Power System Tracking and Dynamic State Estimation
by
Amit Jain, Shivakumar N. R.
in
IEEE PES Power Systems Conference Exposition (PSCE) 2009
Report No: IIIT/TR/2009/213
Centre for Power Systems
International Institute of Information Technology
Hyderabad - 500 032, INDIA
March 2009
POWER SYSTEM TRACKING AND DYNAMIC
STATE ESTIMATION
Amit Jain, Member, IEEE and Shivakumar N. R.
Abstract-- State estimation is a key Energy Management System
(EMS) function, responsible for estimating the state of the power
system. Since state estimation is computationally expensive, it is
not easy to execute it repetitively at short intervals, which is a
requirement for real time monitoring and control. Hence in order
to obtain a computationally inexpensive real time update of the
state vector, tracking state estimation algorithms have been
proposed and discussed in various research papers available in
the literature. Tracking state estimation provides a fast real time
update on the state of the power system with out any physical
modeling of the time varying nature of the system. Dynamic state
estimation models the time varying nature of the system, which
allows it to predict the state vector in advance. Hence proves to
be a major advantage in security analysis and other control
functions. Various techniques for tracking and dynamic state
estimation are available in the literature. This paper presents a
bird’s view on different methodologies and developments in both
of these techniques based on our comprehensive survey of the
available literature.
Index Terms -- Dynamic state estimation, kalman filter, phasor
measurement unit, power systems, square root filter, state
estimation, tracking state estimation.
A
I. INTRODUCTION
S the power system grows larger and more complex, real
time and monitoring and control becomes very
significant in order to achieve a reliable operation of the
power system. The energy management system functions are
responsible for this task of monitoring and control. State
estimation forms the back bone of the energy management
system by providing a real time data base of the state of the
system for using in other EMS functions [1]. Hence an
efficient and accurate state estimation is a pre requisite for an
efficient and reliable operation of the power system.
The vector consisting of bus voltage magnitudes and phase
angles is called the state of an electric power system. Ever
since the concept of state estimation was introduced in to the
field of power systems, by Schweppe et al [2]-[4], in the early
1970s, numerous methods have been proposed to calculate
the state vector of the power system. The state estimation for
Dr. Amit Jain is an Assistant Professor with the Power System Research
Center at the International Institute of Information Technology (IIIT),
Gachibowli, Hyderabad, India (e-mail: amit@iiit.ac.in).
Shivakumar N. R. is currently with ABB, Corporate Research in Bangalore,
India. (e-mail: nrshivakumar@gmail.com)
a power network involves, collecting the real time
measurement data, which includes line flows, injection
measurements and voltage measurements, through the
SCADA and calculating the state vector, using predefined
state estimation algorithms. If the state vector is obtained for
an instant of time k, from the measurement set of the same
instant of time, then such an estimator is called the static state
estimator. In order to know the state of the power system
regularly, this process of calculating the state vector is
repeated at suitable intervals of time. Static state estimators
are widely used in power systems and play a very important
role for the reliable operation of the transmission and
distribution systems.
Under normal conditions, power system is said to be a
quasi-static system and hence changes slowly but steadily.
Hence in order to have a continuous monitoring of the power
system, state estimation must be performed at short intervals
of time. But as the power system expands, with addition of
generations and loads, the system becomes extremely large
for the state estimation to be carried out at short intervals of
time as it consumes heavy computing resources. Hence a new
technique called “Tracking State Estimation” was developed,
wherein the state estimate once calculated, is simply updated
for the next instant of time, with new set of measurement data
obtained for that instant, instead of again running the static
state estimation algorithm fully. Tracking estimators help the
EMS to keep track of the continuously changing power
system without actually performing the whole state
estimation. This allows continuous monitoring of the system,
without excessive usage of the computing resources. Hence
tracking state estimation plays an important role in the energy
management system.
The simplest way of following the changes in the system is
tracking. But tracking does not include any explicit physical
modeling of the time behavior of the system [5]. This allows
room for another set of algorithms called the “Dynamic State
Estimators” (DSE), where the actual physical modeling of the
time varying nature of the system is used. These algorithms
have dual advantages of being more accurate and possessing
the ability to predict the state of the system one step ahead.
