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

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

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CN105846691B
CN105846691B CN201610317491.1A CN201610317491A CN105846691B CN 105846691 B CN105846691 B CN 105846691B CN 201610317491 A CN201610317491 A CN 201610317491A CN 105846691 B CN105846691 B CN 105846691B
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CN105846691A (en
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罗安
岳雨霏
徐千鸣
马伏军
何志兴
周奔
丁红旗
郭鹏
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Hunan University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/02—Conversion of ac power input into dc power output without possibility of reversal
    • H02M7/04—Conversion of ac power input into dc power output without possibility of reversal by static converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0003—Details of control, feedback or regulation circuits

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  • Power Engineering (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
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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

A kind of cascade connection multi-level tundish electromagnetic heating power supply integrated control method
Technical field
The present invention relates to a kind of cascade connection multi-level tundish electromagnetic heating power supply integrated control method.
Background technology
With the progress of power electronics and semiconductor technology, high-power high-efficiency variable-frequency power sources is greatly promoted The development of steel heat treatment induction heating techniques, medium of the tundish induction heating power as its transformation of electrical energy, it is inputted Electric current affects the power quality of utility network, and its output current is directly related to tundish temperature control effect, so right The research of tundish induction heating power control method has good a theory and engineering significance, and tundish induction heating system To power supply energy transmission stability and high current Fast transforms it is more demanding.
Existing high-frequency resonant formula induction heating power is chiefly used in small-power occasion, metallurgical high-power wide size sensing heating Power supply reference frequency output is middle low frequency.The more tundish induction heating power of current application, its prime is using simple and reliable Phase-shifting transformer add diode rectification structure, rear class uses the cascaded H-bridges structure of DC side independence, realizes three-phase to single-phase Conversion, shortcoming is that energy stream is unidirectional from power grid to tundish, so DC capacitor voltage regulating power is limited, at the same time Though multiwinding transformer reduces the harmonic content of power network current to a certain extent, also increase the cost and volume of power supply.
In recent years, it is good that the tundish induction heating power based on the more level blocks of H bridge sub-module cascades has benefited from it Modularization, low harmony wave, more redundancy properties, the more level blocks of extensive concern, especially full-bridge have been obtained handing over alternation to change field Change converter (F-MMC) structure, which possesses buck-boost characteristics, its output frequency and modulation degree are relative to half-H-bridge MMC (H-MMC) scope of module is wider, and this F-MMC structures applied to tundish electromagnetic heating variable-frequency power sources have module Change, low harmony wave, the characteristic of more redundancies, can realize the two-way flow of power, reduce device volume and cost, improve system and stablize Property, the shortcomings that overcoming traditional structure, be a kind of comparatively ideal friendship AC-AC converter.But the discrete energy-storage travelling wave tube of cascaded multilevel structure Larger difficulty is brought to the balance of voltage, seeking a kind of voltage balancing control strategy value being combined with energy stabilization control must visit Rope.
The content of the invention
The technical problems to be solved by the invention are, for realizing energy between tundish inductive electromagnetic heating power supply and power grid The two-way flow of amount and the problems such as solve the cost and volume of power supply and the deficiencies in the prior art, there is provided one kind cascade is more electric Flat tundish electromagnetic heating power supply integrated control method, which uses F-MMC structures, and is based on The structure, the quick tracking problem of solving device input and output electric current, on the premise of control system is stablized, ensures that cascade is more electric The balance of each cascade module capacitance voltage, realizes the efficient of electromagnetic heating power supply energy in flat tundish electromagnetic heating power supply architecture Utilize.
In order to solve the above technical problems, the technical solution adopted in the present invention is：A kind of cascade connection multi-level tundish electromagnetism Heating power supply integrated control method, this method is directed to the more level blocks of F-MMC, using direct Power Control and dead beat electric current control The multi layer control method being combined is made, the input current for having derived the global energy balance in discrete domain instructs, in alternate and phase Energy balance circulation instructs, and premised on voltage close loop control stability, draws the selection model of each layer voltage controller parameter Enclose.
