Competency Training and Certification Program in Electric Power Distribution System Engineering
Certificate in
Power System Modeling and Analysis Training Course in
Power System Reliability Analysis
U. P. NATIONAL ENGINEERING CENTER NATIONAL 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
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Training Course in Power System Reliability Analysis
Reliability Models and Methods
Reliability Definition
Probability Function
The Reliability Function
Availability
System Reliability Networks
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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.
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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
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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 U. P. National Engineering Center National Electrification Administration
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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 U. P. National Engineering Center National Electrification Administration
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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
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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
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m(C) = 2
m(I) = 10
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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, m(Q) = m(Z) = 0
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(F) = m(A+M) = 3 + 5 = 8
m(A+B) = m(A) + m(B) U. P. National Engineering Center National Electrification Administration
if AB = Z
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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 who are both engineers and supervisors (the Set ES). E
ES
S
A
M
C
The size of the Set of all professional employees (engineers and supervisors) is 13 m(E+S) ≠m(E) + m(S) 13 U. P. National Engineering Center National Electrification Administration
≠10
+
5
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Probability Function SET THEORY CONCEPTS Note the Set ES is counted twice. Hence,
m(E+S) = m(E) + m(S) – m(ES) =
10
=
13
+
5
-
2
m(A+B) = m(A) + m(B) – m(AB)
if AB ≠ Z
“NOT MUTUALLY EXCLUSIVE” U. P. National Engineering Center National Electrification Administration
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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 P(A) =
Example:
m(A) M(I)
The probability of the employee of NEC SET Company being both Engineers and supervisor P(ES) =
m(ES) M(I)
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=
2 23
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Probability Function
Random Variable A 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 U. P. National Engineering Center National Electrification Administration
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Probability Function
Random Variable
Results of Tossing two dice
Sample Point
Value of R.V.
Sample Point
Value of R.V.
Sample Point
Value of R.V.
1,1
2
3,1
4
5,1
6
1,2
3
3,2
5
5,2
7
1,3
4
3,3
6
5,3
8
1,4
5
3,4
7
5,4
9
1,5
6
3,5
8
5,5
10
1,6
7
3,6
9
5,6
11
2,1
3
4,1
5
6,1
7
2,2
4
4,2
6
6,2
8
2,3
5
4,3
7
6,3
9
2,4
6
4,4
8
6,4
10
2,5
7
4,5
9
6,5
11
2,6
8
4,6
10
6,6
12
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Probability Function Probability Distribution
Value of R.V.
Occur. m(xi)
Probablity p(xi)
2
1
1/36
3
2
2/36
4
3
3/36
5
4
4/36
6
5
5/36
7
6
6/36
8
5
5/36
9
4
4/36
10
3
3/36
11
2
2/36
12
1
1/36
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0.2 Probability
0.15 0.1 0.05 0 2
3
4
5
6
7
8
9 10 11 12
Random Variable y = x1 + x2
⎧ xi − 1 ⎪ 36 ⎪ p (x i ) = ⎨ ⎪ 13 − x i ⎪ 36 ⎩
x i = 2 , 3, 4, 5, 6, 7 x i = 8, 9, 10, 11, 12
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Probability Function Cumulative Distribution Value of R.V.
Cum. Probablity F(xi)
<2
0
2
1/36
3
3/36
4
6/36
5
10/36
6
15/36
7
21/36
8
26/36
9
30/36
10
33/36
11
35/36
12
36/36 = 1.0
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1 Cum. Probability
0.8 0.6 0.4 0.2 0 2
3
4
5
6
7
8
9 10 11 12
Random Variable y = x1 + x2
F ( xi ) = â&#x2C6;&#x2018; p ( xi ) x â&#x2030;¤ xi
Competency Training & Certification Program in Electric Power Distribution System Engineering
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Probability Function
For Continuous Random Variable Probability Density Function
f (x )
x – random variable
Cumulative Probability Function
F (x ) =
∫
x
−∞
f ( x )d τ
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The Reliability Function
Random Variable
Results of Tossing two dice
Sample Point
Value of R.V.
Sample Point
Value of R.V.
Sample Point
Value of R.V.
1,1
2
3,1
4
5,1
6
1,2
3
3,2
5
5,2
7
1,3
4
3,3
6
5,3
8
1,4
5
3,4
7
5,4
9
1,5
6
3,5
8
5,5
10
1,6
7
3,6
9
5,6
11
2,1
3
4,1
5
6,1
7
2,2
4
4,2
6
6,2
8
2,3
5
4,3
7
6,3
9
2,4
6
4,4
8
6,4
10
2,5
7
4,5
9
6,5
11
2,6
8
4,6
10
6,6
12
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The Reliability Function Probability Distribution
Value of R.V.
Occur. m(xi)
Probablity p(xi)
2
1
1/36
3
2
2/36
4
3
3/36
5
4
4/36
6
5
5/36
7
6
6/36
8
5
5/36
9
4
4/36
10
3
3/36
11
2
2/36
12
1
1/36
U. P. National Engineering Center National Electrification Administration
0.2 Probability
0.15 0.1 0.05 0 2
3
4
5
6
7
8
9 10 11 12
Random Variable y = x1 + x2
⎧ xi − 1 ⎪ 36 ⎪ p (x i ) = ⎨ ⎪ 13 − x i ⎪ 36 ⎩
x i = 2 , 3, 4, 5, 6, 7 x i = 8, 9, 10, 11, 12
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The Reliability Function Cumulative Distribution Value of R.V.
Cum. Probablity F(xi)
<2
0
2
1/36
3
3/36
4
6/36
5
10/36
6
15/36
7
21/36
8
26/36
9
30/36
10
33/36
11
35/36
12
36/36 = 1.0
U. P. National Engineering Center National Electrification Administration
1 Cum. Probability
0.8 0.6 0.4 0.2 0 2
3
4
5
6
7
8
9 10 11 12
Random Variable y = x1 + x2
F ( xi ) = â&#x2C6;&#x2018; p ( xi ) x â&#x2030;¤ xi
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Probability Function
For Continuous Random Variable Failure Density Function
f (t )
t – random variable time-to-failure
Cumulative Probability Function
F (t ) = ∫ f (τ )dτ t
0
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The Reliability Function The probability that a component will fail by the time t can be defined by cumulative distribution function of failure
P(T ≤ t ) = F (t )
t ≥0
where t is a random variable denoting time-tofailure. Since success and failure are mutually exclusive, then the Reliability Function can be defined by
R(t ) = 1 − F (t ) U. P. National Engineering Center National Electrification Administration
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The Reliability Function If the time to failure random variable t has a density function f(t), then t
F (t ) = ∫ f (τ ) dt 0
R (t ) = 1 − ∫ f (τ )dτ t
0
or
f (t )
λ
f(t) F(t)
∞
R (t ) = ∫ f (τ )dτ t
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R(t) t
time
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The Reliability Function Example What is the probability that an equipment will not fail in one year if its failure density function is found to be exponential ( f t = λe − λt ) where λ = 0.01failure/yr
()
The reliability function is
R (t ) = 1 − ∫ λ e t
= 1+ e
= 1+ e
− λτ
0 − λτ t 0
dτ
|
− λt
−e
−0
R(t ) = e − λt = e − (0.01 f / yr )(1 yr ) = U. P. National Engineering Center National Electrification Administration
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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 − ∫0t h (τ )dτ
f (t ) = h(t )e
the Reliability Function in terms of Hazard Function t is h (τ )d τ ∫ 0 R (t ) = e −
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The Reliability Function Example What is the reliability of a component in one year if it has constant hazard function of λ = 0.01failure/yr The reliability function is t
− h (τ )d τ
∫ R (t ) = e 0 t − ∫ λ dτ − λt 0 =e =e = e − (0.01 f / yr )(1 yr ) = U. P. National Engineering Center National Electrification Administration
Note: the failure density function for a constant hazard is exponential − ∫0t h (τ )dτ
f (t ) = h(t )e
∫0 λdτ t
= λe = λ e − λt
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The Reliability Function Component Failure Data Item No.
Time-to-Failure (hrs.)
1
8
2
20
3
34
4
46
5
63
6
86
7
111
8
141
9
186
10
266
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How do you determine the Failure Density and Hazard Functions?
