Power Flow Control using Quadrature Boosters

+-IEEE Proceedings of the IEEE SoutheastCon 2015, April 9 - 12, 2015 - Fort Lauderdale, Florida
Power Flow Control using Quadrature Boosters
With a suggested Optimal Power Flow Analysis
Sandeep Sadanandan
Electrical Engineer
Arlington, Virginia
snsadana@yahoo.com
Abstract-A power system that can be controlled within
security constraints would be an advantage to power planners
and real-time operators. Controlling flows can lessen reliability
issues such as thermal limit violations, power stability problems,
and/or voltage stability conditions. Control of flows can also
mitigate market issues by reducing congestion on some lines and
rerouting power to less loaded lines or onto preferable paths. In
the traditional control of power flows, phase shifters are often
used. More advanced methods include using Flexible AC
Transmission System (FACTS) Controllers. In comparison with
other FACTS controllers Quadrature Boosters (QBs) are not as
complex and not as expensive. QBs have similar structures to
phase-shifters, but allow for higher voltage magnitude during
real power flow control. The present study proposes to use QBs
to control power flows on a power system. With the inclusion of
QBs, real power flows can be controlled to desired scheduled
values. In this paper, the linearized power flow equations used
for power flow analysis were modified for the control problem.
This included modifying the Jacobian matrix, the power error
vector, and calculating the voltage injected by the quadrature
booster for the scheduled real power flow. Two scenarios were
examined using the proposed power flow control method. First,
the power flow in a line in a 5-bus system was modified with a
QB using the method developed in this paper. Simulation was
carried out using Matlab. Second, the method was applied to a
30-bus system and then to a 11S-bus system using several QBs.
In all the cases, the calculated values of the QB voltages led to
desired power flows in the designated line. Lastly, a method for
Optimal Power Flow control was studied.
Keywords-Newton Rapltson, Phase Angle Regulators,
Quadrature Boosters, Reactive Losses, Optimal Power Flow
I. INTRODUCTION
Power system engineers would like to be able to control
power flows to meet thermal limitations, voltage stability
limitations, and angle stability limitations. The last two are a
bit more complex and out-of-the scope of this study. However,
the first must be discussed. The thermal limitations of power
transfer are an essential parameter for analysis. The
transmission line is designed for natural series inductance,
series resistance, and shunt capacitance under load. These
parameters are due to the materials that make-up the conductor,
which can include aluminum and/or steel. Under load (or
active power and reactive power transfer) the transmission line
model must be simplified to a standard pi-model. In this model,
978-1-4673-7300-5/15/$31.00 ©2015 IEEE
Dr. Ghadir Radman
Professor of Electrical Engineering
Tennessee Technological University
Cookeville, Tennessee
shunt capacitance is modeled at the sending end and the
receiving end of the transmission line with a total series
inductance and resistance in between. Power and current will
always flow on the transmission lines that have the least
amount of series resistance and series inductive reactance. The
sum of these two components is called series impedance [1].
Generally, power transfer starts from generators with the active
and reactive power injection into the power system from these
rotating machines. Generators inject power onto the
transmission lines, the power travels along the transmission
lines, and then the power is consumed at the load end. Load
can be industrial, commercial, or residential types of loads.
They can also be designated as motor-loads or non-motor loads
[2]. In either case, the control of this transfer of power across
transmission lines is the concept studied in this paper.
II. LIMITATIONS AND NEED FOR POWER FLOW CONTROL
A. Power Flow Control
Thermal limitations are based on the temperature
constraints of the line. Also, as the temperature increases on the
line, the line tends to sag. This can result in the line sagging
into surrounding trees, causing a line-to-ground fault, and
causing protective relays to trip-out the line [2]. If the series
resistance and series inductance of a line is much lower than
other lines, power will flow on that line. If this is not managed
correctly, the line may violate its thermal limitations and
overload the line. Thus, in terms of temperature violations and
sag considerations, the ability to better control power flows
becomes beneficial.
