This document summarizes a research paper on state estimation of power systems with Interline Power Flow Controllers (IPFCs). The key points are: 1) A new state estimation method is proposed that incorporates an IPFC power injection model into the conventional state estimation algorithm. 2) The IPFC is modeled as injecting both real and reactive power at the buses it connects. This power injection model represents the effect of the IPFC on power flows. 3) The proposed method is tested on the Anderson and Fouad 9-bus system and results are presented. The method allows state estimation of power systems that include FACTS devices like the IPFC.

1. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
State Estimation of Power System with Interline
Power Flow Controller
V.Gomathi1, C.Venkateshkumar2, and Dr.V.Ramachandran3
1, 2
College of Engineering Guindy, Anna University / Department of EEE, Chennai Tamilnadu, India.
Email: gomesvg@annauniv.edu, venkateshceg@gmail.com
3
College of Engineering Guindy, Anna University / Department of CSE, Chennai Tamilnadu, India
Email: rama@annauniv.edu
Abstract— Now-a-days Flexible A.C. Transmission devices have been utilized to meet a growing demand
System (FACTS) controllers are incorporated into the of the transfer capabilities due to developing wheeling
power system network to control the power flow and transactions in the deregulation environment. Some
enhance system stability. Traditional state estimation
interesting applications of FACTS devices can be
methods without integrating FACTS devices will not be
suitable for power systems embedded with FACTS
found to economic dispatch(ED), AC/DC optimal
controller. Based on the conventional power system state power flow (OPF), available transfer capability (ATC),
estimation model, a new method is proposed wherein an contract path based electricity trading, and transmission
IPFC based power injection model is incorporated in the congestion management. [2]-[3].
state estimation algorithm. Interline power flow controller The Interline Power Flow Controller (IPFC) concept
(IPFC) is one of the versatile FACTS device. The provides a solution for the problem of compensating a
proposed method is tested on Anderson and Fouad 9-bus number of transmission lines at a given substation
test system and the results are presented. while the UPFC is used as a powerful tool for the cost
effective utilization of individual transmission lines by
Index Terms— IPFC, Power Injection model, FACTS,
State Estimation, WLS. facilitating the independent control both the real and
reactive power flow. Any inverters within the IPFC are
I. INTRODUCTION able to transfer real power to any other and thereby
facilitate real power transfer among the lines, together
Flexible ac transmission system (FACTS) devices with independently controllable reactive series
enable secure operation of power systems which have compensation of each individual line. The main
to be otherwise upgraded in order to relieve load on objective of the IPFC is to optimize both real and
congested transmission lines or to optimize the system reactive power flow among multi-lines, transfer power
resources. As these devices start populating the from overloaded to underloaded lines. However, it can
transmission systems, monitoring of the system state also be utilized to compensate against reactive voltage
will require detailed models of these devices and their drops and the corresponding reactive line power, and to
integration into the existing power system applications. increase the effectiveness of the compensating system
One of these applications with a critical role in system against dynamic disturbances [4]-[6]. Hence there has
monitoring is the state estimator. This paper presents been increasing interest in the analysis of IPFC in
the formulation, solution and testing results for the power system.However; very limited efforts have been
problem of state estimation of system containing made to study the impact of FACTS devices on power
interline power-flow controller (IPFC). Due to the system state estimation. A new method is introduced to
enlargement of interconnected electric power system incorporate IPFC devices into the power state
and the increasingly complexity of electric power estimation. This paper attempts to deduce the model of
system structure, hence energy management system state estimation with IPFC using the conventional
(EMS) is critical for modern power system State power system state estimation model. A power
estimation plays an important role in EMS, which injection model that transfers the affect of IPFC
provides a reliable and consistent system data by towards the power flow to the transmission lines is
processing real time redundant telemetered and pseudo presented. This method can be integrated to the
measurements. These measurements typically consist conventional state estimation program with the
of bus voltage magnitudes, real and reactive line flows consideration of IPFC.
and power injection. Processing these real time data,
different kinds of advanced application software in II. THE STATE ESTIMATION PROBLEM
EMS are derived, such as voltage stability
analysis, security constraint and transient stability A. Formulation
analysis et al. Since the concept of flexible AC
WLS state estimation minimizes the weighted sum of
transmission systems (FACTS) was proposed by
squares of the residuals.
