Modeling of static var compensator-high voltage direct current to provide power and improve voltage profile

International Journal of Power Electronics and Drive Systems (IJPEDS)
Vol. 12, No. 3, September 2021, pp. 1659~1672
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v12.i3.pp1659-1672  1659
Journal homepage: http://ijpeds.iaescore.com
Modeling of static var compensator-high voltage direct current
to provide power and improve voltage profile
Abdolmajid Javadian1
, Mahmoud Zadehbagheri2
, Mohammad Javad Kiani3
,
Samad Nejatian4
, Tole Sutikno5
1,2,3,4
Department of Electrical Engineering, Yasooj Branch, Islamic Azad University, Yasooj, Iran
5
Department of Electrical Engineering, Universitas Ahmad Dahlan, Yogyakarta, Indonesia
5
Embedded System and Power Electronics Research Group, Yogyakarta, Indonesia
Article Info ABSTRACT
Article history:
Received Apr 14, 2021
Revised Jun 15, 2021
Accepted Jun 27, 2021
Transmission lines react to an unexpected increase in power, and if these
power changes are not controlled, some lines will become overloaded on
certain routes. Flexible alternating current transmission system (FACTS)
devices can change the voltage range and phase angle and thus control the
power flow. This paper presents suitable mathematical modeling of FACTS
devices including static var compensator (SVC) as a parallel compensator
and high voltage direct current (HVDC) bonding. A comprehensive
modeling of SVC and HVDC bonding in the form of simultaneous
applications for power flow is also performed, and the effects of
compensations are compared. The comprehensive model obtained was
implemented on the 5-bus test system in MATLAB software using the
Newton-Raphson method, revealed that generators have to produce more
power. Also, the addition of these devices stabilizes the voltage and controls
active and reactive power in the network.
Keywords:
FACTS devices
High voltage direct current
Newton-Raphson method
Power flow
Static var compensator
This is an open access article under the CC BY-SA license.
Corresponding Author:
Mahmoud Zadehbagheri
Department of Electrical Engineering
Yasooj Branch, Islamic Azad University, yasooj, Iran
Email: Mahmoud.zadehbagheri.2009@gmail.com
NOMENCLATURE
𝑆 : Apparent power 𝑌 : Line and element admittance
𝑃 : Active power 𝐺 : Line and element conductance
𝑄 : Reactive power 𝐵 : Line and element susceptance
𝑈, 𝑉, 𝐸 : Voltages of terminal, effective, bus 𝐽, 𝐽1, 𝐽2, 𝐽3, 𝐽4 : Jacobin matrix and its elements
𝐼 : Line current 𝑥 : State variable in power flow equation
𝛿, 𝛳 : Phase angles f(x) : State variables function
𝑋 : Line and element reactance Rdc : Resistance in the connection line of HVDC
1. INTRODUCTION
The use of flexible alternating current transmission system (FACTS) and high-voltage direct current
(HVDC) equipments are considered by designers of electrical transmission networks due to the increased
demand for transmission networks, the creation of long transmission line routes, long distance of production
centers from consumption centers, accumulation of energy resources in specific places and wide distribution
of consumption centers [1]–[8]. This equipment can control both active and reactive power simultaneously,
regulate voltage range and reduce power flow on overloaded lines by creating the desired voltage level [9]–

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Int J Pow Elec & Dri Syst, Vol. 12, No. 3, September 2021 : 1659 – 1672
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[12]. Flexible alternating current transmission system devices can increase load capacity, portability and
reliability and improve system line density [13]. Load flow studies are essential for the analysis, design,
control, and economic planning of the future of transmission and power systems [11].
The Newton-Raphson power flow method is an effective and practical method due to its quadratic
convergence and the fact that the number of iterations is independent of the system size and has a high
convergence rate [11], [14]. Power transmission capacity is influenced by factors such as thermal constraints,
voltage constraints, and limited stability, which leads to dense lines and reduction of security margins and
definitive load [8], [12], [15], [16].
