CN111931343B - Stability analysis method and system for permanent magnet synchronous motor driving system - Google Patents
Stability analysis method and system for permanent magnet synchronous motor driving system Download PDFInfo
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Abstract
The invention provides a stability analysis method and a system for a permanent magnet synchronous motor driving system, wherein the method comprises the following steps of establishing a permanent magnet synchronous motor driving system model, and further comprises the following steps: and according to the permanent magnet synchronous motor driving system model, carrying out stability analysis on the permanent magnet synchronous motor driving system by adopting a Nyquist stability criterion to obtain a stable condition of the permanent magnet synchronous motor driving system. The stability condition provided by the invention limits parameters such as a filter, a motor, a controller and the like, and provides a basis for the design of a permanent magnet synchronous motor driving system.
Description
Technical Field
The invention relates to the field of stability analysis, in particular to a stability analysis method and system for a permanent magnet synchronous motor driving system.
Background
The permanent magnet synchronous motor is widely applied to the fields of electric automobiles, fully electrically propelled ships, multi-electric airplanes and the like due to the advantages of high efficiency, high response, high power density and the like. The driving system of the permanent magnet synchronous motor is generally composed of an inverter, a controller and the permanent magnet synchronous motor, and is a complex nonlinear system. The permanent magnet synchronous motor generally adopts strict double closed loop control, so that the load power is constant, and the current rises when the voltage drops, thereby presenting a negative impedance characteristic. Research shows that negative impedance characteristics cause system stability to be reduced, even oscillation or collapse of bus voltage in severe cases, so that misoperation of protection equipment or damage of electric equipment is caused, and negative influence is brought to stable operation of the system. In response to these problems, many scholars have conducted extensive research, which can be mainly classified into large signal stability analysis and small signal stability analysis. And the large signal stability analysis adopts an equivalent negative resistance or a current source for analysis, and the system stability is analyzed according to a Lypunov stability criterion. The method is suitable for system stability analysis during low-frequency large-signal disturbance, and analysis of high-frequency small-signal disturbance is lacked. The method is suitable for analyzing the system stability under the condition of high-frequency small signal disturbance, but the analysis process is complex and the calculation difficulty is high.
Disclosure of Invention
The invention provides a stability analysis method and a system for a permanent magnet synchronous motor driving system, wherein the method establishes a system integral mathematical model, defines the system stability condition of the permanent magnet synchronous motor driving system, can simply, conveniently and quickly judge the stability of the system by judging whether a permanent magnet synchronous motor meets the stability condition, and provides a theoretical basis for the design of the permanent magnet synchronous motor driving system.
A first aspect of the present invention provides a stability analysis method for a permanent magnet synchronous motor driving system, the method including the steps of:
establishing a permanent magnet synchronous motor driving system model;
and according to the permanent magnet synchronous motor driving system model, carrying out stability analysis on the permanent magnet synchronous motor driving system by adopting a Nyquist stability criterion to obtain a stable condition of the permanent magnet synchronous motor driving system.
Preferably, the establishing of the permanent magnet synchronous motor driving system model comprises the following steps:
establishing a mathematical model and a small signal model of the permanent magnet synchronous motor;
establishing a mathematical model and a small signal model of the inverter;
establishing a mathematical model and a small signal model of the controller;
and establishing an admittance model of the permanent magnet synchronous motor driving system.
