1. Building Distribution-Level Base Cases Through a
State Estimator
O. Ru´z Garc´a
ı ı E. Romero Ramos A. G´ mez Exp´ sito
o o A. Abur
Applus Norcontrol, SLU University of Sevilla University of Sevilla Northeastern University
Madrid, Spain Sevilla, Spain Sevilla, Spain Boston, USA
M. Ordiales Botija D. Trebolle Trebolle
Soluziona, SA Uni´ n Fenosa Distribuci´ n
o o
Madrid, Spain Madrid, Spain
Abstract—This paper describes the experience of a Spanish a different moment or day. Sometimes, the data is incomplete
distribution utility, Uni´ n Fenosa Distribuci´ n, when implement-
o o and/or contradictory.
ing an off-line state estimation tool intended to work on cases ´
This paper describes the experience of Union Fenosa Dis-
comprising a diversity of voltage levels and coming from a
variety of sources (own SCADA, external equivalent provided by tribuci´ n which decided to resort to a customized state estima-
o
the TSO, past records, etc.). This implies manipulating current tion tool to deal with this challenge, in an attempt to reduce the
magnitudes and transformer tap changer settings along with burden and frustration of former time-consuming procedures
more usual information such as voltage magnitudes and power based on trial-and-error load ﬂow studies and engineering
measurements. This tool has made it possible the automatic experience.
generation of suitable base cases, which can be subsequently
used to undertake routine network studies (contingency analysis, First, noteworthy features of the state estimator developed
planning problems, etc.). for this off-line application, oriented to subtransmission and
distribution networks, are described. These include incorpora-
I. I NTRODUCTION tion of multiple measurements, ampere ﬂows and injections,
In present day electric energy systems two somewhat contra- estimation of transformer taps, bad data detection, pseudomea-
dictory trends are consolidating regarding the type and volume surement generation from historic data, detection of suspect
of data which are handled by the different partners. On the one parameters, etc. A brief explanation will be provided of the
hand, many data that vertically integrated companies used to Windows interface specially designed to help the user when
share are becoming now strictly conﬁdential. On the other, preparing base cases. Then, several application examples are
a much larger volume of data coming from heterogeneous presented and discussed, showing the advantages of using a
sources must be handled by planners and operators. state estimator in this context.
This is aggravated by the relevance and implications of
many decisions nowadays, which makes decision-taking more II. BACKGROUND ON STATE ESTIMATION
risky than ever. State estimators are widely used in today’s Energy Man-
Distribution companies, managing subtransmission and dis- agement Systems. Their role has become signiﬁcantly more
tribution networks ranging from 400V to 132 or even 230kV, important due to the need to closely monitor power transac-
constitute a good example where this situation applies. They tions during the daily operation. State estimators commonly
are investing in new monitoring, protection and automation use measurements such as power ﬂows, injections and voltage
systems, aimed at increasing the quality of service standards. magnitudes at system buses. These measurements are then
This means that systematic network studies are being extended used to obtain the optimal estimate of the system state,
to portions of networks formerly excluded or, at most, man- which is deﬁned as the set of complex voltage phasors at all
ually solved. On the higher voltage side, they receive from system buses. While not as common, there are other types
the ISO, upon demand, snapshots of the bulk power system, of measurements such as line current magnitudes and bus
typically including an equivalent of electrically distant buses. current injection magnitudes, which are available as additional
In this situation, a major problem distribution utilities are measurements at certain control centers. Furthermore, taps
facing is how to efﬁciently match such a diverse information in associated with some transformers with off-nominal taps may
order to build coherent base cases from which reliable network have to be closely monitored, i.e. they may have to be
studies can be performed. For instance, as getting the right data estimated along with the conventional system states.
from the ISO may be difﬁcult, if not impossible, planners may This paper describes a software development project which
have to integrate data corresponding to the transmission system was undertaken in order to address the above mentioned
peak loading condition with those coming from a regional unconventional measurements and unknown variables. In ad-
subtransmission network where the peak demand took place at dition to being able to estimate the system state and unknown
2. transformer taps based on the available conventional and detect, identify and eliminate bad analog measurements. Bad
unconventional measurements, the program aims to detect, data detection is accomplished based on the largest normalized
identify and eliminate any bad data or tap in the system. residual test. If the detection test fails, then the measurement
Hence, it provides a tool which can be used not only to monitor corresponding to the largest normalized residual will be de-
the system operation, but also to improve the system data base. clared bad and its value will be corrected as given in Chapter
5 of [1]:
A. State estimator and bad data processor corrected bad Rkk bad
zk = zk − r
Consider the measurement equation given by: Ωkk k
z = h(x) + e where:
Rkk is the diagonal entry of the measurement error covariance
where: matrix,
z is a vector of power injections, power ﬂows, voltage Ωkk is the diagonal entry of the residual covariance matrix,
magnitudes, line current magnitudes, bus current injection which is deﬁned in Chapter 5 of [1],
magnitudes and monitored taps of some transformers. x is a bad bad
rk = zk − h(ˆ) is the measurement residual,
x
vector of voltage magnitudes and phase angles, plus a set of bad
zk is the bad measurement,
taps associated with those transformers whose taps are to be k is the measurement index for the largest normalized residual.
