A COMPREHENSIVE LOAD FLOW MODEL FOR UPFC AND ITS
COMBINATION WITH ESS
Ahad Kazemi Ahmad Esmaielie
Mohammad.T Hassanzade
R.Rezaiepour
e-mail: kazemi@iust.ac.ir
e-mail:mhasanzadeeng@yahoo.com email: rrezaiepour@yahoo.com
Iran University of Science and Technology
Faculty of Engineering, Department of Electrical & Electronics Engineering, Tehran, Iran
Key words: UPFC, Power flow model, Energy storage system
ABSTRACT
A reliable Power flow model is required to study
Unified Power Flow Controller (UPFC) effects on
power system steady state behavior. A few models
such as decoupled model, power injection and
voltage source model are introduced for this
purpose. In this paper a comprehensive, robust,
complete and flexible load flow model considering
existing decoupled power flow model is presented.
For the first time, UPFC combination with energy
storage system, ESS, is introduced to improve UPFC
capability and performance. The presented model is
incorporated in two different networks to show the
newly developed model to be far more flexible and
efficient. The simulations show the model
capabilities and applications in different UPFC
control strategies considering UPFC losses. Finally,
influence of UPFC location and energy storage
system on converters ratings are studied.
I. INTRODUCTION
N the end of 1980s, appearance of FACTS
controllers opened new ways in power systems.
Various factors such as increasing daily demand,
deregulated power systems and power marketing
motivate FACTS controllers' usage. In power
marketing, it is required to control the whole power
flow of transmission lines. FACTS controllers are the
prime contender to provide many control functions to
handle a wide range of dynamic and steady-state
problems encountered in electrical power networks.
UPFC (Unified Power Flow Controller) is one the most
comprehensive FACTS devices which controls line
active and reactive power flows independently as well
as local bus voltage [1].
However, very little work has been carried in
developing suitable models to assess UPFC behavior in
large-scale power networks and most of them suffer
from restrictions. Therefore, an accurate and
comprehensive model seems to be necessary. In this
paper, existing models such as decoupled, power
injection and voltage source model are reviewed briefly
I
and considering decoupled power flow model, a
comprehensive, complete, robust and flexible model is
presented and generalized for UPFC combined with
ESS.
The model is implemented in two power networks to
show its effectiveness in various UPFC control
strategies considering UPFC losses. Finally, different
parameters effects such as UPFC impedance, location
and energy storage system on UPFC converters rating
are investigated.
II. POWER FLOW MODELS REVIEW
A power flow model is required to study devices effects
on network. In spite of significant importance of these
models, a few UPFC power flow models are proposed.
Decoupled power flow model [4], injection model [3, 7]
and voltage source model [5, 6] can be mentioned as
presented models.
IV. THE PROPOSED POWER FLOW MODEL OF
UPFC
In spite of decoupled model simplicity, it is more robust
than the others and contains unique capabilities. Some
shortcomings such as additional nonlinear equation set
necessity, UPFC parameter initial value choices and
simultaneous control of UPFC objective parameters (i.e.
all three P,Q and V must be varied at the same time) can
be eliminated after some substantial modifications in
this model. Moreover, limit revision of UPFC
parameters would be easily possible in iteration process.
In power flow solution, Pi or one of the Qi or Vi should
be known in every bus. Assuming network stability,
power flow always provides unique solution. In other
words, if the connected elements to the desired bus act
neutral to bus parameters, power flow answer would be
constant. However, power system operation conditions
should be far from critical points.
Having connected UPFC, the receiving end always
injects PBt-QBt to bus j, and sending end voltage
maintain VEt in bus I (see Fig. 5).
According to the above, if UPFC is replaced by
elements which are be neutral to the known bus
parameters, power flow answers remain constant.
These elements should inject PBt-QBt to bus j and keep
VEt at bus i. A load model together with a generator is
capable of injecting PBt-QBt to bus j while maintaining
VEt at bus i. The UPFC model is shown in Fig. 6.
