CN105846691B

CN105846691B - A kind of cascade connection multi-level tundish electromagnetic heating power supply integrated control method

Info

Publication number: CN105846691B
Application number: CN201610317491.1A
Authority: CN
Inventors: 罗安; 岳雨霏; 徐千鸣; 马伏军; 何志兴; 周奔; 丁红旗; 郭鹏
Original assignee: Hunan University
Current assignee: Hunan University
Priority date: 2016-05-13
Filing date: 2016-05-13
Publication date: 2018-05-11
Anticipated expiration: 2036-05-13
Also published as: CN105846691A

Abstract

The invention discloses a kind of cascade connection multi-level tundish electromagnetic heating power supply and its integrated control method, the cascade connection multi-level tundish electromagnetic heating power supply is the more level block structures of cascade connection type full-bridge, and the realization of its integrated control method comprises the following steps：By three-phase power grid voltage, input current transforms to two-phase rest frame respectively with circulation and three-phase stops under coordinate system, using track with zero error input current and circulation；Capacitance voltage inside bridge arm is using balance control strategy, the voltage deviation square chosen in upper and lower bridge arm module capacitance voltage quadratic sum in the horizontal direction, the difference of two squares and vertical direction obtains unbalanced power under 0 rest frames of three-phase α β as voltage control quantity, and then by controlling bridge arm energy come balance module voltage.The present invention realizes the rapid track and control of input and output electric current, improves control efficiency, meets the requirement of induction heating power energy balance and high current Fast transforms.

Description

Comprehensive control method for cascade multilevel tundish electromagnetic heating power supply

Technical Field

The invention relates to a comprehensive control method for a cascade multilevel tundish electromagnetic heating power supply.

Background

With the progress of power electronics and semiconductor technology, the development of steel heat treatment induction heating technology is greatly promoted by the appearance of a high-power high-efficiency variable frequency power supply, a tundish induction heating power supply is used as a medium for electric energy conversion, the input current of the tundish induction heating power supply influences the electric energy quality of a public power grid, and the output current of the tundish induction heating power supply is directly related to the tundish temperature control effect, so that the study on a tundish induction heating power supply control method has good theoretical and engineering significance, and the tundish induction heating system has higher requirements on the stability of power supply energy transmission and the rapid conversion of large current.

The existing high-frequency resonant induction heating power supply is mostly used in low-power occasions, and the output frequency range of the high-power wide-size induction heating power supply for metallurgy is medium-low frequency. The prior tundish induction heating power supply with more applications adopts a simple and reliable phase-shifting transformer and diode rectification structure at the front stage and adopts a cascade H-bridge structure with independent direct current sides at the rear stage to realize the conversion from three phases to single phase, and has the defect that energy flow is unidirectional from a power grid to a tundish, so the capacity of regulating the capacitance and the voltage of the direct current side is limited, and meanwhile, although the multi-winding transformer reduces the harmonic content of the power grid current to a certain degree, the cost and the volume of the power supply are also increased.

In recent years, the tundish induction heating power supply based on the H bridge sub-module cascade multilevel structure benefits from good modularization, low harmonic and multiple redundancy characteristics and gets wide attention in the field of AC-AC conversion, particularly, the structure of a full-bridge multilevel modular converter (F-MMC) has buck-boost characteristics, the output frequency and the modulation degree of the structure are wider than those of an MMC (H-MMC) of a half H bridge sub-module, and the F-MMC structure applied to the tundish electromagnetic heating variable frequency power supply has the characteristics of modularization, low harmonic and multiple redundancy, can realize bidirectional flow of power, reduce the volume and the cost of the device, improve the stability of the system and overcome the defects of the traditional structure, and is an ideal AC-AC converter. However, the discrete energy storage elements of the cascaded multilevel structure bring great difficulty to voltage balance, and it is worth exploring to find a voltage balance control strategy combined with energy stability control.

Disclosure of Invention

The invention aims to solve the technical problems that the bidirectional flow of energy between a tundish induction electromagnetic heating power supply and a power grid is realized, the cost and the volume of the power supply are solved, and the defects of the prior art are overcome, and the comprehensive control method of the cascade multilevel tundish electromagnetic heating power supply is provided.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a comprehensive control method of a cascade multilevel tundish electromagnetic heating power supply is characterized in that a multilayer control method combining direct power control and deadbeat current control is adopted for an F-MMC multilevel structure, an input current instruction of integral energy balance in a discrete domain, an interphase and intra-phase energy balance circulation instruction are derived, and the selection range of parameters of each layer of voltage controller is obtained on the premise of voltage closed-loop control stability.

