Quantifying power system frequency quality and extracting typical patterns within short time scales below one hour

Abstract

This paper addresses the lack of consideration of short time scales, below one hour, such as sub-15-min and sub-1-hr, in grid codes for frequency quality analysis. These time scales are becoming increasingly important due to the flexible market-based operation of power systems as well as the rising penetration of renewable energy sources and battery energy storage systems. For this, firstly, a set of frequency-quality indices is considered, complementing established statistical indices commonly used in power-quality standards. These indices provide valuable insights for quantifying variations, events, fluctuations, and outliers specific to the discussed time scales. Among all the implemented indices, the proposed indices are based on over/under frequency events (6 indices), fast frequency rise/drop events (6 indices), and summation of positive and negative peaks (1 index), of which the 5 with the lowest thresholds are identified as the most dominant. Secondly, k-means and k-medoids clustering methods in a learning scheme are employed to identify typical patterns within the discussed time windows, in which the number of clusters is determined based on prior knowledge linked to reality. In order to clarify the frequency variations and patterns, three frequency case studies are analyzed: case 1 (sub-15-min scale, 10-s values, 6 months), case 2 (sub-1-hr scale, 10-s values, 6 months), and case 3 (sub-1-hr, 3-min values, the year 2021). Results obtained from the indices and learning methods demonstrate a full picture of the information within the windows. The maximum value of the highest frequency value minus the lowest one over the windows is about 0.35 Hz for cases 1 and 2 and 0.25 Hz for case 3. Over-frequency values (with a typical 0.1% threshold) slightly dominates under-frequency values in cases 1 and 2, while the opposite is observed in case 3. Medium fluctuations occur in 35% of windows for cases 1 and 2 and 41% for case 3. Outlier values are detected using the quartile method in 70% of windows for case 2, surpassing the other two cases. About six or seven typical patterns are also extracted using the presented learning scheme, revealing the frequency trends within the short time windows. The proposed approaches offer a simpler alternative than tracking frequency single values and also capture more comprehensive information than existing approaches that analyze the aggregated frequency values at the end of the specific time windows without considering the frequency trends. In this way, the network operators have the possibility to monitor the frequency quality and trends within short time scales using the most dominant indices and typical patterns.