In order to control power flows, we must adjust the original
characteristics of a transmission line. Under load, the series
and shunt elements of a transmission line must be adjusted or
compensated to increase or reduce the series impedance or
shunt capacitance of the line. The generator injects voltage
onto the transmission line. Voltage can be considered the
support network for the transfer of current and power along the
line. We need adequate voltage on the system to transfer power
across the power system. As current flows along the
transmission line it creates a voltage drop along the line
between the sending and receiving ends. The voltage
magnitudes must be about the same throughout the system (i.e.
depending on the voltage ratings of the system), but the voltage
angles must be different for active power transfer. The
difference between the angle of the voltage at the sending end
and the angle of the voltage at the receiving end must be

greater than zero for active power transfer. This difference is
called the power angle and in this study it is the parameter of
the power transfer that will be adjusted or compensated [2].
The power angle can be compensated for the required
active power transfers by injecting a voltage magnitude and
angle in the line or injecting a current magnitude and angle into
the line. This compensation essentially changes the natural
values of the transmission line (i.e. series impedance and shunt
capacitance) to effective values [2]. In this paper we are
injecting a voltage magnitude and angle into the transmission
line with Quadrature Boosters to change natural impedance of
the line to an effective value. This changes the power angle to
an effective value that is higher or lower than the value that
would be the result of the system without a compensation
device or the uncompensated value. Quadrature Boosters are
similar to Phase Angle Regulators which also adjust the power
angle of the line, but QBs allow us to adjust the voltage
magnitude also.
The power angle does not have a great deal of
influence on the reactive power transfer on the system, but
voltage magnitude plays a significant role [2]. Reactive power
transfer can start from the generators, travels along the
transmission lines, and ends at the load. However, reactive
power is a bit more complex than active power that it can start
(i.e. be injected into the system) from capacitor banks and
transmission line capacitance and can be absorbed (or
consumed) by reactors and transformers. Reactive power does
not actually do work on the system, but it is necessary for the
transfer of AC power on the system. AC power transfer
requires magnetic fields for the transfer of power, and reactive
power supports these fields [2]. Quadrature Boosters
inherently maintain and support reactive power transfer on the
line by including a significant voltage magnitude (as compared
to the sending end voltage) onto the system. Thus, it gives
power system management an added benefit over Phase Angle
Regulators, which only inject a significant change to the power
angle on the system.
Often times System Operators will manipulate power flows
by generation redispatch or transmission switching operations
[2]. With Energy Management System (EMS) software tools as
the guide, System Operators develop operating guides for the
switching and outage instructions when lines are overloaded or
when loss of a critical element on the system will overload
lines or power system equipment (such as transformers) [2]. In
the end, without actual devices to compensate the system, the
flows of power still are dependent on the natural impedances of
the lines and of the power system to route power flows.
Currently, some power systems have series capacitors that
can lower impedance of the line and allow more power to flow
on the line [1]. Shunt capacitors can be installed at the load
end to provide reactive power for the local transformers and
motor loads. This allows less reactive power to be sent on the
transmission line from generators; thus, reducing overall losses
on the line and allowing more capacity for active power
transfer [2].
Phase angle regulators (PARs) are another method for
controlling active power flows on the system. PARs can be
used to increase or decrease the power angle. Adjusting the
power angle can significantly change active power transfer on
the system, but does not make much difference in the reactive
power transfer. PARs can adjust active power transfer, but
may do this at the expense of reactive power transfer. Thus,
PARs cannot be relied upon for supporting the voltage on the
system.
A set of power devices called FACTS (Flexible AC
Transmission System) controllers can be used to control both
active and reactive power flows on the power system [3].
FACTS are complex devices with advanced power electronics
and can change the way power flows in a control area and
surrounding areas. Quadrature Boosters are considered a
FACTS device, but these are less complex and less expensive
than other FACTS (e.g. Synchronous Static Series
Compensators). Quadrature Booster can control active power
transfer and inherently support reactive power transfer, but it
cannot do the various functions that more advanced FACTS
controllers can do. The highest level FACTS controllers can
essentially adjust both series impedance of the lines and shunt
capacitance of the lines. The first allows the transfer of more
active power, and the second function can inject more reactive
power on the system.
