Artículo Académico / Academic Paper

Recibido: 28-10-2022, Aprobado tras revisión: 12-01-2023

Forma sugerida de citación: Pereira, O.; Rosés, R.; Giménez, M. (2023). “QV Analysis for the Identification of Vulnerable Zones

to Voltage Collapse: A Study Case”.No. 19, Issue II, Pp. 32-41

ISSN On-line: 2602-8492 - ISSN Impreso: 1390-5074

Doi: https://doi.org/10.37116/revistaenergia.v19.n2.2023.545

QV Analysis for the Identification of Vulnerable Zones to Voltage Collapse: A

Study Case

Análisis QV para la Identificación de Zonas Vulnerables a un Colapso de

Tensión: Un Caso de Estudio

O. Pereira1 R. Rosés1 M. Giménez1

1Institute of Electric Energy, National University of San Juan, San Juan, Argentina

E-mail: opereira@iee.unsj.edu.ar; rroses@iee.unsj.edu.ar; mgimenez@iee.unsj.edu.ar

Abstract

Radial High-Voltage networks have problems

ensuring voltage stability when a fault occurs.

Among preventive actions for these events, installing

reactive power compensation in the most vulnerable

zones to voltage instability is an economical and

simple alternative. Previous works have used the QV

curves methodology based on contingency power

flows to identify such zones. However, this method

has been criticized because it does not consider the

dynamical effect of some network elements that

depend on the voltage levels, especially in

contingency scenarios. This article proposes a QV

curve analysis based on the operating point resulting

from dynamic simulations to amend this critique. To

evaluate the proposed procedure, the model of the

Patagonian High-Voltage Network in southern

Argentina is used through the PSS/E software with

the help of the Python programming language. The

results detect the most vulnerable areas to voltage

instability after a fault occurs and the reactive power

necessary to maintain voltage levels in an acceptable

operating range. The proposed methodology can be

applied to other networks. For example, it can be

used in the Latin-American context to assess future

network expansions, especially on those linking

countries, such as Ecuador with Perú or Colombia,

or even the Centro American Interconnected

System.

Resumen

Las redes radiales de alta tensión son muy propensas

a sufrir inestabilidades de tensión cuando se

presentan fallas. Dentro de las acciones preventivas

ante este tipo de eventos, la instalación de

compensación de potencia reactiva en las zonas con

más problemas de tensión es una alternativa

económica y sencilla de aplicar. Trabajos previos

han utilizado el método de las curvas QV basados en

flujos de potencia en estados de contingencia para

identificar tales zonas. Sin embargo, este

procedimiento es criticado debido a que no

contempla el efecto dinámico de elementos que

cambian su comportamiento de acuerdo a los niveles

de tensión, especialmente en escenarios de

contingencia. Con el fin de subsanar esta crítica, este

artículo propone el uso de las mismas curvas QV

basándose en los puntos de operación resultantes de

simulaciones dinámicas. Para evaluar la

metodología propuesta, se utilizó el modelo de la red

radial de alta tensión de la Patagonia, al sur de

Argentina, por medio del software PSS/E en

conjunto con el lenguaje de programación Python.

Los resultados detectaron las zonas más propensas a

la inestabilidad de tensión y el requerimiento de

potencia reactiva necesaria para que la red opere en

niveles de tensión aceptables. La metodología

propuesta puede ser replicada en cualquier tipo de

red. Por ejemplo, en el contexto latinoamericano, se

podría utilizar en posibles futuras expansiones de

red, especialmente en aquellas que vinculen países

como Ecuador con Colombia o Perú, o también el

Sistema Interconectado Centroamericano.

Index termsVoltage Stability, QV curves,

Dynamic Simulations, Radial High Voltage

Networks, Reactive Compensation, PSS/E.

Palabras claveEstabilidad de tensión, Curvas QV,

Simulaciones dinámicas, Redes de Alta Tensión

Radial, Compensación de Potencia Reactiva, PSS/E.

Edición No. 19, Issue II, Enero 2023

1. INTRODUCTION

The demand growth is a constant concern for

Transmission System Operators (TSO). To address this

situation, TSOs require expansion plans to establish

measures to fulfill the demand projections while

maintaining power quality parameters. In these future

network requirements, besides planning the renewal or

the addition of power plants, it is also mandatory to

consider the grid’s reinforcement to make sure that the

network can transfer this new generation without

compromising the power system stability [1], [2],[3].

