Abstract on the theme of master's work
Content
- Introduction
- 1. Electric arc furnace
- 2. Estimation of nonsinusoidality networks with EAF
- 3. Rating nesimetrii currents and voltages in networks with EAF
- 4. Relay method simulation of the random processes of electric power
- 5. Conclusion
- References
Introduction
Currently, the main equipment in the metallurgical industry for the production of high-quality steels are arc furnace (EAF). These devices are sources of electromagnetic interference: the higher harmonics, voltage fluctuations and unbalance. Calculation and analysis of asymmetric modes arc furnace needed to solve many practical problems: an analysis of automatic regulators the power to select the best parameter of regulation and the development of new regulators, selecting the best network design brief and to develop measures to support all phases of equal capacity furnace settings of relay protection and automatic regulators ovens, etc. For an objective evaluation of voltage unbalance in the existing electricity networks use either specialized instrumentation or digitized curves of the instantaneous phase voltage DSP received at the Registrar RECON. However, RECON does not provide a time schedule recordings voltage sufficient for estimating the asymmetry in accordance with GOST 13109-97.
Purpose: analysis of the possible use of extrapolation of the results for a longer period of time by means of simulation phase voltage EAF.
The idea of ??work: the source data for the job is the distribution function (DF) - the universal characteristic, which is fully characterized by a random variable, and the correlation function (CF), which characterizes the closeness of linear relationships (correlation) between the ordinates of the process, separated by an interval of time τ. Using these functions, you can perform a simulation of the process using StaSim.
The main objectives of research and development: ramp the voltage and current:
- To evaluate the EMC asymmetry and nonsinusoidality;
- To evaluate the accuracy of the program StaSim.
Research methods: used in the methods of the theory of probability and statistical dynamics of electrical systems.
Practical application: prediction of asymmetry and nonsinusoidality voltage on the basis of a simulation model for the solution of practical problems of design and operation.
Review of research and developments on the subject. Questions of EMC and particularly – the statistical simulation of random processes in electrical networks are engaged in DonNTU by E. G. Kourennyi, E. N Dmitrieva, N. N. Pogrebnyak.
The following scientasts greatly contributed to the quetions of power quality: G.Y. Vagin, S. R. Gliternik, A.A. Yermilov, I.V. Zhezhelenko, Y.S. Zhelezko, R.V. Mineev, M.J. Smelyansky, D. Arrilaga etc.
1. Electric arc furnace
Electric Arc Furnace (fig. 1) - is the consumer of the second category of power supply reliability, which is characterized by high unit capacity 0,4-80 MBA, have a power factor of 0,85-0,89 (DSP-5) to 0.7 (ADI -200), non-stop abruptly alternating cyclic operation.
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When the EAF generates an unstable load the phases of the mains supply, thereby generating a wide range of higher harmonics. Inrush current loads cause Motors to supply voltage fluctuation subharmonic and non-sinusoidal current, voltage and arc furnace current supply unbalance cause distortion of the mains voltage - high harmonics [13].
Working arc EAF is a strong non-linear element, which has the following features: a) the arc voltage constant at its constant length b) the curve of non-sinusoidal voltage at the arc, which leads to a distortion of the current waveform and the appearance of the connections with the arc of the higher harmonic components of current and voltage [14]. Higher harmonic components of the arc current passed through the magnetic coupling of the furnace transformer windings on its primary winding and into the network. A non-sinusoidal current causes for heating circuit reactance different voltage drop for each harmonic, which leads to non-linear distortions of the supply voltage. Harmonic structure in the the voltage and current largely depends on the combustion furnace arc. On the mode of combustion are influenced by many factors [15]: change ionization arc gap during melting and evaporation charge, temperature fluctuations and chemical composition of metal and slag, moving charge, tumbling arc arc movement under the action of electromagnetic forces, vibration electrodes, unbalanced load phases separate furnace. These factors contribute to the random nature of the electrical processes in the furnace and the influence on the current-voltage characteristic of the arc that defines the harmonic structure of the current.
Melting charge accompanied by frequent and abrupt changes in the load range from the edge of the arc to short circuit between the electrode and the charge. Single-ended mode of operation of the furnace, and the asymmetry of the current collector affect the harmonious composition of current and supply voltage - the third and multiples of three harmonics occur in all three phases.
