阅读说明：本技术 一种双三电平逆变器开绕组电机模型控制方法 (Method for controlling open winding motor model of double three-level inverter ) 是由 吴迪 陈继峰 朱芮 胡家全 华国武 王影 于 2020-05-19 设计创作，主要内容包括：一种双三电平逆变器开绕组电机模型控制方法,对第k时刻的电压<Image he="72" wi="104" file="DDA0002499093930000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>电流<Image he="66" wi="92" file="DDA0002499093930000012.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>转速<Image he="72" wi="61" file="DDA0002499093930000013.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>以及磁链信号<Image he="81" wi="49" file="DDA0002499093930000014.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>进行采样观测,经过PI调节器后得到定子电流d轴分量的给定值<Image he="78" wi="51" file="DDA0002499093930000015.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>及定子电流q分量的给定值<Image he="99" wi="76" file="DDA0002499093930000016.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>并经过反Park变换数学推导得到两相静止坐标系下α、β轴电流给定值<Image he="94" wi="93" file="DDA0002499093930000017.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>根据定子电流预测模型,代入不同的待选电压矢量可以得到k+1时刻的定子电流预测值,并通过零序电流抑制、电压越级跳变控制、中点电位平衡控制及开关频率抑制,对模型进行优化。本发明在矢量控制的基础上对定子电流的α、β轴分量进行单独控制,采用模型预测控制方式对定子电流进行预测及反馈跟踪,并采用零序电流抑制、电压越级跳变控制、中点电位平衡控制及开关频率抑制,实现了多目标的优化。(A method for controlling the open-winding motor model of dual three-level inverter features that the voltage at the kth time is controlled Electric current Rotational speed And flux linkage signal Sampling and observing, and obtaining the given value of the d-axis component of the stator current after passing through a PI regulator And given value of stator current q component And obtaining α and β shaft current given values under a two-phase static coordinate system through inverse Park conversion mathematical derivation The method comprises the steps of substituting different voltage vectors to be selected according to a stator current prediction model to obtain a stator current prediction value at the moment k +1, and optimizing the model through zero-sequence current suppression, voltage skip jump control, midpoint potential balance control and switching frequency suppression.)

1. A method for controlling a double three-level inverter open winding motor model is characterized by comprising the following steps: the method comprises the following steps of,

(1) for voltage at the k-th timeElectric currentRotational speedAnd flux linkage signalPerforming sampling observation to give signal via flux linkageEstimating flux linkage value psi with flux linkage observer_rMaking difference, and obtaining the given value of the d-axis component of the stator current after passing through a PI regulatorBy setting the speed of rotation omega^*The given value of the stator current q component is compared with the actual measured rotation speed omega of the encoderThe signal is obtained by adjusting a PI regulator;

(2) given value of d-axis component of stator currentAnd given value of stator current q componentObtaining current set values of α and β axes under a two-phase static coordinate system through inverse Park transformation mathematical derivation

(3) Substituting different voltage vectors to be selected according to the stator current prediction model to obtain a stator current prediction value at the moment of k + 1;

(4) comparing a stator current set value with a predicted value by using a cost function from four aspects of zero sequence current suppression, voltage skip jump control, neutral point potential balance control and switching frequency suppression, selecting a stator current predicted value which enables the cost function to be minimum, and outputting a corresponding switching state to two inverters;

(5) and (4) in the (k +1) th control period, repeating the processes of the steps (1) to (4), predicting the stator current value at the k +2 moment, selecting the switch state corresponding to the predicted value of the stator current with the minimum cost function again, and outputting the switch state to the two inverters, and so on, thereby realizing the control of the open-winding motor of the double three-level inverter.

2. The dual three-level inverter open-winding motor model control method according to claim 1, characterized in that: the predicted value of the stator current in the step (3) is obtained by the following steps,

according to the mathematical model formula, the voltage equation and the flux linkage equation of the motor under the two-phase static coordinate system, a current dynamic equivalent expression (4.1) can be obtained,

in the formula: l is_mRepresenting the mutual inductance between the coaxial equivalent windings of the stator and the rotor;

L_s、L_rself-inductance of stator and rotor windings;

R_s、R_rstator and rotor winding resistances;

represents the rotor electromagnetic time constant;

ψ_rα、ψ_rβrepresenting the components of the rotor flux linkage at the α and β axes, respectively;

u_sα、u_sβrepresenting the stator voltage components at the α and β axes, respectively;

i_sα、i_sβrepresenting the components of the stator current in the α and β axes, respectively;

representing a leakage inductance coefficient;

the forward Euler method is adopted to carry out discretization processing on the stator current in the formula to obtain the following result:

in the formulaThe leakage inductance coefficient is represented by the value of,represents the rotor electromagnetic time constant;

model prediction current control is adopted, alpha and beta axis stator currents are used as controlled objects and set as constraint conditions of a cost function:

in the formula:representing stator current set-point on α, β axes, respectively_sα(k+1)、i_sβ(k +1) represents the stator current atα, β axes.