In order to meet the requirements for system control, a set of equipment is used that include tools
that control power and voltage [10]. Low portability means the need for more production resources [13].
Therefore, practical measures should be taken to improve portability. FACTS devices are used for increasing
portability and power quality [13]. Energy systems can be developed by installing HVDC transmission lines
[17]–[20], which resolve the problems of low impedance and unbalanced power flow because they control
power based on electronic power devices [13]. A combination of series and parallel controllers with line
impedance control and voltage regulator manage the active and reactive power in the system [13]. High-
voltage direct current systems are of particular importance due to the accumulation of energy resources in
specific locations, wide distribution of consumption centers, the need to connect to adjacent networks, the
need for transmission by underground and sea routes and the economic benefits of high-power transmission
over long distances [13], [21].
The disadvantages of HVDC lines, on the other hand, include high energy conversion costs and
reactive power requirements of converters [17]. Flexible alternating current transmission system controllers
used in this paper included static var compensator or static var compensator (SVC) and HVDC link was also
used in the transmission line. High-voltage direct current systems are comprised of two converters, one
capable of regulating voltage and the other capable of quickly transmitting and controlling active power [9].
Provided that direct current (DC) converters inherently absorb reactive power, a reactive power source such
as an SVC can be used near the converter [10]. SVC is used to generate or absorb reactive power in parallel
in the network to control the bus voltage [13]. Much research has been carried out on the use of FACTS
devices and HVDC lines, included proposing two suitable multi-terminal VSC-HVDC models for load flow
study using the Newton-Raphson algorithm [22], Newton-Raphson HVDC power flow modeling [23]–[25],
and multi-terminal VSC-HVDC load flow was modeled using the AC/DC load flow algorithm by MATLAB
and MATPOWER software programs [26], [27].
In Vinkovic and Mihalic [28], the general method for dual modeling of FACTS devices and their
series and parallel modeling were studied. SVC has been used to optimize the Newton-Raphson power flow
modeling [29], [30]. In [31], a control method for the coordination of HVDC and FACTS was proposed with
the aim of obtaining small signal stability of the power system, which indicated that by changing the
parameters, the oscillation between adjacent areas for production was reduced. In [32], a multiple optimal
power flow (OPF) solution method was presented with the presence of FACTS devices, which were very
powerful and fine-tuned the unequal constraints of the system. The optimal multi-objective placement of
FACTS controllers including SVC, thyristor-controlled series compensation (TCSC), and unified power flow
controller (UPFC) for power system operational planning has been investigated in [33]–[37]. The optimal
power flow of the HVDC two-terminal system was obtained with the help of a genetic algorithm and a
backtracking search algorithm in [17], [38]. The integration of an SVC into the distribution generator in the
network, led to an improvement in voltage regulation and a reduction in distribution network losses [39]. For
optimal reactive power and coordination between FACTS devices such as SVC and TCSC with other
sources, simple particle swarm optimization (SPSO), evolutionary particle swarm optimization (ESPO), and
adaptive particle swarm optimization (APSO) algorithms were used [40]–[51]. Power flow modeling of the
AC-DC hybrid HVDC multi-terminal system was presented in [52], [53], which achieved a very good power
flow and convergence solution. In [54], a new power flow method including FACTS and HVDC devices was
investigated in which the bass equations included a P-Q bus (in this bus the real power (P) and reactive
power (Q) are specified) in the alternating current (AC) system to remove components from the AC system
and increase the convergence speed. In none of the previous works the simultaneous use of FACTS devices
has been investigated using comprehensive modeling. In this article, the simultaneous combination of two
devices and between two buses has been used, but in previous works, either these devices have been used
individually or not simultaneously between two buses to investigate its effects. We sought to investigate the
modeling of SVC and HVDC devices and to obtain comprehensive modeling of the simultaneous application
of all the two devices by the Newton-Raphson power flow method and determine the effects of series and
parallel compensations on the network. Simulations were implemented with the help of MATLAB software
on a 5-bus test system.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Modeling of static var compensator-high voltage direct current to … (Abdolmajid Javadian)
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2. RESEARCH METHOD
2.1. Modeling of FACTS devices
The general model of FACTS devices when used in series on the network as Figure 1 is formulated
in the manner [28].
