Scientific Paper / Artículo Científico 



https://doi.org/10.17163/ings.n29.2023.01 


pISSN: 1390650X / eISSN: 1390860X 

VOLTAGE STABILITY AND ELECTRONIC COMPENSATION IN
ELECTRICAL POWER SYSTEMS USIGN SIMULATION MODELS 

ESTABILIDAD DE TENSIÓN Y COMPENSACIÓN ELECTRÓNICA EN SISTEMAS ELÉCTRICOS DE POTENCIA USANDO HERRAMIENTAS DE SIMULACIÓN 
Received: 21042021, Received after review:
24092021, Accepted: 08112021, Published: 01012023 
Abstract 
Resumen 
Increased demand in the different electrical
power systems (EPS) has a negative impact in voltage stability, reliability
and quality of the power supply. Voltage profile is reduced
when generation units are not capable of supplying reactive power to the EPS
at the times it is required. With the development of power electronics and
complex control systems, flexible alternating current transmission system
(FACTS) devices have benn introduced. In this
article, the impact of the introduction of a type of FACTS that allows
reactive power compensation in the EPS is analyzed
in detail. Furthermore, a methodology to decide the capacity of the Static
Synchronous Compensator (STATCOM) and its optimal location with the execution
of continuous power flows (CPF) will be analyzed.
Finally, the positive impact of installing a Power System Stabilizer (PSS)
control to ensure voltage stability in the EPS will be
studied. This article is developed using the IEEE 14 bus base system
under two mathematical models for power flow calculation developed in MATLAB
software, which are: i) through the power balance
equations and ii) Newton Raphson with the toolbox PSAT. 
El aumento de la demanda en los distintos sistemas eléctricos de potencia (SEP) tiene un impacto negativo en la estabilidad de la tensión, la confiabilidad y la calidad del suministro eléctrico. El perfil de tensión disminuye cuando las unidades de generación no son capaces de suministrar potencia reactiva al sistema eléctrico en los momentos que se requiere. Con el desarrollo de la ectrónica de potencia y los complejos sistemas de control, se han podido introducir dispositivos de sistemas flexibles de transmisión de corriente alterna (FACTS, del inglés Flexible Alternating Current Transmission System). En este artículo se analiza en detalle el impacto que genera la introducción de un tipo de FACTS que permite la compensación de potencia reactiva en el SEP. Además, se analizará una metodología para decidir la capacidad del compensador síncrono estático (STATCOM), del inglés Static Synchronous Compensator) y su ubicación óptima con la ejecución de flujos de potencia continuos (FCP). Finalmente, se estudiará el impacto positivo de la instalación de un control estabilizador de potencia (PSS, del inglés Power System Stabilizer) para asegurar la estabilidad de tensión en el SEP. Este artículo se desarrolla utilizando el sistema base IEEE de 14 barras bajo dos modelos matemáticos para el cálculo del flujo de potencia desarrollados en el software Matlab, que son: i) utilizando las ecuaciones de balance de potencia y ii) Newton Raphson con el toolbox de MATLAB (PSAT, del inglés Power System Analysis Toolbox). 
Keywords: Load Factor, PSAT, contingency, Continuous
Power Flow, PSS, STATCOM 
Palabras clave: factor de carga, PSAT, contingencia, flujo de potencia continuo, PSS, STATCOM 
^{1,*}^{ }Grupo de Investigación de Redes eléctricas Inteligentes (GIREI), Universidad Politécnica Salesiana – Ecuador. Corresponding autor ✉: mcampana@ups.edu.ec. Suggested
citation: Campaña, M.; Masache,
P.; Inga, E. and Carrión, D. “Voltage stability and
electronic compensation in electrical power systems using simulation models,
“Ingenius, Revista
de Ciencia y Tecnología,
N°. 29, pp.114, 2023, DOI: https://doi.org/10.17163/ings.n29.2023.01. 
1. Introduction Most
interruptions in electric transmission networks (ETN) are due to voltage instability.
Possible causes may be overloaded electric systems, occurrence of faults or
lack of available reactive power in generation units. At present, it is
possible to have a greater control of the voltage margin on each of the buses
of the EPS [1–3]. The ETN are responsible for supplying electric power from
the generation units to the loads, meeting safety and reliability criteria.
