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Article

The Effect of Agricultural Biogas Plants on the Quality of Farm Energy Supply

by
Magdalena Tymińska
1,
Zbigniew Skibko
2,* and
Andrzej Borusiewicz
1,*
1
Department of Agronomy, Modern Technologies and Informatics, International Academy of Applied Sciences in Lomza, Studencka 19, 18-402 Lomza, Poland
2
Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
*
Authors to whom correspondence should be addressed.
Energies 2023, 16(12), 4600; https://doi.org/10.3390/en16124600
Submission received: 28 April 2023 / Revised: 4 June 2023 / Accepted: 5 June 2023 / Published: 8 June 2023
(This article belongs to the Special Issue Biomass, Biofuels and Waste)
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Abstract

Agricultural biogas plants are among the renewable energy sources. While they have many advantages, they are less common than photovoltaic or wind power plants. One of the reasons for the lack of support for the construction of new agricultural biogas plants is the belief that biogas plants will affect the operation of consumers connected in its immediate vicinity through interference introduced into the grid. This article presents the possibilities a biogas plant built on a farm offers. The impact of an on-farm biogas plant on the voltage parameters of a farm specializing in barnless cattle rearing is analyzed in detail. As demonstrated by the authors’ research in one of the agricultural biogas plants (with an electrical capacity of 40 kW), these plants do not introduce significant disturbances to the power quality into the grid. The most significant changes in the parameters of the voltage supplying the farm under study were caused by the operation of the digester mixer installed in the fermenter. Thanks to the research, it was also possible to identify a problem with the effect of the digester mixer on the energy parameters produced in the biogas plant. This problem has so far not been noticed or corrected by biogas plant manufacturers.

