A method for detecting secondary electrical energy in a submerged arc furnace

Abstract

This invention relates to the field of electrical energy detection technology, and more particularly to a method for detecting secondary electrical energy in a submerged arc furnace (SAF). The method includes separately acquiring voltage and current signals from the secondary side of the SAF, performing integration, phase compensation, and calibration on the current signal, and calibrating the voltage signal; processing the voltage and current signals using a Blackman-Harris cubic self-multiplying window and four-line interpolation method; and calculating reactive power based on the processed voltage and current. This invention combines the Blackman-Harris cubic self-multiplying window and four-line interpolation algorithm to analyze harmonic signals, achieving higher accuracy than traditional Blackman-Harris basic window three-line and four-line methods, as well as the Blackman-Harris cubic self-multiplying window and three-line interpolation method, with an amplitude error of less than 3*10. －9 It remains stable even under fundamental wave fluctuations.

Description

Technical Field

[0001] This invention relates to the field of electrical energy detection technology, and in particular to a method for detecting secondary electrical energy in a submerged arc furnace. Background Technology

[0002] Submerged arc furnaces are mainly used for smelting ores to produce ferroalloys such as ferrosilicon and ferronickel. The smelting process primarily involves supplying the furnace with low voltage and high current through a power supply system. An electric arc is generated at the electrode ends, converting electrical energy into heat energy and creating a high-temperature space within the furnace to provide the necessary environment for the oxidation-reduction reaction of the ore. The reactive power compensation device and automatic electrode raising / lowering of the submerged arc furnace rely on secondary-side power detection parameters. Currently, the ADE7758 power metering chip is widely used for power detection. However, the phase-shifting method used by this chip to calculate reactive power does not consider the harmonic components generated by inductive equipment such as transformers and short-circuit power grids, which cause errors in reactive power calculation. This leads to inaccurate signals used for reactive power compensation and electrode raising / lowering control, affecting the submerged arc furnace smelting process and reactive power compensation control. It also results in inaccurate reference calculations for reactive power compensation and electrode raising / lowering, causing power quality problems such as low power factor and three-phase power imbalance. Summary of the Invention

[0003] To address the shortcomings of existing algorithms, this invention improves the FFT algorithm to perform harmonic analysis and reactive power calculation on electrical energy signals.

[0004] The technical solution adopted in this invention is: a method for detecting secondary electrical energy in a submerged arc furnace, comprising the following steps:

[0005] Step 1: Collect the voltage and current signals on the secondary side of the electric arc furnace, and perform integration, phase compensation and calibration on the current signal, and calibration on the voltage signal.

[0006] Step 2: Process the voltage and current signals using the Blackman-Harris cubic self-multiplication window and four-line interpolation method;

[0007] Furthermore, specifically including:

[0008] S21. Extract two spectral lines on the left and right sides of the peak point of the detected signal to obtain four spectral lines, and obtain the corresponding spectral line amplitudes based on the four spectral lines.

[0009] S22. Using the fitting function polyfit, we obtain the approximation formula in the BHSM-3 four-line interpolation correction formula.

[0010] S23. Obtain the modified forms of amplitude and phase in the spectrum expression of the window function based on the approximation formula.

[0011] Furthermore, the four spectral lines are K1, K2, K3, and K4, where k4-k0 = -α+1.5, k3-K0 = -α+0.5, k2-k0 = -α-0.5, k1-k0 = -α-1.5, and α∈(0,0.5).

[0012] Furthermore, the approximation formula is as follows:

[0013] α = 0.0244β + 0.0955β 3 +0.2401β 5 +1.9833β 7 (7)

[0014] h(α) = 0.0738 + 0.0958α 2 +0.0398α 4 +0.0299α 6 (8)

[0015] Where β is the relative deviation between the two spectral lines to the right of the peak point and the two spectral lines to the left.

[0016] Step 3: Calculate the reactive power based on the processed voltage and current values;

[0017] Furthermore, the formula for reactive power is as follows:

[0018]

[0019] Where i is the harmonic order, h is the highest harmonic in the signal, and U i I i Let φ represent the effective values ​​of voltage and current of the i-th harmonic, respectively. i U is the difference between the initial phase angle of the voltage and the initial phase angle of the current at the i-th harmonic. i I i The value is the voltage and current harmonic amplitude, φ i This represents the phase difference between voltage and current.

[0020] The beneficial effects of this invention are:

[0021] 1. Combining the Blackman-Harris cubic self-multiplying window and four-line interpolation algorithm to analyze harmonic signals, the accuracy is higher than that of the traditional Blackman-Harris basic window three-line and four-line methods, as well as the Blackman-Harris cubic self-multiplying window and three-line interpolation method, with an amplitude error of less than 3*10. -9 It remains stable even under fundamental frequency fluctuations.