The shortage of reactive power that a generation unit may supply to the
system may be due to a load increase in the EPS, causing a possible
degradation of the voltage stability in the electric system [4, 5],
especially in buses that operate close to their limits. It is
shown in [6] that the maximum capacity for transferring electric power
through the ETN may be improved installing FACTS devices. Such devices may
anticipate control of power flow and voltage profile, improve voltage
stability and minimize losses. However, their high cost limits the
installation of FACTS controllers in all lines of the EPS. It is assured in [7,8] Thath
the best FACTS devices are those based on converters such as: STATCOM and the
Unified Power Flow Controller (UPFC). The present paper will pay special
attention to the synchronous static compensator and its direc
control on voltage stability. Another detail addressed in this paper is the dynamic analysis in the
presence of electromechanical oscillations in the EPS. These oscillations may
be local (a single generator) or may involve a number of generators widely
separated geographically (oscillations between areas). If they are not
controlled, these oscillations may lead to a partial or total interruption of
the power supply [9]. Electromechanical oscillations may be
damped through the application of PSS. The objective of the PSS is to
modulate the extinction voltage of a synchronous generator acting through the
automatic voltage regulator (AVR) [10, 11], and are economically viable for
improving voltage stability in the presence of small disturbances [1214].
Therefore, PSS use auxiliary stabilizing signals, such as shaft speed,
terminal frequency and power to vary the AVR input signal. The block diagram of the PSS used in this paper may be verified in
[9], [15,16]. Regarding this aspect, one of the main
contributions of this paper is proving that the voltage instability produced
by an N − 1 contingency (opening of a line) may be eliminated
adding a PSS in bus 1 of the proposed EPS (Figure 1). The objective of this paper is to study voltage stability and the direct effects of installing synchronous static compensators in buses whose nominal voltage is critical, i.e., it is below or about to go below the lower voltage limit (0.95 pu). The IEEE 14bus system is used as a base case to validate the proposed methodology. In addition, through the application of PSS and simulations in timedomain with the PSAT toolbox, it will be proven that power stabilizing systems may enable maintaining EPS stability or reducing the negative effect on it of an N −1 contingency. To achieve the objective of this paper, power flows will be simulated in static state under two iterative 
mathematical models based on power balance equations and Newton
Raphson methodology. In addition, this analysis will enable evaluating the
performance and error margins between each model. It is very important to
mention that the Matlab software and the PSAT
toolbox developed by Federico Milano will be used
here.
The power flow
analysis will help to verify the steady state magnitude of voltage, angle and
active and reactive power of both load and generation. The different
operating states will vary according to various initial parameters set on the
EPS obtained from the IEEE 14bus base case. These parameters will enable
generating unstable conditions in the EPS, and further evaluating and beimg able to determine the best technical action to
recover stability in the electric power system. The actions to which the
system will be subject are: i) symmetrical increase
of the load by a load factor λ that will directly multiply the active and reactive power of all
loads and ii) opening of lines that simulate N − 1 contingencies. Figure 1.
IEEE 14bus system base case Section II briefly
analyzes the positive impact on the voltage profiles of an EPS when using
synchronous static compensation in power transfer buses. Section III
formulates the problem and explains the methodology applied in this paper.
Section IV presents the results obtained in the simulations. At last,
conclusions are presented in section V. 2. Materials y
methods The FACTS devices are not only capable of controlling the power transmitted and increasing the capacity of the lines, but also may suppress power fluctuations [4], [17, 18]. These devices are constructed with static elements 
and power electronics
elements which, together, enable improving control and increasing the energy
transfer capacity in alternating current (AC) systems. The
operating principle of the synchronous compensator, which is a type of FACTS,
considers three fundamental criteria i) a direct
current (DC) capacitor after a transformer operates as a controllable voltage
source, (ii) the voltage difference at the transformer reactance produces
exchanges of active and reactive power between the STATCOM and the SEP and
iii) the magnitude of the STATCOM output voltage may be controlled varying
the voltage across the CC capacitor [1921]. Figure 2 Illustrates a
basic structure that summarizes the STATCOM architecture. Figure 2. Basic structure of a type 2 STATCOM There are two types
of synchronous static compensators: the type 1 compensator is able to control
active and reactive power in a transmission line, while type 2 can only
control the angle ψ and the gain c remains fixed. ψ is the angular difference between
V_{1} (voltage at the STATCOM bus) and V_{0}
(Figure 2). In addition, the value of ψ should be kept very
small to be able to control the system reactive power and desired voltage.