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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.
fd
n(ti ) − n(ti + Δti )] N [ (t ) =
Δti
for
ti < t ≤ ti + Δti
where n(t) is the number of survivor at any time t. U. P. National Engineering Center National Electrification Administration
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The Reliability Function Failure Density Function
Time
Δti
f(t)
0–8
8
8 – 20
12
f(t)
20 – 34
14
34 – 46
12
46 – 63
17
63 – 86
23
86 – 111
25
111 – 141
30
141 – 186
45
186 – 266
80
1 10 = 0.0125 8 1 10 = 0.0084 12 1 10 = 0.0074 14 1 10 = 0.0084 12 1 10 = 0.0059 17 1 10 = 0.0043 23 1 10 = 0.0040 25 1 10 = 0.0033 30 1 10 = 0.0022 45 1 10 = 0.0013 80
measure of the overall speed at which failures are occurring.
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f(t) fractional failures/hr.x10-2
The Reliability Function 1.4 1.2 1.0 0.8
0.6 0.4 0.2
0
0
100 200 Operating time, hr.
300
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The Reliability Function 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.
hd
[ n(ti ) − n(ti + Δti )] n(ti ) (t ) = Δti
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for
ti < t ≤ ti + Δti
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The Reliability Function Failure Hazard Function
h(t) measure of the instantaneous speed of failure
Time
Δti
0–8
8
8 – 20
12
20 – 34
14
34 – 46
12
46 – 63
17
63 – 86
23
86 – 111
25
111 – 141
30
141 – 186
45
186 – 266
80
U. P. National Engineering Center National Electrification Administration
h(t) 1 10 = 0.0125 8 19 = 0.093 12 18 = 0.0096 14 17 = 0.0119 12 16 = 0.0098 17 15 = 0.0087 23 14= 0.0100 25 13 = 0.0111 30 12 = 0.0111 45 11 = 0.0125 80
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The Reliability Function h(t) failures/hr.x10-2
1.4 1.2
1.0 0.8
0.6 0.4 0.2 0
0
100
200
300
Operating time, hr.
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The Reliability Function Constant Hazard Model
h(t ) = λ
∫ h(τ )dτ = ∫ λdτ = λt t
t
0
0
h(t )
λ t
f (t ) = λe − λt
F (t ) = 1 − e − λt R(t ) = e − λt U. P. National Engineering Center National Electrification Administration
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h(t )
36
The Reliability f Function (t ) λ
λ
λ e t
t
t =1 λ b. Exponential failure density function
a. Constant Hazard F (t )
R(t )
1 1−1 e
1
t =1 λ
t
c. Rising exponential distribution function U. P. National Engineering Center National Electrification Administration
1e t =1 λ
t
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The Reliability Function Linearly Increasing Hazard Model
h(t ) = Kt
t ≥0
1 2 ∫0 h(τ )dτ = ∫0 Kτ dτ = 2 Kt t
f (t ) = Kte R(t ) = e
t
1 − Kt 2 2
1 − Kt 2 2
h(t )
Kt t
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The Reliability Function h(t )
f (t )
slope K
K K e
Kt t
t
1K
a. Linearly increasing hazard
F (t ) 1
b. Rayleigh density function R (t ) 1
Initial slope = 0
e1 2
1 â&#x2C6;&#x2019; e1 2 1 K
t
c. Rayleigh distribution function U. P. National Engineering Center National Electrification Administration
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t
d. Rayleigh reliability function Competency Training & Certification Program in Electric Power Distribution System Engineering
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The Reliability Function Linearly Decreasing Hazard h (t )
K0
h(t ) =
K0 K1
∫ h(τ )dτ = t
0
∫
K 0 K1
∫
K 0 K1
0
0
0 < t ≤ K0 K1
0 K (t − t0 )
K0 K1 < t ≤ t0 t0 < t ≤ +∞
t
t0
∫0 (K 0 − K 1τ )dτ t
K 0 − K 1t
= K0t −
1 K 1t 2 2
1 K 02 (K 0 − K 1τ )dτ + ∫K 0 dK τ = 0 1 2 K1 t
(K 0 − K 1τ )dτ + ∫K 0 dK τ + ∫t K (τ − t0 )dτ
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t
t
0
1
0
=
1 2 K (t − t0 ) 2
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The Reliability Function Linearly Decreasing Hazard
(K0 − K1t )e f (t ) =
0 < t ≤ K0 K1
0 K (t − t0 )e
e
R(t ) =
1 ⎛ ⎞ −⎜ K 0 t − K 1t 2 ⎟ 2 ⎝ ⎠
1 K 02 − 2 K1
e
2 1 − K (t − t 0 ) 2
1 ⎛ ⎞ − ⎜ K 0 t − K 1t 2 ⎟ 2 ⎝ ⎠
0 −
e
K 02
1 2 K1
e
2 1 − K ( t − t0 ) 2
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K 0 K 1 < t ≤ t0 t0 < t ≤ +∞
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The Reliability Function Weibull Hazard Model
h(t ) = Kt m
m > −1
1 m +1 h ( τ ) d τ Kt d τ Kt = = ∫0 ∫0 m+1 t
t
m
1 − Kt m+1 m m +1
f (t ) = Kt e R(t ) = e
−
1 Kt m+1 m +1
h (t ) K
m=1
2 1
t→ U. P. National Engineering Center National Electrification Administration
m=3 m=2
5 4 3
m = 0 .5 m=0 m = −0 .5
1
2
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The Reliability Function Weibull Hazard Model h (t ) K
f (t ) [(m + 1)] K K
m=3 m=2
5 4 3
m=1
2 1
t→
m = 0 .5 m=0 m = − 0 .5
1
2
a. Hazard function
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m (m + 1 )
5 4 3
m = − 0 .5
2 1
τ →
1
m=0
m = 0 .5 m=1 m=2 m=3
2
b. Density function
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The Reliability Function Weibull Hazard Model F (t )
m=3
5 4 3
m=2 m=1 m = 0 .5 m=0 m = − 0 .5
2 1
R (t )
5 4 3 2 1
τ →
1
2
⎡⎛ K ⎞ 1 ( m + 1 ) ⎤ τ = ⎢⎜ ⎟ ⎥t m 1 + ⎠ ⎝ ⎣⎢ ⎦⎥
c. Distribution function U. P. National Engineering Center National Electrification Administration
τ →
m = − 0 .5 m=0 m = 0 .5
m=1 m=2 m=3
1
2
⎡⎛ K ⎞ 1 ( m + 1 ) ⎤ τ = ⎢⎜ ⎟ ⎥t m 1 + ⎠ ⎢⎣⎝ ⎥⎦
d. Reliability function Competency Training & Certification Program in Electric Power Distribution System Engineering
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The Reliability Function The Bathtub Curve
a. Hazard Function
b. Failure Density Function U. P. National Engineering Center National Electrification Administration
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The Reliability Function Hazard Model for Different System
a. Mechanical
b. Electrical
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The Reliability Function Mean-Time-To-Failure
MTTF = Expected value of t = E (t ) = ∫ tf (t )dt t
0
dF (t ) d [1 − R (t )] dR (t ) = =− but f (t ) = dt dt dt
MTTF = − ∫
∞
0
∞ t tdR(t ) dt = − ∫ tdR(t ) = ∫ R(t )dt 0 0 dt
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1 n MTTF = ∑ t i n i =1
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The Reliability Function RELIABILITY ASSESSMENT of MERALCO Distribution Transformers* Distribution Transformer Failures • 1997: 996 DT Failures • Average of three (3) DT Failures/day • Lost Revenue during Downtime • Additional Equipment Replacement Cost • Lost of Customer Confidence Identify the Failure Mode of DTs Develop strategies to reduce DT failures * R. R. del Mundo, et. al. (1999) U. P. National Engineering Center National Electrification Administration
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The Reliability Function METHODOLOGY: Reliability Engineering (Weibull Analysis of Failure Data) • Gather Equipment History (Failure Data) • Classify DTs (Brand, Condition, KVA, Voltage) • Develop Reliability Model • Determine Failure Mode • Recommend Solutions to Improve Reliability
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Training Course in Power System Reliability Analysis
49
The Reliability Function Parametric Model â&#x20AC;˘ Shape Factor â&#x20AC;˘ Characteristic Life Shape Factor <1 =1 >1
Hazard Function Decreasing Constant Increasing
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Failure Mode Failure Mode Early Random Wear-out
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The Reliability Function MERALCO DTs (1989â&#x20AC;&#x201C;1997) Brand
New
Recond
Rewind
Convert
Total
A
29,960
835
1,333
2,048
34,712
B
5,986
118
