This dissertation studies distribution system reliability and its evaluation methods. It summarizes the basic concepts of distribution system reliability, including reliability indices and their calculation formulas. It analyzes existing distribution system reliability evaluation methods and proposes an optimized minimal path method using Dijkstra's algorithm to simplify reliability calculations for complex grids. The method divides system components into two types - those on the minimum path between loads and power sources, and those off the minimum path. It converts components not on the minimum path into nodes based on their contribution to load point failures. This algorithm is programmed in MATLAB to assess reliability for complex distribution systems like the IEEE RBTS BUS 6 example grid.
10. к⎧⭥࣋ᆖ䲒⺅༛ᆖս䇪᮷
DISTRIBUTION SYSTEM RELIABILITY AND ITS
EVALUATION METHODS STUDY
ABSTRACT
Public Facilities Statistics show that about 80% of the customer average
interruption events were caused by the distribution system failures. Customer
load point reliability depends on the topology, planning and operation of the
local distribution system. Therefore, distribution network reliability assessment
is of great significance.
Based on the study of distribution system reliability development of both
domestic and abroad, the basic concept and structure of distribution system,
and distribution system reliability concepts are summarized and analyzed,
which include distribution system reliability indices and its calculation formula,
the reliability parameters of the system components and its model, distribution
systems modeling and sensitivity analysis methods.
Based on the above, various existing distribution system reliability
evaluation methods are analyzed and studied, and then an optimized minimal