1. Introduction

An agricultural biogas plant is a set of facilities used in the production and processing of agricultural biogas [1], i.e., a gas obtained “by the methane fermentation of agricultural raw materials, agricultural by-products, liquid or solid animal excreta, by-products, waste or residues from the processing of products of agricultural origin or forest biomass, or plant biomass harvested from land other than that registered as agricultural or forestry, excluding biogas derived from raw materials from landfills, as well as from wastewater treatment plants, including on-site wastewater treatment plants from agri-food processing, where no separation of industrial wastewater from other types of sludge and wastewater is carried out” [2]. Agricultural biogas consists mainly of methane (50–75%), carbon dioxide (25–50%) and trace amounts of other elements such as hydrogen sulfide (20–2000 ppm), hydrogen (<1%), carbon monoxide (0–2.1%), nitrogen (<2%) and oxygen (<2%) [3,4,5].
Agricultural biogas is obtained from anaerobic methane fermentation using plants, metabolic by-products and other residual agricultural and food waste as substrates [6,7]. A stable fermentation process and high biogas production efficiency must characterize all substrates used in biogas plants. An essential criterion in substrate selection is the possibility of using the digestate generated in the biogas plant, e.g., as a natural fertilizer [8,9].
In agricultural biogas plants built on farms and generating energy for on-farm use, the most common substrate is slurry, obtained from cattle rearing [10]. The amount of biogas extracted from the slurry primarily depends on the animal husbandry technology (e.g., how the stalls are washed) [11]. Procesy rozkładu na mokro obejmują od 5 do 20% całkowitej zawartości substancji stałych (TS) [12]. Livestock accounts for almost 40% of total agricultural production in high-income countries and 20% in developing countries. As much as 34% of the protein supply in the human diet comes from livestock [12,13]. According to the FAO (Food and Agriculture Organisation of the United Nations), the population in Europe in 2019 consisted of 143 million pigs, 77 million cattle and 74 million sheep and goats [14]. The amount of livestock manure depends on many aspects, which include the feeding regime and the stage of the rearing process [15]. When manure is not properly processed, livestock farming activities negatively impact the environment [16,17,18].
On the other hand, manure is an attractive natural resource for producing renewable energy and significantly improving soil fertility [19,20]. The low C/N ratio found in manure, the high nitrogen content, the low volatile solids (VS) and, in some cases, the high proportion of lignocellulosic biomass are significant limitations to using manure in the fermentation process [21,22,23]. Manure processing (mainly manure and slurry) has more benefits when carried out under anaerobic conditions in biogas plants than directly applying untreated manure on agricultural fields [24,25]. The digested slurry has a less unpleasant odor and a more favorable consistency for further processing than slurry. The digestate has an alkaline reaction with a pH of approximately 7–8 [26]. The ratio of carbon to nitrogen in the raw slurry is 6.8:1, whereas it is much higher in the digestate, ranging from 15:1 to 25:1. As a result, plants can make better use of the components contained in the fertilizer (an increase from 50% to 75–80% was recorded). Digestate as fertilizer also reduces the risk of water eutrophication and groundwater pollution by nitrogen and phosphorus compounds. There is no nitrogen loss during fermentation, only a reduction to ammonium nitrogen, which is more assimilable for plants. Phosphorus and potassium are also present in a form more readily available to plants, and weed seeds lose their germination power [27].
The construction of agricultural biogas plants brings many additional benefits. First and foremost, a farm with a constructed biogas plant is perceived as modern and technology-friendly. Very often, there is a symbiosis between the biogas plant and the scientific, educational or tourism environment [27]. In low-volume biogas installations using slurry from the cattle-rearing process as substrate, it is unnecessary to build additional substrate storage areas (to ensure continuous production) [28,29]. Electricity produced in agricultural biogas turbine sets is characterized by low variability of generated power in time, which influences the stabilization of voltages occurring in individual nodes of the grid and results in a reduction in energy losses occurring in power lines [30]. A properly selected agricultural biogas plant can fully meet the energy needs of the farm on which it is built [31]. The heat of the exhaust gas coming out of the gas turbine can be used both to heat the buildings of the farm in question and can also be used in various technological processes (e.g., drying wood, fruit, grain). A novel use of heat from biogas plants is to heat greenhouses or vegetable tunnels [32]. The combustion of biogas reduces emissions of sulfur dioxide and nitrogen oxides into the atmosphere, leading to a reduction in the formation of so-called acid rain [33]. The production and use of methane in a biogas plant avoids a significant proportion of methane and other greenhouse gas emissions from the decomposition of animal feces (approximately 20 percent of global methane emissions come from the enteric fermentation of ruminants and the decomposition of their feces) [34]. Unused (for legal or economic reasons) permanent grassland can be used as an additional substrate. Using unused plant biomass for biogas production enables these areas to be maintained in good agricultural conditions and increases the amount of biogas produced on the farm [35,36,37].
An agricultural biogas plant, like any energy source installed near the consumer, affects the quality parameters of the farm’s electricity supply. Inadequate energy quality can not only lead to the malfunctioning of sensitive loads (mainly electronically controlled equipment such as milking robots) but, in extreme cases, can damage them. Therefore, before this type of source’s widespread use, it becomes crucial to research the parameters describing the quality of energy produced by agricultural biogas plants.
The research was commissioned by the owner of an agricultural biogas plant due to problems reported (by a customer neighboring the agricultural biogas plant) with the operation of specific equipment, being (according to him) the result of interference in the voltage generated by the biogas plant. As the research has shown, an agricultural biogas plant does not deteriorate the quality parameters of electricity; on the contrary, it improves some of them. On the occasion of the research, it was possible to notice a significant impact of the digester mixer on the network parameters. The manufacturer of small-scale biogas plants operating in Poland has not yet noticed or corrected it. Solutions have been proposed which are not expensive to implement and will significantly help to reduce the problem noted.