Form small values of ψ, the reactive power supplied by the STATCOM has a linear relationship
[22,23]. Therefore, type 2 static synchronous
compensators are not able to supply active power, because they spend active
power to compensate transformer and commutation losses. Consequently,
according to the voltage level of the system and the type of compensator, the
STATCOM may operate as a capacitor or as an inductor. It is important to
mention that the type 2 STATCOM will be used in this
paper. The STATCOM may be modeled as a synchronous voltage source with
maximum and 
minimum limits of voltage magnitude. In
addition, the STATCOM obeys limits and according to the requirements is
capable of generating or absorbing reactive power [24–26]. It is important to
mention that in this paper the STATCOM will be modeled
as a voltage source enabling a rigid voltage support mechanism. The
methodology implemented to analyze the problem considers the following
statements: i) an analysis of the power flow in the
system from differential equations comparing it with the Newton Raphson
method and ii) stability analysis of angle and voltage. The EPS analyzed in
this paper is illustrated in Figure 1. The system
has 5 generation buses, 11 loads and 20 transmission
lines. The base of the system is 100 MVA and bus 1 is
defined as Slack or reference bus. The present paper will be analyzed
at two moments i) power flow and arbitrary
installation of a STATCOM at buses 13 and 14 and ii) it will be analyzed the
voltage stability observing CPFs, which will enable to analyze the EPS
behavior through the load factor increase. The power flow will be analyzed in
two ways i) a mathematical model developed in Matlab considering the power balance equations and ii)
the power flow using the PSAT toolbox. This will enable evidencing the error
margins and performance of each model. It
is known that a load increase both in active and
reactive powers will stress the system, and the reference values of voltage
in each bus will be degraded. It the generation units are not capable of
supplying the reactive power demanded by the system, these voltage values will decrease. This voltage reduction in the buses will
compromise the EPS voltage stability. In the present paper the load factor λ will be increased 50%, i.e., λ will be equal to 1.5 pu. This will stress the system and through a static
state power flow it will be possible to observe the
voltage magnitudes updated with the load increase. Once the system has been stressed due to the load factor, buses 13 and 14
are chosen (Figure 1) as candidate sites for installing the STATCOM. The
fundamental objective is to determine the type of STATCOM and the best
location considering technical criteria at the lowest cost. The basic
criteria for dimensioning and selecting the best location to install a
STATCOM are defined in the literature considering three very important
factors, namely: i) it should be chosen the STATCOM
with minimum Mvar capacity that ii) guarantees that
voltage remains within allowable limits (1.050.95 pu)
verifying that iii) total reactive power losses in the EPS are minimum. At a
second moment, it will be analyzed the stability of the electric system in
the presence of N −1 contingencies in line 24 of Figure 1.
Finally, it will be simulated the effect of the STATCOM on the EPS before and
after its installation. A
modern electric system consists of a large mixture of renewable energy
sources, variable and flexible 
conventional generators are being
replaced by sources based on power electronics [27]. Consequently, the EPS
stabilizers are controllers installed in synchronous generators whose main
function is to dampen the oscillations of the electric system controlling the
excitation, with the purpose of increasing the stability margin in the
presence of low frequency oscillations in the EPS. The PSS controllers have
two structures constituted by i) gain and phase
compensation stages and ii) three bands corresponding to a specific frequency
range (low, intermediate and high frequency) in which each band is
constituted by two branches based on differential filters (with a gain, delay
blocks and a hybrid block) [28]. Consequently, the design of power system stabilizers
is a challenging task that requires long time, and thus an alternative for
controller adjustment is the use of optimization methods [29]. An optimal
design of a multimachine PSS is proposed in [30]
for various simultaneous steadystate operating conditions.
