Probabilistic Transmission System Planning (Li/Transmission System Planning) || Single-Circuit Supply System Planning

283

12.1 INTRODUCTION

A single - circuit supply system is a simple system in which one or more delivery points (substations) are supplied by one single - circuit and an interruption of the circuit will cause load curtailment at all the delivery points. For simplicity of discussion in this chapter, it is assumed that one substation contains one delivery point. The delivery points are divided into two categories: single - circuit - supplied ones and multiple - circuit - supplied ones. The fi rst category can be further classifi ed into two subgroups: single - circuit - radial - supplied delivery points, where only one power source is con-nected to the single - circuit, and single - circuit - network - supplied delivery points, where more than one source is connected to the single - circuit. As shown in Figure 12.1 , DS1, DS2, DS3, and TS1 are the single - circuit - radial - supplied delivery points; TS2 is a single - circuit - network - supplied delivery point; and DS4 and DS5 are the multicircuit - supplied delivery points [129] . Note that a “ transmission customer ” in the fi gure refers to a single industry customer, whereas a distribution customer refers to a distribution substation that will supply its loads through feeders.

Obviously, delivery points supplied by multiple circuits have much higher reli-ability than will those supplied by a single - circuit. Single - circuit - network - supplied

12

SINGLE - CIRCUIT SUPPLY SYSTEM PLANNING

Probabilistic Transmission System Planning, by Wenyuan LiCopyright © 2011 Institute of Electrical and Electronics Engineers

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284 SINGLE-CIRCUIT SUPPLY SYSTEM PLANNING

delivery points have higher availability than do single - circuit - radial - supplied delivery points in terms of outage duration. For example, if circuit L3 shown in Figure 12.1 is interrupted in the upper portion, the load at TS2 will be lost during the outage event. However, it is possible that a crew worker can restore the supply to TS2 by manually isolating the conductor section in the contingency and reenergizing the supply source from the lower portion (via DS5).

There are many single - circuit supply systems in utilities. This may be because some loads located in suburban areas were small and less important historically, and a multicircuit supply could not be justifi ed. However, the loads may gradually grow and become more important over the years with urbanization. The two basic questions facing utilities in single - circuit supply system planning are

• Apparently, the conventional N − 1 criterion cannot be applied in this situation. How can a reinforcement project for a single - circuit supply system be economi-cally justifi ed?

• It is impossible and unnecessary to reinforce all single - circuit supply systems at the same time because of the constraint in the capital budget. Which single - circuit supply system should be reinforced fi rst?

This chapter presents a probabilistic planning approach to address these issues. The contribution of different system components and subnetwork confi gurations to overall system reliability performance is analyzed using the statistics of a utility in Section 12.2 . The probabilistic planning method for single - circuit supply systems is developed in Section 12.3 . An application of the presented method to an actual utility system is demonstrated in Section 12.4 .

Figure 12.1. Examples of single - circuit - supplied and multicircuit - supplied delivery points.

(MC)

(SC)

(MC)

80 MW(8000 distribution

customers)


customers)


customers)


customers)


customers)

100 MW

(1 transmissioncustomer)

10 MW(1 transmission

customer)

Supply source

(SC)

(SC)

(SC)

(SC)

75 km

125 km

20 km

Key:DS1 = distribution customer substation 1

TS1 = transmission customer substation 1SC = single-circuit-supplied delivery point

MC = multicircuit-supplied delivery point

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12.2 RELIABILITY PERFORMANCE OF SINGLE-CIRCUIT SUPPLY SYSTEMS 285

12.2 RELIABILITY PERFORMANCE OF SINGLE - CIRCUIT SUPPLY SYSTEMS

12.2.1 Delivery Point Reliability Indices

The reliability performance seen by customers widely varies at different delivery points. In general, single - circuit - supplied delivery points have relatively low reliability perfor-mance. However, the reliability level at each individual delivery point is quite different because the failure probability of each single - circuit is different. The reliability perfor-mance can be measured from various perspectives, such as

• How often does a supply interruption occur (interruption frequency)?

• How long does a supply interruption last (interruption duration)?

• How severe is the supply interruption (magnitude of load lost)?

• How many customers are affected by a supply interruption?

The answers to these questions can be represented using reliability performance matri-ces. The reliability indices can therefore have various forms, such as a frequency - related index, a duration - related index, or an index that combines all the frequency, duration, and severity factors.

As discussed in Section 7.3.3 , historical outage statistics can be used to calculate the reliability indices at delivery points. The following three indices are selected in this chapter to capture different perspectives of supply interruptions to customer delivery points.

1. Customer Hours Lost ( CHL ) . This is a measure of cumulative interruption duration associated with a number of customers being interrupted on an annual basis. Its unit is customer - hours per year. The CHL index is a combination of frequency, duration, and number of customers being interrupted. The demerit of this index is that it does not include the amount of loss of loads (MW). Also, even if the interruption frequency and duration of transmission lines remain unchanged, the CHL will increase with the number of customers over the years. Such a situation does not represent real degradation of transmission system reliability. Regardless, the CHL index is very commonly used in the utility industry because of its straightforwardness.

2. System Average Interruption Duration Index ( T - SAIDI ) . T - SAIDI is defi ned in Section 7.3.3.1 . Its unit is hours (or minutes) per delivery point per year and represents the average outage duration per delivery point. T - SAIDI is the most popular index in the power industry since many utilities have used it as a cor-porate key performance indicator to measure overall system reliability. It is essential to appreciate that the T - SAIDI used for transmission systems is differ-ent from the SAIDI index used for distribution systems by defi nition and the prefi x T has been used in the book.

3. Delivery Point Unreliability Index ( DPUI ) . DPUI is also defi ned in Section 7.3.3.1 . Its unit is system - minutes per year, and it is calculated as the total

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energy not supplied because of interruption events at all delivery points normal-ized by the system peak load. The DPUI is also known as the severity index , which indicates the time length in minutes for which it would last if an inter-ruption of total system load occurred at the time of system peak load in order to cause the same amount of cumulative energy not supplied occurring at all delivery points in one year. In other words, the DPUI represents the severity related to the magnitude of energy supply lost as a result of interruptions.

12.2.2 Contributions of Different Components to Reliability Indices

An example is used to show the contributions of different system components and con-fi gurations to the reliability indices of overall system based on historical outage statistics [129] . This information is useful for system planners to quantitatively recognize weak components, confi gurations, and locations in terms of reliability performance.

The three indices (CHL, T - SAIDI, and DPUI) were calculated using the historical data of a utility in the 5 years from 2004 to 2008. The outage data causing customer interruptions were categorized in terms of two types of components (substation and transmission components) and further sub - categorized in terms of three types of deliv-ery points as shown in Figure 12.1 (i.e., single - circuit - radial - supplied delivery points, single - circuit - network - supplied delivery points, and multicircuit - supplied delivery points). The results are presented in a percentage contribution of an index due to each category to the overall system index, as shown in Table 12.1 and Figures 12.2 – 12.4 .

The following observations can be made:

• Transmission - line component interruptions make much higher contributions to customer outages than do substation component interruptions. Transmission - line component interruptions contribute to 75% of the total CHL, 91% of the total T - SAIDI, and 80% of the total DPUI.