Further research should be focused on faster and more
accurate controllers and compensation on the system that
provides active power and reactive power adjustments. Active
power flow should be adjusted on the system to meet
scheduled load demands and avoid exceeding limits; while, the
required system voltage is maintained.
A consideration of faster and more accurate
controllers leads to the concept of how often the controllers
should be adjusted. In this study, Quadrature Boosters are
considered the controller of choice to inject voltage for a
specified (or scheduled) active power flow. QBs are at the
transmission line where power flow would be controlled and
the local controllers could receive updates at short time
intervals from a central dispatch location. In reference [4], this
is described for the UK power system where system operators
(at the central dispatch location) analyze the loading patterns
and power flows on the system and optimize the use of their
QBs and send control signals to control their on-load taps and
schedule power flows as calculated by their optimization
software. Power System studies can be performed offline, and
central dispatch energy management software and SCADA
systems should be able to send signals in seconds to the
controllers. Fiber optic connections would be the preference for
the fastest communications with local controllers [2] for the
adjustment of scheduled active power flow for the particular
QB (or QBs) on the system that is to be set.
Certain emergency situations must be considered when the
system operators would not want restrictions to active power
flows on the systems. In this case, QB scheduled active power
flow settings would need to be deactivated. This may allow
interconnections and loading of transmission lines and power
system equipment to emergency limits to keep the integrity of
the power system continuously running during certain
emergency events. Thus, if communications between central
dispatch and the local QBs is not verified every few seconds, it
may be advisable to deactivate the scheduled values of certain

QBs on the system- in particular, those on an interconnection
that could provide power from another area, which has
abundant generation available.
B. ProposedMethod ofPower Flow Control
In this paper, the control of active power flow with
Quadrature Boosters was studied. QBs inject a significant
magnitude of voltage to the system; thereby, supporting
reactive power transfer and voltage on the line. Linearized
power flow equations for active and reactive power transfer
can be derived from the complex power transfer on the line.
These power flow equations were updated such that new
elements were added to the Jacobian matrix to incorporate the
injected Quadrature Booster voltage (Vq). New elements were
added to the Jacobian matrix to incorporate the real power flow
(Pkl) along the line with the inserted QB. The end result was
the ability to specifY a scheduled active (or real) power flow
along the line with the inserted QB and use the Newton
Raphson iteration to calculate the necessary injected
Quadrature Booster voltage (i.e., the voltage needed to allow
the scheduled real power flow).
For this paper, the objective was to control the active power
flow to a scheduled value along a power line from bus k to bus
I using one or more Quadrature Booster. This required using a
power flow program to calculate the QB injected voltage into
the line. In order to properly test the power flow program to
calculate a QB injected voltage for a scheduled active power
flow, the program needed to be implemented for different bus
test systems. Active power flow control using Quadrature
Boosters was studied and simulated on a 5-bus test system, a
30-bus system, and a l1S-bus system.
III. LITERATURE REVIEW
For this study, it is also important to understand the PAR
device and the traditional power flow analysis using the
Newton Raphson method. Quadrature Boosters are similar to
PARs except that the voltage magnitude injected by a QB is
significant (unlike the PAR, where the voltage magnitude is
small). The traditional power flow is the basic Newton
Raphson solution for solving the load flow problem (i.e. 2
known values and 2 unknown values at each bus). With these
two power specific background information, the QB can be
described and its inclusion into traditional power flow analysis
can be described.
