PLACEMENT OF POWER SYSTEM STABILIZER (PSS) IN NIGERIA 28-BUS POWER NETWORK FOR EFFECTIVE VOLTAGE AND DYNAMIC STABILITIES EVALUATION

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PLACEMENT OF POWER SYSTEM STABILIZER (PSS) IN NIGERIA 28-BUS
POWER NETWORK FOR EFFECTIVE VOLTAGE AND DYNAMIC
STABILITIES EVALUATION
Akwukwaegbu, Isdore Onyema1, Obichere Jude-Kennedy Chibuzo2, Raymond Okechukwu
Opara3
1-3Department of Electrical and Electronic Engineering, Faculty of Engineering, Federal University of Technology,
Owerri, Nigeria.
---------------------------------------------------------------------***--------------------------------------------------------------------
ABSTRACT- Nigeria power network has been facing
voltage, steady-state and transient stability problems
with increasing load demand and high population
growth. The major causes of power network instability
include loading of the generators or tie line, power
transfer capability of transmission lines, leading power
factor operation of the generator and automatic voltage
regulator (AVR) gain. The objectives of this work include
overview analysis of the existing Nigeria 10 generators
330kV, 28-bus power network without introduction of
PSS model and develop a workable power network that
can provide dynamic and transient voltage control
during placement of PSS model in order to enhance the
totality of power network stability. The paper presents a
cost-effective and satisfactory design of power system
stabilizers (PSS) capable of solving problems of voltage,
network oscillatory instability and damping for
generator rotor oscillations. The designed PSS are
incorporated into two generators, 3-bus and 10
generators, 28-bus, 330kV Nigeria power network using
MATLAB/SIMULINK Power System Toolbox (PSAT)
program to evaluate voltage and network instability
problems. The dynamic or voltage collapse stability
results obtained from PSAT load flow analysis revealed
that the maximum loading points (MLP) for the network
with and without PSS are 10.1501 pu and 4.5674 pu
respectively.
KEYWORDS: Power System Stabilizers (PSS), Nigeria
28-bus power network, voltage problems, steady state
problems, transient stability problems, instability
problems, MATLAB/SIMULINK Power system Toolbox
(PSAT) program, maximum loading point (MLP).
1 INTRODUCTION
The behavior of synchronous machines following
perturbation lies at the heart of the stability challenge in
the power system. After a change in power, machines
should revert to their former condition if it doesn't alter.
A new operational state is required whenever a change
in load, generation, or network circumstances causes an
imbalance between supply and demand. No matter what
happens, if the system is stable, all linked synchronous
machines should be functioning at the same pace, in
parallel, and in synchronism [1,2]. Even though
synchronous machines and tie lines tend to have stability
issues, other types of power systems with large
capacitances may also have instability. Arrangements
must be taken to avoid damaging equipment and self-
excitation of machinery by avoiding high voltages under
light load situations. Modern synchronous generators
require high-performance excitation systems in order to
maintain steady-state and transient stability. Instabilities
caused by power system disturbances can lead to system
shutdowns. In the event of disruptions, such as three-
phase faults, loss of generators, loss of lines, and loss of
loads, stabilizing measures or controls must be
implemented in the power network to optimize system
performance. The energy supply sector has had its work
cut out for it when it comes to stabilizing and improving
power system oscillators. 330kV Nigeria 28-bus power
network electromagnetic oscillation stability issues may
be addressed using an effective power system stabilizer
(PSS).
Low-frequency power system oscillations were among
the first issues that arose in power systems. Small signal
stability in a power system is compromised by these low
frequency oscillations (LFOs), which jeopardize efforts to
maximize power transmission and secure the power
system. The stability issue was put on hold for a while
after the damper windings on the generator rotors and
turbines were confirmed to be adequate. A poor
synchronizing torque among the generators was shown
to be a substantial contributor to system instability as
power systems were operated closer to their stability
limitations. Improved steady-state stability was achieved
by the use of automatic voltage regulators (AVR).
Concerns about long-distance transmission lines
emerged with the development of massive,
interconnected power networks.
Low frequency oscillations can be reduced by adding a
supplemental controller to the control loop, such as the
addition of power system stabilizers (PSS) to the AVRs
on generator. Designed for a certain network topology
and steady-state circumstances, the power system
stabilizers are excellent at their job. However, as the