• The customer outages due to single - circuit - supplied systems make much higher contributions to the reliability indices than do those due to multicircuit - supplied systems. The impact on the multicircuit - supplied delivery points due to substation

TABLE 12.1. Percentage Contributions of CHL , T - SAIDI , and DPUI Due to Each Category to Overall System Indices

Component Type Type of Delivery Point

Impacted by Outage CHL (%) T - SAIDI (%) DPUI (%)

Transmission - line components

Single - circuit radial 55 74 54 Single - circuit network 10 13 13 Multiple - circuit 10 4 13

Substation components

Single - circuit radial 5 3 2 Single - circuit network 3 2 8 Multicircuit 17 4 10

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12.2 RELIABILITY PERFORMANCE OF SINGLE-CIRCUIT SUPPLY SYSTEMS 287

Figure 12.2. Contributions in CHL categorized by types of component outage and impacts

on types of delivery point.

Outage contributions in the customer hours lost (CHL)

Single-circuit radial

(substation), 5%

Multicircuit (substation), 17%

Single-circuit network

(substation), 3%Single-circuit

radial (transmission),

55%

Multicircuit (transmission),

10%


(transmission), 10%

Figure 12.3. Contributions in T - SAIDI categorized by types of component outage and impacts


Outage contributions in the system average interruption durationindex (T-SAIDI)


(substation), 2%

Single-circuitradial

(substation), 3% Multicircuit

(substation), 4% Multicircuit

(transmission), 4%

Single-circuitnetwork

(transmission),13%

Single-circuit radial

(transmission),74%

Figure 12.4. Contributions in DPUI categorized by types of component outage and impacts


Outage contributions in the delivery point unreliability index (DPUI)


(substation), 2%

Single-circuitnetwork

(substation), 8%

Multicircuit(substation), 10%


(transmission),54%


(transmission), 13%

Multicircuit (transmission),

13%

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and transmission line component interruptions altogether is only 8% (4% + 4%) of the total T - SAIDI. The remaining 92% of the total T - SAIDI originated from single - circuit - supplied systems. The contributions due to single - circuit - supplied systems to the total CHL and DPUI indices are 73% and 77%, respectively.

• In the contributions of the single - circuit - supplied systems, the customer outages due to transmission - line interruptions dominate over those due to substation component interruptions. The single - circuit transmission - line interruptions (including both radial and network delivery point categories altogether) contrib-ute to 65% of the total CHL index, 87% of the total T - SAIDI index, and 67% of the total DPUI index.

• The single - circuit radial transmission lines make the highest contributions to the reliability indices. In the contribution of 65% for the total CHL index, 55% originates from single - circuit redial transmission lines and 10% from single - circuit network lines. In the contribution of 87% for the total T - SAIDI index, 74% originates from single - circuit radial transmission lines and 13% from single - circuit network lines. In the contribution of 67% for the total DPUI index, 54% originates from single - circuit radial transmission lines and 13% from single - circuit network lines.

Obviously, the customer outages in the transmission system of this utility are caused mainly by interruptions of single - circuit transmission lines, particularly by interruptions of single - circuit radial transmission lines. The contribution percentages to the reliability indices due to different types of components and network confi gurations in a transmis-sion system vary for different utilities. However, the general pattern should be similar. The analysis results suggest the importance of single - circuit supply system planning.

12.3 PLANNING METHOD OF SINGLE - CIRCUIT SUPPLY SYSTEMS

This topic is discussed in detail in Reference 130 . It can be seen from the analysis of reliability performance indices above that the impact of transmission lines greatly dominates over that of substation components. In the following discussions for single - circuit supply systems, we will focus on transmission lines.

12.3.1 Basic and Weighted Reliability Indices

As shown in Section 12.2 , the single - circuit supply systems can have different contribu-tion percentages for the three reliability indices (CHL, T - SAIDI, and DPUI) even though they are obtained from the same outages sources. This is due to the fact that each reliability index represents a different reliability perspective. The CHL focuses on the number of customers; the T - SAIDI, on the number of delivery points; and the DPUI, on the outage severity (i.e., magnitude of lost loads). All three indices are therefore used together in order to capture various perspectives associated with power supply outages. The calculation methods of the three basic indices for single - circuit supply

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12.3 PLANNING METHOD OF SINGLE-CIRCUIT SUPPLY SYSTEMS 289

systems are presented and demonstrated using an example. Then a composite index based on weightings of the three basic indices is presented for reliability ranking pur-poses. A circuit that is ranked higher has a greater unreliability impact than do lower - ranked ones.

12.3.1.1 Basic Reliability Indices. The CHL index (in customer - hours per year) for single - circuit supply systems can be calculated by

CHL ===

∑∑ r Nik k

i

f

k

M k

11

(12.1)

where r ik is the interruption duration or restoration time (hours/interruption) in the i th interruption event of the k th circuit, f k is the number of interruptions of the k th circuit in a given year, N k is the number of customers supplied by the k th circuit, and M is the number of circuits considered. When M = 1, the CHL obtained is the index for one circuit.

For the purpose of ranking single - circuits, the CHL of each circuit should be nor-malized by the number of interruption events of the circuit. The normalized CHL is the average customer hours lost per event (ACHL) of each circuit. The measure unit of ACHL is customer - hours per interruption per year. The ACHL for all single - circuit supply systems considered can be calculated by

ACHL = ∑ =

=∑ i

fik k

kk

M k r N

f1

1

(12.2)

where r ik , f k , N k and M are the same as defi ned in Equation (12.1) . If there is no inter-ruption for the k th circuit in a given year (i.e., f k = 0), this circuit is excluded from the calculation for that year.

The T - SAIDI (in hours per delivery point per year) for single - circuit supply systems can be calculated by

T-SAIDI = ∑ ∑= =kM

if

ik Dk

DT

k r N

N1 1 (12.3)

where r ik , f k , and M are the same as defi ned in Equation (12.1) ; N Dk is the number of delivery points on the k th circuit; and N DT is the number of delivery points in the whole system. Note that N DT is not the sum of the numbers of delivery points on the circuits considered. Equation (12.3) has the same implication as Equation (7.44) , except that the counting considerations for single - circuit supply systems are utilized in Equation (12.3) .

The DPUI (in system - minutes per year) for single - circuit supply systems can be calculated by

DPUIsys

= ⋅∑ ∑= =60 1 1kM

if

ik ikk r L

P (12.4)

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where r ik f k , and M are the same as defi ned in Equation (12.1) ; L ik is the actual total load (MW) on the k th circuit that is curtailed in the i th interruption event; and P sys is the annual peak load (MW) of the whole system. The 60 is introduced to convert the unit in hours into the unit in minutes. Similarly, Equation (12.4) has the same implica-tion as Equation (7.48) except for different counting considerations.

In Equations (12.1) – (12.4) , when M = 1, the index is the one for an individual circuit. An index for all single - circuit supply systems considered can be used to refl ect the overall performance of a circuit group. The percentage contribution of the index of each circuit to the index of the whole circuit group can be easily calculated.

