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www.etasr.com Eisa Osman et al.: Application of FVSI, Lmn and CPF Techniques for Proper Positioning of FACTS … 

 

Application of FVSI, Lmn and CPF Techniques for 

Proper Positioning of FACTS Devices and SCIG 

Wind Turbine Integrated to a Distributed Network for 

Voltage Stability Enhancement 
 

Shaheer Hashim Eisa Osman 

Department of Electrical Engineering, 
Pan African University, Institute for 

Basic Sciences Technology and 

Innovation, Nairobi, Kenya 

shaheerkapo2017@gmail.com 

George K. Irungu 

Department of Electrical Engineering, 

Jomo Kenyatta University of 
Agriculture and Technology, 

Nairobi, Kenya 
girungu@jkuat.ac.ke 

David K. Murage 

Department of Electrical Engineering, 

Jomo Kenyatta University of 
Agriculture and Technology, 

Nairobi, Kenya 
davidkinyua76@gmail.com 

 

 

Abstract—Induction power generators are the most popular wind 

energy conversion systems (WECS) because they do not require 

synchronization units. However, they usually draw a huge 
quantity of reactive power during disturbances. Hence, 

incorporating wind power into power networks may cause 

voltage instability. This paper presents the usage of STATCOM 

and SSSC FACTS devices for voltage stability enhancement of a 

distribution network with a squirrel cage induction generator 

(SCIG) wind power turbine. The continuation power flow (CPF) 

approach is utilized as a tool to determine the most suitable 
position of SCIG in the system. Also, voltage stability indices 

(FVSI and Lmn) are employed to estimate the stability margin of 

the system by figuring the weakest transmission lines and buses 

in order to locate the appropriate position where the FACTS 

devices should be installed. A comparison of the suitability of the 

FACTS devices to restore system stability was evaluated under 3-
phase fault conditions. The results illustrated that STATCOM 

behaves better than SSSC when the system is restoring from a 

fault. Simulations and voltage stability assessment were carried 

out on the IEEE 14 bus test scheme using the PSAT simulation 
software package. 

Keywords-squirrel cage induction generator (SCIG); voltage 
stability analysis; continuation power flow (CPF); voltage stability 

indices (VSI); STATCOM; SSSC FACTS devices; PSAT 

I. INTRODUCTION  

The integration of wind energy conversion systems 
(WECS) in electrical power systems can help boosting voltage 
stability. WECS perform a major role in regulating the electric 
power flow and enhance the system voltage profiles [1]. 
Recently, there has been an increase in the use of WECS 
because the cost of generating electricity using this technology 
is cheaper compared to other technologies [2]. Currently, 
several scientific studies have been done on incorporating a 
squirrel cage induction generator (SCIG) wind power turbine 
into an electric power system during normal operation and 
emergencies [3]. By relying on both the wind turbine and 

operational features of the distribution system, the 
incorporation of wind power generators can have negative or 
positive effects on the system’s stability and electric power 
losses [1, 4]. Therefore, it will be necessary to analyze the 
influence of the considered SCIG wind power systems with the 
other electric power system elements. The SCIG was among 
the first induction generators to be used in wind farms. This 
generator can also be used in systems with high penetration of 
wind energy because of features like simple rotor framework 
and minimal maintenance costs [5]. Operators had experienced 
many challenges in incorporating wind energy conversion 
systems in power systems because induction generators always 
absorb huge amounts of reactive power from the system during 
normal operation and during disturbances leading to the 
problem of voltage collapse [5]. Voltage collapse occurs when 
a significant portion of the system has very low voltage profiles 
that can lead to an incomplete or overall blackout of the system 
[6]. In order to alleviate the negative impacts of high-level 
penetration of the wind power conversion system, various 
means can be used such as the instalment of FACTS devices 
which have already been considered as one of the most 
effective solutions to overcome the voltage stability problem 
[7]. FACTS devices refer to flexible alternating current 
transmission systems which can be able to inject or consume 
reactive power into/from the system [8]. 