In any of the above schemes, preferably, the establishing a mathematical model and a small-signal model of the permanent magnet synchronous motor includes:
(11) Determining a stator current equation of the permanent magnet synchronous motor under a dq coordinate system as follows:
wherein i d 、i q Dq-axis stator currents, respectively; u. of d 、u q Dq-axis stator voltages, respectively; r is s Is stator resistance, L d 、L q Respectively, dq-axis inductance,. Psi f Being a permanent magnet flux linkage, omega e The electrical angular velocity of the motor;
(12) Performing Laplace transformation on a stator current equation of the permanent magnet synchronous motor in a dq coordinate system to obtain i d 、i q And u d 、u q Transfer function between:
(13) The dq-axis voltage current is represented in the form of X + δ X, where X is the steady-state operating point and δ X is the small signal disturbance. According to a stator current equation of the permanent magnet synchronous motor, the steady-state working point of the stator voltage is as follows:
the corresponding small signal model is: />
In any of the above aspects, preferably, the establishing a mathematical model and a small-signal model of the inverter includes:
(21) Defining a switching function S j ，j＝a,b,c；S j =1 denotes upper arm closed, S j =0 represents the lower arm closure, thus yielding:
wherein u is an 、u bn 、u cn Three-phase voltage of points a, b and c relative to the negative pole N of the power supply, u dc Is a dc supply voltage.
(22) For symmetrical three-phase loads, there is u on ＝(u an +u bn +u cn ) /3 wherein u on Is the voltage between the load neutral point O and the negative pole N of the power supply, and therefore has
Wherein u is ao 、u bo 、u co The point a, b and c are phase voltages relative to the neutral point O of the load.
(23) Since the inverter switching frequency is much higher than the motor frequency, the switching function S is adjusted j Approximated by duty cycle d j . Performing Park conversion on the formula obtained in the step (22) to obtain
Wherein d is d 、d q Is the duty cycle in dq coordinate system.
(24) Will d d 、d q And u dc Expressed in the form of X + δ X, the steady state operating point is, according to the formula obtained in step (23):
corresponding small-signal pattern is->
Wherein D is d 、D q 、U dc Are respectively d d 、d q And u dc Steady state operating point of (delta d) d 、δd q And δ u dc Corresponding small signal perturbations.
In any of the above aspects, preferably, the establishing a mathematical model and a small-signal model of the controller includes:
(31) The transfer function of the current loop PI controller is G c ＝K p +K i S, wherein K p And K i Respectively a scaling factor and an integration factor.
(32) And after the current given and the current feedback are compared, the output signal passes through a PI controller, and is used as dq axis voltage given after decoupling compensation. Thus, there are
The corresponding small signal model is
(33) The SVPWM modulation scheme can be regarded as an effect of superimposing a zero-sequence component on a corresponding SPWM modulation signal. According to the triangle similarity theorem, for j phase, j = a, b, c, the duty cycle
Wherein T is s Is one sampling period, T j For the on-time of the j-phase arm in a sampling period->
A given phase voltage at points a, b, c with respect to the negative pole N of the power supply, and a given phase voltage ^ based on points a, b, c with respect to the load neutral point O>
Has a zero sequence component e o I.e. is->
Thus, there are
(34) Performing Park transformation on the formula in (33) can obtain:
the corresponding small signal model is
In any of the above aspects, preferably, the establishing an admittance model of the permanent magnet synchronous motor drive system includes:
(41) For a PMSM drive system, there are times when power losses are neglected
Expressing the variables in the formula as X + δ X, and simplifying to obtain the system admittance Y:
(42) From the small-signal models established in (13), (24), (32), and (34), it can be found that:
(43) By substituting the formula in (42) into the formula for admittance Y in (41), Y = Y can be obtained d +Y q Wherein
(44) Let d-axis current be given as 0, U is known from the steady state model d ＝-ω e L q I q ，U dc I dc ＝3U q I q /2, mixing U with d ＝-ω e L q I q And U dc I dc ＝3U q I q The formula of substituting/2 into (43) can be obtained:
in any of the above schemes, preferably, the performing, according to the permanent magnet synchronous motor driving system model, the stability analysis on the permanent magnet synchronous motor driving system by using the Nyquist stability criterion includes:
establishing a transfer function of a driving system of the permanent magnet synchronous motor;
obtaining a permanent magnet synchronous motor driving system stability condition by adopting a Nyquist stability criterion and combining a permanent magnet synchronous motor driving system transfer function;
and analyzing the stability of the permanent magnet synchronous motor driving system according to the stable condition.