The indices are calculated on a yearly basis in Equations (12.1) – (12.4) . When multiple years are considered, an average index per year can be calculated. Obviously, the historical data of each individual interruption event can be directly used in the equations above. If the average interruption frequency and average interruption duration in one year are used, the indices can be expressed as follows:

CHL = ⋅ ⋅=

∑ f r Nk k k

k

M

1

(12.5)

ACHL = ⋅=

∑ r Nk k

k

M

1

(12.6)

T-SAIDI = ∑ ⋅ ⋅=kM

k k Dk

DT

f r N

N1 (12.7)

DPUIsys

= ⋅∑ ⋅ ⋅=60 1kM

k k kf r L

P (12.8)

Here, fk and rk are the average interruption frequency (interruptions/year) and average interruption duration (hours/interruption) for the k th circuit, respectively; L k is the total average load (MW) supplied by the k th circuit; and N k , N Dk , N DT , M , and P sys are the same as defi ned earlier. The fk and rk can be the average values based on the data of either each circuit in multiple interruption events during several years or a group of circuits at the same voltage level and/or under similar operation and environment condi-tions. In cases where there is insuffi cient statistical data for some circuits, it is preferable to use the approach of utilizing the average fk and rk of a group of circuits. The use of the average interruption frequency and duration can reduce the effect due to uncertainty of statistics data of individual circuits. Also, the average interruption frequency and duration can be used to estimate the indices for future years.

The system shown in Figure 12.1 is used to illustrate how to calculate the ACHL, T - SAIDI, and DPUI [129] . It is assumed that the load factor for all the seven delivery points in Figure 12.1 is 0.55. The total system peak is 360 MW. There are three inter-ruption events occurring in a given year. The fi rst interruption event causes line L1 to be out of service for 10 h. The second interruption event causes line L2 to be out of service for 10 h. The third interruption event occurs on the upper portion of line L3 and lasts for 10 h, but the load supply is restored from the lower portion of L3 within 2 h by separating the upper and lower portions of the line.

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Note that the denominator in calculating the T - SAIDI index is the total number of delivery points in the whole system, including those supplied by multiple circuits.

ACHL Index (in customer - hours per interruption per year)

Overall system ACHL(sys) = (7000 × 10)/1 + [(1000 + 1000 + 1) × 10]/1 + (1 × 2)/1 = 90,012

L1 contribution ACHL(L1) = (7000 × 10)/1 = 70,000 [78% contribution to system ACHL(sys)]

L2 contribution ACHL(L2) = [(1000 + 1000 + 1) × 10]/1 = 20,010 [22% contribution to system ACHL(sys)]

L3 contribution ACHL(L3) = (1 × 2)/1 = 2 [rounded to 0.0% contribution to system ACHL(sys)]

DPUI Index (in system - minutes per year)

Overall system DPUI(sys) = 60 × 0.55 × (10 × 70 + 10 × 30 + 2 × 100)/360 = 110.0

L1 contribution DPUI(L1) = 60 × 0.55 × (10 × 70)/360 = 64.2 [58% contribution to system DPUI(sys)]



T - SAIDI index (in hours per delivery point per year)

Overall system T - SAIDI(sys) = (10 × 1 + 10 + 3 + 2 × 1)/7 = 6.00 L1 contribution T - SAIDI(L1) = (10 × 1)/7 = 1.43

[24% contribution to system T - SAIDI(sys)] L2 contribution T - SAIDI(L2) = (10 × 3)/7 = 4.28

[71% contribution to system T - SAIDI(sys)] L3 contribution T - SAIDI(L3) = (2 × 1)/7 = 0.29

[5% contribution to system T - SAIDI(sys)]

The reliability performance of the three circuits can be ranked using the percentage contribution of the index of each circuit to the corresponding system index. For example, if the T - SAIDI index is adopted as the criterion in single - circuit supply system planning, constructing a second circuit in parallel with line L2 will provide more improvements in the system T - SAIDI than will enhancing line L1 or L3. However, utilizing the T - SAIDI alone does not address the severity of load curtailments due to interruption events. The failure of line L1, which supplies a large delivery point (DS1), makes a smaller contribution to the system T - SAIDI index but has the greatest impact on the number of customers affected (the highest ACHL) and the severity of interruption events (the highest DPUI). In order to refl ect all the perspectives in reliability

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performance, the weighted reliability index criterion using a combination of the three reliability indices can be used.

12.3.1.2 Weighted Reliability Index. The weighting factors are introduced to create a composite index using the three basic reliability indices. It should be empha-sized that the percentage contributions of the three indices should be used in weighting instead of using the absolute values of the indices because they have different units and cannot be directly summed up. The weighted reliability index (WRI) for each single - circuit can be calculated by

WRI ACHL T-SAIDI DPUI= ⋅ + ⋅ + ⋅%( ) %( ) %( )W W W1 2 3 (12.9)

where %(ACHL), %(T - SAIDI), or %(DPUI) represents the percentage contribution of each circuit ’ s index to the whole system index, respectively, for each of the three basic indices; W 1 , W 2 , and W 3 are the weighting factors; and W 1 + W 2 + W 3 = 1.0.

Since the interruption frequency and duration are the common parts in all three reliability indices, the effects of the weighting factors are focused on the number of affected customers (ACHL), the number of delivery points (T - SAIDI), and the magni-tude of lost loads (DPUI). Selection of the weighting factors is a management decision of the utility depending on its reliability objective. Since the weighted reliability index is based on the percentage contribution of each single - circuit, it can be used to rank the performance of single - circuit supply systems and to determine an initial short list of circuits for reinforcement. A threshold for the WRI can be specifi ed as a cutoff criterion. The single - circuit supply systems whose WRI is greater than the threshold are the candidates in the initial short list considered for reinforcement.

The weighting factors for the %(ACHL), %(T - SAIDI), and %(DPUI) used in the example shown in Figure 12.1 are 0.3, 0.4, and 0.3, respectively. The percentage con-tributions of each circuit ’ s index to the system index and the weighted reliability indices (%) in the given example are shown in Table 12.2 . It can be seen that if the T - SAIDI is used as a reliability criterion, L2 is ranked at a higher priority for enhancement than are L1 and L3, whereas if the weighted reliability index containing all the three reli-ability measures is used, L1 is ranked at a higher priority for enhancement than are L2 and L3.

TABLE 12.2. Percentage Contributions in Basic Indices and WRI for Each Single - Circuit in Example

Circuit

Percentage Contribution to System Index (%) Weighted Reliability

Index (%) %ACHL %T - SAIDI %DPUI

L1 78 24 58 50.4 L2 22 71 25 42.5 L3 0 5 17 7.1

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12.3.2 Unit Incremental Reliability Value Approach

Although the weighted reliability index can be directly used for ranking the reliability performance of circuits, it does not include any economic consideration for system reinforcement. This section presents the ranking criteria that combine a reliability index with the investment cost for reinforcement.

12.3.2.1 Annual Capital Investment. In principle, a single - circuit supply system can be reinforced by adding a second circuit. For a single - circuit supplying only one delivery point, access to a second power source can also be a reinforcement alter-native. However, such an alternative does not apply to the case in which multiple substations are supplied by a single - circuit. For generality, addition of a second circuit for reinforcement is used as an example in the following discussions. On one hand, the second circuit will greatly improve the system reliability. On the other hand, it requires a capital investment.