The present invention solves above-mentioned technical problem, and the technical scheme comprises the following steps：
1) according to KVL and KCL theorems, the basic structure side based on cascade connection multi-level tundish electromagnetic heating power supply is established Journey is as follows：
Wherein usa,usb,uscWith uoRespectively three-phase alternating current input voltage and single phase ac output voltage, uupxAnd udnxPoint Not Wei x (x=a, b, c) mutually upper and lower bridge arm output voltage, iupx, idnx, izxAnd isxThe respectively upper and lower bridge arm current of x phases and x The circulation and input current of phase, ioFor output load current, L and C are respectively bridge arm reactance value and submodule capacitor's capacity.To upper State the equivalent model that can obtain converter ac circuit and circulation circuit after two formulas simplify；
2) realized using the differential output voltage reference value of input current and circulation to the fast of input current and zero sequence circulation Speed tracking.First by three-phase power grid voltage, input current transforms to two-phase α β rest frames with circulation respectively and three-phase α β 0 are quiet Only under coordinate system, the differential equation of input current and circulation under α β coordinate systems is as follows：
Wherein, isα, isβ, usα, usβ, uinvαAnd uinvβThe respectively common mode of three phase network electric current and voltage and input current Value of the output voltage under two-phase α β rest frames, izα, izβ, iz0, uzα, uzβAnd uz0Respectively three phase circulation voltages, circulation Common mode output voltage and the value under 0 rest frames of three-phase α β, L, RLAnd LeqRespectively bridge arm inductance, resistance and consideration are negative Carry the single-phase circulation equiva lent impedance of reactance；
Using dead-beat control method and forward direction single order Eulerian equation, and think current actual value and the prediction in next cycle Error between value is in allowed band, i.e.,：
Wherein, isα(k+1), isβ(k+1),WithThe k+1 moment is defeated respectively under two-phase α β rest frames Enter electric current and its reference value at the k moment, izα(k+1), izβ(k+1), iz0(k+1),WithRespectively three The circulation at k+1 moment and its reference value at the k moment under 0 rest frames of phase α β.Input current can obtain by above-mentioned two formula Differential output voltage reference valueWithWith the differential output voltage reference value of circulation With
3) using controlling circulation and positive-negative sequence circulation inside converter to realize the alternate balance of voltage.The cascade connection multi-level knot The voltage balancing control of the electromagnetic heating power supply of structure is divided into average voltage control, and the control of horizontal direction balance and vertical direction are put down Weighing apparatus control；Each phase bridge arm cascade module capacitance voltage both horizontally and vertically quadratic sum after discretization, the difference of two squares with The common mode amount of vertical direction voltage deviation square is respectively：
Wherein,(x=a, b, c, similarly hereinafter),WithRespectively In k-th of controlling cycle in x phases bridge arm voltage summation square, square of lower bridge arm voltage summation, upper bridge arm and lower bridge arm electricity The quadratic sum and the difference of two squares of pressure and the common mode part of vertical direction voltage deviation square；
4) control and the control of interior circular current using outer loop voltag in the horizontal direction and the vertical direction, obtains converter Internal active power and the governing equation of reactive power, logical overpowering directly control balance cascade module capacitance voltage；
Step 4) comprises the following steps：Without considering reactive-load compensation, rectification control section reactive command is set to 0, then cascades more Active power and reactive power reference qref P of the power level at the k moment*(k) and Q*(k) it is：
Wherein,WithThe respectively reference of the quadratic sum of the three-phase module voltage of representation transformation device energy storage Value and actual value, kp1And ki1The respectively proportionality coefficient and integral coefficient of average voltage controller.According to instantaneous power theory, The active-power P (k) and reactive power Q (k) of k-th of controlling cycle can be obtained, then the reference value of input current can be by power reference It is worth to, with reference to differential output voltage reference value, can obtain the outer shroud control of average voltage and the inner ring of input current controls in fact Existing direct Power Control.
It may insure the level side between three-phase by the high frequency positive sequence and negative-sequence current of adjusting and output voltage same frequency Zero is arranged to the balance of voltage, and by the voltage reference value of horizontal direction balance control, then the voltage squared of horizontal direction and logical Cross PI controllers and obtain the active power reference value in horizontal direction.
