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CP1 B9 L6 Reliability Analysis
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NATIONAL ELECTRIFICATION ADMINISTRATIONU. P. NATIONAL ENGINEERING CENTER
Certificate in
Power System Modeling and Analysis
Competency Training and Certification Program in Electric Power Distribution System Engineering
U. P. NATIONAL ENGINEERING CENTERU. P. NATIONAL ENGINEERING CENTER
Power System Reliability Analysis
Training Course in
2
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Course Outline
1. Reliability Models and Methods
2. Distribution System Reliability Evaluation
3. Economics of Power System Reliability
3
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Reliability Definition
� Probability Function
� The Reliability Function
� Availability
� System Reliability Networks
Reliability Models and Methods
4
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Reliability Definition
A reliable piece of equipment or a System is understood to be basically sound and give trouble-free performance in a given environment.
Reliability is the probability that an equipment or system will perform satisfactorily for at least a given period of time when used under stated conditions.
5
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
� Subjective Definition (or Man-in-the-Street)� The probability P(A) is a measure of the degree of belief one
holds in a specified proposition A
Example: Out of 100 equipment that were upgraded by introducing a new design, 75 will perform better
P(improved performance) = 75/100 = 0.75
6
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
SET THEORY CONCEPTS
� SET� A finite or infinite collection of distinct objects or elements with
some common characteristics
Venn Diagram of a SET of Geometric Figures
7
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
SET THEORY CONCEPTS
� SUBSET� A partition of the SET by some further characteristics that
differentiate the members of the SUBSET from the rest of the SET
Venn Diagram of the SUBSET “Circles” from the SET of Geometric Figures
8
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
SET THEORY CONCEPTS
� Identity SET� SET that contains all the elements under consideration. Also
called Reference SET and denoted by letter I
� Zero SET� SET with no element denoted by letter Z
9
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability and Statistics
SET THEORY CONCEPTS
� Size of a SET� The number of elements in the SET A is denoted by m(A) and is
referred to as the size of the SET A
Example: The NEC SET company employs ten non-professional workers. Three of these are Assemblers (the Set A), five are Machinists (the Set M), and two are Clerks(the Set C) A M C
m(A) = 3 m(M) = 5 m(C) = 2 m(I) = 10
10
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
SET THEORY CONCEPTS� The SET Q, made up of all workers who are both machinists
and assemblers, does not contain any element (mutually exclusive), i.e., Q = AM = Z. Hence,
� The SET F, consisting of all factory workers (assemblers and machinists), is the Union of SETs A & M, i.e., F = A + M
This SET contains eight distinct elements, three from A and five from M. Thus,
m(Q) = m(Z) = 0
m(F) = m(A+M) = 3 + 5 = 8
m(A+B) = m(A) + m(B) if AB = Z
11
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
SET THEORY CONCEPTS
Example: In addition to the 10 Non-professional workers, the NEC SET Company also employs eight full time Engineers (the Set E), three full time supervisors (the Set S), and two individuals whoare both engineers and supervisors (the Set ES).
The size of the Set of all professional employees (engineers andsupervisors) is 13 m(E+S) ≠ m(E) + m(S)
A M CE ES S
13 ≠ 10 + 5
12
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
SET THEORY CONCEPTSNote the Set ES is counted twice. Hence,
m(E+S) = m(E) + m(S) – m(ES)
= 10 + 5 - 2
= 13
m(A+B) = m(A) + m(B) – m(AB) if AB ≠ Z
“NOT MUTUALLY EXCLUSIVE”
13
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
PROBABILITY AND SET THEORY� The PROBABILITY of some Event A may be regarded as
equivalent to comparing the relative size of the SUBSET represented by the Event A to that of the Reference SET I
� Example: The probability of the employee of NEC SET Company being both Engineers and supervisor
m(A)M(I)
P(A) =
m(ES)M(I)
P(ES) =2
23=
14
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Random VariableA function defined on a sample space
•Tossing two Dice•Operating time (hours)•Distance covered (km)•Cycles or on/off operations•Number of revolutions•Throughput volume (tons of raw materials)
Discrete Random Variable - Countable and Finite
Continuous Random Variable - Measured and Infinite
Probability Function
15
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
21,1
31,2
41,3
51,4
61,5
71,6
82,6
72,5
62,4
52,3
42,2
32,1
Value of R.V.
Sample Point
43,1
53,2
63,3
73,4
83,5
93,6
104,6
94,5
84,4
74,3
64,2
54,1
Value of R.V.
Sample Point
65,1
75,2
85,3
95,4
105,5
115,6
126,6
116,5
106,4
96,3
86,2
76,1
Value of R.V.
Sample Point
Results of Tossing two dice� Random Variable
Probability Function
16
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
1
2
3
4
5
6
5
4
3
2
1
Occur.m(xi)
12
11
10
9
8
7
6
5
4
3
2
Value of R.V.
1/36
2/36
3/36
4/36
5/36
6/36
5/36
4/36
3/36
2/36
1/36
Probablityp(xi)
( )
⎪⎪⎩
⎪⎪⎨
⎧
−
−
=
36
13
36
1
i
i
i
x
x
xp
7 6, 5, 4, 3, 2 ,xi =
12 11,10,9, 8,=ix
� Probability Distribution
0
0.05
0.1
0.15
0.2
2 3 4 5 6 7 8 9 10 11
Random Variable y = x1 + x2
Pro
bab
ility
12
Probability Function
17
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
0<2
12
11
10
9
8
7
6
5
4
3
2
Value of R.V.
36/36 = 1.0
35/36
33/36
30/36
26/36
21/36
15/36
10/36
6/36
3/36
1/36
Cum. ProbablityF(xi)
( ) ( )∑≤
=ixx
ii xpxF
� Cumulative Distribution
0
0.2
0.4
0.6
0.8
1
122 3 4 5 6 7 8 9 10 11
Random Variable y = x1 + x2
Cu
m. P
rob
abili
ty
Probability Function
18
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� For Continuous Random Variable� Probability Density Function
� Cumulative Probability Function
( )xf x – random variable
( ) ( ) τdxfxFx
∫ ∞−=
Probability Function
19
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
The Reliability Function
21,1
31,2
41,3
51,4
61,5
71,6
82,6
72,5
62,4
52,3
42,2
32,1
Value of R.V.
Sample Point
43,1
53,2
63,3
73,4
83,5
93,6
104,6
94,5
84,4
74,3
64,2
54,1
Value of R.V.
Sample Point
65,1
75,2
85,3
95,4
105,5
115,6
126,6
116,5
106,4
96,3
86,2
76,1
Value of R.V.
Sample Point
Results of Tossing two dice� Random Variable
20
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
The Reliability Function
1
2
3
4
5
6
5
4
3
2
1
Occur.m(xi)
12
11
10
9
8
7
6
5
4
3
2
Value of R.V.
1/36
2/36
3/36
4/36
5/36
6/36
5/36
4/36
3/36
2/36
1/36
Probablityp(xi)
( )
⎪⎪⎩
⎪⎪⎨
⎧
−
−
=
36
13
36
1
i
i
i
x
x
xp
7 6, 5, 4, 3, 2 ,xi =
12 11,10,9, 8,=ix
� Probability Distribution
0
0.05
0.1
0.15
0.2
2 3 4 5 6 7 8 9 10 11
Random Variable y = x1 + x2
Pro
bab
ility
12
21
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
The Reliability Function
0<2
12
11
10
9
8
7
6
5
4
3
2
Value of R.V.
36/36 = 1.0
35/36
33/36
30/36
26/36
21/36
15/36
10/36
6/36
3/36
1/36
Cum. ProbablityF(xi)
( ) ( )∑≤
=ixx
ii xpxF
� Cumulative Distribution
0
0.2
0.4
0.6
0.8
1
122 3 4 5 6 7 8 9 10 11
Random Variable y = x1 + x2
Cu
m. P
rob
abili
ty
22
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Probability Function
� For Continuous Random Variable� Failure Density Function
� Cumulative Probability Function
( )tf t – random variable time-to-failure
( ) ( ) ττ dftFt
∫=0
23
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
The Reliability Function
The probability that a component will fail by the time t can be defined by cumulative distribution function of failure
where t is a random variable denoting time-to-failure.
Since success and failure are mutually exclusive, then the Reliability Function can be defined by
( ) ( )tFtTP =≤ 0≥t
( ) ( )tF1tR −= 0≥t
24
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
If the time to failure random variable t has a density function f(t), then
or
( ) ( )∫−=t
0df1tR ττ
( ) ( )∫∞
=t
dftR ττ
∫=t
dtftF0
)()( τ
The Reliability Function
( )tf
timet
λ f(t)
F(t)
R(t)
25
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
Example
What is the probability that an equipment will not fail in one year if its failure density function is found to be exponential ( ) where λλλλ = 0.01failure/yr
The reliability function is
( ) τλ λτ de1tRt
0∫−−=
t0|e1 λτ−+=
0t ee1 −− −+= λ
( ) tetR λ−=
( ) tetf λλ −=
The Reliability Function
( )( ) == − yryr/f.e 1010
26
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
The Reliability Function
� Hazard Function (Failure Rate)
The propones of failure of a system or a component is expressed by a the Hazard Function h(t).
