Static Voltage Stability Analysis with the Integration of Distributed
Generation: An Albanian Case Study
VIKTOR RROTANI*, RAJMONDA BUALOTI, MARIALIS ÇELO
Department of Electric Power Systems,
Polytechnic University of Tirana,
ALBANIA
*Corresponding Author
Abstract: - Modern power networks face significant operational uncertainties that can threaten the stability of
the power grid, due to the rising integration of distributed generation (DG), particularly from renewable energy
sources, such as photovoltaic plants. The integration of distributed generation (DG) into power systems has
become a pivotal factor in enhancing the efficiency and sustainability of electricity supply. This paper presents
a detailed static voltage stability analysis of the Albanian power grid, focused on the effects of the Karavasta
Photovoltaic Park, one of Albania’s largest renewable energy projects. Using a combination of P-V and Q-V
curves, V-Q sensitivity analysis, and modal analysis, the study reveals significant improvements in the system’s
voltage stability following the integration of the PV plant. The NEPLAN software is used for voltage stability
analysis. Particularly, the reactive power margin at the critical node Nst. Babice increased considerably from -
82.009 MVAr to -1061.2 MVAr, while the system’s loading margin improved from 99.08% to 101.97%,
demonstrating that the integration of large-scale PV generation enhances voltage stability by providing
additional reactive power support and improving the grid’s resilience to voltage collapse. Furthermore,
the modal analysis identified the Bistrice-Delvine-Sarande buses as the system’s weakest points, highlighting
areas where additional reinforcement is required. As more renewable energy has to be integrated into the grid,
the study also emphasizes the importance of making targeted interventions at critical buses and branches to
ensure long-term stability. The results of this research are essential for Albania’s energy transition as the
country seeks to diversify its energy sources, especially solar power. More generally, the methodologies and
results in this paper provide a suggestion for maintaining power system voltage stability with increased
renewable energy penetration.
Key-Words: - Photovoltaic Plant, Distributed Generation, Voltage stability, Neplan, Comparison, Static
methods.
Received: April 17, 2024. Revised: September 9, 2024. Accepted: October 13, 2024. Published: November 19, 2024.
1 Introduction
The traditional electricity system is undergoing a
tremendous revolution that is happening rapidly
changing how it is controlled and operated.
Historically, the traditional power system—
especially in Albania—has mostly depended on a
large number of synchronous generators to keep the
grid’s voltage and frequency stable. However, the
operation and control of power systems are
changing with the introduction of renewable energy
sources, such as converter-based generators, [1],
necessitating the development of new services, such
as frequency control reserves, to ensure efficient and
secure operation of power systems, and that presents
challenges due to their impact on grid voltage levels
[2]. Distribution and transmission system operators
need to cooperate to fully understand the integration
of renewable energy sources into the power system.
Photovoltaic plants, installed in the presence of
loads, can improve the quality and security of
energy supply, reducing losses in transmission and
distribution networks. Albania has great potential
for this due to the high number of sunny hours per
year, approximately 2700 hours/year. According to
an IRENA study, by 2030, it is forecasted that
photovoltaic plants with a capacity of 1074 MW
will be installed, with an annual production of 1697
GWh, [3]. However, it is important to highlight that
the inverters used for connecting photovoltaic plants
have a low inertia constant, making them sensitive
to network fluctuations, [1].
Distributed Generation (DG) is typically
considered as electricity produced closer to the end
point of use. DG units have been widely installed in
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demand systems and directly connected to
distribution networks due to the fast development of
DG technologies, [4], [5]. These systems can reduce
power losses and delay investment in distribution
and transmission expansion. Adequate size and
optimal location are essential to achieving it, [6].
However, there are advantages and disadvantages to
the DG connection in terms of environmental,
technical, and economic aspects, [7]. A high level of
DG penetration may affect the control and operation
of the whole system, leading to technical
consequences that must be determined, [8], [9].
Therefore, to avoid instability issues and guarantee
an acceptable system voltage, such aspects need to
be examined.
