CN111817627B - Discrete modeling and control method for double three-phase induction motor under low switching frequency - Google Patents
Discrete modeling and control method for double three-phase induction motor under low switching frequency Download PDFInfo
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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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
- H02P27/08—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 with pulse width modulation
- H02P27/12—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 with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control
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Abstract
The invention discloses a discrete modeling and control method of a double three-phase induction motor under low switching frequency, belonging to the field of electricians, motors and power electronics. Aiming at the working condition of low switching frequency, the discrete modeling method provided by the invention obtains a more accurate motor discrete mathematical model than the traditional Euler discrete modeling by means of Laplace transform and the like. Meanwhile, the double-winding interleaved model predictive control method provided by the invention fully utilizes the characteristic of high degree of freedom of control of the double three-phase induction motor, reduces the control delay caused by low switching frequency by half through the interleaved control of two sets of three-phase windings, reduces the time span of predictive control, effectively improves the control effect and reduces the switching frequency; the positive and negative small vector interleaving control reduces the change rate of the midpoint voltage of the bus by setting two inverters to preferentially output opposite redundant small vectors, thereby further reducing the switching frequency.
Description
Technical Field
The invention relates to the field of electricians, motors and power electronics, in particular to a discrete modeling and control method of a double three-phase induction motor under low switching frequency.
Background
In recent years, in the field of medium-voltage and high-power application, a multi-level driving system of a multi-phase motor draws more and more attention due to the advantages of low stress of power devices, high reliability, high electric energy quality, easiness in realizing low switching frequency operation and the like. The double three-phase induction motor can be obtained by rewinding the stator winding of the three-phase squirrel-cage induction motor, and is a good entry point in the research field of multi-phase motor driving systems. In a driving system with larger power, the switching frequency of a driver is often lower than 1kHz based on the consideration of reducing switching loss and improving heat dissipation conditions, and the existing low-switching-frequency motor control method is often problematic in three aspects: firstly, the influence of coupling factors in a motor driving system is enhanced due to low switching frequency, so that a large deviation exists between a motor discrete model obtained by Euler dispersion and a real system in the traditional control method, and the control effect is seriously influenced; secondly, a low switching frequency causes a higher control signal delay, and a PI regulator is often adopted in the traditional control method to control the motor, so that the bandwidth of the system is reduced, and the control stability is seriously influenced; thirdly, in order to solve the bandwidth problem caused by the PI regulator, the model predictive control method draws wide attention, but in order to obtain a good control effect, the traditional model predictive control method usually has a large calculation amount, and puts a high requirement on the operation performance of the controller, which is not beneficial to practical application.
Disclosure of Invention
The invention aims to provide a discrete modeling and control method of a double three-phase induction motor under low switching frequency aiming at the defects of the background technology. The motor discrete modeling method provided by the invention can accurately predict the running state of the motor system under the working condition of low switching frequency, thereby improving the control effect. Meanwhile, the model predictive control method provided by the invention can effectively inhibit the influence of control signal delay caused by low switching frequency, and an extrapolation method is adopted, so that the calculation amount required by control is smaller than that of the traditional model predictive control.
The invention adopts the following technical scheme for realizing the aim of the invention:
a discrete modeling and control method of a double three-phase induction motor under low switching frequency comprises the following steps:
1) Transforming a dual three-phase motor mathematical model to dualdqIn the coordinate system, performing Laplace transform on the coordinate system, and solving the equation set to obtaind 1 、q 1 、d 2 Andq 2 shaft electric machineA frequency domain representation of the stream;
2) Substituting frequency domain expressions of external input variables such as a voltage source or a current source into the step 1), then carrying out Laplace inverse transformation on the obtained four-axis current frequency domain expression to obtain a mathematical model of a continuous time domain of the motor, taking a time interval as a sampling period to realize discretization of the motor model, and simultaneously obtaining a discrete model of the midpoint voltage of the direct current bus relative to the six-phase current of the motor by using an Euler discrete method;
3) The output signals of the speed sensor and the phase current sensor are acquired and obtained through the double-rotation transformation moduled 1 、q 1 、d 2 Andq 2 an axis current component;
4) According to the motor continuous time domain model obtained in the step 2), a time interval is taken as control signal delay, and a required four-axis current value is predicted, so that the compensation of the control signal delay is realized;
5) Obtaining a torque reference value according to speed closed-loop PI control, and obtaining the torque reference value through efficiency optimization controld 1 、q 1 、d 2 Andq 2 reference value of shaft current.