Another concern for the operator is the system’s

operation after a contingency. In the case of a fault on

High Voltage (HV) networks with radial topology, the

system’s voltage stability is affected due to the lack of

paths to transfer the generated power. The construction

of parallel lines could be a solution to this problem.

Besides increasing the power transfer capacity of the

network, it could also improve reliability in post-fault

scenarios, preventing the disconnection of power plants

and maintaining the reactive power reserves. However,

because of the long-term investment it represents, TSOs

look for more economical alternatives. For example,

countries such as Chile [4] and South Korea [5] have

reported avoiding that kind of investment by installing

significant amounts of reactive power compensation in

the most vulnerable zones of the circuit to a voltage

collapse. It is a more reasonable solution since it is

cheaper and provides more stability and transfer capacity

in the power system.

Different methods are proposed in the literature to

assess the voltage stability in power systems. For

example, four widely used methods are the QV Modal

Analysis, QV Sensitivity Analysis, and the PV and QV

curves. The reason behind the use of these methods is that

they require static power flows to develop the analysis.

However, each method has different purposes and

distinct application advantages as well as disadvantages.

The QV Modal and the QV Sensitivity Analysis are

similar methods. Both of them require as input the

inverse matrix of the resulting Jacobian from the power

flow. The difference between these methods is that the

QV Modal Analysis calculates the matrix eigenvalues to

determine whether a specific bus is stable [6]. Instead, the

Sensitivity Analysis determines the stability of a bus by

looking at the bus’ respective value on the diagonal

components of the matrix. This value corresponds to the

sensitivity of the voltage in the bus with respect to the

change in the reactive power [7]. Both methods check for

the sign of the observed value; if it is positive, then the

bus should not have voltage instability problems.

On the other hand, PV and QV curves are graphical

methods based on the results obtained by a sequence of

power flows in which the voltage levels are continuously

tracked. The PV curves determine the power transfer

limit between generation and load zones by incrementing

the generated power in each simulation until unstable

operating points appear [8]. Alternately, QV curves are

in function of the increment of the reactive power

injection/consumption in a single bus until reaching

voltage levels that are not within an acceptable range.

This characteristic helps to determine the reactive power

requirement of some specific buses in the circuit and how

would the voltage level change according to the reactive

compensation [9].

Among the exposed methods, QV curves, QV Modal,

or QV Sensitivity analyses are more suitable for

identifying and localizing vulnerable zones to voltage

instabilities. Even though the last two methods are

considered to be more straightforward since the results

are obtained directly from the matrix and not from a

number of power flows, these methods have the

disadvantage that they are not available in all the

simulation software, or at least in some cases, it is

required an external program, for example, Matlab, to

extract the information to develop the analysis. Another

problem that these two methods have is that depending

on the size of the network, the computational effort to

invert the Jacobian matrix is a topic of concern [10].

QV curves have many application advantages over

the other methods. It is a fast method compared to

dynamic studies, and unlike PV curves, it has fewer

problems when it comes to convergence [11]. Also, it is

a widely used tool: Recent studies have reported using

simulation software such as PSSE [12], DigSilent [13],

PowerWorld [14], NEPLAN [15], Matlab [16], and

Python [17] to develop QV curves in real and test circuits.

The analysis of these curves, and if possible,

complemented with other voltage stability criteria such

as modal or sensitivity analysis, helps to study the

reactive power margins, determine the most suitable

areas to install reactive compensation, and make planning

decisions in the long and medium term.

Authors in [11] suggest that the results obtained from

the QV curves in post-fault scenarios must be

complemented with dynamic simulations. The traditional

way to obtain the QV curves does not contemplate the

evolutionary behavior of On Load Tap Changers

(OLTC), Overexciting Limiters (OEL), Governors, and

Automatic Voltage Regulators (AVR) during a fault and

their effect on the system, which can guide misleading

conclusions. Hence it opens the door to inaccurate

reactive power compensation sizing and locating. Since

then, no further research has been related to a proposal

that improves the reliability of the results of the QV

curves in the post-fault state.

This paper addresses a different way to obtain the QV

curves in a post-fault state by assessing the operating

points resulting from dynamic simulations instead of the

contingency power flow using a model of a real large-

scale circuit. This methodology evades the disadvantages

of QV curves exposed by [11]. Moreover, by taking the

stabilized operation points after dynamic simulations to

Pereira et. al. / QV Analysis for the Identification of Vulnerable Zones to Voltage Collapse: A Study Case

create the QV curves, it complies with the premise

exposed in [8] by characterizing the steady-state

operation of the system. The main contributions of this

paper are:

 Providing a reliable methodology to obtain QV

curves for post-fault scenarios to be applied on a

real large-scale network model, contemplating the

effect of dynamic elements such as the different

OELs and OLTCs.