Problems related to voltage stability in power
systems are one of the major concerns in power
system planning and operation, [10]. Voltage
stability is concerned with the ability of a power
system to maintain acceptable voltages at all nodes
in the system under normal conditions and after
being subject to a disturbance, [11]. The electrical
system is in a state of voltage instability, when there
is a continuous and uncontrolled decrease in
voltages at voltage buses, due to disturbances. This
phenomenon is known as voltage collapse.
Voltage instability issues are examined through
a variety of both static and dynamic analytical
methods. The P–V and Q–V curves are widely
employed tools for evaluating the static voltage
stability limits of a power system [12], [13], and
[14]. References [15] and [16] utilized the minimum
eigenvalue of the power flow Jacobian matrix as an
indicator of the proximity to voltage collapse. The
concept of the energy function is employed in [17],
[18] to establish a voltage stability index.
Additionally, references [19], [20], [21], and [22]
used a simplified equivalent circuit, derived from
the Thevenin theorem, to evaluate the voltage
stability limit of a power system. Although stability
studies generally require a dynamic model of the
electrical system, this paper focuses on analyzing
voltage behavior through static techniques, which
are commonly used in voltage stability assessments,
[23].
The literature [24] gives a review of bus and
line stability indices to monitor the level of voltage
stability in the electric network. In [25] it is used
MVSI indicator to identify the weak areas of electric
power systems and predict the voltage collapse for
different load conditions.
This paper is organized into seven sections. The
second section provides a detailed explanation of
the voltage stability static methods utilized in the
case study. The third section presents an overview
of the Albanian power system. The fourth section
presents the case study itself. The fifth and sixth
sections delve into results and discussions. Lastly,
the seventh section presents the conclusions.
2 Static Methods
There are several methods to assess the voltage
instability issue, and they can be generally divided
into two groups: static and dynamic. The voltage
stability methods that will be used in the
examination of the Albanian power system are
discussed in this section.
2.1 The P-V and Q-V Curves Methods
P-V and V-Q curves are generated through
continuous load flow calculations. Prior to the
calculation, several selections must be made: a
group of loads and generators whose power will
change during the calculation process within
predefined limits, a group of bus voltages to be
recorded, the loading rate at the beginning of the
simulation, and the loading rate at the end of the
simulation if the process is to be stopped before
voltage collapse occurs, [26]. These methods fail to
give useful information about the causes of voltage
instability and it is not possible to precisely know
the collapse point, [23].
2.1.1 The P-V Curves Methods
The P-V curves are the most commonly employed
method for Voltage Stability Assessment. P-V curve
analysis illustrates the relationship between active
power transfer from a source to a load and its impact
on load voltages. P-V curves are generated through
a parametric study involving a series of AC load
flow calculations, systematically monitoring
changes in one set of load flow variables relative to
another. This process determines transfer limits,
accounting for voltage and reactive power flow
effects. These curves are instrumental in identifying
the loading margin of a power system, where the
margin between the voltage collapse point and the
current operating point serves as a voltage stability
criterion. Figure 1 is depicted a P-V curve. As the
load is gradually increased, there are computed
power flows until reaches the P-V curve’s nose. At
the nose point, additional load growth gives no
feasible operating voltage magnitude, and it is the
point when voltage collapse often occurs, [11], [27].
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Fig. 1: P-V curve, [23]
For a P-V curve, the distance of active power
from the operating point to the nose point of
the curve is called the active power margin and is
calculated below:
Where:
- Pcritical – the value of the active power of the P-V
curve at the nose point
- Poperating – the value of the active power of the P-V
curve at the operating point
The voltage stability margin (VSM) of a bus is
known as the distance between the initial voltage
point and the voltage collapse point and can be
calculated as below:
Where:
- Vinitial – the initial bus operating voltage
- Vcritical – the bus voltage at the collapse point
2.1.2 The Q-V Curves Methods
By the Q-V curve method is possible to know the
maximum reactive power that can be achieved or
added to the weakest bus before reaching
the minimum voltage limit. The Q-V curve can be
used as an index for voltage instability. The point
where dQ/dV is zero is defined as the point of
voltage stability limit, [18]. Figure 2 depicts a Q-V
curve. The operating point is where the curve
intersects the x-axis, and the y-axis displays the
amount of reactive power that must be injected or
absorbed for a bus to operate at a specific voltage. A
reactive power deficiency is indicated if the
minimum point is above the horizontal axis, and
more reactive power sources are required to avoid a
voltage collapse situation [11], [27]. VSM is
calculated as the equation (2).