That is, from the knowledge of the state vector at an instant of
time “t”, and the physical model of the system, the DSE
predicts the state of the power system at the next instant of
time “t+1”. This forecasting ability has tremendous
advantages in performing security analysis and allows more
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time for the operator to take control actions [5]. Hence DSE
algorithms form an important branch of state estimation
techniques, with a potential to impact the very nature of
operation of the real time monitoring and control.
This paper presents a review of the developments in
tracking and dynamic stat estimation techniques based on our
survey of research papers available in literature on these
topics. In our knowledge, no such comprehensive survey has
been done for the review of tracking and dynamic state
estimation techniques and any work in that direction will be of
great importance to the power engineers working on these
topics. We have done a comprehensive survey of the literature
available on tracking and dynamic estimation techniques and
in this paper an attempt has been made to give an overview of
the various algorithms, their applications and future trends, on
these topics.
process all the measurements at one go i.e. the measurements
are read in to the state estimation program as one vector. This
method is called the snap shot processing of measurements.
But if the rate of processing the measurements is greater than
τ, then by the time the entire set of data of data is scanned,
the power system would have changed, rendering the estimate
redundant. Hence we process the measurements as and when
they arrive in to the control center and update the estimate.
This method is called the sequential processing of
measurements [5], [7].
II. TRACKING STATE ESTIMATION
As mentioned earlier, the power system is considered to be
a quasi static system. Hence the changes in the system occur
slowly. It means that the state may not vary much in a short
span of time. But some times it becomes very important to
have a close monitoring of the system, like during the picking
up of load by a generator or during some contingency etc [5].
The SCADA systems, which enable the real time monitoring,
and control of power systems capture the field data through
sensors and deliver them to the control center at regular
intervals of time. In order to have a real time monitoring
system, state estimation must be performed as and when every
new data set arrives. But as state estimation is
computationally heavy (especially as the system size gets
bigger), a lot of control centers will not have sufficient
computing resources to perform an accurate and fast state
estimate at such a high frequency. But if the duration between
two estimates is too large, it results in a week co-relation
between the estimated states, rendering the bad data detection
very difficult [5]. Hence tracking state estimation is used to
in order to give the estimation result with a delay and to keep
up with the result [6]. The difference between the static and
tracking estimators can be understood by the block diagram
[7] shown in Fig. 1. F. C. Schweppe, who is a pioneer in the
development of static state estimation techniques [2]-[4], was
also one of the first to discuss the idea of tracking state
estimation in his paper in 1970 [8].
Tracking state estimator merely adds to the existing value
of the state vector to give the estimate at a delayed instant and
does not need the full execution of the state estimation
algorithm at that instant. Hence tracking allows easy and
fairly accurate monitoring of the power system in real time.
A. Processing of Measurements
The measurements that arrive in the control center through
the SCADA system can be processed using two methods. If
the rate of scanning an entire set of measurements at a given
point of time is lesser than the minimum amount of time the
power system takes to change its state (τ), then we can
Fig. 1. Comparison between static and tracking state estimators
B. Mathematical modeling
The measurements obtained through the SCADA system
include, injection measurements, line flow measurements,
voltage and some times current magnitude measurements.
These measurements have to be represented by a
mathematical model in order to be processed by the
estimation algorithm. The measurement vector is represented
as:
(1)
Z = Hx +ν
Where Z is the measurement vector (m x 1), H is the
Jacobian of measurement function with respect to the state
vectors (m x n), “x” is the state vector (n x 1) and “ν” (m x 1)
is the zero mean Gaussian error factor in the measurement.
Here “m” is the number of measurements and “n” is the
number of states.