The technical scheme for solving the technical problems comprises the following steps:

1) according to KVL and KCL theorem, a basic structural equation based on the cascade multilevel tundish electromagnetic heating power supply is established as follows:

wherein u is_sa,u_sb,u_scAnd u_oA three-phase AC input voltage and a single-phase AC output voltage, u_upxAnd u_dnxX (x is a, b, c) phase output voltage of upper and lower bridge arms, i_upx，i_dnx，i_zxAnd i_sxThe current of the upper and lower bridge arms of the x phase and the circulating current and the input current of the x phase, i_oIn order to output load current, L and C are a bridge arm reactance value and a sub-module capacitance value respectively. The two types are simplified to obtain an equivalent model of the converter alternating current loop and the circulating loop;

2) firstly, the three-phase power grid voltage, the input current and the circulating current are respectively transformed to a two-phase α β static coordinate system and a three-phase alpha beta 0 static coordinate system, and the input current and the circulating current have differential equations under the alpha beta coordinate system, as follows:

wherein i_sα，i_sβ，u_sα，u_sβ，u_invαAnd u_invβvalues of common-mode output voltage, i, of three-phase network current and voltage and input current, respectively, in a two-phase alpha beta stationary coordinate system_zα，i_zβ，i_z0，u_zα，u_zβAnd u_z0three-phase circulating voltage, common-mode output voltage of circulating current and values L, R under three-phase α β 0 static coordinate system_LAnd L_eqBridge arm inductance, resistance and considerations, respectivelySingle-phase circulating current equivalent impedance of load reactance;

adopting a dead beat control method and a forward first-order Euler equation, and considering that the error between the current actual value and the predicted value of the next period is within an allowable range, namely:

wherein i_sα(k+1)，i_sβ(k+1)，Andinput current at the time k +1 in a stationary coordinate system of two phases of alpha and beta and a reference value i at the time k_zα(k+1)，i_zβ(k+1)，i_z0(k+1)，Andthe circulating current at the moment of k +1 under the stationary coordinate system of three-phase α β 0 and the reference value at the moment of k can be obtained by the two formulasAnddifferential mode output voltage reference of sum circulating current And

3) and realizing voltage balance among phases by controlling internal circulation and positive and negative sequence circulation of the converter. The voltage balance control of the electromagnetic heating power supply with the cascade multilevel structure can be divided into average voltage control, horizontal direction balance control and vertical direction balance control; the sum of squares of capacitor voltages of the cascaded module of each phase of bridge arm after discretization in the horizontal direction and the vertical direction, and the common mode quantity of the square difference and the square of voltage deviation in the vertical direction are respectively as follows:

wherein,(x is a, b, c, the same applies below),andthe common mode parts are the square of the sum of the voltages of the x-phase upper bridge arm, the square of the sum of the voltages of the lower bridge arm, the sum of the squares of the voltages of the upper bridge arm and the lower bridge arm, the square difference and the square of the voltage deviation in the vertical direction in the kth control period respectively;

4) the control of the outer ring voltage in the horizontal direction and the vertical direction and the control of the inner ring current are adopted to obtain the control equations of the active power and the reactive power in the converter, and the balance cascade module capacitor voltage is directly controlled through the power;

the step 4) comprises the following steps: and if the reactive command of the rectification control part is set to be 0 without considering reactive compensation, the active power and the reactive power of the cascade multi-level power supply at the moment k are not availableReference value of power P^*(k) And Q^*(k) Comprises the following steps:

wherein,andreference and actual values, k, respectively, representing the sum of the squares of the three-phase module voltages of the converter's stored energy_p1And k_i1Respectively, the proportional coefficient and the integral coefficient of the average voltage controller. According to the instantaneous power theory, the active power P (k) and the reactive power Q (k) of the kth control period can be obtained, then the reference value of the input current can be obtained from the power reference value, and the outer loop control of the average voltage and the inner loop control of the input current can be obtained by combining the reference value of the differential mode output voltage to realize the direct power control.