Hingorani in the 1860s,[1] many various FACTS
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2. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
Consider the set of measurements given by the vector z Vn is the voltage magnitude at bus n, where n= i,j.
: Z = h(x) + e (1)
δij is the difference between the voltage phase
hT=[h1(x),h2(x),…,hm(x)] (2)
hi(x) is the nonlinear function relating measurement i angles at buses i and j,
to the state vector x.
xT=[x1,x2,…,xn ] is the system state vector Gij+jBij is the ijth element of the complex bus
admittance matrix,
eT=[e1,e2,…,em] is the vector of measurement errors.
gij+bij is the series admittance of the branch
Let E(e) denote the expected value of e , with the connecting buses i and j,
following assumptions:
E(e)=0, i=1,2,…,E(eiej)=0 (3) gsi+bsi is the shunt admittance of the branch
Measurement errors are assumed to be independent and connecting buses i and j,
their covariance matrix is given by a diagonal matrix R
N is the number of buses in the system.
:Cov(e)=E[e.eT]=R=diag{�12,�22,…,�m2} (4)
The WLS estimator will minimize the following
objective function: III. INTERLINE POWER FLOW CONTROLLER
Min J(x) =(zi-hi(x))2/Rii= [z-h(x)]TR-1[z-h(x)] It is common that the Interline Power Flow
(5) Controller employs a number of dc to ac inverters in
The objective of weighting the squared differences in order to offer series compensation for each line. As a
eq(5) is to provide a mathematical way of describing new concept for the compensation and effective power
the accuracy of the meters. More precisely, the standard flow management, it addresses the target of
deviation of a meter is a statistical value that describes compensating a number of transmission lines at a given
how tightly the measurements taken are clustered substation.
around the true value. Thus, if the standard deviation is
large, the measurement is relatively inaccurate; while a A. Configuration of Interline Power Flow Controller
small standard deviation value indicates a small error Generally, the Interline Power Flow Controller
range. (IPFC) is a combination of two or more independently
controllable static synchronous series compensators
B. Measurement Functions (SSSC) which are solid-state voltage source converters
According to the previous discussion, the measured which inject an almost sinusoidal voltage at variable
quantities are represented by the vector z, and h(x) magnitude and couples via a common DC link as
represents a set of functions that depend on the values shown in Fig.1.Conventionally, series capacitive
being estimated. These functions are used to calculate compensation fixed, thyristor controlled or SSSC
the estimated values corresponding to measured values based, is employed to increase the transmittable real
z. For this study, only the bus voltage magnitudes, the power over a given line and to balance the loading of a
injected real and reactive powers, and the real and normally encountered multi-line transmission system.
reactive branch power flows will be used as the They are controlled to provide a capability to directly
quantities being measured. With exception of the bus transfer independent real power between the
voltage magnitudes, the corresponding h(x) functions
compensated lines while maintaining the desired
are nonlinear and are calculated as follows:
distribution of reactive flow among the line.
