CN110707949B - Control method of fixed-frequency PWM rectifier - Google Patents

Control method of fixed-frequency PWM rectifier Download PDF

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CN110707949B
CN110707949B CN201910826334.7A CN201910826334A CN110707949B CN 110707949 B CN110707949 B CN 110707949B CN 201910826334 A CN201910826334 A CN 201910826334A CN 110707949 B CN110707949 B CN 110707949B
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beat
rectifier
voltage deviation
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CN110707949A (en
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李飞
王贵峰
刘战
夏正龙
李春杰
白春艳
李洪美
柴艳丽
闫俊荣
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Jiangsu Normal University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/02—Conversion of ac power input into dc power output without possibility of reversal
    • H02M7/04—Conversion of ac power input into dc power output without possibility of reversal by static converters
    • H02M7/12—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/21—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/217—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M7/219—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only in a bridge configuration
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output

Abstract

The invention discloses a control method of a fixed-frequency PWM rectifier, which comprises the following steps: s10, acquiring the current capacitance voltage deviation of the rectifier in the current beat; s20, calculating a first predicted capacitor voltage deviation of the rectifier in the first beat after the current beat according to the current capacitor voltage deviation and a voltage deviation prediction formula; the voltage deviation prediction formula represents the relation between two continuous beats of capacitor voltage deviation of the rectifier; s30, calculating a second predicted capacitor voltage deviation of the rectifier in the second beat after the current beat according to the first predicted capacitor voltage deviation and the voltage deviation prediction formula; and S40, controlling the direct current voltage of the rectifier according to the second predicted capacitor voltage deviation in the first beat after the current beat. By adopting the method, the calculated amount in the control process of the direct-current voltage of the rectifier can be simplified, and the control efficiency is improved.

Description

Control method of fixed-frequency PWM rectifier
Technical Field
The invention relates to the technical field of signal processing, in particular to a control method of a fixed-frequency PWM rectifier.
Background
The three-phase voltage source type Pulse Width Modulation (PWM) rectifier has the advantages of stable and adjustable direct current bus, high sine degree of current on the network side, bidirectional energy flow, adjustable power factor and the like. Therefore, the method is widely applied to the fields of power electronics, alternating current transmission speed regulation, APF, power generation, power transmission and the like. However, with the increase of voltage class and the increase of rectifier capacity, the two-level rectifier cannot meet the requirement of high voltage and large capacity. In order to meet the voltage-bearing capability of the switching device, the multi-level converter and the cascade converter have been the hot research of many researchers, wherein the diode-clamped (NPC) three-level converter is widely applied.
With the intensive research on three-level rectifiers, various control strategies have been proposed in succession. Carrier-based PWM control methods (CBM) are a modulation strategy that was proposed earlier and applied more widely. But the utilization rate of the direct current bus is low and the control of the midpoint potential is difficult. Although the control of the midpoint potential can be realized by injecting zero sequence voltage, the utilization rate of the direct current bus can reach the level same as that of vector PWM (pulse width modulation) by injecting proper zero sequence. But zero sequence voltages are not unique and computationally complex. In recent years, Space Vector PWM (SVPWM) modulation strategies have attracted attention because of their high dc bus utilization and low voltage harmonic distortion. The problem of midpoint potential shift of a three-level rectifier can also be solved by selecting redundant switch states, but the algorithm is more complex. In conclusion, the control scheme of the traditional three-level rectifier has the problems of complex calculation and influence on control efficiency.
Disclosure of Invention
In order to solve the above problems, the present invention provides a control method for a fixed frequency PWM rectifier.
In order to achieve the purpose of the invention, the invention provides a control method of a fixed-frequency PWM rectifier, which comprises the following steps:
s10, acquiring the current capacitance voltage deviation of the rectifier in the current beat;
s20, calculating a first predicted capacitor voltage deviation of the rectifier in the first beat after the current beat according to the current capacitor voltage deviation and a voltage deviation prediction formula; the voltage deviation prediction formula represents the relation between two continuous beats of capacitor voltage deviation of the rectifier;
s30, calculating a second predicted capacitor voltage deviation of the rectifier in the second beat after the current beat according to the first predicted capacitor voltage deviation and the voltage deviation prediction formula;
and S40, controlling the direct current voltage of the rectifier according to the second predicted capacitor voltage deviation in the first beat after the current beat.
In one embodiment, the voltage deviation prediction formula includes:
Figure BDA0002189211880000021
wherein Δ u (k +1) represents a first predicted capacitor voltage deviation of a first beat after the current beat, Δ u (k) represents a current capacitor voltage deviation of the current beat, TsRepresenting the system sampling period of the rectifier, C representing the capacitance parameter of the rectifier, io(k) And representing the current parameters corresponding to the actually measured current of the current beat in the two-phase static coordinate system.
