Abstract
List of contents
- Introduction
- 1. The main theoretical provisions
- 2. Higher harmonics. General information.
- 3. Calculation of the coefficients of the harmonic components of the voltage for a network with gate converters of different power
- 4. Analysis of the effect of harmonic voltage components on individual elements of the electrical system
- Conclusions
- List of sources
Introduction
Non-sinusoidal voltage manifests itself in distortion of the sine wave of the mains voltage, which is created by the appearance of higher harmonics in the network, i.e. voltage with a frequency above 50 HZ. Superimposed on the main frequency of the network, these harmonics create a distortion of the mains voltage curve. The appearance of higher harmonics in the network leads to the following undesirable consequences: increased heating of electrical equipment, interference with the operation of electronic control devices. Connections, etc. Higher harmonics are especially dangerous for capacitor banks and cable lines. Both of these elements of the power supply system have significant capacitive resistance, which decreases with increasing frequency of the voltage applied to them, therefore, the appearance of higher harmonics leads to an increase in current through these capacitances, resulting in increased heating of the insulation, which eventually leads to a sharp decrease in its service life. [4].
The non–sinusoidal voltage is estimated by 2 indicators of the quality of electricity: KU is the distortion coefficient of the sinusoidal voltage curve. KU(n) is the coefficient of the nth harmonic component. To calculate these 2 indicators, it is necessary to make measurements in the considered electrical network with a measuring device that can measure the values of higher voltage harmonics, starting from 2 to 40. In the range 2-40; 100 Hz – 2000. To obtain one KU value, measurements must be carried out within 3 seconds, the number of measurements must be at least 9.
The reasons for the indicators going beyond the norms are the use of various nonlinear electric energy receivers, such as:
-gate converters;
-power electrical equipment with thyristor control;
-arc and induction electric furnaces;
-fluorescent lamps;
-arc and contact welding installations;
-frequency converters;
-household appliances (computers, televisions, etc.).
During operation, these devices consume the energy of the fundamental frequency, which is spent not only on performing useful work and covering losses, but also on the formation of a stream of higher harmonic components that are "thrown out" into the external network.
The main influence is exerted by valve converters, which are currently widely used in industry and transport.
The most common gate converters based on semiconductors (thyristor converters), whose power is constantly growing.
Valve converters are widely used to convert alternating current into direct current and are used as power sources in metallurgical plants for thermal installations, in chemical plants and non-ferrous metallurgy enterprises for electrolysis plants, in machine-building and other enterprises for electric arc and contact welding installations.
1. The main theoretical provisions
To date, valve converters have become widespread in electrical systems, the advantages of which include lower energy losses, smaller dimensions, and ease of maintenance.
The use of gate converters can significantly degrade the quality of the mains voltage.
Non–sinusoidal voltage is a distortion of the sine wave of the mains voltage.
Figure 1.1 – Mains voltage sinusoids Higher voltage harmonics in the electrical network cause additional losses of active power, shortening the service life of equipment insulation, and difficulty compensating reactive power [2].
The power quality indicators [1] related to the harmonic components of voltage are:
a) the values of the coefficients of the harmonic components of the voltage up to the 40th order KU(n), %;
b) the total coefficient of the harmonic components of the voltage KU, %.
According to [1], the norm for the probability of 100% of the time is 1.5 times higher than the corresponding normalized values for the probability of 95%.
2. Higher harmonics. General information
The content of higher harmonics in a three-phase network leads to an increase in current in capacitors, since the reactance of capacitors decreases with increasing frequency.
Contamination of AC networks with higher harmonics can lead to the following consequences:
-reducing the service life of capacitors
-premature operation of protective equipment
-failure or erroneous operation of computers, motor drives, lighting devices, etc. sensitive consumers.
In parallel with the increase in current in capacitors, which can be regulated by constructive measures, in adverse cases, resonant phenomena may occur in networks. Compensating capacitors and inductors of the transformer and the network represent a resonant circuit. If the natural frequency of such a circuit coincides with the frequency of higher harmonics, then fluctuations with significant overcurrents and overvoltages may occur. This leads to reboots and damage to electrical installations.
The purpose of connecting the throttle (reactor) to the capacitor is to reduce the resonant frequency of the network to a value lower than the value of the lowest higher harmonic of this network. This prevents resonance between capacitors and the network, and hence an increase in currents of higher harmonics. In addition, such inclusion has a filter effect, which reduces the degree of voltage distortion. It is recommended in cases where the proportion of consumers polluting the network with higher harmonics is more than 20% of all network consumers.
The reason for the appearance of higher harmonics is the presence of consumers with nonlinear volt–ampere characteristics in the load.