Real and reactive power injection at bus i:
N (6)
P =| Vi | ￥| V j |(Gij cos δij + Bij sin δij )
i j=1
N (7)
Qi =| Vi | ￥| V j |(Gij sin δij − Bij cos δij )
j=1
Real and reactive power flow from bus i to bus k
Pij=Vi2 (gsi+gij)-|Vi|*|Vj|(gij cosδij+bij sinδij)
(8)
Qij=-Vi2 (bsi+bij)-|Vi|*|Vj|(gij sinδij-bij cosδij) Fig.1. Simplified Schematic of the IPFC model
(9) Consider simplified schematic of IPFC model in
Fig.1, each compensating inverters is linked together at
where:
their dc terminals. With this scheme, in addition to
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3. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
providing series reactive compensation, any inverter reactances of the two coupling transformers. Fig.4.
can be controlled to supply real power to the common depicts a two voltage-source model of the IPFC. The
dc link from its own. two voltage sources, Vser are controllable in both
magnitudes and phase angles. Vser should be defined
as:
Vser = r Vi ejγ (10)
The values of r and γ are defined within specified
limits given by equations. The variables r represents
certain percent of the voltage magnitude Vi at bus i.
0 ≤ r ≤ rmax and 0 ≤ γ ≤ 2π
Fig.2. Two-Inverter Interline Power Flow Controller
transmission line. Thus, an overall surplus power can
be transferred from the underutilized lines which can
be used by other lines for real power compensation.
Evidently, this arrangement maintains the overall
power balance at the common dc terminal by
appropriate control action. An elementary IPFC scheme
consisting of two back-to-back dc to ac inverters is
used as a tool to compensate a transmission line by Fig.3. Representation of two series connected voltage sources
series voltage injection. Two synchronous voltage
sources, with phasors V1pq and V2pq, in series with The steady state IPFC mathematical injection model is
transmission line1 and 2 respectively, represent the two developed by replacing voltage source Vser by a current
back-to-back dc to ac inverters as illustrated in Fig2. source Iser parallel with a susceptance bser = 1/ Xser.
B. IPFC Power Injection Model Therefore,the series current Iser is defined by:
This section focuses on the steady-state
Iser = ─ j bser Vser (11)
modeling of IPFC for the implementation of the device
in the conventional power flow program using injection
The current source Iser can be modeled by injected
power flow IPFC model. The injection power flow
power at the three buses i , j and k which the IPFC is
IPFC model is based on the representation of IPFC in
connected as shown in Fig.4. The current sources Iser
steady-state conditions by two voltage sources each are
corresponds to the injection powers Siser , Sjser and Skser
in series with a certain reactance. A MATLAB
where:
conventional N-R power flow program has been
Siser = 2Vi (─ Iser )*
modified in order to incorporate the injection power
IPFC model in power flow program. Sjser = Vj ( Iser )*
The simplest IPFC consists of two back-to- Skser = Vk ( Iser )* (12)
back DC-to-AC converters, which in a substation are
connected in series with two transmission lines via
transformers and the DC terminals of the converters are
connected together via a common DC link as shown in
Fig.1. In the flowing section, a model for IPFC which
will be referred as IPFC injection model is derived.
This model is helpful in understanding the impact of
the IPFC on the power system in steady state.
Furthermore, the IPFC injection model can easily be
incorporated in steady state power flow model. Since
Fig.4. Representation of two series voltages sources by two currents
the series voltage sources converters does the main sources.