By adjusting the balance of voltage adjusted with the fundamental frequency Circulation Components of input voltage same frequency in vertical direction, in order to Prevent occurring undesirable Fundamental-frequency Current component in output current, the fundamental frequency Circulation Components for vertical direction voltage balancing control Comprising positive sequence and negative sequence component, and it is used for realization the three-phase voltage u of the vertical direction balance of voltagesa、usb、uscFor positive sequence property, i.e., Vertical direction balances the Voltage Reference controlledIt is unbalanced between the upper and lower bridge arm of three-phase to have Work(powerWithIt can represent as follows：
Wherein,WithRespectively the k moment obtains through vertical direction balanced voltage controller Active power reference value, kp3And ki3The respectively proportionality coefficient and integral coefficient of vertical balance voltage controller.Thus it is used for The Circulation Components of unbalanced power represent as follows between the elimination upper and lower bridge arm of three-phase：
Wherein,WithRespectively three-phase The general circulation component reference value at k moment under 0 rest frames of α β, positive sequence Circulation Components reference value and the reference of negative phase-sequence Circulation Components Value.
Compared with prior art, the advantageous effect of present invention is that：Cascade connection multi-level tundish proposed by the present invention The integrated control method of electromagnetic heating power supply, outer shroud is by average voltage controller, horizontal equilibrium voltage controller and vertically puts down Weighing apparatus voltage controller is respectively obtained for uneven and elimination three-phase between directly controlling each phase bridge arm energy, eliminating three-phase bridge arm Unbalanced active power reference value between lower bridge arm, and then obtain inner ring and be used for direct Power Control and eliminate three-phase bridge arm power Unbalanced input current amount and circulation, realize the multi layer control that direct Power Control is combined with dead beat current control Method, and the control of horizontal direction balance balances from vertical direction and controls the circulation instruction frequency of output different, control process is mutual It is independent, there is no coupled relation, it can effectively realize the energy conversion of electromagnetic heating power supply.
Brief description of the drawings
Fig. 1 is to be used for cascade connection multi-level tundish electromagnetic heating power supply architecture figure of the present invention.
Fig. 2 is the equivalent-circuit model in one embodiment of the invention AC input current circuit and circulation circuit.
Fig. 3 is the processing and coordinate transform of one embodiment of the invention electromagnetic heating power circuit signal.
Fig. 4 is one embodiment of the invention average voltage outer shroud, input current inner ring control block diagram.
Fig. 5 is one embodiment of the invention horizontally and vertically balance of voltage outer shroud, circulation inner ring control block diagram.
Embodiment
Fig. 1 show the cascaded multilevel structure figure for tundish electromagnetic heating power supply of the present invention, the cascade connection multi-level Structure upper and lower two bridge arms per being mutually made of, it can regard as, and two star-like cascade SVG input terminals are in parallel, and output terminal is connected, direct current Output termination electromagnetic heating power source loads, three-phase AC grid system-level is 10kV/50Hz.In figure, usx(x=a, b, c, under Together) and isxRespectively three-phase AC grid voltage and current, uupx, udnx, iupxAnd idnxThe output of respectively each mutually upper and lower bridge arm Voltage and bridge arm current, the H-type full-bridge submodule that SM cascades for each mutually upper and lower bridge arm, ucix(x=a, b, c, i=1 ..n, under It is together) submodule capacitor's capacity for the DC capacitor voltage of cascade submodule, C, L is bridge arm inductance, ioAnd uoRespectively direct current Lateral load electric current and load voltage.
Fig. 2 is the cascade converter ac circuit and the equivalent model structure chart in circulation circuit.Formula is obtained by KCL and KVL (1) and formula (2) part of differential mode and common mode, is broken down into, as shown in formula (3), the two is respectively the ac circuit electricity in figure Press uinvxWith circulation loop voltage uzx。
In formula, usxAnd isxRespectively three-phase AC grid voltage and current, uupx, udnx, iupxAnd idnxIt is respectively upper and lower The output voltage and bridge arm current of bridge arm, izxEach phase bridge arm circulation, L are bridge arm inductance, ioAnd uoRespectively direct current lateral load electricity Stream and load voltage.After simplification, it can obtain
Wherein uo=io(RL+jωLL),io=iza+izb+izc, formula (4) and (5) are the spatiality side of the equivalent model Journey expression formula.