As an example, the io(k) The determination formula of (2) includes:
io(k)＝iα(k)|sα(k)|+iβ(k)|sβ(k)|，
in the formula iα(k) Represents the value of the measured current of the current beat in the alpha direction in the two-phase static coordinate system, sα(k) Representing the component in the direction alpha of the three-level and three-phase switching state of the rectifier in a two-phase stationary frame, iβ(k) Represents the value of the measured current of the current beat in the beta direction in the two-phase static coordinate system, sβ(k) Representing the component of the rectifier three-level three-phase switch state in the beta direction in the two-phase stationary frame.
In one embodiment, the obtaining of the voltage deviation prediction formula includes:
acquiring a capacitance voltage differential equation of the direct current side of the rectifier;
determining a capacitance midpoint current relational expression of the current beat according to the capacitance voltage differential equation;
discretizing the capacitance midpoint current relation in the sampling period corresponding to the current beat to obtain the voltage deviation prediction formula.
In one embodiment, the method for controlling the fixed-frequency PWM rectifier further includes:
acquiring a first input current of a rectifier at a current beat, a second input current of the rectifier at the first beat before the current beat, and a third input current of the rectifier at the second beat before the current beat;
calculating a first predicted current for the rectifier for a first beat after the current beat according to the first input current, the second input current, the third input current, and a current prediction formula; wherein the current prediction formula characterizes a relationship of input currents of the rectifier between four beats consecutive to each other;
calculating a second predicted current for the rectifier for a second beat after the current beat according to the second input current, the third input current, the first predicted current, and the current prediction formula;
controlling an input current of the rectifier according to the second predicted current for a first beat after the current beat.
As an embodiment, the current prediction formula includes:
i*(k+1)＝3i*(k)-3i*(k-1)+i*(k-2)，
in the formula i*(k +1) represents a first predicted current for the first beat after the current beat, i*(k) A first input current, i, representing the current beat*(k-1) represents a second input current, i, for a first beat prior to the current beat*(k-2) represents a third input current for a second beat prior to the current beat.
As an embodiment, the obtaining of the current prediction formula includes:
acquiring a first mathematical model of a main circuit of the rectifier under a three-phase static coordinate system;
transforming the first mathematical model to a two-phase static coordinate system to obtain a second mathematical model;
discretizing the second mathematical model by adopting a forward Euler method to obtain a system discrete mathematical model;
setting a value function according to the system discrete mathematical model;
solving the value function by adopting a second-order Lagrange interpolation formula to obtain a prediction formula of a first beat after the current beat;
and determining the current prediction formula according to the prediction formula of the first beat after the current beat.
According to the control method of the fixed-frequency PWM rectifier, the current capacitance voltage deviation of the rectifier in the current beat is obtained, the first predicted capacitance voltage deviation of the rectifier in the first beat after the current beat is calculated, the second predicted capacitance voltage deviation of the rectifier in the second beat after the current beat is calculated, so that the direct current voltage of the rectifier is controlled according to the second predicted capacitance voltage deviation in the first beat after the current beat, on the basis of simplifying the calculated amount of the direct current voltage control process and improving the control efficiency, effective compensation of one beat lagging can be achieved, and the control precision is further improved.
Drawings
FIG. 1 is a flow chart of a method for controlling a fixed frequency PWM rectifier according to one embodiment;
FIG. 2 is a schematic diagram of a rectifier main circuit for one embodiment;
FIG. 3 is a sector schematic of an embodiment;
FIG. 4 is a three-phase vector state diagram of an embodiment;
FIG. 5 is a schematic diagram of a vector state after three phases are simultaneously superimposed by Δ T according to an embodiment;
FIG. 6 is a schematic diagram illustrating a comparative flow chart of an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
Referring to fig. 1, fig. 1 is a flowchart of a control method of a fixed-frequency PWM rectifier according to an embodiment, including the following steps:
s10, acquiring the current capacitance voltage deviation of the rectifier in the current beat;
the capacitor voltage parameter of the current beat can be obtained through measurement of the related sensor, and after the sensor obtains the capacitor voltage parameter of the current beat through measurement, the measured capacitor voltage parameter is sent to the controller of the rectifier, so that the controller determines the capacitor voltage deviation of the current beat according to the received capacitor voltage parameter, and stores the first capacitor voltage deviation so as to perform corresponding reading in a subsequent control process.
S20, calculating a first predicted capacitor voltage deviation of the rectifier in the first beat after the current beat according to the current capacitor voltage deviation and a voltage deviation prediction formula; the voltage deviation prediction formula represents the relation between two continuous beats of capacitor voltage deviation of the rectifier;
and the first predicted capacitor voltage deviation of the first beat after the current beat is a predicted value of the capacitor voltage deviation corresponding to the first beat after the current beat.