The voltage balance in the horizontal direction among three phases can be ensured by adjusting high-frequency positive sequence current and high-frequency negative sequence current which have the same frequency with the output voltage, and the voltage reference value for controlling the balance in the horizontal direction is set to be zero, so that the sum of the squares of the voltages in the horizontal direction is obtained through a PI (proportional-integral) controller to obtain the active power reference value in the horizontal direction.

The voltage balance in the vertical direction can be adjusted by adjusting the fundamental frequency circulating current component having the same frequency as the input voltage, and in order to prevent the occurrence of an undesired fundamental frequency current component in the output current, the fundamental frequency circulating current component for the voltage balance control in the vertical direction contains positive sequence and negative sequence components, and the three-phase voltage u for achieving the voltage balance in the vertical direction_sa、u_sb、u_scThe voltage reference for positive sequence properties, i.e. for vertical direction balance control, isUnbalanced active power between upper and lower three-phase bridge armsAndcan be expressed as follows:

wherein,andrespectively an active power reference value k obtained by a vertical direction balance voltage controller at the moment k_p3And k_i3Respectively, the proportionality coefficient and the integral coefficient of the vertical balance voltage controller. Thus, the circulating current component for eliminating the power imbalance between the upper and lower arms of the three phases is represented as follows:

wherein,andthe total circulation component reference value, the positive sequence circulation component reference value and the negative sequence circulation component reference value at the k moment under the three-phase α β 0 static coordinate system are respectively.

Compared with the prior art, the invention has the beneficial effects that: according to the comprehensive control method of the cascade multi-level tundish electromagnetic heating power supply, the outer ring respectively obtains the active power reference values for directly controlling the energy of each phase of bridge arm, eliminating the imbalance among three-phase bridge arms and eliminating the imbalance among three-phase upper and lower bridge arms through the average voltage controller, the horizontal balanced voltage controller and the vertical balanced voltage controller, and further obtains the input current amount and the loop flow rate of the inner ring for directly controlling the power and eliminating the power imbalance of the three-phase bridge arms, so that the multilayer control method combining direct power control and deadbeat current control is realized, the loop current instruction frequencies output by the horizontal direction balanced control and the vertical direction balanced control are different, the control processes are mutually independent, no coupling relation exists, and the energy conversion of the electromagnetic heating power supply can be effectively realized.

Drawings

Fig. 1 is a block diagram of a cascaded multi-level tundish electromagnetic heating power supply used in the present invention.

Fig. 2 is an equivalent circuit model of the ac input current loop and the circulating current loop according to an embodiment of the present invention.

Fig. 3 is a diagram illustrating the processing and coordinate transformation of the electromagnetic heating power circuit according to an embodiment of the present invention.

Fig. 4 is a block diagram of the control of the average voltage outer loop and the input current inner loop according to an embodiment of the present invention.

Fig. 5 is a control block diagram of the outer ring and the inner ring of the ring current for voltage balance in the horizontal direction and the vertical direction according to an embodiment of the present invention.

Detailed Description

Fig. 1 is a diagram showing a cascade multilevel structure used for the tundish electromagnetic heating power supply of the invention, each phase of the cascade multilevel structure is composed of an upper bridge arm and a lower bridge arm, the input ends of the two star cascade SVG can be regarded as parallel, the output ends are connected in series, the direct current output end is connected with an electromagnetic heating power supply load, and the three-phase alternating current network system is 10kV/50Hz in grade. In the figure, u_sx(x ═ a, b, c, the same applies below) and i_sxVoltage and current, u, of a three-phase AC network, respectively_upx，u_dnx，i_upxAnd i_dnxRespectively the output voltage and bridge arm current of the upper and lower bridge arms of each phase, SM is an H-type full-bridge submodule cascaded by the upper and lower bridge arms of each phase, u is_cix(x ═ a, b, C, i ═ 1,. n, the same below) is the dc side capacitance voltage of the cascaded submodules, C is the capacitance value of the submodule capacitor, L is the bridge arm inductance, i is the bridge arm inductance_oAnd u_oRespectively, a dc side load current and a load voltage.