Using the capital return factor discussed in Section 6.3.4.3 , the equivalent annual capital investment (ACI) of a new circuit can be obtained from its total capital invest-ment (TCI) as

ACI TCI= ⋅ ++ +

r r

r

n

n

( )

( )

1

1 1 (12.10)

where ACI and TCI represent the equivalent annual capital investment (k$/year) and the total capital investment (k$) at the beginning, respectively; r is the discount rate; and n is the useful life of a new circuit.

In ranking the priority of reinforcement projects for single - circuit supply systems, an approximate cost estimate is generally acceptable. For example, an average invest-ment cost per km can be applied to the reinforcement projects of circuits at the same voltage level. If necessary, however, more accurate costs for each reinforcement project can be individually estimated through detailed investigation.

12.3.2.2 Unit Incremental Reliability Value. The capital investment required to reinforce the system will lead to system reliability improvement. The unit incremental reliability value (UIRV) concept [131,132] is utilized to evaluate the incremental investment cost for unit reliability improvement. The UIRV is defi ned as follows:

UIRVACI

kk

kR=

Δ (12.11)

Here, ACI k is the annual capital investment cost required by a reinforcement for the k th circuit, and Δ R k represents the reliability improvement due to the reinforcement in a yearly average reliability metric over the planning timespan. Conceptually, the reli-ability metric can be any index. It is noted that Δ R k is expressed in a percentage con-tribution of a circuit ’ s index to the corresponding system index. In other words, the

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improvement in %(ACHL), or %(T - SAIDI), or %(DPUI), or WRI index as defi ned in Equation (12.9) is used as Δ R k .

If a single - circuit supply system is reinforced by adding a second circuit, the ACI k is simply the equivalent annual capital investment of the second circuit addition. The Δ R k is the difference in the selected percentage index between the existing single - circuit and the confi guration with the second circuit addition. The equivalent interruption frequency and duration for a simultaneous outage of two circuits can be calculated using the parallel reliability formulas [see Equations (11.11) and (11.12) in Chapter 11 ], and then Equations (12.5) – (12.8) are still valid for calculating the basic reliability indices for the confi guration with the second circuit addition. In most cases, however, the probability of a simultaneous outage of two circuits is very low. Therefore, the reliability index after the second circuit addition is much smaller than that of the exist-ing single - circuit (often smaller than 1%) and can be neglected in the sense of relative comparison. In this case, the Δ R k can be approximately considered to be the selected percentage index of the existing single - circuit. This approximation basically will not create an effective error in ranking the priority of single - circuits.

Although the UIRV can be directly used for ranking, it is suggested to use the fol-lowing relative UIRV index (RUIRV ), which has no unit and therefore can be combined with another ranking index, the relative cost/benefi t ratio (RCBR) (see Section 12.3.3 ):

RUIRVUIRV

UIRVk

k

kM

kc

=∑ =1

(12.12)

Here, UIRV k is the unit incremental reliability value for reinforcement of the k th circuit, and M c is the number of circuits considered as the candidates in the short list for reinforcement.

12.3.3 Benefi t/Cost Ratio Approach

The deterministic N − 1 criterion is not applicable for judging whether a single - circuit supply system should be reinforced. The benefi t/cost analysis based on reliability worth assessment can be used for this purpose.

12.3.3.1 Expected Damage Cost. The EENS (expected energy not supplied) index (in MWh/year) for each circuit can be calculated by

EENSk k k kf r L= ⋅ ⋅ (12.13)

where fk and rk are the average interruption frequency (interruptions per year) and duration (hours per interruption) for the k th circuit, respectively; L k is the total annual average load (MW) supplied by the k th circuit. When the EENS for different years in the future is estimated, L k for each year should be different and is based on the load forecast and load factor of customers supplied by the circuit.

The EDC (expected damage cost) index (in k$/year) for each circuit can be calcu-lated by

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EDC EENS UICk k k= ⋅ (12.14)

where UIC k represents the composite unit interruption cost (in $/kWh) for the k th circuit.

The composite UIC can be calculated using the unit interruption costs of different customer sectors and the composition of customers supplied by the circuit. This is similar to the approach shown in the example given in Section 9.3.4.1 . The other methods for estimating the UIC given in Section 5.3.1 can also be used.

12.3.3.2 Benefi t/Cost Ratio. In the benefi t/cost analysis, the cost is the capital investment (CI) of the second circuit for reinforcing a single - circuit supply system, whereas the benefi t is the reduction in the expected damage cost (EDC) created by the second circuit addition. The benefi t/cost ratio is calculated by

BCREDC

CIk

k

k

= Δ (12.15)

where CI k is the capital investment of the second circuit addition for the k th circuit over the planning timespan; Δ EDC k is the difference in the EDC index between the existing single - circuit (the k th circuit) and the confi guration with the second circuit addition in the same planning length. Equations (12.13) and (12.14) are still valid for calculation of the EDC of the confi guration with the second circuit if fk and rk are replaced by the equivalent interruption frequency and duration for a simultane-ous outage of two circuits, which can be calculated using the parallel reliability formulas.

The BCR can be used to judge whether the reinforcement for a single - circuit supply system is economically justifi able. Conceptually, if the BCR is greater than 1.0, it is fi nancially acceptable. Otherwise, it cannot be justifi ed. In actual applications, it is usual practice to select a number larger than 1.0 (such as 1.5 or 2.0) as a threshold in order to cover the uncertainty in input data and the errors that may be caused by approxima-tions in calculations.

It should be emphasized that the EENS and EDC indices are different for each year in the future since L k usually increases over the years. A planning timespan (such as 10 – 20 years) needs to be considered. By using the present value method, Equation (12.15) can be expressed in a detailed form

BCREDC

ACIk

jm

kjj

jm

kjj

r

r=

∑ +∑ +

=−

=−

11

11

1

1

{ [( ) ]}

{ [( ) ]}

Δ (12.16)

where Δ EDC kj and ACI kj are the annual reduction of EDC and equivalent annual invest-ment in year j for reinforcement of the k th circuit, respectively; r is the discount rate; and m is the number of years considered in the planning timespan. Note that the reference year in Equation (12.16) is year 1 and the reference year in the corresponding equations of Chapter 6 is the year 0.

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The cost/benefi t ratio (CBR) is the reciprocal of the BCR:

CBRCI

EDCk

k

k

=Δ

(12.17)

Obviously, CBR is in the same form of UIRV. The CBR represents the incremental investment cost for unit improvement in EDC. Therefore the CBR can be also used to rank the priority of single - circuits for reinforcement. Like the UIRV, the relative CBR for a circuit should be used and is defi ned as

RCBRCBR

CBRk

k

kM

kc

=∑ =1

(12.18)

where CBR k is the cost/benefi t ratio for reinforcement of the k th circuit and M c is the number of circuits considered as the candidates in the short list for reinforcement.

