A method for establishing a frequency response model of an electric smelting magnesium furnace based on electrode regulation

Abstract

The application provides a method for establishing a frequency response model of an electric smelting magnesium furnace based on electrode adjustment, which is applied to a high-energy-consumption electric smelting magnesium furnace load participating in primary frequency modulation of a power grid. Steps: 1) studying the electric-thermal conversion process of the electric smelting magnesium furnace and calculating the working resistance, establishing the relationship between the electrode lifting height and the furnace working resistance; 2) describing the power external characteristics of the electric smelting magnesium furnace, and clearly defining the power regulation capability of the electric smelting magnesium furnace; 3) establishing a model of the electrode adjustment system, and verifying the adjustment performance of the lifting electrode. The application realizes the bidirectional regulation of power increase and power decrease through the lifting electrode mode, and can continuously regulate the power. The relationship chain between the electrode lifting force and the frequency response output power is decomposed into several links, the frequency response model under the lifting electrode mode is obtained, and the effectiveness is verified through simulation. The application provides a reasonable frequency modulation control mode and a frequency response characteristic description method for the typical high-energy-consumption industrial load, i.e. the electric smelting magnesium furnace, participating in the primary frequency modulation of the power grid.

Description

Technical Field

[0001] This invention belongs to the field of primary frequency regulation of power systems, and relates to a method for establishing a frequency response model of an electric fused magnesium furnace based on electrode adjustment, and applies it to the participation of high-energy-consuming electric fused magnesium furnace loads in the primary frequency regulation of the power grid. Background Technology

[0002] Driven by the "dual carbon" goals, building a new power system with new energy sources as the mainstay is an inevitable trend in promoting the low-carbon development of modern power systems. With the continuous advancement of clean energy on both the power source and load sides, the proportion of renewable energy integration has increased significantly, resulting in a "dual high" characteristic in the system. On the one hand, the high proportion of renewable energy integration increases the fluctuation of the equivalent load of the grid, leading to greater system uncertainty. Simultaneously, the integration of renewable energy squeezes the grid connection space of conventional units with frequency regulation capabilities. On the other hand, the high proportion of power electronic equipment application means that clean and low-carbon energy itself lacks frequency regulation capabilities. This "dual high" will inevitably lead to an increasingly strong demand for primary frequency regulation in the power grid. Insufficient frequency regulation resources will degrade the frequency quality of the grid; therefore, the power grid urgently needs to find ways to increase primary frequency regulation resources on all sides of the "source-grid-load" chain.

[0003] Under the "dual carbon" target, the issue of improving power grid frequency stability has gradually shifted from technological upgrades on the "source" side to research on methods and approaches for "load" side participation in power grid dispatch and operation. "Load" side resources are crucial for enhancing the primary frequency regulation capacity of the power grid, especially high-energy-consuming industrial loads such as cement plants, electrolytic aluminum plants, and fused magnesium plants. These plants have large load capacities and high levels of automation, making them excellent flexible resources for participating in power grid frequency regulation. Fused magnesium loads are a typical example of high-energy-consuming industrial loads. However, due to their large single-furnace size, complex process constraints, and diverse combinations of furnace operating conditions, their participation in frequency regulation involves complex issues. Currently, there is almost no research on fused magnesium furnaces participating in power grid frequency regulation ancillary services, thus necessitating research in this area.

[0004] To study the operation and control of fused magnesium loads participating in the primary frequency regulation of the power grid, it is first necessary to establish a frequency response model. Only then can the frequency regulation performance be analyzed and an optimized control strategy be formulated. The premise for establishing the frequency response model is to clarify the control mode by which fused magnesium achieves frequency adjustment. That is, while producing fused magnesium products, the enterprise can quickly adjust its power consumption (with small amplitude but rapid and frequent changes, and bidirectional adjustment required) in response to grid frequency fluctuations to participate in the primary frequency regulation of the power grid.

[0005] Short-term shutdown is a method for rapidly adjusting power. Since the electric arc can be re-established after a short power outage, fused magnesia furnaces can be shut down for short periods. However, the shutdown time cannot exceed 30 seconds. Frequent or prolonged shutdowns can lead to a decrease in the molten pool temperature, posing a risk of solidification and hindering product smelting. While shutdown operations can alter the power consumption of fused magnesia, they can only reduce the power output, meaning frequency adjustment is unidirectional. Considering the response characteristics of primary frequency regulation under small disturbances, bidirectional adjustment capability is required. Therefore, short-term shutdown is not suitable for fused magnesia furnaces to participate in primary frequency regulation. In actual production, factors such as process requirements and raw material impurities cause frequent and significant fluctuations in smelting power, which is also detrimental to ensuring product quality and equipment safety.

