Design of Global Controller for Power System Based Neural ...

Design of Global Controller for Power System Based Neural Network
and Gain-scheduling
Rasoul Mohammadi-Milasi
Control and Intelligent Processing Centre of
excellence Electrical and Computer Engineering
Department University of Tehran
rmilasy@ece.ut.ac.ir
Abstract: A global power system transient stabilizer
and voltage regulator is proposed in this paper. Two
independent controllers i.e. transient controller and
voltage regulator are designed. In order to design
voltage regulator we use simple neuro controller and
for transient stabilizer we use Neural PSS. The final
control action is the sum Neural PSS and neuro-voltage
regulator. To achieve the global control action that
guarantees both transient stability and voltage
regulation, we used a membership function that was a
function of measurable parameters of the system. The
proposed global control law acts in a manner in which
in the transient period, the transient stabilizer is the
dominant controller and in the post transient period, the
voltage controller is the dominant one. The effectiveness
of the proposed global control action is demonstrated
through some computer simulations on a Single-
Machine Infinite-Bus (SMIB) power system.
Keywords: Power system stabilization, voltage
regulation, nonlinear system, Single-Machine
Infinite-Bus (SMIB) power system.
1 Introduction
A power system must be modeled as a nonlinear
system for large disturbances. Although power
system stability may be broadly defined according
to different operating conditions [1], an important
problem, which is frequently considered, is the
problem of transient stability. It concerns the
maintenance of synchronism between generators
following a severe disturbance. By the excitation
control in a generating unit, transient stability can
be greatly enhanced. Another important issue of
Parviz Jabehdar-Maralani
Control and Intelligent Processing Centre of
excellence Electrical and Computer Engineering
Department University of Tehran
Pjabedar@ut.ac.ir
power system control is to maintain steady
acceptable voltage under normal operating and
disturbed conditions, which is referred as the
problem of voltage regulation [2, 3, 4, and 5].
So far, a lot of researches about the design of
power system stabilizers have been considered
which consist of wide-range of strategies, such as
adaptive controllers [6, 7] or fuzzy expert systems
[8, 9]. A power system stabilizer (PSS) based on a
neural network is evaluated in this paper. The
neural network is trained using the parameters of
stabilizers which are obtained through a control
design based on the pole-placement method, for
several operation points given by the synchronous
generator active and reactive powers (P and Q)
furnished to the power system.
In the transient stabilizing control, a common
phenomenon is that the post-fault voltage value
varies considerably from the prefault one [5,10,11].
From the practical point of view, voltage quality is
a very important index of power supply in power
system operation. So, the post-fault value is
expected to reach the normal value as closely as
possible. In this work we will use a simple Neuro-
Automatic Voltage Regulator (NAVR) proposed in
[12]. Training of the proposed neuro-controller is
on-line by the back propagation (BP) algorithm
using a modified error function. By representing
the neuro-controller learning equations in the sdomain,
the controller parameters can be
determined analytically. The performance of the
proposed global controller is studied on a Single-

Machine Infinite-Bus (SMIB) power system, which
the simulation results show its effectiveness.
2 Structure of gain-scheduling PSS
A gain-scheduling controller is basically a set of
linear controllers, each one of them designed for a
specific system operation condition. Thus, when
the system is in an arbitrary operation region, the
control signal to be applied is given by the
controller designed for that specific region.
In this work, one PSS based on a gain-scheduling
scheme is first designed only to give the controller
parameters that are used to train the stabilizer
synthesized by an artificial neural network. For the
gain-scheduling PSS (GSPSS) design, the
synchronous machine operation region, in terms of
active and reactive powers (P x Q plane), has been
divided in about 100 regions, presumed to be
sufficient to properly represent the power system.
In each region of the P x Q plane, a discrete linear
system model has been obtained, assuming that the
system operation point is represented by the central
operation point for that specific region (Figure. 1).
These regions, limited by the capability curves of
the generator[13], have the form of circular sectors
and should be in sufficient number to avoid
causing disturbances when the operation point
varies in accordance with the system operating
conditions [14].