In any of the above aspects, preferably, establishing the transfer function of the driving system of the permanent magnet synchronous motor comprises:
according to an impedance analysis method, an admittance Y is used for a permanent magnet synchronous motor driving system to be equivalent, and an impedance Z is used for a direct current end filter in In an equivalent manner, the first and second electrodes,
R f is a line resistance, L f Is a filter inductor and C is a support capacitor.
According to circuit principles, the transfer function of the established system is:
wherein u is in Is the equivalent supply voltage.
In any of the above schemes, preferably, the method for obtaining the stability condition of the driving system of the permanent magnet synchronous motor by using a Nyquist stability criterion in combination with the transfer function of the driving system of the permanent magnet synchronous motor comprises:
in any of the above aspects, preferably, analyzing the stability of the permanent magnet synchronous motor driving system according to the stable condition includes: if the permanent magnet synchronous motor driving system meets the stable condition, the system is stable, or the value range of one or more components of the permanent magnet synchronous motor driving system is judged according to the stable condition, so that the system is stable.
A second aspect of the present invention provides a stability analysis system for a driving system of a permanent magnet synchronous motor, which is configured to operate the stability analysis method for a driving system of a permanent magnet synchronous motor to analyze the stability of the driving system of a permanent magnet synchronous motor.
The stability analysis method and the system for the permanent magnet synchronous motor driving system establish an overall mathematical model of the permanent magnet synchronous motor driving system, and perform stability analysis on the system based on an impedance analysis method. The overall mathematical model of the permanent magnet synchronous motor driving system comprises an inverter model, a motor model and a controller model; establishing a small signal model of the system according to a small signal analysis method, and establishing an admittance model of a permanent magnet synchronous motor driving system; establishing a transfer function model of the system according to an impedance analysis method, and limiting an open-loop transfer function phase angle according to a Nyquist stability criterion to meet the stability requirement; and finally, deducing the stability condition of the system in the whole frequency domain according to the mentioned phase angle limiting condition, thereby meeting the global stability requirement. The stability conditions limit parameters such as a filter, a motor, a controller and the like, and provide a basis for the design of a permanent magnet synchronous motor driving system.
Drawings
Fig. 1 is a schematic flow diagram of a stability analysis method for a permanent magnet synchronous motor drive system according to the present invention.
Fig. 2 is a block diagram of a driving system of a permanent magnet synchronous motor.
Fig. 3 is a three-phase inverter topology.
Fig. 4 is a schematic diagram of the SVPWM modulation process.
Fig. 5 is an overall mathematical model of a permanent magnet synchronous motor driving system for a stability analysis method of the permanent magnet synchronous motor driving system according to the present invention.
Fig. 6 is a small signal model of a permanent magnet synchronous motor driving system for a stability analysis method of the permanent magnet synchronous motor driving system according to the present invention.
Fig. 7 is an equivalent circuit diagram of a permanent magnet synchronous motor driving system for a stability analysis method of the permanent magnet synchronous motor driving system according to the present invention.
Fig. 8 is an admittance phase-frequency diagram of a permanent magnet synchronous motor driving system for a stability analysis method of a permanent magnet synchronous motor driving system according to the present invention.
Detailed Description
For a better understanding of the present invention, reference will now be made in detail to the following examples.
Example 1
As shown in fig. 1, a stability analysis method for a permanent magnet synchronous motor driving system, the method comprising the steps of:
s1, establishing a permanent magnet synchronous motor driving system model;
and S2, according to the permanent magnet synchronous motor driving system model, adopting a Nyquist stability criterion to perform stability analysis on the permanent magnet synchronous motor driving system to obtain a stable condition of the permanent magnet synchronous motor driving system.
