A N OPTIMAL RELIABILITY ALLOCATION METHOD FOR DIGITAL SUBSTATION SYSTEMS Y UZHOU H U, P EICHAO Z HANG, Y ONGCHUN S U, Y U Z OU Adviser: Frank, Yeong-Sung Lin Present by Sean Chou 1

A GENDA Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions 2

A GENDA Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions 3

I NTRODUCTION The applying of the IEC 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

I NTRODUCTION 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

I NTRODUCTION 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

I NTRODUCTION 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

I NTRODUCTION 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

I NTRODUCTION 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. 9

A GENDA Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions 10

R ELIABILITY ALLOCATION MODELING AND SOLVING Basic Concept of Reliability Allocation Model of the cost versus the reliability of components Mathematic Programming 11

R ELIABILITY ALLOCATION MODELING AND SOLVING Basic Concept of Reliability Allocation The goal of reliability allocation is to solve the inequalities: 12

R ELIABILITY ALLOCATION MODELING AND SOLVING The math expression can be defined as Before modeling the math programming, R s and C (R i0, R i )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 R s. 13

R ELIABILITY 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. 14

R ELIABILITY ALLOCATION MODELING AND SOLVING 15

R ELIABILITY 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. 16

R ELIABILITY 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

R ELIABILITY 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. 18

R ELIABILITY 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: 19

R ELIABILITY ALLOCATION MODELING AND SOLVING The cost function is defined as: Considering the optimization objective, we need to find the optimal solution which yields to: 20

R ELIABILITY 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. 21

R ELIABILITY 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? 22

A GENDA Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions 23

E QUIVALENT 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. 24

E QUIVALENT REDUNDANCY COEFFICIENT According to the reliability of parallel- redundancy components, the equivalent redundancy coefficient θ i is introduced which yields to: θ i can measure the gap between the initial reliability and objective reliability of the component i. 25

E QUIVALENT REDUNDANCY COEFFICIENT Because the calculation result R i is solved by the minimum cost allocation method, the equivalent redundancy coefficient θ i 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 θ i becomes. 26

E QUIVALENT REDUNDANCY COEFFICIENT Arrange θ i in descending order and mark the array subscript of the maximum θ i 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. 27

E QUIVALENT REDUNDANCY COEFFICIENT Since the system structure has changed after realizing the redundancy, it is necessary to modify the variable R u in the system reliability function ( ). Check, if can’t meet the objective  Use GRG to find the new θ u 28

E QUIVALENT REDUNDANCY COEFFICIENT The complete process of the method in this paper: 29

A GENDA Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions 30

C ASE 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 31

C ASE STUDY Based on the above protection configuration, we can form the RBD for the transformer bay as shown in Fig.2. 32

C ASE 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. 33

C ASE 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. 34

C ASE 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 , and the optimization objective is set as We implement the GRG method, with the error tolerance to be

C ASE STUDY 36

C ASE STUDY 37

C ASE STUDY 38 The additional costs of quasi-optimal scheme showed in Table V are $9,000, which has risen by 17.51%.

A GENDA Introduction Reliability allocation modeling and solving Equivalent redundancy coefficient Case study Conclusions 39

C ONCLUSIONS 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. 40

C ONCLUSIONS 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 41

Thanks for your listening. 42