Since the tracking state estimation, unlike the static state
estimation has a time factor attached with it, we next have to
consider the mathematical model for the time update of the
state vector. As we have assumed that the power system state
changes very little in a short span of time, we can simply
update the old estimate of the state (at the previous instant of
time) to obtain the new value of state at an instant, after a
short span of time interval. For small time frames, the state is
assumed to change linearly and hence if we know the estimate
( xˆk ) at the instant of‘t’, and with the arrival of measurements
at t+1’ (t+1 = t + Δ t), we can simply update xk , as:
xˆ
k +1
= xˆk + Δx
(2)
Here Δx represents the change in the state due to the changes,
power system undergoes during the time interval between ‘k’
and ‘k+1’ instants. The formula for Δx depends on the
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method used for tracking state estimation. If a simple WLS
method is used, then it is given by:
Δx = Gk−1 H kT R −1[Z k +1 − h( xk )]
(3)
Substituting this in equation (2), we get:
xˆ
k +1
= xˆk + Gk−1 H kT R −1[ Z k +1 − h( xk )]
(4)
−1
Where G = [ H k R H k ] is called the Information Matrix,
T
which remains constant. Hence the computationally heavy G
matrix and its inverse are calculated only once, while the
estimate is updated as and when the new measurements
arrive. It can clearly be seen, that tracking estimation allows
an easy update to the existing state vector without much
computationally complex operations.
Tracking estimation plays its role in between any two
predefined execution instants of static estimation. That is, the
static state estimation will be performed in the control center
at regular intervals or when there is sufficient change in the
power system. But these two instants are separated by a large
amount of time. Tracking estimation helps the control station
to monitor the power system in between these two instants of
time. More over, as seen in the equations above, tracking
helps to get a real time update of the system with out actually
performing the entire state estimation. The concept of
tracking views the estimator as a digital feedback loop which
uses the new measurements to obtain new estimates, by
correcting an old estimate by a feed back gain signal,
operating through a gain matrix [8].
C. Methods of calculating
Δx
Various methods have been proposed to calculate the
update vector or the Δx vector. The WLS method, which is
one of the widely used techniques of calculating the update
vector is as discussed above. In EHV networks, the
decoupled nature of the power system states has been widely
used to simplify calculations in the static state estimation. It
can be easily extended to tracking state estimation as well. In
such a case the Δx vector will be split in to two parts, the
active part representing the voltage angles and the reactive
part representing the voltage magnitudes. This is shown as
below [6].
(5)
Δθ k = [ H PT R −1 H P ]H PT RP−1[ Z P − h( xk )]
ΔVk = [ H RT R −1 H R ]H RT RR−1[ Z R − h( xk )]
(6)
Where the suffix ‘P’ represents the active set and suffix “R”
represents the reactive set. Decoupled estimators are faster,
but somewhat less accurate, although reasonably good, in
comparison with the fully coupled estimation algorithms.
E. Handschin et al [9] suggested associating lesser weight
values to measurements with large residuals, to improve the
performance of the bad data in state estimation. D. M. Falco
et al [6] have suggested that this method can also be
successfully extended to tracking state estimation to improve
the performance under the presence of bad data.
Linear Programming (LP) techniques used in static state
estimation are suggested for tracking state estimation as well.
In [6], the authors extend one of the LP methods available in
literature where, the sum of the moduli of measurement
residuals is minimized. Though the filtering capacity of this
technique is not as good as WLS, it performs better under the
presence of bad data and hence much more robust.
W. W. Kotigua [10] discusses Least Absolute Value
based tracking algorithm. LAV estimation has the property
that the final estimates interpolate a few of the measurements.
Hence it has better bad data rejection properties. More over,
because of its interpolating feature, the tracking estimator can
be updated easily based on the situation, whether interpolated
measurements or non-interpolated or both measurements have
changed. If only non-interpolated measurements have
changed, then the update involves some simple additions else
it involves some calculation. Nevertheless the calculation can
still be carried out faster as the Jacobian matrix in this case is
a very sparse.
S. C. Tripathy et al [11] have used the Hessian matrix
approach to update the state vector. Where Δx is given by:
Δx = M k−1H kT R −1[ Z k +1 − h( xk )]
(7)
One can clearly see that the information matrix G is replaced
by M, which is called the true Hessian matrix. The authors
use the Brown Dennis method to obtain the true Hessian
matrix. Improved convergence even in case of multiple loss of
information or when only injection measurements are used is
the advantage of using this particular technique.