In addition to the arc electrooven DSP circuit has a different nonlinear component - transformer unit consisting of low-power furnaces furnace transformer and current limiting reactor, and for the powerful - from regulating auto transformer and furnace transformer. In nominal operation, steel core transformer, choke and auto-transformer is not saturated (magnetizing current is 0.5-3% of the rated current). In the short-circuit performance with and without the presence of aggregates of transformer iron cores greatly affects the curve of the current in the circuit. At the time of the furnace off-load transformer unit in the network is generated extended (0.01-0.03 s) front pulse frequency of 10-20 kHz and an amplitude (1.5-3.5). These fluctuations are caused not by the linearity of the current-voltage characteristics of the hardware and the arc periodically repeat its ignition.
Non-symmetric modes occur at uneven loading phase furnace. In other words, the length of the rough edges of the individual phases, uneven resistance and vzaimoinduktivnosti supply - causes unbalance [14].
Voltage unbalance is determined by the difference between the current arc of the three phases and characteristics of short network. When voltage unbalance in three-phase networks is reduced throughput power grid, there are additional power losses in the elements of the SES, increased heating of electrical machines, reduced reliability and efficiency of power generation, transmission and consumption of electricity [2].
Nonlinearity of the voltage-current characteristics of the arc chipboard distorts the shape of the current and the generation of higher harmonics. Non-sinusoidal currents through the furnace transformer fall into the electricity network and cause different for each harmonic voltage drop, resulting in a distorted shape of the supply voltage.
A non-sinusoidal curves is due to factors such as: melting chunks of charge, to lengthen the arc, the arc with the throwing of a single piece of the charge on the other, "boiling" of the metal, etc. [4, 5]. In addition to the properties of the arc, the cause of the higher harmonics may be the influence of chain segments with iron magnetic circuits (transformers, inductors), the saturation of which violates the proportionality between the magnetizing current and the magnetic flux.
Non-sinusoidal currents cause a number of unwanted and complicating the work of installation events [6, 7]:
1) increasing the active losses in the wires, since the surface effect of high frequency currents is more pronounced;
2) increase the iron loss (e.g., in the transformer core), since the eddy current loss and hysteresis with increasing frequency;
3) increasing the inductance and reduced since inductance is proportional to the frequency;
4) of a sharp increase of higher harmonics even in comparison with the amplitude of the fundamental harmonic of a series connection of capacitive and inductive impedance (resonance voltage) that can create overvoltage leading to insulation breakdown.
In the range of 0-2.5 Hz (fig. 2) appear interharmonics levels, which can reach 10% of the fundamental frequency current.
Thus, particleboard is "generator" of almost all types of electromagnetic interference. Therefore the need for accurate assessment of the impact of SES on EAF [16].
2. Evaluation nonsinusoidality networks with EAF
2.1 Normalization of nonsinusoidality voltage
A non-sinusoidal voltage in all standards measured by the voltage harmonic distortion factors and the n-th harmonic component [8].
For the averaging interval of N observations must be at least nine. The results of the i-th observation is given by:
The quality of electrical energy at a rate of n-th harmonic component of the voltage at the point of common coupling is considered relevant requirements of GOST 13109-97, if most of all measured within 24 h values ??of the coefficients n-th harmonic component of the voltage does not exceed the limit value, and the value of the coefficient n-th harmonic component of the voltage corresponding to the 95% for a set period of time, normally not exceed the permissible value.
2.2 Initial data for the estimation of nonsinusoidality
The input data for the estimation of nonsinusoidality curves are the the voltage and current CPD received at the Registrar RECON.
RECON allows you to do a spectral analysis of curves. But it is necessary to carry out the whole process of spectral analysis of self-analysis to evaluate the accuracy nonsinusoidality by RECON.
Consider one period of the voltage curve chipboard (fig. 3).
According to [1] characterized by a non-sinusoidal distortion coefficient for which you know the values ??of 40 harmonics. For this we need to find a range of operating currents and voltages.
2.3 Isolation of non-sinusoidal components
Because electricity is transmitted at a frequency of f = 50 Hz, the process u (t) changes the current values ??of the voltage (or current) is naturally represented as a sum of two components: a sine uf (t) with a frequency of 50 Hz and non-sinusoidal, which is called a sine wave and a hindrance.
The case of a periodic noise with a cycle time tf = 1 / f = 0.02 s, which is superimposed on a sine wave with the same cycle time.
Parameters are sinusoids in different ways. A good result is obtained by the method of least squares. Also used the Fourier series expansion. In this case, we use the latter.
Sampling frequency of the curve (Fig. 3) is 2000 Hz. This means that for one period of the curve for 20 points. With so many points of RECON 9 shows the values ??of the harmonics. That is on one harmonic - 2 points, which is not enough for an accurate assessment of nonsinusoidality. In our case, one harmonic will have five points. Therefore, one needs to know the period of at least 200 pixels. To do this, we use an interpolation of a given function using the spline.