[0006] This patent was funded by the National Natural Science Foundation of China Regional Innovation and Development Joint Fund Key Project "Key Technologies for Collaborative Optimization Scheduling of Integrated Energy Systems with Distributed Resources Participating in Primary Frequency Regulation". Summary of the Invention

[0007] To address the problems of existing technologies, this invention provides a control mode for an electric molten magnesium furnace participating in primary frequency regulation. This mode employs an electrode-pulling method during the main melting process, using the electrode adjustment system as the basis for establishing the frequency response model of the electric molten magnesium furnace. The electrode is the device in the electric molten magnesium furnace that converts electrical energy into heat energy. When it is pulled up or down, the working resistance changes, thereby altering the melting power. Therefore, electrode pulling is also a method of power regulation, and adjusting power by pulling the electrode is suitable for primary regulation to handle general frequency disturbances. This adjustment method allows for bidirectional adjustment of power usage (both increasing and decreasing) through the up and down pulling of the electrode, and also enables continuous adjustment.

[0008] Based on the determined primary frequency modulation mode of the lifting electrode, it is necessary to further establish its frequency response model through analysis of the electrothermal conversion process of the fused magnesium furnace, that is, to clarify the relationship between the electrode lifting height and the increase or decrease of the smelting power of the fused magnesium furnace. However, since the fused magnesium furnace is a complex, nonlinear, and strongly coupled system, and research on smelting processes and electrothermal conversion mechanisms is still incomplete, it is difficult to directly obtain a detailed analytical model of its full frequency response parameters. This paper proposes to decompose the relationship chain between electrode lifting force and frequency response output power into several links, and obtain the frequency response model under the lifting electrode mode by determining several intermediate variables and exploring mapping relationships. In the derivation of the corresponding relationships in each link, reasonable simplification and linearization are performed based on the characteristics of frequency adjustment, ultimately obtaining the frequency response model of fused magnesium.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A method for establishing a frequency response model of an electric fused magnesium furnace based on electrode adjustment includes the following steps:

[0011] Step 1: Study the electrothermal conversion process of the fused magnesium furnace and calculate its working resistance;

[0012] The internal structure and electrothermal characteristics of an electric fused magnesium furnace are as follows: Figure 1 As shown, the furnace includes a furnace body, three graphite electrodes, raw materials, an electric arc, slag, and a molten pool resistance heating element. During the smelting process, the graphite electrodes are intermittently embedded in the raw materials, utilizing the electric arc heating generated between the bottom of the electrodes and the raw materials as the heat source for production. In addition to the heat generated by the electric arc, the current in the molten pool also generates resistance heating to maintain the molten pool temperature. Pulling the electrodes changes the distance l between the electrodes and the slag at the bottom of the furnace, thus affecting the resistance R1 of the molten pool below each phase of the electric arc and the resistance R2 of each phase of the electric arc. The material layer is solid granular magnesite ore with high resistivity; the material layer resistance R3 is considered infinite, and the branch containing it is considered an open circuit. This invention does not consider the material layer resistance R3.

[0013] Combined with the energy conversion circuit diagram of fused magnesium furnace smelting Figure 2 and Figure 3 and the internal structure diagram of the molten pool Figure 4 By solving for the molten pool resistance R1 and the arc resistance R2, the relationship between the electrode height h and the working resistance can be obtained. Therefore:

[0014] The electrode adjustment lifting height Δh is:

[0015]

[0016] Where n represents the rotational speed of the lifting motor; t represents the sampling time with an interval of 1 second; λ represents the reduction ratio of the lifting motor; and r1 represents the gear radius of the lifting motor.

[0017] The electrode height h is:

[0018] h=h0+Δh (2)

[0019] Where h0 represents the initial distance between the bottom of the electrode and the slag.

[0020] During the smelting process, an electric field is generated near each phase electrode in the fused magnesium furnace. Using the electric field strength formula and Ohm's law, the resistance R1 of the molten pool below the bottom of the electrode can be calculated as follows:

[0021]

[0022] As can be seen from equation (3), the resistance R1 of the molten pool below the electrode arc of each phase increases with the increase of electrode height (i.e., the increase of the distance h between the bottom of the electrode and the slag).

[0023] There is currently no definitive expression for the arc resistance R2 of a submerged arc furnace. Research indicates that some open-arc characteristics of electric arc furnaces are also applicable to submerged arc furnaces under certain circumstances. Therefore, the calculation of arc resistance in this invention uses the Cassie arc conductance model for open arc furnaces.

