Abstract
When making long-term plans for their asset portfolios, decision-makers have to define a priori a maintenance budget that is to be shared among the several assets and managed throughout the planning period. During the planning period, the a priori budget is then allocated by managers to different operation and maintenance interventions ensuring the overall performance of the system. Because asset degradation is stochastic, a considerable amount of uncertainty is associated with this problem. Hence, to define a robust budget, it is essential to account for several degradation scenarios pertaining to the individual condition of each asset. This paper presents a novel mathematical formulation to tackle this problem in a heterogeneous multiasset portfolio. The proposed mathematical model was formulated as a mixed-integer programming two-stage stochastic optimization model with mean-variance constraints to minimize the number of scenarios with an insufficient budget. A Gamma process was used to model the condition of each individual asset while taking into consideration different technological features and operating conditions. We compared the solutions obtained with our model to alternative practices in a set of generated instances covering different types of multi-asset portfolios. This comparison allowed us to explore the value of modeling uncertainty and how it affects the generated solutions. The proposed approach led to gains in performance of up to 50% depending on the level of uncertainty. Furthermore, the model was validated using real-world data from a utility company working with portfolios of power transformers. The results obtained showed that the company could reduce costs by as much as 40%. Further conclusions showed that the cost-saving potential was higher in asset portfolios in worse condition and that defining a priori operation and maintenance interventions led to worse results. Finally, the results showcased how different decision-maker risk-levels affect the value of taking uncertainty into account.

Abstract
Electrical utilities apply condition monitoring on power transformers (PTs) to prevent unplanned outages and detect incipient faults. This monitoring is often done using dissolved gas analysis (DGA) coupled with engineering methods to interpret the data, however the obtained results lack accuracy and reproducibility. In order to improve accuracy, various advanced analytical methods have been proposed in the literature. Nonetheless, these methods are often hard to interpret by the decision-maker and require a substantial amount of failure records to be trained. In the context of the PTs, failure data quality is recurrently questionable, and failure records are scarce when compared to nonfailure records. This work tackles these challenges by proposing a novel unsupervised methodology for diagnosing PT condition. Differently from the supervised approaches in the literature, our method does not require the labeling of DGA records and incorporates a visual representation of the results in a 2D scatter plot to assist in interpretation. A modified clustering technique is used to classify the condition of different PTs using historical DGA data. Finally, well-known engineering methods are applied to interpret each of the obtained clusters. The approach was validated using data from two different real-world data sets provided by a generation company and a distribution system operator. The results highlight the advantages of the proposed approach and outperformed engineering methods (from IEC and IEEE standards) and companies legacy method. The approach was also validated on the public IEC TC10 database, showing the capability to achieve comparable accuracy with supervised learning methods from the literature. As a result of the methodology performance, both companies are currently using it in their daily DGA diagnosis.