PBt − jQBt
VBt*
P − jQ
I E = Et * Et − I B
VEt
IB =
(1)
(2)
Series source voltage is (3).
VB = VBt − VEt + Z B I B
(3)
Substituting IB from (1) to (3) results in phase and
magnitude of series voltage source. Similarly, for
parallel voltage source (4), substituting IE from (2) to
(4), provides phase and magnitude.
VE = VEt − Z E I E
Fig. 5. Network control by UPFC
Fig. 6. UPFC model for Fig. 5
Assuming free loss UPFC, injected and absorbed power
values to bus j and i would be equal. It can be seen in
Fig. 5 that VEt and PEt are known values of the sending
end of the UPFC.
Contrary to the voltage or reactive power, real power
always is specified in UPFC. In this case, arbitrary
values could be chosen for bus parameter. It is better to
choose 1 p.u for voltage or reactive power of the bus.
Accordingly, the following models (see Fig. 7) can be
considered for UPFC. Regarding to power flow, if the
type of bus i and j are known before UPFC insertion,
they would also be known after insertion. In other
words, a P-Q bus remain P-Q after inserting UPFC if P
and Q in UPFC ends are known, otherwise the bus
always remain P-V bus. Therefore, power flow solution
is always applicable for a power system embedded with
UPFC.
(4)
Therefore, UPFC parameters are obtained as mentioned
above. Note that, in this approach, UPFC parameters are
calculated by linear equations without numerical
solution, so initial values estimation, the main defect of
previous methods, is eliminated.
RB and RE show transformers and power switches
losses, respectively [4]. UPFC losses are calculated by
(5) after power flow solution. Considering power flow
solution inflexibility, it is necessary to assume free loss
UPFC. Also, UPFC losses are so small. Therefore, its
effect on power flow can be ignored. If limit revision of
power flow results is possible in whole iteration process
and verification can be applied on load flow program,
UPFC unknown parameters can be determined easily by
the mentioned equations and their limits can easily be
checked. If the parameters exceed the boundaries, some
strategies seem to be useful during iteration process
contrary to the decoupled model. For example, if VB
increases, QBt or VEt can be reduced and if VE increases,
QEt would be reduced [9].
Fig. 8. UPFC voltage source model
Ploss = RE I E2 + RB I B2
Fig. 7. UPFC applicable power flow models
Unknown system parameters are obtained after power
flow solution, and UPFC parameters would be
calculated considering voltage source model in Fig. 8.
The currents are calculated as follows:
(5)
Considering above, losses would be calculated
accurately by (5) for each iteration and PBt changed to
PBt-Ploss for the next value. Therefore, in the next
iterations accurate solution is achieved for losses.
If UPFC is installed at the beginning or end of the line,
depending on the UPFC model, a bus should be added
to the network. The added bus model can be determined
according to the previous discussion. If a UPFC is
installed in the middle of the line, two buses should be
added to the network. Their models would be
determined considering UPFC models at the two ends.
V. THE PROPOSED GENERALIZED UPFC
POWER FLOW MODEL FOR UPFC/ESS
In spite of various UPFC characteristics involved in
power system efficiency improvement, it suffers from
active power injection disability. Adding this capability
significantly enhances UPFC steady-state performance
[9]. The capability can be achieved by combining
energy storage systems or distributed power generators
with UPFC. There are various systems which can be
combined with UPFC (e.g. combustion turbines or
compact air storage system).
UPFC/ESS steady-state model is shown in Fig. 9[9].
receiving power would be PBt=40-0.0096=39.9904. It is
obvious that, loss value can be ignored.
Assume that a 10MW energy storage system is
combined with the UPFC. UPFC/ESS model is shown
in Fig. 11(c); UPFC parameters are shown in table 1part B.
Easy implementation of this model in load flow
program as well as UPFC parameters easy calculation
significantly shows the priority of the model to the
others. The second network is shown in Fig. 12. Assume
that UPFC is installed at the beginning of the line
between buses 5 and 6. It can be controlled to absorb 30
MW from bus 5 and inject 100 MW to bus 6 in addition
to keep terminal voltages in 1.05 p.u. UPFC parameters
and their losses in each iteration are shown in table 2.