[0024]

[0025] Where E0 represents the instantaneous value of the arc voltage; v represents the arc voltage; i represents the arc current, i = i0 + Δi, i0 represents the initial value of the arc current, Δi represents the change in arc current (caused by the change in electrode position); θ represents the arc time constant.

[0026] During the smelting process, the arc length is kept fluctuating around the rated arc length.

[0027] Δi=KΔl (5)

[0028] Where K represents the arc proportionality coefficient. The relationship between the arc length and the instantaneous value of the arc voltage is as follows:

[0029] E0=a+bl (6)

[0030] Where a represents the voltage drop between the cathode and anode regions; b represents the voltage gradient of the arc column; l represents the arc length, l = l0 + Δl; the change in arc length Δl when the electrodes move up and down is:

[0031] Δl=kΔh (7)

[0032] Where k represents the electrode proportionality coefficient. The inter-electrode conductance G when the arc disappears. min This is also something that needs to be considered during modeling, namely the single-phase electrode arc conductivity model of an electric fused magnesium furnace:

[0033]

[0034] As shown in equation (4-5), the arc current of each phase electrode also increases with the increase of electrode height. As shown in equation (5-8), the arc resistance of each phase electrode also increases with the increase of electrode height. That is, increasing the electrode height can increase the smelting power of the fused magnesium furnace.

[0035] Step 2: Describe the power external characteristics of the fused magnesia furnace. Convert the electrode adjustment system circuit to the secondary side of the furnace transformer. Assume the three-phase electrode parameters are identical. Figure 5 In the fused magnesia furnace, R1 and L1 represent the equivalent resistance and inductance of the molten pool resistance below each phase electrode referred to the secondary side of the transformer at the furnace front; R4 and L2 represent the equivalent resistance and inductance of each phase electrode referred to the secondary side of the transformer at the furnace front; M represents the mutual inductance between the electrodes of the fused magnesia furnace, R... a1 R a2 and R a3The arc resistance model representing the three-phase electrodes A, B, and C (all information regarding the electrode adjustment system itself is known in this invention). Figure 5 , Figure 6 This is the circuit diagram of the predetermined electrode adjustment system. This invention uses this electrode adjustment system to change the power (Equation 11). Step 1 of the arc conductance model has already been given; this part involves solving the differential equations based on the circuit diagram to obtain the arc resistance and power P.

[0036] The electrode adjustment system model established in this invention aims to provide the adjustment capability and performance of the fused magnesia furnace participating in primary frequency regulation. It does not consider all details of the electrical system, and the simultaneous raising and lowering of the three-phase electrodes ignores the coupling effect between the electrodes and the mutual inductance between the electrodes of the fused magnesia furnace, simplifying the circuit as follows: Figure 6 As shown (the electrode adjustment system model established in this invention is to provide the adjustment capability and performance of the fused magnesium furnace participating in primary frequency regulation, without considering all the details of the electrical system, and the coupling effect between the electrodes is ignored when the three-phase electrodes rise and fall simultaneously, and the mutual inductance between the electrodes of the fused magnesium furnace is ignored), the equivalent circuit can be simplified to: R = R1 + R4, L = L1 + L2.

[0037] The following differential equation can be derived from Kirchhoff's laws:

[0038]

[0039] The model of the electrode regulation system is expressed in the form of state equations. The three-phase arc currents i1, i2, and i3 are represented by state variables x1, x2, and x3, respectively, and G1, G2, and G3 represent the arc conductances of the three-phase electrodes A, B, and C, respectively. According to equation (8-9), let the three state variables x4, x5, and x6 represent the three-phase arc conductances G1, G2, and G3, respectively, and the state equation for arc power regulation is obtained:

[0040]

[0041] The smelting power P of an electric magnesia furnace can be obtained by combining the obtained arc power adjustment model with the resistance heating generated by the current passing through the molten pool.

[0042]

[0043] Among them, G j j = 1, 2, 3 represents the conductance of the arc of the three-phase electrodes A, B, and C; i j j = 1, 2, 3 α R1 represents the electrode current; R2 represents the molten pool resistance.

[0044] The electric molten magnesium furnace responds to grid frequency changes using a variable droop coefficient (K coefficient). The real-time adjustable power of the furnace is ΔP. ​​Due to limitations in the furnace's production process, -0.2p ≤ Δp ≤ 0.1p, where p is the furnace's rated operating power. The K coefficient is set based on the frequency difference Δf (Formula 12): If the frequency difference is within the dead zone, the furnace will not operate regardless of its size to prevent encroachment on the frequency regulation space of thermal power units and avoid unnecessary waste; if the real-time frequency difference Δf exceeds the dead zone but does not exceed the grid's frequency quality requirements, the frequency regulation resources will set a certain K value and perform a frequency regulation in droop control mode; if the real-time frequency difference exceeds the grid's frequency quality requirements, the frequency regulation resources will set another K limit value, as shown in the following expression:

[0045]

[0046] Among them, K t Δf is the frequency modulation coefficient of the fused magnesium enterprise at time t; threshold Indicates the threshold value for power grid frequency quality requirements; Δf dead_zone This indicates the frequency dead zone of an electric fused magnesium furnace.