135
269
6,586
C
6,358
49
31
21
6,561
D
2,037
116
90
E
-
-
F
-
G H TOTAL
-
2,344
-
-
192
-
-
-
168
-
-
-
-
79
-
-
-
-
69
1,118
1,588
2,338
44,341
51,129
Note: Total Include Acquired DTs U. P. National Engineering Center National Electrification Administration
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The Reliability Function Reliability Analysis: All DTs Interval 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
Failures 1444 797 638 508 475 363 295 224 159 89 98 51 19 2 0
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Survivors 57095 48852 39997 32802 27515 22129 18200 14690 11865 9010 6473 4479 2254 821 127
Hazard 0.0269 0.0178 0.0174 0.0167 0.0189 0.0178 0.0178 0.0167 0.0151 0.0114 0.0177 0.015 0.0122 0.0042 0
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The Reliability Function Reliability Analysis: All DTs 0.03
Hazard
0.025
Weibull Shape = 0.84
0.02 0.015 0.01
Failure Mode: EARLY FAILURE 0.005
Is it Manufacturing Defect? 0 0
200
400
600
800
1000
1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
Time Interval U. P. National Engineering Center National Electrification Administration
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The Reliability Function Reliability Analysis: By Manufacturer BRAND A B C D E F G H
Size 34712 6586 6561 2344 192 168 79 69
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Shape 0.84 0.81 0.86 0.76 0.85 0.86 0.76 0.98
Failure Mode Early Failure Early Failure Early Failure Early Failure Early Failure Early Failure Early Failure Early Failure
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The Reliability Function Reliability Analysis: By Manufacturer & Condition BRAND A B C D
New 1.11 0.81 0.81 0.67
Reconditioned Rewinded 1.23 1.12 1.29 1.27 1.13 0.77 1.11 1.49
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Converted 1.4 1.23 0.94 -
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The Reliability Function Reliability Analysis: By Voltage Rating PRI 20 20 20 20 13.2 13.2 7.62 7.62 4.8 3.6 2.4
SEC 7.62 120/240 139/277 DUAL 120/240 240/480 120/240 DUAL 120/240 120/240 120/240
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All DTs 0.75 0.79 1.14 0.72 0.88 0.91 0.99 0.77 0.87 0.78 1.15
New DTs 0.94 1.1 1.03 1.54 1.46 1.61 1.17 -
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The Reliability Function Reliability Analysis: By KVA Rating (New DTs) KVA 10 15 25 37.5 50 75 100 167 250 333
Shape 1.3 1.25 0.92 0.83 0.73 1.05 1.04 1.16 1.11 1.46
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The Reliability Function 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 U. P. National Engineering Center National Electrification Administration
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The Reliability Function RELIABILITY ASSESSMENT of MERALCO Power Circuit Breakers* Number of Feeder Power Circuit Breakers VOLTAGE
OCB
VCB
GCB
34.5 KV 13.8 KV 6.24 KV 4.8 KV TOTAL
149 7
160 28 26 2 216
41 2
156
43
MOCB
ACB
36 3
12 122 11 145
39
* R. R. del Mundo (UP) & J. Melendrez (Meralco), 2001 U. P. National Engineering Center National Electrification Administration
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The Reliability Function RELIABILITY ASSESSMENT of MERALCO Power Circuit Breakers Annual Failures of 34.5 kV OCBs Causes of Failure
1997
1998
1999
2000
Installed
Failed
Installed
Failed
Installed
Failed
Installed
Failed
Average Failures (Units/yr)
Contact Wear
158
2
155
2
149
1
145
2
1.15
Bushing Failure
158
1
155
3
149
3
145
1
1.317
Mechanis m Failure
-
-
155
1
-
-
-
-
0.645
3 Circuit Breakers failing per year! Preventive Maintenance Policy: Time-based (Periodic) U. P. National Engineering Center National Electrification Administration
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Reliability Assessment of MERALCO Power Circuit Breakers HAZARD FUNCTION CURVE FOR 34.5 KV OCBs
0.4
0.2 0.1
H a z a rd R a t e
H a za rd R a te
0.3
0.15 0.1 0.05 0
0
6
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Time Interval (months)
6
9 12 15 18 24 30 36 42 48 54 60 Time Interval (months)
6.24 kV MOCBs
0
54 60
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 Time Interval (months)
13.8 kV MOCBs
0.2 0.15 0.1 0.05 0
HAZARD FUNCTION CURVE FOR ALL PCBs CONSIDERED
H a z a rd R a t e
H a z a r d R a te
3
36 42 48
0.1
HAZARD FUNCTION CURVE FOR 6.24 KV ACBs
0.4
0.1 0
18 24 30
0.2
34.5 kV GCBs
HAZARD FUNCTION CURVE FOR 6.24 KV MOCBs
0.3 0.2
12
0.3
Time Interval (months)
34.5 kV OCBS OCBs
H a z a rd R a t e
HAZARD FUNCTION CURVE FOR 13.8 KV MOCBs
0.2
0.4 H a z a r d R a te
HAZARD FUNCTION CURVE FOR 34.5 KV GCBs
6
12 18 24 30 36 42 48 54 60
0.4 0.3 0.2 0.1 0
.
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 Time Interval (m onths)
Time Interval (months)
6.24 kV ACBs
All PCBs
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Reliability Assessment of MERALCO Power Circuit Breakers 0.05
H a z a r d R a te
H a z a r d R a te
H a z a rd R a t e
0.05
0.25 0.2 0.15 0.1 0.05 0
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0
5
10
15
20
25
30
0 25
35
50
34.5 kV OCBS OCBs
0.1 0
Tripping Interval
6.24 kV MOCBs
150
25
50
20
0.1 0 10
15
6.24 kV ACBs
125
150
HAZARD FUNCTION CURVE FOR 34.5 KV OCBs
0.2
Tripping Interval
100
13.8 kV MOCBs
0.3
5
75
Tripping Interval
H a z a rd R a t e
H a z a r d R a te
0.2
15
125
HAZARD FUNCTION CURVE FOR 6.24 KV MOCBs
0.3
10
100
34.5 kV GCBs
HAZARD FUNCTION CURVE FOR 6.24 KV MOCBs
5
75
Tripping Interval
Tripping Interval
H a z a rd R a te
HAZARD FUNCTION CURVE FOR 34.5 KV GCBs
HAZARD FUNCTION CURVE FOR 34.5 KV GCBs
HAZARD FUNCTION CURVE FOR 34.5 KV OCBs
20
0.25 0.2 0.15 0.1 0.05 0 5
10
15
20
25
30
35
Tripping Interval
All PCBs
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The Reliability Function RELIABILITY ASSESSMENT of MERALCO Power Circuit Breakers
Schedule of Servicing for 41XV4
Hazard Rate
0.08 0.06 0.04 0.02 0 0
10
20
30
40
50
60
70
Number of Tripping Operations
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System Reliability Networks Series Reliability Model R(x1)
R(x2)
R(x3)
R(x4)
Series System 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. n
Rs = â&#x2C6;? R( xi ) i =1
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System Reliability Networks 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 位1 = 0.01 failure/year and 位2 = 0.02 failure/year. Calculate the reliability and the mean-time-to-failure for 1 year period.
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System Reliability Networks Parallel Reliability Model R(x1) R(x2) R(x3) R(x4)
This structure represents a system that will fail if and only if all the units in the system fail. n
Rs = 1 − ∏ [1 − R( xi )] i =1
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System Reliability Networks 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 位 = 0.0005 failure/hour, t = 400 hours (operating time) and (b) the mean-time-to-failure (MTTF).
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System Reliability Networks Standby Redundancy Model R(x1) R(x2) R(x3) R(x4) 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. U. P. National Engineering Center National Electrification Administration
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Training Course in Power System Reliability Analysis
System Reliability Networks 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 n
(λt ) i e −λt
i =1
i!
R(t ) = 1 − ∑
The above equation is true if the following are true: 1. 2. 3. 4. 5.