In actual applications, the two relative indices of RUIRV and RCBR can be directly summed up to obtain a combined relative contribution index (CRCI):

CRCI RUIRV RCBRk k k= + (12.19)

In Equation (12.19) , the RUIRV and RCBR have been equally weighted, although dif-ferent weighting factors can be introduced to calculate the CRCI if necessary. Apparently, the value of CRCI ranges between 0.0 and 2.0 since the value of RUIRV or RCBR ranges between 0.0 and 1.0. In fact, the CRCI index is often much smaller than 1.0. A circuit with a smaller CRCI requires a lower investment cost for unit reliability improvement.

12.3.4 Procedure of Single - Circuit Supply System Planning

As mentioned in Section 12.1 , two basic questions in single - circuit supply system plan-ning are: (1) how to justify the reinforcement for a single - circuit supply system and (2) which single - circuit supply system should be reinforced fi rst.

The single - circuit supply system planning procedure includes the following steps:

1. The ACHL, T - SAIDI, and DPUI indices of single - circuit - supplied delivery points for all single - circuit supply systems are calculated using historical outage data.

2. The weighted reliability indices (WRIs) are calculated using the percentage contributions of ACHL, T - SAIDI, and DPUI indices in the form of an individual single - circuit ’ s index to the corresponding system index.

3. The cash fl ows of Δ EDC kj and ACI kj for individual single supply systems in the planning timespan are calculated to obtain their benefi t/cost ratios (BCRs).

4. A short list is created from the information in steps 2 and 3. The single - circuit supply systems whose WRIs are smaller than the specifi ed threshold should be removed from the candidate list for reinforcement. Each candidate in the short

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list should be fi nancially justifi able. If the BCR of a single - circuit supply system is smaller than the selected threshold of BCR, it should also be removed from the short list.

5. The RUIRV and RCBR indices for the individual single - circuit supply systems are calculated.

6. The CRCI indices for the individual single - circuit supply systems are calculated.

7. The priority of the single - circuit supply systems in the short list for reinforce-ment is ranked using their CRCI indices.

8. One or more single - circuit supply systems ranked at the top are selected for reinforcement depending on the constraint of investment budget.

The procedure is summarized in Figure 12.5 .

Figure 12.5. Procedure of single - circuit supply system planning.

Calculate ACHL, T-SAIDI, and DPUI indices using historical outage data

Calculate WRI

WRI of circuit i > or = threshold?

Calculate BCR

Short list for reinforcement

Calculate UIRV

Calculate RUIRV

Calculate CBR

Calculate RCBR

Calculate CRCI

Ranking priority on the short list

BCR of circuit i > or = threshold?

Remove circuit ifrom the list

Remove circuit ifrom the list

No

No

Yes

Yes

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12.4 APPLICATION TO ACTUAL UTILITY SYSTEM

An actual application to BC Hydro system is presented in detail in References 129 and 130 .

12.4.1 Short List Based on Weighted Reliability Index

As pointed out in Section 12.1 , the single - circuit - supplied delivery points are divided into two categories: single - circuit - radial - supplied delivery points and single - circuit - network - supplied delivery points, as demonstrated in Figure 12.1 . Accordingly, all single - circuit supply systems in the BC Hydro system are divided into two groups desig-nated as a single - circuit radial supply group and a single - circuit network supply group.

Tables 12.3 and 12.4 present the weighted reliability indices and the percentage contribution indices %(ACHL), %(T - SAIDI), and %(DPUI) for the single - circuit radial

TABLE 12.3. Circuit Ranking in Single - Circuit Radial Supply Group Based on Weighted Reliability Index

Circuit Voltage (kV)

Percent Contribution to BC Hydro Overall System Index

Weighted Reliability Index (%) %(ACHL) %(T - SAIDI) %(DPUI)

LR1 - 138 138 16.20 34.17 16.21 23.39 LR2 - 138 138 15.52 0.21 1.12 5.08 LR3 - 138 138 2.38 2.55 10.23 4.80 LR4 - 138 138 8.02 1.02 3.33 3.81 LR5 - 138 138 4.25 2.72 3.69 3.47 LR6 - 60 60 2.40 3.04 3.26 2.92 LR7 - 60 60 0.37 3.65 1.42 2.00 LR8 - 60 60 0.00 4.73 0.08 1.92 LR9 - 138 138 0.40 3.61 0.90 1.83 LR10 - 60 60 1.45 1.79 2.12 1.79 LR11 - 60 60 1.05 2.45 1.09 1.62 LR12 - 60 60 1.81 0.75 2.49 1.59 LR13 - 230 230 0.00 0.49 4.52 1.55 LR14 - 60 60 0.43 1.68 1.79 1.34 LR15 - 138 138 1.35 1.34 1.16 1.29 LR16 - 60 60 2.07 1.21 0.40 1.22 LR17 - 60 60 0.51 2.04 0.53 1.13 LR18 - 60 60 1.18 0.91 1.37 1.13 LR19 - 60 60 0.00 1.51 1.48 1.05 LR20 - 230 230 0.28 0.70 2.28 1.05 LR21 - 60 60 0.54 1.46 0.77 0.98 LR22 - 60 60 1.96 0.70 0.42 0.99 LR23 - 60 60 1.50 0.11 0.27 0.57 LR24 - 60 60 1.34 0.29 0.13 0.56 LR25 - 138 138 0.01 1.08 0.05 0.45 LR26 - 230 230 0.86 0.26 0.30 0.45

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12.4 APPLICATION TO ACTUAL UTILITY SYSTEM 299




LR27 - 230 230 0.52 0.43 0.39 0.44 LR28 - 138 138 0.52 0.57 0.16 0.43 LR29 - 138 138 0.33 0.39 0.56 0.42 LR30 - 60 60 0.31 0.64 0.19 0.41 LR31 - 60 60 0.45 0.35 0.46 0.41 LR32 - 230 230 0.00 0.07 1.20 0.39 LR33 - 138 138 0.00 0.77 0.20 0.37 LR34 - 138 138 0.00 0.18 0.94 0.35 LR35 - 138 138 0.20 0.53 0.21 0.33 LR36 - 138 138 0.07 0.32 0.49 0.30 LR37 - 138 138 0.00 0.56 0.17 0.27 LR38 - 60 60 0.04 0.61 0.05 0.27 LR39 - 60 60 0.00 0.66 0.01 0.27 LR40 - 60 60 0.17 0.22 0.44 0.27 LR41 - 138 138 0.53 0.02 0.12 0.20 LR42 - 60 60 0.00 0.13 0.25 0.13 LR43 - 138 138 0.24 0.06 0.04 0.10 LR44 - 138 138 0.00 0.04 0.18 0.07 LR45 - 230 230 0.17 0.01 0.02 0.06 LR46 - 60 60 0.00 0.09 0.06 0.05 LR47 - 138 138 0.00 0.10 0.04 0.05 LR48 - 230 230 0.00 0.04 0.00 0.01 LR49 - 60 60 0.00 0.02 0.00 0.01 LR50 - 138 138 0.00 0.00 0.01 0.00 LR51 - 138 138 0.00 0.00 0.00 0.00 LR52 - 60 60 0.00 0.00 0.00 0.00 LR53 - 230 230 0.00 0.00 0.00 0.00 LR54 - 60 60 0.00 0.00 0.00 0.00 LR55 - 138 138 0.00 0.00 0.00 0.00 LR56 - 138 138 0.00 0.00 0.00 0.00 LR57 - 60 60 0.00 0.00 0.00 0.00 LR58 - 60 60 0.00 0.00 0.00 0.00

TABLE 12.3. Cont’d

and network supply groups, respectively. All circuits in the two tables are listed in descending order of weighted reliability index. The indices were calculated from his-torical data in the 5 years from 2004 to 2008.