A.K. Sinha et al [12] proposed a tracking estimator for
both AC and DC systems, which uses the Tailor’s series
expansion of “h(x)” up to the second order term. This is a
constant gain matrix technique (for a given topology) and
hence helps in faster convergence
Another important technique is the method of tracking by
sequential processing of data. As discussed before, when the
time to scan all measurements is greater than the time for the
system to change its state, then some of the previously
mentioned techniques (snap shot techniques) fail to track the
system accurately. A sequential time scanning based tracking
estimator is needed for that purpose. The expression for time
update of the system in such a scheme is given by [5]:
xˆ k +1 = xˆk + K k +1[ Z k +1 − h( xk )]
(8)
−1
Where, K k +1 = Pk H k +1{H k +1 Pk H k +1 + Rk +1}
T
T
(9)
Where, Pk is Information Matrix at the instant of time k, Hk+1
is a row vector of partial derivatives corresponding to
measurement Zm+1, R is the error covariance of the
measurement corresponding to Zm+1 and K is the gain vector.
The advantage of this scheme is that, it allows faster update of
the system than the snapshot processing by converting the
inversions involved in the update equations to scalar
inversions. Hence this technique is very well suited for online
implementation.
Various methods of tracking state estimation for power
systems and their uses have been discussed so far. A brief
summary of the advantages of tracking state estimators is as
below:
• Continuous tracking of the system helps the system
operator to take better decisions, in case of an
emergency.
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•
•
•
Techniques proposed are computationally lighter and
hence can be easily implemented online
Some of the tracking estimation techniques proposed,
perform well even under loss of information, bad data or
ill conditioning hence make the system more robust.
If scanning of measurements takes longer time (especially
in large networks) sequential processing techniques can
be used to obtain real time update of the system.
III. DYNAMIC STATE ESTIMATION
An easy way of following the changes in a power system
on a real time basis is by using the tracking state estimation
techniques. But these techniques, though computationally
very efficient, do not use any physical modeling of the time
varying nature of the power system [5]. Hence may not be as
accurate as desirable. Lack of any physical modeling also
results in one of the main drawbacks of a tracking state
estimator, which is the lack of the ability to predict the state
vector in advance. Dynamic state estimation uses the present
(and some times previous) state of the power system along
with the knowledge of the system’s physical model, to predict
the state vector for the next time instant. This prediction
feature of the DSE provides vital advantages in system
operation, control, and decision-making. It allows the operator
more time to act in cases of emergency, helps in detection of
anomalies, bad data etc [5]. The main steps involved in DSE
algorithms to achieve an optimized estimate of the state
vector are presented below. Throughout the discussion, “k” is
used to suggest the present instant of time and “k+1” to
suggest the next instant of time.
A. Mathematical Modeling
This is the first step in DSE and involves the identification of
correct mathematical model for the time behavior of the
power system and calculation of the corresponding
parameters. The general mathematical model used for a
dynamic system is given by [1], [13]:
xk +1 = f ( xk , uk , wk , k )
(10)
Where, k is the time sample, x is the state vector, u is the
control actions, w represents the uncertainties in the model
and f represents the non-linear function. But such a model is
extremely complex, costly and impractical. Hence certain
assumptions are made to ease the implementation (some have
already been mentioned earlier). They are:
• The system is quasi static and hence changes extremely
slowly.
• Time frames considered are small enough, for the usage of
linear models to describe the transition of states between
consecutive instants of time
• The uncertainties are described using white Gaussian noise
with zero mean and constant covariance Q.
Considering these assumptions, we can obtain a generic linear
model for the DSE as:
xk +1 = Fk xk + Gk + wk
(11)
Here Fk is the function representing the state transition
between two instants of time, Gk is associated with the trend
behavior of the state trajectory and wk is the white Gaussian
noise with zero mean and covariance Q [1], [13].
B. Parameter Identification
Fk, Gk and Q are the parameters to be calculated online to
evaluate the dynamic model shown in (11). Debs and Larson
[13], credited with the seminal paper on DSE, and Nishiya et
al [14] have assume a simple linear model with Fk assumed to
be an identity matrix and Gk assumed to be zero. But this
makes the estimator very simplistic and hampers the
forecasting ability of the estimator [1]. In the model proposed
by Debs and Larson [13], the change in state vector is
considered to be so small that it is replaced by a zero mean,
white Gaussian noise. Hence the equation (11) reduces to:
xk +1 = xk + wk
(12)
Other authors in [15]-[17] etc have also used similar
mathematical models for describing time update of the state
vector.