Several researchers have examined the utilization of SCIG 
wind turbines for various functions corresponding to enhancing 
voltage profiles and reducing electrical power losses [1] as well 
as increasing the loadability of the system [7]. The 
computational continuation power flow technique has been 
utilized on an IEEE 30 bus test system to find the best position 
in the wind energy conversion system that will result in 
system’s stability enhancement [9] and to get an appropriate 
position of STATCOM as indicated in [10]. Various studies 
have been carried out using numerous voltage stability indices 
(VSI) such as fast voltage stability index (FVSI), line stability 
index (Lmn) for several purposes such as determining the 

Corresponding author: Shaheer Hashim Eisa Osman



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proper placement of SVC and STATCOM [11], identifying the 
weakest buses and lines in order to set up FACT devices [12]. 

The main contributions of the current paper are: (a) The 
CPF approach is presented to examine the influence of SCIG 
wind turbine on various regions of the IEEE 14 bus test system 
for system voltage stability analysis, (b) The FVSI along with 
Lmn indices are presented for the suitable positioning of 
STATCOM and SSSC FACTS devices for voltage stability 
improvement. 

II. WIND ENERGY PLACEMENT 

A. Squirrel Cage Induction Generator (SCIG) 

The SCIG model is driven by a constant speed wind 
turbine. It is also known as a short-circuit induction generator 
that could be coupled straight to the electric grid. The 
configuration and the mathematical equations of the dynamic 
SCIG wind turbine type are based on the induction motor 
equivalent circuit [4, 13], that could be expressed in a 
synchronously rotating real-imaginary frame (r-m) linked with 
the system reference point angle. Therefore, the maximum 
power output obtained by the wind power turbine can be 
expressed mathematically as [13]: 

� = 	
�

�
���	
���� (1) 

where ρ is the air density, S is the swept area by the wind 
turbine, V is wind speed, Cp defines the performance 
coefficient, Λ is the ratio of tip speed of the turbine blade, and β 
is the pitch angle. 

At lower wind speed levels, the performance coefficient 
relies simply on the ratio of tip speed rather than the pitch angle 
that would be equal to zero. This coefficient corresponds to the 
aerodynamic output of the wind turbine providing the highest 
power output. 

B. Continuation Power Flow Method (CPF) 

This particular technique is utilized to measure the 
maximum loadability point (lambda) of the system. Essentially 
in CPF technique there are two phases. The first phase, known 
as the predictor step, is responsible for forecasting the next 
value of lambda (λ) in the case where it shifts from the base 
condition point. The second step attempts to correct the value 
which has been forecasted in the initial phase [14]. The purpose 
of the CPF method is to keep track of the solutions as the 
loading parameter λ varies. This parameter is termed a loading 
point or (factor) which is utilized to the system MW distance 
from a primary operating point to the voltage collapse point 
where the voltages will become critical. The parameter 
modifies load powers as in [1]. 

III. VOLTAGE STABILITY INDICES 

There a number of strategies used to assess the system 
voltage stability which is obtained by the application of indices 
such as the FVSI index and Lmn index that are capable of 
identifying the critical lines and corresponding weak buses by 
measuring the reactive power and voltage of the transmission 
lines in which the system stability may have been violated [15]. 
The basic mathematical formulas for FVSI and Lmn employ 

the general two-bus electric power line model presented in 
[10]. 

A. Fast Voltage Stability Index (FVSI) 

The principle behind this index can be illustrated from (2). 
The more the FVSI is close to 1 in that particular transmission 

line, the more the system will tend to lose stability. 

	���� =
�	���

�
	��

�� 	���
≤ 1		 (2) 

where Zij is the impedance of the transmission line between bus 

i and bus j, Xij is the reactance between bus i and bus j, Qj is the 
reactive power that flows to bus j, Vi is the sending-end 

voltage. 

B. Line Voltage Stability Index (Lmn) 

This index is derived by [20]. Upon examination of (3), it 

can be noted that if the index is≤ 1, the system becomes stable 
otherwise it’s unstable. 

��� =
�	���	��

��
�
	� ��	�!"#�

≤ 1 (3) 

where θ is the line angle and δ is the difference between a 

sending-end angle and receiving-end angle. 

IV. FACTS DEVICES OVERVIEW 

The operation of an alternating current power transmission 
line is generally limited by the constraints of the electrical 
power parameters. FACT devices are a novel technology that 
applies power electronics for controlling voltage, impedance, 
phase angle, current, active and reactive power during normal 
and contingency events in order to improve the system 
controllability, stability and hence increase the power transfer 
capabilities of the system transmission line. FACTS devices 
may either be connected in series or shunt. Their behaviors 
depend on the proper position across the transmission lines and 
buses. In a two-bus transmission line, the active power and the 
current flowing through the transmission line can be controlled 
as stated in [8, 16]. 

