Predicting vegetation-related failure rates for overhead distribution feeders

1170 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 17, NO. 4, OCTOBER 2002

Predicting Vegetation-Related Failure Rates forOverhead Distribution Feeders

Duane T. Radmer, Paul A. Kuntz, Member, IEEE, Richard D. Christie, Member, IEEE,Subrahmanyam S. Venkata, Fellow, IEEE, and Robert H. Fletcher, Member, IEEE

Abstract—Faults on the electric power distribution system areresponsible for a large portion of the interruptions that a customerwill experience. To maintain a high level of system reliability, veg-etation maintenance is often required. Analytical prediction of theeffects of vegetation maintenance on distribution system reliabilityrequires a model of the expected failure rate of line sections thatincludes the effects of vegetation.

Vegetation-related failures are more likely to occur as the vege-tation near the overhead power lines grows, increasing the line-sec-tion failure rate. Due to difficulties in using existing growth models,this paper proposes to use a direct model for failure-rate predictionbased on factors that affect vegetation growth. Four models areconsidered: linear regression, exponential regression, linear mul-tivariable regression, and an artificial neural network (ANN). Themodels are tested with historical vegetation growth parameter dataand feeder failure rates. Results are compared and the features ofeach model are discussed.

Index Terms—Failure-rate modeling, failure-rate prediction,line clearance, neural networks, power distribution systems,regression, reliability, tree trimming, vegetation maintenance.

I. INTRODUCTION

RELIABILITY is an important issue for utilities today be-cause reliable systems maintain customer satisfaction. To

maintain high levels of reliability in the distribution system, lineclearance maintenance (tree trimming and other vegetation con-trol measures) is often required. If left unchecked, trees cangrow tall enough to fall on power lines, initiating faults, and in-terrupting power flow [1]. Since line clearance maintenance isexpensive, devising a cost-effective schedule benefits a utility.For a utility in the northwest U.S., the annual cost of line clear-ance maintenance is approximately 30% of the total distributionsystem maintenance cost and 8% of the total distribution systemoperations and maintenance cost.

To develop cost-effective vegetation maintenance schedules,it is necessary to evaluate the reliability of the distributionsystem. This reliability can be calculated with a distributionsystem reliability program such as the ones found in [2] and[3]. These programs require a failure rateand a repair rate

for each component of the distribution feeder. For overheadline segments, the failure rate is given in per unit length, for

Manuscript received May 21, 2001; revised July 18, 2001. This work wassupported by the Snohomish County PUD #1.

D. T. Radmer, P. A. Kuntz, and R. D. Christie are with the Department ofElectrical Engineering, University of Washington, Seattle, WA 98195 USA.

S. S. Venkata is with the Department of Electrical and Computer Engineering,Iowa State University, Ames, IA 50013 USA.

R. H. Fletcher is with the Snohomish County PUD #1, Everett, WA 98206USA.

Digital Object Identifier 10.1109/TPWRD.2002.804006

example, in failures per mile-year. From these data, load-pointindices and system indices can be calculated.

In distribution system reliability assessment, the componentfailure rates are usually assumed to be constant, given aperiodic maintenance schedule. A better model would predictfailure rates that vary from year to year, increasing until thenext periodic maintenance activity is performed [4]. After lineclearance maintenance, the failure rate is reduced until thevegetation regrows. Since the vegetation-related failure rate ofoverhead feeders is not a constant, it is necessary to develop amodel of the effects of vegetation on the failure rate.

A vegetation growth model is an obvious place to start. Thesemodels predict the diameter or height growth of trees as a func-tion of time or age. However, growth models found in the litera-ture are primarily used by forest managers to predict the lumberproduction expected from a given forest stand. Several difficul-ties exist when attempting to apply these models to the distri-bution system vegetation maintenance problem. Even if a rea-sonably accurate growth model could be found or developed,an additional model is required to link the predicted vegetationgrowth to the overhead line failure rate. Obtaining this modelis not straightforward, as the full range of mechanisms throughwhich vegetation causes faults is still being investigated [5], [6].

In attempting to develop a failure-rate model starting witha growth model, it was realized that a more direct model for-mulation exists. This new technique bypasses growth models,although it is informed by them. It uses historical outage dataand climatic variables that affect tree growth as inputs and di-rectly outputs the time-varying failure rates. The model does notrequire a second model to link predicted vegetation growth tothe failure rate, and so does not need to explicitly model failuremechanisms due to vegetation. The initial formulation using agrowth model and the newly proposed model formulation areillustrated in Fig. 1.