Linear Exponential Smoothing (LES) technique has also
been found to be a widely used technique for this purpose.
Authors in [5], [17], [18] and [19]-[23] have all used the
Holt’s LES technique [24] to obtain the values of Fk and Gk.
In this case the equation (11) is reduces to a form:
xk +1 = Fk xk + Gk
(13)
The next parameter to be identified is the error
covariance Q. Under normal operating conditions of a quasistatic power system, the Fk and Gk are adjusted such that the
value of Q almost remains constant or varies with in a very
small range of values or at a constant noise level. This value
of Q can be obtained by offline simulation studies [5], [22].
The other parameter to be modeled is the measurement
function, which helps to observe the system. The most
common measurement model used in the literature is:
(14)
Z = h( x ) + ν
Most of the techniques linearise the above measurement
model and use the equation after linearization as shown in (1).
C. State Prediction or State Forecasting
State forecasting is the next step in DSE where, the nodal
voltages or the measurements at the next instant of time are
predicted. State vector corresponding to these predicted
values is called the predicted state at the instant k+1. The
forecasted state vector is obtained by performing a
conditional operation on equation (11) [5], [22]. The
forecasted state vector, along with its error covariance is
given by:
xk +1 = Fk xˆk + Gk
(15)
Where, x is the predicted value at instant k+1. If Σ k is the
covariance of the estimate at k, then the covariance of
predicted value is given by:
M k +1 = Fk Σ k FkT + Qk
(16)
Many other techniques can be used to predict the state
vector. Some authors have also used Artificial Neural
Networks (ANN) and Fuzzy Logic techniques [19], [20] to
predict the future values of parameters. Other techniques like
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auto regression and Box & Jenkins method have also been
used as mentioned in [1].
D. State Filtering
Once the predicted state vector for the next time instant
(k+1) is obtained, it can be purified as and when the
measurements arrive at the instant “k+1”, to obtain an
optimized and a higher quality estimate for the instant k+1.
The most commonly used filtering technique is the kalman
filter technique [13], [25]. Since the measurement vector is
non linear in nature, Extended Kalman filter is used in most
cases. As the predicted state vector is used for obtaining the
final estimate in DSE, the objective function is taken as a sum
of measurement residuals and the predicted state vector
residuals. Hence, the objective function becomes:
J ( x) = [ z − h( x)]T R −1[ z − h( x)] + [ x − x ]T M −1[ x − x ]
(17)
Where, M is the covariance of the predicted state vector.
Minimizing this objective function will yield an expression for
the update of the state vector as:
(18)
xˆk = xk +1 + K k +1[ Z k +1 − h( xk +1 )]
Where K = ΣH T R −1 = [ H T R −1 H + M −1 ]−1 H T R −1
(19)
Here H is the Jacobean of h(x) evaluated at xˆ k , ∑ is the
covariance of the estimated state vector and M is the
covariance of the predicted state vector. The term K is called
the Kalman gain, which acts as the gain matrix for the
measurement residuals at instant k+1. The measurement
update is carried out either for the entire measurement set or
for each such sequential measurement. Once all the
measurements at that instant have been processed, the entire
procedure (time and measurement update) is repeated again,
by replacing time instant k with k+1.
The authors in [5], [13]-[16], [19], [21]-[23], [26] and [27]
have all used the Kalman filter or techniques based on
Kalman filter for their DSE algorithms. Other techniques have
also been proposed and implemented in the literature, though
Kalman filter techniques seem to dominate in most of the
DSE algorithms.
As shown in Eq. (18), the filtering step improves up on
the predicted values to obtain an accurate estimate with the
help of measurements at the instant k+1. The equation (18) is
quite similar to the tracking state estimator equation. But the
essential difference between the two is that, on the RHS we
have xk +1 (the predicted state vector) being improved up on
instead of xˆ k (state vector at previous instant) as in case of
tracking state estimation. Hence it is the ability to predict the
state vector, which differentiates the dynamic and tracking
state estimators.
The advantages of using a predicted state vector in filtering
are that it provides additional measurement redundancy,
reduces the effects of bad data and reduces uncertainty levels
of the final estimated values [1].
