# Power distribution system reliability practical methods and applications pdf

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- New Brunswick Power Distribution System Reliability Practical Methods And Applications Pdf
- Reliability assessment of power distribution systems using disjoint path-set algorithm
- Power Distribution System Reliability: Practical Methods and Applications
- Power Distribution System Reliability

Authors: T. Lantharthong , N. Keywords: reliability indices , reliability evaluation , optimization technique.

## New Brunswick Power Distribution System Reliability Practical Methods And Applications Pdf

Finding the reliability expression of different substation configurations can help design a distribution system with the best overall reliability. The algorithm was synthesized and applied for the first time to the determination of reliability expression of a substation to determine reliability indices and costs of different substation arrangements.

The major highlight of this research being that the time consuming procedures of the DSOP solution generated for different substation arrangements using the proposed method is found to be significantly lower in comparison with the time consuming procedures of Monte Carlo-simulation solution or any other method used for the reliability evaluation of substations in the existing literature such as meta-heuristic and soft computing algorithms.

This software tool is capable of handling and modeling a large, repairable system. Additionally, through its intuitive interface it can be easily used for industrial and commercial power systems. Two case studies will be analyzed in this paper. The effects of different substation configurations on the reliability are analyzed and compared. Then, the reliability of a radial distribution system will be evaluated using DSOP solution. Reliability evaluation of distribution power system is of significant importance when performing asset management.

Distribution systems begin at distribution substations, which are the weakest link between the source of supply and the customer load points in a distribution power system, because they comprise switching arrangements that would lead to loss of load.

By knowing how to calculate the reliability of different substation configurations, an engineer can use this information to help design a system with the best overall reliability. But determining the reliability of a substation can also be important for existing installations as it can help locate weak points that may be contributing to overall system unreliability.

The reliability of substation must be high. However, once a reasonable level of reliability is achieved, there must be a means of evaluating the cost of potential changes to the substations to improve their reliabilities. Historically, the results of applying different reliability methodologies and tools varied significantly, and comparisons were difficult.

This paper describes the approach of simulations via reliability block diagrams as applied to the Gold Book standard network. Reliability indices of substations arrangements are presented, and are compared with each other. The research indicated that users were utilizing a wide variety of tools and techniques with different analysis results. The different approaches identified in Hale et al. These analytical approaches are applied to the IEEE Gold Book standard network in a series of papers to determine the accuracy of their results and how closely they can verify operational anomalies Koval et al.

This paper addresses the simulation approach as applied through a reliability block diagram RBD. The presented implementation is of a general-purpose algorithm for producing reliability expressions from reliability blocks diagrams. The algorithm is based on the transformation of the path-set expression Boolean expression derived from the reliability block diagram RBD into a sum of disjoint product.

The final disjoint version of path-set can be interpreted directly as a probabilistic expression system reliability on a one-for-one correspondence. The input to this package would be the sum of the RBD path-sets and the output would be the system reliability expression.

This algorithm could considerably reduce the number of disjoint mutually exclusive terms and save computation time with respect to top-event probability. Four major theorems of this algorithm are given, the use and correctness of which will be analyzed and proven.

In addition, some examples for different substations configurations are illustrated and comparison of their reliability indices is provided to show the superiority and efficiency of the presented algorithm, which is not only easier to understand and implement but also better than the existing known SDP algorithm for large network and complex RBDs. The contribution of this work is to provide a software tool for customers who purchase the critical power systems, the people who sell the systems, engineers who design and test the systems, and managers who make decisions on the systems.

With knowledge of the system design such as a one-line drawing , engineers can easily construct, verify, and modify the RBD, and also communicate with those of different disciplines. Reliability indices of different substations arrangements are presented, and are compared with each other to optimize the choice of the adequate configuration.

There are two types of approaches or models that are used in reliability assessment, namely, non-state space based models such as: network approach or fault trees and state space based models the most common of these is the continuous time Markov chain.

Each of these approaches is used where its advantages are needed, and its disadvantages are harmless. An overview of these analytical methods is presented hereafter.

In this approach, the topology of the network taken into consideration is represented in a logic block diagram RBD. This diagram describes logical connections between components. Each block is a component which is removed when the component fails and replaced when it is repaired. The connections between the blocks describe the success or failure of the system as a function of the states of the component.

Once the block diagram is settled, this approach can be handled in two ways. The method sequentially reduces the simple structures to equivalent units until the whole network reduces to a single unit. The above steps are repeated until the whole network reduces to an equivalent block. If at any stage the network does not reduce any further, the conditional probability theorem is used. The network is decomposed into two networks; in the first, the key component is replaced with a short circuit component success and in the second, the key component is removed component failure.

The overall reliability of the network is as described by the previous formula. When the block diagram is complex, decomposition into simple series and parallel paths may not be easy. The process could be quite difficult to program because it would require a lot of scanning. In this case, using cut sets or path-sets is way better.

A path-set is a set of components whose functioning alone will guarantee system success. A minimal path-set has no subset of components whose functioning alone would ensure system success. In the minimal path all the blocks constituting it are in series. The failure of any one of these blocks would render that ineffective. However, the minimal paths themselves are in parallel as the system will be successful as long as there is one path available between the input and output of the reliability block diagram RBD.

The reliability of the network using this approach, and based on the inclusion—exclusion theorem, is:. The total number of terms in this expression is 2 n -1 where n is the number of tie sets.