Fig. 3 is input signal processing and coordinate transform figure.Bridge arm circulation izxWith output current ioAcquisition can be according to formula (2) Obtain, the conversion of two-phase static coordinate is obtained by the matrix of formula (6)
Fig. 4 is average voltage outer shroud, input current inner ring control block diagram.
Input current inner ring in the control strategy controls the process to be：Obtained by the converter ac circuit model of Fig. 2 defeated Enter electric current isxThe differential equation under α β coordinate systems is
In formula (7), isy(y=α, β, similarly hereinafter), usyAnd uinvyThree-phase alternating current input electricity respectively after α β coordinate transforms Stream, input voltage and differential mode voltage.By the mutual independence of α β components, using track with zero error, the kth th control weeks of formula (7) Phase can be written as
In formula (8), TSFor equivalent switch cycle, isy(k), usy(k) and uinvy(k) it is respectively the defeated of kth th controlling cycles Enter electric current, input voltage and differential mode voltage, isy(k+1) it is the output current predicted value of kth th controlling cycles, if next cycle Output current actual value and predicted valueBetween error in allowed band, then it is believed that
Formula (9) is substituted into formula (8), input current can obtain the ginseng of differential output voltage through the track with zero error device in Fig. 4 Examine valueFor
Inner ring is under α β coordinates, by controlling differential output voltage reference valueRealize to input currentControl.
The process that controls of average voltage outer shroud in the control strategy is：Module voltage is adjusted by controlling power, In the case of reactive-load compensation, rectification control section reactive command is arranged to 0, then overall imbalance power is represented by
Wherein, P*(k) and Q*(k) be respectively k-th of cycle active power reference and reactive power reference,WithThe respectively reference value and actual value of the quadratic sum of the three-phase module voltage of representation transformation device energy storage, kp1And ki1Respectively For the proportionality coefficient and integral coefficient of average voltage controller.According to instantaneous power theory, the active of k-th controlling cycle can be obtained Power P (k) and reactive power Q (k) are respectively
Wherein,For transformation matrix, then reference value of the input current under two-phase rest frame (y=α, β, similarly hereinafter) is represented by：
Wherein, P*(k) and Q*(k) it is value and power reference,For reverse transform matrix, the difference of the input current of convolution (10) Mould output voltage track with zero error, obtains the outer shroud control of average voltage and Direct Power control is realized in the inner ring control of input current System.
Fig. 5 is balance of voltage outer shroud, circulation inner ring control block diagram.
Circulation inner ring in the control strategy controls the process to be：Circulation i is obtained by the transducer loop stream loop model of Fig. 2zx The differential equation of (x=a, b, c, similarly hereinafter) under 0 coordinate systems of α β is
Wherein, izj(j=α, β, 0, similarly hereinafter) and uzjRespectively three phase circulation voltages, the common mode output voltage of circulation is three Value under 0 rest frames of phase α β, L, RLAnd Leq=L+3LL/ 2 be respectively bridge arm inductance, resistance and the list for considering load reactance Phase circulation equiva lent impedance, due to output current ioFor the zero-sequence component of three phase circulations, thus haveCan by formula (14) Know, 0 components of α β of circulation are independent of one another, herein using preceding to single order track with zero error.K-th of controlling cycle of formula (11) is writeable For
Wherein, izj(k), izj(k+1) and uzj(k) it is respectively k moment circulation under 0 rest frames of three-phase α β, the k+1 moment Export circulation and the circulation differential output voltage at k moment, L, RL, LeqAnd TsRespectively bridge arm inductance, resistance, considers load reactance Single-phase circulation equiva lent impedance and the sampling period；If the error between the output current actual value and predicted value in next cycle is permitting Perhaps in the range of, then it is believed that
Wherein, izj(k+1) andThe circulation at k+1 moment and its at the k moment respectively under 0 rest frames of three-phase α β Reference value, formula (16) is substituted into can obtain the common mode output voltage of circulation track with zero error in (15) is referenced as
Wherein,izj(k) andK moment circulation differential mode output electricity respectively under 0 rest frames of three-phase α β The reference value of pressure, loop current value and its reference value, L, RL, LeqAnd TsRespectively bridge arm inductance, resistance, considers load reactance Single-phase circulation equiva lent impedance and sampling period.