Fig. 2 is an equivalent model structure diagram of the ac circuit and the circulating circuit of the cascaded converter. The KCL and KVL are used to obtain an equation (1) and an equation (2), which are decomposed into differential mode and common mode parts, as shown in equation (3), which are respectively the AC loop voltage u in the figure_invxAnd the voltage u of the circulation loop_zx。

In the formula u_sxAnd i_sxVoltage and current, u, of a three-phase AC network, respectively_upx，u_dnx，i_upxAnd i_dnxOutput voltage and bridge arm current i of upper and lower bridge arms respectively_zxEach phase of bridge arm circulating current, L is bridge arm inductance, i_oAnd u_oRespectively, a dc side load current and a load voltage. After simplification, can obtain

Wherein u is_o＝i_o(R_L+jωL_L),i_o＝i_za+i_zb+i_zcEquations (4) and (5) are the spatial equation of state expressions of the equivalent model.

Fig. 3 is a diagram of input signal processing and coordinate transformation. Bridge arm circulation i_zxAnd an output current i_oThe two-phase stationary coordinate transformation is obtained from the matrix of equation (6)

Fig. 4 is a control block diagram of an average voltage outer loop and an input current inner loop.

The control process of the input current inner loop in the control strategy is as follows: obtaining the input current i from the converter AC loop model of FIG. 2_sxthe differential equation in the α β coordinate system is

In the formula (7), i_sy(y ═ α, β, the same applies below), u_syAnd u_invythe three-phase AC input current, the input voltage and the differential mode voltage after the transformation of alpha and beta coordinates are respectively adopted, the dead beat control is adopted by the mutual independence of alpha and beta components, and the kth control period of the formula (7) can be written as

In the formula (8), T_SFor equivalent switching period, i_sy(k)，u_sy(k) And u_invy(k) Input current, input voltage and differential mode voltage, i, of kth control period, respectively_sy(k +1) is the predicted value of the output current in the kth control period, and the output current in the next periodActual and predicted values of currentThe error between the two is within the allowable range, then it can be considered as

By substituting equation (9) for equation (8), the input current can be obtained by the dead-beat controller in FIG. 4 to obtain the reference value of the output voltage of the differential modeIs composed of

the inner ring outputs a voltage reference value by controlling a differential mode under an alpha beta coordinateRealize the input currentAnd (4) controlling.

The control process of the average voltage outer ring in the control strategy is as follows: the voltage of the module is adjusted by controlling the power, under the condition of not considering reactive compensation, the reactive instruction of the rectification control part is set to be 0, and the integral unbalanced power can be expressed as

Wherein, P^*(k) And Q^*(k) Respectively the active power reference and the reactive power reference of the k-th cycle,andreference and actual values, k, respectively, representing the sum of the squares of the three-phase module voltages of the converter's stored energy_p1And k_i1Respectively, the proportional coefficient and the integral coefficient of the average voltage controller. According to the instantaneous power theory, the active power P (k) and the reactive power Q (k) of the kth control period can be obtained as

Wherein,for transforming the matrix, the reference value of the input current in a two-phase stationary coordinate system(y ═ α, β, the same applies below) can be represented as:

wherein, P^*(k) And Q^*(k) In order to be the power reference value,the direct power control is realized by combining the differential mode output voltage dead-beat control of the input current of the formula (10) and outer loop control of the obtained average voltage and inner loop control of the input current as an inverse transformation matrix.

Fig. 5 is a control block diagram of the voltage balance outer ring and the circulating current inner ring.

The control process of the circulation inner ring in the control strategy is as follows: the loop current i is obtained from the converter loop current loop model of fig. 2_zx(x is a, b, c, the same applies hereinafter) a differential equation in α β 0 coordinate system is

Wherein i_zj(j ═ α, β,0, the same applies below) and u_zjthe values of three-phase circulating voltage and circulating common-mode output voltage, L and R, in a three-phase α β 0 static coordinate system_LAnd L_eq＝L+3L_LThe/2 is the equivalent impedance of single-phase circulation with bridge arm inductance, resistance and load reactance considered respectively, because of the output current i_oIs the zero sequence component of three-phase circulating current, and thus hasAs can be seen from equation (14), the α β 0 components of the circulating currents are independent of each other, and forward first-order deadbeat control is employed, and the kth control period of equation (11) can be written as

