CN108521243B - High-speed permanent magnet synchronous motor direct power control method based on space vector modulation - Google Patents
High-speed permanent magnet synchronous motor direct power control method based on space vector modulation Download PDFInfo
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Abstract
The invention discloses a direct power control method of a high-speed permanent magnet synchronous motor based on space vector modulation, which adopts a PI regulator to replace a hysteresis controller so as to realize direct control of instantaneous power. The direct power control method of the high-speed permanent magnet synchronous motor based on space vector modulation is based on two PI regulators, outputs the voltage vector according to the phase magnitude of the voltage vector, and obtains an ideal voltage vector through coordinate transformation and space vector modulation. By utilizing the mode, the accurate control of the stator voltage can be realized so as to achieve the aim of controlling the reactive power to be zero, and the problem of unfixed switching frequency can be overcome. The invention has simple structure and simple algorithm, can reduce the loss of the motor and improve the operation efficiency of the motor, and can be used for the application occasions with long-term steady operation and higher energy-saving requirement, such as a blower, and the like.
Description
Technical Field
The invention belongs to the field of motor control, and particularly relates to a high-speed permanent magnet synchronous motor direct power control method based on space vector modulation.
Background
The permanent magnet synchronous motor utilizes the permanent magnet to provide excitation, reduces the loss of an excitation system compared with an electric excitation motor, and greatly improves the efficiency and the power density of the motor. Meanwhile, the direct current motor overcomes the adverse factors brought by a direct current motor brush and a commutator, and the application range is rapidly developed from the initial military industry to the fields of aerospace, industrial automation and the like.
The current common control methods of the permanent magnet synchronous motor comprise a vector control method and a direct torque control method. The basic principle of vector control is to control the exciting current and the torque current of the motor respectively according to the magnetic field orientation principle by measuring and controlling the stator current vector of the motor, thereby achieving the purpose of controlling the torque of the motor. However, in practical application, because the rotor flux linkage is difficult to accurately observe, the system characteristics are greatly influenced by motor parameters, and the vector rotation transformation used in the motor control process is complex, the actual control effect is difficult to achieve the ideal analysis result. The direct torque control directly controls the torque not by controlling the current and the flux linkage equivalent amount, but directly controls the torque as the controlled amount, the algorithm does not need complex coordinate transformation, the magnitude of the modulus and the torque of the flux linkage is directly calculated on the motor stator coordinate, and the PWM pulse width modulation and the high dynamic performance of the system are realized by directly tracking the flux linkage and the torque, but the direct torque control method has the problem of large ripple torque at low speed, and the calculation amount and the calculation difficulty of the control algorithm are large. The vector control method and the direct torque control method have good effect on the dynamic performance of the system, but the content of reactive power is increased.
Under the large background of building a resource-saving society, in the face of the situation of energy shortage in China, finding a novel and efficient motor control method becomes a research hotspot. The high-speed magnetic suspension motor is used as a core component of high-speed power machinery such as a blower and the like, is in a steady state operation state most of the time, has low requirements on dynamic performance, and has strict requirements on system energy conservation.
In order to reduce the reactive power absorbed by the motor to achieve the aim of energy saving, a direct power control algorithm is adopted to control the motor. The direct power control method has simple structure, and can realize the ideal target that the power factor of the motor is close to 1 by controlling the reactive power of the motor to be zero. The direct power control algorithm has the advantages of high power factor, low harmonic distortion, simple algorithm and system structure and the like, and does not need rotating coordinate transformation. The traditional direct power control algorithm adopts the combination of a hysteresis comparator and a switch table, so that the defects of high requirement on system sampling frequency and time lag caused by unfixed switching frequency exist, and the problem that the control performance of the motor is influenced by factors such as stator parameter change, a switching dead zone of an inverter, error accumulation of an integrator, direct-current temperature drift and the like also occurs. Therefore, a new control method for a high-speed permanent magnet synchronous motor is needed, which can not only achieve the aim of zero reactive power of the motor and improve the working efficiency of the motor, but also overcome the problems of unfixed switching frequency and difficult determination of hysteresis width, avoid the problem of influence on the control performance of the motor caused by a hysteresis controller in the traditional direct control method, and further improve the steady-state performance of the motor.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the invention aims to overcome the defects of the prior art, solve the problems of increased reactive power, large motor loss and low motor efficiency of the traditional blower and other application occasions, and overcome the problem of unfixed switching frequency. The method achieves the aim of controlling the reactive power to be zero, and provides technical support for long-term steady operation of blowers and other application occasions with higher energy-saving requirements.