 Determining zones prone to voltage instability

due to the presence of faults. So that these are later

reinforced through the amount of reactive

compensation specified on the QV curve and help

mitigate voltage instability problems.

The remainder of the paper is organized as follows:

Section 2 presents the classic formulation of the QV

curves, and Section 4 describes the proposed

methodology in this study. Section 4 shows the planned

expansion in Argentina for 2024 and the need for voltage

stability studies. The QV analysis for the Patagonian HV

network is presented in Section 5. Finally, the

Conclusions and Future Work are presented in Sections

6 and 7, respectively.

2. QV CURVES

QV curves depict the reactive power, consumed or

injected, needed to obtain a specific voltage level in a

bus. When plotted, the x-axis corresponds to the voltage

level, and the y-axis to the reactive power compensation.

The positive sign in the y-axis is associated with reactive

power injection and the negative sign with consumption.

Fig. 1 shows an example of three different QV curves 𝒄𝟏,

𝒄𝟐 and 𝒄𝟑 in the voltage range of 0.7 pu to 1.2 pu.

The curve divides into two operating zones according

to the slope of the curve: stable (positive slope, the solid

line in Fig.1) and unstable (negative slope, dotted line).

The unstable part of the QV curve corresponds to

deficient voltage levels, which are undesirable operating

points. Instead, the stable side corresponds to voltage

levels comprehending a range of acceptable values.

Each curve’s knee point reveals the correspondent

bus’s reactive power margin. This point also informs

from what value of reactive power the operation is in the

stable zone of the curve. If the margin is negative, there

exists at least an operation point on the stable zone of the

curve. On the contrary, if the margin is positive, there is

no operation point without the injection of reactive power

(installation of capacitive compensation).

Fig. 1 depicts the margins for curves 𝒄𝟏 and 𝒄𝟑

through the values 𝑸𝟏 and 𝑸𝟑, respectively. In the case

of 𝒄𝟏, it shows that the curve has a range of 𝑸𝟏 MVAr,

where an operating point in the stable zone is ensured

until reaching the point 𝑶𝟏. On the other hand, 𝒄𝟑

corresponds to a curve with a positive margin, a typical

curve of very loaded scenarios. To guarantee an

operating point on the stable side of the curve, the bus

needs the injection of at least 𝑸𝟑 MVAr. However, the

knee point of the curve is not always associated with a

voltage value in an acceptable range, so a higher

compensation is required. Thus, to ensure a 1.00 pu

voltage operation at the bus, 𝑸𝟑

′ MVAr should be

installed, a value greater than 𝑸𝟑.

Figure 1: QV curve example

The methodology to get the curve consists of

installing a fictitious generator with no active power

generation and without reactive power limit in the bus of

interest and then running a series of power flow

simulations. The bus changes from PQ to PV type, setting

the voltage value in a specific range through the power

flow series to obtain the reactive power

injection/consumption to hold the voltage level at the

specified value.

Different ways exist to execute the power flow series

for obtaining the QV curves. One method starts with

identifying the base voltage value from the original

power flow. Then, the simulations could be performed in

two sequential stages: ascending, beginning from the

base voltage and increasing it in small steps until

reaching the established upper limit, then descending

from the base voltage to the lower limit.

In post-fault scenarios, to contemplate the operation

of an isolated area by a three-phase fault, the bus with the

highest rated capacity in the islanded system is selected

as a slack bus, allowing the power flow to reveal the

voltage level status of these zones.

There are some considerations regarding the voltage

range of the curves. When evaluating high or low voltage

values, there exists the risk that the power flow does not

converge. Researchers in [18] used the PSSE software to

perform a QV analysis using the non-divergent power

flow option, which ensures obtaining values that, despite

not being convergent, avoid unrealistic results by

stopping the simulation before getting very high

mismatches. On the other hand, in [1] and [19], they

Edición No. 19, Issue II, Enero 2023

avoid the convergence problem using the Continuation

Power Flow method. The most conservative way to deal

with this problem is taking the recommendation from [9],

which suggests that the most relevant voltage range is

between 0.9 pu and 1.1 pu. Although when evaluating

only in this range of values, the complete behavior of the

curve is not shown, it may be enough to detect voltage

instabilities.