In terms of the Hazard Function, the Failure Density Function is
( )( )∫=
−t
dhetR 0
ττ
( ) ( ) ( )∫−=
t dhethtf 0 ττ
the Reliability Function in terms of Hazard Function is
27
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
Example
What is the reliability of a component in one year if it has constant hazard function of λλλλ = 0.01failure/yr
The reliability function is
The Reliability Function
tdee
t
λτλ−
−
=∫= 0
( )( )∫=
−t
dhetR 0
ττ
( )( )yryr/f.e 1010−=
=
Note: the failure density function for a constant hazard is exponential
( ) ( ) ( )∫−=
t dhethtf 0 ττ
∫=t de 0 τλ
λte λλ −=
28
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
The Reliability Function
Component Failure Data
26610
1869
1418
1117
866
635
464
343
202
81
Time-to-Failure (hrs.)Item No. How do you determine the Failure Density and Hazard Functions?
29
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
The Reliability Function
Estimating Failure Density Function
Data Density Function (fd(t))
The data density function (also called empirical density function) defined over the time interval Δti is given by the ratio of the number of failures occurring in the interval to the size of the original population N, divided by the length of the interval.
where n(t) is the number of survivor at any time t.
( )( ) ( )[ ]
i
iiid t
Nttntntf
Δ
Δ+−= iii tttt Δ+≤<for
30
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Training Course in Power System Reliability Analysis
Failure Density Function f(t)
80186 – 266
45141 – 186
30111 – 141
2586 – 111
2363 – 86
1746 – 63
1234 – 46
1420 – 34
128 – 20
80 – 8
f(t)ΔtiTime
0013.080101
=
0022.045101
=
0033.030101
=
0084.012101
=
0074.014101
=
0084.012101
=
0125.08101
=
The Reliability Function
measure of the overall speedat which failures are occurring.
0059.017
10=
0043.023
101=
0040.025
101=
1
31
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Training Course in Power System Reliability Analysis
0.2
0.4
0.6
0.8
1.0
1.2
1.4
100 200 300
f(t)
frac
tiona
l fai
lure
s/hr
.x10
-2
00
Operating time, hr.
Failure Density Function from Component Failure Data
The Reliability Function
32
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
Data Hazard Rate or Failure Rate [hd(t)]
The data hazard rate or failure rate over the time interval Δti is defined by the ratio of the number of failures occurring in the time interval to the number of survivors at the beginning of the time interval, divided by the length of the time interval.
( )( ) ( )[ ] ( )
i
iiiid t
tnttntnth
Δ
Δ+−=
iii tttt Δ+≤<for
The Reliability Function
33
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Failure Hazard Function h(t)
80186 – 266
45141 – 186
30111 – 141
2586 – 111
2363 – 86
1746 – 63
1234 – 46
1420 – 34
128 – 20
80 – 8
h(t)ΔtiTime
The Reliability Function
0125.08101
=
093.012
91=
0096.014
81=
0119.012
71=
0111.030
31=
0111.045
21=
0125.080
11=
measure of the instantaneous speed of failure
0098.017
61=
0087.023
51=
0100.025
41=
34
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
0.2
0.4
0.6
0.8
1.0
1.2
1.4
100 200 3000
0
h(t)
failu
res/
hr.x
10-2
Operating time, hr.
The Reliability Function
Hazard Function from Component Failure Data
35
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
The Reliability Function
Constant Hazard Model
( ) λ=th
( ) tddht
0
t
0λτλττ == ∫∫
( ) tetf λλ −=
( ) tetR λ−=
( ) te1tF λ−−=
( )th
λ
t
36
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
c. Rising exponentialdistribution function
t
( )tF
1e11−
λ1t =
d. Decaying exponentialreliability function
e1t
( )tR
1
λ1t =
( )th
λ
t t
( )tf
λ
eλ
λ1t =
a. Constant Hazard b. Exponential failuredensity function
The Reliability Function
37
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
( ) Ktth =
( ) 2t
0
t
0Kt
2
1dKdh == ∫∫ ττττ
( )2Kt
2
1
Ktetf−
=
( )2Kt
2
1
etR−
=
0t ≥
The Reliability Function
Linearly Increasing Hazard Model
t
( )th
Kt
38
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Training Course in Power System Reliability Analysis
a. Linearly increasinghazard
t
( )th
Kt
b. Rayleigh densityfunction
( )tf
Kslope
t
K
K1
eK
K1
0slopeInitial =
( )tR
t
121e
K1t
( )tF1
21e1 −
c. Rayleigh distributionfunction
d. Rayleigh reliabilityfunction
The Reliability Function
39
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Linearly Decreasing Hazard( )th
t
0K
10 KK0t
( ) =th
( )0
10
ttK
0
tKK
−
−
+∞≤<
≤<
≤<
tt
ttKK
KKt0
0
010
10
( ) =∫ ττ dht
0
( )
( )
( ) ( ) ( )20
t
t 0
t
KK
KK
0 10
1
20
t
KK
KK
0 10
210
t
0 10
ttK2
1dtKd0dKK
K
K
2
1d0dKK
tK2
1tKdKK
010
10
10
10
−=−++−
=+−
−=−
∫∫∫
∫∫
∫
τττττ
τττ
ττ
The Reliability Function
40
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
( ) =tf
( )
( )( )
2ttK
2
1K
K
2
1
0
tK2
1tK
10
01
20
210
eettK
0
etKK
−−−
⎟⎠⎞
⎜⎝⎛
−−
−
−
( ) =tR
( )2
ttK2
1K
K
2
1
tK2
1tK
01
20
210
ee
0
e
−−−
⎟⎠⎞
⎜⎝⎛
−−
+∞≤<
≤<
≤<
tt
ttKK
KKt0
0
010
10
+∞≤<
≤<
≤<
tt
ttKK
KKt0
0
010
10
Linearly Decreasing Hazard
The Reliability Function
41
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
( ) mKtth =
( ) 1mt
0
mt
0Kt
1m
1dKtdh +
+== ∫∫ τττ
( )1mKt
1m
1meKttf
+
+−
=
( )1mKt
1m
1
etR+
+−
=
1m −>
Weibull Hazard Model
( ) Kth
1
2
3
4
5
1 2→t5.0m −=
0m =5.0m =
1m =
2m =3m =
The Reliability Function
42
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
a. Hazard function b. Density function
( ) ( )[ ] ( )1mm
K
1m
K
tf ++
1
2
3
4
5
1 2→τ
5.0m −=0m =
5.0m =1m =2m =
3m =
( ) Kth
1
2
3
4
5
1 2→t5.0m −=
0m =5.0m =
1m =
2m =3m =
Weibull Hazard Model
The Reliability Function
43
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Training Course in Power System Reliability Analysis
c. Distribution function d. Reliability function
( )
t1m
K1m1
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
+=
+
τ
( )tF
1
2
3
4
5
1 2→τ
5.0m −=0m =
5.0m =1m =2m =3m =
( )tR
1
2
3
4
5
1 2→τ( )
t1m
K1m1
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
+=
+
τ
5.0m −=0m =
5.0m =
1m =2m =3m =
The Reliability FunctionWeibull Hazard Model
44
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a. Hazard Function
b. Failure Density Function
The Bathtub Curve
The Reliability Function
45
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Hazard Model for Different System
a. Mechanical b. Electrical c. Software
The Reliability Function
46
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Training Course in Power System Reliability Analysis
The Reliability Function
( ) ( )∫==t
0dtttftE
( )( ) ( )[ ] ( )
dt
tdR
dt
tRd
dt
tdFtf −=
−==
1
tofvalueExpectedMTTF =
( )( ) ( )∫∫∫ =−=−=
∞∞ tdttRttdRdt
dt
ttdRMTTF
000
Mean-Time-To-Failure
but
∑=
=n
1iitn
1MTTFFor a population of n components
47
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Training Course in Power System Reliability Analysis
• 1997: 996 DT Failures• Average of three (3) DT Failures/day• Lost Revenue during Downtime• Additional Equipment Replacement Cost• Lost of Customer Confidence
Distribution Transformer Failures
RELIABILITY ASSESSMENTof MERALCO Distribution Transformers*
* R. R. del Mundo, et. al. (1999)
� Identify the Failure Mode of DTs� Develop strategies to reduce DT failures
The Reliability Function
48
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Training Course in Power System Reliability Analysis
•Gather Equipment History (Failure Data)• Classify DTs (Brand, Condition, KVA, Voltage)•Develop Reliability Model•Determine Failure Mode• Recommend Solutions to Improve Reliability
METHODOLOGY: Reliability Engineering(Weibull Analysis of Failure Data)
The Reliability Function
49
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Parametric Model• Shape Factor Failure Mode• Characteristic Life
Shape Factor Hazard Function Failure Mode< 1 Decreasing Early= 1 Constant Random> 1 Increasing Wear-out
The Reliability Function
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MERALCO DTs (1989–1997)
51,1292,3381,5881,11844,341TOTAL
69----H
79----G
168----F
192----E
2,344-901162,037D
6,5612131496,358C
6,5862691351185,986B
34,7122,0481,33383529,960A
TotalConvertRewindRecondNewBrand
Note: Total Include Acquired DTs
The Reliability Function
51
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Reliability Analysis: All DTs
The Reliability Function
Interval Failures Survivors Hazard200 1444 57095 0.0269400 797 48852 0.0178600 638 39997 0.0174800 508 32802 0.0167
1000 475 27515 0.01891200 363 22129 0.01781400 295 18200 0.01781600 224 14690 0.01671800 159 11865 0.01512000 89 9010 0.01142200 98 6473 0.01772400 51 4479 0.0152600 19 2254 0.01222800 2 821 0.00423000 0 127 0
52
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0
0.005
0.01
0.015
0.02
0.025
0.03
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
Haz
ard
Time Interval
Weibull Shape = 0.84
The Reliability Function
Reliability Analysis: All DTs
Failure Mode: EARLY FAILURE
Is it Manufacturing Defect?
