CN110690842B - Method for determining main circuit parameter stability region of three-phase asynchronous motor speed regulating system - Google Patents

Method for determining main circuit parameter stability region of three-phase asynchronous motor speed regulating system Download PDF

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CN110690842B
CN110690842B CN201911063367.7A CN201911063367A CN110690842B CN 110690842 B CN110690842 B CN 110690842B CN 201911063367 A CN201911063367 A CN 201911063367A CN 110690842 B CN110690842 B CN 110690842B
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phase
bbmc
inductance
asynchronous motor
converter
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CN110690842A (en
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张小平
张瑞瑞
严颖
陈娟
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Hunan University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/01—Asynchronous machines

Abstract

The invention discloses a method for determining a main circuit parameter stability region of a three-phase asynchronous motor speed regulating system. The method comprises the following steps: establishing a state differential equation by taking the inductive current and the capacitor voltage in the inverter stage of the Buck-Boost matrix converter as state variables; obtaining a discrete iteration mapping model according to the state differential equation of the BBMC inverter stage; establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system, and obtaining a discrete iteration mapping model of the three-phase asynchronous motor according to the state differential equation; obtaining a discrete iteration mapping model of a BBMC-based three-phase asynchronous motor speed regulating system according to the discrete iteration mapping model of the BBMC inverter stage and the discrete iteration mapping model of the three-phase asynchronous motor; according to the discrete iterative mapping model of the BBMC-based three-phase asynchronous motor speed regulating system, the value range of the main circuit parameter of the speed regulating system in stable operation is obtained through numerical simulation.

Description

Method for determining main circuit parameter stability region of three-phase asynchronous motor speed regulating system
Technical Field
The invention relates to the field of three-phase asynchronous motor speed regulation, in particular to a method for determining a main circuit parameter stability region of a three-phase asynchronous motor speed regulation system.
Background
The Buck-Boost matrix converter (BBMC) not only keeps the electrical characteristics of sine input current, adjustable input power factor, capability of realizing four-quadrant operation and the like of the traditional matrix converter, but also has the characteristics of arbitrary adjustable output voltage and frequency, capability of directly outputting high-quality sine waves without a filtering link and the like, so that the Buck-Boost matrix converter is very suitable for being applied to a variable-frequency speed regulation system of an asynchronous motor, and is particularly suitable for application occasions with large voltage fluctuation of a power grid.
However, because the BBMC inverter stage belongs to a strong nonlinear system with a variable structure, bifurcation and chaos phenomena can be generated under certain conditions, so that the problems of unstable performance, intensified oscillation, overlarge irregular electromagnetic noise and the like of the converter are caused, the running quality and reliability of the converter are directly influenced, and the speed regulation performance of the asynchronous motor speed regulation system based on the converter is seriously influenced.
Disclosure of Invention
In order to solve the technical problem, the invention provides a method for determining the stable domain of the main circuit parameters of the speed regulating system of the three-phase asynchronous motor.
The technical scheme for solving the technical problems comprises the following steps:
(1) establishing a state differential equation by taking the inductive current and the capacitor voltage in the BBMC inverter stage as state variables;
(2) obtaining a discrete iteration mapping model of the BBMC inverter stage according to the state differential equation of the BBMC inverter stage obtained in the step (1);
(3) establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system;
(4) obtaining a discrete iteration mapping model of the three-phase asynchronous motor according to the state differential equation of the three-phase asynchronous motor obtained in the step (3);
(5) obtaining a discrete iteration mapping model of the BBMC-based three-phase asynchronous motor speed regulating system according to the BBMC inverter stage discrete iteration mapping model obtained in the step (2) and the three-phase asynchronous motor discrete iteration mapping model obtained in the step (4);
(6) and (4) obtaining the value range of the main circuit parameter of the speed regulating system in stable operation through numerical simulation according to the discrete iterative mapping model of the BBMC-based three-phase asynchronous motor speed regulating system obtained in the step (5).
Preferably, in the step (1), the A-phase inductive current and the capacitor voltage in the BBMC inverter stage are used as state variables to establish a state differential equation, and other two phases are the same; when the power switch tube in A-phase converter
Figure BDA0002256504060000021
When the switch is switched on, the state differential equation is as follows:
Figure BDA0002256504060000022
when the power switch tube in A-phase converter
Figure BDA0002256504060000023
When the switch is switched off, the state differential equation is as follows:
Figure BDA0002256504060000024
wherein: variable of state
Figure BDA0002256504060000025
And
Figure BDA0002256504060000026
respectively representing the inductive current and the capacitive voltage in the a-phase converter,
Figure BDA0002256504060000027
and
Figure BDA0002256504060000028
are respectively state variables
Figure BDA0002256504060000029
And
Figure BDA00022565040600000210
e is the BBMC inverter stage input voltage iAAnd outputting current for the A-phase converter, wherein L and C are inductance parameters and capacitance parameters in the A-phase converter respectively.
