Download Steady state analysis of unified power flow controller: mathematical

Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy
Steady State Analysis of Unified Power Flow
Controller: Mathematical Modeling and
Simulation Studies
A.M. Vural, Student Member, IEEE, and M. Tumay
Abstract--This paper presents an improved steady state
mathematical model for Unified Power Flow Controller
(UPFC), which is necessary for the analysis of the steady state
operation of this device embedded in a power system. The
model is based on the concept of injected powers in which the
operational losses can be taken into account. The model is quite
suitable in load flow studies, since it accepts employing
conventional techniques such as Newton-Raphson method and
even commercial software. The model is verified through a
number of simulation examples, carried out on IEEE 14-bus
and IEEE 30-bus systems by commercial software in which the
model is adapted by means of user-defined modeling technique.
The results of load flow analysis show the effectiveness of the
model. Also the effects of UPFC location on different power
system parameters are entirely investigated.
converters and two coupling transformers, the mathematical
model proposed here is based on the true representation of
them in a computational environment. Converters are
modeled as controllable voltage sources, while the effects of
the transformers are modeled as pure inductances connected
to the lines and real power losses in UPFC. A commercial
software, “Power System Analysis Software Package”
(PSASP) is used in this study to investigate the effects of
UPFC on power system steady state operation [7]. It
provides users to analyze power systems both in steady and
transient states and also has the capability of creating userdefined models of advanced power system equipment.
Index Terms-- FACTS, load flow analysis, modeling, UPFC.
III. MODELING APPROACH
Recent advances in high power electronics has made it
possible to implement all solid state power flow controllers
using power switching converters. Conceptual hardware
configuration of UPFC is schematically drawn in Fig. 1.
Converters labeled as “Series Converter” and “Shunt
Converter”, are operated from a common dc link voltage
provided by a dc storage capacitor. Two coupling power
transformers are also required to isolate UPFC and the
transmission line, and to match the voltage levels between
the power network and voltage produced by the converters.
This arrangement can be functionally treated as an ideal ac
to ac power converter in which the magnitude and phase
shift of the ac output voltages of both converters can be
controlled at any desired value, assuming that the controlled
voltage source in series with the transmission line can be
controlled without restriction. This means that the phase
angle of the series injected voltage can be chosen
independently of the line current. Eventually as seen in Fig.
1, the real power can freely flow in either direction between
ac terminals of the two converters and each converter can
also generate or absorb reactive power independently at its
own ac output terminals. The series converter performs the
main functions of UPFC, while the shunt converter is used
to provide real power demanded by the series converter and
the losses in UPFC. Mathematical model is constructed by
representing the ac output terminals of the two converters
with two ideal voltage sources, Vse and Vsh , respectively in
series with the reactances, Xse and Xsh, denoting the leakage
reactance of the two coupling transformers, respectively, in
Fig. 2. IL represents transmission line current having a phase
angle of φIL.
1.
2.
I.NOMENCLATURE
Complex quantities are represented by upper case
character “~”.
Complex conjugate is denoted by “*”.
II. INTRODUCTION
UPFC is the most comprehensive device of all Flexible AC
Transmission Systems (FACTS) devices, which has arisen
so after the FACTS initiative, is capable of providing
simultaneous active and reactive power flow control, as well
as voltage magnitude control [1]. The versatility provided by
UPFC makes it an advanced power system device and an
important member of FACTS family to provide a number of
control functions required to solve a wide range of problems
encountered in electrical power systems [2], [3].
