Prediction of customer load point service reliability worth estimates in an electric power system

Prediction of customer load point service reliability worth estimates in an electric power system

L. Goel R. Billinton

Indexing terms: Power system optimisation, Reliability test systems

Abstract: The basic concepts associated with quantitative reliability evaluation are reasonably well accepted in the electric power industry. The justification of new facilities and system modifi- cations now normally includes specific reference to reliability and one approach that is receiving con- siderable attention is the assessment of the societal worth or benefit associated with power system reliability, and conversely the costs to consumers of power supply interruptions. The paper presents three different methods for evaluating system customer load point reliability worth factors designated interrupted energy assessment rates (IEAR). These factors consider the influence of outages in all parts of the electric power system. The developed IEAR can be used with the available adequacy indices to assess the severity associated with unsupplied energy owing to supply interruptions. The IEAR can be used as customer related indices in making decisions regarding load curtailment philosophies and reliability related rate setting. The concepts of using a customer damage function in association with customer reliability indices are presented and illustrated using a reliability test system.

1 Introduction

There is an increasing interest in economic optimisation approaches in power system planning and expansion studies. Evaluation of the costs associated with different system configurations and the corresponding customer reliability worth is generally termed as reliability cost/ worth assessment. A basic objective in these evaluations is to determine the optimum level of service reliability. The evaluation of reliability cost through the identifica- tion and analysis of criteria and methods used to predict and quantify reliability levels has progressed significantly during the past two decades. By comparison, the assessment of reliability worth is not as well developed with most approaches providing only an indirect evaluation. This is due to the fact that the assessment of the societal worth of electric service reliability is an extremely complex and subjective task. The worth of reliability

~~~ ~

0 IEE, 1994 Paper 9946C (B), received 5th October 1993 L. Goel is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 2263 R. Billinton is with the Power Systems Research Group, Department of Electrical Engineering, University of Saskatchewan, Canada S7N OW0

390

refers to the value of continuous electrical service. It is more easily estimated and expressed, however, as a function of the costs resulting from the lack of such service. This implies that the losses and damages resulting from interruptions in electrical supply might represent the amount customers and utility management would be willing to pay to prevent such power outages. The worth of reliability can therefore be expressed in terms of customer outage costs.

A wide range of procedures have been used to assess reliability worth. One approach which is finding con- siderable acceptance uses the cost of electric supply interruptions incurred by customers due to power failures [l , 21. Customer interruption costs can be related to the calculated reliability indices used in system planning and operation and provide a practical tool for reliability worth evaluation.

The basic objective of a modern electric power system is to satisfy the system load requirements as economically as possible and with a reasonable degree of continuity and quality. Power system reliability is usually defined as the ability of the system to provide an adequate supply of electrical energy [3]. System reliability can be divided into the two distinct categories of system security and system adequacy [4] in which security relates to dynamic system analysis and adequacy is confined to steady-state long-term assessment. This paper is confined to adequacy assessment of an overall electric power system in regard to measuring the worth of service reliability. Overall adequacy evaluation of an electric power sytem involves a comprehensive analysis of the three principal functional zones of generation, transmission and distribution. These zones can be combined to obtain three distinct hierarchical levels (HL) [4] and adequacy assessment can be conducted at each HL. HLIII adequacy assessment involves the consideration of all three functional zones to assess electric service reliability at specific customer load points [SI. This paper pertains to adequacy assessment at HLIII.

To assess the worth of electric service reliability it is necessary to link the calculated adequacy indices to the consumer costs of interruption. Two sets of reliability indices can be defined at HLIII, namely the customer load point indices and system performance indices [3, 41. The individual load point indices are the average failure rate 1, the average outage duration r and the average annual unavailability U. The most commonly used system indices are those of system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), customer average interruption duration index (CAIDI), energy not supplied (ENS), average service availability index (ASAI) and its com- plimentary average service unavailability index (ASUI).

IEE Proc.-Gem. Transm. Distrib., Vol. 141, No. 4, July 1994

The basic definitions and mathematical formulations of these indices are given in the Appendix.

