# Voltage Problems on Farms with Agricultural Biogas Plants--A Case Study
## 3 Results and Discussion
### Analysis of the Feeding System of the Biogas Plant under Study  
To carry out the analyses, a computer model of the power supply system for the agricultural biogas plant was created using the Neplan program, a global standard in power system analysis. The system data described in Section 2 were used for the calculations. The original power supply system for the biogas plant consisted of a 198-meter-long cable line using YKY 4 \(\times\) 25 mm\({}^{2}\). As shown in Figure 9, this cross-section does not ensure that the voltage remains within legal limits. The cable cross-section should be no smaller than 61 mm\({}^{2}\) to meet the voltage requirements, with the closest standardised cross-section being 70 mm\({}^{2}\). Changing the cross-section of the cable reduces the power loss from 1.82 kW to 0.65 kW. Assuming the biogas plant operates 8400 in annually, this change reduces annual energy losses by 8 MWh. An electricity price of 695/MWh results in an annual cost saving of 6760. A cable with a more considerable cross-section costs \(\copy{23}\) per meter. Considering only the reduction in power losses on the power cable, the upgrade from a 25 mm\({}^{2}\) to a 70 mm\({}^{2}\) conductor will pay for itself in 6 years. Analysis of the Main Supply Parameters of the Studied Agricultural Biogas Plant after Changing the Supply Cable  
The recorded values of the mains frequency after the power system conversion are shown in Figure 10.  
Analysing the course of the variation in the frequency value recorded after the power cable change, repeatability analogous to that before the conversion can be observed. Analysing the recorded voltage waveforms (Figure 11) and voltage deviation (Figure 12), as in the previous case, it is possible to notice a cyclic variation. However, the variations are noticeably more minor--it is much less frequent for the voltage to take values above 250 V, and only one measurement was recorded in which the voltage dropped below 210 V. This is reflected in the voltage deviation values (Figure 12), which were within \(\pm\)10% of the rated voltage throughout the recorded period. Figure 9: Dependence of the voltage value (U) occurring at the connection point of an agricultural biogas plant as a function of the cross-sectional area (s) of the working conductor of the supply cable. Figure 11: Voltage variation waveform recorded after changing the power cable. Figure 12: Voltage deviation variation waveform recorded after changing the power cable. Figure 10: Frequency variation waveform recorded after changing the power cable. The unstable operation of the agricultural biogas plant is reflected in the recorded values of the flicker nuisance index (Figure 13). These are nearly three times lower than the values found in the system before the power cable change (Figure 5). As with the original system, a cyclic variation in the voltage asymmetry factor was also recorded after changing the power cable (Figure 14). This does not show any significant differences in the values achieved, but comparing the two waveforms (Figures 6 and 14), it is clear that the waveform recorded after the power cable change is less 'jagged'. As in the original system, the maximum values of the voltage distortion factor occur in the afternoon and evening (Figure 15). However, these values are almost twice as low as the first biogas plant studied. Figure 14: Variation waveform of the voltage asymmetry factor (\(\alpha_{\mathrm{U}}\)) recorded after changing the power cable. Figure 13: Variation waveform of the long-term flicker nuisance factor (P\({}_{\mathrm{lt}}\)) recorded after changing the power cable. The maximum changes in the recorded active power values of the agricultural biogas plant after changing the feed cable (Figure 16) were due to the operation of the two digester mixers. Notably, at no point during the measurement did the active power reach the generator's rated power. This discrepancy was caused by the energy consumption of the equipment installed in the biogas plant.