3. PROPOSED METHODOLOGY

The classical way to develop QV curves for post-

fault scenarios is through contingency power flows.

These simulations are based on a static power flow (i.e.,

Full Newton Raphson) in an N-k status network. As

stated previously, this procedure does not contemplate

the action of control mechanisms which could be

essential for supporting voltage stability when a

contingency appears. This simplification could lead to

inaccurate conclusions, labeling, for example, voltage

conditions in a bus as unstable when dynamic simulations

show that they are indeed stable, as shown in [11].

A reasonable alternative for tackling this problem is

taking the operating points after a dynamic simulation as

a base to develop the curves. With an adequate base of

dynamic models, these kinds of simulations give accurate

information about the post-fault state, including the effect

of the automatisms that the classic power flow cannot

provide.

Using the resulting operating points from dynamic

simulations means taking a snapshot of the network

condition seconds after the fault is simulated. Ideally, the

time between the fault and the snapshot has to be long

enough so that the oscillating effect does not influence

the operating points. After that, the same sequence

explained in Section II to obtain the QV curve is followed

for the list of buses under study.

In the series of power flows required to obtain the

curves, all the setpoints obtained from the dynamic

simulation are also considered: This includes the

generators’ active power delivered, reactive power

delivered or consumed, and voltage setpoints fixed at the

resulting value. It also comprehends the transformers’

new tap positions, switched shunts’ statuses, and the load

consumption according to the resulting voltage level (ZIP

model).

Since the study focuses on the injection or

consumption of reactive power and its effect on the

voltage levels and also considering that the frequency

levels after the dynamic simulation should be close to

nominal, the methodology assumes the simplification of

fixing the frequency base value at nominal.

Note that the main difference between the classic

method and the one proposed in this study is the choice

of the initial operating points. Taking this into account,

Fig.2 illustrates a diagram for the proposed methodology,

where the variable 𝒌 is the size of the voltage step in the

ascending and descending sequence of power flows, 𝒏

the number of buses under study, and 𝑽𝒉𝒊𝒈𝒉 and 𝑽𝒍𝒐𝒘 are

the upper and lower voltage limits of the QV curve.

4. THE PATAGONIAN EXPANSION PLAN FOR

2022-2024

Due to the long extension of the country and its

geography, the more abundant natural resources in

Argentina vary according to latitude. In the northwest,

there is more potential to exploit solar energy, whereas in

the south, especially in the Patagonian region, hydro and

wind power.

One of the main objectives of the expansion plan in

Argentina for the medium term is to take more advantage

of the resources in the Patagonian Region to supply the

growing demand in the future years [20]. There are

approximately 1.5 GW of wind power installed capacity,

and the expansion plan sets the installation of 25 MW of

wind power and 1.3 GW of hydropower capacity in two

stages: 360 MW for 2024 and 950 MW for 2029.

Argentina relies on 500 kV HV networks to transport

the generated power from the north and south regions to

the main demand centers of the country. In the

Patagonian Region’s case, a radial corridor of 1120 km

goes from La Esperanza 500/220 kV substation to the

Choele-Choel 500/330/132 kV substation. At that point,

the network meshes for approximately 1000 km until the

capital city, Buenos Aires. With the inclusion of future

Figure 2: Proposed QV curves methodology diagram

Pereira et. al. / QV Analysis for the Identification of Vulnerable Zones to Voltage Collapse: A Study Case

power plants, reinforcing the Patagonian HV radial

corridor is a topic of interest for the TSO.

Fig. 3 depicts the 500 kV Patagonian network’s

expansion plan from 2022 to 2024. By 2024, when the

planned 360 MW hydropower plant in La Barrancosa

station comes into operation, three reinforcement

alternatives are considered: A0, A1, and A2. Alternative

A0 corresponds to the original plan for 2024, which in

comparison with 2022, it includes a line series capacitor

after Río Santa Cruz 500/132 kV substation. Alternatives

A1 and A2 are based on A0: A1 incorporates a line series

capacitor right after the Santa Cruz Norte 500/132 kV

substation. On the other hand, A2 contemplates the

partition of the HV line connecting the Santa Cruz Norte

and Puerto Madryn substations to create the Comodoro

Rivadavia Oeste substation. There a line series capacitor

is installed.