2. Materials and Methods

The research was carried out at a biogas plant for agricultural biogas derived from substrate obtained from dairy cows raised in a barnless system. Slurry from the barn was pumped into the lower part of the fermenter, where the fermentation process occurred under anaerobic conditions. The fermenter in the agricultural biogas plant under study had a rated capacity of 1260 m3 (a cylinder with a diameter of 21.75 m and a height of 3.69 m—the total height, including the roof, was 10.7 m). A portion of the digested slurry (depending on the reactor’s capacity and the amount of biogas extracted) was pumped daily into an external digestion tank. A programmable pressure sensor in the digester determined the amount of slurry injected. The average residence time of the feedstock in the digester was between 2 and 3 weeks, with no less than 12 days. Methane fermentation in the reactor occurred at a constant temperature of 42 °C (mesophilic fermentation). According to information received from the developer, the biogas produced in the agricultural biogas plant under study consisted of approximately 60% methane (CH4), 39% carbon dioxide (CO2) and 1% other gases, most of which were hydrogen sulfide (H2S). Throughout the study, the level of biogas accumulated in the reactor was maintained between 210 and 375 cm, allowing the agricultural biogas plant to operate at its nominal capacity. In contrast, the substrate level in the digester at that time was 160 cm ± 10%. The biogas produced in the reactor was burned in an internal combustion engine (the power plant under study used two internal combustion engines of 20 kW each, the technical data of which are shown in Table 1), and the resulting mechanical energy was converted into electricity, which can be used both to power the farm’s equipment and sold to the distribution network. The biogas produced in the reactor was transported through pipes through an airlock and underwent the subsequent treatment stages before being combusted. In the container, the biogas was passed through a system of filters and cleaned of impurities such as foam created during fermentation. The sulfur-hydrogen content was reduced using a carbon filter. The heat from the flue gases was used to maintain a constant temperature in the digester and can also be used to heat buildings on the farm or in other technological processes (e.g., grain drying, greenhouse heating). In the agricultural biogas plant under study, the primary end product was always electricity (irrespective of the outside temperature), the production of which was maintained at the highest possible level. In the event of insufficient heat generation, an additional energy source, such as a gas boiler, was switched on.
A portable SONEL PQM-701 power quality analyzer, certified by the Research and Calibration Laboratory in Świdnica, was used to record parameters characterizing the quality of generated electricity. The analyzer recorded network parameters in accordance with class A of the EN 61000-4-30 standard [38]. It is a programmable device that measures and calculates the parameters of three-phase power networks. The power quality analyzer has nine input channels: five for AC voltages and four for AC currents, making it possible to measure the RMS values of voltage and current for the three phases and the neutral conductor. The measurement results are saved at selected intervals (the minimum measurement time is half the period of the voltage/current waveform) to a memory card (2 GB) and can then be transferred to a computer for further analysis. Measurements were taken at the output terminals of the agricultural biogas plant over a period of one week in accordance with the recommendations of EN 50160:2010 [39].