53
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The Reliability Function
Reliability Analysis: By Manufacturer
BRAND Size Shape Failure ModeA 34712 0.84 Early FailureB 6586 0.81 Early FailureC 6561 0.86 Early FailureD 2344 0.76 Early FailureE 192 0.85 Early FailureF 168 0.86 Early FailureG 79 0.76 Early FailureH 69 0.98 Early Failure
54
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The Reliability FunctionReliability Analysis:
By Manufacturer & Condition
BRAND New Reconditioned Rewinded ConvertedA 1.11 1.23 1.12 1.4B 0.81 1.29 1.27 1.23C 0.81 1.13 0.77 0.94D 0.67 1.11 1.49 -
55
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Reliability Analysis: By Voltage Rating
The Reliability Function
PRI SEC All DTs New DTs20 7.62 0.75 -20 120/240 0.79 0.9420 139/277 1.14 1.120 DUAL 0.72 1.03
13.2 120/240 0.88 1.5413.2 240/480 0.91 -7.62 120/240 0.99 1.467.62 DUAL 0.77 -4.8 120/240 0.87 1.613.6 120/240 0.78 1.172.4 120/240 1.15 -
56
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Reliability Analysis: By KVA Rating (New DTs)
The Reliability Function
KVA Shape Failure Mode10 1.3 Wear-out15 1.25 Wear-out25 0.92 Early
37.5 0.83 Early50 0.73 Early75 1.05 Random100 1.04 Random167 1.16 Random250 1.11 Random333 1.46 Wear-out
57
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MERALCO Distribution Transformer Reliability Analysis: Recommendations
• Review Replacement Policies
- New or Repair
- In-house or Remanufacture
• Improve Transformer Load Management Program
- Predict Demand Accurately (TLMS)
• Consider Higher KVA Ratings
• Consider Surge Protection for 20 kV DTs
The Reliability Function
58
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RELIABILITY ASSESSMENTof MERALCO Power Circuit Breakers*
* R. R. del Mundo (UP) & J. Melendrez (Meralco), 2001
VOLTAGE OCB VCB GCB MOCB ACB
34.5 KV 149 160 4113.8 KV 7 28 2 36 126.24 KV 26 3 1224.8 KV 2 11TOTAL 156 216 43 39 145
Number of Feeder Power Circuit Breakers
The Reliability Function
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Annual Failures of 34.5 kV OCBs
3 Circuit Breakers failing per year!
Preventive Maintenance Policy: Time-based (Periodic)
RELIABILITY ASSESSMENTof MERALCO Power Circuit Breakers
The Reliability Function
0.645----1155--Mechanism Failure
1.3171145314931551158Bushing Failure
1.152145114921552158Contact Wear
FailedInstalled FailedInstalledFailedInstalledFailedInstalled
Average Failures
(Units/yr)
2000199919981997Causes of Failure
60
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All PCBs
34.5 kV OCBS OCBs 34.5 kV GCBs 13.8 kV MOCBs
6.24 kV MOCBs 6.24 kV ACBs
Reliability Assessment of MERALCO Power Circuit Breakers
TIME-BASED HAZARD FUNCTION
HAZARD FUNCTION CURVE FOR 34.5 KV OCBs
0
0.1
0.2
0.3
0.4
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Time Interval (months)
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 34.5 KV GCBs
0
0.05
0.1
0.15
0.2
6 12 18 24 30 36 42 48 54 60
Time Interval (months)
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 13.8 KV MOCBs
0
0.1
0.2
0.3
0.4
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Time Interval (months)
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 6.24 KV MOCBs
0
0.1
0.2
0.3
0.4
3 6 9 12 15 18 24 30 36 42 48 54 60
Time Interval (months)
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 6.24 KV ACBs
00.05
0.10.15
0.2
6 12 18 24 30 36 42 48 54 60Time Interval (months)
Ha
zard
Rat
eHAZARD FUNCTION CURVE FOR ALL PCBs CONSIDERED
00.1
0.20.30.4
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Time Interval (m onths)
Haz
ard
Rat
e
.
61
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TRIPPING OPERATIONS-BASED HAZARD FUNCTION
All PCBs
34.5 kV OCBS OCBs 34.5 kV GCBs 13.8 kV MOCBs
6.24 kV MOCBs 6.24 kV ACBs
Reliability Assessment of MERALCO Power Circuit Breakers
HAZARD FUNCTION CURVE FOR 34.5 KV OCBs
00.050.1
0.150.2
0.25
5 10 15 20 25 30 35
Tripping Interval
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 34.5 KV GCBs
0
0.01
0.02
0.03
0.04
0.05
25 50 75 100 125 150
Tripping Interval
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 34.5 KV GCBs
0
0.01
0.02
0.03
0.04
0.05
25 50 75 100 125 150
Tripping Interval
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 6.24 KV MOCBs
0
0.1
0.2
0.3
5 10 15 20
Tripping Interval
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 6.24 KV MOCBs
0
0.1
0.2
0.3
5 10 15 20
Tripping Interval
Haz
ard
Rat
e
HAZARD FUNCTION CURVE FOR 34.5 KV OCBs
00.050.1
0.150.2
0.25
5 10 15 20 25 30 35
Tripping Interval
Haz
ard
Rat
e
62
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Schedule of Servicing for 41XV4
0
0.02
0.04
0.06
0.08
0 10 20 30 40 50 60 70
Number of Tripping Operations
Haz
ard
Rat
e
Reliability-BasedPreventive Maintenance Schedule
RELIABILITY ASSESSMENTof MERALCO Power Circuit Breakers
The Reliability Function
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System Reliability Networks
Series Reliability Model
This arrangements represents a system whose subsystems or components form a series network. If any of the subsystem or component fails, the series system experiences an overall system failure.
R(x1) R(x2) R(x3) R(x4)
Series System
( )∏=
=n
iis xRR
1
64
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Example:
Two non-identical cables in series are required to feed a load from the distribution system. If the two cables have constant failure rates λλλλ1 = 0.01failure/year and λλλλ2 = 0.02 failure/year. Calculate the reliability and the mean-time-to-failure for 1 year period.
System Reliability Networks
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Parallel Reliability Model
R(x1)
R(x2)
R(x3)
R(x4)
Parallel Network
This structure represents a system that will fail if and only if all the units in the system fail.
( )[ ]∏=
−−=n
iis xRR
1
11
System Reliability Networks
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Example
Supposing two identical machines are operating in a redundant configuration. If either of the machine fails, the remaining machine can still operate at the full system load. Assuming both machines to have constant failure rates and failures are statistically independent, calculate (a) the system reliability for λλλλ = 0.0005 failure/hour, t = 400 hours (operating time) and (b) the mean-time-to-failure (MTTF).
System Reliability Networks
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Standby Redundancy Model
This type of redundancy represents a distribution with one operating and n units as standbys. Unlike a parallel network where all units in the configuration are active, the standby units are not active.
R(x1)
R(x2)
R(x3)
R(x4)
System Reliability Networks
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The system reliability of the (n+1) units, in which one unit is operating and n units on the standby mission until the operating unit fails, is given by
The above equation is true if the following are true:1. The switch arrangement is perfect.2. The units are identical.3. The units failure rate are constant.4. The standby units are as good as new.5. The unit failures are statistically independent.
( )( )∑
=
−
−=n
i
ti
i
ettR
1 !1
λλ
System Reliability Networks
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In the case of (n+1) non-identical units whose failure time density functions are different, the standby redundant system failure density is given by
Consequently, the system reliability can be obtained by integrating fs(t) over the interval [t,∞∞∞∞] as follows:
( ) ( ) ( ) ( )∫ ∫ ∫− =
+ −−=t
y
y
y
y
y
nnn
n
n
n
dy...dydyytf...yyfyf...tf1
2
1 0
21112211
( ) ∫∞
=t
dt)t(ftR
System Reliability Networks
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Training Course in Power System Reliability Analysis
K-Out-of-N Reliability Model
This is another form of redundancy. It is used where a specified number of units must be good for the system success.
