MODELING AND ANALYZING THE EFFECT OF CONNECTION TO THE NETWORK OF A HARMONIC SOURCE HAVING VARIOUS TOTAL HARMONIC DISTORTION FACTORS ON LOAD SIGNAL WAVEFORMS

This article examines the effect of a network connected source of harmonics having a total harmonic distortion factor varying from 5% to 15% on load voltage and current waveforms. When a source of higher harmonics is connected to the network, both in the network and in the load, the effective values of voltage and current increase, that can negatively affect the cable line insulation, accelerating its destruction and aging. To analyze the consequences of a power quality deterioration, a 20 kV network was simulated, consisting of a 20 kV symmetrical generator, an XRUHAKXS-20(1x120/50) power cable line 20 km long, a step-down transformer 20/0.4 kV with a power of 2 MVA, with windings connected in delta-star, and a three-phase symmetrical load. The values of the currents flowing through the cable conductor, obtained as the result of simulation were used to calculate the voltage drop between the cable conductor and its shield. Results obtained show that the connection of a harmonic distortion source to a network leads to a magnification of a current flowing through the cable conductor by more than 2%. The model proposed in the article can be used further for a more detailed study of solar photovoltaic plants connection to the grid. One of the biggest problems regarding solar power plants is that its electricity generation is intermittent. Thus, future efforts should be focused on modeling and studying the higher harmonics generation during switching on and off of the solar photovoltaic plants.

To analyze the consequences of a power quality deterioration, a 20 kV network was considered, consisting of a 20 kV symmetrical generator, an XRUHAKXS-20(1x120/50) power cable line 20 km long, a step-down transformer 20/0.4 kV with a power of 2 MVA, with windings connected in delta-star, and a three-phase symmetrical load. The scheme diagram is shown below in Fig. 1. The electric network simulation was performed with a help of MATLAB® and Simulink® software [10,11]. The obtained voltage and current waveforms are shown in Fig. 2, Fig. 3 and Fig. 4. The graphs show only linear values. . Fig. 4-b. Renewable energy is a relevant and important energy industry, the role of which is growing every year around the world. However, as noted above, an increase in the number of connections of solar photovoltaic cells to the power grid can have an impact on the quality of electricity in the network, and the importance of improving the quality of electricity remains an urgent problem for both electricity producers and consumers, which is especially acute in low voltage networks. The occurrence of non-sinusoidal currents and voltages, voltage unbalance and its fluctuations are associated with a low power factor of non-linear loads on the part of consumers and a high level of current harmonics generated by solar photovoltaic inverters in a low voltage network on the part of electricity producers.  Figure 5 shows the scheme diagram, where a harmonic source is connected to the network from the high voltage side with a total harmonic distortion factor of 5% and a voltage of 20 kV, at the output of which one obtain a non-sinusoidal symmetrical signal, shifted between phases by 120 degrees with the same harmonic content for each of the phases. Three-phase symmetrical voltage with the same harmonic content for each phase of a non-sinusoidal signal with a 20 kV voltage is supplied to the output of the unit, obtained by adding two sinusoids to facilitate observation and control of the influence of a non-sinusoidal signal on a sinusoidal signal in the network. Changes in the 20 kV network will be studied at non-sinusoidal coefficients (total harmonic distortion factor) of 5%, 8% and 15%. In its turn, the obtained voltage and current waveforms are shown in Fig. 6, Fig. 7 and Fig. 8.
According to the results of the virtual experiment, it can be seen that the non-sinusoidal voltage increased due to the connection of a non-sinusoidal power source with a 5% total harmonic distortion factor. According to the graphs, at point after the power line, the non-sinusoidal voltage is increased, and the non-sinusoidal current is decreased. Changes are observed throughout the network, the effective values of line voltages have also changed. Specifically, generator voltage is increased by 170.0 V that is 0.87% greater than at a pure sinusoidal waveform; voltage at the end of line is increased by 190.0 V that is 1.0% greater than at a pure sinusoidal waveform; and finally, load voltage is increased by 3.9 V that is 1.05% greater than at a pure sine wave.
Model in Fig. 5 was used for simulation at 8% total harmonic distortion factor. Simulated voltage and current waveforms obtained in symmetrical network with a connected source of harmonics having an 8% total harmonic distortion factor are shown in Fig. 9, Fig. 10 and Fig. 11. Above plots show an increase in the harmonic content. The changes are more significant than when connecting a source with a total harmonic distortion factor of 5%, the effective values of the line voltages also have changed. Specifically, generator voltage is increased by 180.0 V that is 0.92% greater than at a pure sine wave; voltage at the end of line is increased by 310.0 V that is 1.64% greater than at a pure sine wave; load voltage is increased by 5.6 V that is 1.51% greater than at a pure sinusoidal voltage waveform.
In practice voltage total harmonic distortion factor is rarely higher than 15%. Therefore, such a case is of rather theoretical interest. Simulated voltage and current waveforms obtained in symmetrical network with a connected source of harmonics having a 15% total harmonic distortion factor are shown in Fig. 12, Fig. 13  According to Fig. 12, Fig. 13 and Fig. 14, generator voltage is increased by 200.0 V that is 1.02% greater than at a pure sinusoidal waveform; voltage at the end of line is increased by 790.0 V that is 4.17% greater than at a pure sinusoidal waveform; and finally, load voltage is increased by 12.5 V that is 3.38% greater than at a pure sine wave. The simulation results are summarized in Table I. Since the harmonic issue is one of the most important in power systems, it is important to estimate harmonics risk to cable insulation, shortened life, etc. For a cable line with a given line length of 20 km, a shield grounding scheme with a full transposition cycle was chosen (refer to Fig. 15).

Figure 15 -Cable shield grounding scheme with a full transposition cycle.
Internal cable design is shown in Fig. 16. The values of the currents flowing through the cable conductor, obtained from the simulation above, were used to calculate the voltage drop between the cable conductor and its shield. The calculation results are presented in Table II. According to Table II, the connection of a non-sinusoidal distortion source leads to a magnification of a conductor current by more than 2%. According to experimental measurements presented in [12], the current distortions caused by photovoltaic inverters may reach up to 2% of fundamental frequency current. Following expressions were used for computation.
Longitudinal linear resistance between the conductor and the cable screen (Ω/m) is given as follows: (1) In expressions (1) = N is a number of transposition cycles. Power electronic converters or inverters that do not create pure sinusoidal signals and are components in electricity generation by power plants based on non-traditional renewable energy sources, such as solar power plants, generate harmonics into the system when connected to a low voltage network. With an insignificant power capacity of such power generating installations, they do not cause significant distortions in the waveform of the voltage and current of the general power system into which the generation takes place. But with an increase in the power capacity of these power generating installations, when it becomes commensurate with the power of the general power system, distortions in the waveform of the voltage and current of the general network, which may occur, should be the subject of further study.
Conclusions. This article examines the effect of a network connected source of harmonics having a total harmonic distortion factor varying from 5% to 15% on load voltage and current waveforms. When a source of higher harmonics is connected to the network, both in the network and in the load, the effective values of voltage and current increase, which can negatively affect the cable insulation, accelerating its destruction and aging. Results obtained show that the connection of a harmonic distortion source to a network leads to a magnification of a current flowing through the cable conductor by more than 2%. The model proposed in the article can be used further for a more detailed study of solar photovoltaic plants connection to the grid. One of the biggest problems regarding solar power plants is that its electricity generation is intermittent. Thus, future efforts should be focused on modeling and studying the higher harmonics generation during switching on and off of the solar photovoltaic plants.