1
Some Applications of Distributed Flexible AC
Transmission System (D-FACTS) Devices in
Power Systems
K. M. Rogers, Student Member, IEEE, and T. J. Overbye, Fellow, IEEE

Abstract—Distributed Flexible AC Transmission System (DFACTS) devices offer many potential benefits to power system
operations. This paper examines the impact of installing DFACTS devices by studying the linear sensitivities of power
system quantities such as voltage magnitude, voltage angle, bus
power injections, line power flow, and real power losses with
respect to line impedance. Using these linear sensitivities,
nonlinear problems such as real power loss minimization and
voltage control may be solved; these applications are discussed in
this paper.
Index Terms—power flow control, distributed flexible AC
transmission systems, linear sensitivity analysis
I. INTRODUCTION
C
ONTROLLING real and reactive power flows on
transmission lines has been of interest for many years.
Power flow control is especially applicable now as the
structure of the electric power industry is changing and the
power grid is becoming increasingly more networked.
Interconnecting parts of systems which were previously
independent has benefits such as allowing faulted areas to be
quickly isolated which causes less service interruption to
customers. However, a utility cannot effectively control how
much power flows through its network due to the
interconnections with other systems. These interconnections
can restrict transmission capacity since the available transfer
capability (ATC) of an interface is limited by the first line to
reach its transmission limits.
The ability to effectively control power flow in a network
can allow better utilization of the existing network by routing
power flow away from overloaded lines. The problem of
power flow control is even more compelling when considering
the continually changing network topology and the need to
remain secure under contingency conditions [1]. Also, studies
indicate that transient stability and dynamic stability (damping)
can be improved when reactive compensation is available and
can be varied rapidly by electronic control [2]. System
benefits resulting from power flow control have been the
The authors would like to acknowledge the support of the support of NSF
through its grant CNS-0524695, the Power System Engineering Research
Center (PSERC), City Water Light and Power (CWLP) in Springfield, IL, and
the Grainger Foundation.
The authors are with the University of Illinois Urbana-Champaign, Urbana, IL
61801 (e-mail: krogers6@uiuc.edu; overbye@uiuc.edu).
motivating factors for the use of flexible AC transmission
system (FACTS) devices since the time of their development.
More recently, distributed flexible AC transmission system
(D-FACTS) devices [3],[4] such as the Distributed Static
Series Compensator (DSSC) have been designed to address
power control types of problems. D-FACTS devices attach
directly to transmission lines and can be used to dynamically
control effective line impedance. Also, D-FACTS devices are
smaller and less expensive than traditional FACTS devices
which may make them better candidates for wide scale
deployment.
From a power systems perspective, D-FACTS devices have
many potential benefits. This paper discusses some principles
of power flow control and then examines the impact of using
D-FACTS devices in a power system. In particular, this paper
analyzes some effects of changing transmission line
impedances and the use of D-FACTS devices for loss
minimization and voltage control.
II. POWER CONTROLLER CONCEPTS
To control power flow, it is desirable to be able to maintain
or change quantities such as line impedances, bus voltage
magnitudes, and phase angle differences. There are many
power controller devices which affect some or all of these
parameters. The well-studied FACTS devices are included in
this power controller category.
FACTS devices are different from traditional capacitive
compensators such as static var compensators (SVCs). Instead
of inserting series capacitors or other fixed impedance devices,
FACTS devices typically perform active impedance injection.
Active impedance injection is a term used to describe either
series or shunt compensation achieved by injecting an AC
voltage. The voltage injection is accomplished using a
synchronous voltage source (SVS) which generates sinusoidal
voltages at the fundamental frequency and has controllable
amplitude and phase angle [2]. The SVS is capable of
generating or absorbing reactive power by controlling the
injected voltage magnitude. When the injected voltage is in
quadrature with the line current, only reactive power is
exchanged. Conversely, when the voltage is in phase with the
line current, only real power is exchanged. If an external