IV. ALTERNATIVE FORMULATIONS OF DSE
So far the basic dynamic state estimation technique
available in the literature has been presented. Now we can
look various other techniques, which try to improve up on the
existing technique or have provided a new direction to it.
As discussed earlier, the nonlinear measurement function
is approximated to a linear model in the conventional DSE.
Hence to take care of the error arising due to this, J. K.
Mandal et al in [27] have proposed two schemes to
incorporate non linearities in to the kalman filter based DSE.
In the first method, local iterations are carried out during the
calculation of measurement residuals, at each time sample.
This increases the reference trajectory and hence gives a
better estimate in presence of nonlinearities. In the second
scheme the Tailor’ series expansion of the measurement
function is retained until the second order in rectangular co
ordinates. This helps in retention of full nonlinearity as the
measurement function is related to state vector through
nonlinear quadratic functions [27].
Another method of tackling the problem of non-linearities
has been proposed by Sakr. M. M.F et al in [28], [29]. Here
instead of linearising the measurement vector, a nonlinear
transformation of the measurement vector is carried out. This
transformation is carried out at each node in three different
steps. Once the transformation is completed, the measurement
vector will be related to the state vector by a constant, sparse
matrix, and all linearization errors would be nullified. This
method is also extremely useful in anomaly detection.
The above technique has one difficulty that the
measurement covariance matrix (R) is non sparse and hence
computationally intensive. Hence the authors propose another
method called a two level estimation technique [15]. Here, in
the first level, called the low level estimation, the overall
network is divided in to several small sub systems, which have
small number of buses, and hence there will be no
computation problems related to calculation of R. The next
level of estimation, called the upper level estimation, is only
for coordination among the various sub systems to obtain a
single state vector for the entire system. This technique is
comparable to single level estimator in accuracy, but is much
faster and in most cases the algorithm converges in the first
iteration.
The Kalman filter method has another disadvantage that
it cannot handle large changes in the load and generation.
Hence, K. R. Shih and S. J. Huang in [17], [21] have proposed
an algorithm where the weight vector Wk is replaced with the
term Wk e
−| z − h ( xk )|
. If the load variation is large, the weight
associated with that measurement automatically gets reduced
as the term ‘|z-h(x)|’ appears as a negative exponential term.
Under normal conditions, the value of the residual remains
insignificant, making exponential term close to 1 and allowing
normal weights for the measurements.
Another interesting Kalman filter based DSE technique,
described and analyzed by Da Silva et al in [23], can be found
in [30] and [31]. The technique is primarily used by Da Silva
et al to compare the results of their proposed technique in
[23] with those in [30] and [31]. This technique uses a model
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based on equation (13), to represent the time variation of the
system. To reduce the dimension of the problem, Fk is
assumed diagonal and its elements are used to define a
parameter vector ck . A model for time evolution of ck is
defined based on the measurement model. Then the Kalman
filter technique is used to find out, the value of ck . Once ck
is found, we can calculate the value of Fk based on which the
State-forecasting step is carried out. Once the predicted state
vector is obtained, the Kalman filter technique is applied in
order to filter the predicted state vector and obtain the
estimated state vectors.
So far we have looked at Kalman filter based techniques,
But Isabel et al in 1994 proposed a Square Root Filter (SRF)
for DSE instead of Kalman filter [18]. They used the linear
exponential smoothing for calculating the predicted state
vector and used the SRF for filtering the predicted state vector
and obtaining the optimized state vector. The SRF technique
reduces the uncertainty level in measurements, saves time and
computer memory as compared to the traditional kalman filter
technique.
The kalman filter based techniques assume Gaussian
distribution of noise. But frequently, the noise distribution
deviates from the assumed model resulting in outliers. The
performance of kalman filter based techniques degrades in the
presence of these outliers. Hence, to counter this, G.
Durgaprasad et al [32] and S. S. Thakur et al [33] have come
up with a robust dynamic estimation technique based on Mestimation. The modeling is based on the assumption that the
complex bus voltage at a given point is not only dependent on
the previous voltage level but also on the latest available
voltage change at the buses to which it is connected. The two
essential features based on which the technique has been
developed are realistic modeling based on nodal analysis and
M-estimation to have robust filtering. The M-Estimation
technique reduces the uncertainty level under bad data
conditions, uses a filtering technique which is more effective
in presence of outliers and is also easy to implement in
comparison to the conventional kalman filter based
techniques.
