Power-system state estimator availabilityanalysis

E.P.M. Brown, B.E., M.E., Ph.D., and H.R. Sirisena, B.Sc.(Eng), Ph.D.,C.Eng.. M.I.E.E.

Indexing terms: Power systems and plant, Mathematical techniques

Abstract: A simple technique for determining the probability that a given node will be observable, based onmeasurement-data availability, is presented. In contrast to other methods, the state-estimator nodal-estimatereliability analysis can be carried out without using a computer, and, because all the individual nodal avail-abilities are found, different nodes can be assigned different availabilities during the meter-placement design.The availability analysis also determines the largest number of measurements about each node which cansimultaneously be removed or lost without causing a certain loss of nodal estimate observability, when theremaining measurements are processed. This 'sufficient' test of nodal estimate observability during bad-datadetection and identification can be used in conjunction with the 'power of the J(x) test' in meter-placementdesign.

List of principal symbols

AAPSMTURTUCOMCOMP

= availability= unavailability= probability= complex power measurement pair= master terminal unit= remote terminal unit= communication path= control centre computer

1 Introduction

Power-system metering and communication equipmentcan randomly fail, causing nodes within the power systemto become unobservable to state estimators. The expectedoutage time per year, during which individual nodal esti-mates will be unavailable, depends on the data-acquisition-system availability and on the meter configuration chosen.Recently, Clements et al. [1] numerically evaluated state-estimator reliability using the topological-observabilityproperties of the measurement set. However, their sug-gested method took more than one and half hours CPUtime to evaluate the probability of generating observablenodal estimates for a 137-node power system, which has137 different remote terminal units (RTUs) and 270complex power measurements.

Using the same observability criteria, the authorsapproach the state-estimator reliability problem differ-ently, evolving simple analytical expressions for the prob-ability (availability) that each node will be observable, andthe probability of retaining nodal observability after theloss or removal of suspect measurements. The resultingstate-estimator availability analysis can be performedwithout a computer.

2 Observability criteria and nodal estimateavailability analysis

The probability that a given node i will be observable canbe found by 'removing' the node and its nearest neigh-bours from the power system. Observability to node i ismaintained by any real and reactive line-flow and injectionmeasurements made at node i, any injection measurements

Paper 3233C (P9), received 7th October 1983

Dr. Brown is with New Zealand Electricity, Ministry of Energy, Wellington, NewZealand, and Dr. Sirisena is with the Department of Electrical and Electronic Engi-neering, University of Canterbury, Christchurch 1, New Zealand

made at neighbouring nodes k / and any line-flow mea-surements made at neighbouring nodes on lines connectedto node i [2]. A nodal-voltage-magnitude 'reference' mustalso be monitored [2]. Only one nodal-voltage-magnitudemeasurement must be available because other real andreactive injection and line-flow measurements, which spanthe other nodes in the power system, will link the voltage-magnitude reference to node i. Node i will lose its voltagereference when either all link measurements and/or allnodal voltage measurements are simultaneously unavail-able.

The probability that node i will be unobservable, P,,can be expressed as

Pi = lMTU C0MP

lCOMP ) (1)

where PL is the probability that the link measurementssurround node i, and for all the nodal-voltage-magnitudemeasurements will not reach the control centre, AMTU isthe availability of the master terminal unit (MTU) at thecontrol centre, AC0MP is the availability of the control-centre computers and (1 — AMTU • ACOMP) is the probabil-ity that either the MTU or the control-centre computerswill be unavailable. Also

P, = P, NL + P\ NV (2)

where Pu is the probability that all the line measurementswhich surround node i will not arrive at the control centre,{NL} is the set of all measurement-availability com-binations of nonlink measurements (the probability PNL

that a nonlink-measurement-availability combination willbelong to this set is unity), PV is the probability that allpower-system voltage-magnitude measurements will notarrive at the control centre, {NV} is the set of allmeasurement-availability combinations involving injectionand line-flow power measurements (the probability PNV

that a non-voltage-magnitude measurement-availabilitycombination will belong to this set is unity) and PLV is theprobability that all the link measurements which surroundnode i, and all the power-system voltage-magnitude mea-surements, will not arrive at the control centre. Thus

Py~P LV (3)

Consider the first term in eqn. 3, the probability of losingall the link measurements which surround node i. Theavailabilities of the link measurements which surroundnode i are highly correlated; this is because the link mea-

IEE PROCEEDINGS, Vol. 131, Pt. C, No. 4, JULY 1984 117

surements use the same RTU, the same communicationlink, the same MTU and the same control-centre com-puters. Only the measurement transducers are indepen-dent, thus

= PLIK Llj LIM (4)

where PLlK is the probability that the link measurementsabout node i, which are transmitted to the control centrevia RTU communication link K, will not arrive. Also

I * NCv (5)NMK l NCK

where PNMK is the probability that all the measurementtransducers, which monitor the 'links' surrounding node iand whose indications are transmitted to the controlcentre via RTU K, will be unavailable; and PNCK is theprobability that RTU K and/or communication link Kwill be unavailable. Note that

PNMK — lKPp=i

(6)

where AKP is the availability of the measurement trans-ducers of the Pth 'link'-measurement pair, about node i,which is transmitted to the control centre via RTU K.Link measurements are assumed to occur in pairs. Thecomplex power measurement SKP is a real- and reactive-power-measurement pair (PKP, QKP).