𝑆𝑆𝑇 = 𝑃𝑆𝑇 + 𝑗𝑄𝑆𝑇 = 𝑈𝑆(−𝐼𝑆
∗
) (1)
𝑆𝑅𝑇 = 𝑃𝑅𝑇 + 𝑗𝑄𝑅𝑇 = 𝑈𝑅(−𝐼𝑆
∗
) (2)
𝑃𝑇 = 𝑃𝑆𝑇 + 𝑃𝑅𝑇 (3)
The model of the parallel application of FACTS devices is as Figure 2 [28].
𝑆𝑃𝑇 = 𝑃𝑃𝑇 + 𝑗𝑄𝑃𝑇 = 𝑈𝑃(−𝐼𝑃
∗
) (4)
𝑃𝑃𝑇 = −𝑈𝑃(𝑅𝑒[𝐼𝑃] 𝑐𝑜𝑠 𝛿𝑃 + 𝐼𝑚[𝐼𝑃] 𝑠𝑖𝑛 𝛿𝑃) (5)
𝑄𝑃𝑇 = −𝑈𝑃(𝑅𝑒[𝐼𝑃] 𝑠𝑖𝑛 𝛿𝑃 −𝐼𝑚[𝐼𝑃] 𝑐𝑜𝑠 𝛿𝑃) (6)
In these equations, S, P, Q and I are the apparent power, active and reactive powers, and line current,
respectively. Power control by FACTS devices according to the power as shown in (7) [34].
𝑃 =
𝑉𝑖𝑉
𝑗
𝑋𝑖𝑗
𝑠𝑖𝑛(𝜃𝑖 − 𝜃𝑗)
𝑉𝑖𝑉
𝑗 ===> 𝑆𝑉𝐶 𝑠𝑖𝑛(𝜃𝑖 − 𝜃𝑗), 𝑉𝑖𝑉
𝑗, 𝑋𝑖𝑗 => 𝑈𝑃𝐹𝐶
𝑋𝑖𝑗 ====> 𝑇𝐶𝑆𝐶
(7)
2.2. SVC modeling
In this paper, SVC is modeled as an ideal reactive power source injected into bus A. Static VAR
compensator can continuously generate reactive power compensation by operating in inductive and
capacitive modes. Static VAR compensator model and structure are specified in Figure 3 [55]. The role of
SVC is to keep the voltage in the bus constant, which is done by injecting power into the bus [30]. In
modeling, we considered SVC as a parallel variable susceptance as Figure 3 [9], [30], [55].
𝐼𝑆𝑉𝐶 = 𝑗𝐵𝑆𝑉𝐶𝑉
𝑎 (8)
The power absorbed or injected into the bass is as (9) [30][55].