In [4], multiple Quadrature Boosters were used on the
United Kingdom's transmission network to improve use of
their power system assets (i.e. generators, transmission lines
and networks). The QBs and their tap positions were updated
by system operators to optimize the interaction of the multiple
QBs based on the power flow pattern as system conditions
change. In operational timescales, the quadrature booster tap
positions are optimized to eliminate or minimize any uplift (i.e.
out-of-market payments) in the total generation cost due to
transmission thermal constraints. In planning the development
of the transmission system, a frequent objective is to maximize
the transfer capability of the existing network and thereby
avoid unnecessary reinforcement. The UK's system operators
developed tools to optimize the tap positions of interacting
quadrature boosters. These tools were used to assess network
capability under specific conditions stipulated by the security
standards, and to estimate optimized future operational cost for
specified periods, e.g., a year. Zhu's paper [4] discussed these
developments and some of their applications. In this paper, the
proposed method could be used similarly at a central dispatch
to determine the Quadrature Booster Voltage injection
necessary for a specified active power flow.
In [5], Sharath Vavilala developed a procedure to
calculate the real power flow across a line for a given injected
voltage. He compared the performance of a 30-bus system
with a Quadrature Booster, Phase Angle Regulator, and an
Underload Load Tap Changer. His analysis included effects on
power transfers by combining devices (e.g. PARs and ULTCs).
In the calculation of power transfers, the range of injected
voltage where the load flow would converge was found. This
study builds on Sharath's analysis where he did an analysis of
QBs and how QB injected voltage affects active power flows.
In this study, the injected voltage is calculated for the desired
active power flow. The researchers have so far looked at QB
active power flow control on a system level and analyzed
congested lines to prevent overloads with QB control. The
present study (this paper) provides QB active power flow
control with an emphasis on the analysis and update to the
actual Jacobian elements of the system. The analysis problem
is a necessary preliminary step in understanding how to modifY
the Jacobian to accomplish the control problem in this study.
With modifications to the actual elements, the calculation of
injected QB voltage is evaluated at the coding level.
IV. QUADRATURE BOOSTER FOR POWER FLOW CONTROL
A. General Discussion
The Quadrature Booster inserted into the power system is
shown below:
Fig. I. Model System with the inclusion of QB between buses k & I.
B. Power Flow Control Equations with QBs
Due to the addition of a Quadrature Booster in link k-I, the
power equations at Buses k and I need to be modified. The
traditional power equations for bus i are shown below:
N
Pi=L IVill YmIIVnl{coS(Oi- 8m- on)} (1)
11=1
N
Q,=L IVil1 YinIIVnl{sin(o,- 8in- On)} (2)
11=1
Moreover, addition of QB adds an extra variable (IVql) to the
set of power equations for which we need an additional
equation. This equation is provided by setting the power flow
through the link k-I equal to the desired value. The
modifications needed due to the addition of a QB in link k-I are
derived next.

The power flow through link k-I before the addition of the
QB (or uncompensated system) is:
SkluC = (Vk)hl* = Vk[-Ykl(Vk-VI)]* (3)
= (-Ykl*)IVkI2+ (Ykl*)(Vk)(Vn; Ykl= Gki +jBkI
= -(Gkl -jBkl) IVkI2+ IVkIIVIIIYkdL<Ok-OI-8kl)
From the above, active and reactive power flow from k to I
(Pkl and QkI) can be determined using the real and imaginary
parts of the complex power, respectively.
PkluC = -GkdVkl2+ IVkIIVdIYkllcos(Ok-OI-8kl) (4)
(5)
Similarly, the power equations looking from bus I would
then be as follows.