energy source or load is attached, real power exchange is
possible by controlling the voltage angle with respect to the
line current which corresponds to varying an effective
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2
resistance.
The idea of using a voltage source for reactive power
compensation comes from realizing what a series capacitor is
intended to accomplish. A series capacitor on a line is useful
because it produces the necessary voltage at the fundamental
frequency to cancel some of the inductive voltage drop across
the line causing the line to become electrically shorter. The
same effect is obtained by having an AC voltage source of the
fundamental frequency in quadrature with the line current;
consider the voltage drop across a capacitor:
Vc   jI 1/ C    jIX c
(1)
Lines using capacitors for series compensation face the
problem of subsynchronous resonance (SSR). SSR is a low
frequency transient created when the system reactance and the
line capacitance establish a resonant circuit. The low
frequency transient causes the impedance seen by a relay to
spiral on the R-X plane instead of appearing as a fixed point
which can impair operation of relay elements [5]. SSR also
causes serious damage to generators [6]. The SVS does not
cause the SSR phenomenon, and with proper control, it could
be used to damp oscillations due to SSR by producing voltage
components at non-fundamental frequencies [2].
Some FACTS devices which operate based on the SVS
include the Static Synchronous Series Compensator (SSSC)
[6] and the Unified Power Flow Controller (UPFC) [7]. The
SSSC provides a compensating voltage over both a capacitive
and inductive range irrespective of the line current. Power
control functions encompassed by the UPFC include terminal
voltage regulation, reactive compensation, and phase shifting.
Deployment of FACTS devices has not widely occurred due in
part to size, expense, and installation effort. Distributed Static
Series Compensators (DSSCs) are D-FACTS devices
comprised of a low-rated single phase inverter and a single
turn transformer and provide control similar to the SSSC, but
offer remediation of problems related to size and expense.
Qi ,calc  Vi 2 Bii  Vi  V j Gij sin(i   j )  Bij sin(i   j )  (2c)
jH
q  Qi ,calc   Qi , gen  Qi ,load 
The real power flow from bus i to bus j is given by the
following:
Pflow,ij  Vi 2 Gij   Vi V j Gij cos(i   j )  Bij sin(i   j ) 
Yij   yij   gij  jbij  Gij  jBij
Gij  jBij  
r
x
1
  2 ij 2  j 2 ij 2
rij  jxij
rij  xij
rij  xij
Yii   yij  gii  jbii
Pi ,calc  Vi 2Gii  Vi  V j Gij cos(i   j )  Bij sin(i   j )  (2a)
jH
p  Pi ,calc   Pi , gen  Pi ,load 
(2b)
(4a)
(4b)
(4c)
iH
A. Total Sensitivities for Real Power Losses
Transmission line real power (MW) losses for a system can
be expressed as a summation of the MW losses on all lines.
The losses on a line may be expressed in terms of the current
magnitude and line resistance or as the sum of power flows
from both line ends, Pflow,ij + Pflow,ji. For a system of n buses
and l lines, the total real power losses in the system are given
by both of the following:
n
n
Ploss =  Pflow,ij
i j
(5a)
i 1 j 1
l
Linear sensitivities can be used to express the relationships
between different power system quantities. These
dependencies aid in explaining how quantities of interest
concerning lines, buses, and flows in the system are affected
by a slight change of another quantity somewhere else.
Generalized power system sensitivities for a particular
equation or constraint may be described in terms of controls,
state variables, and bus power injections [8].
The AC power injection equations for a bus i are stated here
for convenience, where the set H is the set of all buses
connected to bus i. Power balance is shown by Δp and Δq
which must equal zero:
(3)
To clarify notation, capital letters Y, G, and B denote matrix
elements where Y is the system admittance matrix and G and
B are the respective real and imaginary parts. Lower case
letters y, g, and b correspond to actual line admittance values.
Recall that for elements in the Y matrix, we have the following
relationships [9], where off-diagonal elements are given by Yij
and self-admittance elements are given by Yii:
Ploss =  I k Rk
III. DEPENDENCIES ON LINE IMPEDANCE
(2d)
2
(5b)
k 1
The sensitivities of real power losses to changing line
impedance are derived from (5a) or (5b) and provide insight
into how much the system’s losses change due to an
incremental change in line impedance. For a given line, this
value is an indication of the amount of control D-FACTS
devices could provide if placed on that line. The following
expression describes the relationships that govern how real
power losses depend on line impedance:
dPloss
Ploss  Pflow,ij s( ,V ) Pflow,ij Gij Pflow,ij Bij  (6)