Fig. 2 is a block diagram of a driving system of a permanent magnet synchronous motor, in which a dc bus supplies power to an inverter after passing through a filter, and the inverter converts dc power into three-phase ac power and supplies power to the motor. The controller adopts a double closed loop PI control structure, a rotating speed loop provides a given signal for q-axis current, and d-axis current is given and usually set to be 0 or determined according to the field weakening degree of the motor. In order to improve the control effect of the dq axis current, a voltage decoupling unit is usually added in a current loop, and a signal output by the current loop is subjected to decoupling compensation and then serves as a dq axis voltage given signal. And after the given voltage signal is converted to an alpha beta coordinate system, the voltage type inverter is controlled by adopting an SVPWM (space vector pulse width modulation) technology to supply power to the permanent magnet synchronous motor, so that the motor drive control is realized. It can be found that the driving system of the permanent magnet synchronous motor is a complex nonlinear system, and includes a motor, an inverter, a controller, and the like, so in step S1, when a driving system model of the permanent magnet synchronous motor is established, the motor, the inverter, and the controller need to be modeled separately.
In the step S1, the establishment of the permanent magnet synchronous motor driving system model comprises the following steps:
s11, establishing a mathematical model and a small signal model of the permanent magnet synchronous motor;
s12, establishing a mathematical model and a small signal model of the inverter;
s13, establishing a mathematical model and a small signal model of the controller;
and S14, establishing an admittance model of the permanent magnet synchronous motor driving system.
In step S11, the permanent magnet synchronous motor model adopts a typical mathematical model in dq coordinate system, and establishes a corresponding motor small signal model according to a small signal analysis method, including:
(11) Determining a stator current equation of the permanent magnet synchronous motor under a dq coordinate system as follows:
wherein i d 、i q Dq-axis stator currents, respectively; u. of d 、u q Dq-axis stator voltages, respectively; r is s Is stator resistance, L d 、L q Respectively, dq-axis inductance,. Psi f Is a permanent magnet flux linkage, omega e The electrical angular velocity of the motor;
(12) Performing Laplace transformation on a stator current equation of the permanent magnet synchronous motor in a dq coordinate system to obtain i d 、i q And u d 、u q Transfer function between:
(13) The dq-axis voltage current is represented in the form of X + δ X, where X is the steady-state operating point and δ X is the small signal disturbance. According to a stator current equation of the permanent magnet synchronous motor, the steady-state working point of the stator voltage is as follows:
the corresponding small signal model is: />
In step S12, a mathematical model and a small-signal model of the inverter are established. The inverter circuit topology is as shown in fig. 3, the inverter adopts a mean value model, a mathematical model under a dq coordinate system is established through Park conversion, and a small signal model of the inverter is established according to a small signal analysis method. The establishment of the mathematical model and the small signal model of the inverter comprises the following steps:
(21) Defining a switching function S j ，j＝a,b,c；S j =1 represents the upper arm closed, sj =0 represents the lower arm closed, thus obtaining:
wherein u is an 、u bn 、u cn Three-phase voltage of points a, b and c relative to the negative pole N of the power supply, u dc Is a dc supply voltage.
(22) For symmetrical three-phase loads, there is u on ＝(u an +u bn +u cn ) /3 wherein u on Is the voltage between the load neutral point O and the negative pole N of the power supply, and therefore has
Wherein u is ao 、u bo 、u co The points a, b and c are phase voltages relative to the load neutral point O.
(23) Since the inverter switching frequency is much higher than the motor frequency, the switching function S is adjusted j Approximated by duty cycle d j . Performing Park conversion on the formula obtained in the step (22) to obtain
Wherein d is d 、d q Is the duty cycle in dq coordinate system.
(24) Will d d 、d q And u dc Expressed in the form of X + δ X, the steady state operating point is, according to the formula obtained in step (23):
the corresponding small-signal pattern is->
Wherein D is d 、D q 、U dc Are respectively d d 、d q And u dc Steady state operating point of (delta d) d 、δd q And δ u dc Is correspondingly smallAnd (6) signal disturbance.