3. The dual three-level inverter open-winding motor model control method according to claim 1, characterized in that: the method for zero sequence current suppression and voltage override jump control in the step (4) comprises the following steps,

establishing a prediction selection vector switching table, sampling a voltage vector at a certain moment, preselecting the voltage vector of the next period by using the vector switching table, selecting a zero common-mode voltage vector as a voltage vector to be selected to predict the future state of the system under an offline condition according to the principle that the voltage vector cannot be selected from 'p → n' or 'n → p' each time, and completely eliminating the zero-sequence voltage and the common-mode voltage of the double-inverter system, wherein the zero common-mode voltage vector is known according to a double-inverter common-mode voltage formula and a zero-sequence voltage formula, and only when the common-mode voltages of the two inverters are both zero (namely U is equal to zero)_cm1＝U_cm20), dual inverter system common mode voltage U_cmAnd zero sequence voltage U_zsThe common-mode voltages of the two inverters are zero at the same time, so that the common-mode voltages of the two inverters are zero voltage vectors.

4. The dual three-level inverter open-winding motor model control method according to claim 3, characterized in that: each voltage vector is synthesized by two inverter output voltage vectors and corresponds to at least one switching state, wherein the switching states "p", "o" and "n" respectively represent the inverter output voltage as V_dc、0、-V_dcAccording to the zero common mode voltage vector diagram of the double three-level inverter system, the switching state corresponding to each zero common mode voltage vector is determined, and then the switching state corresponding to each zero common mode voltage vector can be obtained according to the calculation formula of the common mode voltage and the zero sequence voltage:

U_cm＝[0+V_dc+(-V_dc)+0+(-V_dc)+V_dc]＝0 (4.4)

U_zs＝[0+V_dc+(-V_dc)-0-(-V_dc)-V_dc]＝0 (4.5)

and for other candidate voltage vectors, the generated zero-sequence voltage and the common-mode voltage are zero in the same way.

5. The dual three-level inverter open-winding motor model control method according to claim 1, characterized in that: the method for controlling the midpoint potential balance in the step (4) comprises the following steps,

two supporting capacitors C without considering capacitance difference₁、C₂All the capacitance values of (C, i)_C1And i_C2Respectively, the current, u, flowing through the two supporting capacitors_c1、u_c2Respectively being a supporting capacitor C₁、C₂The voltage at the node is obtained according to the node current law and the capacitance characteristic, and the relation between the capacitance voltage and the capacitance current is as follows:

in the formula, Δ V_NPIs a capacitor C₁And a capacitor C₂Voltage difference between i_NPRepresents the capacitance C₁And a capacitor C₂Current in between, ideally C₁＝C₂According to a state average value method, taking the voltage average value in one period as the voltage difference value at the moment;

discretizing the direct-current side capacitor voltage by using a forward Euler algorithm to obtain an expression of the midpoint potential at the next moment, wherein the expression is as follows:

from this, the expression for the midpoint voltage can be derived:

ΔV_NP(k+1)＝u_C1(k+1)-u_C2(k+1) (4.8)

the midpoint voltage is written into the cost function as a new constraint term, and the new cost function can be obtained as follows:

in order to balance the midpoint voltage, a midpoint potential balance weight factor lambda is introduced into the formula_ΔVBy adjusting λ_ΔVThe balance between the midpoint potential and the output current is dynamically adjusted by the numerical value, and the control effect of the output current of the system can be ensured.

6. The dual three-level inverter open-winding motor model control method according to claim 1, characterized in that: the method for suppressing the switching frequency in the step (4) is that,

after the optimal voltage vector is selected, the optimal switching state with the lowest switching frequency is selected from the corresponding switching states, and the switching frequency expression is as follows:

S＝|S_a1(k+1)-S_a1(k)|+|S_b1(k+1)-S_b1(k)|+|S_c1(k+1)-S_c1(k)|+|S_a2(k+1)-S_a2(k)|+|S_b2(k+1)-S_b2(k)|+|S_c2(k+1)-S_c2(k)| (4.10)

in the formula: s_a1(k)、S_b1(k)、S_c1(k) Respectively showing the switching states of the first, second and third bridge arms of the inverter-1 at the current sampling moment, S_a2(k)、S_b2(k)、S_c2(k) Respectively showing the switching states of the first, second and third bridge arms of the inverter-2 at the current sampling moment, S_a1(k+1)、S_b1(k+1)、S_c1(k +1) represents the switching states to be applied to the first, second and third legs of the inverter-1 at the next sampling time, respectively, S_a2(k+1)、S_b2(k+1)、S_c2(k +1) respectively represents the switching states of a first bridge arm, a second bridge arm and a third bridge arm to be applied to the inverter-2 at the next sampling moment;

the system switching frequency limit is added as a new constraint to the cost function, so the new cost function is:

in the formula of_sIs a switching frequency weighting factor.

7. The double three-level inverter open-winding motor model control method according to claim 5 or 6, characterized in that: the design of the weight factor adopts a half-value approximation method, which comprises the steps of firstly selecting initial values of two orders of magnitude for the weight factor, simulating the two initial values and comparing the result with the expected output, then simulating by taking half of the interval of the initial values as a new weight factor, obtaining where the weight factor should be adjusted by comparing the simulation results, and then continuously calculating by taking the value and the value closest to the value as the initial values of the weight factor until the required weight value is obtained.

Technical Field

The invention relates to a motor model control method, in particular to a double three-level inverter open winding motor model control method.

Background

The common bus structure of the double three-level inverter is similar to that of the double two-level inverter, and when the two inverters share one branch bus, larger zero-sequence current can be generated, so that the system performance is influenced. According to the zero-sequence current loop model, the magnitude of the zero-sequence current is closely related to the magnitude of the zero-sequence voltages of the two inverters, and the fact that a zero-sequence voltage suppression item is directly added to the value function in the third chapter can start a certain suppression effect, but when the optimization target is increased, the value function cannot be biased to a certain control item in each iteration, and therefore the zero-sequence voltage cannot be completely suppressed.

