# Lessons for Data-Driven Modelling from Harmonics in the Norwegian Grid
## 3 Results
### Total Harmonic Distortion, Phases & Voltage Levels  
Figures 5 and 6 show the normalized cumulative distribution functions (CDF) of total harmonic distortion (THD), i.e., the fraction of samples \(N(\geq\text{THD})/N\) found at or above a given THD level. Table 2 shows their respective summary statistics. We observe the following:  
1. Overall, most (99%) of the THD values are small and \(\lesssim\) 1% of their respective fundamental phase voltage. Distributions are narrow with most values concentrated in the range 0.1 to 1%. Difference between different phases at the same voltage level are always smaller than differences between voltage levels;
2. Across phases and voltage levels, the difference between phases is always \(\leq\) 6%. Note that this only means that the phases are STATISTICALLY within 6% of one another. At any given point in time, their difference may be larger than that;
3. Difference between phases cover a wider range of THD for higher voltage levels. The largest integral difference (The area between CDF\({}_{i}\) and CDF\({}_{j}\), i.e., \(\int\sqrt{(\text{CDF}_{i}-\text{CDF}_{j})^{2}}\) dTHD.) between two phases is 0.024, 0.49, and 0.056) for 22, 66, and 300 kV, respectively. For 22 kV, the median values of \(V_{1}\), \(V_{2}\), and \(V_{3}\) remain within 4% of one another. This difference grows to 10% and 15% at 66 and 300 kV, respectively;
4. At higher voltage levels, the distributions of THD consistently shift towards smaller values. For 22 kV (66, 300), 99% of THD measurements (on \(V_{1}\)) are \(\lesssim\)1.48 (\(\leq\)1.01, \(\leq\)0.73). Median THD values shift similarly so that the median THD (on \(V_{1}\)) at 300 kV (66 kV) is half (a fifth) of that measured at 22 kV. The 22 kV site is consistently about half a decade above the 300 kV site, and the 66 kV site is located between these a little towards the 300 kV site.  
Regulatory requirements for THD levels are stricter for higher voltage levels, and more effort is made to keep these disturbances low at transmission level due to the potential impact on all downstream distribution feeders. The THD values are usually higher at lower voltage levels due to the proximity to the non-linear harmonic generating loads and generators. The propagation of harmonics from the polluter to higher voltage levels will usually be damped either by damping in grid components (lines, transformers etc.). However, in some cases, active or passive filters may be necessary to make sure that the harmonics do not propagate and cause damage to grid customers elsewhere in the grid. It is, however, important to understand the frequency-dependent impedance of the grid to understand the harmonic propagation and accurately calculate the resonance frequency [72]. As an example, a temporary change of topology in an area of the power system could cause harmonic levels to increase with several orders of magnitude, which as a consequence could cause instability in the power system. In general, the higher the frequency, the higher the resistance is. Consequently, damping of harmonics is stronger at higher frequencies.  
Researchers or technicians that seek to utilize the development of THD level or the level of specific harmonics for predictive modelling need to take this variation in harmonic levels into account while designing and training models. This variation in harmonic levels may be an underlying reason why general-purpose models trained on data from many sites in different geographic locations may have an inferior performance compared to models trained on specific sites, even though the data volumes are considerably smaller [75].