The The The The The
switch arrangement is perfect. units are identical. units failure rate are constant. standby units are as good as new. unit failures are statistically independent.
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System Reliability Networks 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
f (t ) =
t yn
y2
∫ ∫ ... ∫ f ( y ) f ( y 1
y n y n−1
1
2
2
− y1 )... f n +1 (t − yn )dy1dy2 ...dyn
y1 = 0
Consequently, the system reliability can be obtained by integrating fs(t) over the interval [t,∞] as follows: ∞
R(t ) = ∫ f ( t )dt t
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System Reliability Networks K-Out-of-N Reliability Model R(x1) R(x2) R(x3)
The system reliability for k-out-of-n number of independent and identical units is given by
⎛ n⎞ i Rs = ∑ ⎜⎜ ⎟⎟ R ( 1 − R )n −i i=k ⎝ i ⎠ n
This is another form of redundancy. It is used where a specified number of units must be good for the system success. U. P. National Engineering Center National Electrification Administration
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System Reliability Networks
71 1 2 3 5
4 6
7
Primary side
8
9
10 11 12 13 14 15 17
16 18
Reliability Network Models for Typical Substation Configurations of MERALCO*
19 21
20 22
23 25
24 26
27 28 29 30
31
32
33
34 35
Secondary side
36
37 38
Scheme 1: Single breaker-single bus (primary and secondary side)
39 40 41 42 43 44 45 46 47 48
49
50 51 52 53 54 55
* Source: A. Gonzales (Meralco) & R. del Mundo (UP), 2005 U. P. National Engineering Center National Electrification Administration
56 57
58
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System Reliability Networks Reliability Network Diagram of Single breaker-single bus scheme (Scheme 1) 15λ λc
29λ λct
2λ λbus
4λ λd1
2λ λb1
λp
2λ λb2
3λ λd2
Summary of Substation Reliability Indices for Scheme 1 Event 1
Probability
λs (failure/yr)
Us (hr/yr)
Opened 115kV bus tie breaker & opened 34.5kV bus tie breaker (normal condition)
1.0
0.247152 0.828784
Total
1.0
0.247152 0.828784
where: λs - substation failure rate or interruption frequency Us – substation annual outage time or unavailability U. P. National Engineering Center National Electrification Administration
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System Reliability Networks
L2
1
70 2
71
3
72 5
4
73 6
7
76 77
8
9
78
18
16
127 19
128
129
14 13
22 132
133
12
23 10
134
17
15
20 21
130 131
Reliability Network Models for Typical Substation Configurations of MERALCO
11
92
35 135
136
24
137
34
139
88 31
27
141
81 89
82
32
26 140
80
90 33
25
138
79 91
28
87 30
86
83 84 85 29
36
93
37
Primary side
94 38
Scheme 2: Single breaker-double bus (primary side) and two single breaker-single bus with bus tie breaker (secondary side)
74
75
95
39
96
40
97
41
98
Bank 1
42
99
100
43
101
44
102
45
103
46 104
47 49
48
105
106 107
50
109
52 110
53
111
54 57
112
126 56 125
61
119
124 121
58 59
Secondary side
108
51
55
Bank 2
122
60 123
120
115 117 116
113
114
118
62 63
64 65 66 67 68 69
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Substation Reliability Models Reliability Network Diagram of Single breaker-double bus with normally opened 115kV bus tie breaker (Scheme 2) 16λ λc
29λ λct
2λ λbus
3λ λd1
2λ λb1
Event 1: Opened 115kV and 34.5kV bus tie breakers;
20λ λc
37λ λct
3λ λbus
5λ λd1
2λ λb1
λp
2λ λb2
3λ λd2
2λ λb2
3λ λd2
P1 = 0.997985
λp
Event 2: Closed 115kV bus tie breaker & opened 34.5kV bus tie breaker; P2 = 0.000188
20λ λc
37λ λct
2λ λbus
3λ λd1
2λ λb1
λp
3λ λb2
5λ λd2
Event 3: Closed 115kV bus tie breaker & closed 34.5kV bus tie breaker; P3 = 0.000000344
20λ λc
37λ λct
2λ λbus
3λ λd1
2λ λb1
λp
3λ λb2
5λ λd2
Event 4: Opened 115kV bus tie breaker & closed 34.5kV bus tie breaker; P4 = 0.00182614 U. P. National Engineering Center National Electrification Administration
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Substation Reliability Models Summary of Substation Reliability Indices for Scheme 2 Event
Probability
位s (failure/yr)
Us (hr/yr)
1
0.997985
0.251752
0.848919
2
0.000188
0.302966
1.008374
3
0.000000344
0.308936
1.023840
4
0.001826
0.308936
1.023840
1.0
0.251866
0.849275
Total
Event 1: With two primary lines energized & opened 34.5kV bus tie breaker; P1 = 0.997985 Competency Training & Certification Program in U. P. National Engineering Center Electric Power Distribution System Engineering National Electrification Administration
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Substation Reliability Models Reliability Network Diagram of Single breaker-double bus with normally closed 115kV bus tie breaker (Modified Scheme 2)
λ17
λ54
λΒ3
λΒ4
λΒ1
λΒ1 Β3
λΒ2 Β3
λΒ1 Β3
λΒ1
λΒ2 Β3
λΒ2 Β3
λΒ6
λΒ7
λΒ7 Β4
λλΒ4 29
λΒ9
λΒ6
λΒ4 29
λΒ5
Event 1: With two primary lines energized & opened 34.5kV bus tie breaker; P1 = 0.997985 λ17
λB1
λB2
λB3
Event 2: With one line, L2 interrupted & opened 34.5kV bus tie breaker; λ17
λ29
λB1
λB2
λB5
λB5
λB4
λB8
λB9
P2 = 0.000188 λB10
λB11
Event 3: With one line, L2 interrupted and closed 34.5kV bus tie breaker; P3 = 0.000000344 U. P. National Engineering Center National Electrification Administration
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Substation Reliability Models Reliability Network Diagram of Single breaker-double bus with normally closed 115kV bus tie breaker (Modified Scheme 2)
λ29
λ111
λΒ5
λΒ8
λΒ10
λΒ1
λΒ1
λΒ3 Β2
λΒ3 Β6
λΒ3 Β2
λΒ6
λΒ3 Β7
λλΒ3 Β7
λΒ7 Β3
λΒ6
λΒ7
λΒ7
λλΒ4 17
λΒ4 Β6
λΒ9
λΒ9
λλΒ4 Β8
λλΒ4 17
λΒ11
Event 4: With two lines energized and closed 34.5kV bus tie breaker;
P4 = 0.001826140
Summary of Substation Reliability Indices for Modified Scheme 2
Event
Probability
λs (failure/yr)
Us,(hr/yr)
1
0.997985
0.176076
0.583548
2
0.000188
0.251122
0.847621
3
0.000000344
0.377120
1.261549
4
0.001826
0.233261
0.758472
1.0
0.176194
0.583923
Total
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Substation Reliability Models Comparison of Substation Reliability Indices for Scheme 2 Scheme 2 Original (opened 115kV bus tie breaker) Modified (closed 115kV bus tie breaker)
位s (failure/yr)
Us (hr/yr)
0.251866
0.849275
0.176194
0.583923
Note: A remarkable 30% improvement in the performance of Scheme 2 by making the 115kV bus tie breaker normally closed.