path method is proposed, using Dijkstra’s algorithm to find the minimum path.
Based on the above, various existing distribution system reliability evaluation
methods are analyzed and studied, and then an optimized minimal path method
is proposed, using Dijkstra’s algorithm to find the minimum path in complex
grid. First, the basic concept of algorithm of diagram is described, and then
using Dijkstra’s algorithm to find the minimum path is discussed. Minimal path
algorithm uses the Dijkstra’s algorithm in finding the minimum paths between
load points and power point. Thus, the system components can be divided into
two kinds, components on the minimum path and components off the minimum
path. Components which are not on the minimum path can be converted to the
corresponding nodes according to its contribution to the load points’ failure.
Thus the reliability calculation process of complex gird can be simplified.
This algorithm is programmed based on MATLAB in order to achieve the
II
11. ᪈㾱
reliability assessment of complex distribution system. Then the distribution
system connected to IEEE RBTS BUS 6 is selected as an example to
demonstrate and validate the availability and effectiveness of this algorithm. In
addition, the calculation of reliability indices sensitivity is also performed in
this paper, the result of which can be used to analyze the weaknesses of
distribution system reliability.
KEY WORDS: Distribution System, Reliability, Reliability Sensitivity,
Minimal Path Algorithm, Dijkstra’s Algorithm
III
25. ㅜ 2 ㄐ 䝽⭥㌫㔏৺ަਟ䶐ᙗ࠶᷀
˄4˅ሶ䝽⭥㌫㔏ਟ䶐ᙗᮠᦞؑ⭘Ҿ൘䝽⭥㖁㿴ࡂ䗷〻ѝᵳ㺑ᣅ䍴ᔪ䇮оਟ䶐ᙗ
¦ ˄2.1˅
O O
¦ ˄2.2˅
u O r
11
ᙗ㜭Ⲵ∄䟽DŽ
2.4 䝽⭥㌫㔏Ⲵਟ䶐ᙗ䇴ՠᤷḷ
䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠᤷḷᱟሩ䝽⭥㌫㔏ਟ䶐ᙗ䘋㹼ᇊ䟿࠶᷀Ⲵޣ䭞ˈᱟ䇴ՠ䝽⭥
ਟ䶐ᙗⲴቪᓖˈҏᱟሩ䝽⭥㌫㔏ਟ䶐ᙗ䘋㹼শਢ઼ᵚᶕ䇴ԧⲴส઼สᵜࠪਁ⛩DŽ䝽
⭥㌫㔏ਟ䶐ᙗ䇴ՠवਜ਼є䜘࠶ˈаᱟ㾱ሩ䝽⭥㌫㔏ੁ⭘ᡧⲴ⭥㜭࣋䘋㹼䇴ՠˈҼᱟ