function of the IPFC. The injection powers Siser , Sjser and Skser are simplified
to:
C. IPFC Power Injection Model based on Two Voltage Siser = 2 Vi [ j bser r Vi ejγ]*
Source Representation = ─2 bser r Vi2sin γ ─ j 2 bser r Vi2 cos γ
Piser = ─2 bser r Vi2 sin γ
An IPFC can be represented in steady-state Qiser = ─2 bser r Vi2cos γ (13)
conditions by two voltage sources representing If we define θij = θi ─ θj and θik = θi ─ θk we have:
fundamental components of output voltage waveforms Sjser = Vj [─ j bser r Vi ejγ]*
of the two converters and impedances being the leakage
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4. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
= bser r Vi Vj sin (θij + γ ) + j bser r Vi Vj cos (θij + γ )
Pjser = bser r Vi Vj sin (θij + γ )
(18)
Qjser = bser r Vi Vj sin (θij + γ ) (14)
Table.1. Modification of Jacobian matrix by injection
Skser = Vk [─ j bser r Vi ejγ ]*
power flow IPFC model
= bser r Vi Vk sin (θik + γ ) + j bser r Vi Vk cos (θik + γ )
Pkser = bser r Vi Vk sin (θik + γ ) E (i,i) = Eo (i,i) F (i,i) = Fo (i,i)
Qkser = bser r Vi Vk cos (θik + γ ) (15) E (i,j) = Eo (i,j) F (i,j) = Fo (i,j)
E (i,k) = Eo (i,k) F (i,k) = Fo (i,k)
Based on the explanation above, the injection model of E (j,j) = Eo (j,j) ─ F (j,j) = Fo (j,j) + Pjser
two series connected voltages sources can be seen as Qjser F (j,i) = Fo (j,i) + Pjser
three dependent loads as shown in Fig.5. E (j,i) = Eo (j,i) + F (k,k) = Fo (k,k) +
Qjser Pkser
E (k,k) = Eo (k,k) ─ F (k,j) = Fo (k,j) +
Qkser Pkser
E (k,i) = Eo (k,i) +
Qkser
G(i,i) = Go (i,i) H (i,i) = Ho (i,i) +
G(i,j) = Go (i,j) 4Qiser
G(i,k) = Go (i,k) H(i,j) = Ho (i,j)
G(j,j) = Go (j,j) + H(i,k) = Ho (i,k)
Fig.5. IPFC model Pjser H(j,j) = Ho (j,j) +
G(j,i) = Go (j,i) ─ Qjser
The apparent power supplied by the two series voltages Pjser H(j,i) = Ho (j,i) +
sources is calculated from: G(k,k) = Go (k,k) ─ Qjser
Pkser H(k,k) = Ho (k,k) +
G(k,i) = Go (k,i) + Qkser
Pkser H(k,i) = Ho (k,i) +
Qkser
(16)
Active power and reactive power supplied by
converters 1 and 2 are distinguished as: IV. CO-ORDINATION ALGORITHM FOR STATE
ESTIMATION WITH INTERLINE POWER FLOW
Pser1 = r bser Vi Vj sin ( θij + γ ) ─ r bser Vi2 sin γ CONTROLLER
Qser1 = ─ r bser Vi Vj cos (θij + γ ) + r bser Vi2 cos γ +
r2 bser Vi2 The detailed solution steps of the proposed
Qser2 = ─ r bser Vi Vk cos (θik + γ ) + r bser Vi2cos γ + algorithm can be summarized as follows:
r2 bser Vi2
According to the operating principle of the IPFC, the Step 1: Input system data and telemetered
operating constraint representing the active power measurements load flow;
exchange among the converters via the common DC
link is given by Step 2: Set iteration count k = 0
Pser2 = ─ Pser1 (17)
The equality above is valid when the losses are Step 3: calculate system measurements
neglected.
Step4: Initialize the state vector v(0),e(0)
D. Incorporating IPFC Power Injection Modelinto
Load Flow program Step 5: Compute Jacobin matrix H(x(k)) with IPFC
The IPFC injection model can be incorporated in a
load flow program. If a IPFC is located between nodes Step6: Obtain ΔV(k+1) AND Δ θ(k+1) .
i, j and k in a power system, the admittance matrix is
V(k+1)=ΔV(k)+ΔV(k+1) , θ(k+1)=Δ θ(k)+Δ θ(k+1)
modified by adding a reactance equivalent to X ser
between node i and j and node i and k .The suffix o Step6: Check for convergence. If
indicates without IPFC.
The Jacobian matrix is modified by addition of max {|�v (k+1)| , |�θ(k+1)|} > € go to Step 4
appropriate injection model powers.If we consider the
linearized load flow model as: Otherwise, set k = k + 1 and go to Step 7
Step 7: Print results.