2.1. Methodology for Power Flow
Calculation To know the behavior of the EPS at
an operating point where the power flow is computed; the methodology and
equations that model the power flow are detailed below: · Initialize the unknown variables
of the system. Voltage equal to 1 p. u. and
angles equal to 0 rad. · Admittance of the system (Ybus)
· Equations that govern the power
flow
· Balance of active and reactive
power
· Jacobian matrix 
· Solution of equations
· New iteration values
· Stopping criterion
2.2. System transfer capacity It enables knowing
the maximum power transfer allowed in the electric system when an N −1
contingency occurs; the mathematical model given by equations 1114 is used to calculate this index. · Total transfer capacity
· Real power transmitted
· Transmission margin before reaching instability
· Transfer capacity
2.3.Voltage stability Voltage stability may be verified from CPF usage. The objective of CPF is
periodically increasing λ to reach the maximum inflection point (λ_{max}) where the stability of the electric system
operates at the limit; i.e., when it reaches its maximum value (λ = P_{L}_{max}),
the voltage magnitudes at the different buses of the EPS will decrease until
reaching a voltage collapse. The voltage stability analysis is carried out from the power vs. voltage curve (PV
curves). The PV curve is simulated from the power
flow using equations (1)  (10). 
3.
Results and discussion This section presents a detailed
description of the power flow and voltage stability
analysis results. The magnitudes of voltage, angle, active and
reactive power of both load and generation are obtained
analyzing the EPS at an operating point under specific initial conditions.
The EPS topology and its electric parameters (transmission lines and buses) are detailed in Tables 1 and 2 [31]. Table 1 describes the
EPS topology and the line impedance parameters. Table 2 details the active
and reactive powers of generation, load and base voltage, and also defines
the type of line according to the following nomenclature i)
1 Slack bus ii) 2 PV bus and iii) 3 PQ bus. Table 1.
Data of lines in the IEEE 14 bus base case
Table 2.
Data for cach Bus in the IEEE 14 bus base case
Once the initial
parameters and the features of the ETN have been defined,
it is verified the performance of tho mathematical
models developed in Matlab for power flows. 
The first model provides an
iterative solution based on power balance equations (traditional method),
whereas the second model uses the Newton Raphson algorithm with the PSAT
toolbox. 3.1. Power flow using computational tools Figure 3 enables to verify the
voltage and angle variation ranges obtained from the simulation. Figure 3(a)
shows the node voltage levels at each bus of the EPS for two computation
models. The results of the mathematical model proposed in the PSAT toolbox
are shown in orange, whereas the solution of the
mathematical model proposed in Matlab using power
balance equations is shown in blue. In buses 4, 5, 7, 9, 10, 11 and 14 the
average error is 0.0037 p. u (Figure 3(a)); it can
be seen that the error margin between the two models (Matlab
– PSAT) is minimum, technically zero. Figure 3(b) represents the magnitude of
the angles in each of the buses of the EPS; similarly, the average error
margin in the angle results is 0.0042 radians. Therefore, the two models
proposed for analyzing the power flow at steady state provide reliable
solutions with minimum error margins. An additional detail that may be seen in Figure 3 is that the voltage magnitudes do
not exceed the upper and lower limits of 1.05 p. u. and 0.95 pu, respectively, except for the Slack bus whose voltage
is defined as 1.06 p. u. due to its nature. The error margin in
the active and reactive power is presented in Figure
4. The average error margin in the active power is 0.0019 pu,
as it can be seen in Figure 4(a), whereas the
average error margin in the reactive power is 0.0593 pu.
A detail that should be taken into account is that
both active and reactive power show similar trends, with error margins that
approach zero. Therefore, considering only the comparative analysis of the
results obtained for both models, presented in Figures 3 and 4, it may be concluded that both ways to obtain a solution to
the power flow are reliable. However, Table 3 analyzes the performance of the
methods proposed for power flow calculation. It may be seen in Table 3 that the models execute the same
number of iterations; however, the average margin of total active and
reactive power losses is 0.0006 and 0.0485, respectively, and thus, it may be
concluded that they are minimum and approach zero. It is important to mention
that the same value of 1 × 10^{−5} for the error margin was considered for both methods. On the other hand, the
CPU  Time achieved by the conventional method (power flow solved using power
balance equations) is approximately 65 time larger (Table 3); hence, the PSAT
toolbox is definitely a tool of very good performance, capable of providing
reliable solutions in significantly small machine times. 
Figure 3.
Node Analysis of the IEEE 14 bus EPS
Figure 4.
Node Analysis of the IEEE 14bus EPS 
Table 3. Performance of the
mathematical models proposed for computing the power flow Table
4 presents the initial results obtained for the power flow, which will be
referential magnitudes to start the study of voltage stability. It is very
important to mention that the results achieved were
extracted from the power flow solution provided by the PSAT Toolbox.