ሩ㌫㔏Ⲵᮤփ⣦ߥ䘋㹼ᓖ䟿DŽഐ↔䝽⭥㌫㔏ਟ䶐ᙗᤷḷփ㌫ᓄާᴹԕлࠐ亩สᵜ⢩ᖱ˖
˄1˅䝽⭥㌫㔏ਟ䶐ᙗᤷḷᓄ㜭৽ᓄ㌫㔏Ⲵ䘀㹼⣦ᘱˈሩ⭘ᡧⲴ⭥㜭࣋ˈ৺ަᡰ
㾶ⴆ४ฏ䇮༷Ⲵ䘀㹼ᙗ㜭˗
˄2˅䝽⭥㌫㔏ਟ䶐ᙗᤷḷᓄ㜭⭡㌫㔏⧠ᴹ䘀㹼㔏䇑ᮠᦞ઼ݳԦᮠᦞ䙊䗷䘲ᖃ㇇⌅
䇑㇇ࠪᶕ˗
˄3˅Ӿ䝽⭥ਟ䶐ᙗ䇴ՠⲴⴞⲴࠪਁˈ䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠᤷḷਟԕ㻛࠶Ѫє㊫˖
䍏㦧⛩ਟ䶐ᙗᤷḷ઼㌫㔏ਟ䶐ᙗᤷḷDŽ䍏㦧⛩઼㌫㔏ਟ䶐ᙗᤷḷ䜭ᱟสҾশਢ㔏䇑ᮠ
ᦞ㓿䗷䙫䗁䇑㇇ᗇࡠⲴՠ䇑ᤷḷDŽ
2.4.1 䍏㦧⛩ਟ䶐ᙗᤷḷ
䝽⭥㌫㔏䍏㦧⛩Ⲵਟ䶐ᙗᤷḷ⭘ᶕ䇴ՠঅ⤜䍏㦧⛩Ⲵᤱ㔝⭥㜭࣋DŽ䍏㦧⛩ਟ
䶐ᙗᤷḷवᤜᒣ൷ڌ⭥⦷઼ᒣ൷ڌ⭥ᰦ䰤DŽ
˄1˅䍏㦧⛩ᒣ൷ڌ⭥⦷ᱟᤷ䍏㦧⛩൘аᒤѝ⭡Ҿ⭥㖁䇮༷᭵䳌ᡆỰ؞㘼䙐ᡀⲴ⭥
࣋ѝᯝⲴ⅑ᮠDŽަᮠᆖ㺘䗮ᔿྲл[9]˖
s i
i
s
ަѝˈ s O
Ѫ䍏㦧⛩ᒣ൷ڌ⭥⦷(⅑/ᒤ)˗ i O
ѪݳԦڌ䘀⦷˄वਜ਼᭵䳌઼Ự؞˅˗
˄2˅䍏㦧⛩ᒤᒣ൷ڌ⭥ᰦ䰤ᱟᤷ䍏㦧⛩൘аᒤѝ⭡Ҿ⭥㖁䇮༷᭵䳌ᡆỰ؞㘼ሬ㠤
Ⲵ⭥࣋ѝᯝⲴᰦ䰤DŽަᮠᆖ㺘䗮ᔿྲл˖
s i i
i
s
ަѝˈ s u Ѫ䍏㦧⛩ᒣ൷ڌ䘀ᰦ䰤(ሿᰦ/ᒤ)˗ i r ѪݳԦڌ䘀ᰦ䰤˄वਜ਼᭵䳌઼Ự؞˅˗
˄3˅䍏㦧⛩ᒣ൷ڌ䘀ᤱ㔝ᰦ䰤ᱟᤷ䍏㦧⛩൘аᒤѝᒣ൷⇿⅑⭡Ҿ⭥㖁䇮༷᭵䳌ᡆ
Ự؞㘼䙐ᡀⲴ⭥࣋ѝᯝⲴᰦ䰤DŽަᮠᆖ㺘䗮ᔿྲл˖
26. к⎧⭥࣋ᆖ䲒⺅༛ᆖս䇪᮷
12
i i
s i s
s
s i
i s
r
r u
O
O O
¦
¦ ˄2.3˅
2.4.2 ㌫㔏ਟ䶐ᙗᤷḷ
䝽⭥㌫㔏חਟ䶐ᙗᤷḷਟṩᦞ䇴ՠᇩ࠶Ѫє㊫ˈ㺑䟿⭘ᡧ⭥㜭࣋Ⲵ⭥ਟ䶐
ᙗᤷḷ઼㺑䟿䝽⭥㌫㔏䍏㦧䖜㜭࣋Ⲵਟ䶐ᙗᤷḷDŽ
˄1˅㺑䟿⭘ᡧ⭥㜭࣋Ⲵ⭥ਟ䶐ᙗᤷḷ
㘳㲁ࡠ IEEE 䝽⭥ਟ䶐ᙗᤷḷḷ߶൘ഭ䱵к䟷⭘ᓖ䖳儈ˈᵜ᮷䘹ਆ䈕ḷ߶ᇊѹⲴ
⭥ਟ䶐ᙗᤷḷ䘋㹼䱀䘠˖
1˅⭥࣋⭘ᡧᒣ൷ڌ⭥ᰦ䰤˄Customer Average Interruption Duration Index, CAIDI˅ˈ
ᤷ൘㔏䇑ᰦ䰤˄䙊ᑨѪаᒤ˅ਇڌ⭥һ᭵ᖡ૽Ⲵ⭘ᡧᒣ൷⇿⅑ڌ⭥ᤱ㔝ᰦ䮯ˈঅս
Ѫሿᰦ/ᒤ˗䇑㇇ޜᔿྲл˖
U N
= = i i
i i
CAIDI
O N
¦
¦
ᡰᴹ⭘ᡧڌ⭥ᤱ㔝ᰦ䰤
ᡰᴹ⭘ᡧڌ⭥⅑ᮠ
˄2.4˅
ᔿѝˈ i N ——䍏㦧⛩ i Ⲵ⭘ᡧᮠ˗
i U ——ᒤڌ⭥ᰦ䰤DŽ
2˅⭥࣋⭘ᡧᒣ൷ڌ⭥仁⦷˄Customer Average Interruption Frequency Index, CAIFI˅ˈ
ᤷ൘㔏䇑ᰦ䰤˄䙊ᑨѪаᒤ˅ਇڌ⭥һ᭵ᖡ૽Ⲵ⭘ᡧⲴᒣ൷ڌ⭥⅑ᮠˈঅսѪ⅑/ᒤ˗
䇑㇇ޜᔿྲл˖
¦O
¦
N
' = = i i
i
CAIFI
N
ᡰᴹ⭘ᡧڌ⭥⅑ᮠ
ਇڌ⭥һ᭵ᖡ૽Ⲵ⭘ᡧᮠ
˄2.5˅
ᔿѝˈ '
i N ——䍏㦧⛩ i ༴ਇ⭥࣋ѝᯝһ᭵ᖡ૽Ⲵ⭘ᡧᮠDŽ
3˅㌫㔏ᒣ൷ڌ⭥ᰦ䰤˄System Average Interruption Duration Index, SAIDI˅ˈᤷ൘
㔏䇑ᰦ䰤˄䙊ᑨѪаᒤ˅㌫㔏ѝ⭘ᡧᒣ൷⇿⅑ڌ⭥ᤱ㔝ᰦ䮯ˈঅսѪሿᰦ/ᒤ˗䇑㇇
ޜᔿྲл˖
U N
= = i i
i
SAIDI
N
¦
¦
⭘ᡧᙫڌ⭥ᤱ㔝ᰦ䰤
ᙫ⭘ᡧᮠ
˄2.6˅
4˅㌫㔏ᒣ൷ڌ⭥仁⦷˄System Average Interruption Frequency Index, SAIFI˅ˈᤷ൘
㔏䇑ᰦ䰤˄䙊ᑨѪаᒤ˅㌫㔏ѝ⭘ᡧⲴᒣ൷ڌ⭥⅑ᮠˈঅսѪ⅑/ᒤ˗䇑㇇ޜᔿྲл˖
27. ㅜ 2 ㄐ 䝽⭥㌫㔏৺ަਟ䶐ᙗ࠶᷀
¦O
¦
N
= = i i
! ڌ⭥⅑ᮠབྷҾQⲴ⭘ᡧᮠ
13
i
SAIFI
N
ᡰᴹ⭘ᡧڌ⭥⅑ᮠ
ᙫ⭘ᡧᮠ
˄2.7˅
5˅㌫㔏㕪⭥䟿˄Energy not Served Index, ENSI˅ˈᤷ㌫㔏൘㔏䇑ᰦ䰤˄䙊ᑨѪ
аᒤ˅⭡Ҿڌ⭥һ᭵ᑖᶕⲴ⭘ᡧ⭥䟿ᦏཡ˗䇑㇇ޜᔿྲл˖
= ai i ENS ¦L U ˄2.8˅
ᔿѝˈ
ai L ——䍏㦧⛩ i ༴ᡰ䘎᧕Ⲵᒣ൷䍏㦧࣏⦷˄অս kWh˅DŽ
6˅ᒣ൷⭥ᴽ࣑ਟ⭘⦷˄Average Service Availability Index, ASAI˅ˈᤷ൘㔏䇑ᰦ䰤
˄䙊ᑨѪаᒤ˅⭘ᡧ⭥࣋ਟ⭘ሿᰦᮠо⭥࣋亴ᵏਟ⭘ሿᰦᮠѻ∄˄%˅˗䇑㇇ޜᔿྲ