estimated. State estimation will be repeated as many times as needed
h is the nonlinear function relating error free measurements to after each identiﬁcation and correction of a bad datum. Note
the state variables given in vector x. that, repetitive solutions will start from the most recent esti-
e is the vector measurement errors. mate instead of ﬂat start, and hence will take fewer iterations
Measurement errors are assumed to be independent and have to converge.
a Normal distribution with zero mean and known variance. A Following the bad data identiﬁcation and correction phase,
diagonal covariance matrix, R is assumed as below: transformer taps which are estimated, will be checked to en-
R = E[eeT ] = diag(σ1 , σ2 , . . . , σm )
2 2 2 sure that the estimated taps are within maximum and minimum
operating limits. If there are limit violations, tap values will be
where σi is the standard deviation of the error associated set at the respective limit. If taps are found to be within limits,
with the measurement i and m represents the total number then their values are rounded to the nearest discrete tap value
of measurements. that is physically viable. This will not signiﬁcantly change
Note that multiple measurements of the same quantity are the state estimation solution while providing a physically
allowed and fully compatible with the above formulation. For meaningful answer for the estimated taps.
instance, bus voltage magnitudes may be available from two
or more measuring instruments at a given substation bus. B. Practical issues
Instead of ignoring the extra measurements or using a simple The estimator developed for this project incorporates line
averaging, these measurements are included as separate entries current magnitude and bus current injection magnitude mea-
in the measurement vector z and respective standard deviations surements, which are typically not considered by conventional
of errors are assigned to them. estimators. Furthermore, selected transformer taps are included
The weighted least squares (WLS) estimator will minimize in the unknown variable list, so that their values can be
the weighted squares of residuals of the measurements given estimated as part of the solution. These features call for
below: m derivation of new terms in the measurement Jacobian. Detailed
J= 2
ri derivation of all Jacobian entries can be found in Chapters 2
i=1
and 7 of [1] for the current magnitude measurements and tap
variables respectively. It is worth noting that clever application
where:
of shortcuts proposed in [9] leads to very efﬁcient code for
ri = zi − hi (ˆ) is the measurement residual,
x
computing and updating Jacobian entries for those columns
ˆ
x is the estimated state vector.
corresponding to taps.
The state estimate can be obtained by iteratively solving the
A great deal of effort has been devoted to certain practical
following equation:
aspects of the state estimator that, in spite of not involving new
Gδx = δt
knowledge, play an important role in achieveing a reliable and
where: really accurate application. This is the case of the subroutine
G = H T R−1 H is the gain matrix, devoted to ensure unique observability. After numerous tests it
H = ∂h is the measurement Jacobian,
∂x
has been checked that certain pseudomeasurements result more
δx = xk+1 − xk , k being the iteration counter, appropriate than others in order to get the right estimate. In
δt = H T R−1 [z − h(xk )]. this respect, complex power pseudomeasurements, computed
Iterations are terminated when an appropriate tolerance is from actual current measurements and assumed power factor,
reached on δx. Once the iterations are converged, bad data in places of the system where the power ﬂow direction is well-
processing function is activated. This function’s role is to known, have allowed the state to be estimated in zones where
3. only current measurements exist. It is well documented in the detected and eliminated/substitued. Two different working ﬁles
literature (see references [5], [6], [7]) that ampere measure- result from this preliminary phase of the application:
ments alone are not enough to guarantee unique observability. • A raw data ﬁle containing power ﬂow system speciﬁca-
Also a systematic study has been undertaken to select adequate tion data.
standard deviations for each measurement type. In this sense, • A measurement ﬁle where the available measurements,
not only the precision class of the measurement device, but their values and their standard deviation are listed. The
also its nominal power have been used to better tune this handled measurements can be voltage magnitudes, active
important parameter. In general, all tests have conﬁrmed the and reactive power ﬂows and injections, current ﬂow
improvement of the state estimation results and the bad data and injection magnitudes and transformer taps. Multiple
detection and elimination capability in those cases where measurements for the same magnitude, very frequent in
current measurements are incorporated. practice, are obviously allowed.
