and a ± 0.1 pu
step change in torque reference at G3.
____ GNPSS
-.-.CPSS
Fig. 9 System Response under change in Tref with only GNPSS and only CPSS installed on G1, G2, and G3
____ GNPSS
-.-.CPSS
System response with only GNPSS and only CPSS installed on G1, G2, G3 for 3-phase to ground fault.
____ GNPSS
-.-.CPSS
Fig. 11 System response with GNPSS at G1, G3 and CPSS on G2, G4, G5. for ± 0.2 pu step change in Torque Reference.
CONCLUSION
• GNM has been developed and validated.
• It is successfully used for forecasting, modeling
and control Applications
• The convergence of GNM is much faster as
compared to ANN with standard BKP algorithm.
• The structural complexity as well as computational
complexity in GNM is considerably less in
comparison to ANN.
Applications where GN may be used?
Auto-drive
system
Intelligent
Robot
Pendulum
Control
Motor Speed
Control
MANY MORE . .. . . .. . . .
Acknowledgements
• Prof. P.S. Satsangi, I.I.T. Delhi and Prof.
P.K. Kalra, I.I.T., Kanpur, India
(Development work)
• Prof. O.P. Malik University of Calgary,
Canada (Experimental work)
?
?
?
THANKING YOU
Website: www.works.bepress.com/dk_chaturvedi
SHORT TERM LOAD
FORECASTING PROBLEM
Number of inputs for ANN / GNM
Input 1
-
- Electrical demand of first last Monday (say), at time (t)
Input 2
-
- Electrical demand of second last Monday at time (t)
Input 3
-
- Electrical demand of third last Monday at time (t)
Input 4
-
- Electrical demand of previous day at time (t)
Output
-
- Electrical demand of fourth Monday at time (t)
Where (t) is the time for forecasting.
Electrical Load Forecasting
Models
Training
Epochs
RMS Error
Min Error
Max Error
ANN
3100
0.02535
0.04018
0.05752
GN Model
20
0.021882
0.00379
0.04434
Load Frequency Control Problem
LOAD FREQUENCY CONTROL PROBLEM
 Plant Models used are mostly linearized one.
 The constant Charactering the speed regulator R depends in
a highly non-linear manner upon the turbine power.
 Traditional Integral Controllers are slow.
 GN controller developed.
Electrical Machines Modeling