The technical scheme adopted by the invention for solving the technical problems is as follows: a direct power control method of a high-speed permanent magnet synchronous motor comprises the following steps:
(1) based on the assumption of the permanent magnet synchronous motor under ideal conditions, a three-phase PMSM basic mathematical model is established. The ideal conditions are: the three-phase PMSM is an ideal motor; neglecting the saturation of the motor iron core; eddy current and hysteresis loss in the motor are not counted; the current in the motor is symmetrical three-phase sinusoidal current.
(2) The control target that the reactive power of the motor is zero is realized through a direct power control algorithm, the fixed switching frequency is realized through a space vector modulation algorithm, and meanwhile, the position of the rotor is estimated through a high-speed permanent magnet synchronous motor rotor position information estimation algorithm, so that the implementation of direct power control is guaranteed.
The mathematical model of the high-speed permanent magnet synchronous motor is as follows:
in the ABC coordinate system, the stator current and voltage space vector can be expressed as:
wherein a ═ ej120°Representing an operator space; l issIs equivalent phase inductance, which is the difference between the phase inductance and the mutual inductance; psifIs a permanent magnet excitation space vector; thetarIs the angle of rotation, psi, of the permanent magnet with respect to the A axissA flux linkage for a three-phase winding; u. ofs，Rs，isPhase voltage, phase resistance and phase current of the three-phase winding are respectively;
the direct power control method is a control algorithm which takes two parameters of instantaneous active power and instantaneous reactive power of a motor as control quantity based on a PI regulator, and the method comprises the following specific steps:
(1) in the ABC coordinate system, the state functions of six switching tubes of the inverter are assumed as follows: sA，SBAnd SCRespectively expressed as:
then, the three-phase line voltage can be represented as:
wherein u isdRepresents d-axis voltage, uAB、uBC、uCARepresenting three phase line voltage.
Combined uA+uB+uCWhen the three-phase voltage vector is solved as 0:
wherein u isA、uB、uCRepresents three phase voltage;
(2) through a coordinate transformation method, collecting three-phase current signals iA、iBAnd iCConverted into current vector i under α - β coordinate systemαAnd iβThe conversion relationship is as follows:
(3) and solving α - β coordinate system by using the calculation formula of the instantaneous power, wherein the three-phase instantaneous active power p and the reactive power q of the permanent magnet synchronous motor are obtained.
The instantaneous power is calculated as:
the three-phase instantaneous active power p and the reactive power q are respectively as follows:
(4) given speed of rotation omega*Making a difference with the actually measured rotating speed omega, inputting the difference value into a PI regulator to regulate the rotating speed, and taking the output value of the PI regulator as a given value p of the instantaneous active power*Giving the instantaneous active power a given value p*Making a difference with the instantaneous active power p obtained by actual calculation, and sending the difference value to a PI regulator to obtain a voltage vector uspGiven value of instantaneous reactive power q*Setting the given value q of the instantaneous reactive power as 0*Making a difference with the instantaneous reactive power q obtained by actual calculation, and sending the difference value to a PI regulator to obtain a voltage vector usq。
(5) According to the derivation of the permanent magnet synchronous motor instantaneous power theory, the phase angle information theta of the voltage vector is solveds。
The instantaneous active power under the ABC coordinate system can be obtained according to the scalar product of the instantaneous voltage vector and the current vector, and the instantaneous reactive power can be obtained according to the vector product of the instantaneous voltage vector and the current vector, which are respectively expressed as:
wherein u ═ uA,uB,uC]TAnd i ═ iA,iB,iC]TRepresenting the phase voltage vector and the phase current vector, respectively.
Therefore, the three-phase input instantaneous active power and instantaneous reactive power of the motor are respectively as follows:
the change of the stator current in the d-q coordinate axis is related to the change of the current amplitude and angle, when the motor runs in a steady state, the motor torque is stable, the component of the stator current in the q axis is not changed, so the stator current amplitude is not changed, and the stator current vector and the d axis rotate at the same speed, so the vector angle between the stator current and the d axis is not changed, and in the direct power control process, the instantaneous power is required to be 0, the power factor is 1, so the q is equal to 0.
