Recent Advances in Energy, Environment and Development
Power Flow Using FACTS Devices in Power System
GAGANDEEP SINGH AULUCK
Electrical Engineering Department
RIMT-IET, Mandi-Gobindgarh
Punjab (India)
E-mail: gaganaulakh82@gmail.com
Abstract: The power flow studies with the implementation of FACTS devices are presented in this paper. In this
paper thorough grounding on conventional power flow theory with particular reference to the Newton-Raphson
method has been presented. The main aim of this work is to introduce a systematic and coherent way to study
models and methods for the representation of FACTS controllers in the power flow studies. Aspects of modeling
and implementation of the Thyristor Controlled Series Compensator (Series Controller) and Static VAR
Compensator (Shunt Controller) FACTS controllers are presented with the help of MATLAB simulation &
Newton-Raphson power flow technique in this paper. This technique exhibits very strong convergence
characteristics, regardless of the network size and the number of controllable devices. The results of power flow
have been obtained on the IEEE 5-Bus & 14-Bus system. In this paper the study has been carried to locate the
optimal position of compensating devices in order to reduce the production cost along with the device cost. From
the obtained results the effective regulation of active power has been achieved which leads to reduction in technical
losses.
Key Words: FACTS, TCSC, SVC, Transmission, Distribution.
technologies allow for improved transmission system
operation with minimal infrastructure investment,
environmental impact, and implementation time
compared to the construction of new transmission
lines.
Traditional solutions to upgrading the electrical
transmission system infrastructure have been
primarily in the form of new transmission lines,
substations, and associated equipment. However, as
experiences have proven over the past decade or
more, the process to permit, site, and construct new
transmission lines has become extremely difficult,
expensive, time-consuming, and controversial.
FACTS technologies provide advanced solutions as
cost-effective alternatives to new transmission line
construction.
The power flow problem is formulated as set of
nonlinear equations. Many calculation methods have
been proposed to solve the problem. Among them,
Newton Raphson method and fast decoupled load
flow method are two very successful methods. In
general, the decoupled power flow methods are only
valid for weekly loaded network with large X/R ratio
network. For system conditions with large angle
across lines (heavily loaded network) and with special
control that strongly influence active and reactive
power flows, Newton-Raphson method may be
required. Therefore, when the AC power flow
1. INTRODUCTION
With the ongoing expansion and growth of the electric
utility industry, including deregulation in many
countries, numerous changes are continuously being
introduced to a once predictable business. Although
electricity is a highly engineered product, it is
increasingly being considered and handled as a
commodity. Thus, transmission systems are being
pushed closer to their stability and thermal limits
while the focus on the quality of power delivered is
greater than ever, In the evolving utility environment,
financial and market forces are, and will continue to,
demand a more optimal and profitable operation of
the power system with respect to generation,
transmission, and distribution. Now, more than ever,
advanced technologies are paramount for the reliable
and secure operation of power systems. To achieve
both operational reliability and financial profitability,
it has become clear that more efficient utilization and
control of the existing transmission system
infrastructure is required.
Improved utilization of the existing power system is
provided through the application of advanced control
technologies. Power electronics based equipment, or
Flexible AC Transmission Systems (FACTS), provide
proven technical solutions to address these new
operating challenges being presented today. FACTS
ISBN: 978-1-61804-157-9
41
Recent Advances in Energy, Environment and Development
to SVC Placed at bus i(i = 1,......N i )
calculations is needed in systems with FACTS
devices, Newton-Raphson method is a suitable power
flow calculation in system with TCSC and SVC when
high accuracy is required.
The basic requirement of power system is to meet the
demand that varies continuously. That is, the amount
of power delivered by the power companies must be
equal to that of consumer’s need. Unfortunately
nobody guarantees that unexpected things such as
generator fault or line fault and line tripping would
not happen. Due to its fast control characteristics and
continuous compensation capability, FACTS devices
have been researched and adapted in power
engineering area. There are so many advantages in
FACTS device; it can increase dynamic stability,
loading capability of lines and system security. It can
also increase utilization of lowest cost generation. The
key role of FACTS device is to control the power
flow actively and effectively. In other words, it can
transfer power flow from one line to another within
its capability. This paper focuses on the development
of new SVC and TCSC model and their
implementation in the Newton-Raphson load flow
algorithms.
These factors can be computed at a base load flow
solution as given below.