The voltage deviation prediction formula represents a relationship between two consecutive beats of the capacitor voltage deviation of the rectifier, such as a current relationship between a first beat after the current beat and the consecutive two beats of the current beat, or a current relationship between a second beat after the current beat and the consecutive two beats of the first beat after the current beat, and so on.
S30, calculating a second predicted capacitor voltage deviation of the rectifier in the second beat after the current beat according to the first predicted capacitor voltage deviation and the voltage deviation prediction formula;
and the second predicted capacitor voltage deviation of the second beat after the current beat is a predicted value of the capacitor voltage deviation corresponding to the second beat after the current beat.
And S40, controlling the direct current voltage of the rectifier according to the second predicted capacitor voltage deviation in the first beat after the current beat.
In the step, at the moment k (current beat), the capacitance voltage deviation at the moment k +2 (second beat after the current beat) and the capacitance voltage deviation at the moment k +1 (first beat after the current beat) are obtained, so that the direct current voltage control is carried out at the moment k +1 according to the capacitance voltage deviation corresponding to the moment k +2, and the effective compensation of one beat lagging in the direct current voltage control process of the rectifier can be realized.
According to the control method of the fixed-frequency PWM rectifier, the current capacitance voltage deviation of the rectifier in the current beat is obtained, the first predicted capacitance voltage deviation of the rectifier in the first beat after the current beat is calculated, the second predicted capacitance voltage deviation of the rectifier in the second beat after the current beat is calculated, so that the direct current voltage of the rectifier is controlled according to the second predicted capacitance voltage deviation in the first beat after the current beat, on the basis of simplifying the calculated amount of the direct current voltage control process and improving the control efficiency, effective compensation of one beat lagging can be achieved, and the control precision is further improved.
As an embodiment, the voltage deviation prediction formula includes:
Figure BDA0002189211880000051
wherein Δ u (k +1) represents a first predicted capacitor voltage deviation of a first beat after the current beat, Δ u (k) represents a current capacitor voltage deviation of the current beat, TsRepresenting the system sampling period of the rectifier, C representing the capacitance parameter of the rectifier, io(k) And representing the current parameters corresponding to the actually measured current of the current beat in the two-phase static coordinate system.
As an example, the io(k) The determination formula of (2) includes:
io(k)＝iα(k)|sα(k)|+iβ(k)|sβ(k)|，
in the formula iα(k) Represents the value of the measured current of the current beat in the alpha direction in the two-phase static coordinate system, sα(k) Representing the component in the direction alpha of the three-level and three-phase switching state of the rectifier in a two-phase stationary frame, iβ(k) Represents the value of the measured current of the current beat in the beta direction in the two-phase static coordinate system, sβ(k) Representing the component of the rectifier three-level three-phase switch state in the beta direction in the two-phase stationary frame.
The embodiment can predict the first predicted capacitor voltage deviation of the first beat after the current beat more accurately.
In one embodiment, the obtaining of the voltage deviation prediction formula includes:
acquiring a capacitance voltage differential equation of the direct current side of the rectifier;
determining a capacitance midpoint current relational expression of the current beat according to the capacitance voltage differential equation;
discretizing the capacitance midpoint current relation in the sampling period corresponding to the current beat to obtain the voltage deviation prediction formula.
Specifically, after a capacitance voltage differential equation at the direct current side of the rectifier is obtained, two equations in the capacitance voltage differential equation may be subtracted to obtain an initial capacitance midpoint current relational expression, and then an expression of the capacitance midpoint current in a two-phase stationary α β coordinate system is obtained in a kth sampling period (a kth beat, i.e., a current beat) according to the initial capacitance midpoint current relational expression, so as to obtain a capacitance midpoint current relational expression of the current beat.
The above capacitance voltage differential equation (i.e., differential equation of the dc side capacitance voltage) includes:
Figure BDA0002189211880000052
in the formula idcuRepresenting the current flowing through the upper bus capacitance, idcdDenotes the current flowing through the lower bus capacitance, C denotes the capacitance parameter of the rectifier (bus capacitance), udcuRepresenting the voltage of the upper bus capacitance udcdRepresenting the voltage of the lower bus capacitance.
The initial capacitance midpoint current relationship includes:
Figure BDA0002189211880000061
the capacitance midpoint current relation of the current beat comprises:
io(k)＝iα(k)|sα(k)|+iβ(k)|sβ(k)|
in the formula iα(k) Represents the value of the measured current of the current beat in the alpha direction in the two-phase static coordinate system, sα(k) Representing the component in the direction alpha of the three-level and three-phase switching state of the rectifier in a two-phase stationary frame, iβ(k) Represents the value of the measured current of the current beat in the beta direction in the two-phase static coordinate system, sβ(k) Representing the component of the rectifier three-level three-phase switch state in the beta direction in the two-phase stationary frame.