This paper presents a contingency enumeration method for obtaining the customer load point expected energy not supplied (EENS) index. This index is utilised together with customer outage cost functions to evaluate a factor designated as the interrupted energy assessment rate (IEAR) at HLIII [SI. The IEAR aggregates the costs incurred by a customer for each unit of unsupplied energy due to power interruptions. IEAR have been developed [7, 81 at both HLI and HLII. This paper describes a method for IEAR evaluation at HLIII using the concepts applied to HLI and HLII. Two other methods [9] using the final load point indices of 1, r and U and the system indices SAIFI, SAID1 and C A l D l in conjunction with appropriate cost functions are also presented. The three methods are then compared in terms of their ability to provide a valid IEAR. The concepts presented are illustrated by application to a small but practical test system designated as the RBTS [lo, 111.

2 Customer damage functions

Actual or perceived costs of customer supply interruptions can be used to determine the worth of electric service reliability. A variety of approaches have been used to investigate these costs [l, 23. One method which has been used to establish acceptable reliability worth estimates is to survey electrical consumers to determine the monetary losses associated with supply interruptions. The data compiled from these surveys leads to the formu- lation of sector cost functions, which are referred to as sector customer damage functions (SCDF). The SCDF presents the sector interruption costs as a function of the interruption durations. The customer costs associated with an outage at any point in the system involves the combination of the costs associated with all customers affected by that outage. A composite customer damage function (CCDF) can be created which aggregates the composite costs of the customers in the service area to the interruption duration [Z].

Table 1 shows interruption cost estimates in 1987 C$/kW for five interruption durations for the selected customer sectors [l, 123. The data presented in Table 1

Table 1 : Cost of interruptions in S/kW for various sectors [1, 121

Durn. Sector NDE

(min) Lg.lnd. Sm.lnd. Comm. Agric. Resid. G&l Office

1 1.005 1.625 0.381 0.060 0.001 0.044 4.776 20 1.506 3.866 2.969 0.343 0.093 0.369 9.878 60 2.225 9.085 6.552 0.649 0.482 1.492 21.065

240 3.966 25.163 31.317 2.064 4.914 6.558 68.630 480 8.240 55.808 83.008 4.120 15.690 26.040 119.180

Resid. = residential users Comm. =commercial users G&l =government and institutional users Lg.lnd. = large industrial users (peak demand 2 5 MW) Sm.lnd. =small industrial users (peak demand <5 MW) Agric. =agricultural users Office =office space users

are compiled from two major postal customer surveys conducted by the power systems research group of the University of Saskatchewan. The first one was conducted in 1980 for the residential, commercial and industrial sectors [l], while the second one for the agricultural sector was undertaken in 1985 [12]. The various cus-

1EE Proc.-Gener. Transm. Distrib., Vol. 141, No. 4, July 1994

tomer classes incur different monetary losses due to power supply interruptions. The cost coefficients shown in Table 1 reflect these differences. The cost coefficients for each class are also dependent on whether the interruption occurs during an on or off peak period, etc. It can be easily appreciated from the data given in Table 1 that the interruption cost coefficients vary in a nonlinear manner with the outage duration. The SCDF given in Table 1 are the basic data used in this paper for the evaluation of IEAR at specific customer load points.

3 IEAR evaluation a t HLlll

3.1 Method 1 : Contingency enumeration method The estimation of IEAR at HLIII involves all the customer load points associated with a given load centre or service area. Three basic models are required for customer load point IEAR assessment, viz. the cost model, the load model and the system generation, transmission and distribution model. The cost model is in the form of the sector type and its associated SCDF. The load model involves the loads connected at each customer load point. The combined system model consists of relevant tech- nical and reliability parameters of all major components from the system generating units down to the laterals serving the individual customers. The HLIII adequacy assessment presented in this paper includes independent outages of generating units and transmission lines and also outages owing to station related failures. The method [6] is divided into three distinct steps:

(i) At HLII, a composite generation and transmission system contingency evaluation program termed COMREL was used to obtain the expected load curtailed, probability, frequency and duration of each contingency that leads to load curtailment for each system bus. The contingencies considered include outages of up to four generating units, up to three transmission lines, up to two generators with one line, up to two lines with one generator, all the four outages owing to station related failures and the isolation of up to two load buses owing to station related failures.

(ii) At the subtransmission system level, the impact of all outages were obtained at each distribution system supply point. The contingencies considered include all first-order active failures [3], all first-order permanent outages and all second-order overlapping permanent outages.