6) According to the precise motor discrete model obtained in the step 2), on the basis of dead-beat control, taking the four-axis current reference value obtained in the step 5) as a predicted value when the effect of the current loading vector is finished, and calculating a voltage vector to be loaded at this time, namely a reference voltage vector;
7) According to the reference voltage vector calculated in the step 6), in combination with a three-level inverter voltage space vector distribution diagram, selecting 4 or 5 basic space vectors corresponding to three vertexes of a triangular area where the voltage reference vector is located as candidate vectors, and accordingly simplifying a model prediction control traversal set;
8) And (3) according to the midpoint voltage of the direct-current bus and the discrete model of the motor in the steps 2) and 6), evaluating the candidate vector in the step 7) by using model prediction control, selecting the candidate vector with the optimal control effect as a final loading vector, and outputting a corresponding pulse action signal to control the inverter.
Further, the evaluation objects of the model predictive control method are corresponding windingsdqThe shaft current and the bus midpoint voltage can be divided into two cases, one of which is that at least one candidate vector is provideddqThe predicted value of the shaft current and the predicted value of the midpoint voltage of the bus are within a preset error range, an extrapolation method is used for obtaining an extrapolation step length, the ratio of the switching times required by the vector to the extrapolation step length is used as a cost function, the vector with the minimum cost function is selected as a loading vector, and if at least one index of all candidate vectors exceeds the preset error range, the indexes exceeding the error range are subjected to linear weighting to obtain the cost function, and the loading vector is selected;
furthermore, the model prediction control is performed in two sets of windings in an interlaced manner, when the first set of windings switches vectors, the second set of windings starts to perform model prediction calculation, and then after a half of the vector switching period, the second set of windings performs vector switching, and at this time, the first set of windings calculates vectors to be loaded next time. According to the rule, the two windings carry out staggered predictive control on the motor;
furthermore, in the model predictive control, when the pair of redundant small vectors obtain the same cost function and are both selected as the final loading vector, the two inverters are controlled to preferentially select the redundant small vector which has opposite action on the midpoint voltage as the loading vector, and the positive and negative small vectors of the two inverters are subjected to staggered control.
A discrete modeling and control method of a double three-phase induction motor under low switching frequency is characterized in that a precise discrete model of the motor is established by means of Laplace transform and the like of a differential equation of a continuous time domain of the motor, a current prediction module is established based on the discrete model to compensate control signal delay under low switching frequency, and meanwhile, based on the discrete model, according to the control signal delay under low switching frequencydqShaft reference current, generated by deadbeat controldqAxis reference voltage, selecting four or 5 adjacent inverter basic voltage vectors as candidate voltage vectors to carry out vector simplification, and then selecting the candidate vector with the best control effect as the candidate voltage vector of the control period according to the cost functionAnd outputting vectors, namely reducing the delay of control signals caused by low switching frequency by half in a mode of mutually staggering the control of the two inverters on the motor winding by half of a sampling period, reducing the time span of predictive control, and reducing the change rate of the midpoint voltage of the direct current bus by enabling the two inverters to preferentially output opposite redundant small vectors, thereby further reducing the switching frequency.