dxij
Pflow,ij  s( ,V ) xij
Gij xij
Bij xij 
In (6), the vector s(θ,V) is a concatenated vector of all the
angle and voltage states for the system, and xij is a vector
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3
containing the reactive impedance of every line. The power
flow from bus i to bus j depends explicitly on the angles and
voltages of buses i and j. These angles and voltages have a
dependence on line impedance. The power flow from i to j
also depends explicitly on Y which may be written in terms of
line impedances as shown in (4b).
Expressing elements of matrices G and B in terms of
impedance as in (4b) and taking the derivative of each with
respect to xij yields the following:
Gij

xij
Bij
xij

2  rij  xij
r
2
ij
2 xij 2
 rij  xij
2

 xij 2 
2 2

2
1
 rij  xij 2 
2
(7a)
(7b)
If G and B in the power flow equations are replaced by the
corresponding equations from (4b), then the sensitivity of real
power flow to xij can be calculated directly.
When
differentiating the power flow equations, (7a) and (7b) may be
substituted into the power flow equations in place of the
corresponding Y matrix element. Thus, the equation of
sensitivities in (6) may be expressed with fewer terms:
dPloss
Ploss

dxij
Pflow,ij
 Pflow,ij s( ,V ) Pflow,ij 



xij 
 s( ,V ) xij
(8)
B. Power Injection Sensitivities
The partial derivative of s(θ,V) with respect to xij is needed as
shown in (8), but this cannot be calculated directly. First, the
power flow Jacobian is needed to obtain the relationship
between state variables and bus power injections:
  
 p 
-1
 V  =   J   q 
 
 
(9)
Then, the relationship between power injections and line
impedance is determined. The sensitivities of real and reactive
power injections to a change in line impedance will be denoted
the Power Injection to Impedance (PII) matrix:
 p 


 q  =  PII   xij 


 
 p 
 x 
ij

PII  
 q 


 xij 
bus i. In general, for a bus i, elements of PII are given by the
following:
  Gij 
 (12a)
 Gij 
 Bij 
Pi
 Vi 2  
  Vi  V j  
 cos(i   j )  
 sin(i   j ) 
xij
 xij 
 xij 
  xij 

  G 
 (12b)
 B 
 B 
Qi
 Vi 2   ij   Vi V j   ij  sin(i   j )   ij  cos(i   j ) 


xij

x

x

x

ij 

 ij 
  ij 

From the inverse Jacobian and PII, the relationship between
the state variables and line impedances is determined. Let the
vector f(p,q) consist of Δp (2b) and Δq (2d). From the chain
rule of calculus, the sensitivities of state variables to change in
line impedance are given by the State to Impedance (SI)
matrix:
  


 V  =  SI   xij 


 
s( ,V ) s( ,V ) f ( p ,q )
SI 

  J 1  PII
xij
f ( p ,q ) xij
(13)
(14)
C. Power Flow Sensitivities
To calculate the sensitivities of losses to change in
impedance, the equation for total real power losses used in this
paper is (5a). For any line between buses i and j, the real
power flow is calculated at both line ends. Summing the real
power flow from bus i to bus j and from bus j to bus i results in
the real power losses on that line, and summing the losses for
all lines results in the total losses. Thus, the derivative of
losses (5a) with respect to real power flows (3) is a vector of
ones with a length equal to twice the number of lines in the
system and is denoted the Power Loss to Power Flow (PLPF)
vector:
 P  1
PLPF   loss    
 Pflow,ij   
T
(15)
The sensitivities of the real power flows with respect to
state variables are given in the Power Flow to State (PFS)
matrix:
(10)
 P