In step S13, a mathematical model and a small signal model of the controller are established. The controller comprises two links of PI control and SVPWM modulation. The current loop PI controller inputs signals for current giving and current feedback, the output signals are used as dq axis voltage giving after decoupling compensation, and the specific control process is shown in figure 2. A mathematical model of a PI control link and a corresponding small signal model can be established according to a control block diagram. The SVPWM modulation strategy modulates a given voltage signal output by the PI control link to complete waveform output, and the SVPWM modulation process is as shown in fig. 2. The SVPWM modulation scheme can be regarded as the effect of superimposing zero sequence component on the corresponding SPWM modulation signal, and the points a, b, and c can be regarded as the given phase voltage relative to the negative pole N of the power supply
And a given phase voltage ^ or relative to the load neutral point O at points a, b and c>
Has a zero sequence component e o Therefore, a mathematical relation between the duty ratio and the given phase voltage can be established, and a controller mathematical model under the dq coordinate system can be obtained after Park change. Similarly, a corresponding small-signal model can be established according to the small-signal method. The establishment of the mathematical model and the small signal model of the controller comprises the following steps:
(31) The transfer function of the current loop PI controller is G c ＝K p +K i S, wherein K p And K i Respectively a scaling factor and an integration factor.
(32) And after the current given and the current feedback are compared, the output signal passes through a PI controller and is used as dq axis voltage given after decoupling compensation. Thus, there are
The corresponding small signal model is
(33) Space(s)The vector pulse width modulation SVPWM modulation scheme can be regarded as an effect of superimposing a zero-sequence component on a corresponding SPWM modulation signal. According to the triangle similarity theorem, for j phase, j = a, b, c, the duty cycle
Wherein T is s Is one sampling period, T j For the on-time of the j-phase arm in a sampling period->
A given phase voltage at points a, b, c with respect to the negative pole N of the power supply, and a given phase voltage ^ based on points a, b, c with respect to the load neutral point O>
Has a zero sequence component e o I.e. is->
Thus, there are
(34) Performing Park transformation on the formula in (33) can obtain:
the corresponding small signal model is
In step S14, an admittance model of the driving system of the permanent magnet synchronous motor is established. The overall mathematical model of the permanent magnet synchronous motor driving system is shown in fig. 5, and comprises a dq axis model of the motor, the inverter and the controller, and the corresponding system small signal model is shown in fig. 6. Because the time constant of the rotating speed loop is far longer than that of the current loopThe constants, therefore, the speed loop can be ignored in building a small signal model of the controller, taking into account only the effect of the current loop. After the system model is built, respectively solving according to the small signal model of the system
Substituting into a calculation formula of the system admittance to obtain an expression of the system admittance Y. In particular, by giving the d-axis current 0, a further simplified admittance expression can be obtained. The establishment of the admittance model of the permanent magnet synchronous motor driving system comprises the following steps:
(41) For a PMSM drive system, there are times when power losses are neglected
Expressing the variables in the formula as X + δ X, and simplifying to obtain the system admittance Y:
(42) From the small-signal models established in (13), (24), (32), and (34), it can be found that:
(43) By substituting the formula in (42) into the formula for admittance Y in (41), Y = Y can be obtained d +Y q Wherein
(44) Let d-axis current be given as 0, U is known from the steady state model d ＝-ω e L q I q ，U dc I dc ＝3U q I q /2, mixing U with d ＝-ω e L q I q And U dc I dc ＝3U q I q The formula of substituting/2 into (43) can be obtained:
it should be understood that the above step numbers for establishing the driving system model of the permanent magnet synchronous motor are only used for distinguishing the steps, and not for limiting the sequence of the steps, and those skilled in the art may adaptively adjust the sequence of the steps according to actual situations, and these adjustments do not make the essence of the corresponding technical solution depart from the scope of the technical solution of the present invention, for example, the sequence of the steps S11 to S13 may be arbitrarily adjusted.
The expression of the system admittance Y shows that Y is formed by Y d And Y q Two parts of which Y d Is positive admittance, and Y q Then has a negative admittance characteristic, and in the low frequency band, the amplitude of Y is-I dc /U dc And the negative impedance characteristic can reduce the stability area of the system and even cause the instability of the system in severe cases, so that the stability analysis is carried out on the permanent magnet synchronous motor driving system by adopting a Nyquist stability criterion.