(iii) At the radial distribution level, the effects owing to outages of system components such as primary main/ laterals/low voltage transformers etc. were considered.

The detailed procedure is given in Reference 6 and is summarised below :

Step i (a) At HLII, for a specified load level, the following

Lkj = load curtailed (MW) at bus k owing to contin-

fkj = frequency (occ/yr) of contingency j at bus k, and D, = duration (h) of contingency j at bus k. (b) For contingency j, the load curtailed L , at bus k is

assumed to be shared in proportion to the average load connected at each individual customer load point at that bus. The load curtailed at each customer load point p of bus k owing to contingency j at HLIII is therefore evaluated.

(c) Outage duration Dkj is used to evaluate the cost of unsupplied energy owing to the interruption seen by all

parameters are obtained at each major load centre (bus):

gencyj

391

customers at bus k. The impact of this duration is different for different load points due to the unique customer characteristics and SCDF. Corresponding to this duration, the cost Ck, j , in $/kW is obtained using the SCDF of the respective customer class at the load point. The costs of interruptions longer than 8 h duration are evaluated assuming the SCDF to have the same slope as that for the 4 to 8 h duration.

(d) The unsupplied energy EENS,, j , is obtained using eqn. 1:

EENSk. j . p Lk, j . p fkj D k j (MWh/yr) (1)

(e) The expected cost of unsupplied energy ECOST,,,,. owing to this contingency is obtained using eqn. 2:

ECOST,, j , p = Lk, j , p f k j ck, j , p (MW-WW-Yr) (2) (j) The total EENS and its total cost ECOST at load

point p owing to N k load curtailment events are obtained using eqns. 3 and 4, respectively.

N k

I= 1

N t

j = 1

EENSk, = EENSk, j , (MWh/yr) (3)

ECOST,, = c ECOST,, j , (MW-$/kW-yr) (4)

Step ii Any outage event that causes the isolation of the distribution supply point involves all customers connected at that supply point. Continuity of supply is assumed to be the sole criterion and therefore all the loads at a supply point are completely isolated due to outage of the supply point. The following procedure is followed for estimating the total contribution from this step to the unsupplied energy EENS and its cost ECOST at each system load point.

(a) For each supply point connected to the subtransmission networks at bus &, the outage events contributing to its isolation are evaluated in terms of the average failure rate At, j , average outage time rk, and annual unavailability Ut, j .

(b) Corresponding to outage time rk, owing to event j, for each of the load points isolated by this event, the cost of interruption, Ck, j , using the SCDF of customer cate- gory p are evaluated.

(c) If La,!, is the average connected load at load p, the corresponding ECOST and EENS owing to event j are evaluated using the following equations :

ECoST,, j . p = ck, j . p

E E N S k . 1. p = p A k j

p ukj

Steps (a) to (c) are repeated for each outage event contributing to a supply point. If N , is the number of subtransmission outage events contributing to customer load point p connected to bus k, then the total EENS and ECOST to individual load points is evaluated using the following equations :

Step iii The final contribution to an individual customer load point comes from the radial distribution network. For a given configuration, the outage events contributing to the isolation of load point p are aggregated and EENS

392

and ECOST from each contributing event obtained as in step 2.

The results from the three steps are combined to obtain the HLIII indices. The overall ECOST, EENS and IEAR at load point p associated with bus k are obtained using eqns. 5, 6 and 7, respectively, where i denotes the step number.

($/kwh) (7) HLIII ECOST,, e

HLIII IEAR,. = HLIII EENSk.,

Eqns. 1-7 are formulated for a constant load level. In practice the load does not stay constant throughout the period of study but is best represented by a load duration curve. A seven-step load model [6] was used to incorpor- ate the effect of varying load levels. The unsupplied energy owing to HLII contingencies and its cost for load point p associated with bus k are evaluated using eqns. 8 and 9, where Nkm) is the number of contingencies leading to load curtailment at bus k for load step m and prob(m) is the associated probability.

7 Ndm)

E E N S k , p = 1 [ zl E E N S k , j . p ] prob (m) (8) m = l

7 Nt(m)

EC0ST.p = Jl :l ECOST,, j , p ] Prob (m) (9) [ The contributions from the subtransmission and distribution networks are based on continuity and the average load levels. and are therefore not affected.