The current relation of the midpoint of the capacitor of the current beat is in TsDiscretizing in a sampling period to obtain a voltage deviation prediction formula:
Figure BDA0002189211880000062
in an embodiment, the method for controlling the fixed-frequency PWM rectifier further includes:
s60, acquiring a first input current of a rectifier at a current beat, a second input current of the rectifier at the first beat before the current beat, and a third input current of the rectifier at the second beat before the current beat;
the first input current can be obtained by measurement of a relevant sensor, and after the sensor obtains the input current of the current beat (namely the current moment) by measurement, the sensor sends the measured input current to the controller of the rectifier, so that the controller determines the first input current of the current beat and stores the first input current for corresponding reading in the subsequent control process.
The second input current of the rectifier for the first beat before the current beat may be an input current measured by the corresponding sensor for the first beat before the current beat, and the second input current may be read from a controller of the rectifier.
S70, calculating a first predicted current of the rectifier in the first beat after the current beat according to the first input current, the second input current, the third input current and a current prediction formula; wherein the current prediction formula characterizes a relationship of input currents of the rectifier between four beats consecutive to each other;
the current prediction formula represents a relationship between the input currents of the rectifier and the four consecutive beats, such as a current relationship between the first beat after the current beat, the first beat before the current beat and the second beat before the current beat, or a current relationship between the second beat after the current beat, the first beat after the current beat, the current beat and the first beat before the current beat.
S80, calculating a second predicted current of the rectifier for a second beat after the current beat according to the second input current, the third input current, the first predicted current and the current prediction formula;
the first predicted current is a predicted current for a first beat after the current beat, and the second predicted current is a predicted current for a second beat after the current beat.
S90, controlling the input current of the rectifier according to the second predicted current in the first beat after the current beat.
In the step, at the moment k (current beat), the predicted current at the moment k +2 (second beat after the current beat) and the predicted current at the moment k +1 (first beat after the current beat) are obtained, so that the input current control is performed at the moment k +1 according to the predicted current corresponding to the moment k +2, and the effective compensation of delaying one beat is realized.
The embodiment can also obtain a first input current of the rectifier at the current beat, a second input current of the rectifier at the first beat before the current beat, and a third input current of the rectifier at the second beat before the current beat; the first prediction current of the rectifier in the first beat after the current beat is calculated, and then the second prediction current of the rectifier in the second beat after the current beat is calculated, so that the input current of the rectifier is controlled according to the second prediction current in the first beat after the current beat, the control scheme of the rectifier is further perfected, in addition, effective compensation for lagging one beat can be realized, and the corresponding control precision is improved.
In one embodiment, the current prediction formula comprises:
i*(k+1)＝3i*(k)-3i*(k-1)+i*(k-2)，
in the formula i*(k +1) represents a first predicted current for the first beat after the current beat, i*(k) A first input current, i, representing the current beat*(k-1) represents a second input current, i, for a first beat prior to the current beat*(k-2) represents a third input current for a second beat prior to the current beat.
The present embodiment can accurately predict the input current of the first beat after the current beat.
As an embodiment, the obtaining of the current prediction formula includes:
acquiring a first mathematical model of a main circuit of the rectifier under a three-phase static coordinate system (a three-phase static abc coordinate system);
transforming the first mathematical model to a two-phase static coordinate system (two-phase static coordinate system alpha beta) to obtain a second mathematical model;
discretizing the second mathematical model by adopting a forward Euler method to obtain a system discrete mathematical model;
setting a value function according to the system discrete mathematical model;
solving the value function by adopting a second-order Lagrange interpolation formula to obtain a prediction formula of a first beat after the current beat;
and determining the current prediction formula according to the prediction formula of the first beat after the current beat.
Specifically, the rectifier may be a three-phase three-level PWM rectifier, and a mathematical model (a first mathematical model) of a main circuit of the three-phase three-level PWM rectifier (for example, the topology of the main circuit may refer to fig. 2) under a three-phase stationary coordinate system includes:
Figure BDA0002189211880000081
in the formula, ea、eb、ecRespectively three-phase mains voltage ia、ib、icRespectively three-phase grid current uan、ubn、、ubnThe three-phase output voltage of the rectifier is respectively, and L is a three-phase incoming line inductor; r is three-phase equivalent resistance.
Transforming the first mathematical model in the three-phase stationary abc coordinate system into the two-phase stationary coordinate system (α β coordinate system), and obtaining a second mathematical model comprising:
Figure BDA0002189211880000082
in the formula, eα、eβIs the component of the three-phase grid voltage in the alpha beta coordinate system, eαIs the component of the three-phase grid voltage in the alpha-beta direction in the alpha-beta coordinate system, eβThe component of the three-phase grid voltage in the beta direction in an alpha beta coordinate system is shown;iα、iβis the component of the three-phase network current in the alpha beta coordinate system,iαfor the components of the three-phase network current in the α β coordinate system, iβThe component of the three-phase power grid current in the beta direction in an alpha beta coordinate system; u. ofα、uβIs a component of the three-phase output voltage of the rectifier under an alpha beta coordinate system, uαIs a component of the rectifier three-phase output voltage in the alpha-beta coordinate system in the alpha-beta direction, uβFor three-phase output of rectifierThe component of the voltage in the β direction in the α β coordinate system.