system grows more crowded, its performance suffers
[3,4,5,6].
With the introduction of high-speed exciters and
continuously-acting voltage regulators, the possibility to
manage synchronous machine angular stability through
the excitation system was discovered. Hydraulic and
thermal equipment increasingly employ bus-fed static
exciters with thyristor controllers. Because of
improvements in thyristor controllers, they have a
strong initial reaction and better dependability
[7,8,9,10].
A power system analysis toolkit, MATLAB/SIMULINK, is
used to model the voltage and dynamic stability of two
generators, three-bus and ten generators, 28-bus 330kV
Nigeria power networks (PSAT).
2. MATHEMATICAL ANALYSIS OF POWER SYSTEM
STABILIZER (PSS)
The concepts of stabilization in the power network is
described by a set of non-linear differential and algebraic
equations as follows [4,5]:
PX = F(X, Z), P=d/dt s (1)
Y = H(X, Z) (2)
0 = G(Y, Z) (3)
The oscillatory instability can be viewed as stability of
the operating point, subjected to small, random
perturbations which are always present. The analysis
can be performed by linearizing the system equations
around the operating point (X = X0, Y = Y0, Z = Z0). Where
X are the state variables, Y represent active and reactive
power injections (at buses), Z represent voltage
magnitudes and angles at various buses.
Expressing
X = X0 + ΔX, Y = Y0 + ΔY, Z = Z0 + ΔZ (4)
It is possible to obtain the following equation:
PΔX = [A]ΔX (5)
Where
[ ] [ ( ) ] (6)
The elements of A are functions of the operating point.
The stability of the operating point can be judged by the
location of the eigenvalues of the matrix A. If all the real
points of the eigenvalues are negative, the system is
stable. If one or more has positive real parts, then the
system is unstable
Assuming that the classical model is used to represent
the generators in a multi-machine system, the linearized
system equations may be expressed as follows:
[M] 2Δδ = -[K]Δδ (7)
Where [M] is diagonal matrix Mjj = 2Hj / ωB (Hj is the
inertia constant of the jth synchronous machine).
, where Pei is the power outputs of the ith
machine, is the rotor angle of jth machine referred to a
rotating reference frame (with the operating speed ω0).
If the network can be reduced by retaining, only the
internal buses of the generators and the losses in the
reduced network can be neglected,
( ) (8)
Where Xij is the reactance of the element connecting the
generator buses i and j; Ei and Ej are the generator
voltages.
The solution of equation (7) is represented as
∑ ( )
Where [ ] is the vector of
relative angles ( , C1, … , Cm-1, d1, d2, … ,
dm-1 are scalars depending on the initial conditions, V1,
Vm-1 are vectors. The structure of a vector Vj depicts the
participation of various machines in the oscillation mode
whose frequency is . For a ‘m’ machine system, there
are (m-1) oscillatory modes whose frequency varies in
the range of 0.2 to 3Hz. The frequencies are obtained as
square roots of the non-zero and real eigenvalues of the
matrix[ ] [ ].
The various modes of oscillation are grouped into three
broad categories [9] as follows:
 Power plants can operate in intra-plant modes,
in which only the generators are involved. It is
common for the oscillation frequencies to be
rather high, ranging from 1.5 to 3.0Hz.
 Local modes, in which a number of generators in
a given region collaborate. The oscillations occur
at frequency ranging from 0.8 to 1.8 hertz
(hertz).
 I Inter-area modes, in which generators located
throughout a large geographic region
participate. The oscillation frequencies are
modest, ranging from 0.2 to 0.5 hertz (cycles per
second).