[0047] Step 3: Establish a model of the electrode adjustment system. After determining the smelting power of the fused magnesia furnace, it is also necessary to clarify the adjustment performance of the lifting electrode (such as response time delay caused by the characteristics of various parts of the electrode adjustment system). The electrode adjustment system of the fused magnesia furnace is a typical nonlinear system, and its full parameter description cannot be obtained analytically using mathematical methods. According to the simplification principle of nonlinear systems, it is decomposed into a nonlinear static system and several linear dynamic systems. In this invention, the main circuit of the fused magnesia furnace is simplified into a nonlinear static link. To establish the relationship between the increase or decrease of the smelting power of the fused magnesia furnace and the electrode lifting height, without considering the controller, the equivalent linear dynamic system is decomposed into typical first-order or second-order systems:

[0048] 1. Rectifier and filter stage

[0049] The rectification and filtering stage is actually a nonlinear transformation process, which can be simplified into an inertial stage. This simplification in this invention is to obtain the mathematical model of the object when adjusting the power. The transfer function is:

[0050]

[0051] Among them, K ZL T ZL These represent the equivalent magnification factor and the equivalent time constant, respectively.

[0052] 2. Power Amplification Stage

[0053] The power amplification section of the electrode adjustment system in an electric fused magnesium furnace uses thyristors as the power amplification stage, which can be considered a first-order pure time-delay stage. Its transfer function is:

[0054]

[0055] Among them, K GF T GF These represent the equivalent magnification factor and the equivalent time constant, respectively.

[0056] 3. AC asynchronous motor

[0057] An AC asynchronous motor is a nonlinear object, and strictly speaking, its transfer function cannot be written out. Since the lifting motor in the electrode adjustment system primarily drives the electrode movement, similar to a servo system, the speed accuracy requirement is not very high. Therefore, a linear model can be used to approximate its transfer function:

[0058]

[0059] Where: K DJ The scaling factor of an AC asynchronous motor; T S T represents the electromagnetic time constant; L This represents the electromechanical time constant.

[0060] 4. Mechanical transmission device

[0061] Mechanical transmission devices refer to the speed reduction, conversion, and transmission devices between the output shaft of the lifting motor and the electrodes. Essentially, it's an integral element that converts speed into displacement, and its transfer function is:

[0062]

[0063] Among them, K JX T JX These represent the equivalent magnification factor and the equivalent time constant, respectively.

[0064] 5. Speed ​​Measurement Feedback Process

[0065] This stage can be considered as a proportional stage, and its transfer function is:

[0066] G CS (s)=K CF (17)

[0067] Among them, K CF This is the magnification factor of the tachometer motor.

[0068] 6. Main circuit of fused magnesium furnace

[0069] Considering the main circuit of the fused magnesium furnace as a proportional circuit near the rated operating point, we have:

[0070] G ZDL (s)=K ZDL (18)

[0071] The transfer function of the system is obtained from the Mason gain formula:

[0072]

[0073] To study the operation control of fused magnesium loads participating in the primary frequency regulation of the power grid, it is first necessary to establish its frequency response model before analyzing its frequency regulation performance and formulating optimized control strategies. This invention uses the electrode adjustment system of the fused magnesium furnace as the basis for establishing the furnace's frequency response model. During the main melting operation of the fused magnesium furnace, the furnace power is increased or decreased by lifting the electrodes. Then, the droop coefficient K is varied to respond to changes in the power grid frequency, ultimately establishing a frequency response model for the fused magnesium furnace based on electrode adjustment.

[0074] The beneficial effects of this invention are as follows:

[0075] (1) Since the fused magnesium furnace is a complex, nonlinear, and strongly coupled system, and research on smelting processes and electrothermal conversion mechanisms is still incomplete, it is difficult to directly obtain a detailed analytical model of its frequency response parameters. This invention achieves bidirectional and continuous adjustment of power usage by lifting the electrodes, thereby decomposing the relationship between electrode lifting force and frequency response output power into several links. By determining intermediate variables and mining mapping relationships in several steps, a frequency response model under the lifting electrode mode is obtained.