Power flow results are shown in Fig. 12(b). It can be
seen that UPFC parameters are calculated easily without
initial values requirement and their limits can be revised
easily.
131.1 MW
90.8 MVR
45 MW
15 MVR
0.987 pu
-4.64 Deg
1
1.060 pu
41.79 MW
16.82 MVR
Fig. 9. UPFC/ESS voltage source model
40 MW
5 MVR
3
0.984 pu
4
40.27 MW
17.51 MVR
19.39 MW
2.86 MVR
19.35 MW
4.69 MVR
24.47 MW
-2.52 MVR
27.25 MW
0.83 MVR
6.56 MW
5.17 MVR
86.85 MW
72.91 MVR
It can be seen that power constraint is shown by PBPE=PESS, therefore UPFC/ESS power flow model is as
Fig. 10.
27.71 MW
-1.72 MVR
0.972 pu
2
1.000 pu
5
54.66 MW
5.56 MVR
20 MW
10 MVR
60 MW
10 MVR
40.0 MW
-61.6 MVR
( a).
131.5 MW
85.8 MVR
45 MW
15 MVR
50.34 MW
9.34 MVR
0.997 pu
-2.51 Deg
3
1.000 pu
-6.02 Deg
1
1.060 pu
40 MW
5 MVR
40.01 MW
2.00 MVR
36.57 MW
-11.72 MVR
37.49 MW
-12.97 MVR
4
0.992 pu
6
48.43 MW
8.92 MVR
-40 MW
17.79 MVR
39.85 MW
3.49 MVR
-40 MW
-2 MVR
4.71 MVR
2
1.000 pu
13.31 MW
78.83 MW
75.88 MVR
13.62 MW
1.85 MVR
13.73 MW
-1.78 MVR
5
0.975 pu
46.69 MW
5.29 MVR
47.61 MW
5.14 MVR
20 MW
10 MVR
60 MW
10 MVR
40.0 MW
-75.5 MVR
( b)
120.8 MW
88.6 MVR
Fig. 10. UPFC/ESS applicable power flow models
1.000 pu
-5.25 Deg
1
1.060 pu
40 MW
5 MVR
0.997 pu
-2.33 Deg
3
4
0.992 pu
UPFC/ESS
44.90 MW
10.58 MVR
43.33 MW
11.20 MVR
40.00 MW
2.00 MVR
39.84 MW
3.49 MVR
6
31.67 MW
-9.69 MVR
32.35 MW
-11.64 MVR
-30 MW
13.49 MVR
-40 MW
-2 MVR
13.63 MW
1.85 MVR
13.31 MW
4.71 MVR
73.70 MW
77.76 MVR
VI. POWER FLOW MODEL EVALUATION
In this section, power flow model applications and
efficiency is assessed in two different networks.
At first, a five-bus network is considered (Fig. 11(a))
[10] to show the most important property of decoupled
model, i.e. carrying out capability in common power
flow programs. It is assumed to transfer 40 MW and
2MVAR from bus 3 to bus 4 and keep voltage of bus 4
in 1 p.u. Therefore, UPFC is modeled as Fig. 11(b) and
power flow is implemented by Power World
Simulator®. UPFC parameters are calculated by (3) and
(4) (see table 1-part A). Assuming UPFC impedance as
ZB=ZE=0.05+j0.1 p.u., UPFC losses are 0.0096 p.u. The
45 MW
15 MVR
13.74 MW
-1.78 MVR
2
1.000 pu
0.975 pu
5
46.69 MW
5.29 MVR
20 MW
10 MVR
47.61 MW
5.14 MVR
40.0 MW
-76.0 MVR
60 MW
10 MVR
(c)
Fig. 11. The studied five bus network: (a) without UPFC ;(b) with
UPFC at the beginning of the line, between 3rd and 4th bus; (c) with
UPFC/ESS at the beginning of the line, between 3rd and 4th bus
TABLE I
CALCULATED UPFC PARAMETERS
δB
VB
δE
VE
Part A
0.101pu
86.99o
1.017pu
-6.01o
Part B
0.091pu
87.48o
1.013pu
-4.67o
The parameters calculations impose no influence on
number of iterations for power flow solution
convergence. Also, losses can be calculated easily.