Such consumers include converters based on semiconductor elements, electric welding installations, electric arc furnaces, light sources with gas-discharge lamps, high-voltage power transformers and autotransformers, as well as high-voltage motors. The peculiarity of these devices is that they generate currents of higher harmonics when connected to the terminals of a source with a sinusoidal voltage.
An example is the current curve of a valve converter shown in Figure 2.1.
Any complex harmonic oscillations, i.e. non-sinusoidal current curves, should be considered in such a way that they seem to consist of a combination of some harmonic oscillations of different frequencies.
On the other hand, any periodic function of time satisfying Dirichlet conditions can be represented as a trigonometric Fourier series
where A0 is a certain constant component;
n is the harmonic number of the curve;
an bn are the coefficients of the Fourier series.
For n = 1, the fundamental harmonic is determined by the expression. In another way, it is called the first harmonic.
Then the remaining members of the series (n > 1) will be the higher harmonics.
Figure 2.1 – Curves of the electromotive force (EMF) of the power supply e, terminal voltage and current i of the valve converter To determine the coefficients of the Fourier series, there are formulas:
The amplitude of the nth harmonic is determined from the following expression
the initial phase of the nth harmonic is determined by the formula
Obviously, currents of higher harmonics, as well as the first one, cause voltage drops in the resistances of devices connected to our network. Obviously, these currents of higher harmonic components will be superimposed on the main harmonic. As a result, the shape of the voltage curve on the network elements is distorted (curve and in Figure 2.1). The degree of non-sinusoidal voltage of this network is characterized by the coefficient of non-sinusoidal voltage. This coefficient is the ratio of the equivalent effective value of the voltages of the higher harmonics to the voltage of the first harmonic, which is expressed as a percentage of the voltage of the first harmonic:
where Un , U1 are the effective values, respectively, of the nth and fundamental voltage harmonics
3. Calculation of the coefficients of the harmonic components of the voltage for a network with gate converters of various capacities
In addition to the non-sinusoidal coefficient, GOST normalizes the coefficients of the nth harmonic component [1].
When determining kU, special attention should be paid to the cpr. Most often, it is required to determine kU on the power supply buses of high-power thyristor converters. A converter means a rectifier bridge (or a group of them) and a supply step-down transformer [3].
In this case, the cpr is equal to the resistance of the converter transformer and is determined by the formula:
where Sn,T is the rated power of the converter transformer;
kp is the splitting coefficient of the windings of this transformer;
ir% is the through–circuit voltage of the transformer, reduced to the full rated power of the transformer.
For two-winding transformers used in six-phase (three-phase bridge) rectification circuits, kp=0, three-winding transformers used in converters made according to a twelve-phase circuit, in general
where iR(nh1-nh2) is the short–circuit voltage between the secondary windings of the transformer.
In general, for transformers with split windings, kr = 0/4, if the low voltage branches of the transformer have good electromagnetic coupling with each other, kr = 0; if the NN windings do not have magnetic coupling with each other or the converter is made according to a scheme with two transformers having different connection schemes, then kr = 4.
The effective value of the highest harmonic voltage at any point of the supply network when the converter is operating with any sequence of alternating phases of rectification can be determined by the formula:
where
switching angle,rad.
The effective current value of any harmonic in the converter circuit is determined by:
When working with a group of valve converters, the order of calculation of kU is as follows. According to the above formulas, the levels of higher voltage harmonics for each converter are determined.
The same voltage harmonics of all converters are geometrically summed up.
Then the coefficient of non-sinusoidality is determined:
Special attention should be paid to the number of harmonics taken into account in order to avoid errors in calculating kU. The more converters and rectification phases there are, the more harmonics must be taken into account. The following empirical formula is proposed:
where nmax is the largest harmonic;
q is the number of working converters;
m is the number of rectification phases.
4. Analysis of the effect of harmonic voltage components on individual elements of the electrical system
After the sources of harmonics have been identified and their levels have been determined, it is necessary to find out the nature of the influence of harmonics on the operation of electrical equipment. All elements of power supply systems should be considered in terms of their sensitivity to harmonics. Based on this review, recommendations are then developed on acceptable harmonic levels in networks.
The main forms of influence of higher harmonics on power supply systems are: an increase in harmonic currents and voltages due to parallel and sequential resonances; a decrease in the efficiency of the processes of generation, transmission and use of electricity; aging insulation of electrical equipment and a reduction in its service life as a result; false operation of equipment.
Resonances. The presence of capacitors in networks used to compensate for reactive power can lead to local resonances, which, in turn, can cause an excessive increase in current in the capacitors and their failure.