[0076] (2) This invention explores the control characteristics of the molten magnesium furnace, realizes the adjustment of the molten magnesium furnace smelting power, obtains the adjustment power change curve of the molten magnesium furnace, and finally verifies the effectiveness of the frequency response model of the molten magnesium furnace based on electrode adjustment through simulation. It provides a reasonable frequency regulation control method and frequency response characteristic description method for the molten magnesium furnace, a typical high-energy-consuming industrial load, to participate in the primary frequency regulation of the power grid. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the smelting process in an electric fused magnesium furnace.

[0078] Figure 2 For the electrothermal conversion circuit of the fused magnesium furnace;

[0079] Figure 3 A simplified electrothermal conversion circuit for an electric fused magnesium furnace;

[0080] Figure 4 Diagram of the internal structure of the molten pool;

[0081] Figure 5For the three-phase equivalent circuit of the electrode adjustment system;

[0082] Figure 6 A simplified three-phase equivalent circuit for the electrode adjustment system;

[0083] Figure 7 For the electrode adjustment system of an electric fused magnesium furnace;

[0084] Figure 8 A simulation model for the adjustable capacity of an electric fused magnesium furnace;

[0085] Figure 9 Simulation results of the adjustable capacity of the fused magnesium furnace;

[0086] Figure 10 A simulation model for the performance regulation of an electric fused magnesium furnace;

[0087] Figure 11 Simulation results of performance adjustment for an electric fused magnesium furnace;

[0088] Figure 12 A flowchart of the present invention.

[0089] In the diagram: 1 Furnace body; 2 Electrode; 3 Material; 4 Electric arc; 5 Slag; 6 Molten pool; 7 Resistance heating. Detailed Implementation

[0090] The present invention will be further described below with reference to specific embodiments.

[0091] Based on the determined primary frequency modulation mode of the lifting electrode, it is further necessary to establish its frequency response model through analysis of the electrothermal conversion process of the fused magnesium furnace, that is, to clarify the relationship between the lifting height of the electrode and the increase or decrease of the smelting power of the fused magnesium furnace. However, since the fused magnesium furnace is a complex, nonlinear, and strongly coupled system, and research on smelting processes and electrothermal conversion mechanisms is still incomplete, it is difficult to directly obtain a detailed analytical model of its full frequency response parameters. This paper proposes to decompose the relationship chain between the electrode lifting force and the frequency response output power into several links, and obtain the frequency response model under the lifting electrode mode by determining several intermediate variables and mining the mapping relationships. In the derivation of the corresponding relationships in each link, reasonable simplification and linearization are performed based on the characteristics of frequency adjustment, finally obtaining the frequency response model of fused magnesium. This invention uses the actual parameters of an fused magnesium furnace in a factory in Dashiqiao City, Liaoning Province as an example.

[0092] A method for establishing a frequency response model of an electric fused magnesium furnace based on electrode adjustment includes the following steps:

[0093] Step 1: Study the electrothermal conversion process and calculate the working resistance of the fused magnesia furnace. During the smelting process, graphite electrodes are embedded in the raw materials, and the electric arc generated between the bottom of the electrodes and the raw materials serves as the heat source for production. In addition to the heat generated by the electric arc, the current in the molten pool also generates resistance heating to maintain the temperature of the molten pool. Pulling the electrode changes the distance l between the electrode and the slag at the bottom of the furnace, which in turn affects the resistance R1 of the molten pool below each phase of the electric arc and the resistance R2 of each phase of the electric arc. The material layer is solid granular magnesite ore with high resistivity. The resistance R3 of the material layer is considered infinite, and the branch containing it is considered an open circuit. This invention does not consider the resistance R3 of the material layer.

[0094] Based on the energy conversion circuit and the internal structure of the molten pool during molten magnesium smelting in an electric melting furnace, the resistance R1 of the molten pool and the arc resistance R2 are calculated to obtain the relationship between the electrode height h and the working resistance. The electrode adjustment height Δh is:

[0095] Δh=149.23t(mm / s) (20)

[0096] Where t represents the sampling time, with an interval of 1 second. Electrode height h:

[0097] h=500+149.23t(mm / s) (21)

[0098] During the smelting process, an electric field is generated near each phase electrode in the fused magnesium furnace. Using the electric field strength formula and Ohm's law, the resistance R1 of the molten pool below the bottom of the electrode can be calculated as follows:

[0099] R1≈3.7×10 -3 Ω (22)

[0100] There is currently no definitive expression for the arc resistance R2 of a submerged arc furnace. Research indicates that some open-arc characteristics of electric arc furnaces are also applicable to submerged arc furnaces under certain circumstances. Therefore, the calculation of arc resistance in this invention uses the Cassie arc conductance model for open arc furnaces.