Regarding the detection and identiﬁcation of bad data, the
implemented application allows typical bad performance of Next, the system state is calculated from the state estimator
meters, wrong scale factor or bias, reversed connections, etc., function. At the end of each estimation cycle a bad data pro-
to be identiﬁed. Additionally, topology errors, and in some cessor is executed. If a measurement is identiﬁed as erroneous
cases outstanding parameter errors, have been detected after it is eliminated and a new estimation takes place. This process
carefully and individually analyzing the results of the estimate. ends when no more bad data are detected.
Almost always, those errors were identiﬁed after noticing that Figure 1 depicts a display sample of the application where
large measurement residuals accumulated at certain speciﬁc the state estimator provides the data associated to a particular
points. As the the implemented tool does not incorporate in a bus. In this diagram, actual measurements are shown in blue
systematic manner the topology error and network parameter while estimated ones are green. If a measurement is detected as
estimation functions, this task has been carried out manually. erroneous, it is drawn in red. Notice that several voltage mea-
Examples of such errors include wrong status information surements are available (one for each incident line besides that
transmitted by a switching device or a drastic change in the measured at the bus). Regarding the transformers connected to
parameters of a line that has been redesigned without the new this bus, not only the tap setting but also the regulated voltage
values been adequately updated at the data base. and the percent regulation range are shown. More variables
could be visualized when activating other options offered by
III. S OFTWARE I NTEGRATION the application.
One of the aims of the developed application is to generate
The following modules, characteristic of any estimator, are a power system model so that the PSS/E simulator can operate
developed: topological and observability analysis, the applica- on it. The results of the estimation (voltages magnitudes and
tion of a gross error ﬁlter, the state estimator strictly speaking, power injections) are used to produce the respective power
bad data detection and identiﬁcation and the presentation of ﬂow Raw Data File.
results to operators. However, from the point of view of the
The implemented application also allows working by areas,
system where the state estimator is integrated, three main
that is, by electrical zones that can comprise different voltage
functions can be distinguished:
levels. This possibility is very attractive owing to, among other
1) First, the input data for the state estimator are elaborated. questions, the need to save computation time.
This phase includes the observability analysis and the A ﬁnal remark about the modelling of the external trans-
elimination and correction of gross errors. mission system is needed. As previously pointed out, a net-
2) Secondly, the state estimator is run including the sub- work equivalent could be considered, but keeping the entire
routines of identiﬁcation and detection of bad data. connected network unreduced is another possibility. Both
3) Finally, a power ﬂow network model is built from the possibilities have been considered in this project. However,
state estimation results. a third option proposed in [11] has proved ﬁnally to be the
The data corresponding to the network elements under study most successful. In this last methodology, named “the two-
(e.g. generator, transformer, transmission line, circuit breaker, pass state estimation method”, the state estimator produces an
etc.), their connectivity and the associated measurements are initial estimate of the internal system state. The external model
extracted from the SCADA data base for a particular instant. is then attached in two phases: ﬁrst, branch power ﬂows are
The external equivalent of the higher voltage networks, in- computed for the unobservable network interconnecting the
cluding eventually that of the TSO, is also taken into account internal and external systems; second, a state estimation is
for the speciﬁed day and hour (external equivalents are not run using the internal estimated states as pseudomeasurements
updated so frequently as the SCADA data). Then, a topology along with the power ﬂows of the external system, in order
processor is used to aggregate this detailed model back to a to match the two parts of the network model. The scheduled
bus-branch representation. Moreover, a measurement input ﬁle injections at the inner boundary nodes are used as target
is created by using an observability processor. This procedure values and external telemetry is included when available.
is aimed at adding pseudomeasurements where necessary Additionally, exact null injections for both networks are treated
to make the system fully observable. Gross errors are also as pseudomeasurements.
4. Fig. 1. Detailed bus view display
TABLE I
T ESTED CASES
Tested cases Buses/Branches Variables Measurements
V θ t Total V Pi Qi Ii Pij Qij Iij t
Small case 76/85 76 75 29 180 110 46 41 1 87 86 113 22
Large case 1454/1747 1454 1453 556 3463 3053 851 815 14 2517 2475 2846 446
IV. C ASE STUDIES voltage level is,
The state estimator has been executed on many different • 193 buses with voltage levels greater than or equal
cases. Two of them are discussed here. The ﬁrst one refers to to 220kV. This part of the system is the transmission
a relatively small case on which the main features of the im- network, most of them owned by the Spanish TSO.
plemented system can be tested. This 76-bus network has four • The subtransmission network, comprising voltage levels
voltage levels (in brackets the number of buses for each level): from 132kV to 45kV, contains 754 buses, 470 of them
400kV (3), 132kV (7), 45kV (48) and 15 kV (18); its one-line having a nominal voltage of 45 kV.