Sikuc= (VI)Ilk* = VI[-Ykl(VI-Vd]*
= (-YkI*)(IVd2- VIVk*)
Plkuc= -Gkl1V112+ IVdlVkilYk1ICOS(OI-Ok-8k1)
QlkuC = BkllVd2+ IVIIIVkIIYkllsin(ol-ok-8kl)
(6)
(7)
(8)
Now the compensated Ski (i.e. the Ski with the QB added in)
can be developed:
Sklc= (Vk)hJ*= Vk[-YklVk+Vg-VI)]* (9)
= Vk[-Ykl(Vk-VI) -Ykl(Vg)]*
= Vk[-Ykl(Vk-VI)]* + Vk[(-YkI)(Vg)]*
= SkluC - (Ykl*)(Vk)(Vg*); where Vq=jIVqILtOk)
= SkluC + jIYkdIVkIIVql[cos(8kl)-jsin(8k1)]
From the above, Pkl and Qkl for the compensated system can
be determined using the real and imaginary parts of the
complex power, respectively:
(10)
QkIC=QkIUC +IYkIIIVkIIVql[cos(8kl)]=Qkluc+GkIIVkIIVgl (11)
By defining Pkg=BkllVkllVql and Qkg=GkdVkIIVql, these equations
become:
(12)
Similarly, the compensated power values looking from bus I
would then be:
Slkc= (VI)Ilk*= VI[-Ykl(VI-Vg-Vk)]*= (13)
= SlkuC - jIYkdIVdIVql[coS(OI-Ok-8kl) + jsin(ol-ok-8kl)]
Plkc= Plkuc+ IYkIIIVIIIVql[sin(ol-ok-8k1)] (14)
Qlkc= QlkuC - IYkIIIVIIIVql[coS(OI-Ok-8kl)] (15)
Now by defining Pig = IYkdIVdIVql[sin(ol-ok-8kl)] and
Qlg= -IYdIVdIVql[coS(OI-Ok-8k1)], these equations become:
(16)
Next, the power balance equations for buses k and I were
updated. The power balance equations for the compensated
system at Bus k is as follows:
N
Pk=PkC= I Pkt
)=1
N
=PkIC + I Pkj"C = PklUC +Pkg +
}=I.)#I
N
= Pkq + I Pkt= Pkq + PkUC
}=!
(17)
So, we have: Pk = Pkc= PkuC + Pkg where Pkg was previously
defined. Similar calculations hold for Qb PI, and QI.
Qk=QkC=QkUC + Qkg
PI =Plc=PtC + Pig and QI =Qlc=QluC + Qlg
(18)
(19)
The elements to the Jacobian Matrix (J) that required
update are shown in Figure 2. In Figure 3, the voltage vector
matrix (dV) required an added row for each QB on the system,
and the power balance matrix (dPQ) required an associated
row for Pkl. The Newton Raphson method uses the
relationships of (J x dV = dPQ) and (yl x dPQ = dV) to allow
the use of iteration to determine the unknown bus values.
• • + + •
:---- 10 11 12 13 9
JCI
JIl J12
---- 14 15 16 17 8
Q� 18 19 20 21 7
JC2
hI J22
Q1--+ 22 23 24 25 6
1---- 1 JRI 2 3 JR2 4 5JRC
Fig. 2. Update to the Traditional Newton Raphson Jacobian.
L1P
L1Q
Fig. 3. Update to the Voltage and Power Balance Matrices.

As an example, element 3 would be:
BP
-'-' =-2GkIIVkl + IVdIYkllcos(Ok-OI-8k1) + BkdVql (20)
BI�I
The equations for all the updated elements are derived and
listed in the author's thesis [17].
V.SIMULATED ON IEEE BUS SYSTEMS WITH MATLAB
Using the existing power flow program and modifYing it
for the insertion of a Quadrature Booster, a 5-bus system was
simulated in Matlab with a Quadrature Booster inserted in Line
4-5. Power flow on line 4-5 without an inserted QB or a QB
injecting a 0 voltage was 0.066. As P4•5,scheduled is increased
from 0.066, Vq must be increased. As P4-5,scheduled is decreased
and starts flowing in the opposing direction, Vq becomes
negative and continues to increase in the negative polarity. In
Table I, the results can be seen for the 5-bus system. In Tables
II and III, the results for the analysis of a 30-bus system are
shown. Table II shows the power flows without QBs installed,
and Table III shows the power flows controlled and the
required QB injected voltages (Vq) on lines 5-7, 2-6, and 4-6.
The results for the 118-bus system are available in the author's
thesis [17].