The process that controls of balance of voltage outer shroud in the control strategy is：Process be divided into horizontal direction voltage balancing control and Vertical direction voltage balancing control, balance control operate in discrete domain.
The voltage reference value of horizontal direction balance controlThen the imbalance power between three-phase can table It is shown as
Wherein,WithThe k moment is through horizontal direction balanced voltage control respectively under two-phase α β rest frames The active power reference value that device processed obtains, kp2And ki2The respectively proportionality coefficient and integral coefficient of horizontal equilibrium voltage controller. Thus the high frequency circulating currents component for controlling unbalanced power between three-phase represents as follows under two-phase α β rest frames：
Wherein,WithThe high frequency circulating currents reference value that respectively active power reference value obtains,For Transformation matrix, the form depending on circulation instruction.
Vertical direction voltage balancing control can prevent occurring undesirable Fundamental-frequency Current component in output current, for vertical The fundamental frequency Circulation Components of direction voltage balancing control include positive sequence and negative sequence component, and are used for realization the vertical direction balance of voltage Three-phase voltage usa、usb、uscFor positive sequence property, i.e., the Voltage Reference that vertical direction balance controls is Unbalanced active power between the upper and lower bridge arm of three-phaseWithIt can represent as follows：
Wherein,WithRespectively the k moment obtains through vertical direction balanced voltage controller Active power reference value, kp3And ki3The respectively proportionality coefficient and integral coefficient of vertical balance voltage controller.Thus it is used for The Circulation Components of unbalanced power represent as follows between the elimination upper and lower bridge arm of three-phase：
Wherein,WithRespectively three-phase The general circulation component reference value at k moment under 0 rest frames of α β, positive sequence Circulation Components reference value and the reference of negative phase-sequence Circulation Components Value.The differential output voltage track with zero error of convolution (17) circulation, obtains the control of balance of voltage outer shroud and the control of circulation inner ring, And then realize direct Power Control.

Claims (4)

1. a kind of cascade connection multi-level tundish electromagnetic heating power supply integrated control method, cascade connection multi-level tundish electromagnetic heating electricity Source includes cascaded multilevel structure and the tundish electromagnetic heating power supply in parallel with the cascaded multilevel structure；The cascade is more The each phase of level block is composed in series by upper and lower two bridge arms；Upper and lower bridge arm includes the submodule of multiple cascades；It is special Sign is that this method comprises the following steps：
1) equation below is established：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <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>u</mi> <mi>p</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>a</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>b</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>c</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>a</mi> </mrow> </msub> </mrow> </mtd> <mtd> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mrow> </mtd> <mtd> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>c</mi> </mrow> </msub> </mrow> </mtd> <mtd> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mi>o</mi> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>u</mi> <mi>o</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mi>o</mi> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>u</mi> <mi>o</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mi>o</mi> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>u</mi> <mi>o</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>a</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>b</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>c</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>u</mi> <mi>p</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>a</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>a</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>b</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>b</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>d</mi> <mi>n</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein usa,usb,uscRespectively three-phase alternating current input voltage；uoFor single phase ac output voltage；uupxAnd udnxRespectively x phases The output voltage of upper and lower bridge arm, x=a, b, c；iupx, idnxThe respectively upper and lower bridge arm current of x phases；izxFor the upper and lower bridge arm ring of x phases Stream；isxFor x phase input currents；ioFor output load current；L and C is respectively that upper and lower bridge arm reactance value and submodule capacitance hold Value；The equivalent model in tundish electromagnetic heating capable AC circuit and circulation circuit is obtained after simplifying to above-mentioned two formula；