л˖
8760
= =
¦ ¦
N U N
i i i
8760
i
ASAI
N
¦
⭘ᡧ⭥࣋ਟ⭘ሿᰦᮠ
⭘ᡧ亴ᵏ⭥࣋ਟ⭘ሿᰦᮠ
˄2.9˅
7˅ᒣ൷⭥ᴽ࣑нਟ⭘⦷˄Average Service Unavailability Index, ASUI˅ˈᤷ൘㔏
䇑ᰦ䰤˄䙊ᑨѪаᒤ˅⭘ᡧ⭥࣋нਟ⭘ሿᰦᮠо⭥࣋亴ᵏਟ⭘ሿᰦᮠѻ∄˄%˅˗䇑
㇇ޜᔿྲл˖
= =
8760
i i
i
U N
ASUI
N
¦
¦
⭘ᡧ⭥࣋нਟ⭘ሿᰦᮠ
⭘ᡧ亴ᵏ⭥࣋ਟ⭘ሿᰦᮠ
˄2.10˅
8˅⭥࣋⭘ᡧ㓿ਇཊ⅑ڌ⭥⦷˄Customer Experiencing Multiple Interruption, CEMI˅ˈ
䈕ᤷḷ⭘Ҿ㔏䇑Ḁ⢩ᇊ⭘ᡧ൘а⇥ᰦ䰤Ⲵᤱ㔝ڌ⭥⅑ᮠˈ⭘Ҿ࠶᷀оᒣ൷٬ᐞ䖳
བྷⲴ⢩↺ᛵߥ˗䇑㇇ޜᔿྲл˖
= = k n
i
CEMI CN
N
⭥࣋⭘ᡧᙫᮠ
˄2.11˅
ᔿѝˈ k n CN ! ——㔏䇑ઘᵏڌ⭥⅑ᮠབྷҾ n ⅑Ⲵ⭘ᡧᮠDŽ
9˅ᒣ൷ⷜᰦڌ⭥⅑ᮠ˄Momentary Average Interruption Frequency Index, MAIFI˅ˈ
䈕ᤷḷ⭘Ҿ㔏䇑аᇊᰦ䰤ࠪ⧠ⷜᰦڌ⭥һ᭵Ⲵ仁⦷˗䇑㇇ޜᔿྲл˖
'
IDN
= i i
i
MAIFI
N
ⷜᰦڌ⭥ᙫ⅑ᮠ ¦
⭥࣋⭘ᡧᙫᮠ
˄2.12˅
ᔿѝˈ i ID ——ڌ⭥䇮༷Ⲵ ⅑ᮠDŽ
10˅⭥࣋⭘ᡧ㓿ਇཊ⅑ᤱ 㔝ڌ⭥઼ⷜ ᰦڌ⭥⦷˄Customers Experiencing Multiple
Interruptions and Momentary Interruption Events, CEMSMI˅ˈ䈕ᤷḷ⭘Ҿ㔏䇑㓿ਇᤱ㔝ੜ
28. к⎧⭥࣋ᆖ䲒⺅༛ᆖս䇪᮷
CEMSMI CNT
! ᤱ㔝ڌ⭥઼ⷜᰦڌ⭥⅑ᮠབྷҾQⲴ⭘ᡧᮠ
14
㿱઼ⷜᰦڌ⭥Ⲵ⅑ᮠ˗䇑㇇ޜᔿྲл˖
= =k n
i
N
⭥࣋⭘ᡧᙫᮠ
˄2.13˅
ᔿѝˈ k n CNT ! ——㔏䇑ઘᵏᤱ㔝ڌ⭥઼ⷜᰦڌ⭥⅑ᮠབྷҾ n Ⲵ⭘ᡧᮠDŽ
˄2˅㺑䟿䝽⭥㌫㔏䍏㦧䖜㜭࣋Ⲵਟ䶐ᙗᤷḷ
㚄㔌⦷ਟ䶐ᙗᤷḷѫ㾱⭘Ҿ䇴ԧ䝽⭥㌫㔏ਁ⭏᭵䳌ᰦ䍏㦧⭥Ⲵ䖜〫㜭࣋ˈ⭘Ҿ
䝽⭥㌫㔏ਟ䶐ᙗ亴⍻࠶᷀ѝˈѫ㾱वᤜԕлࠐњᤷḷ[10]˖
1˅㚄㔌⦷ᤷḷˈ⭘ᶕ䇴ՠ䝽⭥㌫㔏᧕㓯㔃ᶴⲴ㚄㔌ᕪᕡˈ᧿䘠Ҷ᭵䳌ᰦ㓯䐟Ⲵق
䘱㜭࣋˗䇑㇇ޜᔿྲл˖
w= u100% ᭵䳌ਁ⭏ᰦਟ࠷ᦒⲴ䍏㦧ח४⇥ᮠ
᭵䳌ਁ⭏ᰦ࠶⇥ᔰޣࣘਾ⭥Ⓚח४⇥ᮠ
˄2.14˅
w=1㺘⽪䈕侸⭥㓯ਟԕ࠷ᦒ˗
2˅ᴹ᭸䘀㹼⦷ᤷḷˈ⭘Ҿ䇴ՠਁ⭏᭵䳌ᰦ࠶ᣵަԆ४⇥䍏㦧Ⲵ㜭࣋ˈᱟ侸㓯ਁ⭏
᭵䳌ᰦᡰᴹ४⇥ᱟ䜭ਟԕ࠷ᦒⲴࡔᦞ˗䇑㇇ޜᔿྲл˖
K = + u100% ↓ᑨᐕᰦ侸㓯䍏䖭⭥⍱ ᡰ㚄㔌४⇥ᴰབྷ䍏䖭⭥⍱
⸝ᰦݱ䇨⭥⍱
˄2.15˅
K =100%ѪѤ⭼٬ˈK 100%㺘⽪ᴹ㼅ᓖ˗
3˅䘲࠷侸㓯⦷ᤷḷˈ⭘Ҿ䇴ԧ䝽⭥㌫㔏᧕㓯⁑ᔿлⲴ侸㓯㼅ᓖ˗䇑㇇ޜᔿྲл˖
q= ᴹ᭸䘀㹼⦷ K
н䏣 100% Ⲵ侸㓯ᮠ
u 100%
侸㓯ᙫᮠ
˄2.16˅
2.5 䝽⭥㌫㔏ݳԦਟ䶐ᙗ৲ᮠ৺⁑ර
൘⭥࣋㌫㔏ਟ䶐ᙗ䇴ՠѝˈݳԦਟԕ࠶Ѫਟ؞༽ݳԦ઼нਟ؞༽ݳԦ˖㤕ݳԦᣅ
ޕ֯⭘ਾаᰖਁ⭏᭵䳌ׯᰐ⌅؞༽ˈᡆ㲭❦؞༽ն䙐ԧᰲ䍥ˈࡉ〠䘉䇮༷Ѫнਟ؞
༽ݳԦˈ㤕ݳԦ֯⭘а⇥ᰦ䰤ਾਁ⭏᭵䳌㓿؞༽ਟԕᚒ༽ࡠ↓ᑨᐕ⣦ᘱˈ䘉䇮
༷ণѪਟ؞༽ݳԦ[11]ˈਟ؞༽ݳԦঐ⭥࣋㌫㔏ѝݳԦⲴ㔍བྷ䜘࠶˗䝽⭥㌫㔏ѝⲴݳԦ
ѫ㾱वਜ਼⇽㓯ǃᷦオ㓯䐟ǃ⭥㔶ǃ䳄ᔰޣǃᯝ䐟ಘǃ䍏㦧ᔰޣ৺䝽⭥ਈಘㅹˈ䘉
Ӌѫ㾱ݳԦ൷Ѫਟ؞༽ݳԦˈഐ↔ˈ൘䝽⭥㌫㔏ਟ䶐ᙗ࠶᷀ѝˈሶ⎹৺ࡠⲴݳԦ൷㿶
Ѫਟ؞༽ݳԦDŽ
29. ㅜ 2 ㄐ 䝽⭥㌫㔏৺ަਟ䶐ᙗ࠶᷀
2.5.1 䝽⭥㌫㔏ݳԦਟ䶐ᙗ৲ᮠ
ݳԦਟ䶐ᙗ৲ᮠҾ㔏䇑㊫ᤷḷˈ৸〠ݳԦ᭵䳌㔏䇑ˈ⺞ᇊݳԦਟ䶐ᙗ৲ᮠˈᱟ
䘋㹼䝽⭥㌫㔏ਟ䶐ᙗ࠶᷀Ⲵㅜа↕DŽݳԦਟ䶐ᙗ৲ᮠѫ㾱वᤜਟ⭘ᓖǃ᭵䳌⦷ǃ؞༽
⦷ǃᒣ൷᭵䳌؞༽ᰦ䰤ǃᒣ൷᭵䳌䰤䳄ǃ䇑ࡂỰ؞⦷ǃ䇑ࡂỰ؞ᰦ䰤ㅹ[10]˖
˄1˅ਟ⭘ᓖ
ݳԦⲴਟ⭘ᓖᱟᤷањݳԦ൘㿴ᇊⲴᶑԦ઼亴ᇊⲴᰦ䰤ˈ㜭ᢗ㹼㿴ᇊ࣏㜭Ⲵᾲ
⦷DŽݳԦⲴਟ䶐ᓖᱟԕᰦ䰤Ѫ㠚ਈ䟿Ⲵ࠭ᮠ R(t).а㡜ᛵߥлˈݳԦⲴਟ䶐ᓖᱟᤷަሯ
ભ T 䎵䗷Ḁ亴ᵏ٬ t Ⲵᾲ⦷ˈণ˖
R(t) P[T ! t] ˄2.17˅