Fig. 2: Q-V curve, [23]
For a Q-V curve, the reactive power margin is
the distance from the operating point to the nose
point of the curve and is calculated as below:
Where:
- Qcritical – the value of the reactive power of the Q-V
curve at the nose point
- Qoperating – the value of the reactive power of the Q-
V curve at the operating point
2.2 The V-Q Sensitivity Analysis Method
The V-Q sensitivity of a bus is the slope of its Q-V
curve at a given operating point and can be
determined much more swiftly than performing a
full Q-V curve calculation. V-Q sensitivity analysis
evaluates the relationship between voltage
variations and changes in reactive power. The
classical reduced Jacobian matrix provides
extensive information regarding V-Q sensitivity,
[11].
– the mismatch of active and reactive power,
, ∆V – the incremental changes in the bus
voltage angle and magnitude,
– the Jacobian matrix.
The ith diagonal element of the matrix [JQV]
represents the VQ sensitivity of the load bus i when
considering changes happen in active and reactive
power. Letting , equation (4) becomes as
below:
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where JR is the reduced Jacobian matrix of the
system.
So, in this way we can take the bellowed equation:
The is the inverse of the reduced Jacobian
matrix and its elements represent the V-Q
sensitivities. The self-sensitivities coefficients are
the diagonal
, and the mutual sensitivities
are the non-diagonal ones
of the reduced
Jacobian matrix. The signs of the sensitivity
coefficients are used to assess system stability. If the
sensitivity coefficients are positive, the system is
considered to be voltage stable. Sensitivity
coefficients indicate system stability, with smaller
coefficients indicating stability. As magnitude
increases, stability decreases, reaching infinite at
the stability limit. Negative coefficients indicate
voltage instability, [11]. For voltage-controlled
buses, the sensitivity coefficients are zero, [11]. The
limitations of this approach are that the linear
characteristics of this method are not good,
especially for complex power systems; hence, it
cannot accurately reflect the critical state of a
system, [23].
2.3 The Modal Analysis Method
The assessment of the system’s voltage stability can
be evaluated by calculating the smallest eigenvalues
and their corresponding vectors of the reduced
Jacobian matrix (7). Eigenvalues are related to
voltage and reactive power variation mode. If all
eigenvalues are positive, the system is considered
stable in terms of voltage. The system’s closeness to
voltage collapse can be determined by measuring
the magnitude of the smallest eigenvalues, [11]. It is
represented by eigenvector matrices as shown in the
following equation, [11]:
where is the right eigenvector matrix of JR, η is the
left eigenvector matrix of JR, and Δ is the diagonal
eigenvalue matrix of JR. From equation (9), the
reduced Jacobian matrix JR can be expressed as
below:
By calculating the bus participation factors, we
can pinpoint areas of voltage weakness or
instability. These factors indicate the amount that a
bus contributes to a particular mode of instability,
highlighting the potential effectiveness of
countermeasures at that bus in stabilizing the mode.
The bus participation factors reveal which areas are
closest to voltage instability for all small
eigenvalues. These factors help in identifying the
voltage stability weakest areas and provide valuable
information into the mechanisms underlying the loss
of stability.
The bus participation factor determines the
contribution of λi to the V-Q sensitivity at bus k. A
high value of Pki at bus k for mode i means this bus
is close to voltage instability in this mode.
The branch participation factors show which
branches, in response to small variations in reactive
load, absorb the most reactive power. High
participation factor branches are typically weak or
heavily loaded. The relative participation of branch j
in mode i is given as below, [11]:
Generator participation factors illustrate which
generators, in response to small variations in system
reactive loading, provide the most reactive power.