Wherein i_zj(k)，i_zj(k +1) and u_zj(k) circulation at the moment k, circulation at the moment k +1 and circulation differential mode output voltage at the moment k, L and R in a three-phase α β 0 static coordinate system respectively_L，L_eqAnd T_sBridge arm inductance and resistance are respectively, and single-phase circulating current equivalent impedance and sampling period of load reactance are considered; if the error between the actual value and the predicted value of the output current of the next period is within the allowable range, the method can be regarded as the method

Wherein i_zj(k +1) andthe ring current at the time k +1 in the stationary coordinate system of three-phase α β 0 and the reference value at the time k are respectively obtained by substituting the formula (16) into the formula (15)Common mode output voltage reference for current deadbeat control is

Wherein,i_zj(k) andreference values of circulation differential mode output voltage at the k moment, circulation current value and reference values thereof, L and R under a three-phase α β 0 static coordinate system_L，L_eqAnd T_sBridge arm inductance and resistance, and single-phase circulation equivalent impedance and sampling period of load reactance are considered.

The control process of the voltage balance outer ring in the control strategy is as follows: the process is divided into horizontal direction voltage balance control and vertical direction voltage balance control, which operate in discrete domains.

Voltage reference value for horizontal direction balance controlThe unbalanced power between the three phases can be expressed as

Wherein,andrespectively is an active power reference value k obtained by a horizontal direction balance voltage controller at the k moment under a two-phase alpha beta static coordinate system_p2And k_i2Respectively horizontal equilibrium voltagethe high frequency circulating current components used to control power imbalance between the three phases are thus represented in the two-phase α β stationary frame as follows:

wherein,andrespectively obtaining high-frequency circulation reference values for the active power reference value,to transform the matrix, depending on the form of the loop instructions.

The vertical direction voltage balance control prevents an undesired fundamental frequency current component from occurring in the output current, the fundamental frequency circulating current component for the vertical direction voltage balance control includes a positive sequence component and a negative sequence component, and the three-phase voltage u for achieving the vertical direction voltage balance_sa、u_sb、u_scThe voltage reference for positive sequence properties, i.e. for vertical direction balance control, isUnbalanced active power between upper and lower three-phase bridge armsAndcan be expressed as follows:

wherein,andthe differential mode output voltage dead-beat control of the combined (17) circulation obtains voltage balance outer ring control and circulation inner ring control, and further realizes direct power control.

Claims

1. A comprehensive control method of a cascade multilevel tundish electromagnetic heating power supply comprises the steps that the cascade multilevel tundish electromagnetic heating power supply comprises a cascade multilevel structure and a tundish electromagnetic heating power supply which is connected with the cascade multilevel structure in parallel; each phase of the cascade multilevel structure is formed by connecting an upper bridge arm and a lower bridge arm in series; the upper bridge arm and the lower bridge arm both comprise a plurality of cascaded submodules; the method is characterized by comprising the following steps:

1) the following equation is established:

wherein u is_sa,u_sb,u_scThree-phase alternating current input voltages respectively; u. of_oOutputting voltage for single-phase alternating current; u. of_upxAnd u_dnxThe output voltages of the upper and lower bridge arms of x phase are respectively, x is a, b and c; i.e. i_upx，i_dnxRespectively x-phase upper and lower bridge arm currents; i.e. i_zxIs x-phase upper and lower bridge arm circulation; i.e. i_sxInputting current for x phase; i.e. i_oTo output a load current; l and C are respectively a reactance value of an upper bridge arm and a lower bridge arm and a capacitance value of a sub-module capacitor; simplifying the two types to obtain an equivalent model of the tundish electromagnetic heating power supply alternating current loop and the circulation loop;

2) according to the equivalent model obtained in the step 1), three-phase alternating input voltage and input current are converted into a two-phase α β static coordinate system, three-phase circulating current is converted into a three-phase alpha beta 0 static coordinate system, a dead beat control method is adopted to obtain differential mode output voltage reference values of the three-phase alternating input voltage, the circulating current and the input current, and the differential mode output voltage reference values are used as control quantities for controlling the input current and the circulating current, wherein differential equations of the three-phase alternating input voltage, the circulating current and the input current in the two-phase α β static coordinate system and the three-phase alpha beta 0 static coordinate system are as follows:

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wherein i_sα，i_sβis the value of three-phase power grid current in a two-phase alpha beta static coordinate system u_sα，u_sβis the value of the three-phase grid voltage in a two-phase alpha beta static coordinate system, u_invαAnd u_invβis the value of the common-mode output voltage of the input current in a two-phase alpha beta stationary frame, i_zα，i_zβ，i_z0is the value of three-phase circulating current in a three-phase α β 0 stationary coordinate system u_zα，u_zβAnd u_z0value of common-mode output voltage in three-phase α β 0 stationary coordinate system, L, R for circular current_LAnd L_eqThe equivalent impedance of the bridge arm inductance, the resistance and the single-phase circulating current considering the load reactance are respectively;

3) the common mode part of the average voltage of the upper and lower bridge arms, the square sum and square difference of the voltage in the horizontal direction and the voltage deviation in the vertical direction is constructed as follows:

andrespectively, in the kth control period, the square of the sum of the x-phase upper bridge arm voltages and the square of the sum of the x-phase lower bridge arm voltages;andthe square sum and the square difference of the voltage of the upper bridge arm and the lower bridge arm of the x phase in the kth control period are respectively;a common mode quantity that is the square of the vertical direction voltage deviation, andthe squares of voltage deviations of the three phases a, b and c in the kth control period in the vertical direction respectively;

4) establishing a common mode quantity based on the square of the voltage deviation in the vertical direction obtained in the step 3)And sum of the squares of the voltages in the horizontal directionThe voltage balance closed loop transfer function is determined by the closed loop transfer function and the Lao Si-Henritz stability criterion, and a proper PI controller is selected to ensure the stability of the system, so that the unbalanced energy of different control targets is obtained.

2. The integrated control method for the cascade multilevel tundish electromagnetic heating power supply according to claim 1, wherein the cascade submodules are in a full-bridge structure.

3. The integrated control method for the cascade multilevel tundish electromagnetic heating power supply according to claim 1, wherein the step 2) comprises the following steps:

1) converting three-phase alternating current input voltage, input current and circulating current into a two-phase α β static coordinate system and a three-phase alpha beta 0 static coordinate system respectively;

2) constructing a differential equation of the input current and the circulating current under an α β coordinate system:

<mrow> <mi>L</mi> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&beta;</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mn>2</mn> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>&alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>&beta;</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mn>2</mn> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&beta;</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>L</mi> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>&alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Li</mi> <mrow> <mi>z</mi> <mi>&beta;</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>z</mi> <mi>&alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>z</mi> <mi>&beta;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mfrac> <mrow> <mn>3</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

wherein i_sα，i_sβis the value u of the three-phase network current in a two-phase α β coordinate system_sα，u_sβis the value of the three-phase grid voltage in a two-phase alpha beta static coordinate system, u_invα、u_invβis the value of the common-mode output voltage of the input current in a two-phase alpha beta stationary frame, i_zα，i_zβ，i_z0are respectively the values u of the three-phase circulation under the three-phase α β 0 static coordinate system_zα，u_zβis the common-mode output voltage of three-phase loop current in two-phase α β static coordinate system_z0is the value of three-phase circulation current in a three-phase α β 0 stationary coordinate system, L, R_LAnd L_eqBridge arm inductance, resistance and single-phase circulating current equivalent impedance considering load reactance respectively;

3) obtaining the reference value of the differential mode output voltage of the input current and the circulation current by adopting a dead beat control method and a forward first-order Euler equation:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>&alpha;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mi>L</mi> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>i</mi> <mrow> <mi>s</mi> <mi>&alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&alpha;</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&beta;</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>&beta;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mi>L</mi> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>i</mi> <mrow> <mi>s</mi> <mi>&beta;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&beta;</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>z</mi> <mi>&alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>L</mi> </mrow> <msub> <mi>T</mi> <mi>S</mi> </msub> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>&alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>&alpha;</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>z</mi> <mi>&beta;</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>L</mi> </mrow> <msub> <mi>T</mi> <mi>S</mi> </msub> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>&beta;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>&beta;</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>L</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mrow> <msub> <mi>T</mi> <mi>S</mi> </msub> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>+</mo> <mn>3</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mn>0</mn> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

wherein,is the reference value of the input current differential mode output voltage at the time k under a two-phase α β static coordinate system_sα(k)，u_sβ(k) is an AC input voltage at the k moment under a two-phase α β static coordinate system i_sα(k)，i_sβ(k) the current value is the alternating current input current value at the k moment under a two-phase alpha beta static coordinate system;andis a reference value of the alternating current input current at the k moment under a two-phase α β static coordinate system; is a reference value of circulation differential mode output voltage at the k moment under a three-phase α β 0 static coordinate system i_zα(k)，i_zβ(k)，i_z0(k) are respectively three-phase alphacirculating current value at k moment under a beta 0 static coordinate system;respectively, reference values of circulating current value at k moment under three-phase α β 0 static coordinate system, L and R_L，L_eqAnd T is bridge arm inductance, resistance, single-phase circulation equivalent impedance considering load reactance and sampling period respectively; t is_SIs an equivalent switching period.