TABLE I
FOR THE IEEE 5-BUS SYSTEM, SCHEDULED POWER AND
CALCULATED INJECTED QB VOLTAGE ON LINE 4-5.
P4-5 sched P4-5 calc Vo
0.25 0.25 0.0910
0.2 0.2 0.0663
0.1 0.1 0.0168
0.066 0.066 0
0.04 0.04 -0.0128
-0.1 -0.1 -0.0818
-0.2 -0.2 -0.l31O
-0.25 -0.25 -0.1555
TABLE II
FOR THE IEEE 30-BUS SYSTEM, REAL POWER FLOWS ON
ALL LINES IN THE 30-BUS SYSTEM (WITHOUT QBS
INSERTED).
Line Pkl
5-7 -0.1409
2-6 0.6193
4-6 0.7155
1-2 l.7778
1-3 0.8335
2-4 0.4557
3-4 0.7814
2-5 0.8312
6-7 0.3742
6-8 0.2996
6-9 0.2730
6-10 0.1613
9-11 0
9-10 0.2730
4-12 0.4270
12-13 0
12-14 0.0774
12-15 0.1712
12-16 0.0664
14-15 0.0146
16-17 0.0308
15-18 0.0582
18-19 0.0258
19-20 -0.0693
10-20 0.0923
10-17 0.0595
10-21 0.1521
10-22 0.0724
21-22 -0.0240
15-23 0.0432
22-24 0.0478
23-24 0.0108
24-25 -0.0287
25-26 0.0355
25-27 -0.0645
28-27 0.1980
27-29 0.0619
27-30 0.0710
29-30 0.0370
8-28 -0.0015
6-28 0.2003
TABLE III
FOR THE IEEE 30-BUS SYSTEM, REAL POWER
FLOWS WITH QBS INSTALLED IN 5-7, 2-6, AND 4-6.
Line PklSched Pkl Vo
5-7 0.5 0.5 0.2798
2-6 0.3 0.3 -0.0554
4-6 0.3 0.3 -0.0565
1-2 Not l.9520 Not
Applicable Applicable
(N/A) (N/A)
1-3 N/A 0.6880 N/A
2-4 N/A 0.2232 N/A
3-4 N/A 0.6448 N/A
2-5 N/A l.5457 N/A
6-7 N/A -0.2747 N/A
6-8 N/A 0.2972 N/A
6-9 N/A 0.2434 N/A
6-10 N/A 0.1439 N/A
9-11 N/A 0 N/A
9-10 N/A 0.2434 N/A
4-12 N/A 0.4839 N/A
12-13 N/A 0 N/A
12-14 N/A 0.0831 N/A
12-15 N/A 0.1956 N/A
12-16 N/A 0.0932 N/A
14-15 N/A 0.0202 N/A

16-17 N/A 0.0573 N/A
15-18 N/A 0.0725 N/A
18-19 N/A 0.0399 N/A
19-20 N/A -0.0552 N/A
10-20 N/A 0.0780 N/A
10-17 N/A 0.0331 N/A
10-21 N/A 01484 N/A
10-22 N/A 0.0699 N/A
21-22 N/A -0.0277 N/A
15-23 N/A 0.0585 N/A
22-24 N/A 0.0417 N/A
23-24 N/A 0.0260 N/A
24-25 N/A -0.0197 N/A
25-26 N/A 0.0355 N/A
25-27 N/A -0.0553 N/A
28-27 N/A 0.l888 N/A
27-29 N/A 0.0619 N/A
27-30 N/A 0.0709 N/A
29-30 N/A 0.0370 N/A
8-28 N/A -0.0038 N/A
6-28 N/A 0.1934 N/A
The IEEE 30-bus system [12] and the IEEE 118-bus system
[13] were similar in analysis to the 5-bus case except with
multiple QBs on different lines, it is clear that real power flow
can be controlled on several lines with the insertion of QBs and
as the bus systems increase in size. The power flow adjusts
and increases (or decreases) the flow on other lines in the
system as needed. Another result of the analysis of the 5, 30,
and 118-bus systems was the increasing CPU times to
complete the power flow solution. The CPU times can be seen
in Table IV.