2) according to the obtained equivalent model of step 1), it is static that three-phase alternating current input voltage, input current are transformed into two-phase α β Under coordinate system, three phase circulations are transformed under 0 rest frames of three-phase α β, it is defeated that three-phase alternating current is obtained using dead-beat control method Enter the differential output voltage reference value of voltage, circulation and input current, and the differential output voltage reference value is defeated as controlling Enter the controlled quentity controlled variable of electric current and circulation；Three-phase alternating current input voltage, circulation and input current are in two-phase α β rest frames and three-phase α The differential equation of 0 rest frames of β is as follows：
<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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&amp;beta;</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
<mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Li</mi> <mrow> <mi>z</mi> <mi>&amp;alpha;</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Li</mi> <mrow> <mi>z</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>z</mi> <mi>&amp;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> <mo>;</mo> </mrow>
Wherein, isα, isβFor value of the three phase network electric current under two-phase α β rest frames；usα, usβIt is three-phase power grid voltage two Value under phase α β rest frames, uinvαAnd uinvβFor input current common mode output voltage under two-phase α β rest frames Value, izα, izβ, iz0For value of the three-phase loop current under 0 rest frames of three-phase α β；uzα, uzβAnd uz0It is defeated for the common mode of circulation Go out value of the voltage under 0 rest frames of three-phase α β, L, RLAnd LeqRespectively bridge arm inductance, resistance and the list for considering load reactance Phase circulation equiva lent impedance；
3) structurally, the average voltage of lower bridge arm, voltage squared in horizontal direction and and the difference of two squares, the voltage in vertical direction The common mode part of deviation, it is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>p</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>d</mi> <mi>n</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>h</mi> <mi>o</mi> <mi>r</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>p</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>d</mi> <mi>n</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
<mrow> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>x</mi> <mn>0</mn> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <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>+</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>+</mo> <msubsup> <mi>u</mi> <mrow> <mi>c</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>c</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
WithWhen being k-th of controlling cycle respectively, in x phases bridge arm voltage summation square and lower bridge arm voltage it is total Square of sum；WithThe quadratic sum of bridge arm and lower bridge arm voltage and flat respectively in k-th of controlling cycle x phase Variance；For the common mode amount of vertical direction voltage deviation square, WithRespectively k-th Square of controlling cycle a, b, c three-phase voltage deviation in vertical direction；
4) the common mode amount of the vertical direction voltage deviation square obtained based on step 3) is establishedWith the voltage of horizontal direction Quadratic sumBalance of voltage closed loop transfer function, by closed loop transfer function, and Lao Si-Hurwitz's stability criterion, selection Suitable PI controllers obtain the uneven energy of different control targes to ensure the stabilization of system.
2. cascade connection multi-level tundish electromagnetic heating power supply integrated control method according to claim 1, it is characterised in that The submodule of the cascade is full bridge structure.