The voltage is the sum of the first (fundamental) u1F (t) and the sum of the canonical harmonic unΣ (t) c order n ≥ 2
[3]:
Substituting (2) into equation (1). We get the equation disturbances:
Assume that the non-sinusoidal component equal to the sum of the higher harmonics, t.e.uf (t) = u1F (t). Equation interference would be:
Fig. 4 shows graphs of the original curve, sinusoidal and noise components.
3. Rating nesimetrii currents and voltages in networks with EAF
3.1 Rationing of unbalance
According to [1] voltage unbalance is as follows:
- coefficient of voltage unbalance on the reverse;
- coefficient of voltage unbalance on the zero sequence.
The coefficient of voltage unbalance on the reverse K2Ui calculated as a percentage as a result of the i-th observation as follows:
where U2 (1) i - the current value of negative sequence voltage fundamental frequency three-phase voltage system in the i-th observation, V, KV;
U1 (1) i - RMS voltage direct-sequence fundamental frequency in the i-th observation, V, kV.
Unbalance voltage residual K0Ui calculated as a percentage as a result of the i-th observation as follows:
3.2 Evaluation of asymmetry in power networks with EAF
EAF settings are powerful three-phase, AC power which is provided from the factory distribution network voltage of 6, 10 and 35 kV. According to the EMP, these networks operate with isolated neutral. When working furnaces due to variations in the electrical load currents and operating at any given time form an asymmetric load. The asymmetry is aggravated by the difference in the settings of the current controllers.
The asymmetry of three-phase currents is characterized by a coefficient of asymmetry, which is defined as the ratio of negative sequence of the module to the module component-sequence [11]:
In the analysis of asymmetrical modes unbalance currents α appropriate to calculate directly through modules (RMS) phase currents IA, IB and IC. The formula for determining the coefficient of asymmetry through the effective values ??of currents is:
4. Relay method simulation of the processes of electric power
Existing methods for simulating random processes do not always provide accurate reproduction of CF. In this case, consideration should be excluded of the SF which does not match. Relay method, developed at the Department of electricity to industrial enterprises and cities Donetsk National Technical University Ph.D. Pogrebnyak N., avoiding repeated simulations by improvement in the quality of EC simulation of random processes obtained by other methods. In addition, the relay method can be used as a standalone: ??simulation of the random processes with a given distribution of ordinates and CF.
Modeling of processes can be done if you know the law of the random variable. Typically, this is used for the distribution function (DF) - the universal characteristic, which is fully characterized by a random velichinu.See can help you identify any numerical characteristics of random variable. The most important of these are secondary to the practice znacheniedispersiya. Fig. 5 shows the statistical distribution function (DF) of the voltage at the terminals of the EAF in the early melting, as well as the hypothetical risk factors with the uniform and the normal laws. Obviously, the change in voltage on the inputs of ADI are well described by a normal distribution. A characteristic feature of the EAF is non-stationary mode during operation. Therefore, the interest is the analysis of changes in the numerical characteristics of three distinct periods: the beginning, middle and end of melting.
However, for the simulation of a random process knowledge only one type of risk factors is not enough, since many indicators of the quality of the voltage (CN) depend not only on the ordinate interference, but their sequence in time. Therefore it is necessary to know also the view of the correlation function (CF), which characterizes the closeness of linear relationships (correlation) between the ordinates of the process, divided by the time interval τ. Fig. 6 shows the three-phase voltages EC EAF for an initial period of melting. Their analysis suggests that the EC can bytapproksimirovany expression:
where D-dispersion process, a, and b - CF parameters defined by the formulas:
Here Tk - constant correlation; t0 - the transition through CF 0.
A simulation of the process is proposed to carry out using the program StaSim, developed by the Department of Master of the ESIS Ivko E. based on the algorithm [12]. This algorithm allows to take into account the law of the distribution process, and CF.
Conclusion
EAF - is many sources of electromagnetic interference. EC to bring the performance of normalized values ??requires significant capital investment and operating costs. Therefore the need for accurate assessment of the impact on the power system EAF.
To evaluate the nonsinusoidality and asymmetry of the original data are recording the instantaneous phase or line voltage at the terminals of chipboard. Constructed and analyzed DF and CF stress for different periods of melting allow a simulation of the process of change in voltage at a desired time interval.
Test problem showed the principal possibility of extrapolation process simulation method for longer periods of time. Simulation error does not exceed 9.7% with an acceptable value of 10%.
On the moment of writing this abstract the master's work was not completed. Its final variant can be obtained from the author or the scientific adviser after December 2013.
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