The forward Euler method is adopted to discretize the formula (2), and the obtained system discrete mathematical model is as follows:
Figure BDA0002189211880000083
in the formula, TsIs the system sampling period.
To improve the current tracking performance of the rectifier, a cost function may be definedgIs the sum of the absolute values of the current deviations, i.e.:
Figure BDA0002189211880000084
in the formula (I), the compound is shown in the specification,
Figure BDA0002189211880000091
iα(k +1) reference current commands (reference current values), i, corresponding to respective directions of the α β coordinate system are taken as k +1, respectivelyα(k +1) and iβAnd (k +1) respectively taking k +1 as an output current corresponding to each direction of the alpha beta coordinate system. For the prediction of the reference current value of the k +1 beat, a second-order Lagrange interpolation formula is adopted for solving, and a prediction formula of the k +1 beat can be obtained:
i*(k+1)＝3i*(k)-3i*(k-1)+i*(k-2) (5)
in the formula i*(k +1) represents the predicted current for k +1 beats, i*(k) Representing the input current of k beats, i*(k-1) represents the input current of k-1 beats, i*(k-2) represents the input current for k-2 beats.
In one example, the above voltage deviation prediction formula may be determined according to a conventional FCS-MPC, and the corresponding determination process includes:
considering that three levels have 27 space voltage vectors, the traditional three-level model prediction scheme is based on a rolling optimization thought and polls the 27 space voltage vectors one by one, so that the output current i under the action of each vector is obtainedα(k+1),iβ(k+1). And selecting a unique voltage vector V that minimizes the value of g by means of the cost function g of equation (4)opAnd the current tracking performance of the three-level rectifier is optimally controlled. And (3) considering the inherent midpoint potential offset problem of the three-level topology, predicting the midpoint potential deviation at the k +1 moment in order to ensure the balance of the midpoint potential, and selecting a voltage vector beneficial to midpoint balance as much as possible during control. According to the capacitor voltage shown in fig. 2, the current direction can be known, and the differential equation of the capacitor voltage on the dc side is:
Figure BDA0002189211880000092
in the formula idcuRepresenting the current flowing through the upper bus capacitance, idcdDenotes the current flowing through the lower bus capacitance, C denotes the capacitance parameter of the rectifier (bus capacitance), udcuRepresenting the voltage of the upper bus capacitance udcdRepresenting the voltage of the lower bus capacitance.
Subtracting the two equations in equation (6) can obtain:
Figure BDA0002189211880000093
wherein, U isdcu-Udcd，UdcuRepresenting the upper bus voltage, U, of the rectifierdcdRepresenting the lower bus voltage, i, of the rectifieroRepresenting the current flowing through the midpoint of the capacitor.
In the k-th sampling period, ioThe expression under the two-phase stationary α β coordinate system is:
io(k)＝iα(k)|sα(k)|+iβ(k)|sβ(k)| (8)
in the formula iα(k) Represents the value of the measured current of the current beat in the alpha direction in the two-phase static coordinate system, sα(k) Representing the component in the direction alpha of the three-level and three-phase switching state of the rectifier in a two-phase stationary frame, iβ(k) Represents the value of the measured current of the current beat in the beta direction in the two-phase static coordinate system, sβ(k) Presentation wholeAnd the component of the three-level and three-phase switch state of the current device in the beta direction in the two-phase static coordinate system.
To formula (7) at a TsDiscretizing in a sampling period to obtain a voltage deviation prediction formula:
Figure BDA0002189211880000101
wherein Δ u (k +1) represents a first predicted capacitor voltage deviation of a first beat after the current beat of k +1, Δ u (k) represents a current capacitor voltage deviation of the current beat of k, and TsRepresenting the system sampling period of the rectifier, C representing the capacitance parameter of the rectifier, io(k) And current parameters corresponding to the measured current of k beats in the two-phase static coordinate system are represented. .
Considering the midpoint potential balance problem, the cost function can now be redefined as follows:
J＝g+λ|△u(k+1)| (10)
in the formula, λ represents a weight factor, and J represents a newly defined cost function. The larger the weight factor, the stronger the constraint on the target. The cost function takes the balance between the tracking command current and the midpoint potential as a target, wherein the optimal current tracking performance is taken as a main control target, and the current tracking performance and the midpoint potential control requirements can be considered through adjusting the weight factor lambda of the midpoint potential item, so that the current tracking performance and the midpoint potential basically achieve the optimal control.