In step S2, according to the permanent magnet synchronous motor driving system model, performing stability analysis on the permanent magnet synchronous motor driving system by using a Nyquist stability criterion includes:
s21, establishing a transfer function of a driving system of the permanent magnet synchronous motor;
s22, obtaining a permanent magnet synchronous motor driving system stability condition by adopting a Nyquist stability criterion and combining a permanent magnet synchronous motor driving system transfer function;
and S23, analyzing the stability of the permanent magnet synchronous motor driving system according to the stable condition.
In step S21, a transfer function of the driving system of the permanent magnet synchronous motor is established.
According to the impedance analysis method, the driving system of the permanent magnet synchronous motor is equivalent to a circuit shown in fig. 7, the driving system of the permanent magnet synchronous motor is equivalent by admittance Y, thevenin is equivalent to the power supply side, and a direct current end filter is equivalent to impedance Z in ，
R f Is a line resistance, L f Is a filter inductor, C is a supporting capacitor, and the power supply voltage u s Is correspondingly equivalent to u in . According to the circuit principle, the closed loop transfer function of the system is established as follows: />
Open loop transfer function of Z in Y。
In step S22, obtaining the stability condition of the driving system of the permanent magnet synchronous motor by using a Nyquist stability criterion in combination with the transfer function of the driving system of the permanent magnet synchronous motor includes:
s221, according to a Nyquist stability criterion, Z in Y cannot encompass the (-1, j0) point, so Z in When the phase angle of Y is equal to +/-180 DEG, the amplitude value should be less than 1, namely Z in The intersection of Y with the real axis is to the right of the point (-1,j0).
In the low frequency band having Z in Y ω→0 ＝-I dc R f /U dc To make Z in Y amplitude is less than 1, and the conditions A and R are satisfied f ＜U dc /I dc 。
In the high frequency band having Z in Y ω→∞ And =0, located to the right of the (-1,j0) point.
At intermediate frequency band Z in The phase angle of Y is limited between (-180 degrees, 180 degrees), so that Z can be ensured in Y does not encompass the (-1,j0) point throughout the band.
Open loop transfer function Z for mid-range in Phase angle analysis was performed for Y: admittance Y of permanent magnet synchronous motor driving system is Y d And Y q Two parts are composed of Y q And Y d Is limited to (0 DEG, 180 DEG), the phase angle of admittance Y must be Y q And Y d The phase angle of (a) is shown in fig. 8 as the phase-frequency diagram of the admittance. According to Y q And Y d Is expressed by q /Y d Is represented by-A 1 (s)A 2 (s) wherein
A is to be 1 (s)、A 2 The phase angles of(s) are all limited to the range of (-90 °,0 °).
If limit A 1 The phase angle range of(s) is (-90 DEG, 0 DEG), and the conditions B and K need to be satisfied p >U q /I q 。
Substituting s = j ω into a 2 The expression for(s) can be found:
due to L d <L q ，A 2 The imaginary part of(s) is determined to be negative, such that A 2 The phase angle of(s) is in the range of (-90 deg., 0 deg.), and A is adjusted to 2 The real part of(s) is positive, and therefore the conditions C and (R) should be satisfied s +K p ) 2 >K i (L d +L q )。
The phase angle of admittance Y being at Y q And Y d And the upper limit of the angle is angle Y q Lower limit of less than Y d Thus, making Z in Y d Is greater than-180 DEG, Z in Y q The phase angle of (A) is less than 180 DEG, that is, Z can be ensured in The phase angle of Y is between (-180 deg., 180 deg.). Z in Has a phase angle range of (-90 deg., 90 deg.) and Y d The phase angle of (1) is in the range of (-90 °,90 °). Thus, Z in Y d The phase angle of (a) is greater than-180 °; substituting s = j ω into Y q And Z in Expression, expressed in complex form, of Z in Y q Is positive, then Z may be made in Y q Is always less than 180 deg.. Therefore, the conditions D,
In summary, satisfying conditions B, C, and D simultaneously in the IF range ensures an open-loop transfer function Z in The phase angle of Y is in the range of (-180 DEG, 180 DEG), and there is no intersection with the real axis, and at the same time, because Z is in The intersection points of Y and the real axis in the low-frequency and high-frequency bands are positioned on the right side of the point (-1, j0), which needs to be satisfiedCondition A, therefore, Z is the frequency domain when conditions A, B, C and D are satisfied in the entire frequency domain in The Y curve does not surround the (-1, j0) point, and the system is stable, namely the stable condition of the permanent magnet synchronous motor driving system is as follows:
in step S23, analyzing the stability of the driving system of the permanent magnet synchronous motor according to the stable condition includes: if the permanent magnet synchronous motor driving system meets the stability condition, the system is stable or the value range of one or more components of the permanent magnet synchronous motor driving system is judged according to the stability condition so as to keep the system stable.