R(x1)
R(x2)
R(x3)
The system reliability for k-out-of-n number of independent and identical units is given by
∑=
−−⎟⎟⎠
⎞⎜⎜⎝
⎛=
n
ki
inis )R(R
i
nR 1
System Reliability Networks
71
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Primary side
Secondary side
1
2
3
45
6
7
89
10
11
12
13
1415
1617
18
19
2021
22
23
2425
2627
2829
30
31
32
33
34
35
3637
38
39
40
4142
43
4445
46
47
4849
50
51
52
5354
55
56
57
58
Scheme 1: Single breaker-single bus(primary and secondary side)
Reliability Network Models for Typical Substation Configurations of MERALCO*
System Reliability Networks
* Source: A. Gonzales (Meralco) & R. del Mundo (UP), 2005
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15λλλλc 29λλλλct 2λλλλbus 4λλλλd1 2λλλλb1λλλλp 2λλλλb2 3λλλλd2
Summary of Substation Reliability Indices for Scheme 1
0.8287840.2471521.0Total
Opened 115kV bus tie breaker & opened 34.5kV bus tie breaker (normal condition)
0.8287840.2471521.0
Us (hr/yr)λs (failure/yr)ProbabilityEvent 1
where: λλλλs - substation failure rate or interruption frequencyUs – substation annual outage time or unavailability
Reliability Network Diagram of Single breaker-single bus scheme (Scheme 1)
System Reliability Networks
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Primary side
Secondary side
12
3
4
7
65
8
9
10 11
12
13
1415
1617
18
1920
2122
23
24
25
26
2728
2930
31
32
3334
35
36
37
38
39
40
41
42
43
44
45
4647
4849
50
51
5253
5455
61
5657
58
5960
62
6364
6566
67
68
69
7071
72
7374
7576
77
78
79
80
8182
8384
8586
8788
89
9091
92
93
94
95
96
97
98
99
100
101
102
103
104105
106107
108
109110
111112
113
114
115
116
117
118
119
120
121
122123
124125
126
127128
129
130131
132133
134
135136
137138
139
140141
L1 L2
Bank 2Bank 1Scheme 2: Single breaker-double bus (primary side) and two single breaker-single bus with bus tie breaker (secondary side)
Reliability Network Models for Typical Substation Configurations of MERALCO
System Reliability Networks
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16λλλλc 29λλλλct 2λλλλbus 3λλλλd1 2λλλλb1λλλλp 2λλλλb2 3λλλλd2
20λλλλc 37λλλλct 3λλλλbus 5λλλλd1 2λλλλb1 λλλλp 2λλλλb2 3λλλλd2
20λλλλc 37λλλλct 2λλλλbus 3λλλλd1 2λλλλb1 λλλλp 3λλλλb2 5λλλλd2
20λλλλc 37λλλλct 2λλλλbus 3λλλλd1 2λλλλb1λλλλp 3λλλλb2 5λλλλd2
Event 1: Opened 115kV and 34.5kV bus tie breakers; P1 = 0.997985
Event 2: Closed 115kV bus tie breaker & opened 34.5kV bus tie breaker; P2 = 0.000188
Event 3: Closed 115kV bus tie breaker & closed 34.5kV bus tie breaker; P3 = 0.000000344
Event 4: Opened 115kV bus tie breaker & closed 34.5kV bus tie breaker; P4 = 0.00182614
Substation Reliability ModelsSubstation Reliability Models
Reliability Network Diagram of Single breaker-double bus with normally opened 115kV bus tie breaker (Scheme 2)
75
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0.8492750.2518661.0Total
1.0238400.3089360.0018264
1.0238400.3089360.0000003443
1.0083740.3029660.0001882
0.8489190.2517520.9979851
Us (hr/yr)λs (failure/yr)ProbabilityEvent
Summary of Substation Reliability Indices for Scheme 2
Event 1: With two primary lines energized & opened 34.5kV bus tie breaker; P1 = 0.997985
Substation Reliability ModelsSubstation Reliability Models
76
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λλλλΒ4λλλλ54 λλλλΒ3
λλλλΒ1
λλλλΒ6λλλλΒ4
λλλλΒ3
λλλλΒ7
λλλλΒ2
λλλλΒ7
λλλλΒ3λλλλΒ1
λλλλΒ4
λλλλΒ3
λλλλ29
λλλλΒ1
λλλλ17
λλλλΒ1
λλλλΒ9λλλλΒ4
λλλλΒ3
λλλλ29
λλλλΒ2
λλλλΒ6
λλλλΒ3λλλλΒ2
λλλλΒ5
Event 1: With two primary lines energized & opened 34.5kV bus tie breaker; P1 = 0.997985
Substation Reliability ModelsSubstation Reliability ModelsReliability Network Diagram of Single breaker-double bus with normally closed 115kV bus tie breaker (Modified Scheme 2)
Event 2: With one line, L2 interrupted & opened 34.5kV bus tie breaker; P2 = 0.000188
λλλλB1 λλλλB2 λλλλB3 λλλλB4λλλλB5λλλλ17
Event 3: With one line, L2 interrupted and closed 34.5kV bus tie breaker; P3 = 0.000000344
λλλλ29 λλλλB1 λλλλB2λλλλ17 λλλλB5λλλλB8 λλλλB9 λλλλB10 λλλλB11
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Event 4: With two lines energized and closed 34.5kV bus tie breaker; P4 = 0.001826140
λλλλΒ1
λλλλΒ6
λλλλΒ10
λλλλΒ1
λλλλΒ7 λλλλΒ4
λλλλΒ3
λλλλ17
λλλλΒ6
λλλλΒ7
λλλλΒ3λλλλΒ2
λλλλΒ5 λλλλΒ8
λλλλΒ4
λλλλΒ3
λλλλΒ6
λλλλΒ2
λλλλ111λλλλ29 λλλλΒ11
λλλλΒ6
λλλλΒ9 λλλλΒ4
λλλλΒ3
λλλλΒ8
λλλλΒ7
λλλλΒ9
λλλλΒ3λλλλΒ7
λλλλΒ4
λλλλΒ3
λλλλ17
λλλλΒ7
Substation Reliability ModelsSubstation Reliability ModelsReliability Network Diagram of Single breaker-double bus with normally closed 115kV bus tie breaker (Modified Scheme 2)
0.5839230.1761941.0Total
0.7584720.2332610.0018264
1.2615490.3771200.0000003443
0.8476210.2511220.0001882
0.5835480.1760760.9979851
Us,(hr/yr)λs (failure/yr)ProbabilityEvent
Summary of Substation Reliability Indices for Modified Scheme 2
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0.5839230.176194Modified (closed 115kV bus tie breaker)
0.8492750.251866Original (opened 115kV bus tie breaker)
Us (hr/yr)λs (failure/yr)Scheme 2
Comparison of Substation Reliability Indices for Scheme 2
Note: A remarkable 30% improvement in the performance of Scheme 2 by making the 115kV bus tie breaker normally closed.
Substation Reliability ModelsSubstation Reliability Models
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Primary side
Secondary side
1
23
4
56
78
9
1011
1213
1415
16
17
18
1920
2122
2324
2526
27
2829
30
31
32
33
34
35
3637
38
3940
4142
43
44 4546
47
48
495051
5253
54
5556
5758
5960
6162
63
64
65
66
67
6869
7071
7273 74
75
7677
7879
8081
82
83
95
8485
8687
88
89 9091
92
9394
96
97
98
99
100101
102
103
104 105106
107
108109
110111
112
113114 115
116
117
118
119
120
121
122
123
124
125
126127
128
129
130
B2
B3
B5
B6
B7 B8
B10
B9
B1 B4
3 69
Bank 1 Bank 2Scheme 3: Ring bus (primary side) and two single breaker-single bus with bus tie breaker (secondary side)
Reliability Network Models for Typical Substation Configurations of MERALCO
System Reliability Networks
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λλλλ17
λλλλB1
λλλλB4
λλλλB1
λλλλB5
λλλλB6
λλλλB4
λλλλB2
λλλλB3
λλλλB2
λλλλB5
λλλλ51 λλλλB7 λλλλB10
Event 1: With two primary lines energized & opened 34.5kV bus tie breaker; P1 = 0.997985
Event 2: With two primary lines energized & closed 34.5kV bus tie breaker; P2 = 0.00182614
λλλλ31
λλλλB1
λλλλB4
λλλλB1
λλλλB5
λλλλB6
λλλλB4
λλλλB2
λλλλB3
λλλλB3
λλλλB6
λλλλB8 λλλλB9 λλλλ51 λλλλB10
Substation Reliability ModelsSubstation Reliability ModelsReliability Block Diagram of Ring Bus Scheme (Scheme 3)
81
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Event 3: With one primary line (L2) interrupted and opened 34.5kV bus tie breaker; P3 = 0.000188056
λλλλ17
λλλλB2
λλλλB3
λλλλB2
λλλλB5
λλλλB7 λλλλ51 λλλλB10λλλλB1
λλλλB2
λλλλ31
λλλλB2
λλλλB6
Event 4: With one primary line (L2) interrupted and closed 34.5kV bus tie breaker; P4 = 0.000000344
λλλλ31
λλλλB2
λλλλB3
λλλλB3
λλλλB6
λλλλB8 λλλλB9 λλλλ51λλλλB1
λλλλB3
λλλλ17
λλλλB3
λλλλB5
λλλλB10
Substation Reliability ModelsSubstation Reliability ModelsReliability Block Diagram of Ring Bus Scheme (Scheme 3)
CONT.