The present example combines the advantages of the three-level PWM modulation strategy and the model predictive control to provide a simplified modulation strategy, and the corresponding control method neither has a complicated rotating coordinate transformation nor does it need to poll 27 discrete vectors, thereby greatly reducing the amount of computation. Meanwhile, the switching frequency of the control strategy is fixed, so that the output filter is simple in design and obvious in harmonic suppression effect. In addition, through constructing a cost function, the neutral point potential balance control of the three-level rectifier is realized.
In an embodiment, the simplified control method of the fixed-frequency PWM rectifier is subjected to verification analysis and simulation analysis, and the corresponding analysis process may include:
when the traditional FCS-MPC selects the optimal voltage vector, each voltage vector needs to be subjected to traversal calculation, 27 discrete voltage vectors exist in the three-level rectifier, and polling brings a large amount of calculation. In addition, the traditional FCS-MPC has the defect of unfixed switching frequency, increases the difficulty of filter reactor and heat dissipation design, and is difficult to apply in industrial fields.
In the implementation of predictive control by the simplified PWM strategy corresponding to the embodiment, 27 voltage vectors do not need to be subjected to polling calculation, the basic voltage vectors are adopted to synthesize the target reference voltage vector, the switching frequency is fixed, and the filter reactor is simple in design. The strategy comprises two major steps: firstly, calculating an optimal target voltage vector, and secondly, calculating the action time of a three-phase high-effective state.
In order to realize fast tracking of the current, the cost function g in the equation (4) is set to 0, that is, the error between the current command of k +1 beat and the output current of k +1 beat is the minimum, so that a fast and accurate tracking effect is achieved. From g ═ 0, one can obtain:
Figure BDA0002189211880000111
when the delay of the digital control system is not considered, order
Figure BDA0002189211880000112
By substituting equation (11) for equation (3), an optimal target reference voltage vector can be obtained:
Figure BDA0002189211880000113
in the formula (I), the compound is shown in the specification,
Figure BDA0002189211880000114
respectively are voltage commands which can enable the current tracking performance to be optimal at the moment k; e.g. of the typeα(k)、eβ(k) Voltages in each direction in the two-phase stationary coordinate system at the time k, and iα(k)、iβ(k) The current quantities of all directions in the two-phase static coordinate system at the moment k are respectively;
Figure BDA0002189211880000115
respectively are reference current commands at the k +1 moment predicted by a Lagrange second-order interpolation formula.
Optimal target voltage vector urefAfter the determination, the basis voltage vectors need to be de-synthesized. As shown in fig. 3, the three-level space vector is divided into six sectors, where P represents the output terminal voltage as a positive half bus voltage, N represents the output terminal voltage as a negative half bus voltage, and O represents the output terminal voltage as 0.
In order to conveniently judge the region where the target voltage vector is located, the target voltage vector is determined by the method
Figure BDA0002189211880000116
Transforming into three-phase abc static coordinate system to obtain
Figure BDA0002189211880000117
By
Figure BDA0002189211880000118
The region where the target voltage vector is located can be conveniently judged, and the sector division can be shown in table 1.
TABLE 1 determination of the region in which the target voltage vector is located
Figure BDA0002189211880000119
The division of the sectors takes the zero crossing point as a positive and negative boundary line, and the boundary of each sector is perpendicular to the axis of one phase. Suppose urefFalling in the first region, i.e., S is 1, and the three-phase vector state is shown in fig. 4, where P denotes that the output terminal voltage is a positive half bus voltage, N denotes that the output terminal voltage is a negative half bus voltage, and O denotes that the output terminal voltage is 0. T in FIG. 4A、TB、TCA high value indicates the effective state action time, i.e. the time at which the vector state is high in each phase, which can be found from the volt-second equilibrium:
Figure BDA0002189211880000121
when the target voltage vector urefWhen falling in other areas, TA、TB、TCThis can be obtained by the same method. The method has small calculation amount and can flexibly inject the zero sequence component, thereby easily realizing multi-target control.
Neutral point potential imbalance is an inherent problem of a three-level NPC rectifier, and a method of injecting zero sequence voltage is generally adopted to solve the neutral point potential offset problem of three levels. The three-phase action time T obtained in the previous section is adopted in the embodimentA、TB、TCThe upper and lower bus capacitance balance is realized by superposing a time quantum at the same time, the zero sequence voltage is still injected essentially, but the expression is more concise and flexible.