Preferably, the specific operation of step (2) is as follows:
let the reference voltage of capacitor in A-phase converter be
Figure BDA0002256504060000031
Then the reference current of the inductor in the A-phase converter is obtained as follows:
Figure BDA0002256504060000032
according to the formula (1) to the formula (3), a discrete iterative mapping model of the A-phase transformer is obtained as follows:
Figure BDA0002256504060000033
wherein:
Figure BDA0002256504060000034
and
Figure BDA0002256504060000035
respectively representing the capacitance voltage and the inductance current of the phase-A converter at the (n +1) T moment,
Figure BDA0002256504060000036
representing the a-phase converter output current at time nT,
Figure BDA0002256504060000037
represents the turn-off time of the A-phase converter power switch tube in the (n +1) th switching period T,
Figure BDA0002256504060000038
represents the conduction time of the power switch tube of the A-phase converter in the (n +1) th switching period T, wherein T is the switching period of the power switch tube in the converter,
Figure BDA0002256504060000039
for inductive reference currents in the A-phase converter at time nT, MA、NAAnd ω are all intermediate variables, and
Figure BDA00022565040600000310
Figure BDA00022565040600000311
Figure BDA00022565040600000312
and
Figure BDA00022565040600000313
respectively representing the capacitive voltage and the inductive current in the a-phase converter at time nT.
Similarly, a discrete iteration mapping model of the B, C two-phase transformer in the BBMC inverter stage can be obtained, so that the total discrete iteration mapping model of the BBMC inverter stage is:
Figure BDA0002256504060000041
wherein:
Figure BDA0002256504060000042
and
Figure BDA0002256504060000043
respectively representing the capacitance voltage and the inductance current of the phase-B converter at the (n +1) T moment,
Figure BDA0002256504060000044
and
Figure BDA0002256504060000045
respectively representing the capacitance voltage and the inductance current of the C-phase converter at the (n +1) T moment,
Figure BDA0002256504060000046
and
Figure BDA0002256504060000047
respectively representing the output currents of the B-phase transformer and the C-phase transformer at nT time,
Figure BDA0002256504060000048
and
Figure BDA0002256504060000049
respectively representing the turn-off time of the B-phase converter power switch tube and the C-phase converter power switch tube in the (n +1) th switching period T,
Figure BDA00022565040600000410
and
Figure BDA00022565040600000411
respectively showing that the B-phase converter power switch tube and the C-phase converter power switch tube are in the (n +1) th switching period TThe on-time of the light source (c),
Figure BDA00022565040600000412
and
Figure BDA00022565040600000413
the inductive reference currents of the B-phase transformer and the C-phase transformer are respectively indicated at nT,
Figure BDA00022565040600000414
and
Figure BDA00022565040600000415
respectively representing the capacitive reference voltages, M, of the B-phase converter and the C-phase converterB、NB、MCAnd NCAre all intermediate variables, and
Figure BDA00022565040600000416
Figure BDA00022565040600000417
Figure BDA00022565040600000418
and
Figure BDA00022565040600000419
respectively representing the capacitance voltage and the inductance current of the B-phase converter at nT time,
Figure BDA0002256504060000051
and
Figure BDA0002256504060000052
respectively representing the capacitance voltage and the inductance current of the C-phase converter at nT time.
Preferably, the step (3) establishes a state differential equation of the three-phase asynchronous motor on the two-phase stationary coordinate system, specifically:
Figure BDA0002256504060000053
wherein: u. ofsαAnd usβRepresenting the stator voltage, i, of the motor in two-phase stationary coordinates, respectivelysαAnd isβRepresenting the stator currents of the motor in two stationary phases, ΨrαAnd ΨrβRespectively representing the rotor flux, T, of the motor in two-phase stationary coordinatesLRepresenting motor load torque, ωrRepresenting the angular velocity, L, of the rotor of the machines、Lr、Lm、Rs、Rr、npAnd J respectively represent the self inductance of the stator, the self inductance of the rotor, the mutual inductance of the stator and the rotor, the resistance of the stator, the resistance of the rotor, the pole pair number and the moment of inertia of the motor,
Figure BDA0002256504060000054
representing the leakage coefficient, T, of the motorr＝Lr/RrRepresenting the rotor electromagnetic time constant.