нਟ䶐ᓖ˄৸〠᭵䳌࠭ᮠ˅ᱟᤷݳԦӾᣅޕ֯⭘ࡠᰦ t ਁ⭏᭵䳌Ⲵᾲ⦷ˈҏᱟᰦ
䰤Ⲵ࠭ᮠˈ䇠 F(t).ݳԦⲴнਟ䶐ᓖਟԕ⭘ݳԦⲴሯભ T ሿҾ઼ㅹҾᰦ䮯 t Ⲵᾲ⦷ᶕ
㺘⽪ˈণ˖
F(t) P[T d t] ˄2.18˅
˄2˅᭵䳌⦷ ( ) R O t ᱟݳԦӾᣅޕ֯⭘ᔰࡠᰦt ӽ↓ᑨᐕⲴᶑԦлˈ൘䈕ᰦ
ѻਾ[t, t+Ƹt]ᰦ䰤䰤䳄ਁ⭏᭵䳌ⲴᶑԦᾲ⦷ᇶᓖˈণ˖
(t)= lim 1 [ | |] R t
(t)= lim 1 [ | |] R t D D
= Rt 1
D
³f ˄2.21˅
15
0
Pt T t t T t
t
O
' o
' !
'
˄2.19˅
᭵䳌⦷ ( ) R O t ᱟᱟԕᰦ䰤 t Ѫ㠚ਈ䟿Ⲵ࠭ᮠˈնݳԦⲴ൘Ḁа䱦⇥Ⲵっᘱ᭵䳌⦷ R O
ਟԕӾݳԦⲴ䈅傼ᡆ䘀㹼䇠ᖅᮠᦞѝ㧧ᗇ˗
˄3˅؞༽⦷ ( ) R P t ᱟᤷݳԦ⭡ڌ䘀⣦ᘱᚒ༽↓ᑨ䘀㹼⣦ᘱⲴᾲ⦷ˈ㺘᰾ݳԦ᭵䳌ਾ
؞༽Ⲵ䳮ԕ〻ᓖ৺᭸᷌DŽ؞༽⦷ⲴᇊѹᱟݳԦ൘ t ᰦѻࡽ༴Ҿ᭵䳌⣦ᘱⲴᶑԦлˈ൘
䈕ᰦѻਾ[t, t+Ƹt]ᰦ䰤䰤䳄㻛؞༽ⲴᶑԦᾲ⦷ᇶᓖˈণ˖
0
Pt T t t T t
t
P
' o
' !
'
˄2.20˅
ᔿѝˈTD——ݳԦⲴ᭵䳌؞༽ᰦ䰤˗
˄4˅ᒣ൷᭵䳌؞༽ᰦ䰤˄Mean Time to Repair, MTTR˅ᤷⲴᱟݳԦᒣ൷⇿⅑᭵䳌
؞༽ᡰ⭘Ⲵᰦ䰤DŽ⭡ҾݳԦ䘎㔝ڌ䘀ᰦ䰤ᱟањ䲿ᵪਈ䟿ˈᡰԕ䙊ᑨ⭘ަᵏᵋ٬ᶕ㺘
⽪ˈ䙊ᑨ䇠Ѫ TD.ᖃ؞༽⦷Ѫᑨᮠˈণ ( )= R R P t P ᰦˈᒣ൷᭵䳌؞༽ᰦ䰤Ⲵᵏᵋ٬Ѫ˖
0
R
T e P dt
P
30. к⎧⭥࣋ᆖ䲒⺅༛ᆖս䇪᮷
⭡ᔿ 2.20 ਟ㿱ˈ൘؞༽⦷Ѫᑨ䟿Ⲵᛵߥлˈᒣ൷᭵䳌؞༽ᰦ䰤 TD о؞༽⦷PR ӂ
= Rt 1
U
³f ˄2.22˅
16
Ѫقᮠ˗
˄5˅ᒣ൷ᰐ᭵䳌ᐕᰦ䰤˄Mean Time to Failure, MTTF˅ᱟݳԦ䘎㔝ᐕᰦ䰤䲿
ᵪਈ䟿Ⲵᵏᵋ٬ˈ䙊ᑨ䇠ѪTU.ᖃ᭵䳌⦷ѪᑨᮠˈণOR (t)=ORᰦˈᒣ൷ᰐ᭵䳌ᐕᰦ䰤
Ⲵᵏᵋ٬Ѫ˖
0
R
T e O dt
O
⭡ᔿ 2.21 ਟ㿱ˈ൘᭵䳌⦷ѪᑨᮠⲴᛵߥлˈᒣ൷᭵䳌؞༽ᰦ䰤 TU о؞༽⦷ ȜR
ӂѪقᮠDŽ
2.5.2 䝽⭥㌫㔏ݳԦਟ䶐ᙗ⁑ර
മ 2.5 ᡰ⽪Ѫ䝽⭥㌫㔏ѝⲴݳԦᡰᴹਟ㜭ࠪ⧠Ⲵ⣦ᘱDŽ
ㅜ1㊫
ㅜ2㊫
ㅜ3㊫
ㅜ4㊫
൘䘀㹼
༷⭘
䇑ࡂỰ؞
ᕪ䘛ڌ䘀
ਟ⭘
нਟ⭘
ᣅޕ֯⭘
ڌ→֯⭘
䝽
⭥
㌫
㔏
ݳ
Ԧ
⣦
ᘱ
മ 2.5 䝽⭥㌫㔏ѝݳԦ⣦ᘱ㊫ර[12]
а㡜ᛵߥлˈн㘳㲁㓶࠶Ⲵ㊫䶎䇑ࡂڌ䘀⣦ᘱˈਚ㘳㲁ݳԦⲴ䘀㹼ǃỰ؞ǃڌ
䘀й⣦ᘱˈᗇࡠݳԦⲴй⣦ᘱ⁑රˈྲമ 2.6 ᡰ⽪DŽ
31. ㅜ 2 ㄐ 䝽⭥㌫㔏৺ަਟ䶐ᙗ࠶᷀
മ 2.6 ݳԦй⣦ᘱ⁑ර
ަѝ N 㺘⽪ݳԦ↓ᑨ䘀㹼Ⲵ⣦ᘱˈM 㺘⽪ݳԦ䇑ࡂỰ؞Ⲵ⣦ᘱˈR 㺘⽪ݳԦⲴ᭵
䳌⣦ᘱDŽȜR ѪݳԦӾ↓ᑨ䘀㹼⣦ᘱੁ᭵䳌⣦ᘱ䖜ᦒⲴᾲ⦷ˈণ᭵䳌⦷˗PR ѪݳԦӾ᭵
䳌⣦ᘱੁ↓ᑨ䘀㹼⣦ᘱ䖜ᦒⲴᾲ⦷ˈণ᭵䳌؞༽⦷˗ȜM ѪݳԦӾ↓ᑨ䘀㹼⣦ᘱੁỰ؞
⣦ᘱ䖜ᦒⲴᾲ⦷ˈণỰ؞⦷˗PR ѪݳԦӾỰ؞⣦ᘱੁ↓ᑨ䘀㹼⣦ᘱ䖜ᦒⲴᾲ⦷ˈণỰ
؞؞༽⦷ˈоỰ؞ᰦ䰤 TM ӂѪقᮠDŽ
㤕ਚ㘳㲁ݳԦⲴڌ䘀઼↓ᑨᐕє⣦ᘱˈሶй⣦ᘱ⁑රѝݳԦⲴ᭵䳌⣦ᘱоỰ
؞⣦ᘱਸᒦˈਟԕᗇࡠݳԦⲴє⣦ᘱ⁑රDŽྲമ 2.7 ᡰ⽪DŽ
മ 2.7 ݳԦє⣦ᘱ⁑ර
ަѝ N ѪݳԦ↓ᑨ䘀㹼⣦ᘱˈF Ѫڌ䘀⣦ᘱˈȜ ѪݳԦӾ↓ᑨ䘀㹼⣦ᘱੁڌ䘀⣦ᘱ
䖜ᦒⲴᾲ⦷ˈণڌ䘀⦷˗PѪݳԦӾڌ䘀⣦ᘱੁ↓ᑨ䘀㹼⣦ᘱ䖜ᦒⲴᾲ⦷ˈণ؞༽⦷DŽ
㓿䗷傜ቄ、ཛ˄Markov˅⣦ᘱ䗷〻࠶᷀ˈݳԦй⣦ᘱ⁑රоє⣦ᘱ⁑රлݳԦⲴ
O O O
R M
P P
R M
17
ਟ䶐ᙗ৲ᮠᴹྲлޣ㌫˖
= +
= +
+
M R R M
P
O P O P
°®°¯
˄2.22˅
2.6 䝽⭥㌫㔏ਟ䶐ᙗᤷḷ⚥ᓖ࠶᷀
䝽⭥㖁ਟ䶐ᙗᤷḷˈަᮠ٬བྷሿо䝽⭥㖁᧕㓯㔃ᶴǃݳԦڌ䘀⦷ˈݳԦڌ䘀ᰦ䰤ǃ
䍏㦧⣦ߥㅹഐ㍐ᇶ࠷ޣˈሩк䘠ഐ㍐ᖡ૽лⲴਟ䶐ᙗᤷḷ⚥ᓖ䘋㹼࠶᷀ˈਟԕѪ
ਟ䶐ᙗ᧗ࡦᯩṸⲴࡦᇊᨀаᇊⲴᦞˈ䘈ਟԕሩн਼᧕㓯⁑ᔿⲴਟ䶐ᙗᴰՈ᧗ࡦㆆ
⮕䘋㹼࠶᷀DŽ
45. ㅜ 4 ㄐ สҾ䘚、ᯟᖫ㇇⌅Ⲵᴰሿ䐟㇇⌅
31
䖳ᘛˈ㘼ф㢲ⴱ䇑㇇ᵪ䍴ⓀDŽ
