Combining Modified Weibull Distribution Models for Power System Reliability Forecast

Ming Dong , Senior Member, IEEE, and Alexandre B. Nassif , Senior Member, IEEE Abstract-Under the deregulated environment, electric utility companies have been encouraged to ensure maximum system reliability through the employment of cost-effective long-term asset management strategies. Previously, the age based Weibull distribution has been used vastly for modeling and forecasting aging failures. However, this model is only based on asset age and does not consider additional information such as asset infant mortality period and equipment energization delay. Some works on modifying Weibull distribution functions to model bathtub-shaped failure rate function can be practically difficult due to model complexity and inexplicit parameters. To improve the existing methods, this paper proposes four modified Weibull distribution models with straightforward physical meanings specific to power system applications. Furthermore, this paper proposes a novel method to effectively evaluate different Weibull distribution models and select the suitable model(s). More importantly, if more than one suitable model exists, these models can be mathematically combined as a joint forecast model, which could provide better accuracy to forecast future asset reliability. Finally, the proposed approach was applied to a Canadian utility company for the reliability forecast of electromechanical relays and distribution poles to demonstrate its practicality and usefulness.

Index Terms-Weibull distribution, power system reliability, asset management.

E LECTRIC utility companies have had to adapt to the dereg- ulated environment and find ways to reduce overall cost while maintaining system reliability performance. To achieve this goal, understanding and forecasting reliability trends of different asset populations is the key. Sophisticated and optimal asset management measures can only be established based on the accurate forecasting of asset reliability change in the future.

Previously, the asset age based Weibull distribution has been the traditional statistical tool to model equipment aging failures in reliability engineering [1]- [4]. However, this classic model cannot effectively incorporate additional information such as asset health condition data, asset warranty, energization delay, asset infant mortality period and minimum spare requirements which many electric utility companies often need to consider for power system asset management. Many recent works to improve Weibull Distribution models [6]- [10] were focused on modeling bathtub-shaped failure rate function. Compared to a standard Weibull function, the bathtub-shaped function can describe the initial asset infant mortality period and the stable low failure rate period before entering into the wear-out period that a standard two-parameter Weibull distribution is able to depict. To achieve this, these previous works proposed modified probability density functions (PDF) that are much more complicated than traditional Weibull PDF [9]. Due to this complication, the estimation of these parameters can be sometimes difficult, computationally costly and inaccurate due to potential over-fitting with multiple parameters. Lack of explicit physical meanings of these parameters made its application even more difficult to electric utility engineers.

To overcome the above problems, this paper proposes four modified Weibull distribution models, which are based on the standard two-parameter Weibull distribution model, except that they can include asset condition information and two additional shifting parameters. These modifications are mathematically simple and straightforward. More importantly, the two shifting parameters have clear physical meanings and can be estimated by domain experts such as utility equipment or maintenance engineers. These parameters reflect the average failure rate during the initial infant mortality period and the stable low failure rate period respectively. In a way, the proposed method represents the bath-tub properties using a different but much simpler approach. Furthermore, these individual modified models can be combined to increase the forecasting flexibility and robustness. The main contributions of this paper are: r Four modified Weibull distribution models with straight- forward physical meanings that incorporate additional information and considerations specific to power system applications; r A novel method to measure the forecast accuracy of dif- ferent Weibull distribution models. Based on this method, suitable Weibull distribution model(s) can be identified for a specific asset population; r A novel method to combine different Weibull distribution models as a joint forecast model. The proposed approach is described as follows and its flowchart is shown in Fig. 1. Firstly, the operation status data of a specific asset population is analyzed and converted to a cumulative failure probability table. This table is then split into training pairs and test

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