The weighted reliability index does not automatically determine a cutoff threshold above which a reinforcement project can be considered. Determination of a threshold depends on multiple factors, including the reliability performance target of the utility and the constraint on the investment budget for reinforcing single - circuit supply systems. The threshold value of 1.5% is used to create an initial short list in the example.

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TABLE 12.4. Circuit Ranking in Single - Circuit Network Supply Group Based on Weighted Reliability Index




LN1 - 138 138 2.47 0.67 1.76 1.54 LN2 - 60 60 0.49 1.15 0.58 0.78 LN3 - 60 60 1.46 0.23 0.43 0.66 LN4 - 138 138 0.24 0.53 0.68 0.49 LN5 - 60 60 0.41 0.41 0.32 0.39 LN6 - 138 138 0.33 0.17 0.58 0.34 LN7 - 60 60 0.39 0.24 0.28 0.30 LN8 - 138 138 0.13 0.28 0.41 0.27 LN9 - 230 230 0.00 0.20 0.59 0.26 LN10 - 60 60 0.00 0.24 0.43 0.23 LN11 - 60 60 0.00 0.25 0.26 0.18 LN12 - 138 138 0.00 0.29 0.18 0.17 LN13 - 60 60 0.00 0.29 0.17 0.16 LN14 - 60 60 0.06 0.21 0.18 0.16 LN15 - 60 60 0.20 0.13 0.11 0.15 LN16 - 60 60 0.33 0.06 0.09 0.15 LN17 - 60 60 0.03 0.18 0.16 0.13 LN18 - 60 60 0.09 0.18 0.06 0.12 LN19 - 60 60 0.21 0.03 0.07 0.10 LN20 - 138 138 0.03 0.12 0.06 0.07 LN21 - 138 138 0.22 0.00 0.01 0.07 LN22 - 60 60 0.00 0.15 0.01 0.06 LN23 - 60 60 0.00 0.08 0.11 0.06 LN24 - 60 60 0.02 0.13 0.01 0.06 LN25 - 60 60 0.02 0.04 0.01 0.03 LN26 - 138 138 0.00 0.03 0.00 0.01 LN27 - 60 60 0.01 0.01 0.01 0.01 LN28 - 230 230 0.00 0.00 0.02 0.01 LN29 - 60 60 0.00 0.00 0.00 0.00

This implies that if any circuit contributes 1.5% or above to the entire BC Hydro transmission system reliability in terms of the weighted reliability index, it should be considered for further investigation using the benefi t/cost analysis.

The rationale for proposing 1.5% as the threshold in this example is based on the comparison between the weighted reliability indices in Tables 12.3 and 12.4 . It is obviously shown that the contribution of the single - circuit radial supply group to the weighted reliability index of the entire BC Hydro transmission system is much greater than the contribution of the single - circuit network supply group. The greatest percent-age contribution in the weighted reliability index shown in Table 12.4 is only 1.54% on the circuit LN1 - 138, whereas the greatest percentage contribution shown in Table

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TABLE 12.5. Average Outage Data of Single - Circuits in Radial and Network Supply Groups

Voltage Class (kV) Interruption Frequency

(interruptions/100 km/year) Repair Time

(h/interruption) Unavailability (per 100 km)

60 4.60 20.29 0.01065 138 1.31 16.91 0.00252 230 1.04 16.57 0.00197

12.3 is 23.39% on the circuit LR1 - 138. Clearly, there is a considerable gap in the impact on the overall system reliability between the two groups. In order to bridge this gap, the threshold value of 1.5% is proposed to bring the unreliability contribution of the circuits at the top in Table 12.3 to be close to the maximum weighted reliability index shown in Table 12.4 , which is 1.54% on the circuit LN1 - 138. Conceptually, this implies that the future reliability of the existing single - circuit radial supply group will be close to the reliability of the single - circuit network supply group after reinforcing the single - circuit radial supply systems at the top in Table 12.3 . Once this target is achieved, a new threshold value can be reestablished using a more aggressive target to rank the remaining single - circuit supply systems that include many circuits in the single - circuit network supply group. Based on the threshold of 1.5%, 13 circuits from the single - circuit radial supply group (italicized entries in WRI column in Table 12.3 ) and 1 circuit from the single - circuit network supply group (italicized entry in WRI column in Table 12.4 ) are selected as the candidates in the initial short list for further investigation.

12.4.2 Financial Justifi cation of Reinforcement

The 14 single - circuit supply systems ranked at the top using the weighted reliability index composed the initial short list. Each candidate in the list must be fi nancially jus-tifi able for reinforcement. The average outage data of both the single - circuit radial and network supply groups are used in the benefi t/cost analysis. Using the average outage data rather than using the outage data of individual circuits can reduce the uncertainty of data in predicting the future reliability performance of the circuits, particularly for those circuits with very few records of outage events. The average outage data of the single - circuits are based on the statistics in the 5 years from 2004 to 2008 and are shown in Table 12.5 . The line lengths and the annual investment costs due to reinforcement by adding a second circuit for the identifi ed 14 single - circuits are presented in Table 12.6 . The annual investment costs were calculated using Equation (12.10) . The load factors and load forecasts of customers on the 14 circuits are given in Table 12.7 .

The benefi t/cost analysis was conducted in the planning timeframe of the 10 years from 2009 to 2018. The EENS indices for each year were evaluated using Equation (12.13) and shown in Table 12.8 . The composite UICs of each circuit, which were estimated using the unit interruption costs of customer sectors and composition of customers on each circuit, are also given in Table 12.8 . The EDC indices were calcu-lated using Equation (12.14) . The reduction ( Δ EDC) in the EDC index due to adding a second circuit represents the benefi t created by reinforcing each single - circuit supply

c12.indd 301c12.indd 301 1/20/2011 10:27:16 AM1/20/2011 10:27:16 AM


system. The present values (in 2009 dollars) of the benefi ts and investment costs due to reinforcement of the 14 circuits in the planning period of the 10 years are presented in Table 12.9 .

The benefi t/cost ratio (BCR) is obtained by dividing the present value of benefi t by the present value of investment cost. The BCR values for reinforcement of the 14 circuits are also given in Table 12.9 . The threshold of BCR is 1.5 in the example. The reinforcement project for each single - circuit supply system is economically justifi able if its BCR is equal to or greater than 1.5. It can be seen from Table 12.9 that the two circuits LR8 - 60 and LR9 - 138 cannot be economically justifi ed since their BCR values are even smaller than 1.0. These two circuits should be excluded from the short list.