Parallel resonance occurs due to the high resistance to current harmonics at the resonant frequency. Since most harmonics are generated by current sources, this causes an increase in the voltage of the harmonics and their large currents in each of the parallel branches.
Parallel resonances can occur under various conditions, the simplest of them correspond to the case of capacitors being connected to the same buses to which the harmonic source is connected. In this case, resonance occurs between the harmonic source and the capacitors.
Assuming the resistance of the source is completely inductive, the resonant frequency is determined by the formula:
where Qk is the power of the power capacitors and the capacity of the supply network; Scz is the short circuit power at the point of common connection (Fig. 3.1.).
Figure 3.1 – Parallel resonance, 1,3 – loads; 2 – harmonic source; TOP – point of common connection. In order to determine the resonance conditions in a particular case, it is necessary to measure the harmonic currents in the branches of each load and power branch, as well as the harmonic voltage on the buses. If the current flowing from the busbars into the power system is small and the voltage is high, this indicates the presence of a resonance between LS and CL, CC.
The sequential resonance is illustrated in Fig. 3.2. This type of resonance occurs in the presence of distortions on the power supply buses. At high frequencies, the load resistance may not be taken into account, while the resistance of the capacitors decreases sharply. The resonant frequency of this circuit is determined by the formula
where Qk is the power of the power capacitors; ST is the power of the transformer; Uk is the short–circuit voltage of the transformer; PH is the load power.
Figure 3.2 – Sequential resonance circuit K is a capacitor,
T is a transformer,
H is an active load
With sequential resonance, a large harmonic current can flow through the capacitor at a relatively low harmonic voltage. The actual value of the current is determined by the quality factor of the circuit. It is usually on the order of 5 at a frequency of 500 Hz.
The effect of resonances on systems. Resonances in power supply systems are usually considered in relation to capacitors, and in particular to power capacitors. When the harmonics of the current exceed the maximum permissible levels for capacitors, the latter do not worsen their performance, but after a while they fail.
Conclusions
The following tasks were set and solved in the study: - the coefficients of the harmonic components of the voltage for a network with gate converters of various capacities are calculated, compliance with the requirements of the standard [1] on non-sinusoidal voltage is estimated; - the effect of harmonic voltage components on individual elements of the electrical system is analyzed.
The tasks have been completed in full.
References
- Э1. ГОСТ 32144-2013. Электрическая энергия. Совместимость технических средств электромагнитная. Нормы качества электрической энергии в системах электроснабжения общего назначения. – Введ. с 01.07.2014.
- Аррилага Д. Гармоники в электрических системах / Аррилага Д., Д. Брэдли, П. Боджер. - М.: Энергоатомиздат, 1990. - 215 с.
- Жежеленко И.В. Высшие гармоники в системах электроснабжения промпредприятий / Жежеленко И.В.. - М.: Энергоатомиздат, 2000.
- Методы уменьшения несинусоидальности напряжения и тока в электрических сетях низкого напряжения: научная статья/ Бирюков К.С. – Марийский государственный университет, 2019 – 32-33 с. – Текст: электронный // Электронно-библиотечная система eLIBRARY : [сайт]. – URL: https://www.elibrary.ru/
- Научная библиотека. URL: https://scask.ru/
- Расчет гармонических составляющих токов в системе электроснабжения с вентильными преобразователями/ Федотов А.И., Чернова Н.В. - Казанский государственный энергетический университет/ Проблемы энергетики ,2004, №11-12. URL: https://cyberleninka.ru/
- КОМПЕНСАЦИЯ РЕАКТИВНОЙ МОЩНОСТИ В СИСТЕМАХ ЭЛЕКТРОСНАБЖЕНИЯ С МАЛОЙ УСТАНОВЛЕННОЙ МОЩНОСТЬЮ/ Михеев Г.М. - Чувашский государственный университет имени И.Н. Ульянова / Диссертация на соискание учёной степени кандидата технических наук. URL: https://www.chuvsu.ru/
- ВЕНТИЛЬНЫЕ ПРЕОБРАЗОВАТЕЛИ ПОСТОЯННОГО И ПЕРЕМЕННОГО ТОКА/ М.В. Гельман, М.М. Дудкин - ЮЖНО-УРАЛЬСКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ / Учебное пособие. URL: https://lib.susu.ru/
- Шабалин, А. И. Влияние несинусоидальности и несимметрии напряжения на протяженные сети 0,4 кВ / А. И. Шабалин. — Текст : непосредственный // Молодой ученый. — 2020. — № 20 (310). — С. 159-161. URL: https://moluch.ru/
- Оценка несинусоидальности напряжения / Куренный Э. Г., Лютый А. П. / Журнал «Электричество», 2005 г., № 8. URL: https://masters.donntu.ru/