[0022] 2. The smelting environment of an electric arc furnace is complex and contains a large number of inductive components, accompanied by complex harmonic interference. The ADE7758 power metering chip does not consider harmonic interference when calculating reactive power. By adopting the method of this invention, the accuracy of reactive power is improved. Attached Figure Description

[0023] Figure 1 This is a flowchart of the secondary electrical energy detection method for a submerged arc furnace according to the present invention;

[0024] Figure 2 This is a hardware structure diagram of the secondary electrical energy detection system for the electric arc furnace of the present invention;

[0025] Figure 3 This is an overall flowchart of the STM32 embedded system secondary electrical energy detection system for a submerged arc furnace according to the present invention;

[0026] Figure 4 The flowchart of the Blackman-Harris cubic self-multiplying window + four-line interpolation algorithm of this invention applied to an embedded system is shown below.

[0027] Figure 5 This is a comparison chart of the relative magnitude errors between the algorithm of this invention and existing algorithms;

[0028] Figure 6 This is a comparison chart of the phase relative error between the algorithm of this invention and existing algorithms. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0030] like Figure 1 As shown, a method for detecting secondary electrical energy in a submerged arc furnace includes the following steps:

[0031] Step 1: Collect the voltage and current signals on the secondary side of the electric arc furnace, and perform integration, phase compensation and calibration on the current signal, and calibration on the voltage signal.

[0032] Step 2: Process the voltage and current signals using the Blackman-Harris cubic self-multiplication window and four-line interpolation method;

[0033] The Blackman-Harris cubic self-multiplying window (BHSM-3) addresses the spectral leakage problem that occurs when using the FFT algorithm to analyze harmonics. When truncating a continuous signal, windowing is used to smoothly connect the beginning and end of the extended period, suppressing jumps. The ideal window function exhibits spectral characteristics such as fast sidelobe decay and low peak level of the first sidelobe. The sidelobe decay rate of BHSM-3 is much faster than that of traditional window functions, and the level of the first sidelobe is lower than that of the first sidelobe of other window functions.

[0034] The time-domain and frequency-domain expressions for BHSM-3 are as follows:

[0035]

[0036] Where N is the number of sampling points, W R (ω) represents the frequency domain of a rectangular window;

[0037] W R The formula for (ω) is:

[0038] Furthermore, the four-line interpolation method extracts two spectral lines on the left and right sides of the peak point K0 of the detected signal, namely K1, K2, K3, and K4; where k4-k0=-α+1.5, k3-K0=-α+0.5, k2-k0=-α-0.5, k1-k0=-α-1.5, α∈(0,0.5);

[0039] Let y1, y2, y3, and y4 be the spectral amplitudes of K1, K2, K3, and K4, respectively;

[0040]

[0041] Where X() is the spectral line function;

[0042] Then the parameter β is introduced as follows:

[0043]

[0044] make

[0045]

[0046]

[0047] The frequency expression corresponding to the window function is:

[0048]

[0049] Where m is the harmonic order, M is the total harmonic order, and A m Let m be the amplitude of the mth harmonic, and N be the number of sampling points.

[0050] Furthermore, using the Matlab polynomial fitting function polyfit, the relevant approximation formula in the BHSM-3 four-line interpolation correction formula is obtained as follows:

[0051] α = 0.0244β + 0.0955β 3 +0.2401β 5 +1.9833β 7 (7)

[0052] h(α) = 0.0738 + 0.0958α 2 +0.0398α 4 +0.0299α 6 (8)

[0053] The frequency domain expression of the signal after windowing is:

[0054]

[0055] Where W(k) is the spectral expression of the window function, and A and θ are the amplitude and phase of the detected signal.

[0056] The corrected expressions for amplitude A and phase θ are obtained as (10) and (11), respectively:

[0057]

[0058]

[0059] Where N is the number of sampling points, α and h(α) are approximations of (7) and (8) respectively, and K i Let Δf be the frequency difference for the i-th spectral line.

[0060] Step 3: Calculate the reactive power based on the processed voltage and current.

[0061] Furthermore, the formula for reactive power is as follows:

[0062]

[0063] Where i is the harmonic order, h is the highest harmonic in the signal, and U i I i Let φ represent the effective values ​​of voltage and current of the i-th harmonic, respectively. i U is the difference between the initial phase angle of the voltage and the initial phase angle of the current at the i-th harmonic. i I i The value is the voltage and current harmonic amplitude, φ i This represents the phase difference between voltage and current.

[0064] like Figure 2The hardware structure diagram of this invention first uses a Rogowski coil to collect the single-phase current on the secondary side of the submerged arc furnace and uses a current transformer to collect the secondary side voltage signal.

