Optimal Power Flow with Injection
Model UPFC Incorporated Power
System
Presented by
Vijaya madhavareddy.D
Dept. of EEE
vijayamadhavareddy@gmail.com
&
Nagarani.N
Dept. of EEE
n.nagarani@gmail.com
Malineni Lakshmaiah
Engineering College
1
Optimal Power Flow with Injection Model
UPFC Incorporated Power System
Abstract: - The unified power flow controller (UPFC) is a flexible and novel power
transmission controller, capable of controlling line flows and minimizing the
losses with out violating the economic generation dispatch. This paper investigates
the performance of injection model of UPFC for power flow control, which shows
that a UPFC has the capability of regulating the power flow and minimizing the
losses at the same time. Tests carried out on 5-bus system [5] are reported.
Keywords: FACTS, UPFC, Optimal power flow, loss minimization, and reduction of
generation cost, injection model.
1. INTRODUCTION:
Investigating the power through a transmission line shows that
reactance and phase angle control of a transmission line are effective means for power
flow in A.C. transmission systems. The possibility of controlling power flow in an
electric power system with generation rescheduling or topology changes can improve the
power system performance. By use for controllable components, the line flows can be
changed in such a way that thermal limits are not exceeded, losses minimized, stability
margins increased, contractual requirements fulfilled, etc. with out violating the
economic generation dispatch.
The concept of using solid-state power electronic converters for power
flow control at the transmission level has been known as FACTS [1]. Among a variety
of FACTS controllers, the unified power flow controller (UPFC) is the most versatile and
is chosen as the focus of investigations, which consists of series and shunt-connected
converters. The UPFC can provide the necessary functional flexibility for optimal power
flow control.
D.Z. Fang et al (2001) [4] proposed an improved injection modeling
approach for power flow analysis of UPFC embedded power system. M. Noroozian et al
(1997) [2] proposed optimal power flow control in electric power system by the use of
UPFC, where it has been shown that UPFC has the capability of regulating power flow
and minimizing power losses. Muwaffaq I. Alomoush (2002) [3] propose an exact pi-
model of UPFC inserted transmission lines, where it has been shown that insertion of
UPFC improves the economic operation of the power system.
In this paper an attempt has been made to incorporate series-injection
model of UPFC in the line between buses 3 and 4 of the 5-bus test system [5] to obtain
the optimal power flow. The test results obtained with and without incorporation of
UPFC in the line between the buses 3 and 4 are compared.
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This paper is organized as follows: section 2 develops a steady state model
of UPFC and discusses the implementation of the model for power flow studies. The case
study and the results are provided in section 3 and the conclusion drawn from this study
is given in section 4.
2. UPFC model for power flow studies:
The following section a model for UPFC, proposed by Noroozian M.
et al (1997), which will be record as UPFC injection model, is derived. This 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 appropriated
to discuss the modeling of a series voltage source converter first.
2.1 Series connected 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 modeled with an
ideal series voltage Vs in series with a reactance Xs. In figure 1, Vs models an ideal
voltage source and V1i represents a fictitious voltage behind the series reactance.
We have:
V1i=Vs+Vi
The series voltage source Vs is controllable in magnitude and phase, i.e.:
Vs=rViejγ
Where 0<r<rmax and 0<γ<2π
Vi∠ θ i Vs V1i Xs Vj∠ θ j
Iij Iji
Fig 1:Representation of series connected VSC
V1i
Vs
Vi γ
Iij
β
3
Fig 2:vector diagram of the equivalent circuit of VSC
The injection model is obtained by replacing the voltage source Vs by the current source
Is= -jbs Vs in parallel with the line where bg=1/Xs
Vi∠ θ I Xs=1/bs Vj∠ θ j
Is
Fig 3:Replacement of a series voltage source by current source
The current source Is corresponds to the injection powers Sis and Sjs, where
Sis=Vi(-Is) ; Sjs=Vj(Is)
The Injection power Sis and Sjs are simplified to:
γ
Sis=Vi[jbs r Viej ]
=-bs r V2i sin γ - j bs r V2i cos γ
If we define: θ ij=θ i-θ j, we have :
γ
Sjs=Vj [-jbs r Viej ]
=bs r Vi Vj sin (θ ij+ γ)+j bs r Vi Vj cos (θ ij+ γ)
Based on the explanation above, the injection model of a series connected voltage source
can be seen as two dependent loads as shown.
Vi∠ θ I Xs=1/bs Vj∠ θ j
Psi = rbs Vi2 sin γ Psj = - rbs Vi Vj sin (θ ji+ γ)
Qsi=rbs V2i cos γ Qsj = - rbs Vi Vj cos (θ ij+ γ)
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Fig 4:Injection model for a series connected VSC
2.2. 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:
Pconv 1 = Pconv 2
The equality above is valid when the losses are neglected. The apparent power supplied
by the series voltage source is calculated from:
γ
Sconv2 = VsIij* = rej Vi . [(Vi – Vj)/jXs]*
’
Active and reactive power supplied by converter 2 are distinguished as:
Pconv2 = r bs Vi Vj sin(θ i- θ j + γ)-r bs V2i sin γ
Qconv2 = -r bs Vi Vj cos(θ i- θ j + γ) + r bs V2i cos γ + r2 bs V2i
The reactive power absorbed or delivered by converter 1 is independently
controllable by UPFC and can be model as separate controllable shunt reactive source.