Preferably, the specific operation of step (4) is:
discretizing a state differential equation shown in the formula (6) by a Runge-Kutta method to obtain:
Figure BDA0002256504060000055
wherein:
Figure BDA0002256504060000061
is the state vector at time (n +1) T,
Figure BDA0002256504060000062
is the state vector at time nT, K1、K2、K3And K4Are all intermediate variables, and K1＝f(xn,yn)，
Figure BDA0002256504060000063
K4＝f(xn+TK0,yn+TK3)，
Figure BDA0002256504060000064
usα(n)And usβ(n)Respectively representing the stator voltage i of the motor at the moment nT on the two-phase stationary coordinatesα(n)And isβ(n)Representing the stator currents of the machine at the moment nT in two-phase stationary coordinates, Ψrα(n)And Ψrβ(n)Respectively representing the rotor flux linkage, omega, at time nT on the two-phase stationary coordinater(n)Representing the angular velocity of the rotor of the machine at time nT.
Preferably, the step (5) obtains a discrete iteration mapping model of the three-phase asynchronous motor speed regulation system based on the BBMC according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (2) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (4), and specifically comprises:
according to the formula (5) and the formula (7) and the transformation formula of the three-phase static coordinate system and the two-phase static coordinate system, a discrete iteration mapping model of the BBMC-based three-phase asynchronous motor speed regulating system can be obtained:
Figure BDA0002256504060000071
preferably, in the step (6), according to the discrete iterative mapping model of the BBMC-based three-phase asynchronous motor speed regulation system obtained in the step (5), the value range of the main circuit parameter of the speed regulation system in stable operation is obtained through numerical simulation.
More preferably, the step (6) specifically includes the steps of:
step A1: setting system parameters, including: self-inductance L of motor statorsSelf-inductance of rotor LrStator and rotor mutual inductance LmStator resistor RsRotor resistance RrN number of pole pairspMoment of inertia J, load torque TLSwitching period T of power switching tube, maximum iteration number N, BBMC capacitance reference voltage
Figure BDA0002256504060000072
Period T of reference voltage of capacitor0(and satisfy T)0kT, k being a positive integer), change parameter increment Δ X, maximum biasThe difference ε, the initial value of the count variable q is 0.
Step A2: firstly, setting the inductance L of the main circuit as a variation parameter X, setting the initial value of the inductance L as 0, and keeping the capacitance C unchanged;
step A3: calculating the state variable at time (n +1) T by equation (8)
Figure BDA0002256504060000073
And
Figure BDA0002256504060000074
step A4: judge this moment
Figure BDA0002256504060000081
And
Figure BDA0002256504060000082
whether or not to simultaneously satisfy
Figure BDA0002256504060000083
Figure BDA0002256504060000084
And
Figure BDA0002256504060000085
if yes, the system is in a stable state, and step A7 is executed; otherwise, go to step A5;
step A5: judging whether the iteration number N is greater than N, if so, executing the step A6; otherwise, adding 1 to the iteration number n, and returning to the step A3;
step A6: adding delta X to the change parameter X, enabling the iteration number n to return to 1, and returning to the step A3;
step A7: let the corresponding change parameter value X at this time be the lower limit value of the parameter stability domain, that is: xmin＝X；
Step A8: the changing parameter X is sequentially increased by delta X, whether the system stably operates is judged according to the methods from the step A3 to the step A4 after each increment, if yes, the increment is continued until the system cannot stably operate, and the corresponding changing parameter value X is made to be the parameter stable at the momentThe upper limit value of localization, namely: xmax＝X；
Step A9: judging whether the counting variable q is equal to 1, if so, executing the step A12, otherwise, executing the step A10;
step A10: let Lmin＝Xmin，Lmax＝XmaxThe value range of the main circuit inductance L is (L) when the speed regulating system stably operatesmin，Lmax) Counting the variable q plus 1, and executing the step A11;
step A11: selecting a value within the stable value range of the inductor L and keeping the value unchanged, setting the capacitance C as a change parameter X, setting the initial value of the change parameter X as 0, and returning to the step A3;
step A12: let Cmin＝Xmin，Cmax＝XmaxThe value range of the main circuit capacitance C is (C) when the speed regulation system stably operatesmin，Cmax)；
Step A13: obtaining the value range (L) of the main circuit inductance L according to the step A10min，Lmax) And the value range (C) of the main circuit capacitor C obtained in the step A12min，Cmax) Specific values of an inductor L and a capacitor C in the BBMC inverter stage are determined, and stable operation of the BBMC-based three-phase asynchronous motor speed regulation system can be achieved.