II. V EGETATION MODELING

Many models have been proposed to describe plant growth[7]–[9]. Two kinds of models are used to describe growthdynamics—process-based models and data-based models [7].Process-based models are aimed at the understanding andexploration of processes that produce tree and stand growth.Data-based models employ an empirical approach that attemptsto mimic field data without much thought about the actualgrowth processes. All models used in forest management aredata based.

Several data-based tree height growth and diameter growthmodels have been developed. These models include the

0885-8977/02$17.00 © 2002 IEEE

RADMER et al.: VEGETATION-RELATED FAILURE RATES FOR OVERHEAD DISTRIBUTION FEEDERS 1171

Fig. 1. Failure-rate model development using a (a) growth model and (b) directmodel.

Gompertz, Logistic, and one of the most popular models, theChapman—Richards model [7]. The Chapman—Richardsmodel is

(1)

where is the height or diameter growth,is the age of the tree,and , , and are regression parameters.

Several problems arise when attempting to apply growthmodels in determining vegetation failure rates. These problemsinclude the time interval of analysis, the modeling of a singletree species, short-term climatic changes, and inadequatemodeling of the vertical and radial growth of trees in theright-of-way. The development of the relationship between treegrowth and failure rate is another key problem.

Most growth models handle variations in climatic factors,such as temperature and water supply, by using long time inter-vals in their modeling process, which has the effect of averagingthese factors. This approach limits the modeling time interval tolarge time spans, in the range of 20–50 yr. The typical main-tenance cycle for distribution right-of-way maintenance rangesfrom two to seven years. Another difficulty is that accurate re-sults may not be reproducible if climatic conditions are widelyvarying [10]. Growth models are also usually limited to con-sidering a single dominant tree species in a forest stand. On adistribution right-of-way, many tree species can exist within asingle pole span, and this can complicate the modeling process.

For line clearance maintenance, vertical growth as well as ra-dial growth is important to analyze. The modeling of the crowngrowth (branch growth) of existing trees on the front edge of theright-of-way can be just as important as modeling the verticalgrowth. Also, vertical and radial growth are closely dependenton how the right-of-way is maintained [1]. Crown diameter isgenerally a function of the tree age, but for vegetation close tothe overhead lines, crown growth becomes also a function ofthe vegetation’s last trim date. In addition, the use of herbicidesor growth regulators also affects the tree growth, and cannot beeasily handled in growth models.

Another key problem encountered when applying a growthmodel to the failure-rate problem is the requirement for an ad-ditional model. This model must develop a relationship betweenthe tree growth, as predicted by the growth model, and the outputfailure rates.

For these reasons, existing tree growth models do not seemwell suited to the distribution system vegetation related failure

rate prediction problem, and this is why a direct failure ratemodel was developed.

III. FAILURE-RATE MODELS

To find the model that best represents the time-varying vege-tation–related failure rate, several regression models were devel-oped [11], [12]. Among these models are parametric models in-cluding a linear model, a multivariable linear model, and an ex-ponential model. The linear model is the simplest model and issimply a function of time since last maintenance. This model isused as a basis for comparison with the other models. The linearmodel can be extended to a potentially more accurate multivari-able linear model by including climatic variables that can affectvegetation growth. For the multivariable linear model developedhere, the variables included are the annual average daily min-imum temperature, annual average daily maximum temperature,and annual average daily precipitation. Temperature and precip-itation are key parameters in vegetation growth processes. Thethird regression model considered was an exponential model.The growth pattern for some trees may be represented by a sig-moidal growth function where the young growth is largely ex-ponential. If overhead line failure rates are directly proportionalto tree growth, their failure rates may also be a sigmoidal func-tion of time. The shortness of trimming cycles compared to treelifetime suggests that the failures might conform to the younggrowth model.

The three regression models described above are parametricmodels. However, the relationships between the climate and treegrowth can be very complex. For this reason, an artificial neuralnetwork (ANN) model was developed. It does not require anexplicit representation of the relationships between the climaticfactors and the resulting failure rates.

The regression models and the ANN model developed in thispaper all require historical data. These data must include thehistorical outage data covering a reasonably long time span,historical climatic data, and the feeder vegetation maintenancehistory. For best model results, a thorough and accurate outagedata-collection effort is required.

The first model for failure rate is a linear regression modelof (2). This model is the simplest model and is a benchmark towhich the remaining three models may be compared. The inde-pendent variable in this model is, which is the time in yearssince the last feeder vegetation maintenance. The regression co-efficients are and .

(2)

The second model is the exponential model of (3). This modelattempts to represent the exponential young growth portion ofthe long-term sigmoidal tree growth pattern.