32 Method 2: basic indices method [9] The three-step contingency enumeration method for IEAR assessment at HLIII described previously can be considered to be reasonably comprehensive as it involves consideration of every possible contingency/outage con- dition which causes load curtailment at customer ter- minals. The expected frequency and duration of each outage, in combination with the expected load curtailed and the appropriate SCDF are used to obtain the HLIII IEAR.

This Section describes a method that uses the average or expected HLIII adequacy indices and sector cost functions. The three basic adequacy indices of average failure rate A, average outage duration r and average annual outage time U evaluated at each HLIII customer load point are used together with the SCDF associated with the customer type at each individual load point.

The HLIII average outage duration index rk. at load point p of bus k is used to obtain the cost ck,q in $/kW from the SCDF of the customer type at load point p . The average load curtailed is the average load connected L,, p . The unsupplied energy EENS and its cost ECOST at each load point are then formulated as follows:

EENSk. p = Lao, p I k , p ' k . p (10)

ECoS&, p = p Lk, p ch. p (1 1)

E = %Z ($/kWh) IEAR = E E N S k , p r k . p

IEE Proc.-Gem. T r a m Disnib., Vol. 141, No. 4, July 1994

T

Eqns. 10 to 12 can then be used to evaluate the IEAR at each load point in the configuration under study. The individual load point IEAR can be multiplied by their respective per units loads and added to obtain a bus IEAR.

3.3 Method 3: system indices method [9] This method combines the system indices at the load bus with the CCDF applicable at that bus. The system CAIDI represents the average duration of outage per system customer interruption. The cost in $/kW from the CCDF using this CAIDI duration value can be obtained and used to obtain the system cost of unsupplied energy. The unsupplied energy is obtained by combining the system SAID1 and the average connected bus load. The overall IEAR reflected at the load centre is then evaluated using eqn. 15. This method, however, cannot be used to obtain individual load point reliability worth factors.

system EENS = (SAIFI)(average bus load)(CAIDl)

= (SAIDIXaverage bus load) (13)

x (cost of CAIDI) (14)

system ECOST = (SAIFIXaverage bus load)

(%/kWh) (15) cost of CAIDI

CAlDJ system IEAR =

The contingency enumeration method designated as method 1 uses a comprehensive failure mode and effects approach which recognises the average frequency and duration associated with each contingency event. This is not the same as recognising each distinct event, as the average frequency and duration are used. Recognition of the average duration of each contingency event permits

the nonlinear nature of the individual load point customer damage functions (SCDF) to be incorporated in the event outage cost analysis. In method 2, designated as the basic indices method, the individual contingency events are aggregated to provide the average load point indices of 1, r and U . These final indices, and not the actual individual event data, are then used in conjunction with the associated SCDF to generate the cost factors, i.e. a single outage duration representing the average interruption duration of the load point is used in conjunction with the SCDF. This is therefore an approximation of the approach used in method 1 where the individual event average costs are aggregated. The process of aggregation is further extended in method 3, in which the basic load point indices are aggregated with the customer (number and load) data to provide the system indices of SAIFI, SAIDI, CAIDI, etc. The primary approximation in method 1 is the use of average event frequencies and durations in obtaining the cost factors. Methods 2 and 3 are successive approximations of method 1.

4 Application to the RETS

A single line diagram of the RBTS with complete subtransmission and distribution facilities at two system buses (2 and 4) is shown in Fig. 1. The RBTS has a peak load of 185 MW and an installed capacity of 240 MW consisting of two generating stations (buses 1 and 2) and five major load centers (buses 2 to 6). The detailed composite generation and transmission system data, load data and cost data are presented in Reference 10. The subtransmission and distribution system data for two system load buses 2 and 4 are provided in Reference 11. HLIII analysis has been conducted for these two system

Fig. 1 Complete

I E E Proc.-Gener. Transm. Distrib., Vol. 141, No. 4, July 1994

LP17 LP19 LP21 LP16 LP18 LP20 LP22

393

I

buses in all the studies reported in this paper. The basic sector cost data required to evaluate reliability worth indices are given in Table 1. Fig. 1 presents the overall test system, which can be used for a wide variety of functional zone and hierarchical level studies.