Performance analysis of UPFC in load flow studies requires
its steady state modeling. There are many papers concerned
with the issue of UPFC modeling. Reference [2] introduces
a steady state UPFC model based on a single, ideal, and
series voltage source. Reference [4] utilizes two ideal
voltage sources, one in series and one in parallel as UPFC
steady- state model. The steady state model suggested in [5]
is based upon one ideal, series voltage source, and one ideal,
shunt current source. In [6], UPFC is represented by two
ideal voltage sources with series source impedances,
connected in series and parallel with the transmission line,
representing the output voltages of series and shunt branches
of UPFC. Because UPFC employs two voltage source
0-7803-7967-5/03/$17.00 ©2003 IEEE
Vi ∠θi
P
Vj∠θ j
- Vse +
Transmission Line
b se = 1 / X se
Vi ∠ θ i
Vj∠ θ j
P
Q
Q
~
Ise
+
V dc
-
SHUNT CONVERTER
SERIES CONVERTER
The effects of the current source Ise and susceptance bse can
be modeled by injection powers at buses i and j.
~
~ ~
Sis = Vi ( − I se )∗
(4)
~
~ ~ ∗
(5)
S js = V j ( I se )
Control Input
Control Unit
system voltage &
current measurement
Fig. 4. Replacement of series voltage source by a current
source.
C
Fig. 1. Conceptual hardware configuration of UPFC.
Vi ∠ θ i
busi
~
Vi '
- ~ +
Vse
X sh
+ ~
Vsh
-
Q SE RIE S
X se
PSE R I ES
V j∠ θ j
IL
busj
PSH U N T
The injected complex powers Sis and Sjs are given as
(See Appendix for derivation)
~
Sis = Pis + jQis = −rbseVi 2 sin γ − jrbseVi 2 cos γ
~
S js = Pjs + jQ js =
(6)
ViV j bse r sin( θ i − θ j + γ ) + jViV j bse r cos( θ i − θ j + γ )
(7)
Based on (6) and (7), power injection model of series
connected voltage source can be seen as two dependent
power injections at buses i and j as shown in Fig. 5.
Fig. 2. Equivalent circuit of UPFC.
A. Series Connected Voltage Source Converter
As seen in Fig. 2, Vi’, represents an imaginary voltage
behind the series reactance Xse.
~
~
~
Vi ′ = Vse + Vi
(1)
Vi ∠θi
Vj∠θ j
X se
Pis + jQ is
EQUIVALENT POWER INJECTION OF
SERIES VOLTAGE SOURCE AT BUS i
Pjs + jQ js
EQUIVALENT POWER INJECTION OF
SERIES VOLTAGE SOURCE AT BUS j
Series voltage source, Vse is controllable both in magnitude
and phase angle.
Fig. 5. Equivalent power injections of series voltage source.
~
~
Vse = rVi e jγ
B. Shunt Connected Voltage Source Converter
(2)
where, 0 ≤ r ≤ rmax and 0 ≤ γ ≤ 2π.
The related phasor diagram of the concerned parameters in
(1) and (2) is drawn in Fig. 3.
~′
Vi
φ IL
IL
~
Vi
~
Vse
γ
PSHUNT = −1.02 PSERIES
In Fig. 3, voltage of bus i, Vi, is assumed to be the reference
vector, i.e., Vi=Vi∠0°. The power injection model can be
obtained by replacing the voltage source Vse by a current
source Ise in parallel with the transmission line as shown in
Fig. 4.
where bse=1/Xse.
(8)
The complex power supplied by the series voltage source
converter is given as (see Appendix for derivation)
Fig. 3. Phasor diagrams of (1) and (2).
~
~
I se = − jb seV se
In UPFC, shunt connected voltage source is used mainly to
provide both real power, PSERIES, which is injected to the
system through the series connected voltage source, and the
total losses within the UPFC. The total switching losses of
the two converters is estimated to be about 2 % of the power
transferred for thyristor based PWM converters [8]. If the
losses are to be included in the real power injection of the
shunt connected voltage source at bus i, PSHUNT is equal to
1.02 times the injected series real power PSERIES through the
series connected voltage source to the system.