4.2 䘚、ᯟᖫ㇇⌅(Dijkstra’s's Algorithm)
4.2.1 䘚、ᯟᖫ㇇⌅สᵜᾲᘥ
䘚、ᯟᖫ㇇⌅ᱟ⭡㦧ޠ䇑㇇ᵪ、ᆖᇦ㢮ީṬ·Wg䘚、ᯟᖫ˄Edsger Wybe Dijkstra’s˅
Ҿ 1959 ᒤᨀࠪⲴDŽ䘚、ᯟᖫ㇇⌅䟷⭘ᒯᓖՈݸᩌ㍒⌅≲䀓䶎䍏ᵳᴹੁമѝⲴঅⓀᴰ⸝
䐟ᖴ䰞仈ˈ㇇⌅ᴰ㓸ਟԕ㧧ᗇањӾⓀ⛩ࡠ㢲⛩Ⲵᴰ⸝䐟ᖴṁˈ䘚、ᯟᖫ㇇⌅Ⲵ䗃
ޕᱟањ䶎䍏ᵳᴹੁമ Gˈԕ৺ G ѝⲴањᶕⓀ㢲⛩ sˈ䘚、ᯟᖫ㇇⌅Ѫ⇿ањ㢲⛩ v
ᆈۘⴞࡽѪ→ᡰࡠⲴӾ s ࡠ v Ⲵᴰ⸝䐟ᖴ[41-43]ˈࡍॆᰦˈሶⓀ⛩ s Ⲵ䐟ᖴ䮯ᓖ d[s]
䍻٬Ѫ 0ˈྲ᷌ᆈ൘㜭ⴤ᧕ࡠ䗮 s Ⲵ䗩˄s, m˅ˈࡉ䇮 d[m]= w˄s, m˅ˈަѝ w˄s, m˅
ᤷⲴᱟ䗩˄s, m˅ⲴᵳˈᒦሶᡰᴹަԆ㢲⛩Ⲵ䐟ᖴ䮯ᓖ䇮Ѫᰐェབྷˈণሩ㢲⛩䳶ਸ V
ѝᡰᴹ㢲⛩ v 䲔 s ઼ m ཆަ։㢲⛩ d[v] = fDŽᖃ㇇⌅㔃ᶏᰦˈӾ s ࡠ v Ⲵᴰ⸝䐟ᖴׯᆈ
ۘ൘Ҷ d[v]ѝDŽ
䘚、ᯟᖫ㇇⌅䙊䗷䗩Ⲵᤃኅ䘋㹼สᵜ˖ྲ᷌ᆈ൘аᶑӾ u ࡠ v Ⲵ䗩ˈ䛓Ѹ䗩˄u,
v˅ਟԕ㻛࣐ࡠӾ s ࡠ v Ⲵᴰ⸝䐟ᖴѝⲴቮ䜘ᶕᤃኅӾ s ࡠ v Ⲵ䐟ᖴˈ䘉ᶑ䐟ᖴⲴ䮯
ቡਈѪ d[u] + w(u, v)ˈ㤕䈕٬∄ⴞࡽⲴ d[v]㾱ሿˈࡉ⭘䈕٬ᴯᦒᖃࡽ d[v]Ⲵ٬ˈⴤࡠᡰ
ᴹ d[v]㺘⽪Ӿ s Ⓚ⛩ࡠ㢲⛩ v Ⲵᴰ⸝䐟ᖴ䮯ᓖᰦˈᤃኅ䗩Ⲵ㔃ᶏDŽ㇇⌅㔤ᣔєњ㢲
⛩䳶 S ઼ Qˈᐢ⸕Ⲵᡰᴹ d[v]٬ᐢ㓿ᱟᴰ⸝䐟ᖴⲴ٬Ⲵ㢲⛩ᆈۘ൘㢲⛩䳶 S ѝˈ䳶ਸ
Q ࡉ؍⮉ަԆ㢲⛩DŽ㇇⌅ࡍॆᰦ䳶ਸ S Ⲵ⣦ᘱѪオ䳶ˈ䲿⵰㇇⌅Ⲵ䘀㹼ˈ⇿а↕ᤃ
ኅ䗩ᆼᡀਾ䜭ᴹањ㢲⛩Ӿ Q 〫ࣘࡠ S ѝDŽ
4.2.2 䘚、ᯟᖫ㇇⌅ᇎ⧠ᙍ䐟
࡙⭘䘚、ᯟᖫ㇇⌅≲ਆӾⓀ⛩ s ࡠ⛩ v Ⲵᴰ⸝䐟ᖴⲴ䇑㇇䗷〻ྲл˖
˄1˅ࡍॆDŽⓀ⛩䇮㖞Ѫ˖d[s] = 0ˈS= ‡˗ަԆᡰᴹ⛩˖d[i] = f˗ሩⓀ⛩䘋㹼
ḷ䇠 k=sˈ਼ᰦሶަԆᡰᴹ⛩൷䇮Ѫᵚḷ䇠ⲴDŽ
˄2˅ḕ傼Ӿᡰᴹᐢḷ䇠Ⲵ⛩ k ࡠަ䛫Ⲵᵚḷ䇠Ⲵ⛩ v Ⲵ䐍ˈᒦ䇮㖞˖
d[v]=min{ d[v], d[k]+w(k, v)}ˈަѝ w(k, v)㺘⽪⛩ k ࡠ v Ⲵⴤ᧕䘎᧕䐍DŽ
˄3˅䘹ਆлањ⛩DŽӾᡰᴹᵚḷ䇠Ⲵ㢲⛩ѝˈ䘹ਆ d[v]ᴰሿⲴањ i. d[i]= min{d[v],
v Ѫᡰᴹᵚḷ䇠Ⲵ⛩}.
˄4˅ࡠ⛩ i Ⲵࡽањ⛩DŽӾᐢḷ䇠Ⲵ⛩ѝࡠо⛩ i 䛫Ⲵ⛩ j*ˈѪࡽа⛩ˈ
ᒦḷ䇠 i= j*.
˄5˅ḷ䇠⛩ iDŽྲ᷌ᡰᴹ⛩䜭ᐢ㻛ḷ䇠ˈࡉ㇇⌅㔃ᶏ˗ࡉ䇠 k= iˈᒦഎࡠ↕僔˄2˅
46. к⎧⭥࣋ᆖ䲒⺅༛ᆖս䇪᮷
㔗㔝⅑ᢗ㹼к䘠↕僔ˈⴤࡠᡰᴹ⛩䜭㻛ḷ䇠ᆼᡀDŽ
䘚、ᯟᖫ㇇⌅Ⲵ՚ԓ⸱ྲлᡰ⽪˖
1 function Dijkstra’s(G, w, s)
2 for each vertex v in V[G] // ㇇⌅ࡍॆ
3 d[v] := f
4 previous[v] := undefined
5 d[s] := 0
6 S := empty set
7 Q := set of all vertices
8 while Q is not an empty set // Dijstra ㇇⌅ѫփ
9 u := Extract_Min(Q)
10 S := S union {u}
11 for each edge (u,v) outgoing from u
12 if d[v] d[u] + w(u,v) // ᤃኅ䗩(u,v)
13 d[v] := d[u] + w(u,v)
14 previous[v] := u
32
4.2 ᴰሿ䐟㇇⌅
4.2.1 ᴰሿ䐟㇇⌅สᵜ⨶
ᴰሿ䐟㇇⌅ѝⲴᴰሿ䐟ᤷⲴᱟ⇿ањ䍏㦧⛩ࡠሩᓄ⭥Ⓚ⛩Ⲵᴰሿ䐟ᖴˈ䙊䗷ሩᴰ
ሿ䐟ᖴⲴ≲ਆˈሶᮤњ㌫㔏ݳԦ࠶Ѫᴰሿ䐟кݳԦ઼䶎ᴰሿ䐟кݳԦє㊫ˈṩᦞ⭥㖁
㔃ᶴ৺㌫㔏ݳԦᇎ䱵ᛵߥˈሶ䶎ᴰሿ䐟кⲴݳԦਟ䶐ᙗ৲ᮠሩ䍏㦧⛩ਟ䶐ᙗᤷḷⲴᖡ
૽ᣈ㇇ࡠሩᓄⲴᴰሿ䐟㢲⛩кˈᴰਾሩᴰሿ䐟кݳԦ઼ㅹ᭸㢲⛩䘋㹼䇑㇇ণਟᗇࡠ
䈕䍏㦧⛩ਟ䶐ᙗᤷḷDŽᴰሿ䐟㇇⌅䴰㾱ާփ㘳㲁䝽⭥㌫㔏Ⲵᇎ䱵ᛵߥˈवᤜ䳄ᔰޣǃ
䍏㦧ᔰޣǃ࠶᭟㓯؍ᣔǃ䇑ࡂỰ؞৺༷⭘⭥ⓀㅹDŽ
л䶒ԕањㆰঅⲴ䗀ሴ㖁㔌Ѫֻᶕ䱀䘠ᴰሿ䐟㇇⌅Ⲵสᵜ⨶DŽ