A computer program was developed to evaluate the HLIII l E A R using the three methods described in this paper. The subtransmission/distribution networks for buses 2 and 4 are shown in Fig. 1. There are three supply points SP1, SP2 and SP3 in the network at bus 4 and only the load points connected to the individual supply points are affected owing to isolation of that supply point. There is, however, only one supply point SP at bus 2 and therefore all customers are disconnected due to an outage of this supply point. This paper illustrates a single case study for the radial distribution system configuration, i.e. presence of the disconnects, 100% reliable fuses in the laterals, 100% available alternate supply and repair of low-voltage transformers. Two subcases are illustrated, as the distribution system is assumed to consist of either underground cables or overhead lines (OHL).

A single aggregate lEAR value for each load bus at HLIII is evaluated using a weighting procedure i.e. individual HLIII IEAR are weighted in proportion to the fraction of bus load and. summed. Reference 10 specifies the customer compositions at the individual load points in the distribution configurations connected to buses 2 and 4. The individual load point IEAR for the various load points at RBTS bus 2 (OHL case) using the contingency enumeration method are shown in Table 2. The HLIII l E A R can also be obtained for each sector class associated with the system buses. The overall sector HLIII IEAR for buses 2 and 4 for the two cases of OHL and cable (using method 1) are shown in Table 3. The

Table 2: HLlll /EAR at bus 2, OHL case: method 1

Load EENS ECOST /EAR %Load Wt. /EAR point

MWh/yr 1000$/yr $/kWh $/kwh 1 2.0648 13.5959 6.5846 0.0435 0.2866 2 2.0996 12.2270 5.8235 0.0435 0.2535 3 2.0996 12.2270 5.8235 0.0435 0.2535 4 2.1845 44.0519 20.1661 0.0460 0.9286 5 2.2212 37.2683 16.7781 0.0460 0.7726 6 1.7743 35.5858 20.0557 0.0369 0.7408 7 1.7640 35.0365 19,8620 0.0369 0.7337 8 0.8271 5.9489 7.1928 0.0814 0.5852 9 0.9063 6.5798 7.2603 0.0936 0.6793

10 11 12 13 14 15 16 17 18 19 20 21 22

2.0666 13.5967 2.0996 12.5251 1.7733 10.2950 2.1 91 9 38.6277 2.201 0 37.2232 1.7537 37.1 549 1.781 7 35.6500 1.7441 11.4464 1.7382 11.4365 1.7675 10.2851 2.2231 37.271 1 2.1919 38.6277 1.7655 35.0494

6.5794 5.9654 5.8054

17.6232 16.9116 21.1 867 20.0084 6.5630 6.5794 5.8190

16.7653 17.6232 19.8524

0.0435 0.0435 0.0366 0.0460 0.0460 0.0369 0.0369 0.0366 0.0366 0.0366 0.0460 0.0460 0.0369

0.2864 0.2597 0.2125 0.81 15 0.7788 0.7826 0.7391 0.2403 0.2409 0.21 30 0.7720 0.81 15 0.7333

Total 41.2395 531.7098 12.1 155

Methods 2 and 3 use eqns. 10-15. Eqns. 12 and 15 are fundamentally the same and simply require the average outage duration and a cost look-up table to evaluate the

Table 3: Sector HLlll /EAR for RETS buses 2844: method 1

Sector OHL case Cable case type

EENS ECOST /EAR EENS ECOST /EAR

MWh/yr 1000$/yr $/kWh MWh/yr 1000$/yr $/kwh Bus 2: Sm.lnd. 1.7333 12.52864 7.23 4.5789 38.39766 8.38 Comm. 8.8393 178.47649 20.1 9 11.971 9 289.06064 24.14 Resid. 17.4534 107,63470 6.1 7 23.7385 196.4331 8 8.27 G&l 13.2136 233.06996 17.64 17.8608 496.98282 27.82

Bus 4: Smhd. 7.2356 56.64048 7.83 14.5261 117.63302 8.10 Comm. 11.0620 230.1 3928 20.80 13.4099 331.91 846 24.75 Resid. 44.5979 276.89380 6.21 54.2726 464.21 31 7 8.55

HLIII IEAR values. The IEAR values obtained for the RBTS using method 2 are shown in Table 4 for bus 2(OHL). The weighted bus HLIII IEAR values are also shown in this table. A comparison of IEAR values obtained for load buses 2 and 4 of the RBTS using methods 1 and 2 is shown in Table 5. The percentage