Consider a line-k connected between bus-I and bus-j
and having series impedance Rk+jXk. Xk is the net
reactance considering the reactance of the series
compensator, if present, in the line. Let the complex
voltage at the bus –I and –j are Vi L I and Vj L j
respectively. φk = δ i − δ j is the phase shifter.
3.
 2R X 
∂PLk
= a 2Vi + V j2 − 2aViV j cos(δ i − δ j ∗  2 k k2 2 
∂xk
 ( Rk + X k ) 
[
Where k=1…N
(3)
For computing the loss sensitivity index with respect
to SVC an exact loss formula has been used, which
expresses PL as,
N
Where a, β is the loss coefficients defined as;
a jk =
β jk =
]
rjk
V jVk
rjk
V jVk
(4)
cos(δ j − δ k )
(5)
sin(δ j − δ k )
(6)
Pi + jQi = Complex injected power at bus-I (7)
rjk = Real Part of the jk element of [Zbus]
At bus-I, sensitivity index with respect to SVC
parameter using above loss formula can be expressed
as:
N
∂PL
= 2∑ (aij Q j + β ij Pj )
∂Qi
j =1
i = 1,......N
(8)
Criteria for optimal placement
The FACTS devices should be placed on the most
sensitive bus or line. With the loss sensitivity indices
computed for each type of the FACTS devices,
following criteria have been used for their optimal
placement.
1. The TCSC should be placed in a line (m)
having most positive loss sensitivity index
(am).
2. The SVC should be placed at a bus -i having
most negative sensitivity index ci.
(1)
to TCSC Placed in line k(k = 1,......N i )
∂P
ci = L Loss sesitivity with respect
∂Qi
(2)
ISBN: 978-1-61804-157-9
[
j =1 k =1
Most of the work, in the past has utilized dynamic
considerations for the placement of the FACTS
devices, as these devices were utilized to mainly
improve the stability of the power system networks.
In this paper, the FACTS devices have been
considered from a static point of view to reduce the
total system real power Transmission loss (PL).
Hence, a new method based on sensitivity approach,
as described below, has been suggested for placement
of the FACTS devices.
Loss sensitivity indices
The proposed method utilizes the sensitivity of total
transmission loss (PL) with respect to the control
parameters of FACTS devices for their optimal
placement. The control parameters for the two
FACTS devices include line net series reactance
(placed in line no-19) for TCSC and reactive power
injection (placed at bus no-5) for SVC. Thus, the loss
sensitivity factors with respect to the parameters of
these devices can be defined as,
∂PL
Loss sesitivity with respect
∂xk
N
PL = ∑∑ a jk ( Pj Pk + Q j Qk ) + β jk (Q j Pk − Pi Qk )
2. OPTIMAL LOCATION OF FACTS
DEVICES
ak =
]
42
Recent Advances in Energy, Environment and Development
possible the development of fast SVC’s in the early
1970’s. The SVC consists of a group of shuntconnected capacitor and reactor banks with fast
control action by the means of thyristor switching.
From the operational point of view, the SVC can be
seen as variable shunt reactance that adjusts
automatically in response to changing system
operative conditions. Depending on the nature of the
equivalent SVC’s reactance, i.e. capacitive or
inductive, the SVC draws either capacitive or
inductive current from the network. Suitable control
of this equivalent reactance allows voltage magnitude
regulation at the SVC points of connection. SVC’s
achieve their main operating characteristics at the
expense of generating harmonic current and filter are
employed with this kind of devices.
Following additional criteria have also been
used while deciding the optimal placement of FACTS
devices.
i)
The TCSC should not be placed between
two generation buses, even though the
line sensitivity is highest.
ii)
The placement of SVC has been
considered at load buses only.
3. POWER FLOW CONSIDERING
FACTS DEVICES
The unified approach blends the AC network and
power system controller state variables in a single
system of simultaneous equations:
f (XnAC, RnF) = 0,
g (XnAC, RnF) = 0,
Where, XnAC stands for the AC network state
variables, namely, nodal voltage magnitude and phase
angle and RnF stands for the power system controller
state variables.
X1
f1
:
:
fnAC
F1
:
:
Fnf
. . . .
xnAC
r1
. . .
rnf
AC network
FACTS
Fig. 1 Augmented Jacobian
3.1 SVC Model Implementation, NewtonRaphson Load Flow
1. SVC total susceptance model: A Changing
susceptence Bsvc represents the fundamental
frequency equivalent susceptance of all shunt
modules making up SVC. This model is an
improved version of SVC models currently
available in open literature.
2. SVC firing angle model: The
equivalent
suscep Beq which is function of a changing
firing angle α, is made up of the parallel
combination of TCR equivalent admittance
and a fixed capacitive susceptance. This is a
new and more advanced SVC representation
than those that are currently available in open
literature. This model provides information
on the SVC firing angle required to achieve a
given level of compensation.
In this work SVC firing angle model has been tested
on IEEE 5 Bus System and IEEE 14-Bus System.
Static VAR Compensator Equivalent Susceptance
Advances in the power electronics technology
together with sophisticated control methods made
ISBN: 978-1-61804-157-9
Fig.2
SVC Structure
Fig.3 SVC equivalent reactance as function of firing
angle.
SVC’s normally include a combination of
mechanically controlled and tyristor controlled shunt
capacitors and reactors. The most popular
configuration for continuously controlled SVC’s is
43
Recent Advances in Energy, Environment and Development
0