PFS   flow,ij 
 s( ,V ) 
(11)
For a single line between buses i and j, in PFS there is a
row for each line end. These two rows contain up to four
nonzero elements which are found from the following
equations:
To calculate PII, the power injection equations at each bus i
are differentiated with respect to xij for all lines connected to
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(16)
4
Pflow,ij
 j
Pflow, ji
 j
Pflow,ij
V j
Pflow, ji
V j
 Vi V j Gij sin(i   j )  Bij cos(i   j ) 
 V j Vi G ji sin( j  i )  B ji cos( j  i ) 
 Vi Gij cos(i   j )  Bij sin(i   j ) 
 2 V j G ji   Vi G ji cos( j  i )  B ji sin( j  i ) 
involves choosing the best lines for placement given that only
(17a) a certain number of lines are available and then controlling the
devices on these lines to minimize losses. This section
addresses the specific problem of loss minimization, but the
(17b) general approach may be extended to other problems.
A. Relevance of Sensitivities to Optimization
The field of optimization is well established and is
(17c)
accompanied by rich theory [10], [11] which includes
comparison of different solution methods. The general form
(17d) of a problem in optimization is
minimize
The sensitivities of real power flows with respect to line
impedances xij are given by the Power Flow to Impedance
(PFI) matrix:
f ( x)
subject to x  X  n
(23)
The optimization problem represented above is to find the
values
of decision variables x in the constraint set X such that
(18)
the objective function f(x) has its minimum value. Finding the
minimum requires knowledge about the shape of f(x) which is
obtained from the first and second derivatives, so the
The structure of PFI is lower bidiagonal. The only
derivatives are important to the solution approach.
impedance that directly impacts the power flow on a line is the
For an unconstrained problem where X is the whole nimpedance on that line. There is a power flow equation for
dimensional space, the first order necessary condition for a
both line ends; thus, each column in PFI consists of two
local minimum is that the gradient of f(x) with respect to x
entries. In PFI and PFS, assume the two rows for both line
must be zero. The second order necessary condition for a
ends are placed adjacently. Then, the two entries in a column
local minimum is that the Hessian, or the matrix of second
of PFI will be on the diagonal and directly beneath the
order variations of f(x), must be positive semidefinite. If the
diagonal. The equations for both entries are identical except
Hessian is positive definite and the first order necessary
with i and j reversed:
conditions hold, then the value of f(x) strictly increases for
small variations in x and x=x* is a local minimum.
  Gij 
 (19)
 Gij 
 Bij 
Pflow,ij
2
If f(x) is convex, the optimization problem (23) exhibits
 Vi  
  Vi V j  
 cos(i   j )  
 sin(i   j ) 
xij
 xij 
 xij 
some unique properties. A function is strictly convex if any
  xij 

chord drawn between two points on the function lies above the
Thus, an incremental change in real power flows with function and the set over which the function is defined is also
respect to changes in state and line impedance may now be convex. Then, the first order necessary condition alone is a
sufficient condition for a local minimum, and any local
expressed in terms of matrices PFS and PFI:
minimum is also a global minimum or a minimum over the
whole set.
  




(20)

P
=
PFS

PFI

x




An important connection exists between optimization
flow
,
ij
ij
 v 








 
theory introduced above and the linear sensitivities of the
previous section. For the situation where f(x) is the sum of the
Finally, the total power loss sensitivities (8) are calculated real power losses in a power system and the decision variables
from the other matrices and are given by the Power Loss to x are the inductive impedances xij of the transmission lines, the
Impedance (PLI) matrix:
gradient of f(x) with respect to x is given by PFI (20). If the
sensitivities in PFI are zero, the function is minimized and
(21) changing xij by a small amount will not change the system
PLI  PLPF PFS  SI  PFI
losses, so the solution cannot be any better. Thus, linear


(22) sensitivities provide a means for doing optimization even when
 Ploss  = PLI xij 
f(x) is nonlinear, an observation which is utilized extensively