3. DESIGN AND IMPLEMENTATION OF POWER
SYSTEM STABILIZERS
In its most basic form, a power system stabilizer (PSS) is
a device that dampens the oscillations of a generator
rotor by managing the excitation of the generator with
supplementary stabilizing signals. A component of
electrical torque in phase with the rotor speed variations
must be produced by the stabilizer in order for it to offer
dampening. The PSS is intended to enhance the amount
of power that can be sent through a network, which is
currently restricted by oscillatory instability. When the
network is subjected to major disruptions such as the
development of a three-phase fault, the unexpected loss
of a line, or the sudden application or removal of loads,
the PSS must function effectively. The block diagram of
the PSS design used in the power network is shown in
figure1.
Fig. 1: Block diagram of power system stabilizer.
Power system stabilization is now presented using the
thyristor excitation system, as seen in Fig 2, as a case
study. The AVR and power system stabilizer are included
in the excitation block diagram for correct modeling. In
this study, small-signal performance, stabilizer and
exciter output limitations, and other parameters, are
taken into consideration. Here's a quick rundown of the
criteria that go into creating different power system
stabilizer setups.
Fig. 2: Thyristor excitation system with AVR and PSS.
Phase correction, signal washout, and gain blocks make
up the power system stabilizer seen in figure 2.
(i) For the exciter-to-generator electrical (air-gap)
torque phase lag, the phase correction block
gives the required phase lead characteristic. A
single first-order block is shown in the diagram.
It is possible to obtain the needed phase
compensation by using two or more first-order
blocks. Second-order blocks with complicated
roots have been employed in several instances.
Phase correction for the Power System Stabilizer [3] is
based on the following criteria:
a) The compensated phase lag (phase of P(s) =
GEP(s)PSS(s)) should pass through 90o at
frequency around 3.5Hz. For frequency input
signal, this can be reduced to 2.0Hz.
b) The compensated phase lag at local mode
frequency should be below 45o, preferably near
20o.
c) The gain of the compensator at high frequencies
(this is proportional to ) should be
minimized.
The first requirement must be met in order to avoid
instability of intra-plant modes at higher frequencies in
the future. Typically, the frequency range of interest is
0.1 to 2.0Hz, and the phase-lead network should offer
compensation throughout the whole frequency range of
interest.
(i) The signal washout block serves as a high-
pass filter, with the time constant Tw high
enough to allow signals associated with
oscillations in wr to pass unchanged.
Washout it, steady changes in speed would
modify the terminal voltage. It allows the
PSS to respond only to changes in speed.
The value of Tw is not crucial from the
perspective of the washout function, and it
can be anything between 1 and 20 seconds
in duration. In particular, it must be long
enough to allow stabilizing signals at the
frequencies of interest to pass through
intact, but not so long that it causes
undesired generator voltage excursions
during system-islanding situations.
(ii) The stabilizer gain, denoted by the letter
KSTAB, regulates the amount of damping
that is introduced by the PSS. (3) The gain is
set to the value that corresponds to the
greatest amount of dampening.
The power system stability should be considered
when applying the PSS to the power network, rather
than merely the small-signal stability, because the
overall system stability should be improved [3].
Using perturbed values, block 4 of figure 2 is considered
to be made up of two blocks:

In this case, becomes the state variable, with
(10)
and the output ΔV2 of the block is given by
(11)
Similarly, block 5 of figure 2 is treated as follows:
In this case, is the state variable, with
(12)
and the output is given by
( ) (13)
The basis for the choice of the time constants of the
phase compensator can be analysed with reference to
the block diagram of the single machine system when
PSS is added as shown in figure 3
Fig. 3: Stabilizer with speed input: system block diagram.
To produce pure damping torque at all frequencies, the
phase characteristics of the power system stabilizer
(PSS) must, in the ideal case, balance the phase
characteristics of the general purpose generator (GEP) at
all frequencies. Specifically, the phase compensator used
in this application is composed of two lead-lag states and
has the following transfer function.
Where Ks is the gain of the PSS and the time constants,
T1, to T4 are chosen to provide a phase lead for the input
signal in the range of frequencies of interest (0.1 to 3.0
Hz). With static exciters, only one lead-lag state may be
adequate. In general, the phase compensator can be
chosen with the following transfer function
(15)
Where:
N(s) = 1+ a1s + a2s2 + … + apsp
D(s) = 1+ b1s + b2s2 + … + bpsp
The zero of D(s) should lie in the left half plane. They can
be complex or real. Some of the zeros of N(s) can lie in
the right half plane making it a non-minimum phase. The
time constants, T1 to T4 in equation (14) are to be chosen
from the requirements of the phase compensation to
achieve damping torque. The gain of PSS is to be chosen
to provide adequate damping of all critical modes under
various operating conditions.
The different values of the centre frequency, fc the
compensator of equation (14) are computed by
√
(16)
It is assumed that
(17)
The plant transfer function, GEP(s) is computed by
(18)
Where Vs is the output of the PSS
4. APPLICATION OF PSS TO NIGERIA POWER
NETWORK
Power system stabilizer behavior is studied using the
current 330kV, 28-bus, 10 generator Nigeria network.
Niger's 28-node, 28-bus system has 10 generators and
18 load (PQ) buses; 16 transformers; 12,426MW grid
capacity and 5,988km transmission lines as seen in fig 4.
The lower reactance and smaller inertias between the
two machines make it possible for the intra-plant
oscillations to have a greater frequency since they are
linked in parallel between the two producing stations in