The ability of artificial intelligence techniques in
prediction and pattern recognition can be put to good use in
DSE. A. K. Sinha and J. K. Mandal [19] have proposed an
Artificial Neural Network (ANN) based DSE algorithm which
is based on the popular Short Term Load forecasting (STLF)
technique. Since the bus loads are the driving factors of
system dynamics, ANN is used to predict the loads at all
buses. From these values the generations at various buses is
also calculated. Once the injections at various buses are
known, it is transformed in to complex bus voltages through
load flow solution. These predicted state vectors are in turn
used in the filtering stage to obtain accurate state estimates.
To counter the linearization errors in Kalman filter based
techniques, the nonlinearities in the measurement were taken
in to account. But this resulted in increased computation time.
Hence to overcome these problems a sliding surface enhanced
Fuzzy logic based technique has been proposed by Jeu-Min
Lin et al in [20]. The sliding surface enhanced fuzzy control
approach to DSE is found to have a higher computational
performance than other methods.
V. PMU BASED DYNAMIC STATE ESTIMATION
In the past two decades a new measuring device called the
Phasor Measurement Unit (PMU) has been developed. Its
advantage lies in the fact, that it can measure both voltage and
current phasors at the installed bus. More over, PMU
measurements are much more accurate than the normal
SCADA measurements. The importance of PMUs can be
gauged by the fact that for the first time both voltage
magnitude and voltage angular measurements could be
obtained directly from PMU. With their high accuracy of
measurement and their ability to directly measure the voltage
phasor, the PMUs are destined to play an important role in
modern day state estimators.
Hui Xue et al. [34] have proposed a technique which
predicts the load flow data at the next instant of time by a
historical data base and combines the PMU data at the next
instant of time for dynamic state estimation of power systems.
Another method presented by the authors in [35], [36] uses
the model proposed by Leite da Silva et al. [23] for the
implementation of PMU based DSE. The DSE technique uses
the Holts double exponential smoothing technique for
predicting the state vector one timestamp ahead and the
extended Kalman filter technique for filtering. To understand
the impact of the PMUs on the DSE, it is important to
understand how the location and the weightage associated
with the PMU measurements affect the estimation procedure.
From the literature it can be seen that PMU measurements are
in general, given a weightage of a few hundred times the
normal SCADA measurements. Hence, in the study presented
[35], PMU measurements are given a weightage of around
100, 200, 400 and 1000 times the normal SCADA
measurements and tested for their effect on the estimation
process. The other implementation and simulation details can
be found in [35].
The paper [35] clearly shows that the PMU based DSE
greatly reduces the estimation errors in comparison to the
case of DSE with no PMU. To obtain a clear of view of how
the addition of PMU affects the error percentages in the
predicted and filtered states, the results of the study on the
variation of the average estimation error when PMU was
placed at each bus of the system with the weight of PMU
measurements being fixed at 100, is as shown in Fig. 2 and
Fig. 3.
From the graphs shown in Fig. 2 and Fig. 3, it is seen that in
most of the cases the error in the predicted angular estimates
of the PMU based DSE is much lower than the filtered values
of no PMU case. This again has a direct impact on the
security analyses performed at the control center, since better
quality of predicted estimate means more accurate prediction
of security risks and hence, enables better risk evading
strategies.
The results also show that location of the PMU is important
to obtain a better estimate. Though a PMU at any location
provided more accurate estimate than the case when there was
no PMU, there are certain PMU locations in the network,
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which seem to provide much higher reduction in error than at
any other bus in the network. Better PMU placement
algorithms can be followed to quickly find out the optimal
location of PMU, especially in the case of large networks.
•
It allows security analysis to be carried out in advance
and hence allows the operator to have more time during
emergencies.
• It helps to identify and reject bad data and hence
improves the estimator performance.
• In cases where pseudo measurements are to be used, DSE
readily provides high quality values and hence avoids ill
conditioning.
• DSE can be used for data validation, as the states are
predicted one time stamp before.