diagram is provided in the Appendix, ﬁgure 2. There are a total • Finally, there are 508 buses associated to the distribution
of 85 branches, 56 lines and 29 transformers, all of them with network with voltages lower than 33kV. This part of the
tap changers. The set of 506 measurements is composed of system is usually operated in a radial manner. There are
voltages, power ﬂows and injections (active and reactive), rms several rated voltages at this level: 33kV, 20kV and 15kV,
current ﬂows and injections, as well as transformer taps (see being 16, 88 and 331 the number of nodes respectively.
the details in table I). Forty complex power injections are exact The rest of the 508 buses are associated to other voltage
null injections. None pseudomeasurement has been needed in levels corresponding to different generating stations. The
this case to make the whole system fully observable. Note also entire network comprises a total of 26 three-winding
the large number of current ﬂow measurements compared to transformers. The star resulting from the electrical model
power ﬂows, reﬂecting the fact that current measurements are of these devices has a rated voltage of 1 kV.
more common than power ones as the voltage goes down. Regarding the largest test case (1454-bus system), the
The largest system presented here incorporates voltage distribution of its 14171 measurements are also detailed in
levels from 440kV to 1kV with a total of 1454 buses. This high table I. Once more, it is to be noted the large number of current
number of buses results from including the subtransmission measurements (2860) and the great deal of exact null complex
power system and a huge number of nodes corresponding power injections (701), over a total of 851 power injection
to lower voltage levels (medium voltage); it is well known measurements. For this system 76 pseudomeasurements have
that the lower the voltage level the higher the ratio of buses been added in order to have a single observable island.
to branches. More speciﬁcally, the number of buses for each Some of them, speciﬁcally 23, are power ﬂow measurements
5. computed from actual current measurements as explained in • Not only measurement errors have been corrected but also
section II-B. errors contained in the information provided by switching
Finally, some comments regarding the tap estimation pro- devices.
cess and identiﬁcation of bad tap measurements are worth • The accuracy of the system data base has been improved
mentioning. Taps of transformers connecting the subtransmis- by correcting parameter errors at speciﬁc points where an
sion network to the distribution feeders usually shift auto- accumulation of bad data were detected.
matically by the action of automatic controllers that try to • Building coherent base cases from which reliable network
maintain voltages as close as possible to speciﬁed values. studies can be performed by different utility departments
As there are so many transformers of this type, not all of (operation, planning, protection, etc.).
their tap settings are telemetered. On the other hand, some • The estimation of tap measurements has also allowed
of these transformers are equipped with two tap changers, associated errors to be detected and corrected.
one at the high voltage side (on-load tap changer), and the The success achieved with the implemented tool has en-
other at the low side that can only be changed upon previous couraged the utility to enhance the possibilities offered by the
disconnection. The state estimator has turned out to be a great estimator, for example: trying to incorporate new functions
help to estimate all these unknown taps, no matter if they are such as estimation of parameters; improving the numerical
ﬁxed or not, since measurement redundancy is sufﬁciently high robustness of the estimator by implementing a QR factoriza-
around these transformers. Other off-nominal tap transformers tion; elaborating a pseudomeasurement data base, etc. Some
are those that step up voltages at generator terminals. Their of these tasks are just being undertaken.
taps are not monitored on-line, but are conveniently estimated
A PPENDIX A
by the developed state estimator.
O NE - DIAGRAM OF THE 76- BUS SYSTEM
The following cases illustrate performance of the state
estimator in detecting tap measurement errors: The meaning of the different symbols used in ﬁgure 2 are:
1) Incorrect model for the transformer. This case may occur
when the initial tap position is assumed to be the upper Voltage measurement
limit of the variable tap range whereas it actually is at Current measurement
the lower limit or vice versa. More speciﬁcally, suppose 6P Active power measurement
a transformer with rated voltages 43/15kV, the regulation Reactive power measurement
6 Q
voltage lying between 38.7kV and 51.3kV. The ﬁrst tap Complex power measurement
6
value could be assigned to the lower value, 38.7kV, when
in fact it should be matched with 51.3kV, or viceversa. A “t” next to a transformer means a tap measurement is
2) Some of the values sent to the SCADA are not exactly available. The color code for the different levels of voltages
the tap setting, but the change in tap position (number of is: red for 440 kV, blue for 132 kV, brown for 45 kV and
steps). If one of those changes is lost for some reason, green for 15 kV.
the next changes will be taken into account by the ACKNOWLEDGMENTS
SCADA from an erroneous tap position. The application
The authors would like to thank the support provided by
has allowed this misleading situation to be detected.
the Spanish MCYT under grant ENE2004-06951/CON.
V. C ONCLUSIONS R EFERENCES
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o o
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