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System Reliability Networks
B1
67
1
B4
17 32
16
15
81 79
78
12 11
B2
82 80
14 13
77
10
76
B5
75
9 7
8
73
6
74 72
71
5
70 4
Reliability Network Models for Typical Substation Configurations of MERALCO
3
69
68
Primary side
2 3
69
18
84
19 20
85 21
86
87
22
B3
83
88
23 24
89 26
B6
90
25
91 92
27 93
28 29
94 95
30 31
96
33
97
B7
Scheme 3: Ring bus (primary side) and two single breaker-single bus with bus tie breaker (secondary side)
34
35
Bank 1
99
36
101
37
40
39
104 105 106 43
107
44 45 46 47
108 109 110 111
48
112 49
52 54
53
B10
113
50
114
130 128
123 125
129
57
58
Secondary side 115
116
55 56
100
103
41
42
Bank 2
102
38
51
B8
98
126 127 124
119 117
121 120
118
122
59 60 62
61 63
B9
64 65 66
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Substation Reliability Models Reliability Block Diagram of Ring Bus Scheme (Scheme 3) λB1
λB4
λB1
λB2 λB5
λ17
λB2
λB4
λ51
λB7
λB10
λB5 λB6
λB3
Event 1: With two primary lines energized & opened 34.5kV bus tie breaker;
λB1
P1 = 0.997985
λB4
λB1
λB3
λB5
λ31
λB2
λB4
λB8
λB9
λ51
λB10
λB6 λB6
λB3
Event 2: With two primary lines energized & closed 34.5kV bus tie breaker; P2 = 0.00182614 U. P. National Engineering Center National Electrification Administration
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Substation Reliability Models Reliability Block Diagram of Ring Bus Scheme (Scheme 3)
CONT. λB2
λB2
λB2
λB2
λ17
λB1
λB3
λ31
λB7
λ51
λB5
λB6
Event 3: With one primary line (L2) interrupted and opened 34.5kV bus tie breaker; λB2
λB3
λB3
λ31
λ17
λB5
P3 = 0.000188056
λB3
λB1
λB3
λB10
λB8
λB9
λ51
λB10
λB6
Event 4: With one primary line (L2) interrupted and closed 34.5kV bus tie breaker; P4 = 0.000000344 U. P. National Engineering Center National Electrification Administration
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Substation Reliability Models Summary of Substation Reliability Indices of Ring Bus (Scheme 3) Event
位s (failure/yr)
Probability
Us (hr/yr)
1
0.997985
0.137928
0.436499
2
0.001826
0.195112
0.618379
3
0.000188
0.147283
0.468233
4
0.000000344
0.204467
0.650114
1.0
0.138034
0.436836
Total
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System Reliability Networks
L 2 1
1 5 1 3 1 1 9
B2
9 9 3 1 8 89 7 8 5 8
B1
1 21 0
B5
8
7
7 8
1 7
1 61 4
6
3
5 4
3
8 1 2
7 9
Reliability Network Models for Typical Substation Configurations of MERALCO
2 2 0 2 2 4 2
B3
9 4
1 9 2 1
62 2 7 8 2 9 3 0
2 5
10 0 10 2 10 4
2 9
4 2
10 6 10 118 0
B9
Scheme 4: Breaker-and-a-half bus (primary side) and two single breaker-single bus with bus tie breaker (secondary side)
Bank 1
5 5 1 3
6 3 6 5
6 4 6 6 6 6 6 7 8 9 7 0 7 1 7 7 2 3 7 4 7 5 7 7 6 7
U. P. National Engineering Center National Electrification Administration
12 1
4 5
12 2
5 5 5 5 6 75 8 5 9 6 6 0 1 15 4
12 5 12 13 8 0
5 4
13 2 13 4
10 1 10 3
9 9
14 14 14 158 6 14 2 4 0 14 14 15 14 14 5 1 9 3 7
Primary side
10 5 10 7 10 9
B8
Bank 2
12 4 12 6 12 7 12 9 13 1 13 3 13 5
13 6 13 13 7 8 14 0 15 2
15 3
9 5 9 7
B10 12 3
4 6 4 8
6 2
4 4
4 7 4 9 5 0 5 2
8 0
11 1 11 11 2 11 3 11 4 5 11 6 11 11 7 8
11 9
1
8 2
10 5
12 0
4 3
3 3 1 3 3 2 3 4 3 5 3 6 3 3 7 83 4 9 0 4
B4
9 96 8
B7
2 3
B6
8 6
8 4
8 0
3 1 8
9 2 9 0 8 8
Secondary side 13 9
14 1
B1 1
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Substation Reliability Models Reliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
λΒ1 λΒ9
λ62
λΒ3
λΒ3
λΒ4
λΒ7
λΒ2 Β3
λλΒ1 6
λλΒ1 6
λΒ6 Β2
λΒ3 33
λλΒ7 7
λΒ8
λΒ7 33
λΒ5 34
λ17
λΒ2 17
λΒ3
λΒ12 λΒ5
A
λΒ3
λΒ1 Β3
λλ119 Β4
λΒ8 Β4
λΒ1 Β3
λΒ1 Β3
λΒ1 Β3
λΒ1 Β3
λλΒ1 6
λλΒ1 6
λΒ3
λΒ3
λλΒ3 6
λλΒ3 6
λλΒ2 17
λλΒ4 33
λΒ2
λλΒ2 33
λλΒ2 7
λΒ2
λΒ5 Β2
λΒ5 33
λλΒ5 7
λΒ5
λλ119 33
λ17 34
λΒ7 33
λλΒ8 34
λ119
λΒ4 Β2
λ17 33
λΒ6 34
λΒ8
λλ119 Β2
Event 1: With two primary lines energized and opened 34.5kV bus tie breaker; U. P. National Engineering Center National Electrification Administration
A
P1 = 0.997985
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Substation Reliability Models Reliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
λΒ7
λΒ1 λΒ10
λ139
λΒ11
λ62
λΒ8
λλ119 Β4
λΒ7
λΒ2 Β3
λλΒ1 6
λλΒ5 6
λΒ6 Β2
λΒ3 33
λλΒ2 7
λΒ8
λλΒ7 33
λΒ5 34
λΒ7
λλΒ2 17
λΒ4 Β3
λΒ12 λΒ5
A
λΒ7 Β3
λΒ3
λΒ1 Β3
A
λΒ7 Β4
λΒ5 Β3
λΒ3
λΒ3
λΒ2 Β3
λλΒ2 6
λλΒ2 6
λΒ5 Β3
λΒ4 Β3
λλΒ4 6
λλ119 6
λλ119 6
λΒ2 17
λΒ5 33
λΒ5 Β2
λΒ5 33
λλΒ5 7
λΒ4
λΒ6 Β2
λΒ5 33
λλΒ5 7
λΒ5
λΒ5
λλ119 33
λ17 34
λΒ6 33
λΒ8 34
λ119
λΒ5 Β2
λΒ8 33
λΒ6 34
λ17
λΒ7 Β2
λΒ6 Β2
Event 2: With two primary lines energized and closed 34.5kV bus tie breaker; P2 = 0.001826 U. P. National Engineering Center National Electrification Administration
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Substation Reliability Models Reliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4) λΒ3
λΒ9
λ62
λΒ12
λΒ6 Β3
λΒ6 Β3
λΒ6 Β3
λΒ6 Β3
λΒ7 Β3
λΒ5
A
λΒ4
λΒ7
λΒ8 Β4
λλ119 Β4
λΒ4
λΒ4 17
λΒ7
λΒ7 Β3
λΒ8 Β3
λΒ8 Β3
λΒ8
λΒ3 17
λΒ3 17
λΒ2 Β3
λλ119 Β3
λλ119 Β3
λΒ2
λΒ3
λΒ4 17
λΒ2 Β4
λΒ3
λ119
λΒ4
λΒ4
λΒ2 Β4
λΒ3 Β4
A
Event 3: With one primary line (L1) interrupted and opened 34.5kV bus tie breaker;
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P3 = 0.000188
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Substation Reliability Models Reliability Block Diagram of Breaker-and-a-half Scheme (Scheme 4)
λΒ10
λ139
λΒ11
λ62
λΒ12
λΒ7
λΒ6 Β3
λΒ7 Β3
λΒ7 Β3
λΒ7
λΒ4 Β3
λλ119 Β3
λΒ8
λΒ7
λλΒ4 17
λΒ2 Β4
λΒ3
λΒ7
λΒ7 Β4
λΒ5
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) Event
Probability
λs (failure/yr)
Us (hr/yr)
1
0.997985
0.137306
0.435214
2
0.001826
0.195120
0.611433
3
0.000188
0.146674
0.466972
4
0.000000344
0.204473
0.643165
1.0
0.137413
0.435545
Total
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System Reliability Networks Substation Reliability Models Comparison of Substation Reliability Indices (Scheme 1 to 4) 位s (failures/yr)
Us (hrs/yr)
Scheme 1 (Single breaker-single bus)
0.247152
0.828784
Scheme 2 (Single breaker-double bus) - with normally opened 115kV tie bkr. - with normally closed 115kV tie bkr.
