advantages and limitations of the interline power flow ... - PSCC

MAIN ADVANTAGES AND LIMITATIONS OF THE INTERLINE POWER
FLOW CONTROLLER: A STEADY-STATE ANALYSIS
R.L. Vasquez-Arnez
USP, São Paulo, Brazil
ricleon@pea.usp.br
F.A. Moreira
UFBA, Bahia, Brazil
moreiraf@ufba.br
Abstract – The IPFC (Interline Power Flow Controller)
main advantages and limitations whilst controlling simultaneously
the power flow in multiline systems are in this
paper presented. In order to observe such advantages and
drawbacks, a mathematical model of a two-converter
IPFC based on the d-q orthogonal coordinates was developed.
Issues like the bus voltage variation in presence of
the IPF, the effect of the transmission angle variation upon
the controlled region of the series voltages injected and
over the compensated system itself, are also presented.
Keywords: FACTS, IPFC, Power flow control, VSC
1 INTRODUCTION
Recently, particular attention was focused on the
FACTS (Flexible AC Transmission Systems) devices,
especially on controllers aimed to control the power
flow in multiline systems. One of these devices is the
IPFC (Interline Power Flow Controller) which unlike
the rest of the multiconverter controllers, GUPFC (Generalized
Unified Power Flow Controller) and GIPFC
(Generalized Interline Power Flow Controller) dispenses
the shunt VSC (Voltage Source Converter) in
charge of locally supporting and compensating the bus
voltage variations. Systems without significant voltage
variation for example, would benefit from the use of
this device. Furthermore, by properly reconfiguring its
arrangement (i.e. using some connection switches between
the VSCs and the line) it can be converted into a
UPFC (Unified Power Flow Controller) and even
adapted to the above mentioned controllers.
Previous publications on controllers of this kind discuss
topics such as its modelling, load flow control and
application to some particular systems [1]-[4]. In [5] a
method for an optimal dimensioning, sizing and steadystate
performance directed to single and multiconverter
VSC-based FACTS controllers, applied to a particular
real world reduced system, is presented. In [6] and [7]
mathematical models for multiterminal VSC-based
HVDC schemes and for the GUPFC addressing optimal
power flow methods are presented. Nonlinear solutions
applied to models of multiline FACTS controllers are
presented in [8]. In [9] the PIM (power injection model)
model for computing the power flow in a large power
system is extended to the IPFC. In [10], where the IPFC
concept has been put forward, a comprehensive study
on its operation as well as some application considerations
are presented. In [11] a control scheme of a 2-
converter IPFC based on a 3-level NPC (Neutral Point
Clamped) VSC aimed at compensating the line impedances
is presented. Reference [12], deals with the implementation
and simulation of an IPFC laboratory
model based on a four-switch single-phase converter.
Both [11] and [12] are chiefly orientated to show the
benefits attained by the IPFC. Very few references [8],
[13] have explored aspects such as the operative limitations
related to this FACTS controller. In this paper, a
mathematical model based on the d-q orthogonal coordinates
will be initially presented. Such a model will be
used to analyse the IPFC steady-state response. Thereafter,
the main limitations related to its operation within a
power system will be presented.
2 IPFC OPERATION AND ANALYSIS
Figure 1 shows the scheme of a multiconverter IPFC.
Basically, the AC side of each VSC is connected to its
respective line through a series transformer. The DC
side of the VSCs share a common circuit. For ease of
analysis, a two-converter IPFC (Figure 2) whose converters
VSC-1 and VSC-2 emulate pure sinusoidal voltage
sources (V C1 and V C2 ) will be considered. The
reader will soon notice that such a model can easily be
extended to a multiconverter IPFC scheme.
The injection of V C1 on System 1 (Figure 2) usually
results in an exchange of P se1 and Q se1 between converter
VSC-1 and the line. Also, for the sake of analysis,
the V C1,2 voltages will be split into its d-q components.
Line 1
Line 2
Series
VSCs
Line 3
VSC-1
VSC-2
VSC-3
Figure 1: Generic scheme of an IPFC
The V C1q component has predominant effect on the
line real power, while the in-phase component (V C1d )
has over the line’s reactive power. The reactive power
exchange Q se1 is supplied by the converter itself; however,
the presence of the active power component (P se1 )
imposes a demand to the DC terminals. Converter VSC-
16th PSCC, Glasgow, Scotland, July 14-18, 2008 Page 1

2 is in charge of fulfilling this demand through the
Pse1 + Pse2
= 0 constraint. Unlike VSC-1 (in the primary
system) the operation of VSC-2 (secondary system) has
its freedom degrees reduced; thus, its series voltage V C2
can compensate only partially to its own line. This is
because converter VSC-2 also has the task of regulating
the dc-link voltage. So, the P se2 component of VSC-2 is
predefined. This imposes a restriction to this line in that
mainly the quadrature component of V C2 can be specified
to control its power flow. Under this condition, the
primary system will have priority over the secondary
system in achieving its set-point requirements.