In addition, the selectable voltage vectors of the double three-level inverter in each control period are various, and even if only the zero common-mode voltage vector is used as a candidate vector, 19 voltage vectors can be selected, which is similar to the selectable vectors of the three-level inverter, so that the difficulty of vector selection is greatly increased. In the process of switching the voltage vector from the previous time to the next time, the step-by-step change of one stage, namely the change from "p → o → n" or "n → o → p" is required to be ensured, and the voltage cannot jump between positive and negative levels directly. When the amplitude of the phase voltage jumps too high, the damage to an inverter circuit is large; when the amplitude of the line voltage jumps too high, the influence on the inverter circuit is small, but the requirement on the load is greatly improved.

Finally, the neutral point potential balance control is a problem that the double three-level inverter must solve, in recent years, the multi-level control technology is continuously perfected, and corresponding neutral point voltage control schemes are more and more. Midpoint voltage control may be achieved by hardware or software methods: the existing hardware control scheme mainly comprises the steps that a direct-current power supply with the same size is connected in series on a direct-current side, a Buck-Boost voltage-boosting circuit is additionally arranged at a rectification output end, and the like, so that the dynamic balance control of the midpoint voltage is realized, and the cost and the complexity of the system can be increased by adopting a hardware control method.

At present, the research of the open winding motor model control of the dual three-level inverter is temporarily absent in China, only the research of the vector control of the open winding motor of the dual two-level inverter is available, the open winding motor is controlled by outputting corresponding voltage vectors through the vector control, the voltage vectors output by the dual two levels are less than that of the dual three levels, and the control targets are fewer.

Disclosure of Invention

The invention aims to solve the technical problem of the prior art and provides a method for controlling a double three-level inverter open winding motor model, which is reasonable in design and realizes multi-objective optimization.

The technical problem to be solved by the invention is realized by the following technical scheme, the invention discloses a double three-level inverter open winding motor model control method which is characterized by comprising the following steps,

(1) for voltage at the k-th timeElectric currentRotational speedAnd flux linkage signalPerforming sampling observation to give signal via flux linkageEstimating flux linkage value psi with flux linkage observer_rMaking difference, and obtaining the given value of the d-axis component of the stator current after passing through a PI regulatorBy setting the speed of rotation omega^*The given value of the stator current q component is compared with the actual measured rotation speed omega of the encoderThe signal is obtained by adjusting a PI regulator;

(2) given value of d-axis component of stator currentAnd given value of stator current q componentObtaining α and β shaft current set values under a two-phase static coordinate system through inverse Park transformation mathematical derivation

(3) Substituting different voltage vectors to be selected according to the stator current prediction model to obtain a stator current prediction value at the moment of k + 1;

(4) comparing a stator current set value with a predicted value by using a cost function from four aspects of zero sequence current suppression, voltage skip jump control, neutral point potential balance control and switching frequency suppression, selecting a stator current predicted value which enables the cost function to be minimum, and outputting a corresponding switching state to two inverters;

(5) and (4) in the (k +1) th control period, repeating the processes of the steps (1) to (4), predicting the stator current value at the k +2 moment, selecting the switch state corresponding to the predicted value of the stator current with the minimum cost function again, and outputting the switch state to the two inverters, and so on, thereby realizing the control of the open-winding motor of the double three-level inverter.

The technical problem to be solved by the present invention can also be achieved by the following technical solution, wherein the predicted value of the stator current in the step (3) is obtained by the following steps,

according to the mathematical model formula, the voltage equation and the flux linkage equation of the motor under the two-phase static coordinate system, a current dynamic equivalent expression (4.1) can be obtained,

in the formula: l is_mRepresenting the mutual inductance between the coaxial equivalent windings of the stator and the rotor;

L_s、L_rself-inductance of stator and rotor windings;

R_s、R_rstator and rotor winding resistances;

represents the rotor electromagnetic time constant;

ψ_rα、ψ_rβrepresenting the components of the rotor flux linkage at the α and β axes, respectively;

u_sα、u_sβrepresenting the stator voltage components at the α and β axes, respectively;

i_sα、i_sβrepresenting the components of the stator current in the α and β axes, respectively;

representing a leakage inductance coefficient;

the forward Euler method is adopted to carry out discretization processing on the stator current in the formula to obtain the following result:

in the formulaThe leakage inductance coefficient is represented by the value of,represents the rotor electromagnetic time constant;

model prediction current control is adopted, alpha and beta axis stator currents are used as controlled objects and set as constraint conditions of a cost function:

in the formula:representing stator current set-point on α, β axes, respectively_sα(k+1)、i_sβ(k +1) represents predicted values of the stator current on the α and β axes, respectively.

The technical problem to be solved by the present invention can also be achieved by the following technical solution, wherein the method for zero sequence current suppression and voltage override jump control in step (4) comprises,

establishing a prediction selection vector switching table, sampling a voltage vector at a certain moment, preselecting the voltage vector of the next period by using the vector switching table, selecting a zero common-mode voltage vector as a voltage vector to be selected to predict the future state of the system under an offline condition according to the principle that the voltage vector cannot be selected from 'p → n' or 'n → p' each time, and completely eliminating the zero-sequence voltage and the common-mode voltage of the double-inverter system, wherein the zero common-mode voltage vector is known according to a double-inverter common-mode voltage formula and a zero-sequence voltage formula, and only when two inverters share the same voltage vectorThe mode voltages are all zero (i.e. U)_cm1＝U_cm20), dual inverter system common mode voltage U_cmAnd zero sequence voltage U_zsThe common-mode voltages of the two inverters are zero at the same time, so that the common-mode voltages of the two inverters are zero voltage vectors.