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0.4368360.1380341.0Total
0.6501140.2044670.0000003444
0.4682330.1472830.0001883
0.6183790.1951120.0018262
0.4364990.1379280.9979851
Us (hr/yr)λs (failure/yr)ProbabilityEvent
Summary of Substation Reliability Indices of Ring Bus (Scheme 3)
Substation Reliability ModelsSubstation Reliability Models
83
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Secondary side
Primary side
1
2
34
56
78
9
10
11
12
13
14
15
16
17
18 1
920 2
122 2
324 2
628
29
30
313
2333
4 353
6 373
8394
0 414
2
119
43
44
45
79
46
474
8 49
505
1 52
53 5
455 5
65758
59 6
061
62
63 6
465
666
7686
9 707
1 72
7374
75
767
7
78
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
959
6979
8 9910
010110
2 10310
4 105
106
10710
8 10911
0 111
112
11311
4 115
116 11
7118
120
121
122
123
124
125 12
612712
812913
0 131
132
13313
4 135
136 13
7138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
3
29
80
105
B1
B2
B3
B4
B5
B8
B6
B7
B9 B10
B11
25
27
L1
L2
Bank 1
Bank 2
Scheme 4: Breaker-and-a-half bus (primary side) and two single breaker-single bus with bus tie breaker (secondary side)
Reliability Network Models for Typical Substation Configurations of MERALCO
System Reliability Networks
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λλλλΒ1
λλλλΒ5
λλλλΒ12
λλλλΒ3
λλλλΒ4
λλλλΒ2
λλλλΒ8
λλλλ6
λλλλ17
λλλλΒ1λλλλ6
λλλλ17
λλλλ7
λλλλΒ1
λλλλΒ7
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλΒ7
λλλλΒ6
λλλλΒ1
λλλλ34
λλλλΒ3
λλλλ33
λλλλΒ5
λλλλΒ2
λλλλΒ3
λλλλΒ4
λλλλΒ3
λλλλ119
λλλλΒ3
λλλλΒ7
λλλλΒ3λλλλΒ3
λλλλΒ9 λλλλ62
λλλλΒ4
λλλλΒ3
λλλλΒ8
λλλλΒ3
A
Event 1: With two primary lines energized and opened 34.5kV bus tie breaker; P1 = 0.997985
λλλλΒ2
λλλλΒ5
λλλλ6
λλλλ119
λλλλΒ3λλλλ6
λλλλΒ8
λλλλ7
λλλλΒ3
λλλλΒ5
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλ17
λλλλΒ5
λλλλΒ3
λλλλ34
λλλλΒ3
λλλλ33
λλλλΒ6
λλλλΒ3
λλλλΒ5
λλλλΒ2
λλλλΒ2
λλλλ6
λλλλΒ4
λλλλΒ1λλλλ6
λλλλ119
λλλλ7
λλλλΒ1
λλλλΒ2
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλΒ7
λλλλΒ2
λλλλΒ1
λλλλ34
λλλλΒ3
λλλλ33
λλλλΒ8
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λλλλΒ2
λλλλ34
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λλλλ33
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λλλλΒ1
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λλλλ33
λλλλΒ2
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λλλλ119
λλλλ17
λλλλΒ1
Substation Reliability ModelsSubstation Reliability ModelsReliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
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λλλλΒ1
λλλλΒ5
λλλλΒ12
λλλλΒ7
λλλλΒ8
λλλλΒ2
λλλλΒ8
λλλλ6
λλλλ17
λλλλΒ5λλλλ6
λλλλΒ7
λλλλ7
λλλλΒ1
λλλλΒ2
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλΒ7
λλλλΒ6
λλλλΒ1
λλλλ34
λλλλΒ3
λλλλ33
λλλλΒ5
λλλλΒ2
λλλλΒ3
λλλλΒ4
λλλλΒ3
λλλλ119
λλλλΒ7
λλλλΒ7
λλλλΒ3λλλλΒ3
λλλλΒ11 λλλλ62
λλλλΒ4
λλλλΒ3
λλλλΒ7
λλλλΒ4
Aλλλλ139λλλλΒ10
λλλλΒ2
λλλλΒ5
λλλλ6
λλλλΒ7
λλλλ119λλλλ6
λλλλ17
λλλλ7
λλλλΒ4
λλλλΒ5
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλΒ8
λλλλΒ6
λλλλΒ5
λλλλ34
λλλλΒ3
λλλλ33
λλλλΒ6
λλλλΒ4
λλλλΒ5
λλλλΒ2
λλλλΒ4
λλλλ6
λλλλΒ5
λλλλΒ2λλλλ6
λλλλ119
λλλλ7
λλλλΒ2
λλλλΒ5
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλΒ6
λλλλΒ5
λλλλΒ3
λλλλ34
λλλλΒ3
λλλλ33
λλλλΒ8
λλλλΒ2
λλλλΒ5
λλλλ34
λλλλΒ3
λλλλ33
λλλλ17
λλλλΒ3
λλλλΒ5A
λλλλ33
λλλλΒ2
λλλλΒ3
λλλλ119
λλλλ17
λλλλΒ5
λλλλΒ2
λλλλΒ5
λλλλ6
λλλλΒ6
λλλλ119
Event 2: With two primary lines energized and closed 34.5kV bus tie breaker; P2 = 0.001826
Substation Reliability ModelsSubstation Reliability ModelsReliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
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λλλλΒ3
λλλλΒ4 λλλλΒ4
λλλλΒ3
λλλλΒ8
λλλλΒ6
λλλλΒ7
λλλλΒ3λλλλΒ6
λλλλΒ4
λλλλΒ3
λλλλ119
λλλλΒ6
AλλλλΒ12λλλλΒ9 λλλλ62 λλλλΒ5
λλλλΒ4
λλλλΒ3
λλλλΒ4
λλλλΒ6
λλλλΒ4
λλλλΒ3
λλλλ17
λλλλΒ7
λλλλΒ8
λλλλΒ3 λλλλΒ4
λλλλΒ3
λλλλΒ4
λλλλ17
λλλλ119
λλλλΒ3λλλλ17
λλλλΒ4
λλλλΒ3
λλλλΒ4
λλλλΒ2
λλλλΒ4
λλλλΒ3
λλλλΒ2
λλλλ119
λλλλΒ4
λλλλΒ3
λλλλΒ3
λλλλ119
λλλλΒ7
λλλλΒ2 λλλλΒ4
λλλλΒ3
λλλλ17
λλλλΒ8
λλλλΒ3
λλλλΒ3λλλλΒ7
λλλλΒ4
λλλλΒ3
λλλλΒ2
λλλλΒ8
A
Event 3: With one primary line (L1) interrupted and opened 34.5kV bus tie breaker; P3 = 0.000188
Substation Reliability ModelsSubstation Reliability ModelsReliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
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λλλλΒ12λλλλΒ11 λλλλ62
λλλλΒ7
λλλλΒ8λλλλΒ4
λλλλΒ3
λλλλ17
λλλλΒ7
λλλλΒ7
λλλλΒ3λλλλΒ6
λλλλΒ4
λλλλΒ3
λλλλΒ2
λλλλΒ7
λλλλ139λλλλΒ10
λλλλΒ7
λλλλΒ3λλλλΒ4
λλλλΒ3
λλλλΒ7
λλλλ119
λλλλΒ7
λλλλΒ3λλλλΒ4
λλλλΒ5
Event 4: With one primary line (L1) interrupted and closed 34.5kV bus tie breaker; P4 = 0.000000344
Summary of Substation Reliability Indices of Breaker-&-a-half (Scheme 4)
0.4355450.1374131.0Total
0.6431650.2044730.0000003444
0.4669720.1466740.0001883
0.6114330.1951200.0018262
0.4352140.1373060.9979851
Us (hr/yr)λs (failure/yr)ProbabilityEvent
Substation Reliability ModelsSubstation Reliability Models� Reliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
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0.4355450.137413Scheme 4 (Breaker-and-a-half bus)
0.4368360.138034Scheme 3 (Ring bus)
0.8492750.583923
0.2518660.176194
Scheme 2 (Single breaker-double bus)- with normally opened 115kV tie bkr.- with normally closed 115kV tie bkr.
