IEEE Transactions on Power Systems, Vol. 13, No. 2, May 1998

704

Distribution System Reliability: Default Data and Model Validation R.E. Brown

J.R. Ochoa

Member

Member

Transmission Technology Institute ABB Power T&D Company Inc. 1021 Main Campus Drive Raleigh, NC 27606

Distribution Information Systlems Development ABB Power T&D Company Inc. 110 Corning Road, Suite 101 Cary, NC 2751 1

Abstract-Distribution system reliability assessment is able to predict the interruption profile of a distribution system based on system topology and component reliability data. Unfortunately, many utilities do not have enough historical component reliability data to perform such an assessment, and are not confident that other sources of data are representative of their particular system. As a result, these utilities do not incorporate distribution system reliability assessment into their design process and forego i t s significant advantages. This paper presents a way of gaining confidence in a reliability model by developing a validation method. This method automatically determines appropriate default component reliability data so that predicted reliability indices match historical values. The result is a validated base case from which incremental design improvements can be explored.

I. INTRODUCTION Customer demands for reliable power are quickly changing. Not only is more energy being demanded, but this energy must be provided at increasing levels of service reliability. A sustained interruption can cost certain customers hundreds of thousands of dollars per hour. Even a momentary interruption can cause computer systems to crash and industrial processes to be ruined. To many customers with sensitive electric loads, reliability as well as the cost of energy may drive decisions such as: where a new plant is to be located, whether an existing plant will be relocated, or whether a switch to a new energy provider will be pursued. PE-870-PWRS-2-06-1997 A paper recommended and approved by the IEEE Power System Planning and Implementation Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power Systems. Manuscript submitted December 27, 1996; made available for printing June 9, 1997.

Since a majority of customer reliability problems stem

from distribution systems [l],utilities must focus on distribution systems if substantial improvement in customer reliability are to be gained. Deregulation of the industry has also made it critical for utilities to provide this level of reliability at the lowest possible cost. To do this, predictive reliability assessment methods are needed [ 2 ] . Distribution system reliability assessment is a quickly maturing field. It has evolved from the first EPRI program in 1978 [ 3 ] , to programs developed and used in-house by utilities [4-71, to commercially available software products. These planning tools are able to predict the reliability of a distribution system based on system topology and component rehability data. Unfortunately, these products will never gain widespread use until utilities are confident that available data is representative of their actual system. Ideally, a utility will have a large amount of historical data from which it can determine the reliability of various components such as lines, prlotection devices, and switches. Most utilities, however, do not have this information available. Values may be obtained from published data corresponding to other systems, but this data may not be representative of the system under consideration. This data discrepancy is most evident when predicted system reliability indices do not agree with historically computed reliability indices. Most utilities do not have a substantial amount of historical component reliability data. Nearly all utilities, however, have historical system reliability data in the form of reliability indices (e.g., SAIFI, SAIDI-see Section 2.1). When a system is modeled, the reliability indices predicted by the assessment tool should agree with these historical values. If so, a certain level of confidence in the model is achieved and more specific reliability results (e.g., the reliability of a specific load point or the impact of a design change) can be trusted to a higher degree. When this confidence has been achieved and predicted results match historical results, the reliability model is said to be validated. This paper presents a new method of distribution system reliability model validation. It first identifies which default component reliability parameters should be modified by performing a sensitivity analysis on a test system. It then presents a method of computing these parameter values so that pre-

0885-8950/98/$10.00 0 1997 IEEE

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dicted system index values match historically computed index values. 11. PREDICTIVE RELIABILITY ASSESSMENT

Predictive reliability assessment can be broken down into three basic steps: defining meaningful measures of reliability, developing a method to compute these measures, and judiciously choosing the best available data to be used by the developed method. This section discusses each of these steps in brief.