(3)
~
~ ~
S SERIES = Vse I L∗ = PSERIES + jQSERIES =
rbseViV j sin( θ i − θ j + γ ) − rbseVi 2 sin γ
− jrbseViV j cos( θ i − θ j + γ ) + jrbseVi 2 cos γ + jr 2bseVi 2
(9)
The reactive power delivered or absorbed by shunt converter
is not considered in this model, but its effect can be
calculated and modeled as a separate controllable shunt
reactive source, The main function of this reactive power is
to maintain the voltage level at bus i within acceptable
limits, in this case shunt converter functions as a static var
compensator. In view of the above explanations, we assume
that QSHUNT=0. Consequently, the UPFC power injection
model is constructed from the series connected voltage
source model with the addition of a power injection
equivalent to PSHUNT + j0 to bus i as shown in Fig. 6.
Vi ∠θ i
Vj∠θ j
X se
Pi ,upfc + jQ i ,upfc
Pj,upfc + jQ j,upfc
EQUIVALENT POWER INJECTION AT
BUS i
EQUIVALENT POWER INJECTION AT
BUS j
cosine constitute the user-defined model. When adaptation,
two imaginary PQ buses (bus i and bus j) are created on line
where UPFC is considered to be located. In order to
represent the model correctly, series reactance Xse is
positioned between these two buses. When the position of
UPFC on the transmission line is changed, the line data, Zkm,
should be modified, depending on the location of the UPFC;
sending-end side, receiving-end side, or middle of line
position. This situation is illustrated in Fig. 8.
Fig. 6. Complete UPFC power injection model.
where Pi,upfc + jQi,upfc and Pj,upfc + jQj,upfc are formulated as
follows
Pi ,upfc = Pis + PSHUNT = 0.02rbseVi 2 Sinγ
−1.02 rbseViV j Sin( θ i − θ j + γ )
(10)
2
Qi ,upfc = Qis = −rbseVi Cosγ
(11)
Pj ,upfc = Pjs = rbseViV j Sin( θ i − θ j + γ )
(12)
Q j ,upfc = Q js = rb seViV j Cos( θ i − θ j + γ )
(13)
IV.ADAPTATION OF MODEL INTO PSASP
To implement UPFC model in PSASP, a user-defined model
is developed. Block diagram of user-defined UPFC model is
schematically drawn in Fig. 7. Operator blocks having basic
functions such as; summing, multiplication, taking sine and
r
g am m a
Y =A
TM1
b se
Y =A
TM2
Y =A
TM3
p i/18 0
Y =A
TM8
TM1
TM2
VT1
VT1
TM4
AX 1 *X 2
AX 1 *X 2
AX 1 *X 2
TM5
TM4
AN G B 1
AN G B 2
AX 1 +B X 2
AX 1 +B X 2
TM3
TM8
TM6
TM7
VT1
VT2
TM1
AX 1 *X 2
TM4
TM3
TM8
AX 1 *X 2
S IN
TM6
COS
TM7
AX 1 *X 2
AX 1 *X 2
P j,up fc
AX 1 *X 2
Q j,u p fc
AX 1 *X 2
TM6
S IN
AX 1 *X 2
AX 1 +B X 2
P i,u p fc
AX 1 *X 2
TM5
COS
AX 1 *X 2
Q i,u p fc
TM5
Fig. 7. Block diagram representation of user-defined model
of UPFC in PSASP.
Fig. 8. Modification of line data due to UPFC position.
V. SIMULATION EXAMPLES
A PC with an Intel Pentium® IV microprocessor at 2.0 GHz
and 256 MB of RAM is used for load flow studies.
A. Simulation Task A
In order to investigate the feasibility of the proposed
technique, load flow studies are carried on IEEE 14-bus
system [9] embedded with a UPFC in PSASP. NewtonRaphson calculation method is selected. Allowed iteration
tolerance is taken as 1E-6. Four different cases are studied in
simulations. First of all and without any compensation, the
electrical system is studied in order to determine the load
flow in each of the transmission line. This allows having a
general idea about system steady state operation. Then
UPFC location is chosen arbitrarily as near bus 2 on line L5,
but thought to be near power generation sections as shown
in Fig. 9. Different UPFC parameters are set to activate
UPFC, the transmitted active and reactive power of all the
lines has remarkably changed. All the results indicate good
convergence and high accuracy achieved by the proposed
method. Case studies show that the results come to a
convergence in 4-6 times of iteration on IEEE 14-bus
system. Table 1 shows the selected results of the load flow
analysis. Comparing load flow solutions without and with
UPFC, power flows can be flexibly controlled by UPFC.