According to [20], the reason behind the installation

of line series capacitors is to increase the power transfer

in the corridor since it has saturation problems. These

devices also can improve the reactive power support to

maintain the voltage levels in an acceptable range.

Nevertheless, when faults occur, the capacitors are

bypassed [9], causing the system to run out of the reactive

compensation they provide in a critical situation,

aggravating the general stability of the system.

Due to the radial topology of the Patagonian system,

faults on the 500 kV network could imply severe

consequences for the system’s voltage stability. Single-

phase faults with successful reclosing can cause back-

swing problems. In addition to violating the security

operation criteria for an adequate voltage level, it could

generate the disconnection of loads or even cause the grid

to operate in weak operating conditions. On the other

hand, three-phase faults can cause the islanding of some

portions of the system and the loss of availability of

reactive power sources to maintain voltage levels.

However, for this kind of fault, there are resources such

as the automatic disconnection of generators through

System Protection Schemes (SPS) to balance the demand

and the generation in an N-1 system condition. Another

possible consequence, depending on where the fault

occurs, is that the power flow intended to be transported

by the 500 kV network diverts to the adjacent 132 kV

network through the Santa Cruz Norte substation,

overloading the lower-voltage network and aggravating

the voltage problems in the area.

5. CASE STUDY

4.1 System description

Fig. 4 shows a single-line diagram of the Patagonian HV

network scheduled for 2024, including the elements of

the three reinforcement alternatives and the adjacent 132

kV part connected to the 500 kV Network between

Puerto Madryn (500-B3) and Santa Cruz Norte (500-B7)

substations. Due to the voltage impact that the 132 kV

network may suffer as a consequence of a fault, it is

necessary to consider it to get a better perspective of the

stability of the whole network.

Figure 3: Expansion plan 2022-2024 for the Patagonian Region

Edición No. 19, Issue II, Enero 2023

4.2 Post-fault Scenarios

The letters from A to G in Fig.4 denote the eight fault

locations to be considered. Each letter is associated with

the line to fault. It must be noted that locations G and H

are exclusive for alternative A2 since substation

Comodoro Rivadavia Oeste (500-B5) splits the 500 kV

line from Puerto Madryn (500-B3) to Santa Cruz Norte

(500-B3). Consequently, location F is only considered by

alternatives A0 and A1. The other fault locations are part

of all three alternatives.

Figure 4: Single Line Circuit of the Patagonian HV Network

Table 1: Considered Fault Scenarios

Fault Scenario

Max-

Disconnected

Generation Units

Equivalent MW

0 MW

360 MW

260 MW

620 MW

F3-F1

16-0

1070 MW

G3-G1

14-0

1038 MW

H3-H1

16-0

1070 MW

Only three-phase and single-phase faults with

successful reclosing are studied regarding the types of

faults to be simulated. Three-phase faults are considered

in all of the described locations in Fig.4, while single-

phase faults are considered only for locations F, G, and

H due to the effect of this type of fault on the main 500

kV corridor (500-B3 to 500-B7) could be detrimental.

When evaluating three-phase faults, the automatic

disconnection of generation units is considered. Table 1

shows the maximum number of disconnected generators

and the corresponding total amount in MW for each fault

location and type of fault (3 for three-phase and 1 for

single-phase faults). In the case of single-phase faults, the

disconnection of generating units is not considered.

Besides contemplating different fault locations and

the automatic disconnection of generation units, the post-

fault scenarios consider four distinct generation cases

that depend on the power delivered by the principal

power plants in the area: La Barrancosa (500-B11) and

Río Turbio (220-B3). These are:

 0G: All generators are turned off (P = 0 MW).

 0G-RT: Generators of 500-B11 are off, but those of

220-B3 are delivering power at 50% of their

nominal capacity (P = 140 MW)

 3G: All generators of 500-B11 are at 95% of their

nominal capacity, and those of 220-B3 are off (P =

342 MW).

 3G-RT: Generators of 500-B11 and the ones of

220-B3 are at 95% and 50% of their respective

nominal capacity (P = 482 MW).

4.3 Previous considerations for the QV curves

The dynamic simulations and the QV curves were

made using PSS/E software version 33.5 and the Python

programming language.

The initial operation points to use in QV curves were

obtained from the result of dynamic simulations. The

dynamic models used are the homologated ones from the

network under study. These simulations considered a

time window of 900 s (15 minutes) after the simulated

fault. At the end of the simulation, if the operating points

are in a steady-state condition, then this point is taken to

develop the QV curves of the corresponding case.