𝑄𝑆𝑉𝐶 = 𝑄𝑎 = −𝑉
𝑎
2
𝐵𝑆𝑉𝐶 (9)
Figure 1. Model of a FACTS series
branch [28]
Figure 2. Model of a FACTS
parallel branch [28]
Figure 3. Model of parallel
variable susceptance for SVC
2.3. HVDC system modeling
A HVDC system consists of two voltage source converters connected to busbars A and B by
transformers. The equivalent circuit of the HVDC system includes a combination of the voltage source and
UT
US UR
SRT
SST
UP
UP
SPT
Bsvc
BUS a
Isvc

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transformer impedance series. Depending on their application, both converters are connected back to back or
by a DC cable [21], [24]. The HVDC system is conveniently modeled with two voltage sources along with an
equation that states the active power condition. With the introduction of HVDC, the range of transmission
power increased (from below 1000 W to 3 to 4 GW) [56]. High-voltage alternative current (HVAC) design
and construction are not economical for long distances, but using HVDC improves the cost and transmission
of high voltages [57]. In the system HVDC and FACTS devices, due to less insulation and resistance DC less
than AC, fewer losses[58], the need for two conductors in the system and as a result of the volume and space
of the less to install, reduce of the thickness and cross-section of the cable in a certain power, use of the
ground as a return wire, it has lower costs than HVAC, which in Figure 4, we see the difference in costs
based on references [59], [60]. Moreover, the HVDC is able to improve stability of inter-connected HVAC
by modulating power in response to small/large disturbances [61]. The DC terminals will always be more
expensive than AC terminals simply because they have to have the components to transform DC voltage as
well as convert the DC to AC. But the DC voltage conversion and circuit breakers have been dropping in
price, the break-even price continues to drop. The HVDC model in power flow studies is as Figure 5 [23],
[24], [62].
Total AC
Cost
Total DC
Cost
DC Line Cost
AC Line
Cost
AC Terminal
Cost
DC
Terminal
Cost
Investment
Costs
Distance
Critical Distance
Figure 4. Compare the costs of HVDC and HVAC systems [60]
BUS a BUS b
I1 I2
E1 E2
Y1 Y2
Ia Ib
Ea Eb
Figure 5. Model of HVDC for power flow [9]
𝐸1 = 𝑉1(𝑐𝑜𝑠 𝛿1 + 𝑗 𝑠𝑖𝑛 𝛿1) (10)

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𝐸2 = 𝑉2(𝑐𝑜𝑠 𝛿2 + 𝑗 𝑠𝑖𝑛 𝛿2) (11)
[
𝐼𝑎
𝐼𝑏
] = [
𝑌1 −𝑌1 0 0
0 0 𝑌2 −𝑌2
] . [
𝐸𝑎
𝐸1
𝐸𝑏
𝐸2
] (12)
𝑃 = 𝑅𝑒{𝐸1𝐼1
∗} (13)
𝑄 = 𝐼𝑚{𝐸1𝐼1
∗} (14)
For both HVDC components connected by a DC cable [9], [23].
𝑅𝑒{𝑉1𝐼1
∗
+ 𝑉2𝐼2
∗
+ 𝑉𝐷𝐶𝐼𝐷𝐶} = 0 (15)
And if Rdc = 0 (That Rdc resistor connection line in HVDC) then: [9], [23].
𝑅𝑒{𝑉1𝐼1
∗
+ 𝑉2𝐼2
∗} = 0 (16)
2.4. Comprehensive SVC-HVDC modeling for power flow
Due to the limitations of transmission lines and the advantages of using FACTS devices as parallel
and series compensators in the network, also, for connecting the power grid and taking into account the
advantages of HVDC lines, establishing HVDC connections as a complement to AC systems is essential. In
this paper, a comprehensive model for modeling SVC and HVDC devices was used as Figure 6. Then, the
Newton-Raphson power flow on the final model was applied. According to the Figure 6, an SVC is used as a
parallel compensator and an HVDC as a link.