Moreover the simulations show that UPFC provides
independent control of active and reactive power transmits.
The model is also efficient on control parameters of UPFC.
From the practical applications aspect, there will be a
maximum value of injected series voltage due to the power
rating of UPFC. Amount of control range of power flow
actually depends on the requirements in real-life
applications.
B12
B13
B14
L16
L9
L1
B5
L10
L9
L2
Gen.
B9
L13
L7
L5
L4
L3
L-12
B3
L-15
B7
L-13
L7
L-12
B 12
C
B 10
L11
B 13
L-16
L-23
Syn. C.
G6
L2
L8
L3
B9
L-14
L-18
L-22
L3
L6
B3
B4
Tr.
L4
L-2
L-7
L-11
B 11
L12
B4
L7
B6
G5
L-11
Tr.
B1
L-4
L6
L6
G1
L-3
L-9
L5
L-10
B8
Tr.
B5
UPFC
G4
L-1
B7
B8
L14
B10
L15
L5
Slack
Bus
L1
B2
L1
L8
B2
L-6
L4
B 16
B 17
L-24
B1
L-8
B11
L10
Syn. C. B6
G2
L-5
G3
L11
L 12
L-25
Gen.
L17
L 11
B 20
L-15
L 15
L-21
L-36
Syn. C.
L-37
B 21
L-20
L 16
L-26
B 18
B 19
L2
L 14
B 22
Fig. 9. IEEE 14-bus system embedded with UPFC.
L 18
L-17
L-28
L-27
B 24
B. Simulation Task B
A comparative study is carried out for investigating the
effects of UPFC location on power system parameters. Case
studies on the IEEE 30-bus system [10], in Fig. 10, are
briefly reported in this section. Two different locations for
UPFC are considered. First position named as “Position A”
refers to UPFC location near bus 6 on line L-6, while second
position named as “Position B” refers to UPFC location at
the middle of line L-6. Comparable simulation results are
graphically represented in Fig. 11. Table 2 summarizes the
percentage changes in parameters when UPFC location is
changed from position A to B. To have a general idea on the
evaluation of UPFC performance, real and reactive power
flows without UPFC on line L-6 is 0.5555 pu and 0.0155 pu,
respectively. While total real and reactive transmission
losses without UPFC are 0.1560 pu and -0.0164 pu,
respectively.
L-19
L 13
L-29
C
B 28
B 26
B 15
L 10
L 19
B 14
L9
B 23
L-31
L-30
L 17
B 27
B 25
L-32
L-34
L-36
L-33
L-35
B 29
L 20
B 30
L 21
Fig. 10. IEEE 30-bus system.