Nigeria's 3-bus power network. Afam and Calabar are
the locations of the two generators. At Alaoji bus 23, fig 5
shows the two generator buses connected to each other
at Afam and Calabar buses 7 and 10 and the line linking
bus-bars. There are two generators at Afam bus 7 and at
Calabar 10, each with a producing capacity of 726
megawatts and 155 megawatts, respectively, and the
transmission line distances between them and Alaoji bus
23 are 25 kilometers and 38 kilometers.
Figure 4: The existing 28 bus 330KV Nigerian
transmission grid.
Fig. 5: Two generating stations, 3-bus power network.
The two generators located at Afam bus7 and Calabar
bus 10 swing together during oscillation. A Power
System Analysis Toolbox (PSAT) specialized tool in
MATLAB environment is deployed for assessing the
behavior of power system stabilizer of 2 generators 3-
bus Nigeria power network. MATLAB/SIMULINK circuit
designed using electrical blocks contained in the
SIMULINK library for 2 generators 3-bus and 10
generators 28-bus Nigeria power networks connected
with power system stabilizers are illustrated in figures 6
and 7 respectively.
Fig. 6: Simulink block representation of two generators,
3- bus power network connected with power system
stabilizer.
Fig. 7: MATLAB /SIMULINK circuit design for
investigating voltage stability of 10 generators 28-bus
Nigeria power network with PSS connected.
5. RESULTS AND DISCUSSION
Using two generators connected in a three-bus power
network without a power system stabilizer, the transient
behavior of line voltage (kV), line power (MW), angle (°),
angular speed (ω), and reference voltage were
demonstrated in Figures 8 and 9. The findings of the
simulation for a two-generator, three-bus power
network following the occurrence of a three-phase
failure revealed that the network is unstable in the
absence of the use of a power system stabilizer. When
the PSS design is connected to the network, the line
power settles after 2.5 seconds, the angle after 4
seconds, the angular speed after 3 seconds, and the
terminal voltage after 2.5 seconds, as illustrated in
figures 10 to 11, respectively.
The 10 generators 28-bus power network with PSS
recorded 14 low and high voltage violations with total
power loading and maximum power factor values of
6.5585pu and 10.1501pu, whereas when this power
network was not connected to a PSS, all buses of the
network recorded voltage violations with total power
loading and maximum power factor values of 2.9501pu
and 4.5674pu, as shown in table 1 and figures 12 to 15,
respectively.

Fig. 8: line power and Vpos for two generators 3-bus
power network without power system stabilizer.
Fig. 9: Angle, angular speed and reference voltage for
two generators 3-bus power network without power
system stabilizer.
Fig.10: line power and Vpos for two generators 3-bus
power network with power system stabilizer.
Fig. 11: Angle, angular speed and reference voltage for
two generators 3-bus power network with power system
stabilizer.
Table 1: PSS Stability analysis result for Nigeria 10
generators, 28-bus power network .
PSS
Designed
scheme
Voltage
profile
Maximum
loadability/collapse
point(PU)
Total
power
loading(PU)
Without
PSS
All
buses
violated
4.5674 2.9501

With
PSS
14 10.1501 6.5585
Fig. 12: Voltage profile for10 generators, 28-bus power
network without PSS.
Fig. 13: P-V curve for 10 generators, 28-bus power
network without PSS.
Fig. 14: Voltage profile for 10 generators, 28-bus power
network with PSS.
Fig. 15: P-V curve for 10 generators, 28-bus power
network with PSS.
6. CONCLUSION
Modern synchronous generators require high
performance excitation systems in order to regulate the
terminal voltage quickly and ensure stable and transient
stability. Two 3-bus and 10 generators, 28-bus 330kV
Nigeria power network electromagnetic damped
oscillation, or swing, of the rotor instability concerns
following disturbances are tackled using
MATLAB/SIMULINK Power System Analysis Toolbox to
create and simulate effective power system stabilizer
models (PSAT). Using power system stabilizers, the 3-
bus Nigeria power network with two generators and a
rotor angle of 4 seconds, angular speed of 3 seconds, and
terminal voltage of 2.5 seconds all settled after 2.5
seconds. There were 14 voltage violations, 6.5585PU
total power loading, and 10.1501PU maximum power
factor in the 330kV Nigeria power network simulated
with the power system stabilizer. Without the PSS, all
buses had low and high voltage violations with total
power loading points and maximum power factors of
2.9501PU and 4.5674PU, respectively.
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PLACEMENT OF POWER SYSTEM STABILIZER (PSS) IN NIGERIA 28-BUS POWER NETWORK FOR EFFECTIVE VOLTAGE AND DYNAMIC STABILITIES EVALUATION

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