The ZIP model considered the load model for the

dynamic simulations and the QV curves, where the

current and impedance constant proportion for the active

power part was 80% and 20%, respectively. Instead, the

reactive power part was 50% - 50%.

The QV curve slope and the base voltage value when

the reactive power is 0 determine if a bus tends to have

voltage problems. If the bus voltage value in the post-

fault cases ranges from 0.95 pu to 1.05 pu for buses in the

500 kV network or from 0.93 to 1.07 for the 132 kV

network, the bus does not tend to have voltage problems.

Pereira et. al. / QV Analysis for the Identification of Vulnerable Zones to Voltage Collapse: A Study Case

Otherwise, the bus requires reactive power compensation

to improve the voltage conditions. On the other hand, the

QV curve slope determines the increment ratio of

reactive power injection with respect to voltage. If this

ratio is high, it could be a problem since high

compensation sizing would be required to achieve small

changes in the voltage level, which depending on the

compensation device, is not always physically possible.

4.4 Results

Figs. 5, 6, and 7 show the QV curves for the

alternatives A0, A1, and A2, respectively, exposing only

the buses in different generation and fault location

scenarios whose voltage is lower than 0.95 pu for 500 kV

buses or 0.93 for 132 kV buses when the reactive power

consumed/injected is 0. Neither of the analyzed cases

presented a base voltage above 1.05 pu.

For the case of the curves shown for alternative A0,

voltage problems occur in bus 500-B7 for two specific

fault locations: A3 and E3. The base voltages of all the

scenarios are slightly lower than 0.95 pu, meaning that

they require low reactive compensation. However, the

slope of the curve reveals that faults in location A are

more problematic than faults in location E, requiring

more reactive compensation than the other case to

maintain the same voltage level.

In the curves shown for alternative A1, bus 500-B3

presents voltage problems in the 3G generation scenario

for three-phase faults in A and D, similar to those in

scenario A0. Nevertheless, the attention is on the single-

phase fault with successful reclosing at location F in the

higher generation scenario (3G-RT). The 132-kV buses

132-B4, 132-B5, and 132-B6 show a different problem:

they have a low slope but require more reactive power

(from 200 to 600 MVAr) to have an operating point

between an acceptable voltage range.

In alternative A2, the same group of 132 kV buses

reported similar voltage problems when evaluating the

3G-RT scenario for single-phase faults with successful

reclosing in locations H and G. When the fault is assessed

on location H, the required compensation ranges from

270 to 550 MVAr. In contrast, location G varies from 145

to almost 500 MVAr. Also, bus 500-B7 presented voltage

problems similar to the ones reported in A0: base voltage

close to 0.95 and high slope.

Fig. 8 shows a results diagram detailing each case

with voltage problems in the three alternatives according

to the generation scenario, fault type, and location. It also

includes the minimum reactive power compensation

required to have a voltage value between acceptable

ranges depending on whether the bus is on the 500 kV or

132 kV network and the required compensation to reach

a 1.00 pu voltage.

The results show that each alternative has localized

and common areas where voltage problems occur in

different fault and generation scenarios. In the case of

alternative A0, the issues are in bus 500-B7. While in

alternatives A1 and A2, the problems mainly occur in the

132 kV buses: 132-B4, 132-B5, and 132-B6.

Also, in terms of the need for reactive power

compensation, the post-fault scenarios with the highest

generation after a single-phase fault with successful

reclosing in the 500-B3 to 500-B7 corridor are more

problematic than three-phase fault scenarios. For each of

the reported 132 kV buses with voltage problems for

these cases, the base voltage values are lower than 0.93

pu and require almost 150 MVAr to 345 MVAr of

compensation to have acceptable voltage levels. It is

worth noting that in both planning alternatives, bus 132-

B5 requires more compensation than the other 132 kV

buses.

Figure 5: QV curves for buses in Alternative A0

Figure 6: QV curves for buses in Alternative A1

Edición No. 19, Issue II, Enero 2023

Figure 7: QV curves for buses in Alternative A2

Figure 8: Summary of reported scenarios with voltage problems

6. CONCLUSION

This paper assessed the QV curves using the post-

fault network operation points obtained from dynamic

simulations under different generation and fault

scenarios. The results identified zones prone to voltage

instability and the approximate amount of reactive

compensation necessary to solve the problem in the

Patagonian HV network under different planning

alternatives.