The technical problem to be solved by the present invention can also be solved by the following technical solution, each voltage vector is synthesized by two inverter output voltage vectors and corresponds to at least one switching state, wherein the switching states "p", "o" and "n" respectively represent inverter output voltages V_dc、0、-V_dcAccording to the zero common mode voltage vector diagram of the double three-level inverter system, the switching state corresponding to each zero common mode voltage vector is determined, and then the switching state corresponding to each zero common mode voltage vector can be obtained according to the calculation formula of the common mode voltage and the zero sequence voltage:

U_cm＝[0+V_dc+(-V_dc)+0+(-V_dc)+V_dc]＝0 (4.4)

U_zs＝[0+V_dc+(-V_dc)-0-(-V_dc)-V_dc]＝0 (4.5)

and for other candidate voltage vectors, the generated zero-sequence voltage and the common-mode voltage are zero in the same way.

The technical problem to be solved by the present invention can also be achieved by the following technical solution, wherein the method for controlling the midpoint potential balance in the step (4) is,

two supporting capacitors C without considering capacitance difference₁、C₂All the capacitance values of (C, i)_C1And i_C2The currents flowing through the two supporting capacitors respectively have the following relationship between the capacitor voltage and the capacitor current according to the node current law and the capacitor characteristic:

in the formula, Δ V_NPIs a capacitor C₁And a capacitor C₂Voltage difference between i_NPRepresents the capacitance C₁And a capacitor C₂Current in between, ideally C₁＝C₂According to a state average value method, taking the voltage average value in one period as the voltage difference value at the moment;

discretizing the direct-current side capacitor voltage by using a forward Euler algorithm to obtain an expression of the midpoint potential at the next moment, wherein the expression is as follows:

from this, the expression for the midpoint voltage can be derived:

ΔV_NP(k+1)＝u_C1(k+1)-u_C2(k+1) (4.8)

the midpoint voltage is written into the cost function as a new constraint term, and the new cost function can be obtained as follows:

in order to balance the midpoint voltage, a midpoint potential balance weight factor lambda is introduced into the formula_ΔVBy adjusting λ_ΔVThe balance between the midpoint potential and the output current is dynamically adjusted by the numerical value, and the control effect of the output current of the system can be ensured.

The technical problem to be solved by the present invention can also be achieved by the following technical solution, wherein the method for suppressing the switching frequency in the step (4) is,

after the optimal voltage vector is selected, the optimal switching state with the lowest switching frequency is selected from the corresponding switching states, and the switching frequency expression is as follows:

S＝|S_a1(k+1)-S_a1(k)|+|S_b1(k+1)-S_b1(k)|+|S_c1(k+1)-S_c1(k)|+ |S_a2(k+1)-S_a2(k)|+|S_b2(k+1)-S_b2(k)|+|S_c2(k+1)-S_c2(k)| (4.10)

in the formula: s_a1(k)、S_b1(k)、S_c1(k) Respectively representing the first bridge arm and the second bridge arm of the inverter-1 at the current sampling momentSwitching states of the strip arm, the third arm, S_a2(k)、S_b2(k)、S_c2(k) Respectively representing the switching states of a first bridge arm, a second bridge arm and a third bridge arm of the inverter-2 at the current sampling moment; s_a1(k+1)、S_b1(k+1)、S_c1(k +1) represents the switching states to be applied to the first, second and third legs of the inverter-1 at the next sampling time, respectively, S_a2(k+1)、S_b2(k+1)、S_c2(k +1) respectively represents the switching states of a first bridge arm, a second bridge arm and a third bridge arm to be applied to the inverter-2 at the next sampling moment;

the system switching frequency limit is added as a new constraint to the cost function, so the new cost function is:

in the formula of_sIs a switching frequency weighting factor.

The technical problem to be solved by the invention can also be solved by the following technical scheme, the design of the weight factor adopts a half-value approximation method, the method comprises the steps of firstly selecting initial values of two orders of magnitude for the weight factor, simulating the two initial values, comparing the result with expected output, then simulating by taking half of the interval of the initial values as a new weight coefficient, obtaining where the weight coefficient should be adjusted by comparing the simulation results, and continuously calculating until the required weight value is obtained by taking the value and the value closest to the value as the initial values of the weight factor, wherein the weight factor comprises a midpoint potential balance weight factor and a switching frequency weight factor.

Compared with the prior art, the method has the advantages that the alpha and beta axis components of the stator current are independently controlled on the basis of vector control, the stator current is predicted and feedback-tracked in a model prediction control mode, and the zero-sequence circulating current of the double three-level common direct current bus is inhibited in a zero-sequence current inhibiting mode; the problem of voltage jump during voltage vector switching is solved by establishing a prediction selection vector switching table; the direct-current side capacitor voltage is discretized by using a forward Euler algorithm to obtain an expression of the midpoint potential at the next moment, so that the problem of double-three-level midpoint voltage balance is solved; after the optimal voltage vector is selected, the optimal switching state which enables the switching times of the switch to be the lowest is selected from the corresponding switching states, the problem of switching frequency suppression is solved, and multi-objective optimization is achieved.