As it can be seen, it is possible to monitor the magnitudes of voltage,
angle, active and reactive power in each of the EPS buses; all the parameters
presented in Table 4 were simulated without constraints in the maximum and minimum
limits of active and reactive power. Therefore,
according to the initial values, the electric system operates at normal
conditions, which indicates that it honors the voltage limits established by
the regulation. In addition, Table 4 shows the total active and reactive
power losses in the EPS. Table 4.
Low NewtonRaphson power flow solution in IEEE 14 bus base case
Table
5 presents the results for a load factor of 50% both in active and reactive
power. In addition, the power flow is constrained to obey the power limits on
the generation buses whose magnitudes oscillate between 0.5 p.u. for the active power and 0.06 p.u.
for the reactive power. If the two cases presented in Tables 4 and 5 are
compared, it may be seen the increase in active and reactive power, both
generated and consumed. However, the voltage magnitudes in bus 14 fell below
the lower limit of 0.95 p. u. (Table 5). 
Table 5. Power flow solution for
50% load increase conditions with respect to the IEEE 14bus base case The new power flow,
considering active power limits with the implementation of STATCOM in buses
13 and 14, is illustrated in Table 6. It is very
important to remember that the STATCOM is modeled as
a voltage source. The initial parameters of the voltage source are fixed at 1 p. u. and 0 degrees, and thus, when a power
flow is executed with the PSAT Toolbox it will be obtained the reactive power
necessary to compensate and maintain the required voltage magnitude at 1 p.u. in the STATCOM installation bus. In other words,
this magnitude of generated reactive power will be necessary to compensate
the system for a load factor increase of λ = 1.5 p. u. of the demand. As it can be seen
in Table 6, the generation reactive power to maintain the voltage in buses 13
and 14 at 1 p. u. at 
different instants, reaches magnitudes of
40.5 and 34.8 Mvar respectively. In addition, it should be noted that when the STATCOM is placed at bus 13
the voltage profiles do not reach the admissible minimum values, whereas when
it is placed at bus 14 the bus voltages have appropriate values. An additional detail is that the EPS at normal and stress
conditions (λ =
1.5 pu) records minimum magnitudes of 0.956 and
0.924, respectively, in bus 14, which implies this is a candidate bus to
install the STATCOM because it exhibits lower voltage magnitudes in pu; therefore, it requires to be compensated with
reactive power to raise the voltage magnitude to appropriate ranges. On the other hand,
Table 6 presents total active and reactive power losses. It may be seen that the active power loss is of equal
magnitude, regardless of the bus where the STATCOM is installed. However,
there is a slight difference in terms of the total reactive power loss if the
STATCOM is installed in buses 13 or 14 (Table 6), with the smaller magnitude
corresponding to the case when the STATCOM is installed in bus 14. Therefore,
when minimizing total losses of reactive power, the optimal location of the
STATCOM is determined by the requirement of
maintaining the voltage profiles in moderate ranges and being the one with
the lowest class. Class refers to the magnitude of Mvar
required for the STATCOM. Finally, when the load factor is increased in 50%
in all PQ buses (load buses), it is required to install a STATCOM of class
34.80 Mvar in bus 14 with the purpose of
maintaining the voltage levels at allowable magnitudes, thus guaranteeing
voltage stability using synchronous static compensation to minimize losses.
When losses are minimized, the power flow transfer
capacity is maximized in the EPS, as specified in the literature. 
Table 6.
