Modeling non-linear loads for low-voltage electric grids

The authors performed the computer modeling of a power distribution grid section comprising a significant non-linear and asymmetric household and office load. The modeling was performed using the SimInTech software. The developed model was used to study the impacts that non-linear single-phase consumers (e.g. computers, printers, TV sets, microwave ovens, etc) have on the distortion of current and voltage curves in the grid and the formation of current in the transformer neutral. The authors demonstrate the dependency between the higher harmonic values of the phase and transformer neutral currents and the total non-linear consumer power, their share in the overall power substation load, and the distribution of non-linear consumer load across the substation feeders. To reduce the level of harmonic current components, the authors suggest using narrow-band passive higher harmonic filters. A computer model was developed for the simultaneous operation of a single-phase non-linear load and a four-link filter compensating device that comprises the filters set for the frequencies of the third, fifth, seventh, and ninth harmonics. The analysis of the non-sinusoidal operating modes of the grids with -harmonic filters connected showed that there is practically no current in the neutral while the distortion factors of the phase currents and grid voltage curves are at the minimum.


Introduction
The extensive introduction of digital technology in all areas of human activity leads to an increase in non-linear loads outside of the industrial sector.The majority of computers and office equipment and household consumers (TV sets, microwave ovens, etc) can be classified as non-linear electrical loads that create distortions in 0.4 kV electrical grids [1,2,3].Modern lighting systems are also sources of harmonic distortions for the current consumed from the grid.
When the power consumption of non-linear consumers is below 10-15%, the operation of the power supply system can operate as usual.When this limit is exceeded, it leads to various problems.Specific problems may become evident immediately in buildings where non-linear loads amount to over 25% [4,5,6].
Harmonics generated by non-linear loads lead to additional power losses due to the hysteresis effect and local currents in power transformers, which, in its turn, leads to the excessive heating and overheating of the transformer and the reduction of the service life of the insulation [7].The service life of the transformer depends on the heating of its components, and the presence of non-sinusoidal currents prevents the transformer to produce its rated power, as it has to be reduced.Harmonics generated by non-linear loads cause the premature wear of insulation as the operating temperature of the conductors rises, as well as the overheating and destruction of zero conductors in cable lines due to their overload with third harmonic currents [8,9,10].When the current is non-sinusoidal, the operating conditions of static capacitor batteries deteriorate [11], and the operation of the power system protection devices is disrupted (or aggravated) because the digital relays and algorithms based on the analysis of data sampling or zero-crossing are especially sensitive to harmonics [12,13].Unsinusoidality also reduced the accuracy of operation and therefore the reliability of electrical meters and devices.TV sets may show distorted images and use improper brightness.Distortions in the grids that supply power to computers and data processing systems are also possible.If higher harmonics are present in 0.4 kV electric grids, there is a risk of resonant phenomena that can have a negative impact on the operability of specific elements and components of the system [14,15].
Recently, there has been an increase in publications and development aiming to reduce the level of higher harmonics in 0.4 kV grids.Nevertheless, this problem still lacks a comprehensive solution.Compensating for the higher harmonic components using various higher-harmonic filters is one of the most efficient methods of improving the quality of electric power in 0.4 kV grids [16].Rational selection of filter types, as well as the number of filter links and their settings, have to be performed during the design and operation of an electric grid with higher-harmonic filters, along with the assurance of the best operating modes for the grid in terms of minimizing additional power losses and maintaining the voltage levels within the set limits [17,18,19,20,21].
The solution to these problems can be facilitated by the usage of a computer model for a 0.4 kV distribution grid comprising asymmetrical and non-linear loads, as well as filter compensating devices [22,23].
This article presents the results of modeling a section of a 0.4 kV power grid with a non-linear load in the SimInTech software.

Modeling a power grid section with a non-linear load
We studied a simplified 220 V power supply modeling diagram as the non-linear consumer (figure 1).The power supply comprised a rectifier, a smoothing capacitor, and an active load.We could connect any number of power supply modules.
The three-phase power supply feeds a 10 kV line that energizes a three-phase double-winding 10/0.4 kV transformer with a power rating of 100 kVA.The power rating of the three-phase load is 30 kW.The consumers were distributed symmetrically across the phases.We used a diode rectifier.The smoothing capacitor was selected to assure a ripple factor of 5%.