Drawings

FIG. 1 is a block diagram of a dual three-level inverter driven open-winding motor according to the present invention;

FIG. 2 is a functional block diagram of a control method according to the present invention;

FIG. 3 is a flow chart of a control method of the present invention;

FIG. 4 is a zero common mode voltage candidate vector diagram;

FIG. 5 is a table of switch states corresponding to a zero common mode voltage vector;

FIG. 6 is a table of preselected vector switches;

FIG. 7 is a topology diagram of a DC side circuit;

FIG. 8 is a schematic diagram of the design of the weighting factors.

Detailed Description

The embodiments of the present invention will be further described with reference to the accompanying drawings so that those skilled in the art can further understand the present invention without limiting the right of the present invention.

Referring to fig. 1-3, a dual three-level inverter open-winding motor model control method includes the steps of,

(1) for voltage at the k-th timeElectric currentRotational speedAnd flux linkage signalPerforming sampling observation to give signal via flux linkageEstimating flux linkage value psi with flux linkage observer_rMaking difference, and obtaining the given value of the d-axis component of the stator current after passing through a PI regulatorBy setting the speed of rotation omega^*The given value of the stator current q component is compared with the actual measured rotation speed omega of the encoderThe signal is obtained by adjusting a PI regulator;

(2) given value of d-axis component of stator currentAnd given value of stator current q componentObtaining α and β shaft current set values under a two-phase static coordinate system through inverse Park transformation mathematical derivation

Substituting different to-be-selected voltage vectors according to a stator current prediction model to obtain a stator current prediction value at the moment of k + 1;

(4) comparing a stator current set value with a predicted value by using a cost function from four aspects of zero sequence current suppression, voltage skip jump control, neutral point potential balance control and switching frequency suppression, selecting a stator current predicted value which enables the cost function to be minimum, and outputting a corresponding switching state to two inverters;

(5) and (4) in the (k +1) th control period, repeating the processes of the steps (1) to (4), predicting the stator current value at the k +2 moment, selecting the switch state corresponding to the predicted value of the stator current with the minimum cost function again, and outputting the switch state to the two inverters, and so on, thereby realizing the control of the open-winding motor of the double three-level inverter.

The stator current prediction model is established by the following steps:

mathematical model under three-phase static coordinate system of (I) open winding induction motor

The open-winding induction motor three-phase stator voltage equation, flux linkage equation, motor torque equation, and motion equation are shown below.

1. Equation of voltage

The voltage equation of the three-phase stator winding of the induction motor in the abc static coordinate system is as follows:

in the formula u_A、u_B、u_C、u_a、u_b、u_cInstantaneous values of stator and rotor phase voltages; i.e. i_A、i_B、i_C、i_a、i_b、i_cInstantaneous values of stator and rotor phase currents; psi_A、ψ_B、ψ_C、ψ_a、ψ_b、ψ_cInstantaneous values of stator and rotor phase currents; r_s、R_rStator and rotor winding resistances. In the formula u_A、u_B、u_C、u_a、u_b、u_cInstantaneous values of stator and rotor phase voltages; i.e. i_A、i_B、i_C、i_a、 i_b、i_cInstantaneous values of stator and rotor phase currents; psi_A、ψ_B、ψ_C、ψ_a、ψ_b、ψ_cInstantaneous values of stator and rotor phase currents; r_s、 R_rStator and rotor winding resistances.

2. Magnetic flux linkage equation

For a traditional induction motor, the flux linkage of a stator winding and a rotor winding is equal to the sum of self-inductance and mutual inductance flux linkage of the stator winding and the rotor winding, and for an open-winding asynchronous motor, only the connection mode of the windings is changed, so that the flux linkage equation of the open-winding induction motor is expressed as shown in the formula.

Or write into

Ψ＝Li

In the formula L_AA、L_BB、L_CC、L_aa、L_bb、L_ccThe elements on the other non-diagonal lines are the mutual inductances between the windings.

3. Equation of torque

Analyzing from the perspective of electromechanical energy conversion, and storing energy W 'of magnetic field'_mAnd magnetic common energy W_mThe relationship under the action of the linear inductor is:

at constant current constraint and at constant mechanical angular displacement theta_m＝θ/n_pWhen the temperature of the water is higher than the set temperature,

in the formula, n_pIs the number of pole pairs of the motor.

Combining a motor flux linkage equation to obtain:

T_e＝n_pL_ms[(i_Ai_a+i_Bi_b+i_Ci_c)sinθ+(i_Ai_b+i_Bi_c+i_Ci_a)sin(θ+120°) +(i_Ai_c+i_Bi_a+i_Ci_b)sin(θ-120°)]

in the formula L_msThe stator inductance is corresponding to the maximum mutual inductance flux interlinked with the stator single-phase winding.

4. Equation of motion

Before describing the motor's equations of motion, usually ignoring viscous friction and torsional elasticity in the electric traction system drive, the motor's equations of motion are:

in the formula T_LIs the motor load torque, J is the rotational inertia of the motor, ω ═ d θ/dt.