俆ݸˈሩ⇿њ䍏㦧⛩≲ਆަࡠ⭥Ⓚ⛩Ⲵᴰሿ䐟ˈᒦሶ㌫㔏ݳԦ࠶Ѫᴰሿ䐟кݳԦ
৺䶎ᴰሿ䐟кݳԦDŽྲമ 4.1 ѝˈѫ侸㓯 AǃB ৺࠶᭟㓯䐟 b ᶴᡀ䍏㦧⛩ 2 ࡠ⭥Ⓚ⛩Ⲵ
ᴰሿ䐟ˈսҾ䈕䐟ᖴкⲴݳԦᡀѪᴰሿ䐟кݳԦˈަԆݳԦণѪ䶎ᴰሿ䐟кݳԦDŽ
47. ㅜ 4 ㄐ สҾ䘚、ᯟᖫ㇇⌅Ⲵᴰሿ䐟㇇⌅
A B C D
DL1 DL2
a b c d
LP1 LP2 LP3 LP4
മ 4.2 ㆰঅⲴ䗀ሴ䝽⭥㖁㔌
༴⨶ᴰሿ䐟кݳԦⲴࡉྲл˖
˄1˅ᖃ㌫㔏ᰐ༷⭘⭥Ⓚᰦˈԫањᴰሿ䐟кݳԦⲴ᭵䳌ᡆỰ؞ˈ䜭Պሬ㠤䍏㦧
⛩ڌ䘀DŽഐ↔ˈሩ䍏㦧⛩ਟ䶐ᙗᤷḷՊӗ⭏ᖡ૽ⲴݳԦਟ䶐ᙗ৲ᮠ࠶࡛ᱟݳԦⲴڌ䘀
33
⦷ i O
˄Oi=ORi +OMi˅৺ڌ䘀ᰦ䰤ti˄ti ORirRi OMirMi˅DŽ൘മ 4.1 ᡰ⽪Ⲵֻᆀѝˈѫ侸
㓯 AǃB ઼࠶᭟㓯䐟 b кⲴݳԦਁ⭏᭵䳌ᡆỰ؞൷Պሬ㠤䍏㦧⛩ 2 ڌ䘀DŽ
˄2˅ᖃ㌫㔏ᴹ༷⭘⭥Ⓚˈ㘼фѫ侸㓯кᆹ㻵ᴹ࠶⇥㻵㖞˄ྲ䳄ᔰޣǃ䍏㦧ᔰޣǃ
࠶⇥ᯝ䐟ಘ˅ᰦˈࡉսҾ࠶⇥㻵㖞ࡽⲴݳԦ᭵䳌ᰦᕅ䎧ਾ⇥䍏㦧⛩Ⲵڌ䘀ᰦ䰤Ѫ max{tb,
tf}ˈަѝ tb Ѫ࠷ᦒ༷⭘⭥Ⓚᡰ⭘ᰦ䰤ˈtf Ѫ࠶⇥㻵㖞ᰦ䰤DŽ࠶⇥㻵㖞ࡽⲴݳԦỰ؞
ࡉнՊ䙐ᡀਾ⇥䍏㦧⛩Ⲵڌ䘀DŽ൘മ 4.1 ѝˈѫ侸㓯 A ᭵䳌ˈ䍏㦧⛩ 2 Ⲵڌ䘀ᰦ䰤Ѫ
max{tb, tf}˗㤕ሩѫ侸㓯 A 䘋㹼Ự؞ˈ䍏㦧⛩ 2 н䙐ᡀڌ䘀˗㘼фѫ侸㓯 Bǃ࠶᭟㓯䐟
b кⲴݳԦ᭵䳌൷Պᕅ䎧䍏㦧⛩ 2 ڌ䘀DŽ
㘼ሩҾ䶎ᴰሿ䐟кݳԦˈ䴰㾱ṩᦞ䝽⭥㖁ᇎ䱵㔃ᶴˈሶݳԦሩᡰ࠶᷀Ⲵ䍏㦧⛩ਟ
䶐ᙗᤷḷⲴᖡ૽ᣈ㇇ࡠᓄⲴᴰሿ䐟㢲⛩кˈӾ㘼⭘ᴰሿ䐟ѝᓄ㢲⛩Ⲵㅹ᭸ਟ䶐ᙗ
ᤷḷ㺘⽪䶎ᴰሿ䐟кݳԦⲴਟ䶐ᙗ৲ᮠDŽ䶎ᴰሿ䐟кݳԦਟԕ᤹ԕлࡉ䘋㹼䇑㇇˖
˄1˅ሩҾ俆ㄟ㻵ᴹ⟄ᯝಘㅹ࠶⇥؍ᣔⲴ࠶᭟㓯ˈྲമ 4.1 ѝⲴ࠶᭟㓯䐟 b ઼ dˈ
ᖃ࠶᭟㓯кݳԦਁ⭏᭵䳌ᰦˈ⟄ᯝಘՊ㠚㹼⟄ᯝˈഐ㘼᭵䳌нՊᖡ૽ަԆ᭟㓯˗
˄2˅㤕࠶᭟㓯俆ㄟ⋑ᴹᆹ㻵࠶᭟㓯؍ᣔˈ䴰㾱ሩ䶎ᴰሿ䐟ݳԦ≲ਆަࡠ⭥ⓀⲴ
ᴰ⸝䐟ᖴˈᒦӾݳԦࠪਁࡠ䈕䐟ᖴкⲴㅜањ䳄ᔰޣᡆ࠶⇥ᯝ䐟ಘˈᒦࡔ࡛䈕࠶
⇥㻵㖞ᱟսҾ䍏㦧⛩ࡠ⭥Ⓚ⛩Ⲵᴰሿ䐟к˗
ᖃ࠶⇥㻵㖞սҾ䍏㦧⛩Ⲵᴰሿ䐟кᰦˈ䶎ᴰሿ䐟кݳԦ᭵䳌Պሬ㠤䍏㦧⛩ڌ䘀ˈ
䈕ݳԦ᭵䳌ᕅ䎧Ⲵ䍏㦧⛩ڌ䘀ᰦ䰤ㅹҾݳԦⲴڌ䘀ᰦ䰤DŽԕമ 4.1 Ѫֻˈ࠶᭟㓯䐟 a
᭵䳌ᰦˈa ࡠ⭥ⓀⲴᴰ⸝䐟ᖴкⲴㅜањ࠶⇥㻵㖞Ѫ QL1ˈսҾ䍏㦧⛩ 2 ࡠ⭥ⓀⲴᴰሿ
䐟кˈ⭡侸㓯 a ᭵䳌ᡆỰ؞䙐ᡀ䍏㦧⛩ 2 Ⲵڌ䘀ᰦ䰤ㅹҾ a Ⲵڌ䘀ᰦ䰤DŽ
ᖃ࠶⇥㻵㖞нսҾ䍏㦧⛩Ⲵᴰሿ䐟кᰦˈ䶎ᴰሿ䐟кݳԦ᭵䳌ᰦਟԕ⭡䈕࠶⇥㻵
59. ৲㘳᮷⥞
[19]ᶘᲃь, ṇ❦. 䝽⭥㖁ਟ䶐ᙗ䇴ՠ㇇⌅[J]. ⭥࣋⧟ຳ؍ᣔ, 2002, 18(4): 33-36.
[20]ߟሿᆱ. ⭥ਟ䶐ᙗ㓿ި亴⍻ᯩ⌅⹄ウ[J]. 、ᢰؑ, 2011 (25): I0366-I0366.
[21]䱸᮷儈. 䜘ḷ߶lj SD137—85 䝽⭥㌫㔏⭥ਟ䶐ᙗ㔏䇑࣎⌅NJᮠᦞ[J]. Ӂই⭥࣋
ᢰᵟ, 1991 (1): 1-4.
[22]䜝≨ส, ᶘࡊ. 䜘࠶ཡ䘀䘎㔝ᙗሩ䝽⭥㌫㔏ਟ䶐ᙗⲴᖡ૽[J]. ॾབྷᆖᆖᣕ: 㠚
❦、ᆖ⡸, 1999, 39(1): 16-18.
[23]ᯩ≤ᒣ, ㇑䵆. ԕ䍏㦧⛩ѪѝᗳⲴ䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠ㇇⌅[J]. ⭥࣋㌫㔏؍ᣔо
᧗ࡦ, 2008, 36(20): 15-19.
[24]䉒ᔰ䍥, ᆉ⊏. สҾ᭵䳌ᢙᮓⲴ༽ᵲѝ䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠ㇇⌅[J]. ⭥࣋㌫
㔏㠚ࣘॆ, 2001, 25(4): 45-48.
[25]Anderson P M, Chintaluri G M, Magbuhat S M, et al. An improved reliability model
for redundant protective systems-Markov models[J]. Power Systems, IEEE Transactions
on, 1997, 12(2): 573-578.
