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AN OPTIMAL RELIABILITY ALLOCATION METHOD FOR DIGITAL SUBSTATION SYSTEMSYUZHOU HU, PEICHAO ZHANG, YONGCHUN SU, YU ZOU
Adviser: Frank, Yeong-Sung Lin
Present by Sean Chou
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AGENDA
Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions
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AGENDA
Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions
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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.
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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.
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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.
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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.
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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.
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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
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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 .
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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
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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.
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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
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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 parallel-redundancy 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
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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
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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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