2.1 Measures of Reliability In the context of distribution systems, reliability has historically been associated with sustained customer interruptions (interruptions lasting more than a few minutes). This is reflected in the predominant use of the reliability indices SAIFI and SAIDI [8]. These values represent the number of sustained interruptions and the number of interruption hours that an average customer experiences in a given year (the reliability indices ASAI and CAIDI are also widely used, but they can be directly computed from SAIFI and SAIDI and offer no new information). Although sustained interruptions have historically received the most attention, the growing sensitivity of electronic loads has made the inclusion of other voltage disruptions necessary when considering customer reliability. The first of these to emerge is momentary interruptions, which is already an indispensable aspect of distribution reliability [9]. Voltage sags are quickly making the transition from a power quality issue to a reliability issue, and voltage spikes and voltage flicker may be soon to follow. The reliability aspects considered in this paper are: momentary interruption frequency, sustained interruption frequency, and sustained interruption duration. The system reliability indices that correspond to these measures are: MAIFI (the Momentary Average Interruption Frequency Index), SAIFI (the System Average Interruption Frequency Index), and SAIDI (the System Average Interruption Duration Index: These indices reflect the overall reliability of a specified area (e.g., an entire system, a single feeder, a region). Equations corresponding to these indices are: MAIFI = SAIFI = SAIDI =

# of Customer Momentary Interruptions

# of Customers Served # of Customer Sustained Interruptions # of Customers Served

Sum of Customer Interruption Durations ## of Customers Served

per year

(1)

per year

(2)

hours/ year

(3)

Reliability indices are typically computed by utilities at the end of each year by using historical outage data recorded

in distribution outage reports. This is important so that utili-

ties know how their systems are performing, but is less useful when the specific impact of various design improvement options wish to be quantified and compared. To do this, a method must be developed which is capable of predicting reliability measures based on system topology, component reliability data, and operational data.

2.2 Reliability Assessment Method The basic methods capable of producing the reliability of a distribution system are: network modeling, Markov modeling, Monte Carlo simulation, and state enumeration. This paper uses state enumeration due to its computational efficiency and its ability to model complex system behavior. In the state enumeration method, system states are dynamically generated by considering each possible primary contingency (including sustained faults, self-clearing faults, and passive outages). For each primary contingency, many possible system responses are considered. System responses include reclosing and sectionalizing behavior, imperfect protection systems, upstream fault isolation, and load restoration. The result is a sophisticated reliability model which can accurately model rare events which can potentially have a large impact on the reliability of the system. For example, if a momentary interruption occurs on a feeder and the recloser at the beginning of the feeder becomes stuck, the substation bus protection must clear the fault. This will result in a sustained interruption for the entire bus. Such a situation is rare, but has a high impact to the system and should therefore be included in the reliability assessment. The above reliability assessment method has been implemented in the engineering tool DISTREL (DISTribution RELiability), which is currently under development. This is an engineering tool which will eventually be an add-on module for ABB’s distribution analysis package CADPAD, and is the radial complement of ABB’s network reliability assessment package NETREL (NETwork RELiability). 2.3 Component Reliability Data Before the reliability assessment described in Section 2.2 can be performed, each component must be assigned reliability data. Descriptions of the various parameters are: Momentary failure rate-this is the frequency of faults that will clear themselves if the fault site is deenergized and then re-energized. Sustained failure rate-this is the frequency of faults Is: that requires a crew to be cleared and repaired. Passive failure rate-this is the frequency of compohp: nent outages that interrupt the flow of current, but do not cause fault current to flow. MTTR: Mean Time To Repair-this is the expected time it will take a crew to repair a component outage and restore the system to its normal operating state.

h,:

706

MTTS: Mean Time To Switch-this is the expected time it will take after a failure occurs for sectionalizing switch to be toggled. PSS: Probability of Successful Switching: the probability of a switching device (a protection device, a loadbreak switch, or a no-load break switch) of actually switching if it is supposed to switch. The complement of PSS is switch unreliability: For a reliability model to produce representative results, component reliability data must be representative of the system being modeled. Ideally, a utility will have a large amount of historical data for each component type under consideration. Unfortunately, most utilities are still many years away from having such data. The alternative is to use previously published data that has been collected for other systems. This data may or may not be representative of the system to be studied. In fact, if predicted system indices do not match historically computed system indices, it is likely that this data is not appropriate. The remainder of this paper discusses a method of determining appropriate component reliability values so that predicted indices match historical indices. This method will then be applied to the test system described in Section 111.

ground line sections might be assigned a different failure rate per unit length. In this way, the number of reliability parameters used in a given system is greatly reduced. There are still, however, many more default parameters than can be effectively adjusted with the limited amount of historical data that is typically available. To help decide which default parameters will be adjusted, a sensitivity analysis will be performed.