Compared with the prior art, the method takes the inductive current and the capacitor voltage in the Buck-Boost matrix converter (BBMC) inverter stage as state variables to establish a state differential equation of the inverter stage; obtaining a discrete iteration mapping model according to the state differential equation of the BBMC inverter stage; establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system, and obtaining a discrete iteration mapping model of the three-phase asynchronous motor according to the state differential equation; obtaining a discrete iteration mapping model of a BBMC-based three-phase asynchronous motor speed regulating system according to the discrete iteration mapping model of the BBMC inverter stage and the discrete iteration mapping model of the three-phase asynchronous motor; according to the discrete iterative mapping model of the BBMC-based three-phase asynchronous motor speed regulating system, the value range of the main circuit parameter of the speed regulating system in stable operation is obtained through numerical simulation. The invention has the advantages that: for a frequency conversion speed regulation system of a three-phase asynchronous motor taking BBMC as a frequency converter, the value range of main circuit parameters, namely main circuit inductance and main circuit capacitance, is researched and determined when the system stably runs, and the method has important significance for guiding the design of the main circuit parameters of the BBMC speed regulation system.
Drawings
FIG. 1 is a topological structure diagram of a BBMC-based three-phase asynchronous motor speed regulation system in the invention;
FIG. 2 is a topology structure diagram of an A-phase Buck-Boost converter in the invention;
FIG. 3 is a flow chart of the present invention;
FIG. 4 is a detailed flow chart of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Fig. 1 is a topology structure diagram of an asynchronous motor speed regulation system based on BBMC according to an embodiment of the present invention. The BBMC adopts the structural form of an AC-DC-AC two-stage converter, the rectifying stage of the BBMC is an 3/2-phase matrix converter, and the inverter stage adopts the structural form of a three-phase Buck-Boost inverter and consists of three Buck-Boost DC/DC converters with the same structure; and three-phase stator windings of the three-phase asynchronous motor are respectively connected to three output ends of the BBMC.
Fig. 2 is a topology structure diagram of an a-phase Buck-Boost converter according to an embodiment of the present invention. The converter includes a power switch
Figure BDA0002256504060000101
And
Figure BDA0002256504060000102
inductance L and capacitance C. Wherein, the power switch
Figure BDA0002256504060000103
The collector of the power switch is connected with the anode of a direct current input power supply E
Figure BDA0002256504060000104
Emitter and power switch
Figure BDA0002256504060000105
Is connected with one end of an inductor L, and a power switch
Figure BDA0002256504060000106
The other end of the inductor L is connected with the anode of the capacitor C and then connected to the cathode of the direct current input power supply E.
Referring to fig. 3, fig. 3 is a flow chart of the present invention. The invention comprises the following steps:
step (1): the method comprises the following steps of establishing a state differential equation by taking inductive current and capacitor voltage in a BBMC inverter stage as state variables, wherein the state differential equation specifically comprises the following steps:
setting a three-phase asynchronous motor in a speed regulation system to be in an electric operation state, namely, the power flow in the BBMC flows from a power supply side to a motor side; meanwhile, considering that the BBMC inverter stage consists of three Buck-Boost DC/DC converters with the same structure, the A phase of the BBMC inverter stage is taken as an example in the following analysis, and the other two phases are the same as the A phase of the BBMC inverter stage, see FIG. 2.
When the power switch tube in A-phase converter
Figure BDA0002256504060000107
When the switch is switched on, the state differential equation is as follows:
Figure BDA0002256504060000108
when the power switch tube in A-phase converter
Figure BDA0002256504060000109
When the switch is switched off, the state differential equation is as follows:
Figure BDA0002256504060000111
wherein: state variable iL AAnd uC ARespectively representing the inductive current and the capacitive voltage in the a-phase converter,
Figure BDA0002256504060000112
and
Figure BDA0002256504060000113
are respectively a state variable iL AAnd uC AE is the BBMC inverter stage input voltage iAAnd outputting current for the A-phase converter, wherein L and C are inductance parameters and capacitance parameters in the A-phase converter respectively.
Step (2): obtaining a discrete iteration mapping model according to the state differential equation of the BBMC inverter stage obtained in the step (1), wherein the discrete iteration mapping model is as follows:
let the reference voltage of capacitor in A-phase converter be
Figure BDA0002256504060000114
Then the reference current of the inductor in the A-phase converter is obtained as follows:
Figure BDA0002256504060000115
according to the formula (1) to the formula (3), a discrete iterative mapping model of the A-phase transformer is obtained as follows:
Figure BDA0002256504060000116
wherein:
Figure BDA0002256504060000117
and
Figure BDA0002256504060000118
respectively representing the capacitance voltage and the inductance current of the phase-A converter at the (n +1) T moment,
Figure BDA0002256504060000119
represents the output current of the a-phase converter at time nT,
Figure BDA00022565040600001110
represents the turn-off time of the power switch tube in the A-phase converter in the (n +1) th switching period T,
Figure BDA00022565040600001111
represents the conduction time of the power switch tube in the A-phase converter in the (n +1) th switching period T, wherein T is the switching period of the power switch tube in the converter,
Figure BDA00022565040600001112
for inductive reference currents in the A-phase converter at time nT, MA、NAAnd ω are all intermediate variables, and
Figure BDA00022565040600001113
Figure BDA0002256504060000121
Figure BDA0002256504060000122
and
Figure BDA0002256504060000123
respectively representing the capacitive voltage and the inductive current in the a-phase converter at time nT.
