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USE OF UPFC FOR OPTIMAL POWER FLOW CONTROL
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Abstract
This paper deals with optimal power flow control in electric
power systems by use of unified power flow controller
(UPFC). Models suitable for incorporation in power flow
programs are developed and analysed. The application of
UPFC for optimal power flow control is demonstrated
through numerical examples. It is shown that a UPFC has the
capability of regulating the power flow and minimising the
power losses simultaneously. An algoriithm is proposed for
determining the optimum size of UPFC for power flow
applications. The performance of UPFC is compared with
that of a phase shifting transformer (PST).
Keywords: FACTS, series connected voltage source, unified
power flow controller, PST, injection model, power flow
control, loss minimisation, optimal powerflow
1. INTRODUCTION
The possibility of controlling power flow in an electric
power system without generation rescheduling or topology
changes can improve the power system performance [ 11. By
use of controllable components, the line flows can be
changed in such a way that thermal limits are not exceeded,
losses minimised, stability margins increased, contractual
requirements fulfilled, etc. without violating the economic
generation dispatch.
Investigating the power through a transmission line shows
that reactance and phase angle control of a transmission line
are effective means for power flow control in AC
transmission systems. In principle, thyristor-switched
series capacitors (TCSC) and thyristor switched phase
shifting transformer (TCPST) could provide fast control of
PE-008-PWRD-0-01-1997 A paper recommended and approved
by the IEEE Transmission and Distribution Committee of the IEEE
Power Engineering Society for publication in the IEEE Transactions
on Power Delivery. Manuscript submitted .January 3, 1996; made
available for printing January 8, 1997.
M. Ghandhari G. Anderson
Non-Member Senior Member
Dept. of Electric Power Engineering
Royal Institute of Technology
S-100 44 Stockholm, Sweden
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active power through a transmission line. Both devices exert
a voltage in series with the line. For a series capacitor, the
inserted voltage lags the line current by 90 degrees. For a
phase shifting transformer, the inserted voltage is in
quadrature to the voltage. Recent advances in high power
technology has made it possible to implement all solid state
power flow controllers using power switching converters.
The unified powerflow controller (UPFC) is a new device in
FACTS family which consists of series and shunt connected
converters.
The unified power flow controller (UPFC) can provide the
necessary functional flexibility for optimal power flow
control. This approach allows the combined application of
phase angle control with controlled series and shunt reactive
compensation. Also, the real-time transition from one
selection compensation mode into another mode for handling
particular system conditions in an optimum manner is
attainable [2, 3,4,5].
This paper investigates the performance of the UPFC for
power flow control. A mathematical model for UPFC
which will be referred as UPFC injection model is derived.
This model is helpful in understanding the impact of the
UPFC on power system. Furthermore, the UPFC injection
model can easily be incorporated in the steady state power
flow model.
The proposed model is used to demonstrate some of the
features of UPFC for optimal power flow control
applications. This paper shows that a UPFC has the
capability of regulating the power flow and minimising the
losses at the same time. This outstanding feature can be
utilised for various power flow control applications, for
example, overload relief, loop flow minimisation, etc. Since
the size of UPFC has a great impact on power system
performance and also in view of the device cost, the optimal
dimensioning of UPFC for a specific application is quite
important. Such a subject is handled in this paper and a
dimensioning algorithm is proposed.
This paper is organised as follows: Section 2 describes the
operating principle of UPFC. Section 3 develops a steady
state model for UPFC and discusses the implementation of
the model for power flow studies. Section 4 demonstrates the
application of UPFC in optimal power flow control through
numerical examples. Section 5 is devoted to dimensioning of
UPFC.
0885-8977/97/$10.00 0 1997 IEEE
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INCIPLE OF UPFC
The unified power flow controller consists of two switching
converters. These converters are operated from a common dc
link provided by a dc storage capacitor (Fig. 1).
Shunt
transformer
Fig. 1: Basic circuit arrangement of UPFC
Converter 2 provides the main function of the UPFC by
injecting an ac voltage with controllable magnitude and
phase angle in series with the transmission line via a series
transformer. The basic function of converter 1 is to supply or
absorb the real power demand by converter 2 at the common
dc link. It can also generate or absorb controllable reactive
power and provide independent shunt reactive compensation
for the line. Converter 2 supplies or absorbs locally the
required reactive power and exchanges the active power as a
result of the series injection voltage.
3. UPFC FLOW STUDIES
In the following section, a model for UPFC which will be
referred as UPFC injection model is derived. This model is
helpful in understanding the impact of the UPFC on the
power system in the steady state. Furthermore, the UPFC
injection model can easily be incorporated in the steady state
power flow model. Since the series voltage source converter
does the main function of the UPFC, it is appropriate to
discuss the modelling of a series voltage source converter
first.
3.1. Series Conneete Voltage Source Converter Model
Suppose a series connected voltage source is located
between nodes i and j in a power system. The series voltage
source converter can be modelled with an ideal series
voltage 5 in series with a reactance X,. In Fig. 2, 5
models an ideal voltage source and represents a fictitious
voltage behind the series reactance. We have:
The series voltage source
and phase, i.e:
is controllable in magnitude
Q = rFeJy ( 2)
where 0 < r < rmaxa nd 0 < y < 276.