0.251866 0.176194
0.849275 0.583923
Scheme 3 (Ring bus)
0.138034
0.436836
Scheme 4 (Breaker-and-a-half bus)
0.137413
0.435545
Configuration
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
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Distribution System Reliability Evaluation
Distribution System Reliability Indices
Historical Reliability Performance Assessment
Predictive Reliability Performance Assessment
Substation 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. classified as momentary
U. P. National Engineering Center National Electrification Administration
An
interruption
not
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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
SAIFI =
T otal number of customer - interrupti ons Total number of customers served
System Average Interruption Duration Index (SAIDI) The average interruption duration per customer served during a period
SAIDI =
Sum of customer interruption duration Total number of customers served
Note: SAIFI for Sustained interruptions. MAIFI for Momentary Interruptions U. P. National Engineering Center National Electrification Administration
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Training Course in Power System Reliability Analysis
Distribution System Reliability Indices CUSTOMER-ORIENTED RELIABILITY INDICES Customer Average Interruption Frequency Index (CAIFI) The average number of interruptions per customer interrupted during the period
Total number of customer interruptions CAIFI = Total number of customers interrupted Customer Average Interruption Duration Index (CAIDI) The average interruption duration of customers interrupted during the period
Sum of customer interruption duration CAIDI = Total number of customers interrupted U. P. National Engineering Center National Electrification Administration
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Training Course in Power System Reliability Analysis
Distribution System Reliability Indices 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 Customer hours of available service
ASAI =
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 C ustomer hours of unavailabl e service ASUI = Customer hours demanded U. P. National Engineering Center National Electrification Administration
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Training Course in Power System Reliability Analysis
Distribution System Reliability Indices 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.
Total load interruption ALII = Total connected load 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.
ASCI =
Total energy curtailment Total number of customers served
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Training Course in Power System Reliability Analysis
Distribution System Reliability Indices LOAD- AND ENERGY-ORIENTED RELIABILITY INDICES Average Customer Curtailment Index (ACCI) The KWh of connected load interruption per affected customer per year.
ACCI =
Total energy curtailment Total number of customers affected
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Historical and Predictive Assessment ORGANIZATION, CUSTOMER, kVA
COMPONENT POPULATION
SYSTEM DEFINITION
INCIDENTS HISTORICAL ASSESSMENT
COMPONENT PERFORMANCE PREDICTIVE ASSESSMENT
HISTORICAL SYSTEM PERFORMANCE MANAGEMENT OPERATIONS ENGINEERING CUSTOMER INQUIRIES
PREDICTED SYSTEM PERFORMANCE COMPARATIVE EVALUATIONS AID TO DECISION-MAKING PLANNING STUDIES
Conceptual Design of an Integrated Reliability Assessment Program U. P. National Engineering Center National Electrification Administration
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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
d1 Number of customers interrupted
d3 d2
N1 N2
N3
Time U. P. National Engineering Center National Electrification Administration
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Historical Reliability Performance Assessment 2
1
S
C
B
A
Source
L2
L1
3
L3
SYSTEM LOAD DATA Load Point L1 L2 L3
Number of Average Load Customers Demand (KW) 200 1000 150 700 100 400 INTERRUTION DATA
Number of Interruption Load Point Average Load Duration of Disconnected Event i Affected Curtailed (KW) Interruption Customers 1 L3 100 400 6 hours U. P. National Engineering Center National Electrification Administration
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Historical Reliability Performance Assessment N ∑ SAIFI = ∑N
C
100 = 200 + 150 + 100
= 0.222222 interruption customer - yr
N d 100 )(6 ) ( ∑ SAIDI = = ∑ N 200 + 150 + 100 C
= 1.333333 hours customer - yr
N d (100 )(6 ) ∑ CAIDI = = 100 ∑N C
C
= 6 hours custumer - interruption
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Historical Reliability Performance Assessment N d ∑ N SAIDI 1.333333 ∑ ASUI = = = C
8760 = 0.000152
8760
8760
ASAI = 1 − ASUI = 1 − 0.000152 = 0.999848
ENS = ASCI = ∑N
∑ L d = (400 )(6 ) ∑ N 200 + 150 + 100 a
= 5.333333 KWh customer − yr
Note: ENS - Energy Not Supplied U. P. National Engineering Center National Electrification Administration
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Historical Reliability Performance Assessment Outage & Interruption Reporting
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Historical Reliability Performance Assessment Outage & Interruption Reporting *Not included in Distribution Reliability Performance Assessment
Date 1 2* 3 4* 5 6* 7 8 9 10* 11 12* 13 14* 15 16 17* 18* 19* 20
01/08/04 02/06/04 02/14/04 03/15/04 04/01/04 05/20/04 05/30/04 06/12/04 07/04/04 07/25/04 07/30/04 08/15/04 09/08/04 09/30/04 10/25/04 11/10/04 11/27/04 12/14/04 12/27/04 12/28/04
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Affected hours 3 All 5, 6 4, 5, 6 3, 4 1, 2, 1 5 All 5 4 2 1, 2, 3 2, 3 3 3, 4, 2, 3 1, 2,
6
3
3
5 3
1.5 4 0.5 3 1.5 3.5 0.5 2 1 5 1 2 1 2.5 1.5 1.5 2 3.5 3 0.075
Line Fault at C Transmission Line Fault at D Pre-arranged Overload Pre-arranged Line Tripped Line fault Line Overload Transmission Line Fault Pre-arranged Line Fault Pre-arranged Line Tripped Line Fault at A Pre-arranged Pre-arranged Pre-arranged Line Fault
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Historical Reliability Performance Assessment Outage & Interruption Reporting Customer Count Month January February March April May June July August September October November December Annual Average
1 900 905 904 908 912 914 917 915 924 928 930 934 916
2 800 796 801 806 804 810 815 815 821 824 826 829 812
3 600 600 604 606 608 611 614 620 622 626 630 635 615
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4 850 855 854 859 862 864 866 872 876 881 886 894 868
5 500 497 496 501 509 507 512 519 521 526 530 538 513
6 300 303 308 310 315 318 324 325 328 331 334 332 319
Total 3,950 3,956 3,967 3,990 4,010 4,024 4,048 4,066 4,092 4,116 4,136 4,162 4,043
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Historical Reliability Performance Assessment Outage & Interruption Reporting Interruption Number
Load Points Affected
1 3
3 5 6 6 1 2 3 1 5 5 2 3 2 3
5 7
8 9 11 13 15 16
Number of Duration Customer Frequency Duration Customers (Hrs.) Hours (Inter/Cust.) (Hrs/Cust.) Affected Curtailed 600 497 303 310 912 804 608 914 512 512 821 626 826 630
1.5 0.5 0.5 1.5 0.5 0.5 0.5 2 1 1 1 1.5 1.5 1.5
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900 248.5 151.5 465 456 402 304 1,828.00 512 512 821 939 1,239.00 945
