AN OPTIMAL RELIABILITY
ALLOCATION METHOD FOR DIGITAL
SUBSTATION SYSTEMS
YUZHOU HU, PEICHAO ZHANG, YONGCHUN SU, YU ZOU
1
Adviser: Frank, Yeong-Sung Lin
Present by Sean Chou
AGENDA
Introduction
 Reliability allocation modeling and solving
 Equivalent redundancy coefficient
 Case study
 Conclusions

2
AGENDA
Introduction
 Reliability allocation modeling and solving
 Equivalent redundancy coefficient
 Case study
 Conclusions

3
INTRODUCTION
The applying of the IEC 61850 standard and the
rapid development of the high-speed Ethernet
technology permit implementation of a digital
substation system.
 Comprises more electronic devices, e.g., merging
units, Ethernet switches and time
synchronization sources [1].
 It is a potential shortcoming of the all-digital
protection system and has a dramatic impact on
the reliability of the system.

4
INTRODUCTION
The digital substation system is expected to have
equal or higher reliability than the conventional
one. Thus, it is necessary to design a robust
system structure.
 Many methods can help to optimize the system
reliability such as the component importance
analysis, the fault tree analysis, and the
reliability allocation methods.

5
INTRODUCTION
Component importance analysis can analyze the
system structure and help to diagnose the
weaknesses of the system.
 But it has three limitations:

It cannot set the system optimization objective
 It does not tell us how the reliability should be
allocated among the components exactly.
 It cannot consider the optimization constraints of
each component.

6
INTRODUCTION
In paper [4], the principle for reliability allocation
is given. Common reliability allocation methods
include proportion method, AGREE method,
minimum cost method, etc. [5]-[8].
 It is unrealistic to discuss the reliability
allocation issues without considering the
economic factors.
 Thus, this paper chooses the minimum cost
method as the basis for analysis to model the
mathematic programming.

7
INTRODUCTION
Using the above method, we can determine the
reliability optimization objective of each
component while obtaining a target level of the
whole system.
 But the analysis result often cannot help to guide
the optimization process directly.
 We usually employ redundancy instead to
increase the reliability of the system effectively.
 Thus the problem turns to decide how to achieve
redundancy in a most cost-effective way.

8
INTRODUCTION
Traditional reliability allocation methods
mentioned above cannot answer the question.
 This paper aims to propose a novel reliability
optimal allocation method based on minimum
cost allocation method, which considers the
cost factors, optimization feasibility, and
constraints for the components of the digital
substation system.

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AGENDA
Introduction
 Reliability allocation modeling and solving
 Equivalent redundancy coefficient
 Case study
 Conclusions

10
RELIABILITY ALLOCATION MODELING AND
SOLVING
Basic Concept of Reliability Allocation
 Model of the cost versus the reliability of
components
 Mathematic Programming

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RELIABILITY ALLOCATION MODELING AND
SOLVING
Basic Concept of Reliability Allocation
 The goal of reliability allocation is to solve the
inequalities:

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RELIABILITY ALLOCATION MODELING AND
SOLVING



The math expression can be defined as
Before modeling the math programming, Rs and C
(Ri0, Ri )should be defined.
Based on the RBD method, we can adopt the minimal
path set and the connection matrix technology to
derive the system reliability function Rs .
13
RELIABILITY ALLOCATION MODELING AND
SOLVING
A Reliability Block Diagram (RBD) performs
the system reliability and availability analyses
on large and complex systems using block
diagrams to show network relationships.
 The structure of the reliability block diagram
defines the logical interaction of failures within a
system that are required to sustain system
operation.
 http://www.reliabilityeducation.com/rbd.pdf

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RELIABILITY ALLOCATION MODELING AND
SOLVING
15
RELIABILITY ALLOCATION MODELING AND
SOLVING
Model of the cost versus the reliability of
components
 The other important element in the minimum
cost allocation is the cost function.
 Classical cost-reliability models :

Lagrange model is based on the assumption that
the logarithm of component unreliability is
proportional to cost, which may not always be the
case.
 Power model has two constants to be calculated,
both of which are not related to reliability.

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RELIABILITY ALLOCATION MODELING AND
SOLVING
Because of these shortcomings, these models are
difficult to be applied in practice.
 The modified “three parameters model” is an
exponential function of manufacturing cost with
respect to reliability, which contains following
parameters.

17
RELIABILITY ALLOCATION MODELING AND
SOLVING


“three parameters model”
Using the above cost model, we can take optimize
costs, feasibility of optimization, and constraints
for the components of the digital substation
system into consideration.
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RELIABILITY ALLOCATION MODELING AND
SOLVING
Mathematic Programming
 Based on the RBD of the system structure, we
have already got the system reliability function.