12.4.3 Ranking Priority of Single - Circuit Systems

The number of candidate circuits in the short list has been reduced to 12 from 14, based on the benefi t/cost analysis. The reinforcements of the 12 circuits not only provide larger contributions to reliability improvement of the overall system than others not in the list but also are all economically justifi able. However, we cannot implement the reinforcement projects of all 12 circuits at the same time. It is necessary to rank their priority to obtain an idea about which one should be reinforced fi rst.

The T - SAIDI index has been used by the utility as a key performance indicator for years and therefore was selected for calculating the UIRV indices of the 12 single - circuits in the updated short list. The relative %(T - SAIDI) index rather than the absolute T - SAIDI value was used. The UIRV index was obtained using the equivalent annual capital investment cost divided by the yearly average reduction in the %(T - SAIDI) index due to addition of a second circuit and was divided by 10. The division by 10 was taken because the reductions in %(T - SAIDI) for some circuits were estimated to be < 1%. This leads to the UIRV values to be expressed in the unit of k$/year for 0.1%

TABLE 12.6. Length and Annual Investment Cost for Reinforcement of the 14 Circuits

Circuit Voltage (kV) Length (km) Annual Investment Cost (k$/year)

LR1 - 138 138 196.63 2411 LR2 - 138 138 79.56 1918 LR3 - 138 138 39.74 958 LR4 - 138 138 41.36 997 LR5 - 138 138 142.29 3430 LR6 - 60 60 132.47 2353 LR7 - 60 60 105.59 1876 LR8 - 60 60 65.00 1155 LR9 - 138 138 174.34 4203 LR10 - 60 60 84.00 1492 LR11 - 60 60 102.35 1818 LR12 - 60 60 30.40 540 LR13 - 230 230 59.99 1903 LN1 - 138 138 105.25 2537

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TABL

E 12

.7.

Load

For

ecas

ts ( M

W ) a

nd L

oad

Fact

ors

of C

usto

mer

s on

the

14 C

ircui

ts

Cir

cuit

Loa

d Fa

ctor

Peak

Loa

d Su

pplie

d by

Eac

h C

ircu

it in

10

year

s (M

W)

2009

20

10

2011

20

12

2013

20

14

2015

20

16

2017

20

18

LR

1 - 13

8 0.

517

72.6

73

.2

73.6

73

.8

74.1

74

.3

74.6

74

.8

74.9

75

.1

LR

2 - 13

8 0.

592

79.7

81

.9

83.6

84

.4

85.2

86

.6

87.6

88

.0

88.4

88

.8

LR

3 - 13

8 0.

682

120.

0 12

1.2

123.

5 12

4.6

123.

1 12

4.9

127.

3 12

8.3

128.

4 12

8.4

LR

4 - 13

8 0.

532

55.4

55

.7

56.0

56

.4

56.5

56

.7

56.9

57

.2

57.3

57

.4

LR

5 - 13

8 0.

572

57.7

60

.8

62.1

62

.4

62.4

62

.8

63.2

63

.5

63.7

63

.8

LR

6 - 60

0.

504

76.5

77

.1

77.5

77

.8

78.0

78

.3

78.5

78

.7

78.9

79

.1

LR

7 - 60

0.

538

11.1

11

.2

11.2

11

.2

11.3

11

.3

11.3

11

.4

11.4

11

.4

LR

8 - 60

0.

508

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

LR

9 - 13

8 0.

555

5.3

5.3

5.3

5.4

5.4

5.4

5.4

5.4

5.4

5.5

LR

10 - 6

0 0.

531

23.5

24

.5

24.5

24

.6

24.6

24

.7

24.9

25

.0

25.1

25

.3

LR

11 - 6

0 0.

486

13.3

13

.3

13.3

13

.3

13.4

13

.4

13.4

13

.4

13.5

13

.5

LR

12 - 6

0 0.

578

17.7

17

.8

17.9

18

.0

18.1

18

.2

18.2

18

.3

18.4

18

.5

LR

13 - 2

30

0.60

0 11

9.2

120.

5 12

2.9

124.

0 12

4.4

124.

4 12

7.0

128.

0 12

8.0

128.

0 L

N1 -

138

0.50

8 29

.2

29.3

29

.4

29.5

29

.6

29.7

29

.8

29.9

30

.0

30.0

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TABL

E 12

.8.

EEN

S an

d U

IC V

alue

s of

the

14 C

ircui

ts

Cir

cuit

UIC

($

/kW

h)

Exp

ecte

d E

nerg

y N

ot S

uppl

ied

(MW

h/ye

ar)

for

Eac

h C

ircu

it in

the

10

Yea

rs

2009

20

10

2011

20

12

2013

20

14

2015

20

16

2017

20

18

LR

1 - 13

8 11

.09

1631

16

44

1653

16

59

1665

16

70

1677

16

81

1684

16

88

LR

2 - 13

8 7.

33

830

853

871

879

887

902

912

916

920

924

LR

3 - 13

8 15

.73

718

726

740

746

737

748

763

769

769

769

LR

4 - 13

8 10

.13

269

271

272

274

275

276

277

278

279

279

LR

5 - 13

8 11

.71

1037

10

95

1118

11

23

1123

11

30

1137

11

42

1145

11

49

LR

6 - 60

10

.27

4759

47

99

4821

48

37

4854

48

70

4883

48

96

4907

49

19

LR

7 - 60

12

.48

590

592

593

595

597

598

601

603

604

606

LR

8 - 60

15

.76

9 9

9 9

9 9

9 9

9 9

LR

9 - 13

8 12

.67

113

114

114

114

115

115

115

116

116

117

LR

10 - 6

0 11

.30

979

1018

10

20

1022

10

25

1030

10

35

1041

10

46

1051

L

R11

- 60

7.92

61

5 61

6 61

7 61

8 61

9 62

1 62

2 62

3 62

5 62

6 L

R12

- 60

6.72

29

1 29

2 29

4 29

5 29

7 29

8 29

9 30

0 30

1 30

2 L

R13

- 230

15

.76

740

749

763

770

773

773

789

795

795

795

LN

1 - 13

8 10

.40

422

424

425

427

429

430

431

432

433

435

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T - SAIDI improvement. The annual investment costs, reductions in the %(T - SAIDI) index, and UIRV indices for the 12 circuits are summarized in Table 12.10 . The CBR index (the reciprocal of BCR) can be used as another ranking criterion. The CBR indices for reinforcement of the 12 circuits, which were calculated by dividing the present values of investment cost by the present values of benefi t listed in Table 12.9 , are also given in Table 12.10 .