[0101]

[0102] Where E0 represents the instantaneous value of the arc voltage; v represents the arc voltage; i represents the arc current, i = i0 + Δi, where i0 represents the initial value of the arc current and Δi represents the change in arc current (caused by the change in electrode position); θ represents the arc time constant. The inter-electrode conductance G when the arc disappears... min This is also something that needs to be considered during modeling, namely the single-phase electrode arc conductivity model of an electric fused magnesium furnace:

[0103]

[0104] Step 2: Describe the power external characteristics of the fused magnesia furnace. Refer to the secondary side of the furnace transformer for the electrode adjustment system circuit. Assume the three-phase parameters are identical. R1 and L1 represent the equivalent resistance and inductance of the molten pool resistance below each phase electrode of the fused magnesia furnace referred to the secondary side of the furnace transformer; R4 and L2 represent the equivalent resistance and inductance of each phase electrode of the fused magnesia furnace referred to the secondary side of the furnace transformer; M represents the mutual inductance between the electrodes of the fused magnesia furnace, R... a1 R a2 and R a3 This represents the arc resistance model of the three-phase electrodes A, B, and C.

[0105] The electrode adjustment system model established in this invention aims to provide the adjustment capability and performance of the fused magnesium furnace participating in primary frequency regulation. Without considering all details of the electrical system, and ignoring the coupling effect between the electrodes during simultaneous raising and lowering of the three-phase electrodes, the simplified equivalent circuit yields: R = 0.596 × 10⁻⁶. -3 Ω, L=3.111μF.

[0106] The following differential equation can be derived from Kirchhoff's laws:

[0107]

[0108] The model of the electrode regulation system is expressed in the form of state equations. The three-phase arc currents i1, i2, and i3 are represented by state variables x1, x2, and x3, respectively, and G1, G2, and G3 represent the arc conductances of the three-phase electrodes A, B, and C, respectively. According to equation (5-6), let the three-phase arc conductances G1, G2, and G3 be represented by three state variables x4, x5, and x6, respectively, and we obtain the state equation for arc power regulation:

[0109]

[0110] The smelting power P of an electric magnesia furnace can be obtained by combining the obtained arc power adjustment model with the resistance heating generated by the current passing through the molten pool.

[0111]

[0112] The electric molten magnesium furnace responds to grid frequency changes using a variable droop coefficient. The real-time adjustable power of the furnace is ΔP. ​​Due to limitations in the furnace's production process, -0.2p ≤ Δp ≤ 0.1p. The K coefficient is set based on the frequency difference. If the frequency difference is within the dead zone, the furnace will not operate regardless of its size to prevent encroachment on the frequency regulation space of thermal power units and avoid unnecessary waste. If the real-time frequency difference exceeds the dead zone but does not exceed the grid's frequency quality requirements, the frequency regulation resources will set a certain K value and perform a frequency regulation in droop control mode. If the real-time frequency difference exceeds the grid's frequency quality requirements, the frequency regulation resources will set another K limit value, as shown in the following expression:

[0113]

[0114] The electrode adjustment system model for the fused magnesia furnace established in this invention is built without considering the controller. To verify the adjustment capability of the model, it is assumed that the height h from the bottom end to the slag is fixed at 1m, which can verify the adjustment capability of equation (7). Figure 6 According to equation (7), a simulation model is built using MATLAB / Simulink as follows: Figure 8 As shown, the smelting characteristic curves of the fused magnesium furnace are obtained as follows: Figure 9 As shown.

[0115] Depend on Figure 9 It is known that since the working curve of fused magnesia at various times differs from the upper / lower limits of the furnace power, there is still some power adjustment space. This adjustment can be achieved by raising the electrodes to change the arc current and thus the smelting power of the fused magnesia furnace. This power adjustment can be used as the primary frequency regulation power of the fused magnesia furnace, and bidirectional frequency regulation can be achieved. However, in some operating conditions (venting and charging conditions), the power fluctuation is too large for power adjustment, such as... Figure 9 Within the square frame area. Melting power can only be achieved in the main melting condition (…). Figure 9 Adjustments are made within the elliptical region. As shown in the figures, the power output of a single boiler is reduced by approximately 0.2MW, and increased by approximately 0.1MW.