The relative participation of generator g in mode i is
given as below, [11]:
Thus, these factors are crucial for understanding
the distribution of reactive power reserves among
generators, to maintain an adequate margin for
voltage stability. The advantage of this approach is
that it gives information about voltage stability
status and the mechanism of instability. The
limitation of this method is that eigenvalues do not
provide an absolute measure of the proximity to
voltage collapse, [23].
3 Albanian Power System Overview
The main challenge dealing with Albania’s electric
power system is that the production is based only on
hydropower and the fast-rising demand for
electricity. Figure 3 illustrates the energy demand
and production from 2009 to 2022. We can see that
the production of electric energy is strongly
influenced by the hydrologic year. Meanwhile,
during this period, the total annual consumption
changed from 6,592 GWh in 2009 to 7,923 GWh in
2022, while the total annual production changed
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from 5,158 GWh in 2009 to 7,002 GWh in 2022
[28].
Fig. 3: Total electricity consumption and production
in the country throughout the years
Due to the power sector’s struggles to meet the
increasing demand, transmission lines, and
transformers are frequently overloaded, which can
cause voltage dips or fluctuations, necessitating
improvements in electricity consumption and
production, the expansion of international
connections and exchanges, and a more accurate
reasoning for the development of new system
infrastructure. The Albanian government granted
concessions for the construction of small and
medium private hydropower plants (HPPs) to meet
the increasing electricity demand. These HPPs
generated 3583.28 GWh in 2023, or approximately
40.7% of total production [28].
It is important to emphasize that, unlike other
European countries that are promoting the use of
renewable energy sources (RES) to replace
traditional generation, Albania produces 100% of its
electricity from renewable sources. Albania’s
electricity generation is heavily reliant on
hydropower, contributing around 95% of the total
electricity supply [28]. This reliance makes the
power grid vulnerable to seasonal fluctuations in
water availability, leading to variable power
generation.
Figure 4 shows the comparison of monthly net
production with monthly net consumption
throughout the months of 2022 in Albania. The
monthly maximum production of electricity for
2022, is marked in March with 649,844 MWh,
while the minimum production was during
September with 314,360 MWh. The monthly
maximum consumption for 2022, is marked in
January with 751,950 MWh, while the minimum
consumption of electricity during 2022 was during
October with 470,160 MWh [28].
From Figure 4, we observe that load surpasses
the production throughout the entire year, except the
months of April and May.
Fig. 4: Comparison of monthly net production with
monthly net consumption in Albania during 2022
During dry seasons or droughts, the reduced
hydropower output can strain the grid and affect
voltage stability. The limited diversification in
energy means there is little backup during periods of
low hydropower production, exacerbating voltage
instability. Due to this reason, Albanian’s National
Energy Strategy sets ambitious targets for
expanding solar capacity in Albania, with plans to
develop more large-scale solar parks and promote
small-scale installations across the country. The
Albanian government has introduced various
incentives to attract investment in solar energy,
including feed-in tariffs for small PV plants,
competitive auctions for larger projects, and long-
term power purchase agreements (PPAs). The PV
plants that have signed connection agreements in
2022, with a total installed capacity of 255.2 MW,
are expected to be energized during the 2022-2023
period, demonstrating the government’s proactive
approach to expanding solar energy, [28]. Alongside
large-scale projects, there has been a growing trend
in small-scale PV installations across Albania.
These include rooftop solar panels on residential,
commercial, and industrial buildings.
4 Case Study
In this paper, the Albanian power system has been
analyzed. The hydropower plants constructed in
Albania’s north, such as the HPP of Koman, Vau
Dejes, and Fierza, are the biggest and meet the most
energy demand. The high nominal voltages that are
present in this system are 400 kV, 220 kV, 154 kV,
and 110 kV. Up to now, it has only been supplied by
the synchronous generators of the hydropower
plants. Because of this heavy reliance on water
flows from snowfall and rainfall, it might be
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challenging to meet the demand for energy
throughout the summer.
