Combining Modified Wei bull Distribution Models for Power System Reliability Forecast
Abstract: Under the deregulated environment, electric utility companies have been encouraged to ensure maximum system reliability through the employment of costeffective long-term asset management strategies. Previously, the age based Wei bull 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 Wei bull 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 Wei bull distribution models with straightforward physical meanings specific to power system applications. Furthermore, this paper proposes a novel method to effectively evaluate different Wei bull 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. Existing system: This paper first describes the required asset operation status dataset as the foundation of this work. It then reviews the standard Wei bull distribution for aging analysis. Based on this review, four modified Wei bull distribution functions (health index based, X-shifting, Y-shifting and XY-shifting) are proposed and discussed considering practical power system conditions. Subsequently, it reviews the existing methods to calculate two-parameter Wei bull distribution parameters, discuss the process of creating training and testing pairs and explain the estimation of the two shifting parameters. After this, the proposed novel methods of evaluating and combining Wei bull distribution models are presented along with the process of forecasting asset reliability by using the produced joint forecast model. Finally, this paper provides two examples of applying proposed methods to forecast future electromechanical relay failures and distribution pole failures, as well as planning spare requirements and replacement strategies for a Canadian utility company. Proposed system: In recent years, to exploit the value embedded in data, many electric utility companies have employed sophisticated Computerized Maintenance Management Systems (CMMS) to track and store various asset data. In particular, asset reliability forecast requires the asset operation status data categorized by asset type and population. Asset operation status data should include age and operating statuses (i.e. working or failed). The data is continuously recorded as new assets get installed and old assets retire due to failures. Similar to any data mining algorithms, the quality of input data will significantly affect the accuracy of data observations and analysis. Understanding the requirements of asset operation status data and preparing qualified asset operation status datasets is a key step towards the successful implementation of the methods proposed in this paper. Advantages:
A good MSE on testing pairs indicate the true forecast accuracy of this model and can describe the forecasting capability for future unknown data using this model. This is especially important for health index based models because a calculated health index using can be any real value in and the original asset operating status dataset used for Wei bull distribution modeling may not contain these values. Furthermore, as explained in Section V, the training pairs are intentionally selected following a uniform distribution so that the corresponding testing pairs will also be able to cover the entire range of available H and F(H) data. The MSE therefore can indicate the forecast capability of the entire failure progression. It is not reliant on a single Wei bull distribution model. Instead, it can leverage multiple modified Wei bull distribution models to incorporate additional information and considerations in the power systems. It uses a unique method to measure the performance of different Wei bull distribution models. The method can better describe the models’ forecasting capability. It can effectively combine different Wei bull distribution models as a joint forecast model which could have a better performance than individual models. Disadvantages: To overcome the above problems, this paper proposes four modified Wei bull distribution models, which are based on the standard two-parameter Wei bull distribution model, except that they can include asset condition information and two additional shifting parameters. In practice, lack of inspection records is a quite common problem for studying aging asset population which covers a relatively long time span. Many old paper based records could be missing. Modules: Distribution Pole Reliability Forecast: The proposed approach was also applied to a sample group consisting of 1000 distribution wood poles selected from one area. Different from electromechanical
relays, these poles were installed from recent time to more than 80 years ago and there are no complete inspection records available for producing their health indices. Only installation and replacement records are available. These records indicate the age of poles and the time when some poles were replaced due to failures. In practice, lack of inspection records is a quite common problem for studying aging asset population which covers a relatively long time span. Many old paper based records could be missing. As discussed in Section IV, in cases like this, if the studied population operates in a homogenous environment, age can be used instead of health index to produce modified Wei bull distribution models. In this case study, all poles were made of western red cedar, treated with the same type of chemical treatment (Chromated copper arsenate) and carrying straight conductors in one geographic area. Therefore, they can be reviewed as one type of asset and rely on age information for further modeling and forecast. Weibull distribution: Electric utility companies have had to adapt to the deregulated 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 Wei bull distribution has been the traditional statistical tool to model equipment aging failures in reliability engineering. 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. Probability density function: Many recent works to improve Weibull Distribution models 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. 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. Asset Operation Status Dataset: In recent years, to exploit the value embedded in data, many electric utility companies have employed sophisticated Computerized Maintenance Management Systems (CMMS) to track and store various asset data. In particular, asset reliability forecast requires the asset operation status data categorized by asset type and population. Asset operation status data should include age and operating statuses (i.e. working or failed). The data is continuously recorded as new assets get installed and old assets retire due to failures. Similar to any data mining algorithms, the quality of input data will significantly affect the accuracy of data observations and analysis. Understanding the requirements of asset operation status data and preparing qualified asset operation status datasets is a key step towards the successful implementation of the methods proposed in this paper. It should be noted that: One type of asset often contains many sub-types due to different technology adoptions and manufacturing standards. Estimation of Model Parameters: The cumulative failure probability data as shown in Table II and Table III can be used to estimate Weibull distribution parameters and establish the models. However, not all data in the tables should be used to establish models. This is because this paper uses a unique method to evaluate and combine multiple Weibull distribution models. Similar to typical supervised machine learning processes, the cumulative failure probability data should be further split into two parts: Training pairs: the data pairs that are used to estimate Weibull distribution parameters. A certain percentage of the data, for example 80%, is randomly selected and grouped
as training pairs. When selecting the training data, a uniform distribution is applied to sample the entire range of H and F(H). This is to ensure the entire failure progression is modeled with enough supporting data. Combining Weibull distribution models as one joint model: After evaluating and selecting the suitable Weibull distribution models, this paper further proposes a powerful method to combine different Weibull distribution models as one joint forecasting model. This is a new approach since traditionally only single Weibull distribution model is applied for a forecasting task. One challenge utility asset engineer’s face is that they cannot pre-determine which Weibull distribution model will be able to yield the most accurate forecast. They also cannot pre-determine the most optimal shifting parameters although they know a probable range these parameters should fall under. A joint model , in comparison, can utilize all the suitable models for the final forecast output and is therefore less biased and more robust. Similar ideas can be found in some ensemble learning methods which attempt to build a joint classifier using multiple weaker classifiers. The joint model can be created. Electromechanical Relay Reliability Forecast: In this utility company, the electromechanical relay operation dataset contains age data, operating status data and three condition attributes for electromechanical relays: enclosure condition, mechanical condition and electrical condition. The substation technicians annually inspect these electromechanical relays for these three conditions. Based on the inspection results, they assign health ratings for the condition attributes. For a limited population, they also perform a low-voltage simulation test and check if the relay can correctly react to the testing signals and control the trip contacts. If the relay fails to make the correct actions, it will be labeled as failed and will get replaced; otherwise it will be labeled as working. The health index H is determined by the normalized relay age, enclosure condition, mechanical condition and electrical condition ratings. Weighting factors are predetermined by equipment engineers based on domain knowledge and experience. They are listed in Table IV.