0.1519 0.1256 0.0766 0.0777 0.2274 0.2005 0.1516 0.2271 0.1265 0.1265 0.2006 0.1521 0.1997 0.1523
Date
0.2278 01/08/04 0.0628 02/14/04 0.0383 0.1165 04/01/04 0.1137 05/30/04 0.1002 0.0758 0.4543 06/12/04 0.1265 07/04/04 0.1265 07/30/04 0.2006 09/08/04 0.2281 10/25/04 0.2996 11/10/04 0.2285
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Historical Reliability Performance Assessment Outage & Interruption Reporting Calculate the Annual Reliability Performance of the Distribution System (according to Phil. Distribution Code)
N ∑ SAIFI = ∑N N d ∑ SAIDI = ∑N N ∑ MAIFI = ∑N C
C
C
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Predictive Reliability Performance Assessment A Source
Distribution System
B Loads
Source
C
位A, rA, UA
A
位B, rB, UB
B Loads
位C, rC, UC
C
Required Data: 1. Component Reliability Data 位i - failure rate of component i ri - mean repair time of component i 2. System Load Data Ni - number of customers at point i Li - the demand at point i U. P. National Engineering Center National Electrification Administration
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Predictive Reliability Performance Assessment Load Point Reliability Equivalents For series combinations:
For parallel combinations: 1
1
2
P
S n
λs = Σ λi i=1 n
Σ λiri
i=1
rs = _________ λs U. P. National Engineering Center National Electrification Administration
2
λp = λ1λ2 (r1 + r2) r1 r2
rp = __________ r1 + r2
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Predictive Reliability Performance Assessment S Source
2
1
3
B
A L1
C L3
L2
COMPONENT DATA Feeder A B C
Load Point L1 L2 L3
r 位 (f/year) (hours) 0.2 6 0.1 5 0.15 8 SYSTEM LOAD DATA Number of Customers 200 150 100
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Load Point Reliability Equivalents For L1 λ1 = λ A
= 0.2 f yr
For L2
λ2 = λ A + λB = 0.2 + 0.1 = 0.3 f yr
For L3
λ3 = λ A + λB + λC
= (0.2 )(6 )
= 6 hrs
r2 =
= 1.2 hrs yr
λ A rA + λB rB λ A + λB
U 2 = λ2 r2
(0.2 )(6 ) + (0.1)(5 ) = 0.2 + 0.1 = 5.666667 hrs
r3 =
= 0.2 + 0.1 + 0.15 = 0.45 f yr
U 1 = λ1r1
r1 = rA
=
λ A rA + λB rB + λC rC λ A + λB + λB
(0.2)(6) + (0.1)(5) + (0.15)(8)
0.2 + 0.1 + 0.15 = 6.444444 hrs
U. P. National Engineering Center National Electrification Administration
= (0.3)(5.666667 ) = 1.7 hrs yr
U 3 = λ3 r3
= (0.45 )(6.444444 ) = 2.9 hrs yr
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Reliability Indices
λ N (0.2 )(200 ) + (0.3)(150 ) + (0.45 )(100 ) ∑ = SAIFI = 200 + 150 + 100 ∑N i
i
i
= 0.288889 interruption customer − yr
U N (1.2 )(200 ) + (1.7 )(150 ) + (2.9 )(100 ) ∑ SAIDI = = 200 + 150 + 100 ∑N i
i
i
= 1.744444 hours customer - yr
UN ∑ CAIDI = ∑λ N i
i
i
i
SAIDI 1.744444 = = SAIFI 0.288889
= 6.038462 hours customer - interruption
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U N ∑N ∑ ASUI = i
i
i
8760 = 0.000199
111
SAIDI 1.744444 = = 8760 8760
ASAI = 1 − ASUI = 1 − 0.000199 = 0.999801
ENS ASCI = = ∑ Ni
∑ L ( )U ∑N a i
i
( 1000 )(1.2 ) + (700 )(1.7 ) + (400 )(2.9 ) = 200 + 150 + 100
i
= 7.888889 KWh customer - yr
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Predictive Reliability Performance Assessment
Source
2
1 a
3 b
4 c
d D
A C B Typical radial distribution system
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SYSTEM RELIABILITY DATA
Lateral
Main
Component Length (km) 位 (f/yr) r (hrs) 1 2 0.2 4 2 1 0.1 4 3 3 0.3 4 4 2 0.2 4 a b c d
1 3 2 1
0.2 0.6 0.4 0.2
2 2 2 2
SYSTEM LOAD DATA Component No. of Customers Ave. Load Connected (KW) A B C D
1000 800 700 500
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5000 4000 3000 2000
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RELIABILITY INDICES FOR THE SYSTEM Load pt. A
Load pt. B
Load pt. C
Load pt. D
Main
U U U U Component λ r λ r λ r λ r (hrs/ (hrs/ (hrs/ (hrs/ failure (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) yr) yr) yr) 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 0.3 0.2
4 4
1.2 0.8
0.3 0.2
4 4
1.2 0.8
0.3 0.2
4 4
1.2 0.8
0.3 0.2
4 4
1.2 0.8
a
0.2
2
0.4
0.2
2
0.4
0.2
2
0.4
0.2
2
0.4
b c
0.6 0.4
2 2
1.2 0.8
0.6 0.4
2 2
1.2 0.8
0.6 0.4
2 2
1.2 0.8
0.6 0.4
2 2
1.2 0.8
d Total
0.2 2.2
2 2.73
0.4 6.0
0.2 2.2
2 2.73
0.4 6.0
0.2 2.2
2 2.73
0.4 6.0
0.2 2.2
2 2.73
0.4 6.0
Lateral
3 4
where : λtotal = ∑ λ ; U total = ∑ U ; rtotal = ∑ U U. P. National Engineering Center National Electrification Administration
∑λ
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λ N (2.2 )(1000 ) + (2.2 )(800 ) + (2.2 )(700 ) + (2.2 )(500 ) ∑ SAIFI = = 1000 + 800 + 700 + 500 ∑N i
i
i
= 2.2 int customer − yr
U N (6.0 )(1000 ) + (6.0 )(800 ) + (6.0 )(700 ) + (6.0 )(500 ) ∑ = SAIDI = 1000 + 800 + 700 + 500 ∑N i
i
i
= 6.0 hours customer - yr
UN ∑ CAIDI = ∑λ N i
i
i
i
=
SAIDI 6.0 = SAIFI 2.2
= 2.727273 hours customer - interruption
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U N ∑N ∑ ASUI = i
i
8760 = 0.000685
i
=
116
SAIDI 6 .0 = 8760 8760
ASAI = 1 − ASUI = 1 − 0.000685 = 0.999315
L U ∑ ASCI = ∑N ai
i
i
5000 )(6.0 ) + (4000 )(6.0 ) + (3000 )(6.0 ) + (2000 )(6.0 ) ( =
1000 + 800 + 700 + 500 = 28.0 KWh customer - yr U. P. National Engineering Center National Electrification Administration
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Predictive Reliability Performance Assessment
Effect of lateral protection Source
2
1 a
3 b
4 c
d D
A C B
Typical radial distribution system with lateral protections
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RELIABILITY INDICES WITH LATERAL PROTECTION Load pt. A
Load pt. B
Load pt. C
Load pt. D
Main
U U U U Component λ r r r r λ λ λ (hrs/ (hrs/ (hrs/ (hrs/ failure (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) yr) yr) yr) 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 0.2
2
0.4
Lateral
a b c d Total
0.6
2
1.2 0.4
1.0
3.6
3.6
1.4
3.14
4.4
1.2
where : λtotal = ∑ λ ; U total = ∑ U ; rtotal = ∑ U U. P. National Engineering Center National Electrification Administration
2 3.33
0.8 4.0
0.2 1.0
2 3.6
0.4 3.6
∑λ
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λ N (1.0)(1000) + (1.4)(800) + (1.2)(700) + (1.0)(500) ∑ = SAIFI = 1000 + 800 + 700 + 500 ∑N i
i
i
= 1.153333 int customer− yr U N (3.6 )(1000 ) + (4.4 )(800 ) + (4.0 )(700 ) + (3.6 )(500 ) ∑ SAIDI = = 1000 + 800 + 700 + 500 ∑N i
i
i
= 3.906667 hours customer - yr
UN ∑ CAIDI = ∑λ N i
i
i
i
=
SAIDI 3.906667 = SAIFI 1.153333
= 3.387283 hours customer - interruption
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U N ∑N ∑ ASUI = i
i
8760 = 0.000446
i
=
120
SAIDI 3.906667 = 8760 8760
ASAI = 1 − ASUI = 1 − 0.000446 = 0.999554 L U ∑ ASCI = ∑N ai
i
i
5000 )(3.6 ) + (4000 )(4.4 ) + (3000 )(4.0 ) + (2000 )(3.6 ) ( =
1000 + 800 + 700 + 500 = 18.266667 KWh customer - yr U. P. National Engineering Center National Electrification Administration
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Predictive Reliability Performance Assessment
Effect of disconnects Source
2
1 a
3 b
4 c
d D
A C B Typical radial distribution system reinforce with lateral protections and disconnects U. P. National Engineering Center National Electrification Administration
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RELIABILITY INDICES WITH LATERAL PROTECTION AND DISCONNECTS Load pt. A
Load pt. B
Load pt. C
Load pt. D
Main
U U U U Component λ r r r r λ λ λ (hrs/ (hrs/ (hrs/ (hrs/ failure (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) yr) yr) yr) 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 0.2