Example 2
A stability analysis system for a permanent magnet synchronous motor driving system is used for operating the method for analyzing the stability of the permanent magnet synchronous motor driving system, and the stable condition of the permanent magnet synchronous motor driving system is determined. It should be understood that all or part of the steps of implementing the method for analyzing the stability of the driving system of the permanent magnet synchronous motor can be indicated by a computer program which can be stored in a non-volatile computer readable storage medium and can implement all or part of the steps of the method. If the stable condition of the permanent magnet synchronous motor driving system is stored in the nonvolatile computer readable storage medium, after the structural parameters of a certain permanent magnet synchronous motor driving system are input, the system automatically establishes a mathematical model for the permanent magnet synchronous motor driving system, and judges the value range of one or more components according to the comprehensive stable condition so as to keep the permanent magnet synchronous motor driving system stable.
It should be noted that the above embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the foregoing embodiments illustrate the invention in detail, those skilled in the art will appreciate that: it is possible to modify the technical solutions described in the foregoing embodiments or to substitute some or all of the technical features thereof, without departing from the scope of the technical solutions of the present invention.
Claims (2)
1. A stability analysis method for a permanent magnet synchronous motor drive system includes the steps of: the method for establishing the permanent magnet synchronous motor driving system model is characterized by further comprising the following steps: according to the permanent magnet synchronous motor driving system model, stability analysis is carried out on the permanent magnet synchronous motor driving system by adopting a Nyquist stability criterion, and a stability condition of the permanent magnet synchronous motor driving system is obtained;
the establishment of the permanent magnet synchronous motor driving system model comprises the following steps:
establishing a mathematical model and a small signal model of the permanent magnet synchronous motor;
establishing a mathematical model and a small signal model of the inverter;
establishing a mathematical model and a small signal model of the controller;
establishing an admittance model of a permanent magnet synchronous motor driving system;
the establishment of the mathematical model and the small signal model of the permanent magnet synchronous motor comprises the following steps:
(11) Determining a stator current equation of the permanent magnet synchronous motor in a dq coordinate system as follows:
wherein i d 、i q Dq-axis stator currents, respectively; u. of d 、u q Dq-axis stator voltages, respectively; r s Is stator resistance, L d 、L q Respectively, dq-axis inductance,. Psi f Is a permanent magnet flux linkage, omega e The electrical angular velocity of the motor;
(12) Performing Laplace transformation on a stator current equation of the permanent magnet synchronous motor in a dq coordinate system to obtain i d 、i q And u d 、u q Transfer function between:
(13) Respectively expressing the dq axis voltage and current into a form of X + delta X, wherein X is a steady-state working point, delta X is small signal disturbance, and according to a stator current equation of the permanent magnet synchronous motor, the steady-state working point of the stator voltage is as follows:
the corresponding small signal model is:
the establishment of the mathematical model and the small signal model of the inverter comprises the following steps:
(21) Defining a switching function S j ，j＝a,b,c；S j =1 denotes upper arm closed, S j =0 represents the lower arm closure, thus yielding:
wherein u is an 、u bn 、u cn Three-phase voltage of points a, b and c relative to the negative pole N of the power supply, u dc Is a direct current power supply voltage;
(22) For symmetrical three-phase loads, there is u on ＝(u an +u bn +u cn ) /3 wherein u on Is the voltage between the load neutral point O and the negative pole N of the power supply, and therefore has
Wherein u is ao 、u bo 、u co Phase voltages of points a, b and c relative to a load neutral point O;