Table 4: HLlll /EAR at bus 2 OHL case: method 2 ~ ~~~

Load Failure Outage Outage /EAR Dt rate duration cost

Vvr h $/kW $/kWh 1 0.3189 12.4481 32.90 2.64 2 0.3319 12.1564 31.62 2.60 3 0.3319 12.1564 31.62 2.60 4 0.3189 12.4481 62.75 5.04 5 0.3319 12.1564 59.86 4.92 6 0.3287 12.2273 150.74 12.33 7 0.3319 12.0389 147.48 12.25 8 0.2195 4.2735 27.15 6.35 9 0.2195 4.0962 25.86 6.31

10 0.3222 12.3327 32.39 2.63 11 0.3320 12.1564 31.62 2.60 12 0.3352 12.0871 31.32 2.59 13 0.3320 12.0000 58.34 4.86 14 0.3352 11.9320 57.68 4.83 15 0.3222 12.3327 152.57 12.37 16 0.3319 12.1564 149.51 12.30 17 0.3222 12.3731 32.57 2.63 18 0.3222 12.3327 32.39 2.63 19 0.3352 12.0484 31.15 2.59 20 0.3352 12.0484 58.81 4.88 21 0.3320 12.0000 58.34 4.86 22 0.3352 11.9320 145.64 12.21

Aggregate: 5.68

Table 5: Comparison of HLlll /EAR (S/kWh) using methods 1 and 2

Bus (case) Method 1 Method 2 Ohdifference

2 (OHL) 12.11 5.68 53.09 2 (cable) 16.63 8.17 50.88 4 (OHL) 8.59 5.24 39.05 4 (cable) 10.28 5.91 42.56

individual customer sector lEAR values shown in Tables 2 and 3 provide valuable information on sector reliability worth at specific points in the system. This information can be used in managerial assessment of reliability worth and in any consideration of assigning customer rates associated with reliability levels.

394

difference between the results obtained using the enumeration method and method 2 with respect to the enumeration method are shown for the weighted bus HLIII IEAR values in Table 5. The results shown in this Table clearly indicate that method 2 does not provide indices comparable to those provided by the basic contingency enumeration approach for the test system studied.

IEE Proc.-Gener. Tmnsm. Distrib., Vol. 141, No. 4, July 1994

Table 6 gives the system performance indices SAIDI, SAIFI, CAIDI, etc. for the RBTS load buses 2 and 4. The values shown in Table 6 were obtained by using the

Table 6: HLlll system indices at buses 2 and 4

Bus SAIFI SAID1 CAlDl ASAl ENS

int./cus-yr hlcus-yr h/cus-int. kWh/yr 2 (OHL) 0.3279 4.0077 12.222 0.999542 42601.8 2 (cable) 0.2382 5.41 14 22.71 9 0.999382 5951 1.3 4 (OHL) 0.4025 3.8864 9.655 0.999556 64675.3 4 (cable) 0.2930 4.71 45 16.089 0.999462 83986.8

equations given in the Appendix and customer data given in Reference 11 in conjunction with the individual load point failure rates and annual unavailabilities. These indices reflect the overall system performance at the load buses and therefore could be used in conjunction with an appropriate composite customer damage function at that bus. The CCDF for any bus within the RBTS can be obtained by suitably combining the customer types and their SCDF with the peak demand and energy consumptions at that load centre.

To obtain the CCDF for load centres 2 and 4 of the RBTS, the sectors allocated at these buses and their peak demand and average load values were used to obtain the percentage peak demand and energy consumptions. These values are given in Table 7. The CCDF at each of

Tabla 7: Percentage peak demand and energy consumptions for buses 2 and 4

Sector Bus 2 Bus 4

Energy Demand Energy Demand

Resid. 36.4087 36.25 47.4980 47.4985 Srn.lnd. 17.4925 17.50 40.6835 40.7500 G &I 27.6300 27.50 Cornrn. 18.4700 18.75 1 1 .81 85 1 1.7495

- -

Total (%) 1OO.OOOO 100.00 100.0000 100.oooO

these buses is obtained by weighting the SCDF from Table 1 with the peak demand (for durations less than 30 min) or the energy consumption (for durations over 30min) values given in Table 7. The CCDF for RBTS buses 2 and 4 are shown in Table 8. Method 3 uses these. data in evaluating IEAR cost factors.