Furthermore, in the discrete motor modeling, firstly, a differential equation of the motor in a continuous time domain based on the selected state variable is listed, then laplace transformation is carried out on the differential equation, the differential equation is substituted into frequency domain constraint conditions of input variables such as a voltage source or a current source, a frequency domain expression of the state variable is solved, then a continuous time domain mathematical model of the relevant state variable is obtained by using inverse laplace transformation, and a time interval is taken as a sampling period, so that the accurate discrete model of the motor based on the laplace transformation can be obtained.
Furthermore, based on the precise discrete model of the motor, precise reference voltage vectors are calculated in advance through dead beat control, and then four or five corresponding voltage vectors in a small area where the reference voltage vectors are located are selected as candidate vectors according to the distribution of the space voltage vectors of the inverter, so that the simplification of a model predictive control traversal set is realized, and the calculated amount is reduced.
Furthermore, the calculated amount of model predictive control is simplified by using an extrapolation method, the state variable at the next moment is calculated only through a discrete model in actual calculation, then linear extrapolation is carried out according to the current value and the predicted value of the state variable, and the control effect is measured according to the step length required by the extrapolated trajectory touching the error range boundary.
Furthermore, the control of the two inverters to the corresponding windings stagger half of the sampling period, so that in the control process of each winding, the delay between the sampling point and the vector loading point is shortened to half of the sampling period, and the time span of the predictive control is reduced.
Furthermore, the two inverters preferentially output the redundant voltage small vectors with opposite effects on the midpoint voltage of the direct-current bus, and the change rate of the midpoint voltage of the direct-current bus is slowed down, so that forced switching points are reduced, and the switching frequency is further reduced.
By adopting the technical scheme, the invention has the following beneficial effects:
(1) Compared with the motor discrete model obtained by the traditional Euler discrete modeling method, the dual three-phase induction motor discrete modeling method provided by the invention is more accurate, optimizes the motor control from the discrete model level, and plays an important role in reducing the switching frequency and improving the control effect.
(2) The invention adopts the model predictive control method, has the effects of fast dynamic response and easy realization of multi-objective optimization, avoids the bandwidth problem of the traditional PI regulator, and simultaneously adopts the extrapolation method to effectively reduce the calculated amount of the model predictive control by linear extrapolation on the premise of ensuring the control effect.
(3) The double-winding staggered prediction control provided by the invention can halve the control delay caused by low switching frequency, reduce the time span of the whole prediction process and effectively improve the control effect.
(4) The positive and negative small vector interleaving control provided by the invention can further reduce the switching frequency under the same midpoint voltage control requirement by slowing down the change rate of the midpoint voltage of the bus.
The foregoing description is only an overview of the technical solutions of the present application, so that the technical means of the present application can be more clearly understood and the present application can be implemented according to the content of the description, and in order to make the above and other objects, features and advantages of the present application more clearly understood, the following detailed description is made with reference to the preferred embodiments of the present application and the accompanying drawings.
The above and other objects, advantages and features of the present application will become more apparent to those skilled in the art from the following detailed description of specific embodiments thereof, taken in conjunction with the accompanying drawings.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following descriptions are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative efforts. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a flow chart of a discrete modeling method of a motor based on Laplace transform;
FIG. 2 is a block diagram of an interleaved model predictive control based on a precise discrete model;
FIG. 3 is a block diagram of a current prediction module compensating for control delays;
FIG. 4 is a distribution diagram of an output voltage vector of a midpoint clamping type three-level inverter;
FIG. 5 isq 1 An axis current model predictive control algorithm graph;
FIG. 6 is a diagram showing a comparison of control signal delays in synchronous predictive control and staggered predictive control;
FIG. 7 is an analysis of the voltage candidate vector selection process for winding one;