Switches* I 0.01 0 00 STS I n ni I o no *Switching times are assumed to be 1 hour

I

4 4

I

0.95

I

099

LP7

111. TEST SYSTEM The test system used in this paper is Bus 2 of the RBTS as described in [lo]. This system consists of four overhead 11-kV feeders (FLF4) fed from a distribution substation and serves 22 load points (LP1-LP22). F1 and F2 are operated in a looped configuration as are feeders F3 and F4. The test system topology is shown in Figure 1 and the component reliability data initially assigned is shown in Table 1. The reliability data of Table 1 will result in certain reliability index values. It is likely that these values will not match historically computed values if the component data is not representative of the equipment being modeled. Predicted and historical index values for this system can be seen in Table 2. As can be seen from Table 2, predicted reliability index values do not match historically computed index values. To validate the system model, certain component parameters should be adjusted so that all values match. Unfortunately, there are hundreds of component parameters to choose from. Section 4 describes how to judiciously choose which parameters will to adjust when validating a distribution system reliability model.

9

IV. SELECTING PARAMETERS TO ADJUST When first creating a predictive reliability model, default values are typically assigned to various classes of components. For example, all overhead lines sections might be assigned the same failure rate per unit length, and all under-

1

LP22

Figure 1. Test System Topology

707

4.1 Sensitivity Analysis

4.2 Selection of Default Component Parameters

The sensitivity of a function to a parameter is defined as the partial derivative of the function with respect to that parameter. This is a measure of how much the value of the function will change if the parameter is perturbed. This can be approximated by actually perturbing the parameter (keeping all other parameters fixed) and measuring how much the function changes. For example, if the default overhead line MTTR is increased by 1%, and the resulting SAIDI value increases by O S % , the sensitivity of SAIDI to default overhead line MTTR is (0.5 / 1) * 100% = 50%. A sensitivity analysis of MAIFI, SAIFI, and SAIDI to all default component parameters has been performed and the results are summarized in Table 3.

Because system reliability indices are most sensitive to changes in overhead line default values, overhead line hM, overhead line is and overhead , line MTTR will be the default values that will be adjusted when validating a reliability model. For a given area under consideration, these results in three degree of freedom in a search space looking for three values: MAIFI, SAIFI, and SAIDI. There is yet another justification for choosing overhead line parameters for adjustment. Since line failure rates and repair rates are largely dependent upon vegetation, treetrimming, and weather, there will likely be significant variation in line failure rates from utility to utility. This means that finding representative data from previously published data will likely be more difficult for overhead lines than for other types of components. Since MAIFI and SAIFI are predominantly affected by overhead line failure rates, model validation will usually results in representative values for these failure rates. SAIDI, however, can be significantly influenced by other component types. For model validation to obtain a representative value of line MTTR, it is essential to obtain the best possible values from other sources for parameters with a high SAIDI sensitivity.

I

d Failure Rate Mean Time To Repair Unreliability * Reclosers Recloser FX Recloser MTTR Unreliablity * Sectionalizing Switches Sustained Failure Rate 'ime To Repair Mean 'I Switching Time ,

... .,

0% -1%

I I I

0% 0% -8%

I

0% 7%

I

I I

4%

0% 15%

I 0% 0% 0% -,"

I I I

6% 12%

I I I

6% 26%

I

I 4% 0% 0%

I I I

3% 3% 22%

*Unreliability is defined as (1 - PSS).

As can be seen in Table 3, MAIFI is much more sensitive to the default overhead line momentary failure rate (AM) than to any other reliability parameter. This is a good indication that if the predicted value of MAIFI does not agree with the historical value of MAIFI, default overhead line A M should be adjusted. Table 3 also shows that SAIFI is much more sensitive to the default overhead line sustained failure rate (As) than to any other reliability parameter. This implies that the default overhead line As should be adjusted if the predicted value of SAIFI does not agree with the historical value of SAIFI. The last set of reliability index sensitivities correspond to SAIDI. Table 3 shows that SAIDI is predominately effected default overhead line hs and default overhead line MTTR. It should be pointed out that the sensitivity of SAIDI to component default parameters is more distributed than MAIFI and SAIFI. This is reflected in relatively high sensitivities to recloser unreliability and switching time. Therefore, if predicted SAIDI values do not match historical SAIDI values, any one or all of these parameters could be undesirable.

