# Lessons for Data-Driven Modelling from Harmonics in the Norwegian Grid
## 3 Results  
### Presence of Harmonics  
Figure 3 shows the fraction of cycles (per month) with power \(>0\) for three sites in the Norwegian power grid between 2015 to 2018. By grouping data by harmonic channel, phase, month, and site, we find the following. 1. Across all voltage levels, non-negligible amounts of non-zero measurements occur only on the third, fifth, and seventh harmonics;
2. At the 22 kV level and across all phases, 95% of measurements of the seventh harmonic are non-zero. For the fifth harmonic, there are non-zero measurements in 70% of cases. The third harmonic differs across phases. On \(V_{2}\), non-zero measurements are more common (40%) than on \(V_{1}\) and \(V_{3}\) (10% each). Non-zero observations on the third and fifth harmonic are clustered in time rather than being spread out evenly. The clusters are not evenly distributed and do not appear to correlate with seasons;
3. At the 66 kV level, we find the same patterns as at the 22 kV level, with most non-zero measurements found in the seventh, fifth, and third harmonics. Across all phases, we find non-zero values for the seventh and fifth harmonics in 75 and 55% of cases, respectively. For the third harmonic, non-zero values are unbalanced across phases. On \(V_{1}\), \(V_{2}\), and \(V_{3}\), we count 55, 65, and 35% of non-zero values, respectively. Observing no differences in the temporal distribution of counts, \(V_{3}\) appears to have a generally lower level of non-zero counts;
4. At the 300 kV level, there is a marked difference between the periods of March 2017 to July 2018 and the remainder of the observation period. Inside this period, 45% of measurements across phases (and for the third, fifth, and seventh harmonic channel) are non-zero. Outside this period (and overall), only 3 (19)% of measurements are non-zero (again, for the third, fifth, and seventh harmonic channel). The temporal patterns (in the period of March 2017 to July 2018) are identical across phases, except for the third harmonic channel on \(V_{2}\), where 87% of all samples are non-zero (compared to 45 and 55% for the third and fifth harmonic, respectively). Figure 3: Fraction of non-zero observations for the first eight harmonics in each voltage channel (denoted as _Instrument Channel_), grouped by harmonic. Data for all three sites are shown, see panel titles. A period of four years is covered for each site. The fraction (see colormap on the right) is calculated over \(\sim\)1.3 \(\times\) 10\({}^{8}\) samples in each month. It is clear that there are some channels (harmonics for each phase) that are clearly more present than others, and that the pattern is to a large degree transferable from phase to phase and from site to site. It is also clear that there is considerably less harmonic content in the higher voltage levels. This is confirmed in Figures 5 and 6. The harmonic levels in Figures 4 and 5 show that there is some variation in harmonic levels on each site. The figures show variation detailed by harmonic number, voltage level and hour-of-day (Figure 4) and the cumulative distribution function (CDF) for each voltage level (Figure 5). As mentioned above, the non-zero values on Site 1 (22 kV) are present on the 3 rd, 5 th and 7 th harmonics. The presence of these odd harmonics is usual in the modern power system, due to a high number of non-linear loads [70]. Both single- and three-phase converters are contributing to this type of harmonic noise, for equipment such as computers and power-intensive industry, respectively. For Site 1, the 7 th harmonic is higher than 1% for the whole analysed period. The 5 th harmonic also has a considerable presence throughout the period. This could suggest that the harmonic noise is caused by power-intensive industry with 6-pulse three-phase rectifiers [71]. Based on the results in Figure 4, it is clear that there is a daily variation in the harmonic levels that backs this claim. Figure 4: Variation in t the occurrence of non-zero values for each node averaged on a daily basis.