in the examples to follow.
 P

PFI   flow,ij 
 xij 


IV. APPLICATION TO LOSS MINIMIZATION
Minimizing total system losses and cost are typical
objective functions for the optimal power flow (OPF) and the
security constrained optimal power flow (SCOPF). The
potential application of D-FACTS for loss minimization
B. D-FACTS Placement for Loss Minimization
Ideally, D-FACTS devices could be placed on all lines for
the greatest amount of control, but this is not a realistic
assumption. Thus, it is necessary to decide which lines are the
best choices for D-FACTS device placement. For the loss
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5
minimization application, the best lines are chosen as the lines
from which the most change in real power losses due to change
in impedance is possible. That is, the best k lines are chosen
corresponding to the k sensitivities in PLI which are the
furthest from zero.
C. Optimization to Determine D-FACTS Settings
Once the best k lines are chosen for D-FACTS device
placement, an optimization algorithm is applied which uses the
linear sensitivities previously introduced.
An algorithm based on the steepest descent method is used
because it is straightforward to implement and is able to show
whether improvement in real power losses is possible by
controlling xij. In the steepest descent algorithm, the direction
of movement is chosen to be the negative gradient direction.
For a small enough step size, each successive iterate results in
a strictly decreased value of the objective function because the
steps taken are perpendicular to the contours of f(x). The
problem of minimizing real power losses is stated as follows:
minimize
n
n
f1   Pij
i j
i 1 j 1
subject to p  0
q  0
xij  xij ,max
(24)
several scenarios are examined to consider different device
placements and amounts of allowed change in line impedance.
The system topology consists of 38 buses, 52 transmission
lines, 6 online generators, and 27 loads.
Figure 2. 38-bus Study System
The properties of convexity mentioned in the previous
section are applicable because system real power losses with
respect to line reactance are convex. In Figure 3, system real
power losses are plotted with respect to line impedance for the
line between buses 2 and 7 to illustrate convexity:
xij  xij ,min
By solving the optimization problem (24), a vector of new
line impedances xij is determined to minimize real power
losses such that the power flow equations are satisfied and the
line impedances may only change by a specified percentage.
The solution procedure is outlined in Figure 1:
Define initial power system state,
admittance matrix, net power injections,
and number of lines (k) to place DFACTS devices
Calculate initial sensitivities (PLI)
Figure 3. Convexity of Losses
Select the best k lines to place D-FACTS
devices
Initially, at a given operating point under high load
conditions, the system has 3.51 MW of real power losses.
Fuel costs are estimated from the Department of Energy [12]
and from CWLP as $2.68/MBTU for coal, $10/MBTU for gas,
and $14.85/MBTU for oil. An estimate of the cost of
generation before any D-FACTS compensation is added is to
be $42,491.33/h. Four D-FACTS scenarios with different
device placements and settings are examined.
The first scenario is unrealistic but one from which the
absolute best results may be achieved for comparison. In this
case, D-FACTS devices are placed on all lines and allowed to
change by any amount. After the loss minimization procedure,
real power losses are reduced to 2.77 MW, and the cost of
generation is estimated at $42,301.71/h which corresponds to a
monetary savings of $189.62/h or $1,661,100.41/yr. Note that
Solve Optimization:
Calculate sensitivities (PLI)
Get new impedance vector xij
Update Y matrix
Solve Power Flow:
Get new state s(θ,V)
Check stopping conditions
Figure 1. Loss Minimization Procedure
D. Loss Minimization Example Case
The study case is based on the system provided by City
Water Light and Power (CWLP) in Springfield, Illinois and is
illustrated in Figure 2. Using code written in Matlab and
system information exported from PowerWorld Simulator,
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6
operating conditions change over the course of the day and