TABLE I
LOAD FLOW RESULTS OF IEEE 14-BUS SYSTEM WITHOUT AND WITH UPFC
((i-j) DENOTES TRANSMISSION LINE i-j)
Without UPFC
UPFC parameters
r=0.0 (pu)
γ=0.0°
Case 1
UPFC parameters
r=0.05 (pu)
γ=45.0°
Case 2
UPFC parameters
r=0.1 (pu)
γ=90.0°
Case 3
UPFC parameters
r=0.12 (pu)
γ=15.0°
Sending node line power flow (pu)
Sending node line power flow (pu)
Sending node line power flow (pu)
Sending node line power flow (pu)
(1-2)
1.5512-j0.2296
(1-5)
0.7774-j0.1363
(2-3)
0.7176+j0.0132
(2-4)
0.5564-j0.1648
(2-5)
0.4183-j0.1927
(4-5)
-0.6114-j0.0556
Transmission losses (pu)
Active
Reactive
0.1383
0.1102
(1-2)
1.2055-j0.1448
(1-5)
0.7002-j0.1770
(2-3)
0.7190+j0.0130
(2-4)
0.5665-j0.2031
(2-5)
0.0777-j0.04151
(4-5)
-0.6052-j0.1587
Transmission losses (pu)
Active
Reactive
0.1191
0.1255
(1-2)
0.6586+j0.0045
(1-5)
0.5223-j0.1303
(2-3)
0.7129+j0.0136
(2-4)
0.5496-j0.1791
(2-5)
-0.4284-j0.1910
(4-5)
-0.6234-j0.0944
Transmission losses (pu)
Active
Reactive
0.1021
0.0961
(1-2)
1.2375-j0.1529
(1-5)
0.6898-j0.2461
(2-3)
0.7009+j0.0149
(2-4)
0.5383-j0.2507
(2-5)
0.1548+j0.02262
(4-5)
-0.6533-j0.2907
Transmission losses (pu)
Active
Reactive
0.1266
0.1303
TABLE II
PERCENTAGE CHANGES IN POWER SYSTEM PARAMETERS
Active power
flow change (%)
increase
r fixed
γ fixed
6.33
2.4
Reactive power
flow change (%)
increase
r fixed
γ fixed
- 120.81
30.91
Total transmission
real loss change (%)
increase
r fixed
γ fixed
1.94
- 0.72
Total transmission
reactive loss change
(%) increase
r fixed
γ fixed
- 30.22
- 30.72
~
S is = −rbseVi 2 sin γ − jrbseVi 2 cos γ
(A.4)
(A.4) can be decomposed into its real and imaginary parts
~
S is = Pis + jQis , where
Pis = −rbseVi 2 sin γ
(A.5)
2
Qis = − rbseVi cos γ
(A.6)
Substituting (2) and (3) into (5), yields
~
~
~
S js = V j ( − jbse rVi e jγ )∗
(A.7)
Using Euler Identity and trigonometric identities, (A.7)
reduces to
~
S js = Pjs + jQ js , where
Fig. 11. Graphical results related with simulation task B.
VI.CONCLUSIONS
A steady state mathematical model for UPFC is studied in
this paper. The most salient features of the model are that it
is capable of taking the losses of UPFC into account and it is
able to keep the traditional techniques, such as NewtonRaphson load flow algorithm intact; as a consequence
conventional techniques and even commercial power system
analysis software can be directly used by means of userdefined modeling techniques. Numerical results verify the
effectiveness of the model in terms of computational speed,
accuracy and computing resources requirement Simulation
studies show that UPFC can handle flexible and independent
control of active and reactive power flow in transmission
lines. Moreover UPFC location factor is an important
criterion, because its choice directly affects system
parameters.
(A.8)
Q js = ViV j bse r cos( θ i − θ j + γ )
(A.9)
Apparent power supplied by the series converter of UPFC is
given in (A.10)
∗
 V~ ′ − V~j 
~
~ ~∗
jγ ~  i

(A.10)
S SERIES = Vse I ij = re Vi
 jX se 


Applying Euler Identity and the trigonometric identities, the
active and reactive powers supplied by the series converter
of UPFC are calculated in (A.11)-(A.15).