FIG. 8 is a graph of bus midpoint voltage rate of change versus switching frequency analysis;
the method comprises the following steps that 1.1, a starting module of a motor discrete modeling flow chart based on Laplace transformation, 1.2, a state variable continuous time domain mathematical model building module, 1.3, a Laplace transformation module used for obtaining a state variable frequency domain equation set, 1.4, a state variable frequency domain equation set solving module, 1.5, an inverse Laplace transformation module used for obtaining a motor continuous time domain model, and 1.6, a motor discrete model building module which sets the time interval of the continuous time domain model as a sampling period;
2.1 is a speed closed-loop PI regulator, 2.2 is an efficiency optimization control module, 2.3 is a dead beat control module based on an accurate discrete model, 2.4 is a polar coordinate transformation module, 2.5 is a model prediction control module, 2.6 is a direct current bus, 2.7 is a six-phase inverter module, 2.8 is a double three-phase induction motor, 2.9 is a speed measurement encoder of the double three-phase induction motor, 2.10 is a double rotation coordinate transformation module, 2.11 is a current prediction module, and 2.12 is a rotating speed calculation module;
3.1 is the time line, 3.2 is the sample points, and 3.3 is the samplekT s The current value at the moment, 3.4 is a current prediction module, 3.5 is a schematic diagram of the current prediction module for compensating the delay between the sampling point and the loading point, and 3.6 is a diagram of the current prediction module according tokT s Prediction of current value at time (k+1)T s The current value at the time, 3.7 is the dead beat control module, 3.8 is: (k+2)T s A reference value of current at the moment, 3.9 is a model prediction control module, 3.10 is control delay between a sampling point and a loading point, and 3.11 is a voltage vector loading point;
4.1 is a reference voltage vector, and 4.2, 4.3, 4.4 and 4.5 are four voltage candidate vectors PON, PNN, ONN and POO corresponding to a triangular area where the reference voltage vector is located;
5.1 is a sampling point, 5.2 is a vector loading point, and 5.3 is a voltage candidate vector VC 3 5.4 is the voltage candidate vector VC 1 5.5 is the voltage candidate vector VC 2 5.6 is the voltage candidate vector VC 4 5.7 isq 1 The upper bound of the permissible error range of the shaft current, 5.8 isq 1 Reference value for the shaft current, 5.9 isq 1 The lower boundary of the allowable error range of the shaft current is 5.10, the prediction process is based on the discrete model of the motor, and 5.11, the linear extrapolation process is carried out according to the prediction result;
6.1 is a time line of winding one, 6.2 is a time line of winding two, and 6.3 shows that the control delay of winding one under synchronous predictive control isT s 6.4 is a sampling point of the first winding and the second winding, 6.5 is a loading point of the first winding and the second winding, 6.6 is a current reference value of the first winding and the second winding, 6.7 is a model prediction calculation process of the first winding and the second winding, and 6.8 represents that the control delay of the second winding under synchronous prediction control isT s 6.9 shows the control delay of winding one under the interleaved predictive control ofT s /2,6.10 is the sampling point of winding one, 6.11 is the loading point of winding one6.12 is the current reference value of winding one, 6.13 is the sampling point of winding two, 6.14 is the loading point of winding two, 6.15 is the current reference value of winding two, and 6.16 shows that the control delay of winding two under the staggered predictive control isT s 2,6.17 is a model prediction calculation process of a winding II, and 6.18 is a model prediction calculation process of a winding I;
7.1 is a time line, 7.2 iskT s The voltage vector POO loaded at the moment, 7.3 iskT s The reference voltage vector of the winding at the moment, 7.4 is: (k+1)T s The reference voltage vector of the winding at the instant 7.5 is: (k+n)T s A reference voltage vector for the winding at the time;
8.1 is the upper boundary of the bus midpoint voltage allowable error range, 8.2 is the lower boundary of the bus midpoint voltage allowable error range, 8.3 is a bus midpoint voltage operation track with a higher voltage change rate, 8.4 is the intersection point of the bus midpoint voltage track with a high change rate and the upper boundary of the allowable error range, which is called a forced switching point, 8.5 is a bus midpoint voltage operation track with a lower voltage change rate, and 8.6 is the intersection point of the bus midpoint voltage track with a low change rate and the lower boundary of the allowable error range, which is called a forced switching point.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. In the following description, specific details such as specific configurations and components are provided only to facilitate a thorough understanding of embodiments of the present application. Accordingly, it will be apparent to those skilled in the art that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present application. In addition, descriptions of well-known functions and constructions are omitted in the embodiments for the sake of clarity and conciseness.