— \\ ~

Also

NCK= {\-ARTUK

lCOMK

(7)

(8)

where ARTUK is the availability of RTU K and ACOMli is theavailability of the communication path from RTU K tothe control centre. Eqn. 5 becomes

'LIK — 1 1p=\

(1-/1 RTUK

1RTUK ACOMK) (9)

and eqn. 4 becomes

pu= n f l ADP + (i - ARTUD • ACOMD)D = K, J M \_P=\.

• (1 " ARTUD • ACOMD)I (10)

Most modern remote data-acquisition systems have mainand standby control-centre MTUs and computers, andmain and standby communication circuits. RTUs andmeasurement transducers are not duplicated. Typicalavailabilities are

AMTU = 0-9998

ACOMP = 0.9998

ACOMD = 0.999

= 0-98

RTUD

ADP = 0.99

Under these conditions AMTU, ACOMP and ACOMD > A

and ADP; and eqns. 9 and 10 can be approximated to

P ~ I n (n\_D = K,J M \P=\

- A RTUD• ACOMDMD))\/J(11)

lMTU (12)

i.e.

nD = K, J, . . . ,

When nD ^ 2, eqn. 11 simplifies to

PLIK — (1 — ARTUK • ACOMfC)

• AC0MP) (13)

(14)

Consider the 2nd and 3rd terms in eqn. 3 which model thenodal-voltage-magnitude measurement availabilities. Mostpower systems have a number of voltage-magnitude mea-surements scattered around the system. These measure-ments are completely independent and are uncorrelated.Consider the IEEE 14-busbar test system with the meter-ing configuration shown in Fig. 1.

tine-flowmeasurement

injectionmeasurement

voltagemeasurement bthree winding

transformerequivalent

Fig. 1 IEEE 14-busbar test systemRTU1 transmits data from node 1RTU2 transmits data from node 2RTU3 transmits data from nodes 4, 8 and 9RTU4 transmits data from nodes 5 and 6

RTU 5 transmits data from node 10RTU6 transmits data from node 12RTU7 transmits data from node 13

Seven nodal-voltage-magnitude measurements and/orsix RTU/communication circuits must be simultaneouslylost before the nodal-voltage reference becomes unavail-able. The probability of this happening is extremely small,and so the 2nd and 3rd terms of eqn. 3 can be neglected.Eqn. 3 becomes

nD=K,J M

fl - A RTVD COMD

+ (1 - AMTU COMP

) (15)

118 IEE PROCEEDINGS, Vol. 131, Pt. C, No. 4, JULY 1984

Grouping RTU/communication paths D = K, J, ..., Minto sets, according to whether or not more than one link-measurement pair surrounding node i is present, results inthe generalised formula:

IIEe{K,J

11Fe{K,J M\nFp=l)

ff *EP + (1 " ARTUE • ACOME)p=l

~ ARTUF • ACOMFI

+ (1 - AMTU

(16)

where E contains only those RTU/communication pathswhich have more than one link-measurement pair and Fcontains only those RTU/communication paths whichhave only one link-measurement pair.

2.1 Availability of zero-injection pseudomeasurementsZero-injection pseudomeasurements occur at nodes wherethere is no generation or load. These pseudomeasurementsdo not require monitoring, yet are always available. Node7 of the IEEE 14 busbar test system, shown in Fig. 1, hasa zero-injection pseudomeasurement. This pseudo-measurement is a 'link' measurement pair to nodes 4, 7, 8and 9, i.e.

* 4 =

0 ~~ ACOM3

RTU2

y\

COMl])

~ A...,~ • ACOMPy\ • A S l (17)

where S denotes a real- and reactive-power link-measurement pair. Since

ASl = 0 (18)

(19)

and

P7 = P8 = P9 = 0 (20)

The only limiting factor is the availability of the nodal-voltage reference at the other end of the link—this nodal-voltage reference has a very high availability, as outlinedearlier, and is assumed to always be available. Eqn. 16 isonly valid when no zero-injection link pseudo-measurements are present. Nodal estimate availabilities forthe 14-busbar IEEE test system are shown in Table 1.

The numerical values shown were obtained by using thetypical availability data suggested earlier.