((
)
~
~
~ ~ ~
S SERIES = re jγ Vi re jγ Vi + Vi − V j / jX se
)
∗
~
j ( θ −θ +γ )
S SERIES = jbse r 2Vi 2 ( 1 + e jγ ) − jbseViV j e i j
~
S SERIES = jbse r 2Vi 2 + jbse rVi 2 cos γ − bse rVi 2 sin γ
− jbse rViV j cos( θ i − θ j + γ ) + bse rViV j sin( θ i − θ j
+bse rViV j sin( θ i − θ j + γ )
(A.11)
(A.12)
+γ)
(A.13)
~
S SERIES = PSERIES + jQ SERIES , where
VII.APPENDIX
Derivation of UPFC power injection model
PSERIES = rbseViV j sin( θ i − θ j + γ )
Substituting (2) and (3) into (4), yields
~
~
~
S is = Vi ( jbse rVi e jγ )∗
Pjs = ViV j bse r sin( θ i − θ j + γ )
(A.1)
jγ
By using Euler Identity, (e = cosγ+jsinγ), (A.1) takes the
form of
~
~
~
S is = Vi ( e − j( γ +90 ) bse rVi ∗ )
(A.2)
~
S is = Vi 2 b se r [cos( −γ − 90 ) + j sin( −γ − 90 )]
(A.3)
By using the trigonometric identities, (A.3) reduces to
− rbseVi 2 sin γ
Q SERIES = − rb seVi V j cos( θ i − θ j + γ )
(A.14)
+ rbseVi 2 cos γ + r 2 bseVi 2
(A.15)
VIII.ACKNOWLEDGEMENT
The authors gratefully acknowledge the contributions of
Professor K.L.Lo from University of Strathclyde for his
valuable supports on this study.
IX. REFERENCES
[1] IEEE Power Engineering Society/Cigre: “FACTS
overview,” IEEE Service Center, Piscataway, N.J., 1995,
Special Issue, 95TP108.
[2] L. Gyugyi, “Unified power-flow control concept for
flexible AC transmission systems,” in IEE Proc.-C, vol.
139, no. 4, pp. 323-331, Jul. 1992.
[3] R. Mihalic, P. Zunko and D. Povh, “Improvement of
transient stability using unified power flow controller,”
IEEE Trans. Power Delivery, vol. 11, pp. 485-492, Jan.
1996.
[4] M.R. Iravani, P.L. Dandeno, K.H. Nguyen, D. Zhu, and
D. Maratukulam, “Applications of static phase shifters in
power systems,” IEEE Trans. Power Delivery, vol. 9, pp.
1600-1608, Jul. 1994.
[5] M. Noroozian, and G. Anderson, “Power flow control by
use of controlled series components,” IEEE Trans. Power
Delivery, vol. 8, pp. 1420-1429, Jul. 1993.
[6] Tsau-Tsung-Ma, K.L.Lo and Mehmet Tumay ,”A
Robust UPFC damping control scheme using PI and ANN
based adaptive controllers,” in Proc. COMPEL 2000, vol.
19, no. 3, pp. 878-902.
[7] Power System Analysis Software Package (PSASP) User
Manual, Electric Power Research Institute (EPRI), China
1993.
[8] Ned Mohan, Power Electronics: Converters,
Applications, and Design, New York: Wiley, 1995
[9] IEEE 14-bus test system data [Online]. Available:
http://www.ee.washington.edu/research/pstca/pf14/pg_tca14
bus.htm
[10] IEEE 30-bus test system data [Online]. Available:
http://www.ee.washington.edu/research/pstca/pf30/pg_tca30
bus.htm
X.BIOGRAPHIES
A.M. Vural (SM’2000) received his B.Sc. and
M.Sc. in Electrical and Electronics Engineering
(EEE) from University of Gaziantep in 1999
and 2001, respectively. He worked as a visitor
scholar in Power Systems Research Group in
EEE, University of Strathclyde, Glasgow, UK
in 2000. He is currently a Ph.D. candidate in
Power Systems Research Group and working as
a research assistant in EEE, University of
Gaziantep. His research interests include
FACTS modeling and system identification.
M. Tumay received a Ph.D. in Electrical
Engineering from The Strathclyde University in
1995, and is presently Associate Professor of
Electrical
and
Electronics
Engineering
Department of Cukurova University. His
research interests include modeling of electrical
machines, current and voltage transformer and
power flow controllers.