Figure1: Regions in the P x Q plane used to design
the GSPSS
The discrete linear model of the plant system to be
used for the controller design has the form:
y(
kT)
= b u(
kT − 1)
+ b u(
kT − 2)
+ b u(
kT − 3)
0
1
2
(1)
− a1
y(
kT − 1)
− a y(
kT − 2)
− a y(
kT − 3)
2
3
Where T is the sample period (in this paper, T =
100ms was used), kT represents the current discrete
time, u is the system input and y is the output.
The parameters ai and bi from equation (1) are
estimated using the recursive least square method
(RLS) [15]. After that, a controller is designed
using a pole-placement technique that consists in
shifting the bad damped poles in a radial direction
towards the origin of the complex z-plane[16].
This can be done by multiplying these bad damped
poles by a real constantα . The well-damped poles
are not changed and if there are any unstable poles,
they are replaced by their reciprocals. Then, the
controller parameters can be represented by the
discrete-time equation:
u(
kT ) = g y(
kT ) + g y(
kT − 1)
+ g y(
kT − 2)
0 1
2 (2)
− h u(
KT − 1)
− h u(
kT − 2)
1
2
The controller parameters gi and hi are determined
by solving the following linear system, obtained
from the diofantine equation of the pole-placement
technique [17]:
⎡ 1 0 b ⎤⎡
⎤ ⎡ ( − 1)
⎤
0
0 0 h α a
1
1
⎢ a
⎥⎢
⎥ ⎢ 2 ⎥
⎢ 1
1 b
1
b
0
0 h
⎥⎢
2 ( α − 1)
a
⎥ ⎢ 2 ⎥
⎢a
⎥⎢
⎥ = ⎢ 3
2
a
1
b
2
b
1
b
0
g
0 ( − 1)
⎥ (3)
α a
3
⎢a
0 ⎥⎢
⎥ ⎢ ⎥
3
a
2
b
2
b
1
g
1 0
⎢
⎥⎢
⎥ ⎢ ⎥
⎣ 0 a
3
0 0 b
2 ⎦⎣
g
2 ⎦ ⎣ 0 ⎦
The α parameter should be chosen between 0 and
1 and, in this application, it was used α = 0.75.
This value allows a very good damping of the
electric power system dominant poles, without
exciting higher frequencies modes[18]. This
approach is repeated for all operation points
mentioned before, resulting in a set of controllers
parameters. If the GSPSS was active in the system,
it would receive the actual system operation point
and chose, among all the controllers, which one
should be used to generate the control signal. In
this work, the sets of controller parameters
obtained are just used as the training set for the
neural PSS, described as follow.
3 Neural PSS
Even though a large number of operation regions
have been used to compose the previous GSPSS, in
certain cases there are some differences, regarding
to the controller parameters, between an operation
point inside a region and the central point that has
been used to represent that same region. For that
reason, a PSS based on a perceptron multi-layer
neural network has been trained (using the error
backpropagation method) to provide a set of
controller parameters, even for operation points
that were not used during training. The proposed
Neural PSS (NPSS) is a static ANN and its inputs
are the actual active and reactive power furnished
by the generator. The network also has 2 hidden

layers composed by 10 neurons each, using a
sigmoid non-linear function. The output layer uses
a linear function and has 5 neurons, representing
the controller parameters (Figure. 2).
After the training process, in order to evaluate how
the controllers parameters change with the
operation point, the NPSS inputs have received a
set of values of active and reactive powers
covering a wide range of operation points (the
active and reactive power have been changed from
0 to 1 pu and 1 to 1 pu, respectively), resulting in a
group of 2500 controllers. It is important to notice
that some of the operation points presented to the
NPSS are not valid operation points (situations that
will never occur in a real power system operation),
but they have not been dropped to show how the
controllers parameters evolve with the changes in
P and Q (Figures 3 to 7).
Analyzing the results supplied by the NPSS, it is
easy to notice that there is not much change in the
controller parameters when the reactive power is
positive. However, all parameters suffer large
variations when the reactive power assumes a
negative value, even for neighbor regions. This is
the main characteristic of the proposed NPSS.
As a CPSS is usually tuned in a region with Q
positive, this could explain the reason why it
presents an acceptable performance in all operation
regions with this characteristic. But, when the
power system is working in regions with Q
negative, the performance of a CPSS (compared
with other methods such as adaptive control, neural
networks or fuzzy logic systems) is usually
unsatisfactory because it could not damp the
oscillations quickly, what could carry the system
even to an unstable condition.