4.3 Default Component Parameter Customized Component Values

Multipliers

and

Although a utility may not have enough historical data to determine the reliability parameters for all components on its system, it may know the relative reliabilities of certain components. For example, it may be known that the overhead line failure rate in a certain heavily treed area is twice as much as in a lightly treed area. Similarly, the MTTR of a component far away from a crew dispatch location may by 50% longer than a component close to the dispatch location. This type of information can be incorporated into the reliability model in the form of default component parameter multipliers. A default component parameter multiplier is simply a number that corresponds to a component parameter. The number that will be assigned to the component parameter is equal to the default component parameter multiplied by the corresponding default component parameter multiplier. For example, if a specific line section has a MTTR multiplier of 1.5 and the default line MTTR is 4 hours, then the line will be assigned a MTTR of (1.5 x 4)= 6 hours. A utility may also have specific component reliability data for certain components on its system, but not for all components. To accommodate this information, each component parameter is allowed to be customized. If a value is customized, is not allowed to be changed during the model validation process.

708 V. DETERMINING DEFAULT PARAMETER VALUES

This section develops a method of determining overhead line section default parameters so that predicted values of MAIFI, SAIFI, and SAIDI agree with historically computed values. Before this method is presented, however, is advantageous to examine how these index values actually change as line section default parameters change. The first default line section parameter that will be examined is AM. MAIFI, SAIFI, and SAIDI as a function of hMcan be seen in Figure 2. The figure reveals that each index varies linearly with failure rate. This makes sense because each momentary failure affects the system in the same manner, regardless of how many occur. The next default line section parameter that will be examined is As. MAIFI, SAIFI, and SAIDI as a function of hs can be seen in Figure 3 . As was seen with AM, all indices vary linearly with As. This also makes sense because our model assumes that each sustained interruption impacts the system in the same way, regardless of the frequency. This assumption is reasonable except during major events when a common mode (e.g., wind, earthquake, icing) is causing many failures to happen at the same time. The method used in this paper does not consider major events. The last default line section parameter that will be examined is MTTR. MAIFI, SAIFI, and SAIDI as a function of MTTR can be seen in Figure 4. Two interesting features can be observed from this figure. First, SAIFI and MAIFI do not change as MTTR changes. Second, SAIDI is piecewise linear with respect to MTTR. The first result is expectedincreasing the repair time of a component will not cause any customers to experience more or less interruptions. The second results is due to switching times. After the MTTR of a component rises above certain levels (corresponding to the MTTS of switches), it will become advantageous to isolate the fault and restore service to some customers. This results in the a piecewise linear relationship between SAIDI and MTTR. Once the MTTR is above the longest MTTS, the relationship remains linear. Determining the appropriate values of default overhead line AM, As, and MTTR (hereafter referred to as h M , hs, and MTTR) can be broken down into two steps. This is possible because MTTR has no effect on MAIFI and SAIFI. Consequently, XM and As can be chosen so that predicted MAIFI and SAIFI values match historical values. After this has been done, MTTR can be adjusted to control SAIDI without impacting MAIFI or SAIFI. The relationship of SAIFI and MAIFI to adjustments of L M and As (AhM and A&) is given in (4):

4.5

,

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0

02

04

06

08

1

Overhead Line Momentary Falure Rate (kmlyr)

Figure 2. Effect of

0

02

04

on ReliabilityIndices

06

08

1

Overhead Line %stained Failure Rate (kmlyr)

Figure 3. Effect of hs on ReliabilityIndices

t 0

2

6

8

Overhead Line Momentary Falure Rate (kmlyr)

Figure 4. Effect of MTTR on Reliability Indices

10

709

SAIFI, MAIFI, SAIFI, MAIFIi

: :

AS

:

hM

:

: :

Target SAIFI value Target MAIFI value Initial SAIFI value Initial MAIFI value Sustained Line Failure Rate (/km/yr) Momentary Line Failure Rate (/km/yr)

default parameters so that predicted values of MAIFI, SAIFI, and SAIDI match historical values. The choice for overhead line default parameters for adjustment is based on a sensitivity analysis. After a distribution system reliability model has been validated, utilities can be reasonable confident that the model is representative of its actual system. This will facilitate the incorporation of the reliability into design and planning procedures which will aid in providing high levels of reliability for the lowest possible cost. VII. REFERENCES

In equation (4), the partial derivatives can be approximated by perturbation methods. This allows AhM and Ahs to be solved for. The new values of are then found by adjusting the old value by the computed change: Le,= Lola+ AL. Once these new values are computed, the relationship between SAIDI and MTTR can be used to find the new value of MTTR. This relationship is:

AMTTR + SAIDI, dMTTR SAIDZ, : Target SAIDI value SAIDI, : Initial SAIDI value MTTR : Mean Time To Repair (hours)