3 Availability during bad-data identification andlocal redundancy

A node which is attached to other nodes by n link-measurement pairs has a nonzero probability of beingobservable after the loss or removal of any 2*(n — 1) mea-surements; and thus the node has an identification 'poten-tial' of 2*(n — 1). Table 2 shows the multiplebad-data-identification 'potentials' for each of the nodes inthe IEEE 14-busbar test system, for the measurement con-figuration shown in Fig. 1. Also shown are the number ofmeasurements which would be lost if the RTU and/or thecommunication link failed.

'Local redundancy' is a figure of merit which is oftenused by meter-placement designers and is found bysumming all the measurements made at a node, and atadjacent nodes, and dividing by the number of unknownstates on, and at, adjacent nodes [3]. The local redundancyof nodes 6 and 12 of the IEEE 14-busbar system, shown inFig. 1, is 1.8 and 3, respectively. However, from Tables 1and 2, node 6 has a greater nodal estimate availability and,therefore, a greater multiple bad-data-identification poten-tial than node 12. Thus nodes which have a high localredundancy will not necessarily have a high nodal-estimateavailability. This is because voltage magnitude measure-ments are included in the local redundancy 'figure ofmerit', as well as measurements made from adjacent nodesto other unrelated nodes. These measurements provide no'linking' to the node of interest.

4 Inclusion of nodal identification 'potentials' inmeter-placement design

Availability has been included in meter-placement designvia simulation studies [4-7]. However, simulations aretime consuming, cannot guarantee to check all measure-ment outage combinations and are usually only used tocheck the validity of a chosen measurement set. With theexception of Arriatti et al. [4], none of the methods gener-ate quantitative availability data which describes the prob-ability of nodes being observable.

The nodal identification potentials, outlined in Section3, can be used as a lower bound on the results of optimalmeter placement. Most of the optimal meter placementmethods maximise the accuracy of the state estimates[4-7]. However, online tracking state estimators try tomaintain a 'reliable' (but not necessarily optimal) database,free from bad data, and the bad-data detection propertiesof the state estimator would normally be optimised.

Nodal identification 'potentials' are a 'sufficient' condi-tion for nodal observability, after the removal of multiplebad data; and are a 'necessary but not sufficient' condition

Table 1 : Estimate availability for the IEEE 14-busbar test system

Node

1234*567*8*9*

1011121314

Probability of unobservable nodal estimates

[d[(1[(10[(1[(1000[(1[(1[(1[(1[(1

-A RTU,

~ A RTU,

~ A RTU2

~ A RTU,

- A RTU.

~ A RTUi- A RTUt

- A RTUt

-A~ A RTU}

' A COM,)

' A COM,)

' A COM2)

' A COM,)

A COM,)

• A COMi) •

• A COM,)

• A COM,) '

' A COM,) '' A COM})

\A s2 + ( ' A RTU2 ' A

(• ~ A RTU2 ' A COM2)

(1 -A A )]

\ ' ~ A RTU2 ' A COM2){A Sii + (1 -A RTUl • >

\ ' ~ A RTUJ • A COM})}

{> ~ A RTUS ' COMiil

(A Si2 i 3 + ( 1 - A RTU6

C * s . 2 - . 3 + ( 1 - A RTU6

(1 - A RTUI • A COM,)]

COM2))~\ + (1 -

V-ARTU}'

\ ' ~ A MTU

• (1 - A

* coMl))f+"(1

+ ( ' ~ ™ MTU+ (i ~A MTu_

' ™ COM6) ' \T

' A coM6) ' (1+ (1 -A MTU

~ A MTU ™ COMP)

A COM})} \' ~ A MTU'

• A COMP)

A coM3)] + {1 ~ A MTU'~ A MTU' A COMP)

' A COMP)

' A COMP)

Sn \' ~ A RTU! ' COt~ A RTU! ' COM7))J

+ (• A COMP)

A COMP)

A COMP)

H7))] + ( 1 - '> ~A MTU' '

" MTU' " COMP)

^ COMP)

Nodal estimateavailability

99.895%99.959%99.916%

100.000%99.959%99.895%

100.000%100.000%100.000%

99.916%99.916%99.959%99.959%99.895%

* Probability of unobservable nodal estimates at nodes 4, 7, 8 and 9 equals zero because of the zero injection at pseudomeasurement 7

IEE PROCEEDINGS, Vol. 131, Pt. C, No. 4, JULY 1984 119

Table 2: Nodal availability for IEEE 14 busbar test system and effect ofcommunication link failure

Node

123456 -

789

1011121314

Number of link-measurementpairs

48487673634453

Multiple bad-dataidentificationcapability

614

614 }12 \_ 9 + : „_„10/ |12 \4 j

1046684

Common mode baddata as a result of RTUcommunication link failure

77

none}

\l (RTU4) :/ T (RTU4) j 22*none •

\)