The equivalent sending and receiving-end sources in
both AC systems are regarded as stiff. The condition for
which the switch CB is closed (i.e. V 11 =V 21 ) also applies
to the analysis presented in this section.
System 1
V 11
V 12 V V P
C1
13
V
I 1 14
14
Z 11
(P
CB
se1
+P se2
) = 0
System 2
V P
C2
I 2
24
Z 21
Z 24
V 21
V 22
V 23 V 24
Figure 2: IPFC scheme used in the analysis
It will also be assumed that both AC systems have
identical line parameters. Likewise, it is assumed that
each converter injects an ideal sinusoidal waveform
with only its fundamental frequency [8], [9], [13]. The
steady-state power balance of the n number of converters
(same number of compensated lines) can be represented
by (1):
n
∑
i=
1
P 0
(1)
se _ i
=
As in our case n=2, we will have,
P + = 0
se1
Pse2 (2)
So for each line it can be written,
P
se1
= VC1d
I14d
+ VC1qI14q
(3)
P = V I + V I
(4)
se2
C2d
24d
C2q
From Figure 2, the following system equations can
be written:
V12d
= V14d
−VC1
d
− X14I14d
(5a)
V12 q
= V14q
−VC1
q
+ X14I14q
(5b)
V22d
= V24d
−VC
2d
− X
24I
24d
(6a)
V22 q
= V24q
−VC
2q
+ X
24I
24q
(6b)
I14 d
= k1( V11q
−V14q
+ VC1
q
)
(7a)
I14q
= k1( −V11
d
+ V14d
−VC1
d
)
(7b)
I
24 d
= k2
( V21q
−V24q
+ VC
2q
)
(8a)
= k −V
+ V V
(8b)
24q
( )
I
24q
2 21d
24d
−
C 2d
Z 14
where k
= 1
( X + )
,
1
11
X
14
k
= 1
( X
2
21
+ X
24
Equations (2) through (8) allow the main parameters
of the elementary IPFC to be calculated (Figure 2).
Unlike the GIPFC case addressed in [13], the unknown
variable V C2d will be a function of V C1 (specified). Once
computed the unknown variables (i.e. the d-q components
of V 12 , V 22 , I 14 , I 24 and V C2d ), the power flow in the
receiving-end of Systems 1 and 2, with or without the
effect of the series voltage, can be calculated through
(9).
*
S
1
= ( P1
+ jQ1
) = V14
I
(9a)
14
*
S
2
= ( P2
+ jQ
2
) = V24
I
(9b)
24
Note that System 1 will have two independently controlled
variables (i.e. V C1 , θ C1 ). Conversely, System 2
will only have one variable (V C2q ) to be independently
controlled.
3 RESULTS
The results shown in Figures 3 and 4 were obtained
using the mathematical model developed in Section 2,
in which θ C1 was varied from 0° through 360°. The area
inside the circle corresponds to the ideal region controlled
by VSC-1, which will be limited by the magnitude
of V C1 (V max C1 ). The series reactive compensation in
System 2 was set to be null (i.e. V C2q =0), thus, only the
V C2d component serves as a parameter through which
active power is passed from Converter 2 to 1. The way
how VSC-2 compensates to its own line, through its
available reactive compensation, will be shown in Section
3(c).
Q (pu)
0.2
0
-0.2
-0.4
-0.6
P 1
, Q 1
(System 1)
330°
75°
240° 60°
255°
θ C2= 0°
30°
300°
120°
150°
210°
P 2
, Q 2
(System 2)
θ C1 =0°
-0.8
0.4 0.6 0.8 1 1.2 1.4 1.6
P (pu)
Figure 3: P-Q plane (receiving-end) showing the operative
region of Systems 1 & 2 when V C1 =0.2 pu & V C2d =ƒ(V C1 )
For this particular case, both AC systems were assumed
to have similar transmission angles, i.e. δ 11_14 =
δ 21_24 = -30°. Should these angles be different, maintaining
the same V C1 = 0.2 pu, the results obtained will be
different. Such a case will also be analysed shortly after.