Three planning alternatives for the year 2024 were

evaluated. The QV curves of each of these alternatives

showed a certain similarity, identifying the 500 kV area

of Santa Cruz Norte (500-B7) and part of its extension at

132 kV (buses 132-B4, 132-B5, and 132 -B6) as areas

prone to voltage instability.

In the cases studied, a pattern was noted for the two

types of faults analyzed. The QV curves for scenarios

where three-phase faults were evaluated generally

showed base voltage values close to the lower allowable

limit with a high slope. On the contrary, single-phase

faults with successful reclosing for alternatives A1 and

A2 showed the need for more significant reactive

compensation than three-phase fault scenarios to achieve

an operating point in an acceptable range.

It is not possible to define a specific amount of

reactive compensation that works for all the post-fault

scenarios evaluated in the three planning alternatives.

However, it was demonstrated that QV curves could give

an insight into a range of possible values, which would

depend on the evaluated case.

7. FUTURE WORK AND RECOMMENDATIONS

The proposed methodology can be extended to

analyze other transmission systems. Nevertheless, it is

important to remember that each network has its own

characteristics, and the results obtained in this study

cannot be extrapolated to other similar networks.

By identifying the location of the most vulnerable

areas to voltage instability and the approximate necessary

size of the reactive compensation needed, it is now

possible to assess the type of element that will have such

work.

Flexible Alternating Current Transmission Systems

(FACTS), specifically the Static Synchronous

Compensator (STATCOM), are gaining a good

reputation worldwide for solving voltage instability

problems. STATCOM devices can improve the power

transfer, support the network under critical conditions

better than shunt capacitors, and do not depend on the

voltage level of the point of connection to inject/consume

reactive power with a fast response. With the

employment of this kind of element, the effects of faults

on the voltage levels can be mitigated, ensuring better

reliability.

Future research aims to evaluate the use of

STATCOM on the Patagonian Network through dynamic

simulations. The WECC-validated generic model

SVSMO3 and the simplified CSTCNT models can be

employed for such labor in PSS/E.

8. REFERENCES

[1] R. Kyomugisha, C. M. Muriithi, and M. Edimu,

“Voltage stability enhancement of the Uganda

power system network,” in 2021 IEEE PES/IAS

PowerAfrica, PowerAfrica 2021, 2021, pp. 1–5.

[2] S. Opana, J. K. Charles, and A. Nabaala,

“STATCOM Application for Grid Dynamic Voltage

Regulation: A Kenyan Case Study,” 2020 IEEE

PES/IAS PowerAfrica, PowerAfrica 2020, 2020.

Pereira et. al. / QV Analysis for the Identification of Vulnerable Zones to Voltage Collapse: A Study Case

[3] P. Chawla and B. Singh, “Voltage Stability

Assessment and Enhancement Using STATCOM -

A Case Study,” Eng. Technol. Int. J. Electr. Comput.

Eng., vol. 7, no. 12, p. 148, 2013.

[4] CIGRE, CIGRE Green Books: Flexible AC

Transmission Systems: FACTS, 1st ed. Springer

International Publishing, 2020.

[5] J. Park, S. Yeo, and J. Choi, “Development of ±

400Mvar World Largest MMC STATCOM,” in

2018 21st International Conference on Electrical

Machines and Systems (ICEMS), 2018, pp. 2060–

2063.

[6] B. Gao, G. K. Morison, and P. Kundur, “Voltage

Stability Evaluation using Modal Analysis,” IEEE

Power Eng. Rev., vol. 12, no. 11, p. 41, 1992.

[7] F. Ruiz-Tipan, C. Barrera-Singana, and A.

Valenzuela, “Reactive power compensation using

power flow sensitivity analysis and QV curves,” in

2020 IEEE ANDESCON, ANDESCON 2020, 2020.

[8] T. Van Cutsem and C. Vournas, Voltage stability of

electric power systems. 2008.

[9] C. W. Taylor, N. J. Balu, and D. Maratukulam,

Power System Voltage Stability. McGraw-Hill,

1994.

[10] X. Liang, H. Chai, and J. Ravishankar, “Analytical

Methods of Voltage Stability in Renewable

Dominated Power Systems: A Review,” Electricity,

vol. 3, no. 1, pp. 75–107, 2022.

[11] B. H. Chowdhury and C. W. Taylor, “Voltage

stability analysis: V-Q power flow simulation versus

dynamic simulation,” IEEE Trans. Power Syst., vol.

15, no. 4, pp. 1354–1359, 2000.