Fig. 2: Representation of a series connected VSC
The equivalent circuit vector diagram is shown in Fig. 3:
.,P
'ij
Fig. 3: Vector diagram of the equivalent circuit of VSC
The injection model is obtained by replacing the voltage
source E by the current source I, = - jb, in parallel with
Fig. 4: Replacement of a series voltage source by a current
source
The current sources 7, corresponds to the injection powers
S,, and SI,, where:
- -
S,, = V , ( -is )*
s,, = v/ ( I, )*
(3)
(4)
-
The injection power $, and S,s are simplified to:
- si, =Q [ jb, r vi e j r I*
= -b, rQ2 sin y- jb, rQ 2 cosy
If we define: Bij = 8, - 8 j , we have:
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=b,rV,. Vj sin 0 . , + y +jbsrVi V j c o s ( 0 o + y ) ( 6 )
( l J
Based on the explanation above, the injection model of a
series connected voltage source can be seen as two
dependent loads as shown in Fig. 5.
v;. L O vi Le,
Fig. 5: Injection model for a series connected VSC
3.2. UPFC MODEL
In UPFC, the shunt connected voltage source ( Converter 1)
is used mainly to provide the active power which is injected
to the network via the series connected voltage source. We
have:
'CONVl = 'CONV2 (7 )
The equality above is valid when the losses are neglected.
The apparent power supplied by he series voltage source
converter is calculated from:
Active and reactive power supplied by Converter 2 are
distinguished as:
PcoNv=z r b, y V,s in (0, - 0, + y)- r b, y' sin y (9)
&orjvz =-rb,y ?cos (0,-0,+y)+rb,yZcosy+rZb,y2
(10)
The reactive power delivered or absorbed by converter 1 is
independently controllable by UPFC and can be modelled as
a separate controllable shunt reactive source. In view of
above, we assume that GoNV= Ol (In Sec. 3.2, the
possibility to control GoNVis li nvestigated). Consequently,
the UPFC injection model is construcled from the series
connected voltage source model (Fig. 5) with the addition of
a power equivalent to PcoNV+, j O to node i. Thus, the UPFC
injection model is shown in Fig. 6. The model shows that the
net active power interchange of UPFC with the power system
is zero, as is it expected for a lossless UPFC.
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v;. L O vj Lej
.I
P,; = rb, y Vj sin ( 0 +~ y )
QSi =rb,r/;.2cosy
P,. = -rbs V, vj sin (e ji + y)
Qs, =-rb, V, V, cos(6,.+y)
Fig. 6: UPFC model
3.3. UPFC Injection Model For Load Flow Studies
The UPFC injection model can easily be incorporated in a
load flow program. If a UPFC is located between node i and
node j in a power system, the admittance matrix is modified
by adding a reactance equivalent to X, between node i and
node j. The Jacobian matrix is modified by addition of
appropriate injection powers. If we consider the linearized
load flow model as:
The Jacobian matrix is modified as given in Table 1. (The
superscript o denotes the Jacobian elements without UPFC).
Table 1: Modijication of Jacobian matrix
4. UPFC IN OPTIMAL POWER FLOW
The possibility of controlling the magnitude and angle of the
series voltage source in a UPFC, makes it a powerful device
for optimal power flow control applications. This section
examines, through numerical examples, some applications
which can be realised in a power system.
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60
A UPFC is assumed to be located on the line between North-
Lake in Hale network [7]. The base active power flow
through the line is about 41 MW. 40
20
0-
-20
Q [Mvarl r=0,09 - @@-)
y=90
-
y=270
y=O
[MWl
The UPFC is planned for: The results of a study to achieve minimum losses are shown
in Fig. 10. (The minimum losses are determined by varying
rand Y for a given PI. Also, the results of a study using a
phase shifting transformer (PST) is shown for comparison.
The following data for PST is selected:
rmax = 0.09p.u.,
'shunt-eans = 'series-trans = 6MVA
e Regulating the active power flow ( p in Fig. 7) by
120 MW (f50%).
Minimising the total power losses.
= tan-' rmax = 5.40
Based on the algorithm which is discussed in Section 4 the
following UPFC data is selected (It is assumed that
= 0 in this design):
Fig. 10 shows that a UPFC can regulate the power flow and
rmax= 0.0%. u., ScONVl = 4.8 MVA, S,--NV* = 6 MVA minimise the total power losses simultaneously with the
Figs. 8 show the influence of UPFC on active power flow of
the line for variations of y from zero to 277 and r from zero
properly selected control parameters. The change in the total
system losses for the base loading (41 MW) is negative(-
3.67%) and for the variation of power flow from 26 MW to
54 MW, the trend is still remained. PST can also affect the
power flow and minimise losses, but the impact is less when
compared to UPFC. This is because a UPFC yields two
choices of reactive power flow for any desired active power
flow and a given r , while the irelation of active and reactive
power flows for PST is unique.
Y Ldeg.1
0
0 90 180 270 360
Fig. 8: Variation of P against rand y
.4 20 30 40 50 60
The variation of Q against P for the same variation of r and
y are shown in Fig. 9. Fig 10: Optimum powerPow for UPFC and PST ( P~ooisss t he
total system losses for base loading and without any FACTS
device
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