0
∆Pk  
 ∆θ k 
2
∆Q  = 0 2Vk [cos(2a − 1)] ∆a 
svc
 k 
  svc 
 πX L
the combination of either fix capacitor and tyristor
controlled reactor. As for as steady state analysis is
concerned, both configuration can be modeled along
similar lines. SVC structure shown in the figure above
is used to drive a SVC model that considers the tCR
firing angle α as state variable. This is a new and
more advanced SVC representation than those
currently available in open literature.
The Variable TCR equivalent reactance, XLeq, at
fundamental frequency, is given by
(13)
At the end of iteration I, the variable firing angle α is
updated according to equation mentioned below:
a i +1 = a i + ∆a i
The firing angle model is better than variable
susceptance model as variable susceptance model
requires an additional iterative procedure, after the
load flow solution has converged, to determine the
firing angle.
π
X Leq = X L
2(π − a ) + sin 2a
(9)
Where the thyristor is’s firing angle.
The SVC effective reactance Xeq is determined by the
parallel combination of Xc and XLeq,
X eq =
3.2 TCSC Model Implementation in NewtonRaphson Load Flow
XLXC
XC
(2(π − a) + sin 2a) − X L
π
Variable Series Impedance Power Flow Model: The
TCSC power flow model presented in this section is
based on the simple concept of variable series
reactance, the value of which is adjusted
automatically to constrain flow across the branch to a
specified value.
(10)
Depending on the ratio Xc/XL there is a value of firing
angle that causes a steady state resonance to occur.
The SVC equivalent susceptance is given as
XC
Beq = π
(2(π − a ) + sin 2a ) − X L
XL XC
The changing reactance XTCSC shown in figure
below:
(11)
Beq varies in a continuous, smooth fashion in both
operative regions as shown in graph below:
Fig .5
The transfer admittance matrix of the variable series
compensator shown figure-(a) is given by:
 I k   jBkk
 I  =  jB
 m   mk
Qk = −
V
XC XL
Bkk = Bmm = −
Bkm = Bmk =
1
X r csc
(15)
1
X r csc
(16)
And for capacitive operation the signs are reversed
The active and reactive power equation at bus k is:
XC