It should be appreciated that reference throughout this specification to "one embodiment" or "the embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present application. Thus, the appearances of the phrase "one embodiment" or "the present embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
Example one
The invention provides a discrete modeling and control method of a double three-phase induction motor under low switching frequency, aiming at the problems of inaccurate discrete model, serious control signal delay influence and large calculation amount of a model prediction control method in the existing motor low switching frequency driving technology. Meanwhile, the model predictive control method provided by the invention can effectively inhibit the influence of control signal delay caused by low switching frequency, and the required calculation amount is less than that of the traditional model predictive control method.
The invention provides an accurate discrete modeling method based on Laplace transform for low switching frequency operation of a double three-phase induction motor driving system, which comprises a modeling starting step 1.1, a state variable continuous time domain mathematical model establishing step 1.2, a Laplace transform step 1.3 for obtaining a state variable frequency domain equation set, a state variable frequency domain equation set solving step 1.4, an inverse Laplace transform step 1.5 for obtaining a motor continuous time domain model, and a motor discrete model establishing step 1.6 for setting the time interval of the continuous time domain model as a sampling period.
The specific modeling process of an embodiment of the precise discrete modeling method of the present invention is as follows. According to 1.2, a mathematical model of the continuous time domain of a double three-phase induction machine is first listed:
wherein, the first and the second end of the pipe are connected with each other,L s , L r andMrespectively a stator winding inductance, a rotor winding inductance and a mutual inductance among windings after coordinate transformation,L ls is the leakage inductance of the stator winding,L lr is the leakage inductance of the rotor winding and meets the following requirements:L s =L ls +M, L r =L lr +M, M=3L ms ；R s is the resistance of the stator winding and is,R r is the resistance of the rotor winding and,τ r is the rotor time constant, andτ r =L r /R r ，ω 1 is the electrical angular velocity of the stator,ω s is the difference between the electrical angular velocity of the stator and the electrical angular velocity of the rotor,σis the leakage coefficient of the motor, andσ=1-M 2 /(L r L s )，pis a differential operator which is a function of the differential,u d1 , u q1 , u d2 andu q2 respectively two stator windingsdqThe voltage of the shaft is set to a value,i d1 , i q1 , i d2 andi q2 respectively two stator windingsdqThe shaft current. Since the mechanical time constant of the motor is much larger than the sampling period, it can be considered that the angular velocityω 1 Andω s held constant for a single sampling period. According to 1.3 and 1.4, laplace transform is carried out on the continuous time domain model of the motor, and the following matrix equations can be arranged out:
considering that the neutral-point clamped three-level inverter belongs to the voltage source type inverter,dqthe shaft input voltage should satisfy the constraint condition shown in equation (7):
substituting equation (7) into equation (4) according to 1.5 and 1.6, and performing inverse laplacian transform on the result, taking the time interval as the sampling periodT s Thenk+1)T s The four-axis current of the time can be usedkT s The information prediction of (1):
wherein the coefficient matrix elementsB ij Setting the time to be from the inverse Laplace transform resultT s And (4) obtaining. The equation is the precise discrete model of the motor.
Example two
The invention provides a double-winding interleaving model prediction control system based on positive and negative small vector interleaving for the low switching frequency operation of a double three-phase induction motor driving system, which comprises a speed closed-loop PI regulator 2.1, an efficiency optimization control module 2.2, a dead-beat control module 2.3 based on an accurate discrete model, a polar coordinate transformation module 2.4, a model prediction control module 2.5, a direct current bus 2.6, a six-phase inverter module 2.7, a double three-phase induction motor 2.8, a speed measurement encoder 2.9 of the double three-phase induction motor, a double rotation coordinate transformation module 2.10, a current prediction module 2.11 and a rotating speed calculation module 2.12.