SAIDI, =-

If all parameterhndex relationships are linear within the ranges considered, equations (4) and ( 5 ) will results in predicted MAIFI, SAIFI, and SAIDI values which exactly match historical values. If an exact match is not found, the process can be repeated iteratively until a certain error tolerance is reached. This model validation method has been applied to the test system described in Section 3 on a feeder by feeder basis. For the reliability data given in Table 2 and Table 3, solutions converged for each feeder in a single iteration. After model validation, all predicted reliability indices matched historical values to within 0.1%. This method was also been tested for a wide variety of other reasonable data sets, and converged in a single iteration for all cases. The only difficulty encountered when using this model validation method occurs when the system is not completely controllable. An example of when this occurs is when there are no reclosers on the system. In this situation, no momentary interruptions can occur and MAIFI is not controllable. To handle this, equation (4) should be reworked to only consider SAIFI. VI. CONCLUSIONS Distributions system reliability models can be validated by adjusting default component reliability parameters so that predicted results match historical results. This has been dem-

onstrated on a 4 feeder test system by adjusting overhead line

R. Billinton and S. Jonnavitihula, ‘A Test System for Teaching Overall Power System Reliability Assessment,’ IEEWPES 1996 Winter Meeting, Baltimore, MD, IEEE, 1996. R. Brown, S. Gupta, S.S. Venkata, R.D. Christie, and R. Fletcher, ‘Distribution System Reliability Assessment: Reliability and Cost Optimization,’ 1996 IEEE Transmission and Distribution Conference Proceedings, Los Angeles, CA, September, 1996. EPRI Report EL201 8, Development of Distriburion Reliability and Risk Analysis Models, Aug. 1981. (Report prepared by Westinghouse Corp.) R. Brown, S. Gupta, S.S. Venkata, R.D. Christie, and R. Fletcher, ‘Distribution System Reliability Assessment Using Hierarchical Markov Modeling,’ IEEE PES Winrer Meeting, Baltimore, MD, January, 1996. S. R. Gilligan, ‘A Method for Estimating the Reliability of Distribution Circuits,’ IEEE Transactions on Power Delivery, Vol. 7 , No. 2, April 1992, pp. 694-698. G. Kjfille and Kjell Sand, ‘RELRAD - An Analytical Approach for Distribution System Reliability Assessment,’ IEEE Transacrions on Power Delivery, Vol. 7, No. 2, April 1992, pp. 809-814. Yuan-Yih Hsu, Li-Ming Chen, Jiann-Liang Chen, et al., ‘Application of a Microcomputer-Based Database Management System to Distribution System Reliability Evaluation,’ IEEE Transactions on Power Delivery, Vol. 5, No. l , Jan. 1990, pp. 343-350. R. Billinton and J. E. Billinton, ‘Distribution System Reliability Indices,’ IEEE Transactions on Power Delivery, Vol. 4, No. 1, Jan 1989, pp. 561-568. R. Brown, S. Gupta, S.S. Venkata, R.D. Christie, and R. Fletcher, ‘Distribution System Reliability Assessment: Momentary Intemptions and Storms,’ IEEE PES Summer Meeting, Denver, CO, June, 1996. [IO] R. N.Allan, R. Billinton, I. Sjarief, L. Goel, and K. S. So, ‘A Reliability Test System for Educational Purposes - Basic Distribution System Data and Results,’ IEEE Transactions on Power Systems, Vol. 6, No. 2, May 1991, pp. 813-820.

VIII. BIOGRAPHIES Richard E. Brown received his Ph.D. in electrical engineering from the University of Washington in 1996. Before beginning graduate studies, Dr. Brown worked as a consulting engineer designing industrial distribution systems. He is currently a senior engineer at ABB’s Transmission Technology Institute and specializes in the areas of distribution systems, reliability, power quality, and design optimization.

J. Rafael Ochoa received his Ph.D. from the University of Manchester Institute of Science and Technology (UMIST) in 1986. He is currently the manager of ABB’s Distribution Information System’s development group. Prior to this position, Dr. Ochoa was the Reliability and Power Quality Group’s team leader at the Transmission Technology Institute. From 1987 to 1992, Dr. Ochoa was a Lead Engineer at Ferranti Intemational Controls Corporation (HCC). From 1978 to 1987, Dr. Ochoa was a Senior Engineer at the Electrical Power Research Institute of Mexico.