will result in different amounts of actual savings for any real
system. Payback period is calculated by determining the
number of years which elapse before annual savings becomes
equivalent to the initial cost [13]. Assuming initial costs of
$100/kVA [3] for installing D-FACTS devices and an interest
rate of 6%, the payback period is found to be 4.62 years.
The next scenario again places D-FACTS devices on all
lines, but now impedances are only allowed to change by +/50% of the original values. After optimization, real power
losses are reduced to 2.91 MW. The cost of generation
becomes $42,376.94/h corresponding to savings of
$1,002,076.88/yr. The payback period is now 8.53 years,
nearly double that of the unrestricted case.
In a third case which is much more realistic, D-FACTS
devices are installed on the five best lines and impedances are
allowed to change no more than +/- 20%.
A list of the
selected lines for each case is shown in Table 1. After
optimization, losses reduce to 3.35 MW and cost savings are
$103,909.05, but the payback period is now 14.14 years. A
significant benefit owed to the distributed nature of D-FACTS
devices is that they may be installed incrementally, thus
reducing the initial expense.
To illustrate that selecting D-FACTS device locations using
PLI is advantageous, a fourth case is studied. D-FACTS
devices are now placed on the five worst lines, the lines where
sensitivities in PLI are the closest to zero. Real power losses
are reduced from the original 3.512 MW to 3.5116 MW,
which results in annual savings of just $315.97. The initial
cost based on line MVA limits is $360,000, which results in
the calculation of an infinite payback period, so this
installation can not be justified. Thus, if cost is a concern,
choosing an appropriate number of lines and choosing the
most beneficial lines are crucial and will require some analysis
by the utility company prior to installation.
Table 1 summarizes the results, where the term (i,j) denotes
a line between bus i and bus j:
Original
Case 1
Case 2
Case 3
(5 best
lines)
Case 4
(5 worst
lines)
Table 1. Loss Minimization Results Summary
Controlled Lines
xij Max
Final
(from i, to j)
Change
Losses
none
none
3.51 MW
all
any
2.77 MW
all
50%
2.91 MW
(1,35), (2,7),
20%
3.35 MW
(12,13), (13,14),
(14,15)
(10,34), (12,21),
20%
3.51 MW
(19,24), (23, 24),
(23,25)
Payback
Period
N/A
4.62 years
8.53 years
14.14 years
∞
(never)
V. APPLICATION TO VOLTAGE CONTROL
Capacitor banks and reactive vars produced by generators
provide a means of keeping system voltages high. However,
in some systems, it may also be desirable to lower voltages
slightly if they become too high. During off-peak periods,
large generators are producing high amounts of reactive power
which is not able to be absorbed, thus boosting voltages in the
system. This may be a concern when a neighboring system has
nearby large generating units and no transformers or other
regulating devices are in place between the two systems. The
objective of interest is to determine if voltage control can be
provided by D-FACTS devices. In particular, this application
examines the use of D-FACTS devices as a means to lower
voltages.
Solving the voltage control problem using D-FACTS
devices uses many of the same concepts and derivations as
solving the problem of real power losses. Since D-FACTS
devices behave like series connected voltage sources, they are
a logical choice for consideration in voltage control
applications.
A. Voltage Control Problem Formulation
When voltages are higher than a certain threshold in a
system containing D-FACTS devices, the system may benefit
from changing the settings such that voltages return to a more
normal level. Voltage control may be done by determining the
required line impedance settings on lines with D-FACTS
devices to minimize the square of the difference between the
voltage states in the system and the corresponding reference
voltages.
Once again, the sensitivities derived for PLI are useful for
solving this problem. However, the only sensitivities needed
in this application are the sensitivities of voltage with respect
to line impedance which are found in the lower block of SI,
SIV:
SI 
s( ,V )
xij
  