VII. INFLUENCE OF VARIOUS FACTORS ON
UPFC COVERTERS RATINGS
Various factors influence UPFC performance,
converters ratings and range of UPFC parameters
variations. These factors are studied in previous papers
for special case of two machine system [1, 8]. The
offered model can be used to perform these studies in a
real network without simplifying and the results would
be more reliable. On the contrary of two machines
system, the main advantage of real networks studies is
to consider network
n
1
2
VE (pu)
δE ( )
Ploss (pu)
0.27
72.5
1.24
-8.1
0.060
72.0
1.22
-9.5
6
33.09 MW
36.22 MVR
2
70 MW
70 MVR
150.0 MW
147.9 MVR
116%
38.43 MW
25.85 MVR
-75.99 MW
-75.38 MVR
0.95 pu
-1.23 MW
-2.82 MVR
1.07 pu
δB ( )
0.30
3
0.94 pu
111.11 MW
0.00 MVR
VB (pu)
o
1.05 pu
-2.84 MW
-6.88 MVR
TABLE II
UPFC PARAMETERS IN EACH ITERATION
o
but it is not so significant to restrict UPFC location.
UPFC can be installed in vast range of a line
considering low variations of rating and voltage UPFC
converters.
A UPFC is installed in the middle of the line between
buses 5 and 6 to study transferring power effects on
UPFC converters (see Fig. 12). UPFC converters rating
in terms of transferred power of UPFC are shown in
Fig. 13(b).
Transferring power increment results in almost linear
increment of converters rating. Therefore, converters
rating limitation affect severely on maximum
transferring power. The increment affect ignorantly
parallel converters voltage, but severely affects series
converters voltage. Series converters voltage is another
constraint for maximum transferring power.
Now, consider energy storage influence on UPFC
converters ratings. Assume that UPFC is installed
between buses 5 and 6 (see Fig. 12) and absorbs 30MW
at the receiving end and deliver the same amount plus
exiting energy storage power at another end. UPFC
converter ratings in terms of energy storage delivered
power are shown in Fig. 13(c).
1
55.52 MW
39.59 MVR
5
-3.09 MW
-5.51 MVR
34.34 MW
35.59 MVR
145.8 MW
138.7 MVR
0.058
55.95 MW
63.52 MVR
2.72 MW
-1.70 MVR
70 MW
70 MVR
0.94 pu
85%
4
70 MW
70 MVR
-14.61 MW
3
0.29
71.0
1.23
-8.6
0.060
-10.34 MVR
70 MW
70 MVR
0.92 pu
4
0.29
71.4
1.23
-8.8
0.059
5
0.29
71.3
1.22
-8.8
0.059
6
7
0.29
0.29
71.3
71.3
1.22
1.22
-8.8
-8.8
0.059
(a)
1.05 pu
3
0.97 pu
70 MW
70 MVR
150.0 MW
76.1 MVR
6
38.93 MW
24.72 MVR
2
85%
-17.17 MW
-2.64 MVR
0.059
0.98 pu
8
0.29
71.3
1.22
-8.8
1.07 pu
0.059
47.82 MW
29.37 MVR
1
-9.93 MW
17.26 MVR
5
Operational restrictions and UPFC parameters
constraints effect on UPFC performance. For instance,
in some cases, network topology-structure as well as
constraints makes UPFC unable to increase lines
transmission capacity.
UPFC can be installed in every point of a line. UPFC
location affects on converters ratings and parameters
range. Assume that UPFC is installed between buses 5
and 6 to transfer 30 MW (see Fig. 12). UPFC converters
ratings variations in terms of UPFC location in a line is
shown in Fig. 13(a). On the contrary of significant
changes of series converters rating, parallel converter
rating can be ignored. Parallel converters have
minimum rating at 70% of line sending end of the line.