Mathematical model under (two) open winding induction motor two-phase static coordinate system

According to the definition of the two-phase stationary coordinate system, a transformation matrix (i.e. Clark transformation matrix) for transforming from the three-phase stationary coordinate system to the two-phase rotating coordinate system can be obtained as follows:

wherein K is a transformation coefficient for transforming a three-phase stationary coordinate system into a two-phase stationary coordinate system, K is 2/3 under the condition of constant amplitude transformation, and K is 2/3 under the condition of constant power transformation

1. Equation of voltage

By using Clark transformation matrix, an equation of voltage, current and flux linkage under a two-phase static coordinate system can be obtained, and the equation is combined with a formula u_a+u_sab2＝u_b+u_sab1And obtaining a voltage equation under the two-phase static coordinate system as follows:

in the formula: u. of_sα、u_sβRepresenting the stator voltage components at the α and β axes, respectively;

u_rα、u_rβrepresenting the components of the rotor voltage at the α and β axes, respectively;

i_sα、i_sβrepresenting the components of the stator current in the α and β axes, respectively;

i_rα、i_rβrepresenting the components of the rotor current at α and β axes, respectively;

L_mrepresenting the mutual inductance between the coaxial equivalent windings of the stator and the rotor;

2. magnetic flux linkage equation

3. Electromagnetic torque equation

T_e＝n_pL_m(i_sβi_rα-i_sαi_rβ)

Mathematical model under (three) open winding induction motor two-phase rotating coordinate system

And (3) carrying out Park transformation on the mathematical model of the open-winding induction motor in the static coordinate system to obtain the mathematical model in the synchronous rotation dq coordinate system. The two-phase stationary coordinate system can be transformed into a two-phase rotating coordinate system through Park transformation, and the transformation matrix form is as follows:

1. equation of voltage

After Park transformation, a matrix equation of the stator voltage and the rotor voltage on d and q coordinate axes is as follows:

in the formula: omega_dqsIs the angular velocity, ω, of the dq coordinate system relative to the stator_dqrIs the angular velocity of the dq coordinate system relative to the rotor.

2. Magnetic flux linkage equation

3. Equation of torque

The torque equation in dq coordinate system is:

T_e＝n_pL_m(i_sqi_rd-i_sdi_rq)。

the predicted value of the stator current in the step (3) is obtained by the following steps,

according to the mathematical model formula, the voltage equation and the flux linkage equation of the motor under the two-phase static coordinate system, a current dynamic equivalent expression (4.1) can be obtained,

in the formula: l is_mRepresenting the mutual inductance between the coaxial equivalent windings of the stator and the rotor;

L_s、L_rself-inductance of stator and rotor windings;

R_s、R_rstator and rotor winding resistances;

represents the rotor electromagnetic time constant;

ψ_rα、ψ_rβrepresenting the components of the rotor flux linkage at the α and β axes, respectively;

u_sα、u_sβrepresenting the stator voltage components at the α and β axes, respectively;

i_sα、i_sβrepresenting the components of the stator current in the α and β axes, respectively;

representing a leakage inductance coefficient;

wherein, the voltage equation under the two-phase static coordinate system is,

in the formula: u. of_sα、u_sβRepresenting the stator voltage components at the α and β axes, respectively;

u_rα、u_rβrepresenting the components of the rotor voltage at the α and β axes, respectively;

i_sα、i_sβrepresenting the components of the stator current in the α and β axes, respectively;

i_rα、i_rβrepresenting the components of the rotor current at α and β axes, respectively;

L_mrepresenting the mutual inductance between the coaxial equivalent windings of the stator and the rotor;

p represents the number of pole pairs;

the flux linkage equation in the two-phase stationary coordinate system is,

in the formula: l is_s、L_rSelf-inductance of stator and rotor windings;

L_mrepresenting the mutual inductance between the coaxial equivalent windings of the stator and the rotor;

ψ_rα、ψ_rβrepresenting the components of the rotor flux linkage at the α and β axes, respectively;

ψ_sα、ψ_sβrepresenting the components of the stator flux linkage at the α and β axes, respectively;

representing a leakage inductance coefficient;

the forward Euler method is adopted to carry out discretization processing on the stator current in the formula to obtain the following result:

in the formulaThe leakage inductance coefficient is represented by the value of,represents the rotor electromagnetic time constant;

model prediction current control is adopted, alpha and beta axis stator currents are used as controlled objects and set as constraint conditions of a cost function:

in the formula:representing stator current set-point on α, β axes, respectively_sα(k+1)、i_sβ(k +1) represents predicted values of the stator current on the α and β axes, respectively.

The control method comprises the following specific steps of zero-sequence current suppression, voltage override jump control, midpoint potential balance control and switching frequency suppression:

(1) and (3) zero-sequence current suppression:

fig. 4 shows a zero common mode voltage candidate vector diagram of a dual three-level inverter system, and fig. 5 shows a switching state corresponding to each zero common mode voltage vector. Wherein, the switch states "p", "o" and "n" respectively represent that the output voltage of the inverter is V_dc、0、-V_dcEach voltage vector is synthesized by two inverter output voltage vectors and corresponds to at least one switching state. Taking a zero common mode voltage vector I as an example, when I is an action vector, the switching states corresponding to the two inverters are respectively: o, p, n, o, n and p can be obtained according to a calculation formula of the common-mode voltage and the zero-sequence voltage:

U_cm＝[0+V_dc+(-V_dc)+0+(-V_dc)+V_dc]＝0 (4.4)

U_zs＝[0+V_dc+(-V_dc)-0-(-V_dc)-V_dc]＝0 (4.5)

similarly, for other vectors to be selected in the graph, the generated zero sequence voltage and the common mode voltage are both zero.