Notice how the power flow in System 2 is forced to
vary (P 2 ≅0.8pu → 1.2pu, Q 2 ≅-0.6pu → +0.1pu) on
account of helping to control P 1 & Q 1 in System 1. For
example, when V C1 =0.2 pu∠60°, with which System 1
increases its active power to about P 1 ≅1.4 pu, System 2
(straight line) will need to reduce its active power to
)
16th PSCC, Glasgow, Scotland, July 14-18, 2008 Page 2

P 2 ≅0.94 pu. As seen in these figures, for the full rotation
of the series angle (θ C1 =0→360°), the reactive
power Q 2 will experience a broader variation.
The model presented in Section 2 can also be extended
to observe the IPFC behavior, mainly the degradation
experienced by System 2, when it assists to more
than one line. Figure 4 shows the result of an IPFC
simultaneously controlling three lines such as those
shown in Figure 1. In this case, the primary systems are
constituted by Systems 1 and 3, whereas System 2 remains
as the secondary (assisting) system. The main
consideration to be done falls again onto eq. (1). In this
case n=3, then (2) will turn into:
P
se1
+ Pse2 + Pse3
= 0
(10)
The rest of the procedure will be analogous to that
developed while dealing with only 2 series VSCs (same
number of compensated lines).
Q (pu)
0.2
0
-0.2
-0.4
-0.6
-0.8
System 1
240°
System 3
30°
0°
75°
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Figure 4: (a) Three-converter IPFC, (b) P-Q plane (receiving-end)
of Systems 1, 2 and 3 when V C1 =0.2 pu∠0→360°,
V C3 =0.1pu∠0→360° & V C2d = ƒ(V C1 , V C3 )
Similarly to the conditions imposed in Figure 3, the q
component of V C2 was set to be null (i.e. no series reactive
compensation was applied to System 2). Notice that
in this case, the power flow over System 2 is significantly
degraded on account of the help provided to
Systems 1 and 3.
a) Bus Voltage Variation due to the Series Voltage
Injection – IPFC Primary System
The insertion of the series voltage in both lines of the
IPFC causes the voltages in the non-stiff buses to vary.
This variation can trespass some predefined operative
limits of the bus voltages (e.g. 0.9 pu

In this case, the operation of the series voltage will
be limited to the area below the shaded areas shown in
Figure 6(b). So, any value of V C1 within such areas will
cause overvoltage in the operative range of bus V 13 . The
same effect will occur in System 2, although this system
can utilise its available reactive compensation (through
the V C2q component) to raise or lower to a certain extent
voltage V 23 .
(b) Transmission Angle Effect over the Controlled Region
– IPFC Secondary System
It is well established that the increase/reduction of
the transmission angle causes the line current to also
increase/decrease, if the line impedance does not vary.
In this section, the effect of the transmission angle upon
the power flow of the assisting system will be shown.
Figure 7 shows the receiving-end ∆P-∆Q behaviour
corresponding to Line 2. Such results represent the
incremented power around the uncompensated case (P 0
& Q 0 ). Generally, the total power flow in both systems,
regarding the effect of V C1 & V C2 , can be expressed as
P = [ P ∆P]
0 + and Q = [ Q ∆Q]
0 + . When δ 21_24 =-30° the
uncompensated power at the receiving-end was equal to
P 0 =1.0 and Q 0 =-0.2679 pu. When δ 21_24 =0°, the reactive
power flow in the receiving-end, ∆Q 2 (Figure 7a), can
be controlled in the range ∆Q 2 =±0.4 pu, without affecting
the active power flow at all. An opposite effect