The principle of the midpoint potential control is described in detail in the second chapter, and the midpoint control is optimal when Δ u (k +1) is 0 in equation (9). To optimize midpoint control, equation (9) can be written as:
Figure BDA0002189211880000122
generally, when the sampling frequency is sufficiently high, the current can be approximately considered to be constant within one sampling period. The average value of the current flowing through the midpoint during a sampling period can be written as:
Figure BDA0002189211880000123
in the formula io_newThe average current flowing through the midpoint during a cycle without considering midpoint balance is shown. When zero-sequence components are injected simultaneously in three phases to suppress midpoint potential offset, the midpoint current average value can be rewritten as:
Figure BDA0002189211880000124
where Δ T represents the amount of time superimposed on the three-phase action time to suppress the midpoint potential shift.
The united type (14), (16) can obtain:
Figure BDA0002189211880000125
therefore, the three-phase vector action time T 'of the midpoint balance algorithm is added'A、T′B、T′CComprises the following steps:
Figure BDA0002189211880000131
the vector state after three phases are simultaneously superposed with Δ T can be referred to as fig. 5, wherein P represents that the output end voltage is a positive half bus voltage, N represents that the output end voltage is a negative half bus voltage, and O represents that the output end voltage is 0; Δ T represents the amount of time superimposed on the three-phase action time to suppress midpoint potential shift; t isA’、TB’、TC' is the three-phase vector action time with the addition of the midpoint balancing algorithm. In fig. 5, (a) indicates a vector state corresponding to a decrease in the high-activity state, and (b) indicates a vector state corresponding to an increase in the high-activity state.
In a digital control system of a rectifier, when a control delay is taken into consideration, control delayed by one beat is actually performed. This means that the command voltage calculated at time k is applied to the control system only at time k + 1.
In order to eliminate the influence of lagging one beat on the control system, the reference voltage applied at the moment k +1 needs to be calculated at the moment k in advance of one beat. The cost function of equation (4) needs to be modified as follows:
Figure BDA0002189211880000132
similarly, to realize fast tracking of the current, the cost function g is made 0, so that the current command of k +2 beats is equal to the output current of k +2 beats. From g ═ 0, one can obtain:
Figure BDA0002189211880000133
meanwhile, the reference voltage at the time k +1 can be derived from the reference voltage at the time k by equation (12):
Figure BDA0002189211880000134
in equation (21), since the sampling frequency is high, the grid voltage e at the time k +1α(k+1)，eβ(k +1) can be considered to be equivalent to the grid voltage e at time kα(k)，eβ(k)。
Figure BDA0002189211880000135
The predicted current command indicating the time k +2 can be derived from equation (5):
i*(k+2)＝3i*(k+1)-3i*(k)+i*(k-1) (22)
the command current needs to be predicted in two steps, and the command current at the moment of k +1 is predicted by formula (5)
Figure BDA0002189211880000136
Figure BDA0002189211880000137
Then, the command current at the time k +2 is predicted from equation (22)
Figure BDA0002189211880000138
Therefore, at the time k, the reference voltage command at the time k +1 can be calculated in advance by one beat by using the predicted current command at the time k +2 and the predicted output current at the time k +1, and effective compensation for one beat delay is realized.
The midpoint potential delay compensation mechanism is similar to that of current, and further forward estimation is carried out on the formula (9) on the basis of the formula (9), so that the following can be obtained:
Figure BDA0002189211880000141
in one example, the algorithm of the MPC-based simplified PWM strategy (i.e., the control method of the fixed-frequency PWM rectifier provided by the present invention) is compared with the algorithm of the conventional MPC by simulation analysis, the flowchart of the simplified PWM strategy provided by the present invention is shown in fig. 6(a), and the flowchart of the conventional MPC can be referred to in fig. 6 (b). As can be clearly seen from the two algorithm flowcharts, the simplified PWM modulation algorithm proposed herein does not need to perform polling calculation on 27 space voltage vectors, obtains an optimal reference voltage command by setting the cost function g to 0, and then realizes PWM output by judging the sector where the reference voltage vector is located, thereby greatly improving the algorithm execution efficiency.
The embodiment provides a simplified fixed-frequency PWM control strategy based on the MPC, which overcomes the defects of the traditional FCS-MPC. In the optimal vector derivation process, it is not necessary to poll all 27 vectors. The controller has good dynamic and static control performance, and the calculated amount is greatly reduced. In order to compare the calculated amount, the traditional FCS-MPC algorithm and the simplified algorithm proposed herein are respectively run in TMS320F28335 DSP by using a C language program, and the same code writing style and compiler option setting are adopted. It was measured that the conventional FCS-MPC algorithm required 37.95us to operate, while the simplified algorithm required only 19.66 us.