Fig. 5: Schematic design of the Albanian Power System
In addition to small and medium hydropower
plants, which have contributed to the energy balance
[29], new wind and PV plants are going to be
constructed in the next years.
The Karavasta photovoltaic plant (140 MW or
approximately 9,08% of peak load) is an energy
source that has started producing in the last
few years. The impact of this PV plant will be
analyzed in this paper.
The maximum regime for the year 2023 will be
taken as the base case analysis. In this scenario, the
generation is 1409.942 MW active power and
405.435 MVAr reactive power, also the imported is
92.942 MW and 120.129 MVAr.
In this paper, we have conducted the Voltage
Stability Analysis in the condition of PV penetration
and small and medium HPPs. Two case studies have
been analyzed:
– Base case
– PV penetration
Figure 5 shows a schematic representation of
the electricity system of Albania, but the system
under consideration with several voltage levels
consists of many layers built into Neplan software.
5 Results and Analysis
In the following we have analyzed Voltage Stability
for Albanian power system, using P-V and Q-V
curves, Q-V sensitivity analysis, and modal
analysis. Analyzing P-V and Q-V curves, we have
identified the critical node.
5.1 P-V and Q-V curves
In Figure 6 are shown the P-V and Q-V curves
obtained for the Nst. Babice node, which is
considered the critical node, for the base case, with
the lowest active and reactive power reserves.
In Figure 6(a), are presented Q-V curves of Nst.
Babice for both study cases, where we can see the
improvement of reactive power margin after the
integration of PV plant, respectively from -82.009
MVAr to -1061.2 MVAr. We can do the same
analysis, by observing the P-V curves in Figure
4(b). The margin between the voltage collapse point
and the current operating point is used as voltage
stability criterion. In Figure 6(b), are presented P-V
curves of Nst. Babice for both study cases, where
we can see the improvement of loading margin with
2,89 %, respectively from 99.08 % to 101,97 %.
Equations (1) and (3) are used to evaluate the
loading margin. After the integration of the
Karavasta photovoltaic plant, there has been a
noticeable increase in both active and reactive
power reserves. This positive impact is attributed to
the increased reactive power support provided by
the PV plant which reduces grid strain and lowers
the possibility of voltage dips, especially in weak
areas in the system.
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(a)
(b)
Fig. 6: Q-V a) and P-V b) curves
5.2 Q-V Sensitivity Analysis
Table 1 presents the V-Q sensitivity coefficients for
both scenarios: without the integration of the
Karavasta photovoltaic plant and with its
integration. In both instances, the system is
observed to be voltage stable, indicated by the
positive coefficients. Additionally, there is a
noticeable decrease in the coefficients after the
integration of the photovoltaic plant. Smaller
coefficients signify enhanced voltage stability in the
system. A decrease in V-Q sensitivity coefficients
for the critical node, Nst, was observed. Babice,
specifically from 0.0649 to 0.0351.
Table 1. V-Q sensitivity coefficients
Node
V-Q sensitivity coefficients
(%/MVAr)
With PV
Without PV
Nst. Tirana 2
0.0243
0.0536
Nst. Babicë
0.0351
0.0649
Nst. Fier
0.0396
0.0507
5.3 Modal Analysis
Modal analysis has an advantage over other
methods by providing detailed insights into the
mechanisms of instability. To investigate static
voltage stability through this analysis, it is essential
to calculate eigenvalues, node participation factors,
branch participation factors, and generator
participation factors. Using Neplan software for
simulation, the eigenvalues for both scenarios have
been computed and are illustrated in Figure 7.
Fig. 7: Eigenvalues (MVAr/%)
In Figure 7, the system remains stable in both
scenarios, indicated by the positive coefficients.
However, the smaller the eigenvalue, the closer the
voltage is to instability. The magnitude of the
eigenvalue serves as a measure of the system’s
proximity to instability. A recalculation of
the system’s eigenvalues identifies an increase in
the smallest eigenvalue, specifically from 0.252 to
0.442.