(3)

The third model is the multivariable linear model of (4). Anextension of (2), it includes the effects of temperature and pre-cipitation on the failure rate. The model is

(4)


Fig. 2. ANN failure-rate model.

where and are the annual average daily minimumand maximum temperatures, respectively, andis the annualaverage daily precipitation.

Each regression is a weighted least squares regression, wherethe regression minimizes the sum of weighted squared error(SWSE).

SWSE (5)

The weights are the feeder lengths, is the actual failurerate, and is the estimated failure rate.

The fourth model is an ANN model [13], [14] that uses thesame inputs as the multivariable linear model. The advantageof this model is that it does not require that the relationships be-tween the independent variables be explicitly known. The modeluses the data to learn the relationships between the inputs andthe output. One of the most common networks is a feedforwardnetwork that is trained with backpropagation. The backpropa-gation algorithm is used because it has the ability to generalizebeyond the training data.

After extensive experimentation, an ANN model with onehidden layer and seven neurons in the hidden layer yielded thebest results. A diagram of the ANN failure-rate model is shownin Fig. 2. A learning rate of was used with no mo-mentum, . Bias was incorporated in the model, and abinary sigmoid activation function was used. There is little the-oretical justification for these parameter values, but they provedto work well in practice. The weighting of the training datapoints as a function of feeder length was accomplished by pre-senting the ANN with feeder data points at a frequency in roughproportion to the feeder length. Thus, a data point from a feeder10 miles long would be presented to the ANN during training10 times more often than one from a feeder one mile long.

The ANN consistently converged after approximately 4000epochs, where one epoch is one sweep of the training data set.This took approximately 30 min on a 300-MHz PC.

IV. RESULTS

The four failure-rate models were fit with a small dataset. The historical outage information was obtained from the

TABLE IWEIGHTED MEAN FAILURE RATES (FAILURES/MILE-YEAR) FOREACH MODEL

Snohomish County PUD #1 distribution system from years1993 through 1996, and the climatic data were taken fromseveral weather stations in Snohomish County. The Snohomishsystem has approximately 280, mostly overhead, distributionfeeders.

The historical outage data base included the following fields:the time/date of a sustained outage, the outage cause (such asvegetation, equipment failure, animal, or other), the outagestreet address, the outage the feeder occurred on, the number ofcustomers affected, and the restoration time. From the historicaloutage data base, the overhead line failure rates were recordedby feeder and included only outages caused by vegetation.Only the 32 feeders, which were trimmed in the 4-yr period, areincluded in this data set. Each year for each feeder represents adata point, yielding 128 data points for the following analysis.These data points are provided in Table IV in the Appendix.The results presented in this section are based on a seven-yeartrimming cycle, that is, the year before a known trim date wastaken to be seven years since the previous trim date, which wasunknown.

The mean failure rate for each year following trimming wascalculated from the data and is shown in Table I in the secondcolumn. The mean failure rates calculated using estimated indi-vidual feeder failure rates from each of the four models are alsoshown in this table. A graphical comparison between the esti-mated weighted mean failure rates given by each model and thefailure rate calculated from the data is shown in Fig. 3.

Note that the failure rate for the first year is higher than thefollowing years. The first year since trimming is taken as the endof the year in which the feeder was trimmed. The trimming isassumed to occur at the beginning of the year. However, feedersare sometimes trimmed in the middle or later part of the year.Hence, the failures before the feeder was trimmed inflate thefailure rate for the first year. To account for this, the estimatedyear one failure rate is taken as the average of the estimatedfailure rate at the end of the cycle (year seven) and the beginningof the cycle (year two).

After the model parameters were determined, theroot-weighted mean-square error (RWMSE) was calcu-lated for each model using (6). The results are summarized inTable II.

RWMSE (6)


Fig. 3. Predicted versus actual failure rates for the (top) linear and exponential,and (bottom) the multivariable linear and neural network models.

TABLE IIRWMSEFOR FAILURE–RATE MODELS

The RWMSE is large compared to the mean failure rates, in-dicating large random variation in failure rates. The neural net-work model fits the data slightly better than the other models.The predicted failure rate closely follows the yearly mean failurerate, with the exception of the small differences in years twoand four. Both the neural network model and the multivariablelinear model perform better than the other two models. This in-dicates that weather parameters may be used to better predictyear-to-year variation in the failure rate.

Each model can also be evaluated for generality (i.e., howwell it predicts unknown values). One feeder at a time is ex-cluded from the test data, and the model is evaluated and thenused to estimate failure rates for the excluded feeder. The gen-eralization RWMSE from this process, shown in Table II, is anindication of the ability of the model to estimate failure ratesfor new data. Based on this test, the multivariable linear modeldoes slightly better at predicting unknown failure rates. Thelinear and exponential models had a generalization error thatwas slightly higher than their fitting error. The ANN had theworst generalization error. This error reflects the limitations ofa very small data set. When the long feeders are removed, a sig-nificant portion of the training set is lost (due to the weightingof the frequency of use of the values in the training set), and theANN loses accuracy.