When voltage vector selection is carried out, the common mode voltage and the zero sequence voltage of the common bus system are restrained only by adopting a zero sequence voltage vector mode. According to a common-mode voltage formula and a zero-sequence voltage formula of the double invertersIt can be seen that the common-mode voltage of the two inverters is zero (i.e., U)_cm1＝U_cm20), dual inverter system common mode voltage U_cmAnd zero sequence voltage U_zsCan be zero at the same time, so that the voltage vector in which the common-mode voltages of the two inverters are both zero is called a zero common-mode voltage vector. The application of the zero common mode voltage vector essentially cuts off the sources of the generation of the common mode voltage and the zero sequence voltage, so that the system does not need to rely on the constraint of a value function to realize the suppression of the zero sequence current. If the zero common-mode voltage vector is used as a candidate vector to predict the future state of the system before voltage vector screening is carried out, the zero common-mode voltage vector can be used as a candidate vector, and therefore the zero sequence voltage and the common-mode voltage of the double-inverter system can be completely eliminated no matter which voltage vector is selected.

Because the magnitude of the zero sequence current is closely related to the zero sequence voltage, when the output voltage of the inverter is zero sequence voltage, the zero sequence current is zero, so that the zero sequence current is inhibited, the zero sequence current is eliminated, the output of the system can be kept stable, the operation in a common direct current bus mode is realized, and the operation and maintenance cost of the system is reduced. According to the zero common mode voltage vector diagram shown in fig. 4, after the double three-level inverter completely adopts the zero common mode voltage vector as the candidate vector, the linear modulation region of the double three-level inverter is an inscribed regular hexagon of the normal region, so that the modulation range is 86.6% of the original modulation range. Therefore, in order to obtain the loading capacity of the vector system using the conventional voltage vector as the candidate vector, the voltage level on the direct current side needs to be properly increased.

In addition, it can be seen from the zero common mode voltage candidate vector diagram that if the zero sequence voltage is eliminated in the dual two-level inverter by using this method, the number of candidate voltage vectors will be very small, and although the constraint of zero sequence voltage suppression can be satisfied, the control effect on the motor flux linkage and the torque will be difficult to guarantee.

(2) Voltage skip control

Referring to fig. 6, to avoid phase and line voltage overshoot, switching to adjacent voltage vectors is only allowed. Therefore, the voltage vector at the next moment of the system is selected in an off-line selection mode, a predictive selection vector switching table is established, and fig. 6 is a preselected vector switching table. The voltage vector at this moment is sampled first, and then the voltage vector of the next period is preselected by using a vector switching table according to the principle that the voltage vector can not be from 'p → n' or 'n → p' every time.

(3) Midpoint potential balance control

The magnitude of the midpoint potential is related to the selected voltage vector, and referring to the conventional three-level inverter voltage vector classification method, the zero common mode voltage vector shown in fig. 4 can be divided into: zero, small, medium and large vectors. Where only the small and medium vectors will produce the corresponding midpoint current, while the zero and large vectors will not. If only the voltage vector which does not generate the midpoint current is adopted during vector selection, the midpoint current can be restrained, but after zero-sequence current and voltage jump limiting vector screening, a small number of vectors can be selected. Therefore, the method is not adopted for carrying out neutral point potential balance control, the problem of neutral point load potential fluctuation is firstly analyzed, and the neutral point potential control is effectively realized by adopting a model prediction control method.

Referring to FIG. 7, FIG. 7 shows a DC side capacitor topology, which is analyzed for a DC side circuit, and two supporting capacitors C without considering the capacitor difference₁、C₂All the capacitance values of (C, i)_C1And i_C2Respectively, the current, u, flowing through the two supporting capacitors_c1、u_c2Respectively being a supporting capacitor C₁、C₂The voltage at the node is obtained according to the node current law and the capacitance characteristic, and the relation between the capacitance voltage and the capacitance current is as follows:

in the formula, Δ V_NPIs a capacitor C₁And a capacitor C₂Voltage difference between i_NPRepresents the capacitance C₁And a capacitor C₂Current in between, ideally C₁＝C₂Taking the average value of voltage in one cycle as C according to the state average methodThe voltage difference at that moment. From the quantitative relationship between the capacitor voltage and the capacitor current, the magnitude of the midpoint potential is closely related to the midpoint current. Discretizing the direct-current side capacitor voltage by using a forward Euler algorithm to obtain an expression of the midpoint potential at the next moment, wherein the expression is as follows:

from this, the expression for the midpoint voltage can be derived:

ΔV_NP(k+1)＝u_C1(k+1)-u_C2(k+1) (4.8)

the midpoint voltage is written into the cost function as a new constraint term, and the new cost function can be obtained as follows:

in order to balance the midpoint voltage, a midpoint potential balance weight factor lambda is introduced into the formula_ΔVBy adjusting λ_ΔVThe balance between the midpoint potential and the output current is dynamically adjusted by the numerical value, and the control effect of the output current of the system can be ensured.

(4) Switching frequency suppression

After the control targets are restrained, the optimal voltage vector corresponding to each sampling period can be obtained through the iterative solution of the cost function. Since the switching states of a dual three-level inverter system are much more than the voltage vectors, there are cases where the switching states are redundant, i.e. each voltage vector corresponds to more than one switching state. Therefore, after the optimal voltage vector is successfully screened out, the switching state with the minimum switching frequency of the switching state is selected according to the corresponding relation between the zero sequence voltage vector diagram shown in fig. 4 and the switching state shown in fig. 5. The optimal voltage vector screened out after multi-objective optimization is assumed to be the A vector in FIG. 4, that is, all the above limitations can be satisfied when the A vector is output in two or three levels. However, the voltage vector a corresponds to four switching states, and the inverter outputs different voltage vectors depending on the corresponding switching states, so that the switching states cannot be switched at will and a certain restriction rule is necessary.