We should also define the following vectors:
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RELIABILITY ALLOCATION MODELING AND
SOLVING


The cost function is defined as:
Considering the optimization objective
, we
need to find the optimal solution
which yields
to:
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RELIABILITY ALLOCATION MODELING AND
SOLVING

Then, we get the mathematic programming:
The GRG (Generalized Reduced Gradient)
method [13] is employed to solve the problem and
calculate the optimal feasible solution
.
 Thus, the
vector is the reliability optimization
objective of each component.

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RELIABILITY ALLOCATION MODELING AND
SOLVING
However, the solution of the reliability allocation
tells only one part of a story.
 When the results are generated, follow-up
question arises: how to improve the reliability of
the components in practice?

How?
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AGENDA
Introduction
 Reliability allocation modeling and solving
 Equivalent redundancy coefficient
 Case study
 Conclusions

23
EQUIVALENT REDUNDANCY COEFFICIENT

Two ways to improve the reliability of
components:
substitution (with more reliable components)
 redundancy (achieved in the component level)

The former way is often unavailable, whereas the
latter is more effective.
 Based on the optimal feasible solution
, this
section further demonstrates the above
discussions.

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EQUIVALENT REDUNDANCY COEFFICIENT


According to the reliability of parallelredundancy components, the equivalent
redundancy coefficient θi is introduced which
yields to:
θi can measure the gap between the initial
reliability and objective reliability of the
component i.
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EQUIVALENT REDUNDANCY COEFFICIENT
Because the calculation result Ri is solved by the
minimum cost allocation method, the equivalent
redundancy coefficient θi has already taken the
cost factors into consideration.
 When all the other conditions remain the same,
the higher the initial cost of the component is,
the smaller the equivalent redundancy coefficient
θi becomes.

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EQUIVALENT REDUNDANCY COEFFICIENT

Arrange θi in descending order and mark the
array subscript of the maximum θi as u, namely:
Then the component u is the critical component
in the optimization process.
 If we reduplicate the component u, the total
system reliability will improve in the most
effective way, while the additional cost remains
minimum.
 Thus, reduplicating the component u is an
effective quasi-optimal method in engineering
practice.

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EQUIVALENT REDUNDANCY COEFFICIENT
Since the system structure has changed after
realizing the redundancy, it is necessary to
modify the variable Ru in the system reliability
function ( )
.
 Check
, if can’t meet the objective
 Use GRG to find the new θu

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EQUIVALENT REDUNDANCY COEFFICIENT

The complete process of the method in this paper:
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AGENDA
Introduction
 Reliability allocation modeling and solving
 Equivalent redundancy coefficient
 Case study
 Conclusions

30
CASE STUDY
We apply the method of the preceding section to a
practical digital protection system at the
transformer bay of a typical 110kV digital
substation to demonstrate the effectiveness.
 Includes the following components:


Protection
Main protection (PR)
 Zero-sequence protection
 Breaker failure protection






Merging unit (MU)
Circuit breaker IED (CB IED)
Time source (TS)
Ethernet media (EM).
Transformer auxiliary relay
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CASE STUDY

Based on the above protection configuration, we
can form the RBD for the transformer bay as
shown in Fig.2.
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CASE STUDY
This paper assumes that the life of all the
components accord with exponential distribution.
 It means that the failure rate of each component
is constant and their mean time to failure(MTTF)
is the reciprocal of the average life expectancy.

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CASE STUDY

Referring to the parameters listed in paper [2]
and [3], this paper estimates the cost, MTTF, and
the optimization feasibility parameters of all the
components as showed in Table I.
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CASE STUDY
According to the system RBD, this paper employs
minimal path set method to solve the system
reliability function, and calculates the reliability
of the components as well as the whole system.
 The initial reliability of the system is 0.9552, and
the optimization objective is set as 0.99.
 We implement the GRG method, with the error
tolerance to be 0.001.

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CASE STUDY
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CASE STUDY
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CASE STUDY

The additional costs of quasi-optimal scheme
showed in Table V are $9,000, which has risen by
17.51%.
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AGENDA
Introduction
 Reliability allocation modeling and solving
 Equivalent redundancy coefficient
 Case study
 Conclusions

39
CONCLUSIONS
The novel method proposed in this paper
provides the quasi-optimal redundancy scheme
which can be used in practice directly.
 The methodology proposed in this paper is easy
to implement using software and suitable to
analyze the digital substation system with
arbitrary architectures.

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CONCLUSIONS

In this research


A resource allocation method
Other issues

Internal factor


Component geographic location
External factor
Nature disaster
 Attacker


Confidential issue about storage

Secret sharing
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Thanks for your listening.
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