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Nand Kishor AE P. R. Sharma AE A. S. Raghuvanshi
An investigation on pruned NNARX identif i cation model
of hydropower plant
Received: 13 December 2004 / Accepted: 26 January 2006 /Published online: 19 May 2006
'O Springer-Verlag London Limited 2006
Abstract The aim of this paper is to determine an
accurate nonlinear system model for identif i cation of
dynamics. A small hydropower plant connected as single
machine inf i nite bus (SMIB) system is considered in the
study. It is modeled by a neural network conf i gured as a
feedforward multilayer perceptron neural network
(MLPNN). An investigation is conducted on various
NN structures to determine the optimally pruned neural
network nonlinear autoregressive with exogenous signal
(NNARX) identif i cation model. The structure selection
is based on validation tests performed on these network
models. The proposed structure identif i es the model
characteristics, which represent the dynamics ofa power
plant accurately. The results show an improved perfor-
mance in identif i cation of power plant dynamics by
optimal brain surgeon (OBS) pruned network as com-
pared to un-pruned (i.e., fully connected) network.
Keywords Hydroturbine AE Single machine inf i nite bus AE
Identif i cation AE Neural network AE Pruned AE
Governor AE Exciter
List of symbols
m mechanical torque
m l load torque
w 0 base angular speed (377.16 rad/s)
w rotor angular speed (p.u.)
d l load angle (rad)
D damping torque
T a mechanical time constant
ec q internal transient voltage in the q-axis (p.u.)
V t terminal voltage (p.u.)
x d d-axis synchronous reactance (p.u.)
xc d d-axis transient reactance (p.u.)
r e + jx e transmission line impedance (p.u.)
x q q-axis synchronous reactance (p.u.)
K A , K E voltage regulator gains
T A , T E voltage regulator time constants
K F , T F stabilizing transformer gain, time constant
K 1 –K 6 constants of the linearized model of synchro-
nous machine
P e , Q e active and reactive power output from syn-
chronous machine
V f stabilizing transformer voltage
E FD f i eld voltage
V ref reference voltage
V a regulator voltage
s c d0 d-axis open circuit f i eld time constant
1 Introduction
A hydroturbine is a nonlinear nonstationary multivari-
able system whose characteristics vary signif i cantly with
unpredictable load. It is dif f i cult to obtain nonlinear
simulation model ofthe hydroturbine. The conventional
characteristic curves of hydroturbine do not provide
suf f i cient insight into nonlinear simulation. This presents
a dif f i culty in designing an ef f i cient and reliable governor.
At present linear control theory based PID controller
f i nds its application in the power plant. Thus it is nec-
essary to ef f ectively design its control action with proper
model representation of the system. The modeling of
dynamic interaction between the gate position (input)
and turbine mechanical power (output) is important as it
regulates the operation of governor action.
As such, system identif i cation technique provides an
ef f ective means of plant modeling. With system identi-
f i cation it is inferred to obtain the accurate characteris-
tics ofa particular system from its input–output data. In
general, one seeks to obtain a system representation,
which is as accurate and close to the original system as
possible. Over the last one decade, neural networks have
been considered as promising approach in system iden-
tif i cation. A black-box nonlinear mathematical model
N. Kishor (&) AE P. R. Sharma AE A. S. Raghuvanshi
Department of Electrical Engineering, Royal Bhutan Institute
of Technology, Phuentsholing, Bhutan
E-mail: nand_research@yahoo.co.in
Engineering with Computers (2006) 21: 272–281
DOI 10.1007/s00366-006-0016-z
An Investigation on Pruned NNARX Identification Model of Hydropower Plant.pdf
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