A. Static Synchronous Compensator (STATCOM) 

STATCOM is a voltage source converter (VSC) that is 
connected in parallel to the bus for the purpose of providing 
dynamic reactive power and thus regulating the system voltage. 
Both STATCOM and synchronous condenser have the same 
functionality. They can deliver or consume the reactive power 
for the system. The basic STATCOM topology can be found in 
[17]. STATCOM is shunt-connected and therefore functions to 
control the voltage at the connecting bus with respect to the 
reference by adjusting the voltage and angle of the internal 
voltage source. When E=V, the reactive current output is zero. 
When E>V, the current will flow to the converter from the AC 
system, absorbing reactive power, whereas when E<V, the 
currents will flow through the converter to the AC system 
generating reactive power. When δ=0, the reactive current 
absorbed (Ir) is given by: 

�$ =
%"�

&'(�
	 (4) 



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B. Static Synchronous Series Compensator (SSSC) 

SSSC is basically consisting of a VSC, a coupling 
transformer and a voltage source. The flow of the power can be 
regulated by controlling the magnitude of the voltage source 
(Vc) and hence, control the active and reactive power flow in 
the network. SSSC is connected in series to power transmission 
lines through a transformer and this is the only difference with 
STATCOM [17]. The steady-state power in the absence of the 
energy source between Vc and the DC side is shown by: 

�)�
∗ = 0 (5) 

This equation illustrates that Vc is in quadrature with the 
flowing current I, meaning that there are two operating modes 
for reactive power compensation (capacitive mode and 
inductive mode) depending on the phase displacement between 
the Vc and I. So, generally 

�)
∧ = �)�cos 0 1 2 sin 0�5

(∅ (6) 

where γ is the angle by which �)
∧ lags the current, ∅ is line 

current phase angle. 

V. DESCRIPTION OF THE SYSTEM MODEL 

In this study, the basic IEEE 14 bus test system as indicated 
in Figure 1 has been considered. 

 

 
Fig. 1.  Illustration of the standard IEEE 14-bus test system with wind 

incorporated to bus 14 

The system comprises of two synchronous power 
generators, three synchronous condensers, joined together by 
using numbers of twenty transmission lines to supply eleven 
load buses [11]. The SCIG model from the PSAT library is 
employed on this simulation. The chosen MVA and rated 
frequency are 100MVA and 50Hz respectively. The wind farm 
comprises of 25 units of 2MW, 0.69kV, 50Hz, a SCIG type 
with 15m/s average wind speed is integrated to the standard 
IEEE 14 bus system by adding an extra PV bus type at bus 15 
through a power transformer. A standard PQ type is utilized for 

the loads while the generator limitations are dismissed. The 
SCIG and wind turbine data used in wind farms simulation are 
found in [18]. The simulation has been executed with the use of 
PSAT. PSAT is a power system analysis toolbox incorporating 
various tools such as load flow analysis (LFA), time domain 
simulation (TDS) and continuation electrical power flow (CPF) 
[19]. Employing the CPF method of PSAT, the system voltage 
stability is examined. 

VI. SIMULATION, RESULTS, AND DISCUSSION 

To examine the effects of wind power integration on 
voltage stability, the simulation was carried out in various 
stages. 

A. Identifying the Proper Location of the Wind Turbine 

In this stage, the SCIG wind power turbine model from the 
PSAT library was used. The location was identified as an 
outcome of the CPF approach, on which the system stability 
was enhanced and electric power losses were minimized. The 
CPF approach is used to identify voltage levels along with the 
maximum loadability element of the presented system after 
introducing the SCIG wind turbine into the system. From the 
IEEE 14 bus dynamic model base case, a CPF is performed and 
the voltage profiles were obtained. Figure 2 shows that buses 9, 
10, 11, 13, and 14 are the critical buses. Among them, bus 14 is 
considered the most critical one due to the small value of the 
voltage profile which is 0.69p.u. 