Therefore, the three-phase input instantaneous active power of the motor can be written as:
wherein gamma is a current vector isAngle with q axis, δ being voltage vector usAnd theta is the angle between the voltage vector and the current vector.
Since γ is θ + δ, and when the reactive power is zero, i.e. the power factor is 1, the power factor angle is zero, i.e. isAnd usIt should be coaxial, i.e., γ ═ δ. Order:
therefore, the above equation may become:
phase angle information theta of voltage vectorsCan be determined from gamma and rotor position angle thetarThe determination can be expressed as:
θs＝90°+δ+θr(14)
wherein, δ and θrThe expression of (c) can be expressed as:
wherein P represents the number of pole pairs of the motor.
(6) Outputting the obtained voltage vector signal u by a PI regulator through a coordinate transformation methodspAnd usqFrom phase angle information theta of the voltage vectorsAnd calculating a voltage vector u under α - β coordinate systemsαAnd usβThe conversion relationship is as follows:
wherein, thetasAs a voltage space vector usThe angle between the axis α.
The direct power control method is a permanent magnet synchronous motor direct power control algorithm based on space vector modulation, and the method specifically comprises the following steps:
(1) and establishing a space vector modulation model.
Assuming a calculated vector usIs a non-zero vector us1And us2Between and utilize us1Equivalent us2The equivalence relation is as follows:
us·Ts＝us1·Ts1+us2·Ts2(17)
wherein, TsRepresents a PWM cycle; t iss1And Ts2Each represents us1And us2The action time of (1).
(2) Voltage vector u of α axissαβ axis of voltage vectorusβPerforming vector decomposition to obtain ideal voltage vector uαAnd uβThe equivalent relationship is rewritten as follows under the α - β coordinate system:
solving for exact Ts1And Ts2A fixed switching frequency can be achieved.
(3) Ideal voltage vector uαAnd uβOutputting three-phase current signals i through PWM inverterA、iB、iCSo as to regulate the amplitude of the stator current vector to change the instantaneous reactive power and output three-phase current iA、iB、iCObtaining a current vector i under α - β coordinate system through coordinate transformationαAnd iβAnd a voltage vector uαAnd uβThe instantaneous active power p and the instantaneous reactive power q are used as the input of the actual calculated instantaneous active power p and the instantaneous reactive power q together, and the closed-loop control of direct power control is realized.
The principle of the invention is as follows: the invention relates to a space vector modulation algorithm-based direct power control algorithm for a high-speed permanent magnet synchronous motor used in occasions with long-term steady-state operation and high energy-saving requirements. Firstly, acquired three-phase current signals are subjected to coordinate transformation to obtain two-phase current signals, instantaneous active power and reactive power of a motor are calculated in real time, then difference comparison is carried out on the two-phase current signals and the given instantaneous active power and reactive power respectively, the two-phase current signals are adjusted through two PI regulators, the two-phase current signals are processed through coordinate transformation according to a phase angle of a voltage vector, finally, an ideal voltage vector is obtained through a space vector modulation algorithm, and zero reactive power control is carried out on the motor.
Compared with the prior art, the invention has the advantages that: the invention provides a direct power control algorithm, namely, based on a PI regulator, two parameters of instantaneous active power and instantaneous reactive power of a motor are used as control quantities, the method is simple and convenient, the aim of zero reactive power of the motor is realized, and the operating efficiency and the energy-saving index of the high-speed motor are greatly improved. Meanwhile, a method combining direct power control and a space vector modulation algorithm is provided, and the problems that the switching frequency is not fixed and the hysteresis loop width is not easy to determine are solved. In addition, in the control process, the problem that the control performance of the motor is influenced by factors such as stator parameter change, the switching dead zone of an inverter, error accumulation of an integrator, direct-current temperature drift and the like under the condition of low frequency brought by the output of a hysteresis controller and a sector where a stator flux linkage is required to be estimated in the traditional direct control method is solved, and the steady-state performance of the motor is effectively improved.
Drawings
FIG. 1 is a block diagram of the system architecture of the present invention;
FIG. 2 is a schematic diagram of the coordinate relationship of the present invention;
FIG. 3 is a schematic diagram of the space vector modulation of the present invention;
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1-3, the specific method of the present invention is as follows:
the first embodiment is as follows: referring to fig. 1 to explain the present embodiment, the direct power control method for a high-speed permanent magnet synchronous motor according to the present embodiment is a method based on a space vector modulation algorithm, and includes a mathematical model part 1 of the permanent magnet synchronous motor, a direct power control part 2, and a space vector modulation part 3.