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5. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
V. TEST SYSTEM AND RESULTS power system state estimation model, this paper
introduces the model of state estimation embedded with
In this section, Anderson and Fouad 9- bus
IPFC. A power injection model that transfers the effect
test system has been used to validate the effectiveness
of IPFC on the power flow between the interconnected
of the proposed method. The IPFC is incorporated in
lines is presented. It is demonstrated that the algorithm
the buses 4, 5, and 6. The measurement data for testing
retains good convergence property as the traditional
the modified state estimation algorithm are obtained
WLS method and it possess the main merit of
using the results from power flow analysis. The results
extending the state estimation algorithm including the
of the proposed method are verified with the results
effects of Interline Power Flow Controller.
obtained from traditional state estimation method. The
solution is found to be more accurate, the
REFERENCES
computational effort is reduced and there is an
improvement in the voltage profile. The tolerance [1] SUN Guo-qiang ,WEI Zhi-nong “Power System State
assumed for convergence is 10−4. Estimation with Unified Power Flow Controller”
DRPT2008 6-9 April Nanjing China 2008.
[2] Jun Zhang and Akihiko Yokoyama “A Comparison
between the UPFC and the IPFC in Optimal Power Flow
Control and Power Flow Regulation” IEEE 2006
[3] Nursyarizal Mohd and Ramiah Jegatheesan “WLS
modification Power Systems State Estimation Embedded
with FACTS Devices” Proceedings of the International
Conference on Electrical Engineering and Informatics
Institut Teknologi Bandung, Indonesia 2007.
[4] Satish Kumar Singh, and Jaydev Sharma” A Hopfield
Neural Network based Approach for State Estimation of
Power Systems Embedded with FACTS Devices” vol.4
IEEE 2006.
[5] Bei Xu and Ali Abur ,“State estimation of System With
UPFCs Using the Interior Point Method”, IEEE
Fig.6. Anderson Fouad 9-Bus with IPFC Transactions on Power Systems, vol.19, n 3, pp. 1635-
1641 ,August, 2004.
Table. 2. STATE ESTIMATION RESULTS FOR [6] B. Xu, A. Abur, "State Estimation of Systems with
Embedded FACTS Devices," in Proc. IEEE Power Tech
9- BUS SYSTEM
Conf,vol.5 2003.
WITHOUT IPFC WITH IPFC [7] A.J. Wood, B.F. Wollemberg, Power Generation,
BUS Operation and Control, 2nd. Ed. (New York: Wiley,
NO. V/pu δ(°) V/pu δ(°) 1996,453-513).
1 1.0400 0 1.0400 0 VII. BIOGRAPHIES
2 1.0250 9.280 1.0256 8.817
Gomathi Venugopal received the Bachelors degree from
University of Madras, in 2002 and the Masters degree from
College of Engineering, Anna University, Chennai in 2004.
3 1.0250 4.665 1.0250 4.043
She is presently working as a Lecturer in College of
Engineering, Anna University; Chennai.Her fields of interest
4 1.0258 -2.217 1.0259 -2.217
include Power System control and operation, Service
Oriented Architecture and Web Services.
5 0.9956 -3.989 0.9972 -4.306
Venkateshkumar Chandrasekaran received his
6 1.0127 -3.687 1.0129 -4.464 Bachelors degree from Anna University, Chennai, in 2006.He
is presently pursuing his Masters in College of Engineering,
7 1.0258 3.720 1.0254 3.254 Anna University, Chennai.His fields of interest include Power
System Operation and Control, FACTS and Power System
8 1.0159 0.728 1.0155 0.195 Planning.
9 1.0324 1.967 1.0321 1.345
Ramachandran Veilumuthu received his Masters degree
and Ph.D in Electrical Engineering from College of
Engineering, Anna University, Chennai, India. He is currently
working as a Professor in the Department of Computer
VI. CONCLUSION Science, College of Engineering, Anna University, Chennai.
In the proposed method the state estimation of His research interests include power system reliability
engineering, network security, soft computing and Web
power system embedded with Interline power flow technology.
controller is presented. Based on the conventional
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