Table 8: Compoaite customer damage functions for b u m 2 and 4

Duration Interruption cost

Bus 2 Bus4

$/kW $/kW 1 min 0.3683 0.7074 20min 1.3688 1.9692 l h 3.7564 4.9357 4 h 13.7866 16.2724 8 h 38.0000 39.9674

IEAR values obtained using eqn. 15, the CCDF and the system indices given in Table 6 are shown in Table 9. This table also shows the percentage difference with respect to the enumeration method values. As in the case of method 2, the results obtained by method 3 do not compare well1 with those obtained by the enumeration method.

The results shown in Tables 5 and 9 clearly indicate that IEAR values obtained using either method 2 or 3 for RBTS buses 2 and 4 are not comparable to those obtained using the enumeration method for the test system studied. The IEAR from methods 2 and 3, however, are quite comparable to one another. This can be explained from the fact that these two methods use ‘single event’ parameters in conjunction with a single nonlinear cost curve. Method 3 uses CCDF and CAIDI which are directly aggregated from the SCDF and individual load point indices, respectively. It can therefore be concluded that these two methods, in general, do not provide correct estimates of the system IEAR and that a detailed contingency enumeration technique should be used to obtain practical estimates. The main advantage of method 2, however, is that if the average outage duration at a given customer load point and its associated cost function are known, the IEAR can be readily evaluated using eqn. 12. Similarly, if the average system CAIDI and the CCDF are available, the system IEAR can be easily obtained using method 3 (eqn. 15). The results obtained from methods 2 and 3 may be used as starting values to make planning decisions in the absence of more accurate values. The error in these results may also be system specific and therefore detailed studies should be conducted before deciding which method is appropriate for a given configuration.

5 Conclusions

Owing to emerging market pressures and the regulatory environment, and changes in the cost structure of the power industry, the traditional system planning practices are being expanded to facilitate an explicit examination of the cost and benefit implications from the customer’s perspective. This paper concerned the assessment of the societal worth of electric service interruptions at the overall system level (HLIII). Three methods have been presented for evaluating reliability worth in an electric power system. The first method uses a contigency enumeration technique and a failure mode and effects analysis procedure in association with appropriate customer cost functions to evaluate the bulk system load point IEAR and customer load point IEAR values. This procedure involves a comprehensive analysis of all major component outages in an electric power system. The second method uses the average HLIII adequacy indices at each customer load point together with the sector customer cost characteristics, and the third method makes use of the HLIII system performance indices in conjunction with appropriate composite customer cost characteristics. All three methods are illustrated by application to

Table 9: Comparison of HLlll EAR using method. 1 and 3

Bus (case) CADI Cost of IEAR IEAR %Difference CAlDl (method 3) (method 1) in IEAR

h/cus-int $/kW $/kWh $/kWh 2 (OHL) 12.22 70.63 5.78 12.1 1 52.30 2 (cable) 22.72 174.92 7.70 16.63 53.71

4 (cable) 16.09 98.88 6.14 10.28 40.25 4 (OHL) 9.65 51.00 5.28 8.59 38.54

IEE Proc-Gem. Tramm. Djstrib.., Vol. 141, No. 4, July 1994 395

I

the RBTS, a small but comprehensive test system. The results indicate that methods 2 and 3 can be used to obtain approximate customer interruption costs in the absence of a detailed study. To obtain accurate values, however, a detailed procedure such as the contingency enumeration method must be used.

The IEAR values obtained at both HLII and HLIII can be used to relate customer interruption costs with the worth of electric service reliability in an electric power system [13, 141. The individual customer load point IEAR values and the customer sector IEAR values at each bulk system load point can be used to make decisions on preferred load curtailment strategies or in studies considering reliability based electric utility customer rates.