 SI   xij 
 
 SIV   V 


 xij 
(25)
Thus, the information needed to solve the voltage control
problem is a subset of the information previously used to solve
the loss minimization problem. The voltage control problem
may be stated as follows:
minimize
n
f 2   Vi  Vi , spec 
2
i j
i 1
subject to p  0
q  0
xij  xij ,max
(26)
xij  xij ,min
The objective function has changed, but the constraints for
this problem are the same as in the loss minimization
application. That is, the power flow equations must be
satisfied, and the line impedances may change only by a
specified amount.
B. D-FACTS Placement for Voltage Control
By the same reasoning as the loss minimization application,
beneficial choices of lines for D-FACTS placement may be
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7
determined from SIV. Lines that have higher sensitivities are
better choices because changing the impedance on that line has
a higher impact on the system voltages. The gradient of the
objective function f2 with respect to xij is given by the
following:
 n

f 2  2   Vi  Vi , spec   SIV
 i 1

(27)
Lines for placement of k D-FACTS devices may be chosen
by selecting the k lines with entries in f 2 which are furthest
from zero.
C. Voltage Control Example Case
To illustrate the use of D-FACTS devices in a voltage
control application, several scenarios are examined for the
study system in Figure 2. The system’s load level is lower than
for the loss minimization case which causes voltages to be as
high as 1.041 per unit.
A steepest descent algorithm which follows basically the
same procedure as in Figure 1 is applied to determine DFACTS settings such that the system voltages will be
controlled to 1.00 per unit. It is important to note that these
results depend heavily on operating conditions. The voltages
at each bus in the system are shown in Figure 4 before and
after the optimization algorithm was applied:
Figure 4. Study System Voltage Control
The initial high voltage (HV) condition caused by low load
levels is shown in Figure 4. Several control scenarios illustrate
the results of the optimization procedure. In the first three
scenarios, D-FACTS devices are allowed to change xij by 20%,
50%, and 90%. The results indicate that voltages are only
significantly affected when D-FACTS devices are allowed to
cause a large percent change in effective line impedance.
However, during these low load conditions, it could be
acceptable for D-FACTS devices to change effective
impedances by more than +/- 20% because the corresponding
current flows will be lower for the same voltage drop as in (1).
To illustrate the importance of device placement, in a fourth
scenario, D-FACTS devices are placed on the 10 best lines
determined by SIV: (1,26), (1,28), (1,35), (2,5), (3,29), (3,37),
(5,9), (6,7), (13,33), and (14,15). Line impedances are
allowed to change by +/- 90% to correspond with the previous
scenario which allowed the most control. An interesting
conclusion is that the results of placing D-FACTS on all lines
and the results of placing D-FACTS devices on only the 10
best lines are very similar. Thus, these 10 lines are good
choices for use in voltage control. Conversely, there is little
benefit to be gained by placing devices on ineffective lines.
Additionally, lines (1,35) and (14,15) selected for this
application are among the top five lines previously selected for
loss minimization, which suggests versatility.
The final voltages in Figure 4 illustrate that in all cases, the
use of D-FACTS devices will lower system voltages, but the
amount of the change depends strongly on the range over
which D-FACTS devices are allowed to change. Thus, it is
important to determine what amount of voltage reduction is
sufficient for the situation of interest and more exactly what
the device limitations are.
VI. CONTROL AND COMMUNICATIONS REQUIREMENTS
An important caveat to the benefits and usefulness of DFACTS is that their potential applications may not be practical
or even possible in the absence of secure control and
communications. Determining the communication and control
requirements for D-FACTS devices is a task which is relevant
only after the devices are shown to be valuable to the power
system. Increasing ATC was previously shown [3] to be a
possible use of D-FACTS devices. Providing a means to
minimize losses and to regulate system voltages, as shown in
this paper, is also useful. Thus, now it is reasonable to
consider how communication and control of D-FACTS
devices should be done.
Perhaps the control for D-FACTS devices could be
decentralized. The idea of decentralized control is not new in
the power industry and has been studied as a means for devices
to damp electromechanical oscillations [14]. Decentralized
control has recently been gaining attention as more devices are
equipped with fast communication capabilities. One approach
to implementing decentralized control is through the use of
intelligent agents [15].
Regardless of the type of control chosen and its
implementation, one must consider the timing with which
commands are given to the D-FACTS devices, especially as
the number of devices increases. It must be proven that the
system stability does not suffer due to transients caused by
giving commands to change settings of multiple devices in a
short time span. On the other hand, with the proper control, it
has been mentioned [1], [2] that SVS devices may actually be
used to improve system stability. The impact of D-FACTS
devices on system stability still requires investigation.
Furthermore, communications between power system
devices are crucial from a cyber security standpoint. Because
of the amount of control which is possible, integrity of the
control messages is extremely important. Changing device
settings incorrectly either accidentally or maliciously could
cause significant damage.
VII. CONCLUSIONS
As verified in the two applications studied in this paper, D-
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8
FACTS devices are compelling candidates for power flow
control. By producing a series compensating voltage which
can effectively change transmission line impedances, DFACTS devices may be applied to problems such as
minimizing real power losses and controlling system voltages
after they have become too high.
Although the benefits of D-FACTS devices discussed in
this paper provide strong arguments for their use, there is work
to be done to understand the effects of D-FACTS devices on
system stability and to develop a corresponding cyber-secure
method for control.
Thomas J. Overbye (S’87-M’92-SM’96-F’05) received the B.S., M.S. and
Ph.D. degrees in electrical engineering from the University of WisconsinMadison. He is currently the Fox Family Professor of Electrical and
Computer Engineering at the University of Illinois Urbana-Champaign. He
was with Madison Gas and Electric Company, Madison, WI, from 19831991. His current research interests include power system visualization,
power system analysis, and computer applications in power systems.
VIII. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
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Katherine M. Rogers (S’06) received the B.S. degree in electrical
engineering from the University of Texas at Austin in 2007 and is currently
working toward the M. S. degree in the department of Electrical and
Computer Engineering at the University of Illinois Urbana-Champaign. Her
interests include sensitivity analysis, power system analysis, and power
system protection.
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