BUS a
BUS b
I1 I2
E1 E2
Y1 Y2
Ia
Bsvc
Isvc
Ea
Eb
SVC
HVDC
Ib
Figure 6. Model of SVC-TCSC-HVDC for power flow
By writing the relations of currents passing through buses and lines and the relation of power and
separation of their real and imaginary parts,
𝑆𝑖 = 𝑃𝑖 + 𝑗𝑄𝑖 = 𝐸𝑖𝐼𝑖
∗
(17)
𝐸𝑖 = 𝑉𝑖(𝑐𝑜𝑠 𝜃𝑖 + 𝑗 𝑠𝑖𝑛 𝜃𝑖) (18)
𝐸𝑎 = 𝑉
𝑎(𝑐𝑜𝑠 𝜃𝑎 + 𝑗 𝑠𝑖𝑛 𝜃𝑎) (19)
𝐸𝑏 = 𝑉𝑏(𝑐𝑜𝑠 𝜃𝑏 + 𝑗 𝑠𝑖𝑛 𝜃𝑏) (20)
𝐸1 = 𝑉1(𝑐𝑜𝑠 𝛿1 + 𝑗 𝑠𝑖𝑛 𝛿1) (21)
𝐸2 = 𝑉2(𝑐𝑜𝑠 𝛿2 + 𝑗 𝑠𝑖𝑛 𝛿2) (22)

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𝑌𝑖 = 𝐺𝑖 + 𝑗𝐵𝑖 (23)
𝑌0 = 𝑗𝐵𝑆𝑉𝐶 (24)
𝑌1 = 𝐺1 + 𝑗𝐵1 (25)
𝑌2 = 𝐺2 + 𝑗𝐵2 (26)
𝑌3 = 𝑌0 + 𝑌1 = 𝐺1 + 𝑗𝐵3 (27)
𝐵3 = 𝐵𝑠𝑣𝑐 + 𝐵1 (28)
where:
𝑃𝑎 = 𝐺1𝑉
𝑎
2
− 𝐺1𝑉1𝑉
𝑎 cos(𝜃𝑎 − 𝛿1)−𝐵1𝑉1𝑉
𝑎 sin(𝜃𝑎 − 𝛿1) (29)
𝑄𝑎 = −𝐵3𝑉
𝑎
2
− 𝐺1𝑉1𝑉
𝑎 sin(𝜃𝑎 − 𝛿1) +𝐵1𝑉1𝑉
𝑎 cos(𝜃𝑎 − 𝛿1) (30)
𝑃𝑏 = −𝐺2𝑉𝑏
2
+ 𝐺2𝑉2𝑉𝑏 cos(𝜃𝑏 − 𝛿2)+𝐵2𝑉2𝑉𝑏 sin(𝜃𝑏 − 𝛿2) (31)
𝑄𝑏 = 𝐵2𝑉𝑏
2
+ 𝐺2𝑉2𝑉𝑏 sin(𝜃𝑏 − 𝛿2) −𝐵2𝑉2𝑉𝑏 cos(𝜃𝑏 − 𝛿2) (32)
𝑄𝑆𝑉𝐶 = −𝑉
𝑎
2
𝐵𝑆𝑉𝐶 (33)
𝑃1 = −𝐺1𝑉1
2
+ 𝐺1𝑉1𝑉
𝑎 cos(𝜃𝑎 − 𝛿1)−𝐵1𝑉1𝑉
𝑎 sin(𝜃𝑎 − 𝛿1) (34)
𝑄1 = 𝐵1𝑉1
2
− 𝐺1𝑉1𝑉
𝑎 sin(𝜃𝑎 − 𝛿1) −𝐵1𝑉1𝑉
𝑎 cos(𝜃𝑎 − 𝛿1) (35)
𝑃2 = −𝐺2𝑉2
2
+ 𝐺2𝑉2𝑉𝑏 cos(𝜃𝑏 − 𝛿2)−𝐵2𝑉𝑏𝑉2 sin(𝜃𝑏 − 𝛿2) (36)
𝑄2 = 𝐵2𝑉2
2
− 𝐺2𝑉2𝑉𝑏 sin(𝜃𝑏 − 𝛿2) −𝐵2𝑉2𝑉𝑏 cos(𝜃𝑏 − 𝛿2) (37)
where Va, Vb, V1, V2, ϴa, ϴb, δ1, and δ2 are the voltage and angles of the bus a, b, and HVDC link,
respectively. B1, B2 and BSVC are susceptance for the rectifier, inverter and SVC, respectively. G1 and G2 are
the side conductance of the rectifier and inverter, respectively. P1, P2, Pa, Pb are the active powers of rectifier
and inverter, buses a, and b, respectively. Finally, Qa, Qb, QSVC, Q1, and Q2 are the reactive powers for a, and
b buses, the SVC reactive power and the rectifier and inverter sides of the model, respectively.