3. cascade connection multi-level tundish electromagnetic heating power supply integrated control method according to claim 1, it is characterised in that The step 2) comprises the following steps：
1) by three-phase alternating current input voltage, input current transforms to two-phase α β rest frames with circulation respectively and three-phase α β 0 are quiet Only under coordinate system；
2) differential equation of input current and circulation under α β coordinate systems is built：
<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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Li</mi> <mrow> <mi>z</mi> <mi>&amp;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>&amp;alpha;</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>z</mi> <mi>&amp;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, isα, isβFor value of the three phase network electric current under two-phase α β rest frames, usα, usβIt is three-phase power grid voltage two Value under phase α β rest frames, uinvα、uinvβFor input current common mode output voltage under two-phase α β rest frames Value, izα, izβ, iz0Value of respectively three phase circulations under 0 rest frames of three-phase α β, uzα, uzβIt is three phase circulations in two-phase α β Common mode output voltage under rest frame；uz0For value of three phase circulations under 0 rest frames of three-phase α β；L, RLAnd LeqRespectively For bridge arm inductance, resistance and the single-phase circulation equiva lent impedance for considering load reactance；
3) dead-beat control method and forward direction single order Eulerian equation are used, obtains the differential output voltage ginseng of input current and circulation Examine value：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>v</mi> <mi>&amp;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>&amp;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>&amp;alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&amp;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>&amp;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>&amp;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>&amp;beta;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>&amp;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>&amp;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>&amp;alpha;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>&amp;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>&amp;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>&amp;beta;</mi> </mrow> <mo>*</mo> </msubsup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>z</mi> <mi>&amp;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,For the reference of k moment input current differential output voltages under two-phase α β rest frames Value；usα(k), usβ(k) it is k moment AC-input voltages under two-phase α β rest frames；isα(k), isβ(k) it is static for two-phase α β K moment AC input currents value under coordinate system；WithInput electricity is exchanged for the k moment under two-phase α β rest frames Flow reference value； For the reference of k moment circulation differential output voltages under 0 rest frames of three-phase α β Value；izα(k), izβ(k), iz0(k) it is k moment loop current values under 0 rest frames of three-phase α β to be respectively；K moment loop current value reference values respectively under 0 rest frames of three-phase α β；L, RL, Leq, T point Wei not bridge arm inductance, resistance, the single-phase circulation equiva lent impedance for considering load reactance and sampling period；TSFor the equivalent switch cycle.
4. cascade connection multi-level tundish electromagnetic heating power supply integrated control method according to claim 2, it is characterised in that The specific implementation process of the step 4) comprises the following steps：
1) rectification control section reactive command is set to 0, active power of the cascade connection multi-level tundish electromagnetic heating power supply at the k moment With reactive power reference qref P*(k) and Q*(k) it is：
<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>&amp;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>&amp;rsqb;</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mrow> <mo>&amp;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>&amp;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,WithRespectively represent the three-phase cascade of cascade connection multi-level tundish electromagnetic heating power supply energy storage The reference value and actual value of the quadratic sum of module voltage, kp1And ki1The respectively proportionality coefficient and integration of average voltage controller Coefficient；
2) according to instantaneous power theory, the active-power P (k) and reactive power Q (k) of k-th of controlling cycle are obtained, then input electricity The reference value of stream is by value and power reference P*(k) and Q*(k) obtain, with reference to differential output voltage reference value Obtain the outer shroud control of average voltage and the inner ring of input current controls, realize direct Power Control；
3) the high frequency positive sequence and negative-sequence current with output voltage same frequency are adjusted, it is ensured that the horizontal direction voltage between three-phase is put down Weighing apparatus, and the voltage reference value of horizontal direction balance control is arranged to zero, then the voltage squared of horizontal direction and controlled by PI Device obtains the active power reference value in horizontal direction；
4) the fundamental frequency Circulation Components with input voltage same frequency are adjusted, the balance of voltage in vertical direction are adjusted, for Vertical Square Positive sequence and negative sequence component are included to the fundamental frequency Circulation Components of voltage balancing control, is used for realization the three-phase of the vertical direction balance of voltage Voltage usa、usb、uscFor positive sequence property, i.e., the Voltage Reference that vertical direction balance controls is Unbalanced active power between the upper and lower bridge arm of three-phaseWithRepresent 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>&amp;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>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mo>&amp;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>&amp;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>&amp;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>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mo>&amp;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>&amp;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>&amp;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>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>k</mi> </munderover> <mo>&amp;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>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein,WithRespectively the k moment obtains active through vertical direction balanced voltage controller Value and power reference, kp3And ki3The respectively proportionality coefficient and integral coefficient of vertical balance voltage controller；
5) Circulation Components for being used to eliminate unbalanced power between the upper and lower bridge arm of three-phase represent 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>&amp;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>&amp;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>&amp;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>&amp;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>&amp;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>&amp;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,For the general circulation component reference value at k moment under 0 rest frames of three-phase α β；For the positive sequence Circulation Components reference value at k moment under 0 rest frames of three-phase α β；For the negative phase-sequence Circulation Components reference value at k moment under 0 rest frames of three-phase α β.
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