Figure 1. The structural diagram of the grid in question
We used the model to analyze the impact the consumers have on the distortion of phase current and voltage curves, as well as the current in the transformer neutral.We assessed how the grid reacted on a non-linear load of three, thirty, and sixty consumers with the same power rating that were distributed symmetrically across the phases.In this article, we review the results for the third and fifth harmonics because they have a greater significance compared to the higher-order harmonics.Figure 2 shows a diagram for the relative value of these harmonics (Ch factor) depending on the number of non-linear consumers.The results of modeling a grid with three consumers show that the usage of non-linear consumers had a great impact on the harmonic composition of the current.Some fuzzy harmonics appeared on the low-voltage side of the transformer.The value of the fifth harmonic reached 4.5% (the GOST standard allows up to 6%).When the load is absolutely symmetrical, the third harmonic current with an amplitude close to the rated value appears in the transformer neutral.The transformer load in this case was assumed to be 30%.
As the number of consumers increased from three to thirty, the third-order current harmonic increased by 4%, while the fifth-order harmonic increased by 12%.However, the harmonic composition of voltage did not change.When the number of consumers increased to sixty, the voltage sine wave did not receive any extra distortions, and the harmonic composition of current increased by 4% for the third harmonic and 3% for the fifth harmonic.

Modeling a grid section with a mixed load
Figure 3 shows the diagram of the modeled grid with a mixed load (both linear and non-linear).The linear load is represented as an active resistance.We used this model to analyze the changing of the harmonic components of current and voltage against the varying proportion of the non-linear and linear loads and the same transformer load.We reviewed the situations where the transformer neutral was grounded through the resistance or a fixed connection.To build the 0.4 kV line, we used the SIP-4 4х95 wire.The overall load power was the same and it amounted to 60 kW, while the power rating of the transformer reached 100 kVA.The distribution of the load across the phases was uneven: the load of phase A was 25 kW, phase B -20 kW, and phase С -15 kW.
We analyzed the distortion of the phase current and neutral current depending on the share of nonlinear consumers within the load.Figure 4 shows a diagram of the relative values of the third and the fifth harmonics (Ch factor) depending on the proportion of non-linear consumers in the load (13% and 50%).Additionally, it shows the results for the situation when one of the three feeders only has a linear load, while two others have a non-linear load.The spectral analysis of the neutral current and the phase current was carried out for the most remote linear consumer.The analysis showed that as the share of non-linear load increases, neutral and phase current sine waves become distorted on the low-voltage side of the transformer, while the amplitude of the current increases in each of the phases.When the share of non-linear load is 50%, the amplitude increases by two times.If the grid with a non-linear load third harmonic fifth harmonic 3 consumers 30 consumers 60 consumers of 30 kW is connected to a linear load of the same rating, the fuzzy harmonic currents in the transformer reduce significantly.A high-power non-linear consumer or multiple low-power consumers that use a greater total power impact the operating parameters of the transformer, as well as the remote linear consumers connected to the same power grid.Figure 5 shows the oscillogram of the transformer neutral current for the situation when the share on the non-linear load is 13% and Figure 6 shows the current oscillogram on the 10 kV side of the

Modeling a power grid section with a non-linear load and passive filters
The installation of three-phase narrow-band passive higher harmonic filters helps reduce the adverse distortions of phase currents and voltages in the grid, as well as the transformer neutral current.Figure 7 shows the diagram of the grid model with a non-linear single-phase load and passive filters set for the third, fifth, seventh, and ninth harmonics.The filter capacity was selected based on the current value of the respective harmonic.The results of the analysis (including the overview of the oscillograms) demonstrate that the usage of a narrow-band filter helped compensate for the harmonics of the third, fifth, seventh, and ninth order on the high-voltage and low-voltage sides of the transformer substation.This helps assure the normal operation of the transformer and, consequentially, the quality of electric power in terms of unsinusoidality in a 10 kV grid.The amplitude of the current in the neutral was reduced by 12 times in this case.

Conclusion
In this work, we obtained the following results: • A digital load model was developed in the Simintech software.
• We analyzed the potential consequences of higher harmonics in a 0.4 kV distribution grid powered from a 10/0.4kV transformer substation.

Figure 2 .
Figure 2. Harmonic component factors when the power rating of non-linear consumers changes.

Figure 3 .
Figure 3.The structural diagram of the grid with a mixed load.

Figure 4 .
Figure 4. Harmonic component coefficients under the uneven distribution of the non-linear consumer load.
feeders have a non-linear load APITECH-V-2023 Journal of Physics: Conference Series 2697 (2024) 012075 transformer for the same situation.Both figures show current sine wave distortions on the low-voltage side of the transformer and the presence of the third-harmonic currents in the transformer neutral.

Figure 5 .
Figure 5.The current oscillogram for the transformer neutral (the share of the non-linear load is 13%).

Figure 6 .
Figure 6.The current oscillogram for the 10 kV side of the transformer (the share of the nonlinear load is 13%).

Figure 7 .
Figure 7.The structural diagram for the no-linear single-phase load and passive filters.

Figure 8
Figure8shows the oscillogram of the transformer neutral current for the situation with a non-linear load in three 10 kW consumers, and Figure9shows the current oscillogram on the 10 kV side of the transformer for the same situation.

Figure 8 .
Figure 8.The current oscillogram for the transformer neutral.

Figure 9 .
Figure 9.The current oscillogram for the 10 kV side of the transformer.