[26]Billinton R, Wang P. Reliability-network-equivalent approach to distribution system
reliability evaluation[J]. IEE Proceedings-Generation, Transmission and Distribution, 1998,
145(2): 149-153.
[27]ᕐ䘎᮷, 䜝⎧呿. 䍍ਦᯟ㖁ᕅ䇪[M]. 、ᆖࠪ⡸⽮, 2006.
[28]ᕐሿ၏, ᵾ⌭㦓, ᕐ䟽䘌, ㅹ. สҾᴰሿ䐟⌅Ⲵ䝽⭥㖁ਟ䶐ᙗ䇴ՠ[J]. ⭥㖁о⌱
㜭Ⓚ, 2010 (008): 24-28.
[29]Xie K, Zhou J, Billinton R. Reliability evaluation algorithm for complex medium
voltage electrical distribution networks based on the shortest path[J]. IEE
Proceedings-Generation, Transmission and Distribution, 2003, 150(6): 686-690.
[30]ᡤ䴟䵎, ᦧ. สҾᴰሿ䐟Ⲵ䝽⭥㖁ਟ䶐ᙗᘛ䙏䇴ՠ⌅[J]. ⭥࣋㠚ࣘॆ䇮༷, 2002,
22(7): 29-31.
[31]Billinton R, Allan R N, Allan R N. Reliability evaluation of power systems[M]. New
York: Plenum press, 1984.
[32]㼤咯ᡀˈ ⦻Ԣཷ. 㫉⢩㖇ᯩ⌅৺ަᓄ⭘: 1993-1997[M]. ⎧⌻ࠪ⡸⽮, 1998.
[33]व・ޜ, ᕐ⪎⾕. Ӫᐕ⾎㓿㖁㔌ᢰᵟ൘⭥࣋㌫㔏ѝⲴᓄ⭘[J]. ⊏㣿⭥ᵪᐕ〻, 2010
(005): 52-55.
[34]El-Sayed M A H, Seitz T, Montebaur A. Fuzzy sets for reliability assessment of
electric power distribution systems[C]//Circuits and Systems, 1994., Proceedings of the
37th Midwest Symposium on. IEEE, 1994, 2: 1491-1494.
[35]⦻ጫጠ, ઘᇦ, 䉒ᔰ䍥. ѝ䝽⭥㖁ਟ䶐ᙗⲴ⁑㋺䇴ՠ[J]. 䟽ᒶབྷᆖᆖᣕ: 㠚❦
、ᆖ⡸, 2006, 29(2): 45-49.
[36]Zhang P, Li W. Boundary analysis of distribution reliability and economic
assessment[J]. Power Systems, IEEE Transactions on, 2010, 25(2): 714-721.
45
60. к⎧⭥࣋ᆖ䲒⺅༛ᆖս䇪᮷
[37]ᵡᥟݳ, ᵡ. ᮠᦞ㔃ᶴ: 䶒ੁሩ䊑ᇎ⧠ᯩ⌅[M]. 㾯ᆹ⭥ᆀ、ᢰབྷᆖࠪ⡸⽮,
2000.
[38]ᔰ▴, ॾ᰾. മ䇪৺ަᓄ⭘[M]. ॾབྷᆖࠪ⡸⽮, 1995.
[39]ᕐ՟᰾ˈ䱸ሯᆉˈѕ↓. 儈ㅹ⭥࣋㖁㔌࠶᷀[M]. ॾབྷᆖࠪ⡸⽮, 2007.
[40]䲦ॾ, ᶘ䴷, ᕐ≁, ㅹ. สҾ␡ᓖՈݸᩌ㍒㇇⌅Ⲵ⭥࣋㌫㔏⭏ᡀṁⲴᇎ⧠ᯩ⌅[J].
⭥㖁ᢰᵟ, 2010, 34(2): 120-124.
[41]⊸㦓㣣. 䘀ㆩᆖ[M ]. ेӜ: ᵪỠᐕъࠪ⡸⽮, 1997.
[42]䫡亲䘚. 䘀ㆩᆖ[M ]. ेӜ: ॾབྷᆖࠪ⡸⽮, 1999
[43]ᵾᒶᢜ, ⦻㜭䎵, ᱃བྷѹ. ᮠ٬࠶᷀[M ]. ↖≹: ॾѝ⨶ᐕབྷᆖࠪ⡸⽮, 1986.
[44]95 GB. 䝽⭥㌫㔏䇮䇑㿴㤳[S][D] , 1995.
[45]䏳. 䝽⭥㌫㔏㿴ࡂⲴਟ䶐ᙗ࠶᷀⹄ウоᇎ⧠[D]. ཙ⍕བྷᆖ, 2008.
[46]哴㢪. 䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠ㇇⌅Ⲵ⹄ウ[D]. ॾे⭥࣋བྷᆖ (ेӜ), 2007.
[47]⦻ᡀኡ, ᷇⪎ޤ. ѝ䝽⭥㖁н਼᧕㓯⁑ᔿ㓿⍾ᙗ઼ਟ䶐ᙗ࠶᷀[J]. ⭥࣋㌫㔏㠚
ࣘॆ, 2002, 26(24): 34-39.
[48]䠁ѹ䳴, ࡈ㦾, 䛃⎙. ༽ᵲ䝽⭥㖁ਟ䶐ᙗ᭩䘋㇇⌅৺㕆〻ᇎ⧠[J]. ьे⭥࣋ᢰᵟ,
2012 (9): 1-6.
[49]䠁ѹ䳴, ည㓒Տ, 䳽ࢁҖ, ㅹ. 䝽⭥㖁ਟ䶐ᙗ䇴ՠ㌫㔏Ⲵ䇮䇑[J]. к⎧⭥࣋ᆖ䲒ᆖ
ᣕ, 2010, 26(1): 1-4.
[50]ᕐ呿, ⦻ᆸ. བྷ㿴⁑䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠⲴ४䰤㇇⌅[J]. ѝഭ⭥ᵪᐕ〻ᆖᣕ,
2004, 24(3): 77-84.
[51]䎥⅒. 䝽⭥㌫㔏ਟ䶐ᙗ൘㓯䇴ՠᯩ⌅Ⲵ⹄ウ[D]. ॾे⭥࣋བྷᆖ (ेӜ), 2007.
[52]༿ዙ, 䛡ᵍ᰾. ᑖᴹ༽ᵲ࠶᭟ᆀ侸㓯Ⲵ䝽⭥㌫㔏ਟ䶐ᙗ䇴ՠ[J]. ⭥࣋㌫㔏㠚ࣘॆ,
2002, 26(4): 40-44.
[53]࡛ᵍ㓒, ⦻⿰ѭ. ༽ᵲ䝽⭥㌫㔏Ⲵਟ䶐ᙗ䇴ՠ[J]. 㾯ᆹӔ䙊བྷᆖᆖᣕ, 2000, 34(8):
9-13.
[54]㫉⢩㖇ᯩ⌅[M]. к⎧、ᆖᢰᵟࠪ⡸⽮, 1985.
[55]Billinton R, Jonnavithula S. A test system for teaching overall power system reliability
assessment[J]. Power Systems, IEEE Transactions on, 1996, 11(4): 1670-1676.
[56]Allan R N, Billinton R, Sjarief I, et al. A reliability test system for educational
purposes-basic distribution system data and results[J]. Power Systems, IEEE Transactions
on, 1991, 6(2): 813-820.
46