(23) Since the inverter switching frequency is much higher than the motor frequency, the switching function S is adjusted j Approximated by duty cycle d j Performing Park conversion on the formula obtained in the step (22) to obtain
Wherein d is d 、d q Is the duty cycle in the dq coordinate system;
(24) Will d d 、d q And u dc Expressed in the form of X + δ X, the steady state operating point is, according to the formula obtained in step (23):
the corresponding small signal model is
Wherein D is d 、D q 、U dc Are respectively d d 、d q And u dc Steady state operating point of (delta d) d 、δd q And δ u dc Perturbing for a corresponding small signal;
the establishment of the mathematical model and the small signal model of the controller comprises the following steps:
(31) The transfer function of the current loop PI controller is G c ＝K p +K i S, wherein K p And K i Respectively a proportional factor and an integral factor;
(32) The current is given and compared with the current feedback, then the current passes through a PI controller, and the output signal is given as dq-axis voltage after decoupling compensation, so that
The corresponding small signal model is
(33) The SVPWM modulation scheme can be regarded as the effect of superimposing a zero-sequence component on the corresponding SPWM modulation signal, and according to the triangle similarity theorem, for j phase, j = a, b, c, the duty ratio
Wherein T is s Is one sampling period, T j For one mining of j-phase bridge armThe on-time within a sample period,
given phase voltages of points a, b and c relative to the negative pole N of the power supply and given phase voltages of points a, b and c relative to the neutral point O of the load
Has a zero sequence component e o I.e. by
(34) Performing Park transformation on the formula in (33) can obtain:
the corresponding small signal model is
The establishment of the admittance model of the permanent magnet synchronous motor driving system comprises the following steps:
(41) For a PMSM drive system, there are times when power losses are neglected
Expressing the variables in the formula as X + δ X, and simplifying to obtain the system admittance Y:
(42) From the small-signal models established in (13), (24), (32), and (34), it can be found that:
(43) By substituting the formula in (42) into the formula for admittance Y in (41), Y = Y can be obtained d +Y q In which
(44) Let d-axis current be given as 0, U is known from the steady state model d ＝-ω e L q I q ，U dc I dc ＝3U q I q /2, mixing U with d ＝-ω e L q I q And U dc I dc ＝3U q I q The formula of substituting/2 into (43) can be obtained:
according to the permanent magnet synchronous motor driving system model, the stability analysis of the permanent magnet synchronous motor driving system by adopting a Nyquist stability criterion comprises the following steps:
establishing a transfer function of a permanent magnet synchronous motor driving system;
obtaining a permanent magnet synchronous motor driving system stability condition by adopting a Nyquist stability criterion and combining a permanent magnet synchronous motor driving system transfer function;
analyzing the stability of the permanent magnet synchronous motor driving system according to the stable condition;
the method for establishing the transfer function of the permanent magnet synchronous motor driving system comprises the following steps:
according to an impedance analysis method, equivalence is carried out on an admittance Y for a permanent magnet synchronous motor driving system, and impedance Z for a direct current end filter in In an equivalent manner, the first and second electrodes,
R f is a line resistance, L f The filter inductor and the support capacitor are C, and according to the circuit principle, a transfer function of the system is established as follows:
wherein u is in Is an equivalent supply voltage;
and (2) obtaining the stability condition of the permanent magnet synchronous motor driving system by adopting a Nyquist stability criterion and combining the transfer function of the permanent magnet synchronous motor driving system as follows:
2. a stability analytic system for permanent magnet synchronous machine actuating system, its characterized in that: the stability analysis method for a permanent magnet synchronous motor driving system according to claim 1 is operated to analyze the stability of the permanent magnet synchronous motor driving system.
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