Under the condition of adopting the same sampling frequency, the simplified algorithm has lower current harmonic content on the network side and better control effect. In essence, a conventional FCS-MPC can only select an optimal discrete voltage vector within one cycle. And the optimal vector selected by the simplified algorithm is a virtual voltage vector constructed by adopting the latest three-vector principle. Therefore, the control effect is more excellent, the harmonic content is lower, and the tracking precision is higher.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
It should be noted that the terms "first \ second \ third" referred to in the embodiments of the present application merely distinguish similar objects, and do not represent a specific ordering for the objects, and it should be understood that "first \ second \ third" may exchange a specific order or sequence when allowed. It should be understood that "first \ second \ third" distinct objects may be interchanged under appropriate circumstances such that the embodiments of the application described herein may be implemented in an order other than those illustrated or described herein.
The terms "comprising" and "having" and any variations thereof in the embodiments of the present application are intended to cover non-exclusive inclusions. For example, a process, method, apparatus, product, or device that comprises a list of steps or modules is not limited to the listed steps or modules but may alternatively include other steps or modules not listed or inherent to such process, method, product, or device.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (5)

1. A control method of a fixed-frequency PWM rectifier is characterized by comprising the following steps:
s10, acquiring the current capacitance voltage deviation of the rectifier in the current beat;
s20, calculating a first predicted capacitor voltage deviation of the rectifier in the first beat after the current beat according to the current capacitor voltage deviation and a voltage deviation prediction formula; the voltage deviation prediction formula represents the relation between two continuous beats of capacitor voltage deviation of the rectifier; the voltage deviation prediction formula includes:
Figure FDA0003013992610000011
wherein Δ u (k +1) represents a first predicted capacitance voltage deviation for a first beat after the current beat, Δ u (k) represents a current capacitance voltage deviation for the current beat, and TsRepresenting the system sampling period of the rectifier, C representing the capacitance parameter of the rectifier, io(k) Representing current parameters corresponding to the actually measured current of the current beat in a two-phase static coordinate system;
i is describedo(k) The determination formula of (2) includes:
io(k)＝iα(k)|sα(k)|+iβ(k)|sβ(k)|，
in the formula iα(k) Represents the value of the measured current of the current beat in the alpha direction in the two-phase static coordinate system, sα(k) Representing the component in the direction alpha of the three-level and three-phase switching state of the rectifier in a two-phase stationary frame, iβ(k) Represents the value of the measured current of the current beat in the beta direction in the two-phase static coordinate system, sβ(k) Representing the component of the three-level and three-phase switch state of the rectifier in the beta direction in a two-phase static coordinate system;
s30, calculating a second predicted capacitor voltage deviation of the rectifier in the second beat after the current beat according to the first predicted capacitor voltage deviation and the voltage deviation prediction formula;
and S40, controlling the direct current voltage of the rectifier according to the second predicted capacitor voltage deviation in the first beat after the current beat.
2. The method for controlling the fixed-frequency PWM rectifier according to claim 1, wherein the obtaining of the voltage deviation prediction formula comprises:
acquiring a capacitance voltage differential equation of the direct current side of the rectifier;
determining a capacitance midpoint current relational expression of the current beat according to the capacitance voltage differential equation;
discretizing the capacitance midpoint current relation in the sampling period corresponding to the current beat to obtain the voltage deviation prediction formula.
3. The method for controlling the fixed-frequency PWM rectifier according to claim 1 or 2, further comprising:
acquiring a first input current of a rectifier at a current beat, a second input current of the rectifier at the first beat before the current beat, and a third input current of the rectifier at the second beat before the current beat;
calculating a first predicted current for the rectifier for a first beat after the current beat according to the first input current, the second input current, the third input current, and a current prediction formula; wherein the current prediction formula characterizes a relationship of input currents of the rectifier between four beats consecutive to each other;
calculating a second predicted current for the rectifier for a second beat after the current beat according to the second input current, the third input current, the first predicted current, and the current prediction formula;
controlling an input current of the rectifier according to the second predicted current for a first beat after the current beat.
4. The method of controlling a fixed frequency PWM rectifier of claim 3, wherein said current prediction formula comprises:
i*(k+1)＝3i*(k)-3i*(k-1)+i*(k-2)，
in the formula i*(k +1) represents a first predicted current for the first beat after the current beat, i*(k) A first input current, i, representing the current beat*(k-1) represents a second input current, i, for a first beat prior to the current beat*(k-2) represents a third input current for a second beat prior to the current beat.
5. The method for controlling the fixed-frequency PWM rectifier according to claim 3, wherein the obtaining of the current prediction formula comprises:
acquiring a first mathematical model of a main circuit of the rectifier under a three-phase static coordinate system;
transforming the first mathematical model to a two-phase static coordinate system to obtain a second mathematical model;
discretizing the second mathematical model by adopting a forward Euler method to obtain a system discrete mathematical model;
setting a value function according to the system discrete mathematical model;
solving the value function by adopting a second-order Lagrange interpolation formula to obtain a prediction formula of a first beat after the current beat;
and determining the current prediction formula according to the prediction formula of the first beat after the current beat.
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