Power flow solution applying STATCOM to the IEEE 14 bus base case


3.2. Continuous power flow in voltage
stability analysis This section presents the voltage
stability analysis before and after a contingency. In addition, it is analyzed
the response of the system after installing the synchronous static
compensation. Figure 5 presents
the voltage stability analysis in bus 11 of the EPS. It may be seen the
behavior of the bus in three scenarios: i) normal
operation (yellow curve), ii) disconnection of lines L2 and L4 (blue curve)
and iii) voltage stability analysis when reactive compensation is
incorporated through a STATCOM (red curve). Figure 5 presents the behavior of
bus 11 in normal operating conditions with λmax = 3.7 (approximately). When the load
increase occurs with λmax = 3.2, the stability margin is reduced. This occurs because the
EPS is stressed and its maximum power transfer
capacity is reduced, as shown in points 24 of Figure 5. The yellow and blue
metrics represent the PV curve in conditions before and after the contingency
without synchronous static compensation. An additional detail
shown by Figure 5 is that the capacity of keeping the system stable decreases
when the contingency occurs. When STATCOM is used, the voltage level
increases and it is able to transmit slightly more power, as can be seen in
points 46 of Figure 5. Therefore, the load factor level
does not vary significantly when synchronous compensation is used, however, the profile improves. Points 1, 3, 5 of Figure 5
represent the optimal operating levels of the system where it can be seen more clearly that the power transmission
capacity increases if the system has STATCOM to provide reactive power in
specific operating conditions. 
Figure 5.
Voltage level as a function of the normal operating parameter, N 1
contingency using reactive compensation The Available Transmission Capacity (ATC) is calculated in Table 7. This analysis is carried out considering the worst contingency that may occur in the system; for this case, the worst contingency is when the line 2–4 is disconnected, TPlo represents the power demanded, i.e., the power required by the system for its normal operation. Pl are the losses present in the entire EPS, TTC is the maximum power value that may be present in the system, ETC represents the actual power in the EPS and TMR is the available power margin in which the electric system should remain before a voltage collapse occurs. Finally, it is proven that the STATCOM is capable of adjusting the voltage magnitudes in the buses of the EPS. A particular detail is that the STATCOM does not modify the active power values of the electric system. Based 
on the above, it may be inferred
that the STATCOM adjusts the voltage levels injecting reactive power in the
buses and maintains stable the voltage parameters under normal operating
conditions, and increases the voltage in case of a fault so that the system
remains stable. Table 7. Availabre
transfer capacity in the N1 contingency The voltage
stability analysis is performed with the metrics of
Figure 6 considering different scenarios. The continuous power flow in
initial conditions is computed 
with Figures 6(a, b and c), i.e.,
without contingencies and without the installation of synchronous static
compensators. The voltage stability when a contingency is
applied in lines L2  L4 is analyzed in Figures 6(d, e and f). For the
analysis mentioned it is proven the behavior of the
PV curve for different values of λ. The PV curves shown in Figure 6 illustrate
the magnitudes of the variables in the PQ buses. In the reference and
generation buses, the voltage level is constant. From Figures 6(ab) and
6(df) it may be inferred that as λ increases, the transmission capacity
(resulting λ)
decreases, and this occurs because the capacity of the electric transmission
system operates inversely to the load, i.e., as the load increases the
maximum electric power transfer capacity decreases. When a fault occurs
(Figures 6(df) and the load factor increases, the voltage levels drop
drastically putting the system in critical operating conditions, potentially
leading it to experience a voltage collapse. An additional detail is that
through the voltage stability analysis it is verified
that, when a disconnection or fault occurs in the system, the voltage in all
its PQ buses is reduced, mainly because they are load buses, but voltage
drops are not significant in the generation buses. 


Figure 6.
PV curves with Continuous Power Flow (CPF) analysis. Figure a, b and c
correspond to a CPF without STATCOM and without contingencies, and Figures d,
e and f include a CPF without STATCOM and a contingency produced by the
opening of the 24 line 

Figures 7 and 8 and
Table 8 display the metrics for analyzing voltage stability and angular behavior
in the buses considered; the voltage variable is analyzed with Figure 7; the
angular variation analysis corresponds to Figure 8 together with Table 8. The
PV curve that enables analyzing the voltage stability when line L2L4 is
disconnected is identified in Figure 7; this is considered 
the worst contingency of the electric
system. In addition, it is seen the load factor variation reducing the stable
operation margin of the electric system in the PQ buses when the load factor
increases to λ =
1.3 pu. The voltage drop is seen
in Figure 8. When a fault occurs, the voltage stability margin decreases, and
this may be seen in Figure 7(b). 