occurs when δ 21_24 = -90°, for which ∆Q 2 =0 and
∆P 2 =±0.4 pu, though the operation under both angles is
in practice remote. Figure 7(b) shows the effect of the
transmission angle upon the ∆P-∆Q plane for the condition
V C2d =0 (similarly to an SSSC – Static Synchronous
Series Compensator) with V C2q being specified. The
positive (Figure 7a), negative (Figure 7b) or even zero
slope of the control lines can be calculated through (see
also Figure 2):
*
S = V
(10)
I
2 24I
24
24
⎛ V21
− V24
+ V
=
⎜
⎝ jX
C2
⎞
⎟
⎠
(11)
In this case X = (X 21 +X 24 ). So, the d-q components of
I 24 can be written as:
⎛V21q
−V24q
⎞ VC2q
⎛ V
0 C2q ⎞
I =
⎜
⎟ + =
⎜ I +
⎟ (12a)
24d
d
⎝ X ⎠ X ⎝ X ⎠
⎛ V21d
− V24d
⎞ VC2d
⎛ 0 VC2d
⎞
I = ⎜−
⎟ − = ⎜ I − ⎟ (12b)
24q
q
⎝ X ⎠ X ⎝ X ⎠
Substituting (12) into (10) yields,
0
0
⎛ VC2q
V ⎞
C2d 0
P2 ( V24d
I
d
V24qI
q
) ⎜V24d
V24q
= ( P + ∆P2
)
X X
⎟ (13a)
= + + −
⎝
⎠
0
0
⎛ VC2q
V ⎞
C2d 0
Q2 ( V24qI
d
V24d
I
q
) V24q
V24d
= ( Q + ∆Q2
)
(13b)
= − +
⎜ +
X X
⎟
⎝
⎠
Writing ∆P 2 and ∆Q 2 in a matrix form, we obtain:
⎡ ∆P2
⎤
⎢ ⎥ =
⎣∆Q2
⎦
1
X
⎡V
⎢
⎣V
24d
24q
−V
V
24q
24d
⎤⎡V
⎥⎢
⎦⎣V
C2q
C2d
⎤
⎥
⎦
(14)
If V C2q =0 and as V C2d is a function of V C1
(V C1 =0.2pu∠0°→360°) then:
∆P V
2 24q
= −
(15a)
∆Q2
V24d
V24d
∆Q2 = − ∆P
(15b)
2
V
24q
Which draw the positive slopes of the control lines
shown in Figure 7(a).
0.4
0.2
∆Q 0
-0.2
δ 21−24
= 0°
System 1
V C1
=0.2 pu (0° to 360°)
-0.4
-0.4 -0.2 0 0.2 0.4
P
0.4
0.2
∆Q 0
-0.2
−30°
δ 21−24
= 0°
− 60°
∆
(a)
−30°
−60°
δ 21−24
= −90°
System 2
− 90°
System 2
-0.4
-0.4 -0.2 0 0.2 0.4
∆ P
Figure 7: Power flow in Line 2 (receiving-end) for several
values of δ 11_14 : (a) V C2q =0 and V C2d =ƒ(V C1 ), positive slope;
(b) V C2d =0 and V C2q =0.2 pu, negative slope
(b)
If V C2d = 0 and as V C2q =0.2 pu, then (14) becomes:
∆P2
V24d
= −
(16a)
∆Q V
2
V
24q
24q
∆Q
2
= ∆P
(16b)
2
V24d
Which draw the positive slopes of the control lines
shown in Figure 7(b).
c) Control Area of the IPFC Secondary System
Since the primary system of the IPFC behaves similarly
to a line compensated through a UPFC, its control
area in the P-Q plane will correspond to that shown in
Figure 3. Due to the inherent restrictions of the secondary
system, each value of V C2q will create parallel line
leftwards of the M-N line (if V C2q is inductive) or rightwards
of it (if V C2q is capacitive); thus, giving place to
16th PSCC, Glasgow, Scotland, July 14-18, 2008 Page 4

the skewed area shown in Figure 8. The M-N line
shown in this figure has no series reactive compensation
(i.e. V C2q = 0).
Apparently, the secondary system might have a bigger
control area than the primary system. However,
because both converters are rated with the same capacity,
this control area will be basically limited to the
same circular area as that of Line 1. For example, if we
consider point B in Figure 8, which is out of the circular
area, converter VSC-2 would not be able to fully accomplish
its compensation function on both lines. This
can be verified by comparing the boundaries of the
controlled regions, which should be equal.
For any point inside the circle, it can be verified that:
max
∆ = ( ∆P
+ j∆Q
) 0.4 pu.
S1 1 1
≤
As for point B, outside the circle, the pu value will
be:
B
∆S
2
= ∆P2
+ ∆Q
2
2
2
=
2
0.2 + ( −
0.4)
2
= 0.447 pu
This value is greater than the maximum value corresponding
to that drawn by converter VSC-1
B max
B
( ∆ S2 > ∆S1
), thus, ∆ S 2
can not be considered
as an operative point of System 2.
0.6
0.4
0.2
C
V C2q
(ind.)