In (29) to (37) we see that the hybrid model is effective in active and reactive powers related to
buses and lines. For example, in (30) B3 is used which is a combination of SVC and HVDC. These show a
comprehensive hybrid model that can be generalized to larger networks, and this model can also be used in
load flow and stability analysis, etc. To solve the Newton-Raphson power flow (38)-(44). The Newton-
Raphson method is scientifically efficient due to quadratic convergence and high convergence velocity,
which is obtained by extending the Taylor series [63]–[67].
[𝑓(𝑥)] = [𝐽]. [𝑥] (38)
The matrix [J] is the Jacobin matrix obtained by the partial derivatives of each function as shown in
(29)-(37) relative to the variables:
𝑥 =
[
∆𝜃𝑎
∆𝑉𝑎
𝑉𝑎
∆𝐵𝑆𝑉𝐶
𝐵𝑆𝑉𝐶
∆𝛿1
∆𝑉1
𝑉1
∆𝛿2 ]
, 𝐹(𝑥) =
[
∆𝑃𝑎
∆𝑄𝑎
∆𝑄𝑆𝑉𝐶
∆𝑃1
∆𝑄1
∆𝑃𝐻𝑉𝐷𝐶]
, 𝐽 = [
[𝐽1] [𝐽2]
[𝐽3] [𝐽4]
] (39)

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𝐽1 =
[
𝜕𝑃𝑎
𝜕𝜃𝑎
𝜕𝑃𝑎
𝜕𝑉𝑎
𝑉
𝑎 0
𝜕𝑄𝑎
𝜕𝜃𝑎
0
𝜕𝑄𝑎
𝜕𝑉𝑎
𝑉
𝑎
0
𝜕𝑄𝑎
𝜕𝐵𝑆𝑉𝐶
𝐵𝑆𝑉𝐶
𝜕𝑄𝑎
𝜕𝐵𝑆𝑉𝐶
𝐵𝑆𝑉𝐶]
(40)
𝐽2 =
[
𝜕𝑃𝑎
𝜕𝛿1
𝜕𝑃𝑎
𝜕𝑉1
𝑉1 0
𝜕𝑄𝑎
𝜕𝛿1
0
𝜕𝑄𝑎
𝜕𝑉1
𝑉1
0
0
0]
(41)
𝐽3 =
[
𝜕𝑃1
𝜕𝜃𝑎
𝜕𝑃1
𝜕𝑉𝑎
𝑉
𝑎 0
𝜕𝑄1
𝜕𝜃𝑎
𝜕𝑄1
𝜕𝑉𝑎
𝑉
𝑎 0
𝜕𝑃𝐻𝑉𝐷𝐶
𝜕𝜃𝑎
𝜕𝑉𝑎
𝑉
𝑎 0
]
(42)
𝐽4 =
[
𝜕𝑃1
𝜕𝛿1
𝜕𝑃1
𝜕𝑉1
𝑉1 0
𝜕𝑄1
𝜕𝛿1
𝜕𝑄1
𝜕𝑉1
𝑉1 0
𝜕𝛿1
𝜕𝑉1
𝑉1
𝜕𝛿2 ]
(43)
Where in the above relations 𝐽, 𝐽1, 𝐽2, 𝐽3, 𝐽4 are the Jacobin matrix and its components and f(x) are
the function of state variables and x are state variables in load flow equations and we have:
𝑃𝐻𝑉𝐷𝐶 = 𝑃1 − 𝑃2 (44)
Since the active power is set at the end of the rectifier in the HVDC line and the voltage range at bus
b is kept constant, the equations of active and reactive power of the inverter are additional [9].