The direct power control part 2 is based on a PI regulator, takes two parameters of instantaneous active power and instantaneous reactive power of the motor as control quantities, outputs the initial control of a voltage vector, establishes three corresponding coordinate systems in the rotation process of a motor rotor, namely an ABC coordinate system, a static α - β coordinate system and a rotating d-q coordinate system, and gives a given rotating speed omega*Making a difference with the actually measured rotating speed omega, inputting the difference value into a PI regulator for rotating speed regulation, and taking the output value of the PI regulator as the instantaneous active power p*Given value of, instantaneous reactive power q*Is set to 0, in a stationary α - β coordinate system, using voltage vectors and currentsVector information, and calculating three-phase instantaneous active power and reactive power of the motor. Will instantaneously active power p*Reactive power q*And respectively subtracting the instantaneous active power p and the reactive power q obtained by actual calculation, respectively sending the difference values to the two PI regulators for regulation, and outputting the two PI regulators according to the voltage vector phase angle thetasTransforming the coordinate into a stationary α - β coordinate system to obtain a α -axis voltage vector usαVoltage vector u of axis βsβ。
The space vector modulation part 3 is a control algorithm for further obtaining an ideal voltage vector on the basis of direct power control, and α -axis voltage vector usαVoltage vector u of axis βsβPerforming vector decomposition to obtain ideal voltage vector uαAnd uβ. The voltage signal passes through a PWM inverter to output a three-phase current signal iA、iB、iCThereby adjusting the stator current vector magnitude to vary the instantaneous reactive power. Simultaneously, three-phase current signals iA、iB、iCObtaining a current vector i under α - β coordinate system through coordinate transformationαAnd iβAnd a voltage vector uαAnd uβTogether as the actual calculated instantaneous active power p*And instantaneous reactive power q*Is input.
The second embodiment is as follows: the embodiment is a further limitation on the method for controlling the direct power of the high-speed magnetic suspension synchronous motor based on space vector modulation in the first embodiment, and the mathematical model part 1 of the permanent magnet synchronous motor comprises a system current vector equation, a voltage vector equation, a flux linkage equation and an electromagnetic torque equation.
In the ABC coordinate system, the stator current, voltage space vector, and stator flux linkage can be expressed as:
wherein a ═ ej120°Representing an operator space; rsIs a phase resistance; l issIs equivalent phase inductanceThe difference between the phase inductance and the mutual inductance; psisA flux linkage for a three-phase winding; u. ofs，Rs，isPhase voltage, resistance and current of the three-phase winding respectively; psifIs a permanent magnet excitation space vector; thetarIs the rotation angle of the permanent magnet relative to the A axis, and satisfies the following conditions:
The third concrete implementation mode: referring to fig. 1 and fig. 2, the present embodiment is further limited to the method for controlling direct power of a high-speed magnetic levitation synchronous motor based on space vector modulation according to the first embodiment, and the direct power control section 2 includes the following steps:
step one, solving a three-phase voltage vector u by using the state of a switching tube of an inverterA、uBAnd uC。
In the ABC coordinate system, the state functions of six switching tubes of the inverter are assumed as follows: sA，SBAnd SCRespectively expressed as:
then, the three-phase line voltage can be represented as:
wherein u isdRepresents d-axis voltage, uAB、uBC、uCARepresenting three phase line voltage.
Combined uA+uB+uCWhen the three-phase voltage vector is solved as 0:
wherein u isA、uB、uCRepresenting three phase voltage.
Step two, acquiring a three-phase current signal i by a coordinate transformation methodA、iBAnd iCConverted into current vector i under α - β coordinate systemαAnd iβ. According to the schematic diagram of the coordinate relationship shown in fig. 2, the transformation relationship is:
and step three, solving α - β coordinate system by using the calculation formula of the instantaneous power, wherein the three-phase instantaneous active power p and the reactive power q of the permanent magnet synchronous motor are obtained.