Current prediction according to the inventionThe module 2.11 implementation is shown in fig. 3. As shown in 3.10, in practical control, a sampling period exists between the sampling point and the loading pointT s So that the current parameter input in the deadbeat control 3.7 existsT s Causing control inaccuracies. The invention predicts the sampling value 3.3 obtained by sampling point 3.2 according to the formula (8) to obtaink+1)T s The predicted value of the time current is used as the input of the dead-beat control module, and then a loading vector is selected by the model prediction control MPC module 3.9 for loading. Therefore, based on the prediction of the accurate model, the problem of control signal lag is solved.
The model predictive control of the invention is divided into two steps, wherein the first step is to obtain a reference voltage vector according to dead beat control so as to determine 4 or 5 candidate voltage vectors, as shown in 2.3 and 2.4; and secondly, predicting and comparing the control effect of the candidate vector according to the motor discrete model, and selecting the finally loaded voltage vector as shown in 2.5.
The dead-beat control calculation formula can be obtained according to the motor accurate discrete model of the formula (8). Taking the current reference value as (k+1)T s The current prediction value of the time can be calculatedkT s Given at the timedqMagnitude of input voltage to the shaft, i.e.kT s Reference voltage of time:
wherein the coefficient matrix elementsC ij Obtained by deformation from equation (8).
The candidate voltage vector determination method of the present invention is shown in fig. 4. Fig. 4 is a space voltage vector distribution diagram of a midpoint clamp type three-level inverter, which divides a plane into 24 small triangular regions. And selecting voltage vectors corresponding to three vertexes of a triangular area where the reference voltage vector obtained by the dead-beat control is located as candidate vectors. When the reference voltage vector 4.1 is located as shown in fig. 4, the vectors PON, PNN, ONN and POO are selected as candidate vectors as shown in 4.2, 4.3, 4.4 and 4.5 according to the above-described principle.
The specific implementation method of an embodiment of the candidate vector selection method of the present invention is as follows. There are two cases. The first one is: when at least one of the candidate vectors is presentdqIf the axis current and the predicted value of the bus midpoint voltage are within the predetermined error range, the candidate vector is determined by extrapolation, as shown in fig. 5. 5.3, 5.4, 5.5 and 5.6 are vectors VC 3 、VC 1 、VC 2 And VC 4 Predicted and extrapolated trajectories. The solid line part is the predicted trajectory based on the discrete model, as shown in 5.10; the dashed portion is the linear extrapolation trace, as shown at 5.11. The step size required for the candidate vector trajectory to reach the upper or lower error boundary 5.7, 5.9 is defined as the extrapolation step size for the vector. Taking candidate vectorsdqThe minimum value of the extrapolation step length under three indexes of the shaft current and the bus midpoint voltage is used as the final extrapolation step length of the vectorN. For example, if not taken into accountd 1 Prediction of shaft current and bus midpoint voltage, VC in FIG. 5 3 、VC 1 、VC 2 And VC 4 Are 1, 2, 3 and 4, respectively. In order to introduce an evaluation index of the switching frequency, the method is defined fromkT s Number of switching times of time-loaded vector to candidate vectorn s Comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other, (ii) (k) RepresentkT s The state of the switch at the time of operation,S x is a switching function defined as:
obviously, the larger the total extrapolation step size and the smaller the number of switching times, the better the control and the smaller the switching frequency. Thus, the cost function is defined as:
the candidate vector selection problem in the first case can be solved accordingly. The second vector evaluation case is: when at least one index of all the candidate vectors exceeds a preset error range, linear weighting is carried out on the index exceeding the error range to obtain a cost function, which is specifically shown as follows:
whereinλ V , λ id Andλ iq respectively the bus midpoint capacitance voltage andd 1 、q 1 the weighting factor of the axis current. When the predicted value of the weight coefficient corresponding variable is within the allowable error range, the weight coefficient is given as 0. For example, wheni d1 In (1)k+1)T s If the predicted value of time is within the error range, the coefficient in the cost functionλ id Given as 0.