Hence, it is assumed that Qconv 1=0. Consequently, the UPFC injection model is
constructed from the series connected voltage model with the addition of power
equivalent to voltage 1+j0 to node i. Thus the UPFC injection model as shown in figure
5. The model shows that the reactive power inter change of UPFC with the power system
is zero, as is it expected for a loss less UPFC.
Vi∠ θ I Xs=1/bs Vj∠ θ j
Psi = rbs Vi Vj sin (θ ij+ γ) Psj = - rbs Vi Vj sin (θ ji+ γ)
Qsi=rbs V2i cos γ Qsj = - rbs Vi Vj cos (θ ij+ γ)
2.3 UPFC injection model for load flow studies:
The UPFC injection model can easily be incorporated in a load flow program. If a
UPFC is locate between node i and node j in a power system, the admittance matrix is
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modified by adding a reactance equivalent to Xs between node i and node j. The Jacobian
matrix is modified by addition of appropriate injection powers. If the linear zed load flow
model is considered as below:
∆P H N ∆θ
=
∆Q J L ∆ V/V
The Jacobian matrix is modified as given in table 1 (where the super script 0 denotes
the Jacobian elements with out UPFC)
Table1: modification of Jacobian matrix
H(i,i)=H0(i,i)-Qsj N(i,i)=N0(i,i)-Psj
H(i,j)=H0(i,j)+Qsj N(i,j)=N0(i,j)-Psj
H(j,i)=H0(j,i)+Qsj N(j,i)=N0(j,i)+Psj
H(j,j)=H0(j,j)-Qsj N(j,j)=N0(j,j)+Psj
J(i,i)=J0(i,i) L(i,i)=L0(i,i)+2Qsj
J(i,j)=J0(i,j) L(i,j)=L0(i,j)
J(j,i)=J0(j,i)-Psj L(j,i)=L0(j,i)+Qsj
J(j,j)=J0(j,j)+Psj L(j,j)=L0(j,j)+Qsj
3. CASE STUDY AND RESULTS
In this paper the 5-bus test system [5] is considered which consists of 5 buses
and 7 lines in which 3 generators at buses 1, 2 and 3, with bus 1 as slack bus and four
loads at buses 2, 3, 4 and 5. The total load on the system is 150 Mw+j90MVAR. The
system will be tested for the OPF, where the objective is to minimize the total generation
cost.
The cost functions, and the minimum and maximum limits of 3 generators G 1,
G2 and G3 are given by
G1:C1=200+7.0PG1+0.008PG12 $/hr, (10,85)Mw
G2:C2=180+6.3PG2+0.009PG22 $/hr, (10,80)Mw
G3:C3=140+6.8PG3+0.007PG32 $/hr, (10,70)Mw
The UPFC data are assumed :
r=0.02 and γ =900
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The results of this test system are shown in table2 for two cases: (1) case1: OPF
results with out UPFC and (2) case2: OPF results with the UPFC inserted between buses
3 and 4.
As can be seen from table 2, the power generations from generators 1 and 3 are
reduced and there is an increase in power from generator 2 with the inclusion of UPFC.
For the case when the UPFC is utilized (case2), we notice that the UPFC makes it
possible to take more power from the cheapest generator and the more expensive
generators now are dispatched back to provide power out puts less than those obtained in
case1. Compared to case 1 we notice that the total generation cost in case 2 is decreased
by $ 0.16/hr, total reactive power generation has reduced and also the total losses are
minimized .
Table2: OPF results
Case (1) Case (2)
PG1 (MW) 33.4558 33.4712
PG2 (MW) 64.1101 65.2773
PG3 (MW) 55.1005 53.9122
Total Loss (MW) 2.66645 2.66079
Total Gen. (MW) 153.051 152.982
Total Gen. (MVAR) 73.230 72.518
Total Cost ($/hr) 1599.97 1599.81
Table 2: Case (1): OPF results with out UPFC.
Case (2): OPF results with the UPFC inserted between bus3 and bus 4.
4. CONCLUSIONS
The injection model of UPFC incorporated in one the lines of the power system
was proposed. The capability of UPFC in optimal power flow applications was
demonstrated and the results for OPF with and with out UPFC incorporated in the line
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between the buses 3 and 4 of 5-bus system were compared. It was shown that a UPFC
can be incorporated in a poser system to minimize the total losses and the cost of
generation.
REFERENCES:
1.N.G. Hingorani and L.Gyugyi, Understanding FACTS, Newyork, IEEE Press, 2000
2. Noroozian M., Angquist L, Ghandhari.M, Anderson. G, ‘Use of UPFC for optimal
power flow control’, IEEE Trans. On power Delivery, Vol. 12, Oct 1997, pp 1629-1633
3. Muwaffaq I. Alomoush, “Exact pi-model of UPFC-Inserted Transmission Lines in
power flow studies”, IEEE Power Engg. Review, Dec. 2002.
4. Fang.D.Z, Fang .Z, Wang .H.F, ‘Application of the injection modeling approach to
power flow analysis for systems with unified power flow controller’, International
Journal on Electric Power and Energy Systems, Vol. 23, 2001, pp 421 – 425.
5. Hadi Saadat, ‘Power System Analysis’, 2002, Tata McGraw-Hill edition.