Similarly, a discrete iteration mapping model of the B, C two-phase transformer in the BBMC inverter stage can be obtained, so that the total discrete iteration mapping model of the BBMC inverter stage is:
Figure BDA0002256504060000124
wherein:
Figure BDA0002256504060000125
and
Figure BDA0002256504060000126
respectively representing the capacitance voltage and the inductance current of the phase-B converter at the (n +1) T moment,
Figure BDA0002256504060000127
and
Figure BDA0002256504060000128
respectively representing the capacitance voltage and the inductance current of the C-phase converter at the (n +1) T moment,
Figure BDA0002256504060000129
and
Figure BDA00022565040600001210
respectively representing the output currents of the B-phase transformer and the C-phase transformer at nT time,
Figure BDA00022565040600001211
and
Figure BDA00022565040600001212
respectively representing the turn-off time of the B-phase converter power switch tube and the C-phase converter power switch tube in the (n +1) th switching period T,
Figure BDA00022565040600001213
and
Figure BDA00022565040600001214
respectively representing the conduction time of the B-phase converter power switch tube and the C-phase converter power switch tube in the (n +1) th switching period T,
Figure BDA00022565040600001215
and
Figure BDA00022565040600001216
the inductive reference currents of the B-phase transformer and the C-phase transformer are respectively indicated at nT,
Figure BDA0002256504060000131
and
Figure BDA0002256504060000132
respectively representing the capacitive reference voltages, M, of the B-phase converter and the C-phase converterB、NB、MCAnd NCAre all intermediate variables, and
Figure BDA0002256504060000133
Figure BDA0002256504060000134
Figure BDA0002256504060000135
and
Figure BDA0002256504060000136
respectively representing the capacitance voltage and the inductance current of the B-phase converter at nT time,
Figure BDA0002256504060000137
and
Figure BDA0002256504060000138
respectively representing the capacitance voltage and the inductance current of the C-phase converter at nT time.
And (3): establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system, which specifically comprises the following steps:
Figure BDA0002256504060000139
wherein: u. ofsαAnd usβRepresenting the stator voltage, i, of the motor in two-phase stationary coordinates, respectivelysαAnd isβRepresenting the stator currents of the motor in two stationary phases, ΨrαAnd ΨrβRespectively representing the rotor flux, T, of the motor in two-phase stationary coordinatesLRepresenting motor load torque, ωrRepresenting the angular velocity, L, of the rotor of the machines、Lr、Lm、Rs、Rr、npAnd J respectively represent the self inductance of the stator, the self inductance of the rotor, the mutual inductance of the stator and the rotor, the resistance of the stator, the resistance of the rotor, the pole pair number and the moment of inertia of the motor,
Figure BDA00022565040600001310
representing the leakage coefficient, T, of the motorr＝Lr/RrRepresenting the rotor electromagnetic time constant.
And (4): obtaining a discrete iteration mapping model according to the state differential equation of the three-phase asynchronous motor obtained in the step (3), specifically:
discretizing a state differential equation shown in the formula (6) by a Runge-Kutta method to obtain:
Figure BDA0002256504060000141
wherein:
Figure BDA0002256504060000142
is the state vector at time (n +1) T,
Figure BDA0002256504060000143
is the state vector at time nT, K1、K2、K3And K4Are all intermediate variables, and K1＝f(xn,yn)，
Figure BDA0002256504060000144
K4＝f(xn+TK0,yn+TK3)，
Figure BDA0002256504060000145
usα(n)And usβ(n)Respectively representing the stator voltage i of the motor at the moment nT on the two-phase stationary coordinatesα(n)And isβ(n)Representing the stator currents of the machine at the moment nT in two-phase stationary coordinates, Ψrα(n)And Ψrβ(n)Respectively representing the rotor flux linkage, omega, at time nT on the two-phase stationary coordinater(n)Representing the angular velocity of the rotor of the machine at time nT.