 

 
Fig. 2.  The voltage profiles of the basic case using CPF method 

The active power-voltage (P-V) curve of each bus is 
obtained through the employment of CPF approach, in which 
CPF starts with primary operating point and then expanding the 
load to the maximum loading point. Figure 3 illustrates the P-V 
curve of each weak bus of the basic case. Maximum loading 
factor or (point) which is where the Jacobian matrix turns out 
to be singular, takes place at λ=1.7p.u. Bus 14 is demonstrated 
as the weakest load bus that needs voltage support. 

 

 
Fig. 3.  Shows the IEEE 14 bus P-V curves of the basic case 



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The maximum loading point for the modified system with 
the wind generator located at bus 14 happened at λ=1.72p.u, 
and this is due to the positioning of the wind generator at the 
weak bus. When the wind energy conversion system is 
connected at bus 14, there is an increase in the maximum 
loading factor of the system and an improvement in the voltage 
levels in the weak buses as shown in Figure 4. 

 

 
Fig. 4.  The voltage levels of the integrated system using CPF method 

B. The Modified IEEE 14 Bus System Under 3-phase Fault 

The considered test system has been divided into three 
areas which are high voltage side, medium voltage side and 
low voltage side based on the working voltages 69KV, 18KV, 
13.8KV respectively of the IEEE 14 bus system. On this stage 
a three-phase fault has been applied on bus 1 which represents 
the high voltage side, bus 8 which represents the medium 
voltage side, and on bus 14 which represents the low voltage 
side. The 3-phase fault occurred at the 1.0s instant and was 
cleared at the 1.25s instant. To examine the effects of the three-
phase fault on the system, the electrical variables active power, 
reactive power, and voltage have been monitored on the wind 
bus which represents bus 15. From the results shown in Figure 
5, during the occurrence of the faults at bus 14 the voltage 
dropped from 1.045p.u to almost 0p.u and therefore, the 
acceleration of the wind rotor reduced making the transmitted 
active power by the wind generator to the system equal to 0p.u 
as shown in Figure 6. 

 

 
Fig. 5.  Voltage profiles response at the wind bus with fault applied at bus 

1, bus 8, and bus 14 

It was noted that when the fault was cleared the system 
attempted to restore back to its original operating point making 
the SCIG wind power generator to absorb a huge reactive 
power amount equal to -0.8p.u from the distribution portion of 
the system as shown in Figure 7. When the fault occurred at 

bus 14 the wind system became unstable. This was because the 
reactive power demanded by the SCIG wind turbine was not 
enough for the rotor magnetization of the wind generator, while 
in the other fault cases (fault at bus 1 and bus 8) the wind 
system kept its stability although reactive power had been 
consumed. 

 

 
Fig. 6.  Active power transmitted by a wind turbine with fault applied at 

bus 1, bus 8, and bus 14 

 
Fig. 7.  Reactive power transmitted by wind turbine with fault applied at 

bus 1, bus 8, and bus 14 

C. Determination of the Weakest Lines and Buses for an 

Integrated System with the Wind at Bus 14 

From sub-section B it is evident that the SCIG wind turbine 
required huge reactive power when the fault was close to the 
wind bus. Also, the distribution part as shown in Figure 5 
describing the installed wind turbine has some nodes needing 
reactive power support which may lead to instability. 
Therefore, it is recommended to apply the VSI for the 
integrated IEEE 14 bus system, to determine the weakest lines 
and corresponding buses for reactive power support. 

1) Procedures of Computing the VSI 

The steps that have been followed are: 

• Perform the Newton-Raphson method for the integrated 
IEEE 14 bus test system and obtain the load flow report. 

• From load flow results and by the use of (7) and (8) the 
FVSI and the Lmn for all buses and lines of the system are 
computed. 

• The reactive power at the receiving-end bus for the selected 
load bus progressively increases until the load flow process 
fails to converge to a solution. This is followed by the 
calculation of FVSI. 



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• The line index with the highest values shall be taken out as 
the most significant weak line with reference to a bus. 

• Another load bus is chosen and the previous procedures are 
repeated.  

2) Calculation of FVSI and Lmn for the Integrated IEEE 14 

Bus System. 

Figure 8 shows the obtained values from the calculation of 
FVSI and Lmn. 

 

 
Fig. 8.  Bar graph of the calculated values of FVSI, Lmn of the integrated 

IEEE 14 bus test system. 