[0065] First, the acquired signal is processed. First, according to the detection principle of Rogowski coil, the output signal and the detected signal are differentially related. The signal is restored using an integrating circuit, and the detection accuracy is ensured using a phase compensation circuit.

[0066] Secondly, the voltage transformer needs to go through protection circuits and amplification and correction circuits to complete the acquisition of voltage signals. Since there are range requirements when voltage and current signals enter ADE7758 and STM32, they need to be processed by signal correction circuits.

[0067] The DZ1022Z signal generator from Rigol Corporation was selected to output two synchronous harmonic signals for easy power calculation. Voltage and current detection modules were used for signal detection. Since the sampling range of the ADE7758 is ±0.5V, an amplification and processing module was designed to process the signals. Then, the ADE7758 and STM32F103 synchronously sampled the two signals, and the STM32 performed harmonic analysis and reactive power calculation on the signals.

[0068] like Figure 3 The main program flowchart shows that the ADE7758 and STM32 communicate via SPI to transmit data. Finally, all power parameters are calibrated on the STM32 and displayed on the host computer via RS-485 communication. The microcontroller is an STM32F103ZET6, which contains three ADCs with a minimum conversion time of 1μs. Voltage and current signals are synchronously acquired through two ADCs. The ADE7758 uses an online periodic accumulation mode. After the ADE7758 has measured for a certain time, it sends an interrupt request to the MCU to read the calculated power parameters via SPI, calibrates the parameters, and displays them on the host computer via RS-485 communication. The priority order is: sampling interrupt priority > ADE7758 interrupt request priority > data processing priority, to ensure synchronous signal processing.

[0069] Figure 4 To apply the interpolation algorithm to the embedded system flowchart, the BHSM-3 four-spectrum-line algorithm is adopted. The number of sampling points for calculating reactive power is 256. 256 points are extracted at equal intervals from the BHSM-3 function as a constant array. The sampling points are multiplied with the constant array to complete the windowing process. The peak value k and the points on both sides of k are taken. According to the parameter fitting formula, a more accurate amplitude, phase and frequency are obtained, and then the reactive power is obtained.

[0070] like Figure 5 , 6For analyzing harmonic signals using the Blackman-Harris cubic self-multiplying window and four-line interpolation algorithm, this invention compares its amplitude error with the Blackman-Harris basic window + three-line difference algorithm, the Blackman-Harris basic window + four-line difference algorithm, and the Blackman-Harris cubic self-multiplying window + three-line interpolation algorithm. The results show that the amplitude error of the Blackman-Harris cubic self-multiplying window and four-line interpolation algorithm is less than 3*10^6. -9 Phase error less than 3*10 -6 It has higher accuracy than existing algorithms and remains stable under fundamental wave fluctuations.

[0071] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for detecting secondary electric energy of an electric arc furnace, characterized in that The method comprises the following steps: Step one, collecting the secondary side voltage and current signal of the ore smelting furnace respectively, and integrating, phase compensation and calibration for the current signal, and calibration for the voltage signal; Step two, processing the voltage signal and current signal by using Blackman-Harris cubic self-multiplication window and four-spectrum line interpolation method; The time domain and frequency domain expression of BHSM-3 is: （1） where N is the number of sampling points, Rectangular window frequency domain; S21, extracting two spectrum lines on the left and right sides of the peak point of the detection signal to obtain four spectrum lines, and obtaining the corresponding spectrum line amplitude according to the four spectrum lines; The four spectral lines are respectively K 1、 K 2、 K 3、 K 4, wherein , is to determine the interpolation range of the peak point of the detection signal The frequency expression corresponding to the window function is: (6) wherein, m is the harmonic number, M is the total number of harmonics, A m is m is the amplitude of the sub-harmonic, N is the number of sampling points; S22, using the fitting function polyfit to obtain the approximation formula in the BHSM-3 four-spectrum line interpolation correction formula; S23, obtaining the correction formula of the amplitude and phase in the window function spectrum expression according to the approximation formula; The formula of the approximation formula is: （7） （8） wherein, is the relative deviation of the two spectra on the right side of the peak point from the two spectra on the left side of the peak point. （10） （11） wherein, N is the number of sampling points, and are the approximations of (7) (8), respectively, K i is the first i spectrum line, is the frequency difference; Step three, calculating the reactive power according to the processed voltage and current values.

2. The method of detecting secondary electric energy of an arc furnace according to claim 1, characterized by, The calculation formula of the reactive power is: （12） wherein i is the harmonic number, h is the highest harmonic in the signal, U i , I i denote the voltage, current effective value of the i harmonic, respectively, is the difference between the voltage initial phase angle and the current initial phase angle at the i harmonic, U i , I i the value of the voltage and current harmonic amplitude, is the phase difference value of the voltage and the current.

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