The implementation and effect analysis of the dual winding interleaving prediction control of the invention are shown in fig. 6. Fig. 6.1 to 6.8 are timing charts of synchronous predictive control, and fig. 6.9 to 6.18 are timing charts of interlace predictive control. As shown in fig. 6, the control strategy of dual winding simultaneous sampling, simultaneous loading vectors is called synchronous control, and the control strategy of interleaved sampling, interleaved loading vectors is called interleaved control. In synchronous predictive control, as shown in 6.4 and 6.5, the selected candidate vector needs to start loading vectors at the same time after two sets of windings finish model prediction calculation, and the delay of the sampling point and the loading point of each set of windings isT s . And in the interleaving prediction process, as shown in 6.10, 6.11, 6.13 and 6.14, winding one is in (k+1/2)T s Sampling of time instants immediately after the completion of the calculation of the winding model prediction in (k+1)T s Loading the vector at a moment, controlling the delay onlyT s /2. The delay of the second winding is also reduced toT s /2. In addition to the effect of reducing the delay of the control signal, the total prediction time span in the interleaved predictive control is 1.5T s Less than synchronous predictive control 2T s The overall time span, and therefore the predictive and control effect of the interleaved predictive control will be more accurate. Furthermore, in terms of dynamic response, the interleaved predictive control is at the latestT s Response is started after/2, and synchronous predictive control is needed at the latestT s The response is started after time. Therefore, the dynamic response speed of the staggered predictive control is improved.
The principle analysis of the positive and negative small vector interleaving control method of the present invention is shown in fig. 7 and 8. First, the bus midpoint voltage variation rule in the present embodiment will be described with reference to fig. 7. As shown in figure 7 of the drawings,kT s the time voltage reference vector is located at the position shown at 7.3, assuming that it finally selects vector POO as the loading vector, as shown at 7.2. In consideration of the actual operation, the candidate vectors are selected in the first case described above, and therefore, in the cost functiong 1 The analysis was performed as an example. (k+1)T s The reference voltage vector at the moment is located at the position shown by 7.4, and the candidate vector still compriseskT s The vector POO is loaded at a time, so that if the corresponding switch switching times are 0, the cost function of the POO vector is 0, so that POO is (k+1)T s The loading vector of the moment. Therefore, when the vector loaded at the previous time is still a candidate vector at the next time, the vector at the previous time will be continuously output at the next time. It is not assumed that the reference vector is ink+n)T s At the position shown by 7.5 at time instant, the POO is no longer a candidate vector. According to (A)k+1)T s Vector law of time of day fromkT s To (a)k+n)T s POO is selected as a loading vector at any time between the times, and the bus midpoint potential therefore continuously rises. At the same time, observek+n)T s The new candidate small vector at the moment can find the positive small vector PPOIs 1 and the negative small vector OON is 2. This means that instead of OON being selected as a loading vector only if its prediction step exceeds more than twice PPO, i.e. positive small vectors still have a higher probability of being selected as loading vectors relative to negative small vectors. Thus, unless the bus midpoint voltage is sufficiently close to the error upper bound, the midpoint voltage will continue to rise. Therefore, it can be concluded that the change rule of the midpoint voltage of the bus is as follows: the rise continues until the upper error boundary is sufficiently approached, and then the fall continues until the lower error boundary is sufficiently approached, with a waveform like a sawtooth waveform. When the voltage waveform of the midpoint changes the rising and falling trend each time, the required switching times are larger than the common operation condition due to the switching problem of the positive and negative small vectors. When the moment of the bus midpoint voltage changing the ascending and descending trend is called the forced switching point, the key point of further reducing the switching frequency is to reduce the frequency of the forced switching point. The most effective method is to reduce the change rate of the midpoint potential of the bus. Due to the control freedom degree provided by the double windings, the two windings can preferentially output opposite redundant small vectors on the premise of not influencing model prediction control. Fig. 8 shows a relationship between the change rate of the neutral point potential and the switching frequency of the bus bar. The bus midpoint potential trace 1 with the higher rate of change has 7 forced switching points in the time period shown in fig. 8, while trace 2 has only 3 forced switching points because of the lower rate of change. Therefore, on the premise of similar current tracking effect, the average switching frequency of the track 2 is lower than that of the track 1 due to fewer forced switching points.