0.8287840.247152Scheme 1 (Single breaker-single bus)
Us (hrs/yr)λs (failures/yr)Configuration
Comparison of Substation Reliability Indices (Scheme 1 to 4)
Note: Scheme 3 & 4 - better than Scheme 1 & 2 by 44% & 45% respectively for substation failure rates.Scheme 3 & 4 - better than Scheme 1 & 2 by 47% & 49% respectively for substation interruption duration or unavailabilty.Scheme 3 & 4 - better than Modified Scheme 2 by 22% & 25% for substation failure rates & unavailability, respectively
Substation Reliability ModelsSubstation Reliability ModelsSystem Reliability Networks
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� Distribution System Reliability Indices
� Historical Reliability Performance Assessment
� Predictive Reliability Performance Assessment
� Substation Reliability Evaluation
Distribution System Reliability Evaluation
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Outages, Interruptions and Reliability Indices
� Outage (Component State)Component is not available to perform its intended
function due to the event directly associated with that component (IEEE-STD-346).
� Interruption (Customer State)Loss of service to one or more consumers as a result of
one or more component outages (IEEE-STD-346).
� Types of Interruptions(a) Momentary Interruption. Service restored by
switching operations (automatic or manual) within a specified time (5 minutes per IEEE-STD-346).
(b) Sustained Interruption. An interruption not classified as momentary
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Distribution System Reliability Indices
CUSTOMER-ORIENTED RELIABILITY INDICES
System Average Interruption Frequency Index (SAIFI)*The average number of interruptions per customer served during a period
System Average Interruption Duration Index (SAIDI)The average interruption duration per customer served during a period
servedcustomersof numberTotal
onsinterrupti-customerof numberotalTSAIFI =
servedcustomers of number Total
duration oninterrupti customerof umSSAIDI =
Note: SAIFI for Sustained interruptions. MAIFI for Momentary Interruptions
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CUSTOMER-ORIENTED RELIABILITY INDICES
Customer Average Interruption Frequency Index (CAIFI)
The average number of interruptions per customer interrupted during the period
Customer Average Interruption Duration Index (CAIDI)
The average interruption duration of customers interrupted during the period
dinterrupte customers of number Total
onsinterrupti customerof number otalTCAIFI =
dinterrupte customers of number Total
duration oninterrupti customerof umSCAIDI =
Distribution System Reliability Indices
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CUSTOMER-ORIENTED RELIABILITY INDICES
Average Service Availability Index (ASAI)
The ratio of the total number of customer hours that service was available during a year to the total customer hours demanded
Average Service Unavailability Index (ASUI)
The ratio of the total number of customer hours that service was not available during a year to the total customer hours demanded
Distribution System Reliability Indices
demanded hours Customer
serviceavailableof hoursustomerCASAI =
demanded hours Customer
serviceeunavailablof hoursustomerCASUI =
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LOAD- AND ENERGY-ORIENTED RELIABILITY INDICES
Average Load Interruption Index (ALII)
The average KW (KVA) of connected load interrupted per year per unit of connected load served.
Average System Curtailment Index (ASCI)
Also known as the average energy not supplied (AENS). It is the KWh of connected load interruption per customer served.
Distribution System Reliability Indices
loaddconnecte Total
oninterrupti load TotalALII =
servedcustomers of number Total
tcurtailmenenergy TotalASCI =
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LOAD- AND ENERGY-ORIENTED RELIABILITY INDICES
Average Customer Curtailment Index (ACCI)
The KWh of connected load interruption per affected customer per year.
Distribution System Reliability Indices
affected customers of number Total
tcurtailmenenergy TotalACCI =
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Historical and Predictive Assessment
INCIDENTS
HISTORICALASSESSMENT
COMPONENTPERFORMANCE
PREDICTIVEASSESSMENT
ORGANIZATION,CUSTOMER, kVA
COMPONENTPOPULATION
SYSTEMDEFINITION
HISTORICAL SYSTEMPERFORMANCE
MANAGEMENTOPERATIONSENGINEERINGCUSTOMER INQUIRIES
PREDICTED SYSTEMPERFORMANCE
COMPARATIVE EVALUATIONSAID TO DECISION-MAKINGPLANNING STUDIES
Conceptual Design of an Integrated Reliability Assessment Program
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Historical Reliability Performance Assessment
Required Data:1. Exposure Data
N - total number of customers served
P - period of observation
2. Interruption Data
Nc - number of customers interrupted on interruption i
d - duration of ith interruption, hours
Number of customers interrupted
Time
1N
1d
2N2d
3N
3d
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L1 L2 L3
A B CSource
S 1 2 3
Load PointNumber ofCustomers
Average LoadDemand (KW)
L1 200 1000L2 150 700L3 100 400
SYSTEM LOAD DATA
InterruptionEvent i
Load PointAffected
Number ofDisconnected
Customers
Average LoadCurtailed (KW)
Duration ofInterruption
1 L3 100 400 6 hours
INTERRUTION DATA
Historical Reliability Performance Assessment
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yr-customeroninterrupti 222222.0
100150200
100
N
NSAIFI C
=
++==
∑∑
( )( )
yr-customerhours 333333.1
100150200
6100
N
dNSAIDI C
=
++==
∑∑
( )( )
oninterrupti-custumerhours 6
100
6100
N
dNCAIDI
C
C
=
==∑∑
Historical Reliability Performance Assessment
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000152.0 8760
333333.1
8760
SAIDI
8760
NdNASUI C
=
===∑∑
999848.0
000152.01ASUI1ASAI
=
−=−=
( )( )
yrcustomerKWh 333333.5
100150200
6400
N
dL
N
ENSASCI a
−=
++===
∑∑
∑
Note: ENS - Energy Not Supplied
Historical Reliability Performance Assessment
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Training Course in Power System Reliability Analysis
Outage & Interruption Reporting
Historical Reliability Performance Assessment
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1 01/08/04 3 1.5 Line Fault at C2* 02/06/04 All 4 Transmission3 02/14/04 5, 6 0.5 Line Fault at D4* 03/15/04 4, 5, 6 3 Pre-arranged5 04/01/04 6 1.5 Overload6* 05/20/04 3, 4 3.5 Pre-arranged7 05/30/04 1, 2, 3 0.5 Line Tripped8 06/12/04 1 2 Line fault9 07/04/04 5 1 Line Overload
10* 07/25/04 All 5 Transmission11 07/30/04 5 1 Line Fault12* 08/15/04 4 2 Pre-arranged13 09/08/04 2 1 Line Fault14* 09/30/04 1, 2, 3 2.5 Pre-arranged15 10/25/04 3 1.5 Line Tripped16 11/10/04 2, 3 1.5 Line Fault at A17* 11/27/04 3 2 Pre-arranged18* 12/14/04 3, 4, 5 3.5 Pre-arranged19* 12/27/04 2, 3 3 Pre-arranged20 12/28/04 1, 2, 3 0.075 Line Fault
Outage & Interruption Reporting
*Not included in Distribution Reliability Performance Assessment
Historical Reliability Performance Assessment
hoursAffectedDate
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Month 1 2 3 4 5 6 TotalJanuary 900 800 600 850 500 300 3,950February 905 796 600 855 497 303 3,956March 904 801 604 854 496 308 3,967April 908 806 606 859 501 310 3,990May 912 804 608 862 509 315 4,010June 914 810 611 864 507 318 4,024July 917 815 614 866 512 324 4,048August 915 815 620 872 519 325 4,066September 924 821 622 876 521 328 4,092October 928 824 626 881 526 331 4,116November 930 826 630 886 530 334 4,136December 934 829 635 894 538 332 4,162Annual Average 916 812 615 868 513 319 4,043
Outage & Interruption Reporting
Historical Reliability Performance Assessment
Customer Count
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Interruption Number
Load Points
Affected
Number of Customers Affected
Duration (Hrs.)
Customer Hours
Curtailed
Frequency (Inter/Cust.)
Duration (Hrs/Cust.)