4. The integrated control method for the electromagnetic heating power supply of the cascade multilevel tundish according to claim 2, wherein the specific implementation process of the step 4) comprises the following steps:

1) the reactive instruction of the rectification control part is set to be 0, and the active power and reactive power reference value P of the cascade multilevel tundish electromagnetic heating power supply at the moment k^*(k) And Q^*(k) Comprises the following steps:

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>P</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>&lsqb;</mo> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>h</mi> <mi>o</mi> <mi>r</mi> <mn>0</mn> </mrow> <mrow> <mo>*</mo> <mn>2</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>h</mi> <mi>o</mi> <mi>r</mi> <mn>0</mn> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mrow> <mo>&lsqb;</mo> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>h</mi> <mi>o</mi> <mi>r</mi> <mn>0</mn> </mrow> <mrow> <mo>*</mo> <mn>2</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>h</mi> <mi>o</mi> <mi>r</mi> <mn>0</mn> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>Q</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

wherein,andrespectively representing the reference value and the actual value, k, of the square sum of the voltages of the three-phase cascade module of the cascade multi-level tundish electromagnetic heating power supply energy storage_p1And k_i1Proportional coefficient and integral coefficient of the average voltage controller respectively;

2) according to the instantaneous power theory, the active power P (k) and the reactive power Q (k) of the kth control period are obtained, and then the reference value of the input current is the power reference value P^*(k) And Q^*(k) Obtaining, in combination with the differential mode, a voltage reference Obtaining the outer ring control of the average voltage and the inner ring control of the input current to realize direct power control;

3) adjusting high-frequency positive sequence current and negative sequence current with the same frequency as the output voltage to ensure voltage balance in the horizontal direction among three phases, and setting a voltage reference value for balance control in the horizontal direction to be zero, so that the sum of squares of the voltage in the horizontal direction is used for obtaining an active power reference value in the horizontal direction through a PI (proportional-integral) controller;

4) adjusting fundamental frequency circulation components with the same frequency as the input voltage, adjusting voltage balance in the vertical direction, wherein the fundamental frequency circulation components for vertical voltage balance control comprise positive sequence components and negative sequence components, and three-phase voltage u for realizing vertical voltage balance_sa、u_sb、u_scThe voltage reference for positive sequence properties, i.e. for vertical direction balance control, isUnbalanced active power between upper and lower three-phase bridge armsAndis represented as follows:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>a</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mn>3</mn> </mrow> </msub> <mo>&lsqb;</mo> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>a</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mo>&lsqb;</mo> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>a</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>b</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mn>3</mn> </mrow> </msub> <mo>&lsqb;</mo> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>b</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mo>&lsqb;</mo> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>b</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mn>0</mn> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mn>3</mn> </mrow> </msub> <mo>&lsqb;</mo> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mn>0</mn> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mo>&lsqb;</mo> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mn>0</mn> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

wherein,andrespectively an active power reference value k obtained by a vertical direction balance voltage controller at the moment k_p3And k_i3Proportional coefficient and integral coefficient of the vertical balance voltage controller respectively;

5) the circulating current component for eliminating the power imbalance between the upper and lower bridge arms of the three phases is expressed as follows:

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>&alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>&beta;</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>&alpha;</mi> <mo>+</mo> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>&beta;</mi> <mo>+</mo> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>&alpha;</mi> <mo>-</mo> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>i</mi> <mrow> <mi>z</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>&beta;</mi> <mo>-</mo> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

wherein,the total circulating current component reference value at the k moment under the three-phase α β 0 static coordinate system;the reference value of the positive sequence circulation component at the k moment under the three-phase α β 0 static coordinate system;the reference value of the negative sequence circulation component at the k moment under the three-phase α β 0 static coordinate system.