[0116] Step 3: Establish a model of the electrode adjustment system. After determining the smelting power of the fused magnesia furnace, it is also necessary to clarify the adjustment performance of the lifting electrode (such as response time delay caused by the characteristics of various parts of the electrode adjustment system). The electrode adjustment system of the fused magnesia furnace is a typical nonlinear system, and its full parameter description cannot be obtained analytically using mathematical methods. According to the simplification principle of nonlinear systems, it is decomposed into a nonlinear static system and several linear dynamic systems. In this invention, the main circuit of the fused magnesia furnace is simplified into a nonlinear static link. To establish the relationship between the increase or decrease of the smelting power of the fused magnesia furnace and the electrode lifting height, without considering the controller, the equivalent linear dynamic system is decomposed into typical first-order or second-order systems:

[0117] 1. Rectifier and filter stage

[0118] The rectification and filtering stage is actually a nonlinear transformation process, which can be simplified into an inertial stage. This simplification in this invention is to obtain the mathematical model of the object when adjusting the power. The transfer function is:

[0119]

[0120] 2. Power Amplification Stage

[0121] The power amplification section of the electrode adjustment system in an electric fused magnesium furnace uses thyristors as the power amplification stage, which can be considered a first-order pure time-delay stage. Its transfer function is:

[0122]

[0123] 3. AC asynchronous motor

[0124] An AC asynchronous motor is a nonlinear object, and strictly speaking, its transfer function cannot be written out. Since the lifting motor in the electrode adjustment system primarily drives the electrode movement, similar to a servo system, the speed accuracy requirement is not very high. Therefore, a linear model can be used to approximate its transfer function:

[0125]

[0126] 4. Mechanical transmission device

[0127] Mechanical transmission devices refer to the speed reduction, conversion, and transmission devices between the output shaft of the lifting motor and the electrodes. Essentially, it's an integral element that converts speed into displacement, and its transfer function is:

[0128]

[0129] 5. Speed ​​Measurement Feedback Process

[0130] This stage can be considered as a proportional stage, and its transfer function is:

[0131] G CS (s)=0.05s (33)

[0132] 6. Main circuit of fused magnesium furnace

[0133] Considering the main circuit of the fused magnesium furnace as a proportional circuit near the rated operating point, we have:

[0134] G ZDL (s)=0.009s (34)

[0135] Combination Figure 8 Using the principles of automatic control, substituting the transfer functions of each stage and omitting higher powers, we have:

[0136]

[0137] The state equation expression for the electrode adjustment system of the fused magnesium furnace is then derived as follows:

[0138]

[0139]

[0140] in: t represents the state variables of the electrode adjustment system; A represents the transmission coefficient matrix of the lifting motor; x(t) represents the system state variables of the fused magnesium furnace; B represents the transmission coefficient matrix of the actuator; u(t) represents the speed of the lifting motor; y(t) represents the actual smelting power of the fused magnesium furnace; C represents the arc coefficient matrix.

[0141] The initial height of the electrode bottom from the slag was set to 1m. The state equation (7) of the established electric molten magnesium furnace electrode adjustment system, combined with the state equation (18) of the arc power adjustment, was used for simulation in MATLAB / Simulink. The simulation duration was set to 20s. At the 10th second, the electrode was pulled up and lowered. The electrode height was raised to 1050mm from the slag at the bottom, and lowered to 900mm from the slag at the bottom. The simulation model is as follows. Figure 10 As shown. After the adjustment action occurs, the performance simulation results are as follows. Figure 11 As shown.

[0142] Depend on Figure 11 It can be seen that the active power response speed of the fused magnesium furnace is on the order of seconds. Regardless of the direction of adjustment, the time for the power change to first reach 10% of the target control power is approximately 1.2 seconds, and the time for the power change to first reach 90% of the target control power is approximately 2.1 seconds. According to the latest "Implementation Rules for the Management of Ancillary Services of Grid-Connected Power Plants and the Implementation Rules for the Management of Grid-Connected Operation of Power Plants" issued by China, the start-up time (from receiving the control signal until the power change first reaches 10% of the target control power) should not exceed 3 seconds, and the response time (from receiving the control signal until the power change first reaches 90% of the target control power) should not exceed 12 seconds. Therefore, the adjustment time for regulating the active power of the fused magnesium furnace by controlling the electrode lifting meets the regulatory requirements.

[0143] In summary, previous research on the participation of high-energy-consuming industrial loads in power system frequency regulation ancillary services has focused primarily on electrolytic aluminum plants, steel mills, and cement plants, lacking research on the frequency response power characteristics of fused magnesia furnaces. This invention, through exploring the control characteristics of fused magnesia furnaces, achieves the adjustment of the furnace's smelting power, obtaining the adjustment power variation curve. Finally, simulations verify the effectiveness of the frequency response model of the fused magnesia furnace based on electrode adjustment, providing a reasonable frequency regulation control method and a frequency response characteristic description method for this typical high-energy-consuming industrial load to participate in the primary frequency regulation of the power grid.