Date
1 3 600 1.5 900 0.1519 0.2278 01/08/045 497 0.5 248.5 0.1256 0.06286 303 0.5 151.5 0.0766 0.0383
5 6 310 1.5 465 0.0777 0.1165 04/01/041 912 0.5 456 0.2274 0.11372 804 0.5 402 0.2005 0.10023 608 0.5 304 0.1516 0.0758
8 1 914 2 1,828.00 0.2271 0.4543 06/12/049 5 512 1 512 0.1265 0.1265 07/04/04
11 5 512 1 512 0.1265 0.1265 07/30/0413 2 821 1 821 0.2006 0.2006 09/08/0415 3 626 1.5 939 0.1521 0.2281 10/25/04
2 826 1.5 1,239.00 0.1997 0.29963 630 1.5 945 0.1523 0.2285
11/10/0416
3
7 05/30/04
02/14/04
Outage & Interruption Reporting
Historical Reliability Performance Assessment
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Outage & Interruption Reporting
Historical Reliability Performance Assessment
Calculate the Annual Reliability Performance of the Distribution System (according to Phil. Distribution Code)
∑∑
=N
NSAIFI C
∑∑
=N
dNSAIDI C
∑∑
=N
NMAIFI C
106
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Required Data:1. Component Reliability Data
λi - failure rate of component iri - mean repair time of component i
2. System Load Data
Ni - number of customers at point iLi - the demand at point i
DistributionSystemSource
A
B Loads
C
λB, rB, UBSource
A
B Loads
C
λA, rA, UA
λC, rC, UC
Predictive Reliability Performance Assessment
107
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1 2 S
1
2
P
For series combinations:
n
λλλλs = Σ λλλλii=1
n
Σ λλλλirii=1
rs = _________
λλλλs
λλλλp = λλλλ1λλλλ2 (r1 + r2)
r1 r2rp = __________
r1 + r2
For parallel combinations:
Predictive Reliability Performance Assessment
Load Point Reliability Equivalents
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L1 L2 L3
A B CSource
S 1 2 3
Feederλλλλ
(f/year)r
(hours)A 0.2 6B 0.1 5C 0.15 8
COMPONENT DATA
Load PointNumber ofCustomers
Average LoadDemand (KW)
L1 200 1000L2 150 700L3 100 400
SYSTEM LOAD DATA
Predictive Reliability Performance Assessment
109
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Load Point Reliability Equivalents
� For L1
� For L2
� For L3
yrf 0.2 A1
=
= λλ
hrs 6
rr A1
=
=( )( )
yrhrs 1.2
62.0
rU 111
=
=
= λ
yrf 0.3
0.10.2 BA2
=
+=
+= λλλ
( )( ) ( )( )
hrs 676666.5 1.02.0
51.062.0
rrr
BA
BBAA2
=
+
+=
+
+=
λλ
λλ
( )( )yrhrs 1.7
5.6666673.0
rU 222
=
=
= λ
yrf 0.45
0.150.10.2 3
=
++=
++= CBA λλλλ
( )( ) ( )( ) ( )( )
hrs 4444446 1501020
8150510620
3
....
...
rrrr
BBA
CCBBAA
=
++
++=
++
++=
λλλ
λλλ
( )( )yrhrs 9.2
6.44444445.0
rU 333
=
=
= λ
110
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�Reliability Indices
( )( ) ( )( ) ( )( )
yrcustomeroninterrupti 288889.0
100150200
10045.01503.02002.0
N
NSAIFI
i
ii
−=
++
++==
∑∑λ
( )( ) ( )( ) ( )( )
yr-customerhours 744444.1
100150200
1009.21507.12002.1
N
NUSAIDI
i
ii
=
++
++==
∑∑
oninterrupti-customerhours 038462.6
288889.0
744444.1
SAIFI
SAIDI
N
NUCAIDI
ii
ii
=
===∑∑
λ
111
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000199.0 8760
744444.1
8760
SAIDI
8760
NNUASUI iii
=
===∑∑
999801.0
000199.01ASUI1ASAI
=
−=−=
( ) ( )( ) ( )( ) ( )( )
yr-customerKWh 888889.7
100150200
9.24007.17002.11000
N
UL
N
ENSASCI
i
iia
i
=
++
++===
∑∑
∑
112
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Training Course in Power System Reliability Analysis
A
B
C
D
1 2 3 4Sourcea b c d
Typical radial distribution system
Predictive Reliability Performance Assessment
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Length (km) λλλλ (f/yr) r (hrs)
1 2 0.2 42 1 0.1 43 3 0.3 44 2 0.2 4
a 1 0.2 2b 3 0.6 2c 2 0.4 2d 1 0.2 2
Lat
eral
Component
SYSTEM RELIABILITY DATA
Mai
n
Component No. of Customers Ave. Load Connected (KW)
A 1000 5000B 800 4000C 700 3000D 500 2000
SYSTEM LOAD DATA
114
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λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
1 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8
2 0.1 4 0.4 0.1 4 0.4 0.1 4 0.4 0.1 4 0.4
3 0.3 4 1.2 0.3 4 1.2 0.3 4 1.2 0.3 4 1.2
4 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8
a 0.2 2 0.4 0.2 2 0.4 0.2 2 0.4 0.2 2 0.4
b 0.6 2 1.2 0.6 2 1.2 0.6 2 1.2 0.6 2 1.2
c 0.4 2 0.8 0.4 2 0.8 0.4 2 0.8 0.4 2 0.8
d 0.2 2 0.4 0.2 2 0.4 0.2 2 0.4 0.2 2 0.4
2.2 2.73 6.0 2.2 2.73 6.0 2.2 2.73 6.0 2.2 2.73 6.0
RELIABILITY INDICES FOR THE SYSTEM
Total
Load pt. A Load pt. B Load pt. C Load pt. DM
ain
Lat
eral
Componentfailure
∑∑∑∑ === λλλ Ur ;UU ; :where totaltotaltotal
115
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
( )( ) ( )( ) ( )( ) ( )( )
yrcustomerint 2.2
5007008001000
5002.27002.28002.210002.2
N
NSAIFI
i
ii
−=
+++
+++==
∑∑λ
( )( ) ( )( ) ( )( ) ( )( )
yr-customerhours 0.6
5007008001000
5000.67000.68000.610000.6
N
NUSAIDI
i
ii
=
+++
+++==
∑∑
oninterrupti-customerhours 727273.2
2.2
0.6
SAIFI
SAIDI
N
NUCAIDI
ii
ii
=
===∑∑
λ
116
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
000685.0 8760
0.6
8760
SAIDI
8760
NNUASUI iii
=
===∑∑
999315.0
000685.01ASUI1ASAI
=
−=−=
( )( ) ( )( ) ( )( ) ( )( )
yr-customerKWh 0.28 5007008001000
0.620000.630000.640000.65000
N
ULASCI
i
iai
=
+++
+++=
=∑∑
117
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Effect of lateral protection
A
B
C
D
1 2 3 4Source
a b c d
Typical radial distribution system with lateral protections
Predictive Reliability Performance Assessment
118
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
1 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8
2 0.1 4 0.4 0.1 4 0.4 0.1 4 0.4 0.1 4 0.4
3 0.3 4 1.2 0.3 4 1.2 0.3 4 1.2 0.3 4 1.2
4 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8
a 0.2 2 0.4
b 0.6 2 1.2
c 0.4 2 0.8
d 0.2 2 0.4
1.0 3.6 3.6 1.4 3.14 4.4 1.2 3.33 4.0 1.0 3.6 3.6
RELIABILITY INDICES WITH LATERAL PROTECTION
Total
Load pt. A Load pt. B Load pt. C Load pt. DM
ain
Lat
eral
Componentfailure
∑∑∑∑ === λλλ Ur ;UU ; :where totaltotaltotal
119
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
( )( ) ( )( ) ( )( ) ( )( )
yrcustomerint 153333.1
5007008001000
5000.17002.18004.110000.1
N
NSAIFI
i
ii
−=
+++
+++==
∑∑λ
( )( ) ( )( ) ( )( ) ( )( )
yr-customerhours 906667.3
5007008001000
5006.37000.48004.410006.3
N
NUSAIDI
i
ii
=
+++
+++==
∑∑
oninterrupti-customerhours 387283.3
153333.1
906667.3
SAIFI
SAIDI
N
NUCAIDI
ii
ii
=
===∑∑
λ
120
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
000446.0 8760
906667.3
8760
SAIDI
8760
NNUASUI iii
=
===∑∑
999554.0
000446.01ASUI1ASAI
=
−=−=
( )( ) ( )( ) ( )( ) ( )( )
yr-customerKWh 266667.18 5007008001000
6.320000.430004.440006.35000
N
ULASCI
i
iai
=
+++
+++=
=∑∑
121
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Effect of disconnects
A
B
C
D
1 2 3 4Source
a b c d
Typical radial distribution system reinforce withlateral protections and disconnects
Predictive Reliability Performance Assessment
122
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
1 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8
2 0.1 0.5 0.05 0.1 4 0.4 0.1 4 0.4 0.1 4 0.4
3 0.3 0.5 0.15 0.3 0.5 0.15 0.3 4 1.2 0.3 4 1.2
4 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 4 0.8
a 0.2 2 0.4
b 0.6 2 1.2
c 0.4 2 0.8
d 0.2 2 0.4
1.0 1.5 1.5 1.4 1.89 2.65 1.2 2.75 3.3 1.0 3.6 3.6
RELIABILITY INDICES WITH LATERAL PROTECTION AND DISCONNECTS
Total
Load pt. A Load pt. B Load pt. C Load pt. DM
ain
Lat
eral
Componentfailure
∑∑∑∑ === λλλ Ur ;UU ; :where totaltotaltotal
123
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
( )( ) ( )( ) ( )( ) ( )( )
yrcustomerint 153333.1