The instantaneous power is calculated as:
the three-phase instantaneous active power p and the reactive power q are respectively as follows:
step four, setting the rotation speed omega according to the block diagram of the direct power control algorithm shown in the figure 1*Making difference with the actually measured rotating speed omega, inputting the difference value into a PI regulator for rotating speed regulation, and taking the output value of the PI regulator as the given value p of the instantaneous active power*. Setting the given value p of instantaneous active power*Making a difference with the instantaneous active power p obtained by actual calculation, and sending the difference value to a PI regulator to obtain a voltage vector usp. Given value q of instantaneous reactive power*Setting the given value q of the instantaneous reactive power as 0*Making a difference with the instantaneous reactive power q obtained by actual calculation, and sending the difference value to a PI regulator to obtain a voltage vector usq。
Step five, benefitThe phase angle information theta of the voltage vector is solved by derivation of the permanent magnet synchronous motor instantaneous power theory according to the coordinate relation diagram shown in figure 2s。
The three-phase instantaneous power under the d-q coordinate system can be calculated according to a complex power definition method:
S＝p+jq＝us×is* (8)
wherein S represents complex power; p represents instantaneous active power; q represents the instantaneous reactive power; i.e. is *Represents isThe complex conjugate of (a).
The instantaneous active power under the ABC coordinate system can be obtained according to the scalar product of the instantaneous voltage vector and the current vector, and the instantaneous reactive power can be obtained according to the vector product of the instantaneous voltage vector and the current vector, which are respectively expressed as:
wherein u ═ uA,uB,uC]TAnd i ═ iA,iB,iC]TRepresenting the phase voltage vector and the phase current vector, respectively.
Voltage vector usRewriting in the d-q coordinate system is as follows:
wherein psis d-q＝ψd+jψq＝(Ldid+ψf)+j·Lqiq＝ψf+Lsis d-qRepresenting the stator flux linkage in the d-q coordinate system. Therefore, the instantaneous active power and the instantaneous reactive power of the three-phase input of the motor are respectively as follows:
due to isCan also be expressed as
Its differential can be expressed as:
wherein, theta1Representative current vector isAnd the angle between the d-axis.
Therefore, it can be seen from the above formula that the change of the stator current in the d-q coordinate axis is related to the change of the current amplitude and angle, and when the motor operates in a steady state, the motor torque is stable, the component of the stator current in the q axis is not changed, so the stator current amplitude is not changed, and the stator current vector and the d axis rotate at the same speed, so the vector angle between the stator current and the d axis is also not changed. In the direct power control, since the instantaneous power is required to be 0 and the power factor is 1, d is made 0, that is:
wherein gamma is a current vector isThe angle between the q axis and the axis.
Therefore, the three-phase input instantaneous active power of the motor can be written as:
where δ is the voltage vector usAnd theta is the angle between the voltage vector and the current vector.
Since γ is θ + δ, and when the reactive power is zero, i.e. the power factor is 1, the power factor angle is zero, i.e. isAnd usIt should be coaxial, i.e., γ ═ δ. Order:
therefore, the above equation may become:
phase angle information theta of voltage vectorsCan be determined from gamma and rotor position angle thetarThe determination can be expressed as:
θs＝90°+δ+θr(14)
wherein, δ and θrThe expression of (c) can be expressed as:
wherein P represents the number of pole pairs of the motor.
Step six, outputting the obtained voltage vector signal u by using a PI regulator through a coordinate transformation methodspAnd usqFrom phase angle information theta of the voltage vectorsAnd calculating a voltage vector u under α - β coordinate systemsαAnd usβ. According to the schematic diagram of the coordinate relationship shown in fig. 2, the transformation relationship is:
wherein, thetasAs a voltage space vector usThe angle between the axis α.
The fourth concrete implementation mode: the present embodiment is described with reference to fig. 1, fig. 2, and fig. 3, and the present embodiment is further limited to the method for controlling direct power of a high-speed magnetic levitation synchronous motor based on space vector modulation according to the first embodiment, and the space vector modulation section 3 includes the following steps:
step one, establishing a space vector modulation model.
Assuming a calculated vector usIs a non-zero vector us1And us2Between and utilize us1Equivalent us2According to the space vector modulation diagram of fig. 3, the equivalence relation is as follows:
us·Ts＝us1·Ts1+us2·Ts2(17)
wherein, TsRepresents a PWM cycle; t iss1And Ts2Each represents us1And us2The action time of (1).