3. RESULTS AND DISCUSSION
We applied the model obtained in the previous section on a 5-bus test system according to Figure 7,
where all the information about the buses and lines and the whole network was extracted from reference [38].
The information required for the test system is provided in Appendix. First, power flow was without adding
FACTS devices, and then in this network, we added the SVC and HVDC devices individually to the network
and observed the results. Finally, based on the SVC-HVDC model obtained in the previous section of this
paper, all the both devices were added to the system and the results were recorded. In this paper, the focus
was on load flow in buses on which the devices have a direct effect, such as buses 3 and 4 (Lake and Main),
although they affect the whole network.
Lake
North
South Elm
Main
D
D
D
D
SVC
REC INV
HVDC

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Figure 7. System test 5 buses with SVC-HVDC
In Figure 8, which shows voltage changes in the presence of various FACTS devices, the voltage state for
stabilization at 1p.u. is presented. Using SVC, was better than the mode without FACTS devices and the
mode of using HVDC, and in buses 3 and 4, it was 1p.u. closer. But the best state and voltage stabilization
occurred in the case that the SVC-HVDC combination was used. Also, compared to the different references
in Figure 9, the SVC-HVDC model hasd the best state of recovery and voltage stabilization. The best state
for voltage improvement was the mode of using SVC in reference [9].
Figure 8. Voltage of models
Figure 9. Voltage in different model of references
In all diagrams and figures, PG1, PG2, P3-4 and P4-3 are the active powers produced by the North
and South generators, and the active powers are between buses 3 and 4, respectively. In addition, QG1, QG2,
Q3-4 and Q4-3 are the reactive powers generated by the North and South generators, and the reactive powers
are between buses 3 and 4, respectively. By applying Newton-Raphson load flow in the final model and
different models in Figure 10 and Figure 11 (by keeping the output of the South generator constant at 40
MW), an increase in active and reactive power between the buses used by the devices is noted, which is the
best way to use SVC-HVDC. It is the most efficient model in compensating active and reactive power. In the
final hybrid model, the generators are forced to produce more power, which is more costly for the system and
is among the disadvantages of the system.

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Figure 10. Result of active power flow
Figure 11. Result of reactive power flow
By comparing load flow in the models used in this paper and the different references in Figure 12
and Figure 13, we see a further spike in active and reactive power, which indicates the efficiency of the
proposed SVC-HVDC hybrid model in the network. Comparing this model with the references in Figure 12
and Figure 13, it can be concluded that good compensation is obtained for the system. Besides, an increase in
active and reactive power between the buses and lines, and at the same time, voltage stabilization in the Main
and Lake Buses in this SVC-HVDC model were obtained. However, this paper examined a comprehensive
model for the simultaneous effects of all the two types of devices for power flow and controlled the active
and reactive power simultaneously, which had not been done in any of the previous studies [9], [23]–
[25],[29]–[31], [33], [34], [40], [52], [54], [57],[68]–[70].

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Figure 12. Active power flow indifferent model of references
Figure 13. Reactive power flow indifferent model of references
4. CONCLUSION
In this paper, models for the use of different flexible alternating current transmission system
(FACTS) devices were presented, and finally a hybrid model including static var compensator (SVC) as a
parallel compensator and high voltage direct current (HVDC) link was modeled for simultaneous use in a
5-bus network and Newton-Raphson load flow. According to the results, the installation of several types of
FACTS devices simultaneously with SVC-HVDC, by increasing the flexibility of the power network to
achieve better results, improved the voltage profile and compensation to increase the active and reactive
power in the network. In this model, we observed an increase in the power generation of generators, which
increases the production cost in the network and is one of the disadvantages of the model. The results showed
that the proposed method had good performance. This study obtained a suitable hybrid model for load flow
studies that can be generalized to larger networks and this model can be used in stability discussion studies
and other power system studies. Future studies are needed to examine the optimal load flow of this model
and optimal placement of these devices in the network.