Also, converters voltages increase at the end of the line,
30 MW
-100 MVR
30 MW
13 MVR
UPFC model
43.21 MW
51.34 MW
-8.40 MVR
-58.40 MW
-55.29 MVR
70 MW
70 MVR
7
30.00 MW
13.18 MVR
1.05 pu
2.70 Deg
7.23 MVR
144.4 MW
86.3 MVR
53.34 MW
49.67 MVR
1.01 pu
-6.41 Deg
4
-19.38 MW
-7.26 MVR
0.20 MW
11.93 MVR
70 MW
70 MVR
70 MW
70 MVR
0.95 pu
(b)
Fig. 12. The studied 6 bus network: (a) without UPFC; (b) with UPFC
at the beginning of the line between bus 5 and 6
Both series and parallels converters ratings almost
increase equal to injected power of energy storage
system. Therefore, converters ratings limitation restricts
energy storage system power injection. Converters
voltages vary in terms of injecting power of energy
storage system. Parallel converters variation can be
ignored, but series one increases rapidly. Voltage
constraint of series converter is another limiting factor
for injection power of energy storage system.
Another effective parameter is UPFC parallel
impedance. A 30MW UPFC is installed on a line
between buses 5 and 6 (Fig. 12) to assess UPFC
converters ratings (Fig13(d)).
[9] A.Esmaili, "UPFC efficiency improvement by energy storage
systems", MSc thesis, Mazandaran University, 2004
[10] G.W. Stagg, A.H. El-Abiad, ‘Computer Methods in Power System
Analysis’, McGraw-Hill Inc., New York, 1968
PS=30 MW , VS=1.02pu , V R=1.02pu
1
0.9
shunt conv.
0.8
Converters rating (pu)
0.7
0.6
0.5
0.4
0.3
0.2
series converter
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
UPFC locataion in line(%)
0.8
0.9
1
(a).
UPFC in middle of line , VS=1.02pu , V R=1.02pu
2.5
2
shunt conv.
Converters rating (pu)
VIII. CONCLUSION
Investigating various power flow models shows their
shortcoming and constraints. Decoupled power flow
model is modified to a comprehensive and robust one to
eliminate available defects and limitations. Model
capability to implement in available load flow programs
without changing the context is considered as a unique
property. In the proposed model, two decoupled buses
are added for each UPFC. Therefore, Jacobean matrix
dimension increases by two and convergence speed
changes, but especially in large networks this case can
be ignored. In this model, UPFC constraints and losses
are considered. Also, the model can be easily performed
in power networks and UPFC combined with ESS. The
performed simulations confirmed the two proposed
models capabilities and efficiencies in various UPFC
control strategies.
According to the investigation performed on UPFC
converters rating using the offered models in this
research, converters rating, voltages, limitations of
converters voltage and rating affect severely the
maximum transferring power. These limitations restrict
injection power of energy storage system as well.
1.5
1
series conv.
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
UPFC Sending Power (pu)
0.8
0.9
1
0.9
1
(b).
UPFC in middle of line , PS=30MW, VS=1.02pu , VR=1.02pu
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1.8
1.6
1.4
Converters rating (pu)
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1.2
shunt conv.
1
0.8
0.6
0.4
series conv.
0.2
0
0.1
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0.3
0.4
0.5
0.6
ESS Power (pu)
0.7
0.8
(c).
UPFC in middle of line , PS=30MW, VS=1.02pu , VR=1.02pu
0.8
0.7
0.6
Converters rating (pu)
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0.2
shunt conv.
0.5
0.4
0.3
0.2
series conv.
0.1
[7] A. L’Abbate, M. Trovato, C. Becker, E. Handschin, “Advanced
Steady-State Models of UPFC for Power System Studies”, IEEE Trans.
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Canada, May 2002, pp. 103-107
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Shunt reactance(pu)
0.7
0.8
0.9
1
(d).
Fig. 13-UPFC converters ratings related to : (a) location;(b)
transferring power ;(c) ESS delivered power ;(d) parallel reactance