3. Results and Discussion

A summary of the analysis results of the active and three-phase reactive power levels generated by the agricultural biogas plant is shown in Figure 1 and Figure 2, respectively, while Figure 3 shows the corresponding power factor variation.
The change in the value of active power generated in the biogas plant was mainly caused by the operation of the mixer installed in the digester (the mixer had a power of about 15 kW) and caused analogous changes in the recorded waveforms of reactive power and power factor. It is worth highlighting that the biogas plant did not reach its rated power at the recording time. This was most likely caused by the power consumption of the individual electrical devices of the biogas plant and the losses occurring in their current paths. The waveform shown in Figure 3 shows the biogas plant’s failure to meet the requirement for a power factor value tg ϕ, which should be between 0 and 0.4 [34], and on many occasions, took values several times higher than required. The power generated in the agricultural biogas plant was produced with a power factor tg ϕ between −0.3 and −0.55. When the agitator was switched on, this value dropped to around −1. This was mainly due to a delay in the response of the compensation system installed in the biogas plant. The higher value of the three-phase apparent power recorded at the agricultural biogas plant under study (compared with the active power—Figure 1) shown in Figure 4 was due to including the generated reactive power in the analyzed waveform—Figure 2.
Analyzing the recorded voltage waveforms (Figure 5), it is possible to notice a cyclical pattern of changes in its values. The lowest voltage values occur when the power system experienced maximum loads (the afternoon peak). The statistical analysis (Figure 6) showed that for most of the recording time, the phase-to-phase voltage value was between 410 and 430 V. Voltage decreases were accompanied by voltage deviation values (Figure 7). The high variability of the recorded voltage values (from about 210 V to more than 250 V) can cause equipment malfunction sensitive to supply voltage changes. A solution to this problem can be provided by introducing energy through renewable energy sources when the lowest voltage occurs. As these are usually in the evening hours, a biogas plant that can produce energy regardless of the time of day and weather conditions would be the most effective for regulation.
In the case of the waveform of the voltage asymmetry factor (Figure 8), certain repeatability can also be observed. The maximum values usually occurred in the afternoon, while the minimum was recorded during the night hours. An asymmetry in the voltage values in the individual phases is also noticeable (the recorded waveforms do not overlap). This can cause incorrect operation of some equipment (especially rotating machinery). Voltage asymmetry values were mostly between 0.2 and 0.6% (Figure 9) and were more than three times lower than the values required by European regulations.
The asymmetry of the current generated in the biogas plant was more significant than the voltage asymmetry but, in most cases, did not exceed 12% (Figure 10), usually taking values between 4 and 8% (Figure 11). Such high values of current asymmetry were due to the amount of single-phase equipment installed and operating in the biogas plant (mainly water and gas pumps), causing phase load imbalance.
By comparing the voltage distortion of the waveform generated at the biogas plant to the sinusoidal waveform, it can be seen that the permissible values of the 9th, 15th and 21st harmonics (Figure 12) were not met. The total voltage distortion factor values recorded at the biogas plant (Figure 13 and Figure 14) also varied in the diurnal system, with minimum values occurring at night and peaks in the afternoon (usually around 3 p.m.). This was due to the operation of non-linear loads (drawing current from the grid distorted from the sinusoidal waveform) in the analyzed power system.
Table 2 shows the correlation coefficients between the apparent power generated by the agricultural biogas plant under study and the voltage U, voltage asymmetry factor kU2, current asymmetry factor kU2 and voltage distortion factor THDU. The best correlations were observed using the r-Pearson and Spearman coefficients.
Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20 show the correlation between the analyzed quantities describing the quality of the electricity generated at the agricultural biogas plant under study and the apparent power generated. As expected, voltage values were increased as the generated power increased (Figure 15). The low value of the correlation coefficient was mainly due to the occurrence of voltage drops during the operation of the agitator in the digester.