5none

25

none

(RTU1)(RTU2)

(RTU3)

(RTU3)(RTU3)(RTU5)

(RTU5)(RTU7)

* total (RTU3) = total (node 4) + total (node 7) + total (node 8)t total (RTU4) = total (node 5) + total (node 6)

for the detection of multiple bad data. The 'power of theJ(x) test' optimal meter-placement method maximises thedetection capabilities of a measurement set for a givencapital resource. However, the 'power of the J(x) test' onlymodels the distortion caused by single and multiple nonin-teracting bad data. Using the nodal identification poten-tials as a lower bound on the results of the 'power of theJ(x) test' optimal meter placement guarantees a predeter-mined level of observability when attempting to identifymultiple interacting bad data.

5 Comparison with the Clements et al. method ofanalysing state estimator reliability

(a) Both the Clements et al. [1] method and the methodoutlined in Section 2 assume that a voltage magnitude ref-erence will always be available, and that real- and reactive-power measurements occur in pairs.

(b) The Clements et al. [1] method considers only thefailure of RTU/communication channels. The methodadvocated in Section 2 also considers individual measure-ment failures.

(c) The Clements et al. [1] method uses all the measure-ment data present to assess only the probability that theentire system will be observable, whereas the method out-lined in Section 3 only uses the 'link' measurements whichsurround the node in question; determining the probabil-ity of the node being observable. The Clements et al. [1]method takes more than lj h CPU time to evaluate thereliability of the 137-node power system, whereas avail-ability analysis can be done by hand using the method out-lined in Section 2.

Also, calculating individual nodal-estimate availabilitiesallows meter-placement designers to selectively increasethe availability of important nodes, simply by adding extra'link' measurements in the vicinity of the node in question,or by upgrading the RTU or communication paths.

6 Conclusion

A novel technique for determining power-system state-estimator availability has been presented. Rather thansimply calculating the probability that the power system asa whole is observable, the suggested method calculates theprobability that an individual node within the powersystem will be observable. The resulting availabilityexpressions are so simple that the availability analysis canbe done without recourse to a computer.

The availability-based analysis can also determine theidentification potential of each node. The identification

potential is the largest number of measurements, abouteach node, which can simultaneously be removed or lostwithout causing a zero probability of that node beingobservable when the remaining measurements are pro-cessed. These potentials are a sufficient condition forobservability, during multiple-bad-data identification, andare a 'necessary but not sufficient' condition for the detec-tion of multiple bad data. The 'power of the J(x) test'optimal meter-placement technique is used to maximisethe detection capabilities of measurement sets. However,the 'power of the J(x) test' only models the distortioncaused by single and multiple noninteracting bad data.The availability-based nodal identification potentials canbe used as a lower bound on the results of the power of theJ(x) test. This guarantees observability when attempting toidentify interacting bad data.

Reliability aspects of online state estimators have oftenbeen neglected in meter-placement studies in the past. Theuse of the simple expressions outlined in this paper willgive designers a guide to state-estimator availability.

7 Acknowledgment

The authors are grateful to Mr. K.D. McCool, GeneralManager of New Zealand Electricity, for permission topublish this paper'.

8 References

1 CLEMENTS, K.A., KRUMPHOLZ, G.R., and DAVIS, P.W.: 'Stateestimator measurement system reliability evaluation—An efficientalgorithm based on topological observability theory', IEEE Trans.,1982, PAS-101, pp. 997-1004

2 CLEMENTS, K.A., and WOLLENBERG, B.F.: 'Observability deter-mination for networks containing bus injection and line flow measure-ments'. 1975 IEEE Power Engineering Society Summer Meeting, SanFransisco, California, 20th-25th July, 1975, Paper A75, 447-3

3 HANDSCHIN, E.J., and BONGERS, C : Theoretical and practicalconsiderations in the design of state estimation for electric powersystems'. 3rd international symposium on computerised operation ofpower systems, San Carlos, Brazil, 1975

4 ARIATTI, F., MARZIO, L., and RICCI, P.: 'Designing state estima-tion in view of reliability'. 5th power systems computations conference,Vol. 1, Cambridge, 1975* Paper 2.3/8

5 MASIELLO, R.D., and HORTON, J.S.: 'On-line decoupled observa-bility processing'. 1977 power industry computer applications con-ference, pp. 420—426

6 LE ROY, A., and VILLARD, P.: 'Applications of state estimationmethods to evaluation of a telemeasurement configuration for energypower systems'. 3rd international symposium on computerised oper-ation of power sytems, San Carlos, Brazil, 1975

7 PHUA, K., and DILLON, T.: 'Optimal choice of measurements forstate estimation'. 1977 power industry computer applications con-ference, pp. 444-456

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