[2(π − a svc ) + sin(2a svc )]
X L −
π


Pk = VkVm Bkm sin(θ k − θ m )
(12)
The Linearised SVC equation for ith iteration is given
as:
ISBN: 978-1-61804-157-9
(14)
For Induct Operation, we have:
Fig .4. SVC equivalent susceptance as function of
firing Angle
FA model is an optimized iterative process, consists
in handling the TCR firing angle as a state variable
in the power flow formulation.
Injected Bus Power by SVC:
2
k
jBkm  Vk 
jBmm  Vm 
Qk = −V Bkk − VkVm Bkm cos(θ k − θ m )
2
k
44
(17)
(18)
Recent Advances in Energy, Environment and Development
The set of Linearised power flow equation is:

∆Pk




∆Pm 





∆Q
k





∆Q
 m 


 TCSC 
∆Pkm 
 ∂P ∂P ∂P
∂Pk
∂Pk
k
k
 k
Vk
Vm
X TCSC
∂V m
∂X TCSC
 ∂θ k ∂θ m ∂V k

 ∂Pm ∂Pm ∂Pm V ∂Pm V ∂Pm X
 ∂θ k ∂θ m ∂V k k ∂V m m ∂X TCSC TCSC

 ∂Q k ∂Q k ∂Q k V ∂Q k V ∂Q k X
TCSC
 ∂θ k ∂θ m ∂V k k ∂V m m ∂X
TCSC

∂Q m
∂Q m
 ∂Q m ∂Q m ∂Q m
X TCSC
 ∂θ ∂θ ∂V V k ∂V V m ∂X
m
k
m
TCSC
 k
X
X
 ∂P X TCSC ∂P X TCSC ∂P X TCSC
∂P TCSC
∂P TCSC
km
km
 km
V k km V m km
∂θ m
∂V k
∂V m
∂X TCSC
 ∂θ k
