M
V C2q
(cap.)
d) Transmission Angle Effect upon the Converters
This section shows the steady-state response of the
series converters when the transmission angle is simultaneously
varied. This analysis resulted also from the
model developed in Section 2. In order to observe the
effect of transmission angle, the series voltage in both
systems were kept constant at V C1 =0.2 pu ∠0→360°
and V C2q =0. Once computed the line current in each
line, eqs. (19a) and (19b) were used to compute P se and
Q se in also each converter.
*
S
se1
= ( Pse1
+ jQse1
) = VC1I
(17)
L1
V11
−V14
+ VC1
I
L1
= (18)
jX
1
from which it can be obtained:
V
C1
Pse1
= [ V11
sin ( δ11
− θ
C1
) − V14
sin ( δ14
− θ
C1
)]
(19a)
X
1
VC1
Q
se1
= [ V11cos( δ11
- θC1
) −V14cos( δ14
- θC1
) + VC1
] (19b)
X
1
Figure 9(a) shows the case when the transmission
angle in System 1 is varied (δ 11_14 = -10°, -20°, -30°)
while that of System 2 was kept constant at δ 21-24 = -
30°.
0.3
0.2
0.1
Q se
VSC - 1
-10°
-20°
-30°
∆ Q
0
System 1
0
-0.2
System 2
-0.1
VSC - 2
-0.2 -0.1 0 0.1 0.2
-0.4
N
-0.6
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
∆ P
Figure 8: Ideal control region (IPFC Secondary system) at
the receiving-end: V C2q =0→±0.2 pu, V C2p =ƒ(V C1 ) e
V C1 =0.2∠0→360°
Actually, as V C2q increases from V C2q =0→±0.2pu (inductive
or capacitive mode) the V C2d component will
decrease. Similarly to Section 3(b), the ∆P-∆Q controlled
region shown in this figure does not correspond
to the capacity of the converters, but to the incremented
power around P 0 &Q 0 in the receiving-end. Also, as V C2q
is increased (i.e. displacing the M-N line leftwards or
rightwards) the V C2d component will decrease. This
occurs so as to maintain the capacity of converter VSC-
2, which should not be trespassed. Should the M-N line
be displaced even further, for example reaching point C,
both converters will be operating as independent SSSCs
with angles 75° (inductive mode of V C2q ) or 255° (capacitive
mode of V C2q ). Thus, the active power exchange
between the converters will be zero.
B
0.6
0.5
0.4
0.3
Q se 0.2
0.1
0
-0.1
-0.2
VSC - 2
P se
(a)
VSC - 1
-10°
-0.2 -0.1 0 0.1 0.2
P se
-20°
-30°
(b)
Figure 9: Control region of converters VSC-1 & VSC-2
when V C1 =0.2 pu ∠0→360° and V C2q =0: (a) δ 11_14 = -10°, -
20°, -30° and δ 21_24 = -30°, (b) δ 11_14 = -30° and δ 21_24 = -10°,
-20°, -30°
It can be seen that the active power demand P se1 increases
proportionally to δ 11_14 . Likewise, P se2 varies
16th PSCC, Glasgow, Scotland, July 14-18, 2008 Page 5

according to δ 11_14 (blue curves) as it has to fulfil the
demand of P se1 . The reactive power Q se2 (at VSC-2)
shows a less variation compared to that experienced by
P se2 .
Once reversed this condition, that is, the transmission
angle in System 2 is varied (δ 21_24 = -10°, -20°, -
30°) while the angle of System 1 is kept constant (δ 11_14
= -30°), the reactive power Q se2 (blue curves) becomes
highly affected (Figure 9b). Conversely, the real power
of VSC-2 (P se2 ) operates nearly in the same range (-0.2,
+0.2 pu). Obviously, the variation of δ 21_24 will be also
reflected in the variation of the power flow (P 2 ) in System
2.
4 CONCLUSIONS
This paper showed the main attributes and disadvantages
characterising the operation of the IPFC whilst
controlling the power flow in multiline systems.
Issues like the power flow degradation in the system
termed as secondary and the bus voltage variation in
both systems on account of helping to manipulate the
series voltage in the primary system(s), were also addressed.
It was also shown that maintaining the bus
voltage within certain technical limits, it was the case of
voltage V 13 , imposes some restrictions to the operative
region of the series voltage (V C1 ). Some other steadystate
operative conditions such as the variation of the
transmission angle and its effect over both systems were
also analysed in the paper.
Despite the above mentioned drawbacks the IPFC,
even in its simplest form (i.e. with only two series converters)
can be very attractive and useful for relieving
congested systems.
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