2
0.4
Lateral
a b c d Total
0.6
2
1.2 0.4
1.0
1.5
1.5
1.4
1.89 2.65
1.2
where : λtotal = ∑ λ ; U total = ∑ U ; rtotal = ∑ U U. P. National Engineering Center National Electrification Administration
2 2.75
0.8 3.3
0.2 1.0
2 3.6
0.4 3.6
∑λ
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λ N (1.0 )(1000) + (1.4 )(800 ) + (1.2 )(700 ) + (1.0 )(500 ) ∑ SAIFI = = 1000 + 800 + 700 + 500 ∑N i
i
i
= 1.153333 int customer − yr
U N (1.5 )(1000 ) + (2.65 )(800 ) + (3.3)(700 ) + (3.6 )(500 ) ∑ SAIDI = = 1000 + 800 + 700 + 500 ∑N i
i
i
= 2.576667 hours customer - yr
UN ∑ CAIDI = ∑λ N i
i
i
i
=
SAIDI 2.576667 = SAIFI 1.153333
= 2.234105 hours customer - interruption
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U N ∑N ∑ ASUI = i
i
8760 = 0.000294
i
=
124
SAIDI 2.576667 = 8760 8760
ASAI = 1 − ASUI = 1 − 0.000294 = 0.999706 L U ∑ ASCI = ∑N ai
i
i
5000 )(1.5 ) + (4000 )(2.65 ) + (3000 )(3.3 ) + (2000 )(3.6 ) ( =
1000 + 800 + 700 + 500 = 11.733333 KWh customer - yr U. P. National Engineering Center National Electrification Administration
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Effect of protection failures RELIABILITY INDICES IF THE FUSES OPERATE WITH PROBABILITY OF 0.9 Load pt. A
Load pt. B
Load pt. C
Load pt. D
Main
U U U U Component λ r r r r λ λ λ (hrs/ (hrs/ (hrs/ (hrs/ failure (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) yr) yr) yr) 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 Lateral
a b c d Total
0.2 2 0.06 0.5 0.04 0.5 0.02 0.5 1.12 1.39
0.4 0.03 0.02 0.01 1.56
0.02 0.5 0.6 2 0.04 0.5 0.02 0.5 1.48 1.82
0.01 0.02 0.5 1.2 0.06 0.5 0.02 0.4 2 0.01 0.02 0.5 2.69 1.3 2.58
where : λtotal = ∑ λ ; U total = ∑ U ; rtotal = ∑ U U. P. National Engineering Center National Electrification Administration
0.01 0.03 0.8 0.01 3.35
0.02 0.5 0.06 0.5 0.04 0.5 0.2 2 1.12 3.27
0.01 0.03 0.02 0.4 3.66
∑λ
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Effect of load transfer to alternative supply RELIABILITY INDICES WITH UNRESTRICTED LOAD TRANSFERS Load pt. A
Load pt. B
Load pt. C
Load pt. D
Main
U U U U Component λ r r r r λ λ λ (hrs/ (hrs/ (hrs/ (hrs/ failure (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) yr) yr) yr) 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 0.2
2
0.4
Lateral
a b c d Total
0.6
2
1.2 0.4
1.0
1.5
1.5
1.4
1.39 1.95
1.2
where : λtotal = ∑ λ ; U total = ∑ U ; rtotal = ∑ U U. P. National Engineering Center National Electrification Administration
2
0.8
1.88 2.25
0.2 1.0
2 1.5
0.4 1.5
∑λ
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Effect of load transfer to alternative supply RELIABILITY INDICES WITH RESTRICTED LOAD TRANSFERS Load pt. A
Load pt. B
Load pt. C
Load pt. D
Section
U U U U Component λ r r r r λ λ λ (hrs/ (hrs/ (hrs/ (hrs/ failure (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) (f/yr) (hrs) yr) yr) yr) 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 Distributor
a b c d Total
0.2
2
0.4 0.6
2
1.2 0.4
1.0
1.5
1.5
1.4
1.59 2.23
1.2
where : λtotal = ∑ λ ; U total = ∑ U ; rtotal = ∑ U U. P. National Engineering Center National Electrification Administration
2
0.8
2.23 2.67
0.2 1.0
2 2.3
0.4 2.3
∑λ
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SUMMARY OF INDICES Load Point A 位 (f/yr) r (hrs) U (hrs/yr) Load Point B 位 (f/yr) r (hrs) U (hrs/yr) Load Point C 位 (f/yr) r (hrs) U (hrs/yr) Load Point D 位 (f/yr) r (hrs) U (hrs/yr)
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
2.2 2.73 6.0
1.0 3.6 3.6
1.0 1.5 1.5
1.12 1.39 1.56
1.0 1.5 1.5
1.0 1.5 1.5
2.2 2.73 6.0
1.4 3.14 4.4
1.4 1.89 2.65
1.48 1.82 2.69
1.4 1.39 1.95
1.4 1.59 2.23
2.2 2.73 6.0
1.2 3.33 4
1.2 2.75 3.3
1.3 2.58 3.35
1.2 1.88 2.25
1.2 2.23 2.67
2.2 2.73 6.0
1.0 3.6 3.6
1.0 3.6 3.6
1.12 3.27 3.66
1.0 1.5 1.5
1.0 2.34 2.34
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SUMMARY OF INDICES (cont.) Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Sytem Indices SAIFI 2.2 1.15 1.15 1.26 1.15 1.15 SAIDI 6.0 3.91 2.58 2.63 1.80 2.11 CAIDI 2.73 3.39 2.23 2.09 1.56 1.83 ASAI 0.999315 0.999554 0.999706 0.999700 0.999795 0.999759 ASUI 0.000685 0.000446 0.000294 0.003000 0.000205 0.000241 ENS 84.0 54.8 35.2 35.9 25.1 29.1 ASCI 28.0 18.3 11.7 12.0 8.4 9.7 Case 1. Base case. Case 2. As in Case 1, but with perfect fusing in the lateral distributors. 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. U. P. National Engineering Center National Electrification Administration
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Economics of Power System Reliability
Impact of Power Interruptions
Reliability Worth
Optimal Power System Reliability
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Impact of Power Interruptions 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
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Impact of Power Interruptions Impact to National Economy: NEDA Study (1974)
P 342,380 per day – losses due to brownout in Cebu-Mandaue area
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)
Sinay
Report (1989)
P 25 – losses in Value Added per kWh curtailment 45% – loss in Value Added in the manufacturing sector in Cebu due to power outages U. P. National Engineering Center National Electrification Administration
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Impact of Power Interruptions 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
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Reliability Worth Outage Cost to Industrial Sector in Luzon (0.0086 + 0.0023D)F + 0.1730 Pesos/kWh Where, F â&#x20AC;&#x201C; Frequency of Interruptions D â&#x20AC;&#x201C; Average Duration of Interruptions
Losses of MERALCO Industrial Customers in 1989 Energy Sales: 3.781 billion kWh Outage Cost: Php 0.3544/kWh Total Losses: Php 1.34 billion Source: del Mundo (1991) U. P. National Engineering Center National Electrification Administration
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Reliability Worth
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Reliability Worth Luzon Grid Outage Cost* LOLP (days/yr)
Frequency (per year)
Duration (Hours)
Outage Cost (Php/kWh)
12.26
70
2.11
1.12
6.25
38
2.00
0.68
1.88
13
1.73
0.34
0.94
7
1.61
0.26
0.45
4
1.50
0.22
0.21
2
1.38
0.20
0.08
0.73
1.31
0.18
0.04
0.31
1.30
0.18
Source: del Mundo (1991) U. P. National Engineering Center National Electrification Administration
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Reliability Worth
Luzon Grid Outage Cost Source: del Mundo (1991) U. P. National Engineering Center National Electrification Administration
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Reliability Worth Luzon Grid Total Cost
ATC = ASC + AOC
LOLP (days/yr)
Supply Cost (Php/kWh)
Outage Cost (Php/kWh)
Total Cost (Php/kWh)
12.26
0.90
2.11
2.02
6.25
0.94
2.00
1.62
1.88
1.01
1.73
1.35
0.94
1.03
1.61
1.29
0.45
1.06
1.50
1.28
0.21
1.09
1.38
1.29
0.08
1.11
1.31
1.29
0.04
1.14
1.30
1.32
Source: del Mundo (1991) U. P. National Engineering Center National Electrification Administration
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Optimal Power System Reliability
Luzon Grid Total Cost Source: del Mundo (1991) U. P. National Engineering Center National Electrification Administration
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Competency Training & Certification Program in Electric Power Distribution System Engineering