# Lessons for Data-Driven Modelling from Harmonics in the Norwegian Grid
## 5 Conclusions & Future Work  
We have presented a statistical analysis of time-series of harmonic components for three sites in the Norwegian power system. Variations between voltage levels, over different time periods (hourly, monthly, and seasonally), and between individual harmonics were quantified. The findings can be condensed into four major points:  
1. The distribution of harmonics differs with phases and voltage level (site);
2. There is little power (below the Elspec instrument cut-off) beyond the 13 th harmonic;
3. There is temporal clumping of events;
4. There is seasonality on different time-scales.  
Each of these has an implication for the development of data-driven (machine learning) models of power system behaviour. In particular:  
1. Variations in harmonic power with phase and voltage level suggests that two-step training procedures akin to transfer learning may be useful. In such a scheme, one would (i) train a baseline model on data from all nodes and all harmonics, and then (ii) fine-tune the model to with data from specific sites. This will result in a model specific to each site;
2. The lack of power beyond the 13 th harmonic suggests that including higher-order harmonics will not increase the predictive power of models;
3. Clumping suggests that models should include features such as the time-since-last-event to distinguish between grid states (frequent alarms vs. nominal operations);
4. Seasonality suggests that models should include features such as the hour of the day or the month of the year.  
Strictly speaking, these conclusions are only valid for the set of three sites we have analyzed. However, Norwegian grid operators have deployed PQA instruments at 49 sites (with more being rolled out). Most of these have at least a few years worth of measurements (and some more than a decade). Future work should therefore focus on adapting and scaling the analysis to (a) include more sites, (b) account for grid topology (and switching), as well as (c) explicitly account for local production and consumption profiles. Additionally, the statistical properties of voltages, currents, and power should be included to generalize the work even further. An early draft of this work included a preliminary statistical analysis of cycle-by-cycle RMS voltage, but we were forced to drop it due to resource constraints.  
A separate thread of work should focus on applying these lessons to the development of predictive models. The development of predictive (machine learning) models comes with its own set of challenges and choices--the inclusion of which we deemed to have gone beyond the scope of this contribution.  
**Author Contributions:** Conceptualization, V.H., B.N.T. and G.H.R.; Data curation, V.H.; Formal analysis, B.N.T. and C.A.A.; Funding acquisition, C.A.A.; Investigation, V.H., B.N.T. and G.H.R.; Methodology, V.H., B.N.T., G.H.R. and C.A.A.; Project administration, C.A.A.; Software, V.H.; Validation, V.H.; Visualization, V.H. and C.A.A.; Writing--original draft, V.H., B.N.T., G.H.R. and C.A.A.; Writing--review & editing, V.H., B.N.T., G.H.R. and C.A.A. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was funded by the Research Council of Norway via the EnergyX grant number 268193 and the project partners Statnett, Tensio TN, Lyse Elnett, Nettalliansen, Hydro Energi, Haugaland Kraft Nett and the Norwegian University of Science and Technology (NTNU).  
**Data Availability Statement:** Due to the sensitive nature of the data used in this article the underlying data are not made public as required by Norwegian Law. The methodology should however be readily transferable to data obtained from similar instruments measuring power quality in other grids.  
**Conflicts of Interest:** The authors declare no conflict of interest.