However, no correlation was observed between the voltage asymmetry factor values and the generated power (Figure 16). This means that the value of the short-circuit power at the point of connection of the agricultural biogas plant was sufficiently large that the generation of approximately 40 kVA (despite the current asymmetry registered at the biogas plant) did not affect the voltage asymmetry in the grid. Therefore, the over-recorded voltage asymmetry was an “incoming” asymmetry from the electricity grid and may have resulted from asymmetrical loading of the individual phases of the line to which the biogas plant under study was connected.
As can be seen from Figure 17 and Figure 18, as the power generated in the agricultural biogas plant increased, the value of the current asymmetry factor and the voltage distortion (THDU) decreased. The decrease in the value of the kI2 coefficient was mainly due to an increase in the ratio between the power generated by the turbogenerators and the power consumed by the single-phase equipment operating in the biogas plant. The fact that the agricultural biogas plant did not introduce distortions in the supply voltage waveform can be seen from the waveform shown in Figure 18. As the generated power increased, the value of the THDU coefficient decreased. The noticeable scatter in the recorded values was mainly due to the digester mixer’s operation, and the greater the ratio between generated power and mixer power, the smaller the scatter.
As expected, the correlation between the voltage deviation value and the power generated in the agricultural biogas plant (Figure 19) was the same as the corresponding correlation of the voltage values. The correlation was increasing. Similarly, the values of the power coefficient behaved similarly, clearly increasing with increasing apparent power generated (Figure 20). The significant reduction in the tgφ value (to nearly −1.2) was due to the operation of the digester mixer. When the agitator is not running, the tgφ is closer to the regulatory required values (−0.4). Even then, an apparent increase in the value of this coefficient can be seen as the generation in the biogas plant increased.
Table 3 shows the descriptive results of the statistical analysis of the waveforms recorded at the agricultural biogas plant. The highest standard deviation value (expressed as a percentage of the mean value) was observed for the voltage asymmetry factor. This was primarily due to the fact that the value of this coefficient was mainly influenced by loads connected to the same line as the biogas plant, whose total variability in time was low. Above all, it is essential to draw attention to the high value of the maximum voltage distortion factor, which far exceeded the values permitted by European regulations. During such a high voltage distortion, malfunctions may occur in some types of equipment, especially those using rotating electromagnetic fields. Nevertheless, the duration of the exceedances during the recording week was short, as evidenced by the calculated mean and median values.
In summary, of the analyzed parameters of the energy produced at the agricultural biogas plant, all the requirements of the current regulations for power quality parameters were not met. A non-fulfilment of the voltage distortion requirements from the sinusoidal waveform was observed. The recorded maximum value of the total voltage distortion coefficient THDU was more than 1.6 times higher than the value required by current regulations [39,40,41]. These exceedances were correlated with the voltage drops occurring in the power network. A similar situation occurred for the voltage’s 9th, 15th and 21st harmonics. The operation of the biogas plant caused an increase in voltage at its connection point. The measurements show that the voltage was kept near the upper limit regulations allow. Switching on the digester mixer reduced generation by almost half, resulting in a drop in voltage values. Switching off the agitator drive caused the voltage value to rise again, and this cycle was repeated many times a day. The cyclic, step-by-step changes in voltage generated on the farm can negatively impact the quality of electricity produced and the durability of consumer equipment. The changes were most noticeable in the intensity of the farm’s lighting and can lead to malfunctioning voltage-sensitive electronic equipment, ultimately resulting in deactivation or damage. An increase in the power generated by the agricultural biogas plant increased the voltage value and the power factor, tgφ, occurring at its connection point. In doing so, a slight reduction in the value of the recorded voltage distortion and current asymmetry coefficients was noticeable. The operation of the analyzed agricultural biogas plant did not change the value of the voltage asymmetry factor, mainly due to the low ratio of the power generated in the gas generator to the short-circuit power occurring at the connection point of the biogas plant.