[12] A. Rijesh and S. Chakraborty, “Performance

analysis of smart device : STATCOM for grid

application,” in 2017 IEEE Region 10 Symposium

(TENSYMP), 2017, pp. 1–5.

[13] N. Manjul and M. S. Rawat, “PV/QV Curve based

Optimal Placement of Static Var System in Power

Network using DigSilent Power Factory,” in 2018

IEEE 8th Power India International Conference

(PIICON), 2018.

[14] R. Kumar, A. Mittal, N. Sharma, I. V. Duggal, and

A. Kumar, “PV and QV Curve Analysis Using

Series and Shunt Compensation,” in 2020 IEEE 9th

Power India International Conference (PIICON),

2020.

[15] M. Khaled and A. O. A. Elsayed, “Voltage Profile

Enhancement in Middle District of Sudan Electric

Grid Using Neplan Software,” in 2019 International

Conference on Computer, Control, Electrical, and

Electronics Engineering (ICCCEEE), 2019, pp. 1–6.

[16] J. E. Sarmiento et al., “Finding unstable operating

points via one-dimensional manifolds,” 2019 IEEE

Milan PowerTech, PowerTech 2019, 2019.

[17] V. N. Sewdien, R. Preece, J. L. R. Torres, and M. A.

M. M. Van Der Meijden, “Evaluation of PV and QV

based voltage stability analyses in converter

dominated power systems,” Asia-Pacific Power

Energy Eng. Conf. APPEEC, vol. 2018-Octob, pp.

161–165, 2018.

[18] T. Van Cutsem et al., “IEEE PES Task Force on Test

Systems for Voltage Stability Analysis and Security

Assessment Technical Report,” 2015.

[19] Y. Lou, Z. Ou, Z. Tong, W. Tang, Z. Li, and K.

Yang, “Static Volatge Stability Evaluation on the

Urban Power System by Continuation Power Flow,”

in 2022 5th International Conference on Energy,

Electrical and Power Engineering (CEEPE), 2022,

pp. 833–838.

[20] TRANSENER S.A, “Guía de Referencia del Sistema

de Transporte de Energía Eléctrica en Alta Tensión

2022-2029,” 2021.

Orlando Pereira Guzmán. -

Nació en San José, Costa Rica en

1994. Recibió su título de

Bachillerato y Licenciatura en la

carrera de Ingeniería Eléctrica de la

Universidad de Costa Rica en 2017

y 2020, respectivamente.

Actualmente es becario del DAAD

en el programa de Maestría en Ingeniería Eléctrica de la

Universidad Nacional de San Juan, Argentina. Sus

campos de investigación se relacionan con el modelado y

simulación de Redes de Transmisión y Distribución y la

incorporación de tecnologías emergentes en las mismas.

Rodolfo Edgar Rosés. - nació en

San Juan, Argentina en 1960. Se

graduó como Ingeniero Electricista

y Doctor en Ingeniería Eléctrica en

la Universidad Nacional de San

Juan. Su experiencia incluye el

análisis de funcionamiento de

Sistema Eléctricos, Operación en

Tiempo Real, Restauración de Cargas, desarrollo de

Software e implementación de metodologías para

operación de Sistemas Eléctrico en Centros de Control

con Sistemas SCADA. Es Docente-Investigador en el

Instituto de Energía Eléctrica de la U. N. de San Juan

desde 1986 y dicta cursos de grado, postgrado y

capacitación profesional.

Edición No. 19, Issue II, Enero 2023

María del Carmen Giménez. -

Ingeniera Electromecánica, 1989 –

Universidad Nacional de San Juan,

Argentina. Investigador, Profesor y

Consultor en Sistemas Eléctricos.

Profesor en el área de posgrado para

las carreras de Doctorado y

Maestría en Ingeniería Eléctrica.

Codirección de Becarios de la carrera de Maestría en el

área de los Sistemas de Potencia y empleo de nuevas

tecnologías (Líneas de Corriente Continua, STATCOMs

y Energías Renovables). Dirección, Codirección y

participante en Proyectos de Transferencia Tecnológica

en el área de Análisis de Funcionamiento de Sistemas

Eléctricos. Especialidad: Análisis de Funcionamiento de

Sistemas de Potencia. Análisis de Contingencias,

Análisis de Estabilidad de Tensión, Transitoria y de

Pequeñas Señales. Especialista en modelación Dinámica

de Sistemas Eléctricos.