The previous description of all disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (5)
1. The control system of the driving system of the double three-phase induction motor under the low switching frequency is characterized by comprising a speed closed-loop PI regulator (2.1), an efficiency optimization control module (2.2), a dead-beat control module (2.3) based on a motor accurate discrete model, a polar coordinate transformation module (2.4), a model prediction control module (2.5), a direct current bus (2.6), a six-phase inverter module (2.7), the double three-phase induction motor (2.8), a speed measurement encoder (2.9) of the double three-phase induction motor, a double rotation coordinate system transformation module (2.10), a current prediction module (2.11) and a rotating speed calculation module (2.12);
obtaining a torque reference value (Te) from a speed closed-loop PI regulator (2.1) * ) D is obtained by the efficiency optimization control module (2.2) 1 、q 1 、d 2 And q is 2 Reference value (i) of the shaft current d1 * 、i q1 * 、i d2 * And i q2 * ) Then the data is input to a dead beat control module (2.3) based on a motor accurate discrete model;
the current prediction module (2.11) works as follows: predicting a sampling value (3.3) obtained by sampling the sampling point (3.2) to obtain (k + 1) T s The predicted value of the time current is used as the input of the dead-beat control module, and then a loading vector is selected by the model prediction control module (3.9) to load, so as to control the six-phase inverter module (2.7);
the formula for predicting the sample value (3.3) obtained by sampling the sample point (3.2) is:
wherein i d1 ,i q1 ,i d2 And i q2 The two stator windings are dq axis currents respectively; coefficient matrix element B ij Setting time T from the inverse Laplacian transformation result s Obtaining wherein T is s Is a sampling period, u d1 ,u q1 ,u d2 And u q2 The voltages of the dq axes of the two stator windings are respectively obtained, and the equation is an accurate discrete model of the motor;
the model prediction control method of the model prediction control module comprises the following specific steps:
s1, obtaining a reference voltage vector according to dead-beat control, and determining 4 or 5 candidate voltage vectors;
and S2, predicting and comparing the control effect of the candidate voltage vector according to the accurate discrete model of the motor, and selecting the finally loaded voltage vector.
2. The control system of the driving system of the dual three-phase induction motor with low switching frequency according to claim 1, wherein the step-less control in S1 for obtaining the reference voltage vector comprises the following specific steps: the current reference value is taken as (k + 1) T s Substituting the predicted current value into the precise discrete model of the motor to calculate the kT s Given the magnitude of the dq-axis input voltage, i.e. kT s The reference voltage of time.
3. The control system of a dual three-phase induction motor drive system with low switching frequency of claim 1 wherein the candidate voltage vector determination method comprises: and dividing the plane into 24 small triangular areas, and selecting voltage vectors corresponding to three vertexes of the triangular area where the reference voltage vector obtained by dead-beat control is located as candidate vectors.
4. The control system of a dual three-phase induction motor driving system with low switching frequency according to claim 3, wherein the control of the corresponding windings by the two inverters are staggered by half of the sampling period, so that the delay between the sampling point and the vector loading point is shortened to half of the sampling period in the control process of each winding.
5. The control system according to claim 4, wherein the two inverters output small redundant voltage vectors having opposite effects on the midpoint voltage of the DC bus, and slow down the change rate of the midpoint voltage of the DC bus, thereby reducing forced switching points.
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