TABLE IV
CPU TIMES FOR POWER FLOW SOLUTION.
IEEE Bus System NoQBs With QBs Included
Included
5 0.007694 sec 0.008348 sec
30 0.192628 sec 0.198784 sec
118 2.315 sec 4.543 sec
VI.OPTIMAL POWER FLOW ANALYSIS
In this OPF analysis, the total reactive power loss on the
system is minimized, and a Performance Indicator (PI) is
discussed. In order to minimize the reactive loss on the system,
the derivative of the reactive power flow loss on the line with
the quadrature booster with respect to the quadrature booster
injected voltage (Vq) needs to equal O. In order to determine
this, our Newton Raphson analysis is similar to above except
there is no need to have another row for Pkl in the Jacobian and
in the power balance matrix. The reactive power loss equation
for link k-I with the QB inserted is:
QkUoss= Qklc + Qlkc (21)
The derivative with respect to Vq is:
(22)
For a 5-bus system, with a QB inserted in Line 4-5, the
derivative was 0 at an injected Vq=0.0220. The minimized
Qloss on the system was found to be -0.0115 (down from
Qloss equal to -0.1078 for the system without a QB).
A Performance Indicator was developed using the complex
power flow conservation equation: Sgen-Sload-Sloss = Schek,
where Schek should be the error in our power flow. Similarly
for active power and reactive power conservation: Pgen-Pload
Ploss=Pchek and Qgen-Qload-Qloss=Qchek. From these
equations, the following system Qloss equation can be
developed:
jQloss = Sgen-Sload-Ploss-Schek (23)
jQloss = Pgen+jQgen-Pload-jQload-Ploss-Pchek-jQchek (24)
Finding the magnitude ofboth sides ofthe complex equation gives:
Qloss2=(Pgen-(Pload+Ploss+Pchek»2 + (Qgen-(Qload+Qchek)2 (25)
In Figure 4, a circle diagram from the above equation can
be developed with radius=abs(Qloss) and center point of
«Qload+Qchek), (Pload+Ploss+Pchek or Pgen».
Center Point:
«Qload+Qchek), (Pload+Ploss+Pchek or Pgen))
P
Pgen.. .........
Q
Qgen
(Qload+Qchek)
Fig. 4. Capability Circle for Active and Reactive Power Injection
With our 5-bus power flow system at min Qloss, we would like
to use the capability circle to reduce our PI. As Qloss on the
system is reduced, the new requirements for Pgen and Qgen
can be determined on the circle diagram. As we reduce Qloss,
the requirements for reactive power generation on the system
reduce allowing more capacity for active power generation.
Minimizing the following Performance Indicator (PI), the
optimal performance can be certified:
min PI = min{(System Ploss) + alpha*(System Qloss)} (26)
At Point A in Figure 4, there is no reduction in Qloss, so
the system allows values of Pgen and Qgen for an IEEE 5-bus

system to flow. Alpha is 0 and PI=Ploss=0.0654. If Qloss is
reduced by 40% (alpha=O.4) to Point B in Figure 4, the system
requires less Qgen equal to Qgen-abs(Qloss)*O.4 and more
active Pgen can flow, equal to
Pgen+abs(Qloss)*sin(arccos(0.6». The PI is now 0.060S. If
Qloss is reduced further, by 100% (alpha=l), the system
requires less Qgen, equal to Qload+Qchek, and maximum
active Pgen, equal to Pgen+abs(Qloss) at Point C in Figure 4, is
available for the test system. The PI is now at 0.0539. The
resulting 5-Bus Matlab simulation capability circle is shown in
Figure 5.
·1
d
.
3
0
�
.�
"
Study of Qlos$ Reduction
Radiu$"'abs(sum(Qloss))
CenterPoint=(s um(Qld)+Qchek, sum(PG))
1.725
,--,--,--,--,------,------,------,------,
1.72
1.715
1.71
1.705
Reactive PowerGeneration
Fig. 5. Matlab Simulation result for an IEEE 5-Bus System
The Performance Indicator (PI) allows for a metric to relate
different power system losses- Ploss and Qloss- in the power
flow analysis.