8 References

1 BILLINTON, R., WACKER, G., and WOJCZYNSKI, E.: ‘Cus- tomer damage resulting from electric service interruptions’. Cana- dian Electrical Association, R&D project 907 U 131 Report, 1982

2 BILLINTON, R., and WACKER, G.: ‘Customer cost of electric service interruptions’, Proc. IEEE, June 1989,77, (a), pp. 919-930

3 BILLINTON, R., and ALLAN, R.N.: ‘Reliability evaluation of power systems’(Plmum, New York, 1984)

4 BILLINTON, R., and ALLAN, R.N.: ‘Reliability evaluation of large elecuic power systems’ (Kluwer, Boston, MA, USA, 1988)

5 BILLINTON, R., and GOEL, L.: ‘Overall adequacy assessment of an electric power system’, IEE Proc. C, 1992,139, (l), pp. 57-63

6 GOEL, L., and BILLINTON, R.: ‘A procedure for evaluating interrupted energy awxsment rates in an overall electric power system’, IEEE Trans., 1991, PWRS6, (4), pp. 1396-1403

7 BILLINTON, R., OTENG-ADJEI, J., and GHAJAR, R.: ‘Compari- son of two alternate methods to establish an interrupted energy assessment rate’, IEEE Trans., Aug. 1987, PWRS2, pp. 751-757

8 OTENG-ADJEI, J., and BILLINTON, R.: ‘Evaluation of interrupted energy assessment rates in composite systems’, IEEE Trans., 1990, PWRSS, (4), pp. 1317-1323

9 GOEL, L., and BILLINTON, R.: ‘Evaluation of interrupted energy aSScSSment rates in distribution systems’, 1EEE Trans., 1991, PD-6, (4), pp. 1876-1882

10 BILLINTON, R., KUMAR, S., GOEL, L., CHOWDHURY, N.,

G., and OTENG-ADJEI, J.: ‘A reliability test system for educational purposes - basic data’, IEEE Trans., 1989, PWRS-4, (3), pp. 1238-1244

11 ALLAN, R.N., BILLINTON, R., GOEL, L., SJARIEF, I., and SO, K.S. : ‘A reliability test system for educational purposes - basic distribution system data and results’, IEEE Trans., 1991, PWRS-6, (2), pp. 813-820

12 WACKER, G., and BILLINTON, R.: ‘Farm losses resulting from electric service interruDtions - a Canadian survey’. 1EEE Trans.,

cnu, K. DEBNATH, K., KHAN, E., KOS, P., NOURBAKHSH,

1989, PwRsq (2), pp.b72-478 13 BILLINTON, R., and OTENG-ADJEI, J.: ‘Utilization of inter-

~ p t e d energy assessment rates in generation and transmission system planning’, IEEE Trans., 1991, PWRS-6, (3), pp. 1245-1253

14 GOEL, L., and BILLINTON, R.: ‘Utilization of interrupted energy assessment rates to evaluate reliability worth in electric power systems’, IEEE Trans., 1993, PWRS8, (3), pp. 929-936

7 Appendix

SAIFl is defined as the average number of interruptions per customer served per time unit :

K

C l i N i - S A I F I = (interruptions/system-customer)

1 Ni i = 1

(16)

SAlDI is defined as the average interruption duration for customers served per time unit:

K

1 UiNi SAlDI = (h/system-customer) (17)

1 N i i = 1

CAIDI is defined as the interruption duration for CUS- tomers interrupted per time unit:

K

1 UiNi CAlDI = (h/interruption)

Ai Ni i = l

ASAI is defined as the ratio of the total number of customer hours that service was available during a year to the total customer hours demanded. The complement to this index is the system ASUI:

f 8760Ni i = l

ENS is defined as the energy not supplied due to supply unavailability :

K ENS = 1 U i L i (MWh/yr)

i = 1

The symbols used are defined as

li = average failure rate of load point i U i = average unavailability of load point i N i = number of customers connected to load point i Li = average load (MW) connected to load point i,

K = number of load points in the system. and

396 IEE Proc.-Gener. Transm. Distrib., Vol. 141, No. 4, July 1994

-- I

Documents

Prediction of customer load point service reliability worth estimates in an electric power system