APPENDIX

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The information required for the test system in Figure 6 and the range of selected parameters for the
equipment is as:
SVC
BSVC0 = 0.02
BLO = -0.2
BHi = 0.2
V0 = 1.00 QSVC0 = -100 MVAr 100 MVAr
HVDC
Rdc = 0.00
V1’ = 1.00
V2’ = 1.00
VLO =0.9
VHi = 1.1
PHVDC0 = 0.4 MW 300 MW
Where BSVC0, BLO, BHi, V0 and QSVC0 are the initial values and upper and lower limits of the susceptance,
the initial voltage and range of change of reactive power values in SVC, respectively. Also, V1’, V2’, VLO and
VHi are the initial voltage values on the rectifier and inverter side and their change amplitude, respectively.
PHVDC0 the range of change of active power values is HVDC. The rest of the information related to buses,
lines and generator information is available in reference [38].
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BIOGRAPHIES OF AUTHORS
Abdolmajid Javadian, he was born in December 1989 in Yasuj, Iran. In 2013, he received
his bachelor's degree in electrical engineering from Jundishapur University of Dezful, Iran.
In 2015, he received a master's degree in electrical engineering from the Islamic Azad
University, Yasouj Branch, Iran. He is currently studying for his doctorate at the Islamic
Azad University of Yasouj Branch. His research interests include context FACTS and Power
flow in power systems.
Mahmoud Zadehbagheri was born in Yasouj, Iran in October 1989. In 2003 he received his
B.S. in Electrical Engineering from Kashan University and in 2008 he received his M.S. in
Electrical Engineering from the Islamic Azad University, Najafabad Branch. He received the
PhD degree in Electrical Engineering from Sabzevar Hakim Sabzevari University in 2017.
He is with the faculty of the Electrical Engineering Department, Islamic Azad University of
Yasouj. His research interests include the fields of power electronics, electrical machines and
drives, FACTS devices and power quality.
Mohammad Javad Kiani was born in Yasouj, Iran in. In 2003 he received his B.S. in
Electrical Engineering from K. N. Toosi University of Technology and in 2008 he received
his M.S. in Electrical Engineering from the K. N. Toosi University of Technology. He
received the PhD degree in Electrical Engineering from UTM University of Malaysia in
2017. He is with the faculty of the Electrical Engineering Department, Islamic Azad
University of Yasouj. His research interests include the fields of Electronic and Power
electronics.
Samad Nejatian was born in Yasouj, Iran, in 1981. He received his B.S. degree in Electrical
Engineering from Zahedan University, Zahedan, Iran, in 2003; his M.S. degree in Electrical
Engineering from the Ferdowsi University of Mashhad, Mashhad, Iran, in 2007; and his
Ph.D. degree in Electrical Engineering from the UTM University of Malaysia, Skudai,
Malaysia, in 2014. He is presently a faculty member and an Associate Professor in the
Department of Electrical Engineering, Islamic Azad University, Yasouj, Iran. His current
research interests include intelligent networks, control systems, reliability in power systems,
and neural networks.
Tole Sutikno is a Lecturer in Electrical Engineering Department at the Universitad Ahmad
Dahlan (UAD), Yogyakarta, Indonesia. He received his B.Eng., M.Eng. and Ph.D. degrees in
Electrical Engineering from Universitas Diponegoro, Universitas Gadjah Mada and
Universiti Teknologi Malaysia, in 1999, 2004 and 2016, respectively. He has been an
Associate Professor in UAD, Yogyakarta, Indonesia since 2008. He is currently an Editor-in-
Chief of the TELKOMNIKA and the Head of the Embedded Systems and Power Electronics
Research Group. His research interests include the field of digital design, industrial
applications, industrial electronics, industrial informatics, power electronics, motor drives,
renewable energy, FPGA applications, embedded system, artificial intelligence, intelligent
control and digital library.

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