V. CONCLUSIONS
In the case of a 5-bus system with a Quadrature Booster
inserted in Line 4-5, it was shown that real power flow can be
controlled by compensating the line with an injected voltage in
quadrature to the sending end voltage. As expected the injected
voltage for the QB is 0 when the desired (scheduled) power
flow is set to the value obtained when there is no QB installed
on the system. As the scheduled power flow value is increased
(from the case when no QB is installed), the injected QB
voltage on to the transmission line is greater than zero. As the
scheduled power flow is decreased, the QB injected voltage
goes negative and continues going more negative as the power
flow is reduced and changes direction. Similarly, using a 30-
bus and lIS-bus system multiple QBs were used to control the
power flows on several lines. Optimal power flow can be used
to minimize reactive losses on the system.
REFERENCES
I. J Duncan Glover, Mulukutla S. Sarma and Thomas J Overbye, POlVer
System Analysis andDesign. Thomson, 2008.
2. EPR! Power Systems Dynamics Tutorial. EPR!, Palo Alto, CA: 2009.
3. N. G. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and
Technology of Flexible AC Transmission Systems. New York: IEEE
Press, 2000.
4. Zhu, M, "Application and Modelling of Quadrature Boosters for the HV
Transmission System", POWERCON '98, 1998 International
Conference on Power System Technology, August 1998.
5. Vavilala, Sharath, "Inclusion of Quadrature Booster (QBs) in Power
Flow Analysis", Tennessee Technological University, Master of Science
in Electrical Engineering Thesis, December 201I.
6. Gaswami, P.K, Quadrature Booster for Optimization of Power flow;.;
Electric Power Engineering, 1999 International Conference on
PowerTech Budapest 99.
7. Luiz A. C. Lopes, G. Joos, Boon-TeckOoi;A PWM quadrature-booster
phase shifter for AC power transmission;IEEE Transactions on Power
Electronics - IEEE TRANS POWER ELECT , vol. 12, no. I, pp. 138-
144, 1997.
8. E. Wirth and A. Kara,"Innovative power flowmanagement and
voltagecontrol technologies", IEEE Power Engineering Journal, June
2000.
9. ZbigniewFedyczak, Maciej Jankowski, PawelSzczesniak, "Modelling
and analysis of the quadrature-booster phase shifter with PWM AC
bipolarMC and passive load", University of ZielonaGora, Institute of
Electrical Engineering,uL Podgorna 50, 65-246, ZielonaGora, Poland.
Available: http://www.pszczesniak.cba.pI/Robocze/EPQU_2006.pdf
10. Jan Machowski, JanuszBialek, Dr Jim Bumby;PolVer System Dynamics:
Stability and Control; Wiley Publishing Company. Wirth and A.
Kara,"lnnovative power flowmanagement and voltagecontrol
technologies", IEEE Power Engineering Journal, June 2000.
II. IEEE5-BusTestSystemData, Available:
http://www.ee.washington.edu/research/pstca/
12. IEEE30-BusTestSystemData, Available:
http://ietd.inflibnetac.inlbitstreaml1060311271118118_appendix.pdf
13. IEEEI18-BusTestSystemData, Available:
http://www.ee.washington.edu/research/pstca/pflI8/pg_tcaI18bus.htm
14. N.G. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and
Technology of Flexible AC Transmission Systems.New York: IEEE
Press, 2000.
15. Kalyan K. Sen and Mey Ling Sen, Introduction to FACTS Controllers:
Theory, Modeling and Applications. IEEE Press 2009.
16. Matlab Software (www.mathworks.com).
17. Sadanandan, Sandeep, "Power Flow Control Using Quadrature
Boosters", Tennessee Technological University, Master of Science in
Electrical Engineering Thesis, December 2013.

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