Figure 7. PV
curves in normal conditions and temporary opening of line 24, λ = 1.3, t = 1 s, t = 1 s Figure 8. Time domain curve in N1 contingency in line 24 
Table 8. Magnitudes of voltage and angle
Figure 8(a) enables performing a wide
analysis, because it shows an evaluation of the behavior of the buses in time
domain when there is a 30% increment in the load, and the disconnection
occurs in 1 second; the behavior of all buses is similar, therefore, Figure
8(a) will only present the buses in which there are significant variations
due to the contingency generated. Therefore, when there is an unscheduled
opening of any element of the electric system, mainly lines, this contingency
affects all PQ buses since the supply of reactive power from the generation
nodes to the loads is cut. Figure
8(b) presents the behavior of the angle in time domain. The
angular level varies according to the power flow and the initial conditions
considered for the calculation; Figure 8(a) represents the angular variation
in the PQ buses where there is a larger angular variability; it may be
observed that the larger angular variation occurs in buses 9, 10, 13 and 14,
where there is a drastic change in the voltage levels, as may be seen in
Table 8. Consequently, it is concluded that the disconnection of an
element of the system or a fault modify the system operating parameters and
affect the maximum and minimum voltage operating limits. Another
very important aspect revealed by Table 8 is a summary of the voltage level
variations and angular variation in each of the buses in time domain. Table 8
shows the voltage variations in all the buses; no changes are
observed in the PV buses, but in the PQ buses the voltage varies due
to the line disconnection. This occurs because the system power flow changes,
due to the drastic topology change and the redirection of the power flow due
to the opening of line 2 – 4; an important point is that under operating
conditions of 30% overload in the EPS, the voltage level in bus 14 is below
0.95 p.u.; a critical point of analysis is when the
line is disconnected at bus 14 and its voltage magnitude is below 0.93 p. u.;
i.e., the disconnection or fault in the system is affected 
by the connection to bus 14; a way
to stabilize the parameters at such bus is through synchronous static
compensation, which demonstrates that a candidate location to place the
STATCOM is bus 14. Table
8 enables analyzing the behavior of all system buses. The angular variation
is different in all PQ buses and, unlike the voltage level, when an angular
analysis is performed there is a variation in the PV buses; the only bus that
remains under the same operating levels, both in voltage and angle, is the
Slack bus, because when the power flow varies, the angle also varies.
Consequently, Figure 8 shows the angular variation and Table 8 the voltage
and angular variation in all system buses. Figure
9 illustrates the voltage stability when a type II PSS controller is used,
which implies that the possibility of analysis varies according to the PSS
input signal (angular speed, voltage and power); when a speed controller is
used, it is fundamental to assign various parameters for its full operation,
namely, maximum and minimum voltage, stability gain. Figure 9 has a gain of
100 and it is seen that the generator controller
starts to operate after line 24 is disconnected to maintain system
stability. This type of control is known as primary
voltage control, where the important issue is to stabilize voltage levels
after the EPS experiences any contingency.
Figure 9. Voltage
as a function of time in N1 Contingency with the opening of line 24 with
PSS voltage regulation 4.
Conclusions It has been possible
to verify the reliability of the data obtained from the PSAT Toolbox and the
performance, to provide results of voltage stability analysis and angular
variation. Consequently, it is a reliable tool to perform detailed voltage
stability analyses, considering the installation of STATCOM and PSS. The use
of STATCOM FACTS devices has demonstrated to be an effective method to reduce
the stress of the electric 
transmission network, and thus be able to
maximize the power flow exchange from generation units to the different
consumption points. In addition, the present research evidences that there
are alternatives such as the PSS controllers to adjust the voltage in buses
before deciding to install STATCOM, which has a higher cost. On the other hand,
the main contribution of this paper is considering a load factor that leads
the EPS to operate in congestion conditions. Such congestion produces
marginal operating costs, which raise the electric power transportation
costs. In addition, contingencies are considered to be able to evaluate and
select the most critical node (lowest voltage level), and thus be able to
determine the location of reactive compensation. Therefore, this paper
guarantees the optimal dimensioning of the STATCOM, to minimize power losses. There is a big
difference between the use of a FACTS compensator and the use of a PSS
controller in the generator. FACTS is a device that improves stability of the
voltage at the bus where it is located, and modifies voltage levels in most
of the buses of the EPS seeking to maintain them at 1 pu.
On the other hand, a PSS voltage control enables stabilizing the voltage
levels in the generation buses through a control additional to the AVR. The
gain is one of the fundamental variables to model PSS in the PSAT. The PSS
gain is directly proportional to the voltage magnitude increase in the
desired bus. Therefore, PSS only
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