∆θ k


∆θ m

 ∆V k
 Vk

 ∆V m
V
 m
 ∆X TCSC

 X TCSC
is the active power flow mismatch for the series
reactance; ∆X r csc , given by:-














(i )
( i −1)
∆X TCSC = X TCSC
− X TCSC
4. Load Flow Test Case
Sensitivity index of the transmission line no-19 has
been come out most positive so TCSC should be
placed on the transmission line no-19 only making the
operation highly cost effective. And sensitivity index
of bus no-5 has been come out as most negative
among all the indices. So SVC should be placed at the
bus no-5 only.
Where ∆PkmX TCSC
(19)
∆PkmX TCSC = Pkmreg − PkmTCSC ,cal
(21)
X
(20)
TABLE.1 VOLTAGE PROFILE OF 5-BUS SYSTEM
Bus
No
1
2
3
4
5
Base Load Flow
Magnitude
Phase angle
(p.u.)
(deg)
1.06
0
1
-2.06
0.987
-4.64
0.984
-4.96
0.972
-5.77
Load Flow with TCSC on TL-6
Magnitude
Phase angle
(p.u.)
(deg)
1.06
0
1
-2.04
0.987
-4.73
0.9844
-4.81
0.972
-5.7
Load Flow With SVC on Bus-3
Magnitude (p.u.)
Phase angle (deg)
1.06
1
1
0.994
0.975
0
-2.05
-4.83
-5.11
-5.8
TABLE.2 POWER FLOW RESULTS OF 5-BUS SYSTEM
TL
No
Active/
Reactive
Powers
P
6
Q
P
7
Q
Total Loss
Base Load Flow
Sending Receivin
Loss
End
g End
0.000
-0.1935
4
0.1939
+
0.018
0.0286i - 0.0469i
2i
0.000
0.066
-0.0656
4
+
0.046
0.0052i - 0.0517i
5i
6.1222 -10.7773i
Load Flow with TCSC on TL-6
Sending Receiving
Loss
End
End
-0.2095
0.0005
0.1965
+
0.0251i
- 0.0432i
0.0180i
0.0713
-0.0709
0.0005
0.21
+
0.0041i
- 0.0505i 0.0464i
6.1272 -10.7650i
-0.1959
0.0005
+
0.1119i
- 0.1302i
0.0183i
0.0678
-0.0671
0.0006
+
0.0325i
- 0.0791i
0.0466i
6.0560 -11.2543i
sensitive line to get placed with TCSC and bus no 3
with SVC device. After placing these devices, above
results have been obtained from Matlab simulation.
After analyzing the results it can be observed that
TCSC maintains active power from Bus no-3 to Bus
no-4 at 21 MW. We have set the starting value of the
TCSC at 50% of the value of the transmission-line
5. Discussion on Load Flow Results
with TCSC Model
On the basis of sensitivity indices obtained,
Transmission line no 6 has been considered as most
ISBN: 978-1-61804-157-9
Load Flow With SVC on Bus-3
Sending Receiving
Loss
End
End
45
Recent Advances in Energy, Environment and Development
Power flows and nodal voltages are shown in table
drawn below. Convergence is achieved in 5 iterations,
satisfying a pre specified tolerance of 1e-12 for all the
variables involved. SVC injects 20.5 MVAR into bus
no 3 and keeps the nodal voltage magnitude at 1 p.u.
The action of SVC results in an overall improved
voltage profile as detailed in the Table drawn below.
The svc generates reactive power in excess of the
local demand, which stands at 15 MVAR and,
compared with the base case, there is an almost four
times export increase of reactive power to bus no-4.
Also there is an export of reactive power to bus no-2
via transmission line 3-2 with larger amount of
reactive power available at the bus being absorbed by
the generator. It draws 77.1 MVAR as opposed to
61.59 MVAR in the base case.
inductive reactance i.e. X=0.015 p.u. Convergence is
obtained in 6 iteration to a power mismatch tolerance
of 1e-12. The connected TCSC device upholds the
target value of 21 MW, which is achieved with 70%
series capacitive compensation of the transmission
line 3-4. It can also be observed that nodal voltage
magnitudes and reactive power flows do not change
appreciably compared with the base case.
5.1 Discussion on Load Flow Results with SVC
Model
The inductive and capacitive reactance is taken to be
0.288p.u. and 1.07 p.u., respectively. The SVC firing
angle is set initially at 140 deg, a value that lies on the
capacitive region of the SVC characteristics. The
SVC upholds its target value and, as expected,
identical power flows and bus voltages are obtained.
TABLE.3 Power Flow Results of IEEE-14 Bus System:
TL
No
Active/
Reactive
Powers
Base Load Flow
Total Loss
Sendi Receiving
ng
End
End
0.017 -0.0174
5
+0.01 -0.0127i
28i
0.059 -0.0581
1
+0.04 -0.0416i
36i
15.1549+34.6678i
Bus No
TABLE.4
Base Load Flow
P
19
Q
P
20
Q
4
5
6
Magnitude
(p.u.)
0.9829
0.9908
0.9939
Phase angle
(deg)
-5.897
-4.390
-10.936
Loss
Load Flow with TCSC on TL–
19
Sending Receiving
Loss
End
End
0.000
1
+0.00
1i
0.001
0.0198
-0.0197
+0.0136
i
0.0606
-0.0135i
+0.00
20i
+0.0482 -0.0460i
i
15.1623+34.5359i
Sendi Receiving
ng
End
End
0.017 -0.0176
7
+0.01 -0.0131i
32i
0.059 -0.0584
4
+0.04 -0.0437i
57i
15.0800+34.0456i
Loss
0.0001
+0.001i
0.001
+0.0021
i
Voltage Profile of IEEE-14 Bus System:
Load Flow with TCSC on TL–
Load Flow with SVC on
19
Bus–5
Magnitude
Phase angle
Magnitude
Phase angle
(p.u.)
(deg)
(p.u.)
(deg)
0.9839
-5.897
0.9889
-5.946
0.992
-4.390
1
-4.499
1
-10.936
1
-10.958
After analyzing the results it can be observed that
TCSC maintains active power from Bus no-12 to Bus
no-13 at 1.98 MW. We have set the starting value of
the TCSC at 50% of the value of the transmission-line
inductive reactance i.e. X=0.09994 p.u. Convergence
is obtained in 7 iteration to a power mismatch
tolerance of 1e-12. The connected TCSC device
upholds the target value of 1.98 MW, which is
achieved with 64% series capacitive compensation of
5.2 Discussion on Load Flow Results with
TCSC Model
On the basis of sensitivity indices obtained,
Transmission line no 19 has been considered as most
sensitive line to get placed with TCSC and bus no 5
with SVC device. After placing these devices, above
results have been obtained from Matlab simulation.
ISBN: 978-1-61804-157-9
-0.0595
0.000
1
+0.00
01i
0.001
1
+0.00
22i
Load Flow with SVC on Bus–5
46
Recent Advances in Energy, Environment and Development
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the transmission line 12-13. It can also be observed
that nodal voltage magnitudes and reactive power
flows do not change appreciably compared with the
base case.
5.3 Discussion on Load Flow Results with SVC
Model
The inductive and capacitive reactances are taken to
be 0.288p.u. and 1.07 p.u., respectively. The SVC
firing angle is set initially at 140 deg, a value that lies
on the capacitive region of the SVC characteristics.
The SVC upholds its target value and, as expected,
identical power flows and bus voltages are obtained.
Power flows and nodal voltages are shown in table
drawn above. Convergence is achieved in 7 iterations,
satisfying a pre specified tolerance of 1e-12 for all the
variables involved. SVC injects 18.5 MVAR into bus
no 5 and keeps the nodal voltage magnitude at 1 p.u.
The action of SVC results in an overall improved
voltage profile as detailed in the Table drawn above.
The svc generates reactive power in excess of the
local demand, which stands at 1.6 MVAR. It can be
analyzed that the reactive power loading of Line No-2
(Between Bus-1 & Bus-5) has been reduced to 22% in
comparison with base case and, compared with the
base case, there is an almost two times export increase
of reactive power to bus no-2. Voltage regulation is
achieved by controlling the production, absorption
and flow of reactive power throughout the network.
Reactive power flows are minimized so as to reduce
system losses. This fact is justified in the Table where
the decrement of 0.5% in total system losses has been
mentioned by embedding the SVC on the key location
in the 14-Bus system.
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