TABLE IIIAVERAGE CLIMATE DATA

V. CONCLUSIONS

This paper investigated models that could be used to predictthe time-varying, vegetation-related failure rates of overheaddistribution power lines. Existing vegetation growth modelswere found to be unsuitable for this purpose, as they were notdeveloped for the vegetation encountered along distributionfeeders, and operate over a long time period. Instead, severaldirect failure-rate models based on vegetation growth parame-ters were developed and evaluated using historical data. Whilethe ANN model fits the data well, the multivariable linearmodel proved to be the most accurate in predicting unknownfailure rates.

In the future, the accuracy of the failure–rate models may beenhanced by the inclusion of additional climatic and environ-mental inputs such as tree density, soil characteristics, and sun-light exposure. The inclusion of the type of maintenance activityperformed and major outage causing events such as wind, ice,and snow storms in the failure-rate determination may also yielda more accurate model.

The vegetation-related failure rate model is a key componentfor line clearance maintenance scheduling. It provides thenecessary link between a particular vegetation maintenanceschedule and line-segment failure rates.

APPENDIX

The climate data, including the average annual daily precip-itation, average annual maximum temperature, and average an-nual minimum temperature for years 1993 through 1996 aregiven in Table III. These data are used in the multivariable linearregression and the neural-network failure-rate models.

The historical outage data and historical maintenance dataused in development of the regression models and the neuralnetwork model are given in Table IV. The fields labeled “Trim,”display the feeder’s year in the maintenance cycle.

REFERENCES

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[4] L. Dai and R. D. Christie, “The optimal reliability-constrained lineclearance scheduling problem,” inProc. 26th Annu. North Amer. PowerSymp., vol. 1, Manhattan, KS, Sept. 1994, pp. 244–249.


TABLE IVFEEDERFAILURE- RATE AND TRIMMING CYCLE DATA

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[12] I. Miller and J. E. Freund,Probability and Statistics for Engi-neers. Englewood Cliffs, NJ: Prentice-Hall, 1985.

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Duane T. Radmerreceived the B.Sc. degree in electrical engineering from Gon-zaga University, Spokane, WA, in 1994, and received the M.Sc. degree in elec-trical engineering from the University of Washington, Seattle, in 1999.

Currently, he is an Electrical Enginner at Itronix Corporation, Spokane, WA.His fields of interest include distribution system reliability assessment and mo-bile computing electronics.

Mr. Radmer is a member of Tau Beta Pi.

Paul A. Kuntz (M’99) received the B.Sc. and M.Sc. degrees in electrical en-gineering from Gonzaga University, Spokane, WA, in 1993 and 1995, respec-tively. He is currently pursuing the Ph.D. degree in electrical engineering at theUniversity of Washington, Seattle.

His fields of interest include distribution system reliability assessment andpower system optimization.

Richard D. Christie (M’76) received the B.Sc. and M.E. degrees in electricpower engineering from Rensselaer Polytechnic Institute, Troy, NY, in 1973 and1974, respectively, and the Ph.D. degree in electrical and computer engineeringfrom Carnegie Mellon University, Pittsburgh, PA, in 1989.

Currently, he is Associate Professor at the University of Washington, Seattle.He has served in the U.S. Navy nuclear power program and has also worked atLeeds & Northrup, North Wales, PA.


Subrahmanyam S. Venkata(F’89) received the Ph.D. in electrical engineeringfrom the University of South Carolina, Columbia, in 1971.

Currently, he is Chairman of the Electrical and Computer Engineering De-partment at Iowa State University, Ames. He has published and presented morethan 130 papers and is coauthor ofIntroduction to Electric Energy Devices(En-glewood Cliffs, NJ: Prentice-Hall, 1987).

Dr. Venkata is a member of Tau Beta Pi, Sigma Xi, Eta Kappa Nu, and severalIEEE committees and subcommittees.

Robert H. Fletcher (M’80) received the M.Sc. degree from the University ofWashington, Seattle, in 1994.

Currently, he is the Principal Planning Engineer at Snohomish County PUD#1, Everett, WA.

Mr. Fletcher is a member of the Risk, Reliability, and Probability Apllica-tions IEEE subcommittee, Working Group on Distribution System Design ofthe IEEE Distribution subcommittee, and Working Group of Distribution Plan-ning of the IEEE Power System Planning and Implementation committee.

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Predicting vegetation-related failure rates for overhead distribution feeders