4. Conclusions

A biogas plant caters to a farm’s energy needs and produces surplus energy that can be sold for profit. Furthermore, using digestate as a valuable fertilizer reduces the cost of procuring artificial fertilizers necessary for optimal crop growth. Access to in-house energy resources enhances the profitability of livestock farming while reducing the operational expenses of the farm. Research findings demonstrate that agricultural biogas plants do not significantly disrupt the power grid, although voltage quality parameters are primarily affected upon activating the fermentation mass mixer. To maintain the required power factor range, fast-changing thyristor compensation systems or more expensive active filters may need to be incorporated. Consideration should also be given to installing several agitators in the digester with lower specific power and designing their cycles so that one agitator is always running (alternating with the others). This will avoid power and voltage variations in the system resulting from the operation of the mixer. The above solutions can be applied to all small-scale agricultural biogas plants equipped with a single digestate agitator, regardless of location.

Author Contributions

Conceptualization, M.T.; methodology, M.T.; software, M.T.; validation, M.T.; formal analysis, M.T.; investigation, M.T.; resources, Z.S. and M.T.; data curation, Z.S. and M.T.; writing—original draft preparation, Z.S. and M.T.; writing—review and editing, Z.S. and A.B.; visualization, Z.S.; supervision, A.B.; project administration, M.T.; funding acquisition, M.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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  40. Regulation of the Minister of Economy of 4 May 2007 on Detailed Conditions for the Operation of the Electricity System. Available online: https://isap.sejm.gov.pl/isap.nsf/DocDetails.xsp?id=wdu20070930623 (accessed on 4 June 2023).
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Figure 1. Recorded course of the variation in three-phase active power values generated in an agricultural biogas plant.
Figure 1. Recorded course of the variation in three-phase active power values generated in an agricultural biogas plant.
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Figure 2. The recorded waveform of the variation in three-phase reactive power values generated at an agricultural biogas plant.
Figure 2. The recorded waveform of the variation in three-phase reactive power values generated at an agricultural biogas plant.
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Figure 3. The recorded waveform of the variation in the power factor value tgφ.
Figure 3. The recorded waveform of the variation in the power factor value tgφ.
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Figure 4. The recorded course of variation in the value of three-phase apparent power generated in an agricultural biogas plant.
Figure 4. The recorded course of variation in the value of three-phase apparent power generated in an agricultural biogas plant.
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Figure 5. Recorded waveform of voltage variation at the biogas plant.
Figure 5. Recorded waveform of voltage variation at the biogas plant.
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Figure 6. Distribution of voltage values recorded at the agricultural biogas plant under study.
Figure 6. Distribution of voltage values recorded at the agricultural biogas plant under study.
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Figure 7. Voltage deviation variation waveform recorded at the biogas plant.
Figure 7. Voltage deviation variation waveform recorded at the biogas plant.
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Figure 8. The voltage asymmetry factor value variation waveform was recorded at the biogas plant.
Figure 8. The voltage asymmetry factor value variation waveform was recorded at the biogas plant.
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Figure 9. Distribution of voltage asymmetry values recorded at the agricultural biogas plant under study.
Figure 9. Distribution of voltage asymmetry values recorded at the agricultural biogas plant under study.
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Figure 10. The recorded waveform of the variation in the current asymmetry factor at the biogas plant.
Figure 10. The recorded waveform of the variation in the current asymmetry factor at the biogas plant.
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Figure 11. Distribution of current asymmetry values recorded at the studied agricultural biogas plant.
Figure 11. Distribution of current asymmetry values recorded at the studied agricultural biogas plant.
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Figure 12. Voltage harmonic distribution recorded at the biogas plant.
Figure 12. Voltage harmonic distribution recorded at the biogas plant.
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Figure 13. The total voltage distortion coefficient THDu variation waveform was recorded at the biogas plant.