The subsequent results will focus exclusively on
the smallest eigenvalue under conditions where the
limit of mutual sensitivity or participation factors
exceeds 20%. This implies that the analysis is
conducted for those eigenvalues where the node,
branch, and generator participation factors have the
most significant impact on the assessment of voltage
stability.
5.3.1 Participation Factors
In the following, we have presented which buses,
branches, and generators and to what extent they
influence the system so that appropriate measures
can be taken to improve the situation, using the
smallest Eigenvalue. Equations (11)-(13) are used to
evaluate the participation factors. Referring
to Figure 7, we see that the smallest Eigenvalue is
0.252.
In Figure 8(a), are shown the buses which have
the most influence for the smallest Eigenvalue. We
see, that the Bistrice-Delvine-Sarande is the closest
node to voltage instability. To prevent a voltage
collapse, this node needs to be continuously
monitored and corrective measures (such as reactive
power compensation) should be taken.
Figure 8(b) illustrates the branches that are
proximate to instability or experiencing overload.
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These branches are identified as those absorbing the
highest amounts of reactive power, corresponding to
the smallest eigenvalue. In Figure 8(b), we observe
that AT-Tirana 2 is the branch absorbing the most
reactive power, highlighted as the most vulnerable
to becoming overloaded. The results obtained
provide important information regarding the
identification of the critical branches of the network,
those branches with the highest participation factors.
These elements consume more reactive power
during a small increase in load. This is valuable
information that can be used by system operators,
who classify branches with the highest participation
factors that should be disconnected during a fault.
Disconnecting these branches from the network
could cause a loss of voltage stability.
(a)
(b)
(c)
Fig. 8: Bus Participation Factors a) Branch
Participation Factors b) Generator Participation
Factors c) for the smallest Eigenvalue
Figure 8(c) presents the generator participation
factors. The reactive power generated changes
drastically with the increase in load. These
generators need to provide reactive power reserves
to maintain the static voltage stability of the power
system. However, not all generators provide reactive
power in the same amount, and some might be more
effective in stabilizing the system than others. The
ability of these generators to provide reactive power
becomes even more crucial in preventing voltage
collapse when they are located nearby to critical
nodes. Observing Figure 8(c), GVD5 results as the
most effective generator for maintaining voltage
stability by providing reactive power reserves.
Overall, participation factors are crucial in
pinpointing the exact locations within the power
grid that are most vulnerable to voltage instability.
They allow operators to prioritize interventions,
monitor key branches, and optimize generator
control.
6 Discussions
The analysis conducted in this paper emphasizes
that the integration of DG, particularly PV plants,
into traditional power systems presents both
opportunities and challenges for voltage stability.
Through static methods, this research has
highlighted key results that are relevant for both
technical advancement and practical
implementation. These methods demonstrated that
the integration of the 140 MW PV plant
significantly enhances the voltage stability of the
Albanian power grid. In particular, significant
improvements were found at critical nodes, such as
Nst. Babice, based on the examination of P-V and
Q-V curves. The reactive power margin increased
from -82.009 MVAr to -1061.2 MVAr following
PV integration, while the loading margin improved
from 99.08% to 101.97%. This positive impact is
attributed to the increased reactive power support
provided by the PV plant which reduces grid strain
and lowers the possibility of voltage dips, especially
in weak areas in the system. The degree of
improvement is highly dependent on the specific
characteristics of the system, as demonstrated by the
unique challenges faced by the Albanian power
system dominated by hydropower plants.
The bus participation factors identified the
Bistrice-Delvine-Sarande buses as the most critical.
Similarly, critical transmission lines, which absorb
the greatest reactive power and are vulnerable to
overloading during periods of high load demand,
were identified using the branch participation
factors. Moreover, modal analysis suggests that the
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system is still close to its stability limits in certain
areas, despite the improvements by the 140 MW
Karavasta PV plant.