It can be observed from the results in Table 12.10 that reinforcing the LR6 - 60 circuit would reduce the T - SAIDI contributed by the single - circuit supply system by ∼ 9.4%. The UIRV for reinforcement of the circuit LR6 - 60 is $25 k/year for 0.1%

TABLE 12.9. Present Values of Benefi ts and Capital Investment Costs and BCR s for Reinforcement of the 14 Circuits

Circuit Present Value of

Benefi t (k$) Present Value of

Investment Cost (k$) Benefi t/Cost Ratio (BCR)

LR1 - 138 143,851 18,314 7.9 LR2 - 138 50,577 14,571 3.5 LR3 - 138 91,490 7,278 12.6 LR4 - 138 21,677 7,575 2.9 LR5 - 138 101,942 26,059 3.9 LR6 - 60 388,397 22,293 17.4 LR7 - 60 58,137 17,770 3.3 LR8 - 60 1,136 10,939 0.1 LR9 - 138 11,330 31,929 0.4 LR10 - 60 90,267 14,136 6.4 LR11 - 60 38,275 17,225 2.2 LR12 - 60 15,525 5,116 3.0 LR13 - 230 94,821 16,628 5.7 LN1 - 138 34,755 23,581 1.5

TABLE 12.10. UIRV and CBR Indices for Reinforcement of the 12 Circuits

Circuit Annual Investment

Cost (k$/year) Reduction in

(T - SAIDI) Index (%) UIRV (k$/year for 0.1% T - SAIDI Improvement) CBR

LR1 - 138 2411 5.65 42.7 0.13 LR2 - 138 1918 0.38 504.7 0.29 LR3 - 138 958 0.48 199.6 0.08 LR4 - 138 997 0.20 498.5 0.35 LR5 - 138 3430 2.73 125.6 0.26 LR6 - 60 2353 9.38 25.1 0.06 LR7 - 60 1876 2.14 87.7 0.31 LR10 - 60 1492 0.85 175.5 0.16 LR11 - 60 1818 4.14 43.9 0.45 LR12 - 60 540 0.31 174.2 0.33 LR13 - 230 1903 0.11 1730.0 0.18 LN1 - 138 2537 0.50 507.4 0.68

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T - SAIDI reduction, which is the lowest unit investment cost for unit reliability improve-ment among all the listed circuits. Also, its cost/benefi t ratio is the lowest. The circuit LR13 - 230 results in the highest UIRV ($1730 k/year for a 0.1% T - SAIDI reduction), and the circuit LN1 - 138 has the largest CBR (0.68). The observations enable us to make a judgment that the circuit LR6 - 60 should be reinforced fi rst whereas the circuits LR13 - 230 and LN1 - 138 should be ranked last.

However, there is inconsistency if the UIRV and CBR are separately used to rank the priority of all the circuits. This is because the UIRV and CBR indices represent different reliability perspectives. The UIRV indices refl ect the incremental cost for unit improvement in T - SAIDI, and the CBR indices provide the information on the incre-mental cost for unit improvement in the EDC index. In order to overcome this disad-vantage, the relative contribution indices of RUIRV and RCBR were calculated using Equations (12.12) and (12.18) and combined into the CRCI indices for ranking. The RUIRV, RCBR, and CRCI indices for reinforcement of the 12 circuits in the increasing order of CRCI are given in Table 12.11 . The circuit with a smaller CRCI has a higher priority for reinforcement.

It can be seen that the circuit LR6 - 60 has the smallest CRCI (0.024) since both its RUIRV and RCBR values are the smallest, and therefore it ranks at the top of the list over the other 11 circuits. This implies that the LR6 - 60 reinforcement project can maximize the improvements of both T - SAIDI and EDC while minimizing the invest-ment cost for enhancing reliability. The circuit LR13 - 230 has the largest value of CRCI and is consequently ranked at the bottom of the list. It is worth to noting that LR13 - 230 is a single radial circuit serving one transmission customer, which is the largest single customer in this study. The RCBR (0.055) of LR13 - 230 based on the EDC is smaller than that of other 7 circuits in the list. This means that the improvement of EDC after the reinforcement is relatively signifi cant. However, the RUIRV (0.420) of LR13 - 230 based on the T - SAIDI is the largest because the T - SAIDI reduction due to reinforcing this circuit is very small: only 0.11% T - SAIDI reduction, as shown in Table 12.10 . For

TABLE 12.11. RUIRV , RCBR , and CRCI Indices for Reinforcement of the 12 Circuits

Circuit RUIRV

(Based on T - SAIDI) RCBR

(Based on EDC) CRCI Ranking Index Rank

LR6 - 60 0.006 0.018 0.024 1 LR1 - 138 0.010 0.040 0.050 2 LR3 - 138 0.049 0.024 0.073 3 LR10 - 60 0.043 0.049 0.091 4 LR5 - 138 0.031 0.079 0.110 5 LR7 - 60 0.021 0.095 0.116 6 LR12 - 60 0.042 0.101 0.143 7 LR11 - 60 0.011 0.137 0.148 8 LR2 - 138 0.123 0.088 0.211 9 LR4 - 138 0.121 0.107 0.228 10 LN1 - 138 0.123 0.207 0.331 11 LR13 - 230 0.420 0.055 0.475 12

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12.5 CONCLUSIONS 307

this reason, the combined CRCI ranking index of the circuit LR13 - 230 becomes the largest (0.475), meaning that this reinforcement can be benefi cial only from the EDC perspective (as a large industrial customer) but is not benefi cial from the T - SAIDI improvement viewpoint. It can be noted that the ranking order obtained using the CRCI index for the circuits in the middle rows in the list is different from that based on the RUIRV or RCBR. This indicates that using a single reliability or economic index for ranking is not suffi cient in decisionmaking for single - circuit supply system planning.

12.5 CONCLUSIONS

Conceptually, it is apparent that single - circuit supply systems are the weakest network confi gurations in a transmission system in terms of power supply reliability. The reli-ability performance indices based on historical outage statistics can quantitatively provide the information on contributions of different components and subnetwork confi gurations to the overall transmission system unreliability. This information is useful for enhancement direction in transmission planning. An actual example is used for demonstration.

A decision on reinforcement of single - circuit supply systems has been a challenging issue in transmission planning for years because the deterministic N − 1 criterion is not applicable in this case. This chapter proposed a probabilistic reinforcement planning method for single - circuit supply systems, which includes the following three main steps:

• An initial short list is determined. The three reliability performance indices, which are called the ACHL, T - SAIDI, and DPUI, are calculated using historical outage statistics. The three indices not only provide the information about the existing reliability status of each individual circuit in different performance per-spectives but also are used to develop the weighted reliability index (WRI) for establishing the initial short list for reinforcement.

• The short list is modifi ed. A benefi t/cost analysis, which is based on the reduction in the expected damage cost and the investment cost, is conducted for reinforce-ment of each circuit in the list. Any circuit whose reinforcement cannot be eco-nomically justifi ed in the analysis is removed from the initial short list.

• A set of circuits recommended for reinforcement are identifi ed. The UIRV and CBR indices, which represent the incremental cost for unit reliability improve-ment in the different metrics, are estimated fi rst. The RUIRV and RCBR indices in a relative contribution form of UIRV and CBR indices are calculated to develop the CRCI index for ranking the priority of the circuits.

All single - circuit supply systems at BC Hydro are used as an example to demonstrate the application of the probabilistic planning method presented in this chapter. A total of 12 out of 87 single - circuit supply systems are recognized for reinforcement. The 12 circuits are most critical in light of the weighted reliability index, and all of them are fi nancially justifi able. The ranking order for the 12 circuits using the CRCI index indi-cates the priority for reinforcement.

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Probabilistic Transmission System Planning (Li/Transmission System Planning) || Single-Circuit Supply System Planning