Step two, converting the voltage vector u of the α axissαVoltage vector u of axis βsβPerforming vector decomposition to obtain ideal voltage vector uαAnd uβAccording to the space vector modulation diagram of fig. 3, the equivalent relationship is rewritten as follows under the α - β coordinate system:
solving for exact Ts1And Ts2A fixed switching frequency can be achieved.
Step three, according to the block diagram of the direct power control algorithm based on space vector modulation shown in fig. 1, an ideal voltage vector uαAnd uβOutputting three-phase current signals i through PWM inverterA、iB、iCAnd thus the stator current vector magnitude is adjusted to vary the instantaneous reactive power. Simultaneously, three-phase currents iA、iB、iCObtaining a current vector i under α - β coordinate system through coordinate transformationαAnd iβAnd a voltage vector uαAnd uβThe instantaneous active power p and the instantaneous reactive power q are used as the input of the actual calculated instantaneous active power p and the instantaneous reactive power q together, and the closed-loop control of direct power control is realized.
The method can be used as a novel high-speed magnetic suspension synchronous motor direct power control method based on space vector modulation, is simple and convenient, can achieve the aim of controlling the reactive power to be zero, greatly improves the operation efficiency and energy-saving index of the high-speed motor, overcomes the problems of unfixed switching frequency and difficult determination of hysteresis loop width, is simple in engineering realization, does not need a hysteresis loop controller and complex flux linkage angle calculation, and improves the operation efficiency of the high-speed permanent magnet synchronous motor.
The invention has not been described in detail and is within the skill of the art.
Claims (1)
1. A direct power control method of a high-speed permanent magnet synchronous motor based on space vector modulation is characterized by comprising the following steps:
(11) based on the assumption of the permanent magnet synchronous motor under ideal conditions, a three-phase PMSM basic mathematical model is established, wherein the established permanent magnet synchronous motor model is as follows:
in the ABC coordinate system, the stator current and voltage space vector can be expressed as:
wherein a ═ ej120°Representing an operator space; l issIs equivalent phase inductance, which is the difference between the phase inductance and the mutual inductance; psifIs a permanent magnet excitation space vector; thetarIs the rotation angle of the permanent magnet relative to the A axis; psisA flux linkage for a three-phase winding; u. ofs，Rs，isPhase voltage, phase resistance and phase current of the three-phase winding are respectively;
(12) obtaining voltage vector under α - β coordinate system by direct power control method, and setting given rotation speed omega*Making difference with the actually measured rotating speed omega, inputting the difference value into a PI regulator for rotating speed regulation, and taking the output value of the PI regulator as the given value p of the instantaneous active power*Given value of instantaneous reactive power q*Setting the given value p of the instantaneous active power as 0*Given value q of reactive power*And respectively subtracting the instantaneous active power p and the reactive power q obtained by actual calculation, respectively sending the difference values to two PI regulators for regulation, and obtaining a voltage vector u of an α axis through coordinate change according to phase information of the voltage vector by the output of the two PI regulatorssαVoltage vector u of axis βsβ；
(13) Obtaining ideal voltage signal by space vector modulation, and converting α -axis voltage vectorusαVoltage vector u of axis βsβPerforming vector decomposition to obtain ideal voltage vector uαAnd uβ(ii) a The voltage signal passes through a PWM inverter to output a three-phase current signal iA、iB、iCSo as to adjust the amplitude of the stator current vector to change the instantaneous reactive power; simultaneously, three-phase current signals iA、iB、iCObtaining a current vector i under α - β coordinate system through coordinate transformationαAnd iβAnd a voltage vector uαAnd uβTogether as the input of the actually calculated instantaneous active power p and the instantaneous reactive power q;
the direct power control method is a control method which takes two parameters of instantaneous active power and instantaneous reactive power of a motor as control quantity based on a PI regulator, and comprises the following specific steps:
(21) in the ABC coordinate system, the state functions of six switching tubes of the inverter are assumed as follows: sA，SBAnd SCRespectively expressed as:
then, the three-phase line voltage can be represented as:
wherein u isdRepresents d-axis voltage, uAB、uBC、uCARepresents a three-phase line voltage;
combined uA+uB+uCWhen the three-phase voltage vector is solved as 0:
wherein u isA、uB、uCRepresents three phase voltage;
(22) by coordinate transformationThe collected three-phase current signal iA、iBAnd iCConverted into current vector i under α - β coordinate systemαAnd iβThe conversion relationship is as follows:
(23) solving α - β coordinate system by using an instantaneous power calculation formula, wherein the three-phase instantaneous active power p and reactive power q of the permanent magnet synchronous motor are obtained;
the instantaneous power is calculated as:
the three-phase instantaneous active power p and the reactive power q are respectively as follows:
(24) given speed of rotation omega*Making difference with the actually measured rotating speed omega, inputting the difference value into a PI regulator for rotating speed regulation, and taking the output value of the PI regulator as the given value p of the instantaneous active power*Giving the instantaneous active power a given value p*Making a difference with the instantaneous active power p obtained by actual calculation, and sending the difference value to a PI regulator to obtain a voltage vector uspGiven value of instantaneous reactive power q*Is set to 0, the instantaneous reactive power is set to a given value q*Making a difference with the instantaneous reactive power q obtained by actual calculation, and sending the difference value to a PI regulator to obtain a voltage vector usq；
(25) According to the derivation of the permanent magnet synchronous motor instantaneous power theory, the phase angle information theta of the voltage vector is solveds；
The instantaneous active power under the ABC coordinate system can be obtained according to the scalar product of the instantaneous voltage vector and the current vector, and the instantaneous reactive power can be obtained according to the vector product of the instantaneous voltage vector and the current vector, which are respectively expressed as:
wherein u ═ uA,uB,uC]TAnd i ═ iA,iB,iC]TRespectively representing phase voltage vectors and phase current vectors;
therefore, the three-phase input instantaneous active power and instantaneous reactive power of the motor are respectively as follows:
the change of the stator current in the d-q coordinate axis is related to the change of the current amplitude and the angle, when the motor runs in a steady state, the motor torque is stable, the component of the stator current in the q axis is unchanged, so the stator current amplitude is unchanged, and the stator current vector and the d axis rotate at the same speed, so the vector angle between the stator current and the d axis is also unchanged, and in the direct power control process, the instantaneous power is required to be 0, the power factor is 1, so the q is 0;
therefore, the three-phase input instantaneous active power of the motor can be written as:
wherein gamma is a current vector isAngle with q axis, δ being voltage vector usAn included angle between the voltage vector and the q axis, and theta is an included angle between the voltage vector and the current vector;
since γ is θ + δ, and when the reactive power is zero, i.e. the power factor is 1, the power factor angle is zero, i.e. isAnd usShould be coaxial, i.e., γ ═ δ, let:
therefore, the above equation may become:
phase angle information theta of voltage vectorsCan be determined from gamma and rotor position angle thetarThe determination can be expressed as:
θs＝90°+δ+θr(14)
wherein, δ and θrThe expression of (c) can be expressed as:
wherein, P represents the number of pole pairs of the motor;
(26) outputting the obtained voltage vector signal u by a PI regulator through a coordinate transformation methodspAnd usqFrom phase angle information theta of the voltage vectorsAnd calculating a voltage vector u under α - β coordinate systemsαAnd usβThe conversion relationship is as follows:
wherein, thetasAs a voltage space vector usAngle to the α axis;
the direct power control method is a high-speed permanent magnet synchronous motor direct power control method based on space vector modulation, and the method specifically comprises the following steps:
(31) establishing a space vector modulation model
Assuming a calculated vector usIs a non-zero vector us1And us2Between and utilize us1Equivalent us2The equivalence relation is as follows:
us·Ts＝us1·Ts1+us2·Ts2(17)
wherein，TsRepresents a PWM cycle; t iss1And Ts2Each represents us1And us2The action time of (c);
(32) voltage vector u of α axissαVoltage vector u of axis βsβPerforming vector decomposition to obtain ideal voltage vector uαAnd uβThe equivalent relationship is rewritten as follows under the α - β coordinate system:
solving for exact Ts1And Ts2Fixed switching frequency can be realized;
(33) ideal voltage vector uαAnd uβOutputting three-phase current signals i through PWM inverterA、iB、iCSo as to regulate the amplitude of the stator current vector to change the instantaneous reactive power and output three-phase current iA、iB、iCObtaining a current vector i under α - β coordinate system through coordinate transformationαAnd iβAnd a voltage vector uαAnd uβThe instantaneous active power p and the instantaneous reactive power q are used as the input of the actual calculated instantaneous active power p and the instantaneous reactive power q together, and the closed-loop control of direct power control is realized.
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