[0144] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for establishing a frequency response model of an electric fused magnesium furnace based on electrode adjustment, applied to the participation of a high-energy-consuming electric fused magnesium furnace load in the primary frequency regulation of the power grid, characterized in that... First, the electrode adjustment system of the fused magnesia furnace is used as the basis for establishing the frequency response model of the fused magnesia furnace. During the main melting operation of the fused magnesia furnace, the power of the fused magnesia furnace is increased or decreased by lifting the electrodes. Then, the frequency response of the power grid is responded to by changing the droop coefficient K. Finally, a frequency response model of the fused magnesia furnace based on electrode adjustment is established. Specifically, the following steps are included: Step 1: Analyze the electrothermal conversion process of the fused magnesium furnace and calculate the working resistance to obtain the single-phase electrode arc conductivity model of the fused magnesium furnace; During the smelting process, the graphite electrodes inside the fused magnesia furnace are embedded in the raw materials. Pulling up the electrodes changes the distance between the electrodes and the slag at the bottom of the furnace. This further affects the resistance of the molten pool beneath each phase arc. and the arc resistance of each phase Effects; Material layer resistance The value is considered infinite, and the corresponding branch is considered an open circuit. The resistance of the material layer is not considered. Electrode adjustment lifting height for: (1) in, This indicates the rotational speed of the lifting motor; This indicates the sampling time, with an interval of 1 second; This indicates the reduction ratio of the lifting motor. Indicates the gear radius of the lifting motor; Electrode height for: (2) in, This indicates the initial distance between the bottom of the electrode and the slag. The single-phase electrode arc conductivity model of the fused magnesium furnace during the smelting process is as follows: (3) in, This is the inter-electrode conductance when the electric arc disappears; Indicates the instantaneous value of the arc voltage; Indicates arc voltage; Represents arc current. , This represents the initial value of the electric arc current. This indicates the change in arc current; Indicates the arc time constant; During the smelting process, the arc current of each phase electrode increases with the increase of the electrode height, and the arc resistance of each phase electrode also increases with the increase of the electrode height. That is, increasing the electrode height can increase the smelting power of the electric fused magnesium furnace. Step 2: Convert the electrode adjustment system circuit to the secondary side of the furnace transformer. Assume that the three-phase electrode parameters are exactly the same and that the three-phase electrodes rise and fall simultaneously. Ignore the coupling effect between the electrodes and the mutual inductance between the electrodes of the fused magnesia furnace to simplify the circuit. The following differential equation is derived from Kirchhoff's laws: (4) The model of the electrode regulation system is expressed in the form of state equations, and the three-phase arc current is... , and Using state variables respectively , and express, , and Let the arc conductances of the three phase electrodes A, B, and C be represented respectively; and let three state variables be defined. , , Indicates the arc conductance of the three-phase electrodes , , The state equation for arc power regulation is obtained as follows: (5) The smelting power of an electric magnesia furnace can be obtained by combining the obtained arc power adjustment model with the resistance heating generated by the current passing through the molten pool. : (6) in, This represents the electrical conductance of the arc between the three phase electrodes A, B, and C; , Indicates electrode current; Indicates the resistance of the molten pool; By employing a variable droop K-coefficient to respond to changes in grid frequency, the power of the electric magnesia furnace can be adjusted in real time. , ,in The rated operating power of the fused magnesia furnace; determined by the actual production process of the fused magnesia furnace. coefficient; Step 3: Establish a frequency response model of the fused magnesium furnace based on electrode adjustment; after determining the smelting power of the fused magnesium furnace, it is also necessary to clarify the adjustment performance of the lifting electrode; the electrode adjustment system of the fused magnesium furnace is a typical nonlinear system. The main circuit of the fused magnesium furnace is simplified into a nonlinear static link. In order to establish the relationship between the increase or decrease of the smelting power of the fused magnesium furnace and the lifting height of the electrode, without considering the controller, the equivalent linear dynamic system is decomposed into a typical first-order or second-order system.

2. The method for establishing a frequency response model of an electric fused magnesium furnace based on electrode adjustment according to claim 1, characterized in that, In step 2, the following steps are set: The coefficients are based on frequency difference. Determined by size Value magnitude: If the frequency difference is within the dead zone, the electric fused magnesium furnace will not operate regardless of the frequency difference, to prevent it from encroaching on the frequency regulation space of the thermal power unit and causing unnecessary waste; if the real-time frequency difference... If the frequency regulation resource exceeds the dead zone but does not exceed the frequency quality requirements of the power grid, a certain frequency regulation resource will be set. If the real-time frequency difference exceeds the grid frequency quality requirements, the frequency regulation resources will be set again. The limit value; the specific expression is as follows: (7) in, for Frequency modulation coefficient of fused magnesium enterprises at all times; This indicates the threshold value for power grid frequency quality requirements; This indicates the frequency dead zone of an electric fused magnesium furnace.

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