Measurement of currents and voltages non-sinusoidal parameters in power supply systems with rectifier load

The use of frequency-controlled electric drives in industry and municipal services is accompanied by the problem of their negative impact on the distribution network. As examples, the results of measurements of power quality indices in the power supply system of an oil producing enterprise and on the supply input of a railway traction substation are given. It is shown that the voltage subgroup total harmonic distortions (THDS) can exceed their rated permitted values in 100% of the measurement time.


Introduction
In industry and municipal services, the use of frequency-controlled electric drives is increasing. Frequency-controlled drives provide operation of own-use mechanisms at power plants, are used in traction substations of electrified transport, oil and gas production facilities, in water and heat supply systems. Their total capacity in the total load of the power supply system of the enterprise can be significant [1]. The application of frequencycontrolled drives allows to reduce power consumption and provides advantages in the operation of electric motors. But the use of frequency converters in them, consuming nonsinusoidal current, leads to the power quality deterioration in the power supply system.
Non-sinusoidal voltage is characterized by the voltage subgroup harmonic distortions KU(n) and the voltage subgroup total harmonic distortions (THDS) KU.. The results of the assessment of the power quality state in the electrical grids of the Russian Power System confirm that the highest levels of harmonic distortions are observed in electric grids feeding the electrified railway, oil and gas transportation and mining enterprises, metallurgical and aluminum enterprises [2][3][4][5].
The purpose of the work is to measure and analyze the current and voltage harmonic components in electrical networks with rectifying converter load and to assess the compliance of the power quality indices (PQI) KU and KU(n) with the rated values. The measurements were performed in the distribution network of the oil producing enterprise and at the 110 kV input of the railway traction substation. During the measurements, BINOM3 specialized devices were used. Devices BINOM3 are certified for compliance with the requirements of standards for measurement methods and norms for power quality [14][15][16][17][18]

Methods and results
The PQI measurements and statistical analysis algorithms are established in GOST 30804.4.7 and GOST 30804.4.30-2103 [14,15]. The phase voltages instantaneous values are measured on the main time interval equal to 10 periods of the industrial frequency. Using the Fourier Transform, the r.m.s. values of the 1 st -and n th -order voltage harmonics and the n th -order voltage harmonics distortions KU(n)i are calculated: where nis the harmonics order; U(n)iis the r.m.s. value of the n th -order voltage harmonic on the i-th main time interval (harmonic subgroups are applied); U(1)iis the r.m.s. value of the 1 st -order (fundamental frequency) voltage harmonic on the ith main time interval (harmonic subgroups are applied).
The voltage harmonic distortions are calculated on the aggregated time interval equal to 10 min, KU(n): • 100, % (2) where Nis the number of 10-period intervals (main time intervals) in the 10-minute interval (N = 3000).
The voltage THDS on the i-th main time interval equal to 10 periods of the industrial frequency, KUi, is calculated as the ratio of the r.m.s. value of the sum of all the harmonics up to the n th -order to the r.m.s. value of the fundamental frequency voltage: The voltage THDS on the aggregated time interval equal to 10 min, KU is: GOST 32144-2013 [15] establishes rated values for the voltage harmonics distortions and limits the range of harmonics to be considered 40 th . PQI measurement devices should provide the measurement of harmonics distortions of voltage and current to 50 th -order [15,19]. The current harmonics levels are normalized in foreign standards [20].
The type of the non-linear electric receiver and its operation modes stipulate the spectral composition of the current being consumed and the voltage spectrum due to the current harmonics flowing along the electrical network elements. The order of the higher harmonics of current consumed by the rectifier converters depends on the circuit and the number of phases of the converter and is determined by the formula: = ± 1 (5) Depending on the conversion scheme, a number of harmonics are compensated, their orders are determined by the formula: where pis the number of conversion phases, kis a natural number (k = 1, 2, 3, ...), nis the order of the harmonic. For example, for a three-phase bridge converter scheme (Fig. 1), p = 6 and are characterized by 5 and 7, 11 and 13, 17 and 19, 23 and 25, etc. harmonics in the consumed current. The measurements were performed in switchgear 6 kV of the power plant at the line feederbay towards the transformer substations. The odd harmonics of the 5 th and 7 th , 11 th and 13 th , 17 th -orders, characteristic of the three-phase bridge rectification scheme, are expressed in the spectrum of the current consumption (Fig. 2) in all phases. In the voltage spectrum (Fig. 3), harmonics of the same order as in the current spectrum are expressed, and additionally there are 3 rd and 15 th -orders harmonics.
Based on the results of measurements conducted during the week, it was recorded that in the busbar section of the power plant switchgear in 100% of the measurement time the normative levels of the THDS of voltage were exceeded (Fig. 4 -table 5).  The normative levels of the 5 th -and 7 th -, 11 th -and 13 th -, 17 th -orders characterizing of the three-phase bridge rectification scheme (Figure 4 -table 6) are violated. These frequencies are present in the currents spectrum, which may indicate the contribution of this load to the deterioration of the power quality of electrical energy. Exceeding the voltage harmonic distortions of the 3 rd and 15 th -order can be caused by the influence of other distorting receivers connected to the 6 kV busbars.
For the scheme with a series connection of two three-phase bridges (Fig. 5) p = 12. There are 11 th and 13 th , 23 rd and 25 th , 35 th and 37 th , 47 th and 49 th -order harmonics in the current. Such schemes are used in rectifier units of traction substations of the railway.  Taking into account formulas (5) and (6), the presence of the corresponding orders harmonics (11 th and 13 th , 23 rd and 25 th , 35 th and 37 th ) in the currents and voltages confirms the presence of a scheme with two three-phase bridges in the rectifier converter in the substation load. The voltage subgroup total harmonic distortions at frequencies present in the current and voltage spectrums go beyond the normative levels ( Fig. 8) established in [16]. Harmonic components of 3 rd , 5 th , 7 th order in the current consumed can indicate another distorting load receiving power at the substation input.  Based on the results of practical measurements containing arrays of values of the nth harmonic components of currents, voltages, and power, the actual contribution of the distorting receivers to the deterioration of the electric power quality at the point of common connection can be determined [21].

Conclusions
1. The results of measurements show that rectifier converters consume a current with a characteristic composition of harmonics, depending on the conversion scheme.
2. Using rectifiers reduces the quality of the network voltage. Voltage harmonic distortions can exceed standard and threshold permissible levels during 100% of the observation time.
3. It is necessary to carry out measures to reduce the influence of electric receivers with rectifier converters on the electric power quality