Figure 2: NPSS structure
Fig. 3: Parameter g0
Figure 4: Parameter g1
Figure 5: Parameter g2
Figure 6: Parameter h1
Figure 7: Parameter h2
4 Structure of Neuro Voltage Regulator
In order to regulate generator terminal voltage to
the prefault value a simple Neuro-AVR proposed
in [12] is used. The overall control system with the
proposed neuro-controller consisting of one neuron
is shown in Figure. 8. The neuro-controller uses a
linear hard limit activation function and a modified
error feedback function.
This error is back propagated through the single
neuron to update its weight. Then, the output of the
neuro-controller is computed, which is equal to the
neuron weight.

Figure 8: Overall control system with simple neurocontroller.
The neuro-controller output can be derived as:
u ( t)
= W ( t)
(4)
W ( t)
= W ( t −1)
+ η × WCT(
t)
(5)
where WCT is the neuron weight correction term
based on the modified error function. W (t), u(t), η
are neuron weight, neuron output and the learning
rate respectively.
Based on equations (4) and (5), the neurocontroller
model in s-domain can be derived as
presented in the [12]. The derived model is shown
in Figure. 9.
Figure 9: Neuro-controller model in s-domain.
The proposed modified feedback function in this
case is:
f ( s)
= 1+
kv
s
(6)
In[12] it is shown that best parameter for this
controller areη 1 = 500,
kv
= 0.
23 . We show the
performance of this neuro controller for tracking of
reference voltage with these parameters in Figure.
10 again. (System response to a 0.055pu step
increase in reference voltage at 1s)
Figure 10: Neuro-controller performance using
modified error function for the simple model of the
synchronous generator
5 Design of global control law
In the previous sections, the local controllers, i.e.
transient stabilizer and voltage regulator were
designed based on one neuron structure. The global
control law is the average of the signals from the
local controllers, each weighted by the value of its
operating region membership function. Since the
membership function can be determined by direct
measurable variables of power systems. Indeed, the
controller structure for synchronous generator is
obtained by combination of two neuro-controllers,
which is getting feedback of output voltage and
angle. We used the following trapezoid-shaped like
membership functions which are able to indicate
different operating stages [19]:
1
µ = 1 −
(7)
δ
1 + exp( −120(
z − 0.
08))
µ v = 1−
µ δ
(8)
where
2
2
z = a1
∆ω
+ a2(
∆V
)
(9)
and
∆ ω = ω −ω
o
(10)
Where a 1 , a 2 are positive design constants
providing appropriate scaling which can be chosen
according to the different sensitivity requirement
of power frequency and voltage.
Membership function (7,8) is plotted in Figure. 11.
It can be seen that µ δ (z)
gets its dominant value
when z is far away from the origin, which
corresponds to the transient period: on the other
hand µ v (z),
does so when z is close to the origin,
which indicates the post-transient period. Since the
membership function values are determined by the
directly measurable variables, ω andV t , the fault
sequence need not to be known beforehand.
Figure11:Membership function, µ
δ
" − − −"
and µ " ___". .
v
Therefore, the whole operating region is
partitioned into the following two subspaces by the
membership functions, where S 1 indicates the
transient period and 2
S indicates the post transient
period.

⎪⎧
S1
= {( ∆ω,
∆Vt
) µ v ≤ µ δ }
⎨
(11)
⎪⎩ S 2 = {( ∆ω,
∆Vt
) µ δ ≤ µ v}
The characteristic function of each subspace
Sl ( l = 1,
2)
defined by:
⎧1 z ∈ Sl
τ l = ⎨
(12)
⎩0
otherwise
Note that τ 1 +τ 2 = 1.
It should be pointed out that ω and V t are chosen
as the index variables in (9) since they sufficiently
represent operating status for the problem transient
stability and voltage regulation. If the problem
under consideration is voltage stability, reactive
power could be included in the index.
Similarly the proposed method can be extended to
other power system control issues. The chosen
membership functions have a trapezoid-shaped like
which is well known in fuzzy control to separate
operating conditions. The system performance is
not sensitive to different parameters a 1 and a 2 .