And (5): obtaining a discrete iteration mapping model of the BBMC-based three-phase asynchronous motor speed regulating system according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (2) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (4), and specifically:
according to the formula (5) and the formula (7) and the transformation formula of the three-phase static coordinate system and the two-phase static coordinate system, a discrete iteration mapping model of the BBMC-based three-phase asynchronous motor speed regulating system can be obtained:
Figure BDA0002256504060000151
and (6): according to the discrete iterative mapping model of the BBMC-based three-phase asynchronous motor speed regulating system obtained in the step (5), the value range of the main circuit parameter in the stable operation of the speed regulating system is obtained through numerical simulation, wherein the main circuit parameter specifically refers to the L parameter of the main circuit inductance and the C parameter of the main circuit capacitance in the BBMC, and referring to fig. 4, the detailed flow chart for obtaining the value range of the main circuit parameter in the stable operation of the speed regulating system provided by the embodiment of the invention specifically comprises the following steps:
step A1: setting system parameters, including: self-inductance L of motor statorsSelf-inductance of rotor LrStator and rotor mutual inductance LmStator resistor RsRotor resistance RrN number of pole pairspMoment of inertia J, load torque TLSwitching period T of power switching tube, maximum iteration number N, BBMC capacitance reference voltage
Figure BDA0002256504060000161
Period T of reference voltage of capacitor0(and satisfy T)0kT, k being a positive integer), the change parameter increment Δ X, the maximum deviation ∈, and the initial value of the count variable q is 0.
Step A2: firstly, setting the inductance L of the main circuit as a variation parameter X, setting the initial value of the inductance L as 0, and keeping the capacitance C unchanged;
step A3: calculating the state variable at time (n +1) T by equation (8)
Figure BDA0002256504060000162
And
Figure BDA0002256504060000163
step A4: judge this moment
Figure BDA0002256504060000164
And
Figure BDA0002256504060000165
whether or not to simultaneously satisfy
Figure BDA0002256504060000166
Figure BDA0002256504060000167
And
Figure BDA0002256504060000168
if yes, the system is in a stable state, and step A7 is executed; otherwise, go to step A5;
step A5: judging whether the iteration number N is greater than N, if so, executing the step A6; otherwise, adding 1 to the iteration number n, and returning to the step A3;
step A6: adding delta X to the change parameter X, enabling the iteration number n to return to 1, and returning to the step A3;
step A7: let the corresponding change parameter value X at this time be the lower limit value of the parameter stability domain, that is: xmin＝X；
Step A8: the changing parameter X is sequentially increased by delta X, whether the system stably operates or not is judged according to the method from the step A3 to the step A4 after each increment, if yes, the increment is continued until the system cannot stably operate, and the corresponding changing parameter value X at the moment is made to be an upper limit value of a stable domain of the parameter, namely: xmax＝X；
Step A9: judging whether the counting variable q is equal to 1, if so, executing the step A12, otherwise, executing the step A10;
step A10: let Lmin＝Xmin，Lmax＝XmaxThe value range of the main circuit inductance L is (L) when the speed regulating system stably operatesmin，Lmax) Counting the variable q plus 1, and executing the step A11;
step A11: selecting a value within the stable value range of the inductor L and keeping the value unchanged, setting the capacitance C as a change parameter X, setting the initial value of the change parameter X as 0, and returning to the step A3;
step A12: let Cmin＝Xmin，Cmax＝XmaxThe value range of the main circuit capacitance C is (C) when the speed regulation system stably operatesmin，Cmax)；
Step A13: obtaining the value range (L) of the main circuit inductance L according to the step A10min，Lmax) And the value range (C) of the main circuit capacitor C obtained in the step A12min，Cmax) Specific values of an inductor L and a capacitor C in the BBMC inverter stage are determined, and stable operation of the BBMC-based three-phase asynchronous motor speed regulation system can be achieved.