Figure 13. The total voltage distortion coefficient THDu variation waveform was recorded at the biogas plant.
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Figure 14. Distribution of total voltage distortion coefficient values recorded at the agricultural biogas plant under study.
Figure 14. Distribution of total voltage distortion coefficient values recorded at the agricultural biogas plant under study.
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Figure 15. Correlation between voltage values and apparent power recorded at an agricultural biogas plant.
Figure 15. Correlation between voltage values and apparent power recorded at an agricultural biogas plant.
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Figure 16. Correlation recorded at an agricultural biogas plant between voltage asymmetry values kU2 and apparent power.
Figure 16. Correlation recorded at an agricultural biogas plant between voltage asymmetry values kU2 and apparent power.
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Figure 17. Correlation recorded at an agricultural biogas plant between the values of current asymmetry kI2 and apparent power.
Figure 17. Correlation recorded at an agricultural biogas plant between the values of current asymmetry kI2 and apparent power.
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Figure 18. Correlation recorded at an agricultural biogas plant between THDU voltage de-ratio values and apparent power.
Figure 18. Correlation recorded at an agricultural biogas plant between THDU voltage de-ratio values and apparent power.
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Figure 19. Correlation recorded at an agricultural biogas plant between voltage deviation values and apparent power.
Figure 19. Correlation recorded at an agricultural biogas plant between voltage deviation values and apparent power.
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Figure 20. Correlation recorded at an agricultural biogas plant between power factor values tgφ and apparent power.
Figure 20. Correlation recorded at an agricultural biogas plant between power factor values tgφ and apparent power.
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Table 1. Impact of the wind turbine on farm supply voltage values.
Table 1. Impact of the wind turbine on farm supply voltage values.
Internal Combustion Engine
Engine typeWG1605
CycleOtto
Number of cylinders4
Speed2700 rpm
Rated active power20 kW
Nominal apparent power26 kVA
Primary energy consumption62.5 kW
Electrical efficiency32%
Total efficiency97%
Thermal power40.9 kW
Maximum flue gas temperature110 °C
Rated voltage400 V
Rated current29 A
Power factor cos ϕ rated0.97
Generator
TypeAsynchronous 4P/IE2
Rated speed1500 rpm
Rated frequency50 Hz
Rated voltage3 × 400 V
Winding connectiontriangle
Table 2. Correlation coefficients between selected quantities recorded at the studied agricultural biogas plant.
Table 2. Correlation coefficients between selected quantities recorded at the studied agricultural biogas plant.
VariableApparent Power S
Pearson CorrelationsSpearman Rank Order CorrelationsGamma CorrelationsKendall Tau Correlations
Voltage U0.3633760.3908000.2959680.295949
Voltage deviation ΔU0.3627250.3903000.2955350.295524
Power factor tgφ0.5859010.4607400.3137090.313709
Voltage asymmetry factor kU20.011067−0.015419−0.009762−0.009762
Current asymmetry factor kI2−0.268349−0.270219−0.179850−0.179850
Voltage distortion factor THDU−0.347478−0.284441−0.197056−0.196958
Marked correlations were significant at p < 0.05000
Table 3. Summary of results of statistical analysis of selected electrical quantities recorded at the biogas power plant under study.
Table 3. Summary of results of statistical analysis of selected electrical quantities recorded at the biogas power plant under study.
Voltage U
[V]		Voltage Asymmetry Factor kU2
[%]		Current Asymmetry Factor kI2
[%]		Voltage Distortion Factor THDU
[%]		Apparent Power S
[kVA]
Valid N99989998999899989998
Mean417.81390.35125.61344.245435.6261
Median420.66520.32865.36024.143336.9863
Minimum366.39670.02120.90052.533326.8018
Maximum435.48281.117117.777910.436742.2088
Lower Quartile410.71670.24374.25373.236731.9492
Upper Quartile427.22630.44546.67715.091437.7431
Std. Dev.11.99510.14921.85681.05423.4882
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Tymińska, M.; Skibko, Z.; Borusiewicz, A. The Effect of Agricultural Biogas Plants on the Quality of Farm Energy Supply. Energies 2023, 16, 4600. https://doi.org/10.3390/en16124600

AMA Style

Tymińska M, Skibko Z, Borusiewicz A. The Effect of Agricultural Biogas Plants on the Quality of Farm Energy Supply. Energies. 2023; 16(12):4600. https://doi.org/10.3390/en16124600

Chicago/Turabian Style

Tymińska, Magdalena, Zbigniew Skibko, and Andrzej Borusiewicz. 2023. "The Effect of Agricultural Biogas Plants on the Quality of Farm Energy Supply" Energies 16, no. 12: 4600. https://doi.org/10.3390/en16124600

APA Style

Tymińska, M., Skibko, Z., & Borusiewicz, A. (2023). The Effect of Agricultural Biogas Plants on the Quality of Farm Energy Supply. Energies, 16(12), 4600. https://doi.org/10.3390/en16124600

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