The global control law is the average of the
individual control laws, weighted by the operating
region membership functions,
i.e., the input u f takes the form:
u f = eδ
µ δ + evµ
(13)
v
Where
e = δ − δ
(14)
δ
ref
ev = Vt
−V
(15)
ref
Figure. 12 depicts the block diagram of proposed
global control law for power systems.
6 Dynamic Model of Power System
Simulation tests have been performed using a
single machine connected to an infinite-bus by a
double circuit tie-line.
The classic third order single-axis dynamic model
of the SMIB power system can be written as
follows [1,10]:
A. Mechanical equations
& δ ( t) = ω(
t)
− ω
(16)
o
D
ω 0
ω& ( t) = − ( ω(
t)
− ω o ) − ( Pe
( t)
− Pm
) (17)
2H
2H
The mechanical input power Pm is treated as a
constant in the excitation controller design, i.e., it
is assumed that the governor action is slow enough
not to have any significant impact on the machine
dynamics.
Figure 12: Global controller for synchronous Generator
B. Generator electrical dynamics
1
E& q′
( t)
= ( E f ( t)
− Eq
( t))
(18)
Tdo
′
C. Electrical equations (Assumed x ′ d = xq
)
( t)
= E′
( t)
+ ( x − x′
) I ( t)
(19)
Eq q d d d
E f ( t)
= kcu
f ( t)
(20)
Eq′
( t)
Vs
Pe
( t)
= sinδ
( t)
(21)
xds
′
Eq′
( t)
−V
s cosδ
( t)
I d ( t)
=
(22)
x′
ds
Vs
I q ( t)
= sin δ ( t)
(23)
x′
ds
Eq′
( t)
V
2
s Vs
Q(
t)
= cosδ
( t)
−
(24)
xds
′
xds
′
Eq ( t)
= xad
I f ( t)
(25)
1
2
2
V ( t)
[( E ( t)
x I ( t))
( x I ( t))
] 2
t = q′
− d′
d + ′ d q
(26)
More details about power system modeling are in
[1,10].
7 Simulation Results
In this section, some simulations are provided to
study the performance of the proposed controller
law. The simulations are carried out using
SIMULINK toolbox of the MATLAB software
package. The prefault conditions of the system
o
are: δ o = 30 , Pmo
= . 7,
Vto
= 1.
1
To investigate the performance of the proposed
controller, a symmetrical three-phase short circuit
fault in the middle of one of transmission lines

short circuit was applied at half of one
transmission line at 5sec, and the fault was cleared
100 ms later by disconnecting the line. The
disconnected line is successfully reconnected after
1 sec. The responses of the closed-loop system
with different controllers for the above fault are
depicted in Figures. 13, 14, and 15. Figure. 13
shows the close-loop system response using the
neuro-voltage regulator. As it can be seen, the
synchronous generator’s terminal voltage is
regulated to its prefault value but the angle
oscillates very much, which is not desired for
power system. In this case, the stability of the
systems needs to be improved using a transient
stabilizer. In Figure. 14 the responses using the
transient control law is depicted. Evidently, the
stability of the closed-loop system has been
considerably improved in comparison with the
former but the post fault value of terminal voltage
differs from its prefault value. So, we have to trade
off between the transient stability improvement
and voltage regulation. To this end, the global
control law is proposed as in (13). The closedloop
response using the global controller is shown
in Figure. 15. In this case, in the transient period,
the transient controller is the dominant control
action and in the post transient period, the voltage
controller is dominant one.
As it can be seen, the post fault terminal voltage
value is regulated to its prefault one and the
stability of the system is better than that of the case
of voltage controller.
Figure 13: System response to a three -phase to a
ground fault with voltage controller.
Figure 14: System response to a three -phase to a
ground fault with transient controller.
Figure 15: System response to a three -phase to a
ground fault with general controller.
8 Conclusion
In this paper, a global control law for transient
stabilization and voltage regulation of power
systems was presented. To achieve the global
control action that guarantees both transient
stability and voltage regulation, we used a
membership function that was a function of
measurable parameters of the system (rotor relative
speed and generator terminal voltage). Then, the
global control law was formed as a weighted
summation of both transient controller and voltage
regulator with respect to their membership
functions. The simulation results showed the
effectiveness of the proposed global controller.
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