Claims (2)

1. A method for determining a main circuit parameter stability region of a three-phase asynchronous motor speed regulating system is characterized by comprising the following steps:
(1) the method comprises the following steps of establishing a state differential equation by taking inductive current and capacitor voltage in a BBMC inverter stage as state variables, and specifically comprising the following steps:
establishing a state differential equation by taking the A-phase inductive current and the capacitor voltage in the BBMC inverter stage as state variables, wherein other two phases are the same; when the power switch tube in A-phase converter
Figure FDA00031255707500000111
When the switch is switched on, the state differential equation is as follows:
Figure FDA0003125570750000011
when the power switch tube in A-phase converter
Figure FDA00031255707500000112
When the switch is switched off, the state differential equation is as follows:
Figure FDA0003125570750000012
wherein: variable of state
Figure FDA0003125570750000013
And
Figure FDA0003125570750000014
respectively representing the inductive current and the capacitive voltage in the a-phase converter,
Figure FDA0003125570750000015
and
Figure FDA0003125570750000016
are respectively state variables
Figure FDA0003125570750000017
And
Figure FDA0003125570750000018
e is the BBMC inverter stage input voltage iAOutputting current for the A-phase converter, wherein L and C are inductance parameters and capacitance parameters in the A-phase converter respectively;
(2) obtaining a discrete iteration mapping model according to the state differential equation of the BBMC inverter stage obtained in the step (1), wherein the specific steps are as follows:
let the reference voltage of capacitor in A-phase converter be
Figure FDA0003125570750000019
Then the reference current of the inductor in the A-phase converter is obtained as follows:
Figure FDA00031255707500000110
according to the formula (1) to the formula (3), a discrete iterative mapping model of the A-phase transformer is obtained as follows:
Figure FDA0003125570750000021
wherein:
Figure FDA0003125570750000022
and
Figure FDA0003125570750000023
respectively representing the capacitance voltage and the inductance current of the phase-A converter at the (n +1) T moment,
Figure FDA0003125570750000024
representing the a-phase converter output current at time nT,
Figure FDA0003125570750000025
represents the turn-off time of the A-phase converter power switch tube in the (n +1) th switching period T,
Figure FDA0003125570750000026
represents the conduction time of the power switch tube of the A-phase converter in the (n +1) th switching period T, wherein T is the switching period of the power switch tube in the converter,
Figure FDA0003125570750000027
for inductive reference currents in the A-phase converter at time nT, MA、NAAnd ω are all intermediate variables, and
Figure FDA0003125570750000028
Figure FDA0003125570750000029
Figure FDA00031255707500000211
and
Figure FDA00031255707500000210
respectively representing the capacitance voltage and the inductance current in the A-phase converter at the nT moment;
similarly, a discrete iteration mapping model of the B, C two-phase transformer in the BBMC inverter stage can be obtained, so that the total discrete iteration mapping model of the BBMC inverter stage is:
Figure FDA0003125570750000031
wherein:
Figure FDA0003125570750000032
and
Figure FDA0003125570750000033
respectively representing the capacitance voltage and the inductance current of the phase-B converter at the (n +1) T moment,
Figure FDA0003125570750000034
and
Figure FDA0003125570750000035
respectively representing the capacitance voltage and the inductance current of the C-phase converter at the (n +1) T moment,
Figure FDA0003125570750000036
and
Figure FDA0003125570750000037
respectively representing the output currents of the B-phase transformer and the C-phase transformer at nT time,
Figure FDA0003125570750000038
and
Figure FDA0003125570750000039
respectively representing the turn-off time of the B-phase converter power switch tube and the C-phase converter power switch tube in the (n +1) th switching period T,
Figure FDA00031255707500000310
and
Figure FDA00031255707500000311
respectively representing the conduction time of the B-phase converter power switch tube and the C-phase converter power switch tube in the (n +1) th switching period T,
Figure FDA00031255707500000312
and
Figure FDA00031255707500000313
the inductive reference currents of the B-phase transformer and the C-phase transformer are respectively indicated at nT,
Figure FDA00031255707500000314
and
Figure FDA00031255707500000315
respectively representing the capacitive reference voltages, M, of the B-phase converter and the C-phase converterB、NB、MCAnd NCAre all intermediate variables, and
Figure FDA00031255707500000316
Figure FDA00031255707500000317
Figure FDA00031255707500000318
and
Figure FDA00031255707500000319
respectively representing the capacitance voltage and the inductance current of the B-phase converter at nT time,
Figure FDA0003125570750000041
and
Figure FDA0003125570750000042
respectively representing the capacitance voltage and the inductance current of the C-phase converter at the nT moment;
(3) establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system, which comprises the following specific steps:
Figure FDA0003125570750000043
wherein: u. ofsαAnd usβRepresenting the stator voltage, i, of the motor in two-phase stationary coordinates, respectivelysαAnd isβRepresenting the stator currents of the motor in two stationary phases, ΨrαAnd ΨrβRespectively representing the rotor flux, T, of the motor in two-phase stationary coordinatesLRepresenting motor load torque, ωrRepresenting the angular velocity, L, of the rotor of the machines、Lr、Lm、Rs、Rr、npAnd J respectively represent the self inductance of the stator, the self inductance of the rotor, the mutual inductance of the stator and the rotor, the resistance of the stator, the resistance of the rotor, the pole pair number and the moment of inertia of the motor,