The network approach when applicable usually provides a shorter route to solution. The network approach is usually not suitable when dependent failures or repairs are involved common cause failures, restricted repairs, warm standby unit, etc. It is not necessary to assume the event independence in this approach, but dependent events can greatly increase the algebra of the computations. A component may assume various states depending upon its failure and restorative modes.

The system state describes the states of the components and the environment in which the system is operating. The set of all the possible states of the system is called the state space or event space. The number of states is, however, modified because of the dependency restrictions. The state space approach involves the following steps:. Indentify all possible states: describe all state space and transitions among states Fig. Form transition rate matrix: this matrix is formed from the state vectors of the different components using Kronecker product and Kronecker sum.

This matrix is also known as transition matrix. In case of dependency between components, the matrix is modified accordingly. The probability of every single state can be calculated by solving the Kolmogorov equations, written in matrix form hereafter:. This approach is conceptually general and flexible and makes it possible to take into account various dependent failures Dr Nahman ; Anderson ; Billinton and Allan The most often used performance measurement for a sustained interruption is the system average interruption duration index SAIDI.

This index measures the total duration of an interruption for the average customer during a given time period. SAIDI is normally calculated on either monthly or yearly basis; however, it can also be calculated daily, or for any other time period Brown Once an outage occurs the average time to restore service is found from the customer average interruption duration index CAIDI. The system average interruption frequency index SAIFI is the average number of times that a system customer experiences an outage during the year or time period under study.

The SAIFI is found by dividing the total number of customers interrupted by the total number of customers served. It is simply the number of interruptions that occurred divided by the number of customers affected by the interruptions. The average service availability index ASAI is the ratio of the total number of customer hours that service was available during a given time period to the total customer hours demanded.

This is sometimes called the service reliability index. However, applying the previously discussed methods will result in a NP-hard problem.

Heuristic algorithms do not provide an assurance for optimization of the problem. These methods are an approximation Bashiri and Karimi They have an additional property that worst-case solutions are known. Meanwhile, none of meta-heuristic algorithms are able to present a higher performance than others in solving all problems.

Also, existing algorithms suffer from some drawbacks such as slow convergence rate, trapping into local optima, having complex operators, long computational time, need to tune many parameters and design for only real or binary search space. Hence, proposing new meta-heuristic algorithms to minimize the disadvantages is an open problem Beheshti Also, Neuro computing and evolutionary computation usually need a lot of computational time, which is the disadvantage of the implementation of soft computing Dote and Ovaska State space approach: with n components, the event space consists of 2 n states.

The probability of each of the states is to be computed. Fault trees: requires the use of cut-set or tie-set. Network approach: either use of network reduction method, which is impractical.

Or path-set method that will lead to same result as fault tree approach. To overcome the previous difficulties, an algorithm for calculating system reliability by sum of disjoint products SDP , based on Boolean algebra, is presented. This algorithm is applied to sum of minimal path-sets Xing The first step to decompose a sum of product is rather simple.

The recursive method can be used for example. Assume that M 1 , M 2 , M 3 … M n , are minimal path-sets, and T is a sum of minimal path-sets, Then, using recursive method:. Obviously, disjoint products between items of formula 2 can be achieved, but each item is crossed. If the probabilities are known as. The first input to the program is the sum of minimal path-sets. Therefore, the first thing to do is decomposing it into a sum of mutually exclusive products.

## Reliability assessment of power distribution systems using disjoint path-set algorithm

A holistic analysis of distribution system reliability assessment methods with conventional and renewable energy sources[J]. AIMS Energy, , 7 4 : Article views PDF downloads Cited by Tables 2. AIMS Energy , , 7 4 :

## Power Distribution System Reliability: Practical Methods and Applications

Mohammoud M. Hadow, Ahmed N. Abd Allah, Sazali P. In order to assess the reliability of distribution systems, more and more researchers are directing their attention to the artificial intelligent method, and several reliability indices have been proposed, such as basic load point indices and system performance indices.

Finding the reliability expression of different substation configurations can help design a distribution system with the best overall reliability. The algorithm was synthesized and applied for the first time to the determination of reliability expression of a substation to determine reliability indices and costs of different substation arrangements. The major highlight of this research being that the time consuming procedures of the DSOP solution generated for different substation arrangements using the proposed method is found to be significantly lower in comparison with the time consuming procedures of Monte Carlo-simulation solution or any other method used for the reliability evaluation of substations in the existing literature such as meta-heuristic and soft computing algorithms. This software tool is capable of handling and modeling a large, repairable system.

### Power Distribution System Reliability

ALI A. He has nearly thirty years of experience in teaching, research and development, electric utility industry, electric equipment manufacturing, and consulting in power system reliability and security assessments. DON O. Previously, he worked as a distribution special studies engineer for B.

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Scientific Research An Academic Publisher. Power system reliability is a key aspect in power distribution system planning, design, and operation. Electric power utilities are required to provide uninterrupted electrical services to their customers at the lowest possible cost while maintaining an acceptable level of service quality. The importance of reliability arises as it can express the cost of service outages. Reliable power distribution networks are those managing a high level of reliability. The traditional power distribution grid is radial in nature, the power flows in one direction from the distribution substation to the load point. The radial system has low reliability, and those customers who are located at the end of the circuit, tend to be more prone to power outages than any other customers.

POWER DISTRIBUTION. SYSTEM RELIABILITY. Practical Methods and Applications. Ali A. Chowdhury. Don O. Koval. IEEE. PRESS. SERIES. ON POWER.