The results from this study have several
practical implications for system operators. Using a
combination of static analysis techniques, this paper
addresses the impact of integrating a large PV plant
into the voltage stability of the Albanian power grid,
which is historically reliant on hydropower. Firstly,
the improvements in voltage and the reactive power,
generated by transmission lines, indicate that
the future incorporation of renewable energy, such
as wind or PV plants, could continue to enhance
the grid’s voltage stability. However, this also
requires careful management of the system’s
weakest points, which have been identified through
participation factor analysis. The other contribution
of this paper is that using modal analysis, identified
the critical components of the power system. In
scenarios with high load demand or low generation,
targeted interventions at critical buses, branches,
and generators will be necessary to avoid voltage
collapse. While the study focuses on the Albanian
power grid, its approach and results are relevant to
any power system, which is integrating renewable
energy sources into the system.
Despite the comprehensive insights into voltage
stability provided by this study, there are some
limitations that should be considered. Initially, the
investigation concentrated primarily on static
voltage stability techniques, which are valuable but
do not fully capture the dynamic behavior of the
system in the presence of external disturbances. To
evaluate how the grid reacts to more complex and
transient events, further study could expand on this
by analyzing dynamic stability, including time-
domain simulations. Furthermore, the analysis
assumes a constant PV-generating output, but solar
power can be highly variable due to weather
variations, so stochastic models that simulate the
variations in sun irradiance and how they affect
voltage stability might offer more accurate insights
into the system’s performance under fluctuating
renewable generation.
Finally, future research could investigate the
effects of combining PV plants with other
renewable energy sources, including wind power.
This would offer an expanded awareness of how
multi-source renewable energy systems affect the
stability of the grid and interact with it.
7 Conclusions
This paper presents the impact of the integration of
PV generators on voltage stability. The static
voltage stability analysis used various techniques: P-
V and Q-V curves, V-Q sensitivities, and modal
analysis. Using a combination of these methods, this
study provided a detailed assessment of how large-
scale PV plant integration affects the stability of a
power system that is traditionally dominated by
hydropower. Following the integration of the PV
plant, the P-V and Q-V curve methods showed
improvements both in voltage and reactive power
margin at the critical node, indicating increased grid
resilience against possible voltage collapse. The
reactive power margin was increased from 82.009
MVAr to -1061.2 MVAr, while the loading margin
from 99.08% to 101.97%, in this way lowering the
risk of voltage collapse. Also, the V-Q sensitivity
analysis demonstrated a decrease in sensitivity
coefficients after PV integration, indicating
enhanced voltage stability throughout the system.
Among the methods used, modal analysis turned
out to be the most effective in locating the areas,
that are vulnerable to voltage instability, providing
detailed information about the weakest buses,
generators, and branches, allowing for
countermeasures. In this way, helps the system’s
operators prioritize interventions, optimize
production control, and monitor critical branches.
Overall, the Albanian power grid’s voltage
stability is improved with the integration of the
Karavasta Photovoltaic Plant. The results from this
study serve as a valuable guide for operators and
policymakers as they seek to integrate more
renewable energy sources into the grid while
maintaining reliability and stability, but with careful
planning and targeted interventions, the voltage
stability can be enhanced. This research underscores
the importance of a balanced energy mix and the
strategic placement of distributed generation to
support voltage stability.
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Contribution of Individual Authors to the
Creation of a Scientific Article
- Viktor Rrotani conducted the literature review,
conceptualized and formulated the case study,
modeled the power system in Neplan, carried out
the simulations, and analyzed the results.
- Rajmonda Bualoti has carried out the Static
Methods, developed the mathematical models,
contributed to the discussions and conclusions
sections, and provided revisions and advice.
- Marialis Celo has carried out the Albanian Power
System Overview, analyzed the results obtained
from the simulations, contributed to the
discussions section, and drew the conclusions.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This publication was made possible with the
financial support of the Polytechnic University of
Tirana (PUT) under the Research Project
“Interaction of Information and Energy
Technologies for a Smart Power System”.
Conflic of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.37
Viktor Rrotani, Rajmonda Bualoti, Marialis Çelo
E-ISSN: 2224-350X
437
Volume 19, 2024