If the switching frequency is increased due to the excessively high switching frequency, the system loss is increased, and the normal operation of the system is not facilitated. After the optimal voltage vector is selected, the optimal switching state with the lowest switching frequency is selected from the corresponding switching states, and the switching frequency expression is as follows:

S＝|S_a1(k+1)-S_a1(k)|+|S_b1(k+1)-S_b1(k)|+|S_c1(k+1)-S_c1(k)|+ |S_a2(k+1)-S_a2(k)|+|S_b2(k+1)-S_b2(k)|+|S_c2(k+1)-S_c2(k)| (4.10)

in the formula: s_a1(k)、S_b1(k)、S_c1(k) Respectively showing the switching states of the first, second and third bridge arms of the inverter-1 at the current sampling moment, S_a2(k)、S_b2(k)、S_c2(k) Respectively representing the switching states of a first bridge arm, a second bridge arm and a third bridge arm of the inverter-2 at the current sampling moment; s_a1(k+1)、S_b1(k+1)、S_c1(k +1) represents the switching states to be applied to the first, second and third legs of the inverter-1 at the next sampling time, respectively, S_a2(k+1)、S_b2(k+1)、S_c2And (k +1) respectively represents the switching states of the first bridge arm, the second bridge arm and the third bridge arm to be applied to the inverter-2 at the next sampling moment. The system switching frequency limit is added as a new constraint to the cost function, so the new cost function is:

in the formula of_sFor the weighting factor of the switching frequency, it should be noted that, since the switching frequency is limited to the weakest constraint of the system, that is, the system should consider the problem of the switching frequency limitation on the premise of satisfying the first several constraints. If the system and the most basic control can not be realized, the methodIt does not make sense how low the switching frequency is. Thus λ_sThe values cannot be very large and should be an order of magnitude smaller than the first few terms, and details will be given in the next subsection as to how the weighting factors are designed. And finally, realizing multi-objective optimized current prediction control by dynamically adjusting the numerical values of the weight factors.

(5) Weight factor design

One of the advantages of model predictive control is multi-objective optimization, and the key to realizing the multi-objective optimization is the design of weight factors in the cost function. The main variables such as current, voltage, motor torque or magnetic flux and the like are controlled by adjusting the weight factor, and meanwhile, additional control requirements such as midpoint voltage control, common-mode voltage suppression, switching frequency limitation and the like can be met. Combining two or more variables into one variable can be a complex and difficult task given the differences in the nature, units and orders of magnitude of the control variables. In order to balance the quantity relationship between the additional control requirements and the main variables, corresponding weight factors are required to be added before each additional control requirement, the weight factors with corresponding numbers can be set according to the number of the additional items, and the weight factors are used for balancing and adjusting the importance degree or the weight relationship between the corresponding additional items and other control items. Only by properly designing and adjusting these weighting factors will the system meet the desired performance requirements. However, there is no mature theory, numerical derivation or control design theory in the literature data at present, which can provide effective guidance for the adjustment of the weight factor, and although the design of the weight factor does not affect the application of the MPC in the multilevel inverter, it is still necessary to make a set of rules or determine some basic guidance methods to reduce the uncertainty in the cost function design stage, reduce the design difficulty and improve the design efficiency.

The subject double-inverter open-winding motor control is a typical constrained multi-objective optimization problem, optimization performance indexes comprise current following control, zero-sequence current suppression, voltage jump limitation, neutral point potential balance control, switching frequency suppression and the like, and the design and setting of weight factors are difficult due to mutual conflict among different control objectives. This subsection proposes a method for designing weight factors, which classifies the weight factors in MPC merit function according to the characteristics of the control target, and aims to make a preliminary classification and evaluation of the influence of the weight factor coefficients on the system.

For a dual three-level inverter system, the main control objective that must be achieved is the control of the motor current, providing the system with the correct system input-output characteristics, so the current control term has the highest rank. Additional secondary constraints or requirements are included that are needed to achieve the goal of improving system performance, efficiency, or power quality. At the moment, the motor current is a main item of the cost function, other control targets are secondary items, and the secondary items are designed differently according to different application requirements. Secondary control items such as switching frequency control, common mode voltage suppression, reactive compensation and the like control the system auxiliary performance optimization degree through weight factor balance, and the weight factor setting of the system does not have a unified method at present and mostly depends on experience or is set through a simulation experiment method.

Meanwhile, it is obvious that the design difficulty of the weight factors is positively correlated with the number of the weight factors, and the design process is more complicated when the number of the weight factors to be designed is larger. To reduce the design process required to determine the weight factor values, a half-value approximation algorithm is used herein. Referring to fig. 8, when using the algorithm, first two orders of magnitude initial values are selected for the weight factors, which should contain a large range of different orders of magnitude, e.g. λ₁0 and λ₂10. Two initial values are simulated and the result is compared with the expected output, and then the simulation is performed with half of the interval of the initial values, for example, λ ═ 5, as the new weighting factor. The comparison of the simulation results shows where the weighting factor should be adjusted, for example, if the simulation result of λ ═ 5 is better than the simulation result of λ ═ 10, it indicates that the weighting factor should be adjusted when λ ═ 0. Again with 0 and 5 as initial values of the weight factors, the calculation is continued until the appropriate weight values are obtained.

The above embodiments are only for more clearly illustrating the technical solutions of the present invention, and the scope of the present invention includes but is not limited to the above embodiments, and any suitable changes or substitutions that are consistent with the claims of the present invention and are made by those skilled in the art shown should fall within the scope of the present invention.