Figure FDA0003125570750000044
representing the leakage coefficient, T, of the motorr＝Lr/RrRepresents the rotor electromagnetic time constant;
(4) and (4) obtaining a discrete iteration mapping model according to the state differential equation of the three-phase asynchronous motor obtained in the step (3), wherein the specific steps are as follows:
discretizing a state differential equation shown in the formula (6) by a Runge-Kutta method to obtain:
Figure FDA0003125570750000045
wherein:
Figure FDA0003125570750000051
is (n +1) TThe state vector of the moment is calculated,
Figure FDA0003125570750000052
is the state vector at time nT, K1、K2、K3And K4Are all intermediate variables, and K1＝f(xn,yn)，
Figure FDA0003125570750000053
K4＝f(xn+TK0,yn+TK3)，
Figure FDA0003125570750000054
usα(n)And usβ(n)Respectively representing the stator voltage i of the motor at the moment nT on the two-phase stationary coordinatesα(n)And isβ(n)Representing the stator currents of the machine at the moment nT in two-phase stationary coordinates, Ψrα(n)And Ψrβ(n)Respectively representing the rotor flux linkage, omega, at time nT on the two-phase stationary coordinater(n)Representing the angular speed of the motor rotor at the moment nT;
(5) obtaining a discrete iteration mapping model of the BBMC-based three-phase asynchronous motor speed regulating system according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (2) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (4), and specifically comprises the following steps:
obtaining a discrete iteration mapping model of the three-phase asynchronous motor speed regulating system based on the BBMC according to the formula (5) and the formula (7) and a transformation formula of the three-phase static coordinate system and the two-phase static coordinate system:
Figure FDA0003125570750000061
(6) and (5) obtaining the value range of the main circuit parameter when the three-phase asynchronous motor speed regulating system stably operates through numerical simulation according to the discrete iterative mapping model of the three-phase asynchronous motor speed regulating system based on BBMC obtained in the step (5).
2. The method for determining the main circuit parameter stability region of the speed regulating system of the three-phase asynchronous motor according to claim 1, wherein the method comprises the following steps: the specific steps of the step (6) are as follows:
step A1: setting system parameters, including: self-inductance L of motor statorsSelf-inductance of rotor LrStator and rotor mutual inductance LmStator resistor RsRotor resistance RrN number of pole pairspMoment of inertia J, load torque TLSwitching period T of power switching tube, maximum iteration number N, BBMC capacitance reference voltage
Figure FDA0003125570750000062
Period T of reference voltage of capacitor0And satisfy T0K is positive integer, the increment of the change parameter is delta X, the maximum deviation is epsilon, and the initial value of the counting variable q is 0;
step A2: firstly, setting the inductance L of the main circuit as a variation parameter X, setting the initial value of the inductance L as 0, and keeping the capacitance C unchanged;
step A3: calculating the state variable at time (n +1) T by equation (8)
Figure FDA0003125570750000071
And
Figure FDA0003125570750000072
step A4: judge this moment
Figure FDA0003125570750000073
And
Figure FDA0003125570750000074
whether or not to simultaneously satisfy
Figure FDA0003125570750000075
Figure FDA0003125570750000076
And
Figure FDA0003125570750000077
if yes, the system is in a stable state, and step A7 is executed; otherwise, go to step A5;
step A5: judging whether the iteration number N is greater than N, if so, executing the step A6; otherwise, adding 1 to the iteration number n, and returning to the step A3;
step A6: adding delta X to the change parameter X, enabling the iteration number n to return to 1, and returning to the step A3;
step A7: let the corresponding change parameter value X be the lower limit value at this time, that is: xmin＝X；
Step A8: the change parameter X is sequentially increased by delta X, after each increment, whether the system stably operates is judged according to the method from the step A3 to the step A4, if yes, the increment is continued until the system cannot stably operate, and the corresponding change parameter X at the moment is made to be an upper limit value, namely: xmax＝X；
Step A9: judging whether the counting variable q is equal to 1, if so, executing the step A12, otherwise, executing the step A10;
step A10: let Lmin＝Xmin，Lmax＝XmaxThe value range of the main circuit inductance L is (L) when the speed regulating system stably operatesmin，Lmax) Counting the variable q plus 1, and executing the step A11;
step A11: selecting a value within the stable value range of the inductor L and keeping the value unchanged, setting the capacitance C as a change parameter X, setting the initial value of the change parameter X as 0, and returning to the step A3;
step A12: let Cmin＝Xmin，Cmax＝XmaxThe value range of the main circuit capacitance C is (C) when the speed regulation system stably operatesmin，Cmax)；
Step A13: obtaining the value range (L) of the main circuit inductance L according to the step A10min，Lmax) And the value range (C) of the main circuit capacitor C obtained in the step A12min，Cmax) The specific values of the inductance L and the capacitance C in the BBMC inverter stage are determined, so that the stability of the three-phase asynchronous motor speed regulation system based on the BBMC can be realizedAnd (5) operating constantly.
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