5007008001000
5000.17002.18004.110000.1
N
NSAIFI
i
ii
−=
+++
+++==
∑∑λ
( )( ) ( )( ) ( )( ) ( )( )
yr-customerhours 576667.2
5007008001000
5006.37003.380065.210005.1
N
NUSAIDI
i
ii
=
+++
+++==
∑∑
oninterrupti-customerhours 234105.2
153333.1
576667.2
SAIFI
SAIDI
N
NUCAIDI
ii
ii
=
===∑∑
λ
124
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
000294.0 8760
576667.2
8760
SAIDI
8760
NNUASUI iii
=
===∑∑
999706.0
000294.01ASUI1ASAI
=
−=−=
( )( ) ( )( ) ( )( ) ( )( )
yr-customerKWh 733333.11 5007008001000
6.320003.3300065.240005.15000
N
ULASCI
i
iai
=
+++
+++=
=∑∑
125
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Effect of protection failures
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
1 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8 0.2 4 0.8
2 0.1 0.5 0.05 0.1 4 0.4 0.1 4 0.4 0.1 4 0.4
3 0.3 0.5 0.15 0.3 0.5 0.15 0.3 4 1.2 0.3 4 1.2
4 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 4 0.8
a 0.2 2 0.4 0.02 0.5 0.01 0.02 0.5 0.01 0.02 0.5 0.01
b 0.06 0.5 0.03 0.6 2 1.2 0.06 0.5 0.03 0.06 0.5 0.03
c 0.04 0.5 0.02 0.04 0.5 0.02 0.4 2 0.8 0.04 0.5 0.02
d 0.02 0.5 0.01 0.02 0.5 0.01 0.02 0.5 0.01 0.2 2 0.4
1.12 1.39 1.56 1.48 1.82 2.69 1.3 2.58 3.35 1.12 3.27 3.66
RELIABILITY INDICES IF THE FUSES OPERATE WITH PROBABILITY OF 0.9
Total
Load pt. A Load pt. B Load pt. C Load pt. DM
ain
Lat
eral
Componentfailure
∑∑∑∑ === λλλ Ur ;UU ; :where totaltotaltotal
126
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Effect of load transfer to alternative supply
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
1 0.2 4 0.8 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1
2 0.1 0.5 0.05 0.1 4 0.4 0.1 0.5 0.05 0.1 0.5 0.05
3 0.3 0.5 0.15 0.3 0.5 0.15 0.3 4 1.2 0.3 0.5 0.15
4 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 4 0.8
a 0.2 2 0.4
b 0.6 2 1.2
c 0.4 2 0.8
d 0.2 2 0.4
1.0 1.5 1.5 1.4 1.39 1.95 1.2 1.88 2.25 1.0 1.5 1.5
RELIABILITY INDICES WITH UNRESTRICTED LOAD TRANSFERS
Total
Load pt. A Load pt. B Load pt. C Load pt. D
Mai
nL
ater
al
Componentfailure
∑∑∑∑ === λλλ Ur ;UU ; :where totaltotaltotal
127
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
λλλλ
(f/yr)r
(hrs)
U(hrs/yr)
1 0.2 4 0.8 0.2 1.9 0.38 0.2 1.9 0.38 0.2 1.9 0.38
2 0.1 0.5 0.05 0.1 4 0.4 0.1 1.9 0.19 0.1 1.9 0.19
3 0.3 0.5 0.15 0.3 0.5 0.15 0.3 4 1.2 0.3 1.9 0.57
4 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 4 0.8
a 0.2 2 0.4
b 0.6 2 1.2
c 0.4 2 0.8
d 0.2 2 0.4
1.0 1.5 1.5 1.4 1.59 2.23 1.2 2.23 2.67 1.0 2.3 2.3
RELIABILITY INDICES WITH RESTRICTED LOAD TRANSFERS
Total
Load pt. A Load pt. B Load pt. C Load pt. D
Sec
tion
Dis
trib
uto
r
Componentfailure
∑∑∑∑ === λλλ Ur ;UU ; :where totaltotaltotal
� Effect of load transfer to alternative supply
128
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
λ (f/yr) 2.2 1.0 1.0 1.12 1.0 1.0r (hrs) 2.73 3.6 1.5 1.39 1.5 1.5U (hrs/yr) 6.0 3.6 1.5 1.56 1.5 1.5
λ (f/yr) 2.2 1.4 1.4 1.48 1.4 1.4r (hrs) 2.73 3.14 1.89 1.82 1.39 1.59U (hrs/yr) 6.0 4.4 2.65 2.69 1.95 2.23
λ (f/yr) 2.2 1.2 1.2 1.3 1.2 1.2r (hrs) 2.73 3.33 2.75 2.58 1.88 2.23U (hrs/yr) 6.0 4 3.3 3.35 2.25 2.67
λ (f/yr) 2.2 1.0 1.0 1.12 1.0 1.0r (hrs) 2.73 3.6 3.6 3.27 1.5 2.34U (hrs/yr) 6.0 3.6 3.6 3.66 1.5 2.34
SUMMARY OF INDICES
Load Point A
Load Point B
Load Point C
Load Point D
129
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
SAIFI 2.2 1.15 1.15 1.26 1.15 1.15SAIDI 6.0 3.91 2.58 2.63 1.80 2.11CAIDI 2.73 3.39 2.23 2.09 1.56 1.83ASAI 0.999315 0.999554 0.999706 0.999700 0.999795 0.999759ASUI 0.000685 0.000446 0.000294 0.003000 0.000205 0.000241ENS 84.0 54.8 35.2 35.9 25.1 29.1ASCI 28.0 18.3 11.7 12.0 8.4 9.7
Case 3. As in Case 2, but with disconnects on the main feeders.Case 4. As in Case 3, probability of successful lateral distributor fault clearing of 0.9.Case 5. As in Case 3, but with an alternative supply.Case 6. As in Case 5, probability of conditional load transfer of 0.6.
Sytem Indices
SUMMARY OF INDICES (cont.)
Case 1. Base case.Case 2. As in Case 1, but with perfect fusing in the lateral distributors.
130
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� Impact of Power Interruptions
� Reliability Worth
� Optimal Power System Reliability
Economics of Power System Reliability
131
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
� To Electric Utility• Loss of revenues• Additional work• Loss of confidence
� To Customers• Dissatisfaction• Interruption of productivity• Additional investment for alternative
power supply
� To National Economy• Loss value added/income• Loss of investors• Unemployment
Impact of Power Interruptions
132
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Impact to National Economy:�NEDA Study (1974)
� P 342,380 per day – losses due to brownout in Cebu-Mandauearea
�Business Survey (1980)� P1.4 Billion – losses due to brownouts in 1980
�CRC Memo No. 27 (1988)� P 3.4 Billion – loss of the manufacturing sector in 1987 due to
power outages
�Viray & del Mundo Study (1988)� P 25 – losses in Value Added per kWh curtailment
�Sinay Report (1989)� 45% – loss in Value Added in the manufacturing sector in
Cebu due to power outages
Impact of Power Interruptions
133
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Impact to Customers:A. Short-Run Direct Cost
• Opportunity losses during outages• Opportunity losses during restart period• Raw materials spoilage• Finish products spoilage• Idle workers• Overtime• Equipment damage• Special operation and maintenance during restart period
B. Long-Run Adaptive Response Cost• Standby generators• Power plant• Alternative fuels• Transfer location• Inventory
Impact of Power Interruptions
134
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
(0.0086 + 0.0023D)F + 0.1730 Pesos/kWh
Source: del Mundo (1991)
Outage Cost to Industrial Sector in Luzon
Where, F – Frequency of Interruptions
D – Average Duration of Interruptions
Reliability Worth
Losses of MERALCO Industrial Customers in 1989
Energy Sales: 3.781 billion kWhOutage Cost: Php 0.3544/kWhTotal Losses: Php 1.34 billion
135
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Reliability Worth
136
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Reliability Worth
0.181.310.730.08
0.181.300.310.04
0.201.3820.21
0.221.5040.45
0.261.6170.94
0.341.73131.88
0.682.00386.25
1.122.117012.26
Outage Cost(Php/kWh)
Duration(Hours)
Frequency(per year)
LOLP(days/yr)
Luzon Grid Outage Cost*
Source: del Mundo (1991)
137
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Reliability Worth
Luzon Grid Outage Cost
Source: del Mundo (1991)
138
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Reliability Worth
ATC = ASC + AOC
1.291.311.110.08
1.321.301.140.04
1.291.381.090.21
1.281.501.060.45
1.291.611.030.94
1.351.731.011.88
1.622.000.946.25
2.022.110.9012.26
Total Cost(Php/kWh)
Outage Cost(Php/kWh)
Supply Cost(Php/kWh)
LOLP(days/yr)
Luzon Grid Total Cost
Source: del Mundo (1991)
139
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
Optimal Power System Reliability
Source: del Mundo (1991)
Luzon Grid Total Cost
140
Competency Training & Certification Program in Electric Power Distribution System Engineering
U. P. National Engineering CenterNational Electrification Administration
Training Course in Power System Reliability Analysis
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