The modified system has 21 transmission lines, but only 15 
transmission lines have been considered. This is because they 
connect load buses, which are line numbers 4, 5, 7, 8, 9, 11, 12, 
13, 15, 16, 17, 18, 19, 20, and 21. Among the considered lines, 
the ones with the highest values (greater or equal to 0.04) of 
FVSI and Lmn have been taken as critical lines, which are lines 
8, 9, 11, 12, 13, 15, 18 and 20 as shown in Figure 8.The results 
showed that load bus 14 is the weakest bus and exposed to 
voltage instability. It has the lowest maximum allowable 
reactive power of 63MVAR compared to the other load buses 
as shown in Figure 9. Bus 14 has three lines connected to it and 
the weakest line with respect to load bus 14 is the line 13-14. 
Hence this implies that any absorption of 63MVAR or more 
will tend to voltage collapse. 

 

 
Fig. 9.  Maximum allowable reactive power on load buses 

D. Comparison of the FACTS Devices Used 

At this stage, two types of FACTS devices, STATCOM and 
SSSC FACTS devices, were compared. By the utilization of 
PSAT platform, the time domain simulation (TDS) approach 
have been examined to evaluate the performance of FACTS 
when a three-phase fault occurs at bus 14. 

1) Performance of STATCOM and SSSC FACTS Devices 

During a Three-phase Fault. 

The scenario that was discussed in sub-section B has been 
repeated again with the presence of 100MVA SSSC and 
STATCOM FACTS devices. SSSC is connected to line 20 
(between bus 13 and bus 14) and STATCOM is connected to 
bus 14. Comparison analysis between the SSSC and 

STATCOM has been made based on the responses of the 
electrical variables voltage, active and reactive power with 
respect to the considered system under three-phase faults. 
Figure 10 shows the voltage responses of the wind bus before 
and after the connection of SSSC and STATCOM FACTS 
devices. It is evident that the system was able to revert back to 
the normal operation and this is attributed to the consumed 
reactive power amount by SCIG wind turbine that has been 
generated from SSSC and STATCOM FACTS devices making 
the system stable. Although both types of FACTS devises 
performed well in the system, STATCOM settled down before 
SSSC. This is attributed to the effectiveness of STATCOM at 
low voltage levels which has made the system stability better 
than when using SSSC. With regards to active power response, 
SSSC has better performance than STATCOM as shown in 
Figure 11. STATCOM oscillated higher and delayed in the 
settlement compared to SSSC. 

 

 

Fig. 10.  Voltage responses at wind bus 15 with fault applied at bus 14 

 

Fig. 11.  Active power responses at wind bus 15 with fault applied at bus 14 

Finally, the analysis was extended to the reactive power 
response that was delivered by both FACTS devices. Figure 12 
shows the reactive power drawn by the SCIG wind turbine. As 
mentioned above, the instability occurred because of SCIG 
wind turbine reactive power absorption goes more than 
63MVAR. Therefore, in SSSC and STATCOM cases even if 
the reactive power demand goes beyond 63MVAR these 
devices were able to support the excess reactive power demand 
which makes the system stable. STATCOM reacted faster than 
SSSC. Furthermore, STATCOM started to settle down before 
SSSC. 



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Fig. 12.  Reactive power responses at wind bus 15 with fault applied at bus 

14 

VII. CONCLUSION 

The computation of VSI of the standard IEEE 14 bus after 
the integration of the SCIG wind power turbine was calculated 
along with the comparative investigation of STATCOM and 
SSSC FACTS devises. The results were drawn for simulations 
with the SCIG wind power turbine incorporated to the 
distribution network at bus 14. There was an enhancement of 
the voltage levels at some load buses with a difference of 
0.2p.u, and the loadability margin increased from 1.7 to 1.72. 
There was also a reduction in the active and reactive electric 
power losses from 1.3p.u and 5.18p.u to 0.97p.u and 3.59p.u 
respectively. Furthermore, there was a massive reactive power 
amount at the time of fault occurrence. The weak parts of the 
system were determined and the maximum permissible reactive 
power for load buses was computed. To prevent voltage 
collapse, STATCOM and SSSC have been employed and 
comparatively STATCOM provided more effective outcomes 
than SSSC. 

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