Similarly, with the help of the predicted state vector we can
identify sudden changes in the system, topological errors and
other anomalies.
VII.
Figure 2. Variation of predicted and filtered voltage magnitude estimate errors,
when weight of PMU is fixed at 100
Figure 3. Variation of predicted and filtered voltage angular estimate errors,
when weight of PMU is fixed at 100
Simulation studies with multiple PMUs have also been
presented in [35]. An important observation in the study of
multiple PMUs is that the reduction in error with increase in
the number of PMUs seems to saturate after a particular
point. Though a great reduction in estimation error can be
obtained from a few PMUs, the optimal number of PMUs for
a given network should ideally be chosen from the point of
view of both state estimation accuracy and observability of
the network. This helps to improve the ability of the estimator
to detect bad data in the measurement set, especially in
critical SCADA measurements.
Since DSE can play a major role in monitoring and risk
prediction with their unique ability of predicting the state
vector one time stamp ahead, their association with phasor
measurement units is a great advantage for real time
monitoring, detection and control of power systems. From this
point of view the PMU based DSE techniques are of extreme
importance for the modern day energy management systems.
VI. ADVANTAGES OF DYNAMIC STATE ESTIMATION
The ability of predicting the state vector one step ahead is a
very important advantage of DSE. Some of the advantages of
that includes:
CONCLUSIONS
Real time monitoring and control of power systems is
extremely important for an efficient and reliable operation of
a power system. Sate estimation forms the backbone for the
real time monitoring and control functions. Since a repeated
operation of state estimation functions with in short intervals
of time is computationally expensive, tracking estimation has
been conceived to update the state vector at instant of time. In
tracking estimation the changes in the system between two
successive instants of time is assumed to be extremely small
and hence the state vector is simply updated by an amount
proportional to the measurement residual at every instant.
Various techniques proposed in the literature to improve the
computability, accuracy and the ease of implementation have
been discussed. Certain techniques also help in better
detection of bad data, anomalies and perform well even under
the presence of ill conditioning.
Since power system changes continuously, the operator
has to be extremely alert in taking decisions on real time,
especially in cases of emergency. In such a scenario a
technique which can predict the possible state of a power
system in the immediate future is a boon. Though tracking
monitors the power system continuously, it lacks any physical
modeling of the system and hence no realistic prediction of
the states can be obtained. Hence researchers have proposed
dynamic state estimation techniques, which provide the
predicted state vector at the next time instant to the operator,
with which the operator will be able to take any suitable
control actions. Once the measurements at the next instant
arrive, the predicted state vector is filtered to obtain an
optimized estimate. Various DSE techniques proposed in the
literature, their advantages, disadvantages and specialties if
any, have been briefly described in this paper.
Keeping in mind the importance of a review paper for
future research in the area, a comprehensive survey of the
available literature on tracking and dynamic state estimation
techniques has been presented. It is sincerely hoped that this
will help the community of power engineers to further
research on tracking and dynamic state estimation topics.
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IX. BIOGRAPHIES
Amit Jain graduated from KNIT, India in Electrical
Engineering. He completed his masters and Ph.D.
from Indian Institute of Technology, New Delhi,
India.
He was working in Alstom on the power SCADA
systems. He was working in Korea in 2002 as a
Post-doctoral researcher in the Brain Korea 21
project team of Chungbuk National University. He
was Post Doctoral Fellow of the Japan Society for
the Promotion of Science (JSPS) at Tohoku
University, Sendai, Japan. He also worked as a Post Doctoral Research
Associate at Tohoku University, Sendai, Japan. Currently he is an Assistant
Professor in IIIT, Hyderabad, India. His fields of research interest are power
system real time monitoring and control, artificial intelligence applications,
power system economics and electricity markets, renewable energy, reliability
analysis, GIS applications to power systems, parallel processing and
nanotechnology.
Shivakumar N R has obtained his Electrical
Engineering Degree from RVCE Bangalore and his
masters in Power Systems, from IIIT, Hyderabad. He
is currently working in ABB Corporate Research
Center, Bangalore, India. His areas of interest include
real time monitoring and control of power systems,
power system protection, AI applications to power
systems and condition monitoring and diagnostics of
electrical equipment.
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