CN104393813A - Method for measuring direct-axis inductance of permanent magnet synchronous motor - Google Patents

Abstract

The invention discloses a method for measuring direct-axis inductance of permanent magnet synchronous motor, and belongs to the technical field of electric power and electronic. The method comprises the following steps: firstly, driving the permanent magnet synchronous motor twice by the same control method to achieve no-load steady state operations, wherein in two no-load steady state operation states, amplitudes of driving signals are different, while the frequencies of the driving signal are the same and are smaller than the fundamental frequency of the permanent magnet synchronous motor; secondly, according to currents and voltages of the driving signals in the two no-load steady state operation states, computing to obtain the direct-axis inductance. By the method, the direct-axis inductance of the permanent magnet synchronous motor can be measured relatively accurately, voltage detection equipment and a voltage detection component are not required additionally, and direct-axis positioning of the synchronous motor is not required; the method is simple in operation and strong in robustness.

Description

The d-axis inductance measurement method of permagnetic synchronous motor

Technical field

The present invention relates to a kind of basic parameter method of measurement of permagnetic synchronous motor, particularly relate to a kind of d-axis inductance measurement method of permagnetic synchronous motor, belong to electric and electronic technical field.

Background technology

Along with the application of Frequency Conversion and Speed Regulation Technique in synchronous machine, the range of application of synchronous machine is more and more extensive, conventional high performance variable frequency speed regulation control technology comprises the vector control technology of Speedless sensor and the technology of direct torque, these two kinds of control technologys are all based on the Mathematical Modeling of synchronous machine, need the parameter obtaining motor, such as: stator resistance, ac-dc axis inductance, linkage coefficient.

The method of traditional measurement d-axis inductance is to motor d direction of principal axis generating pressure pulse vector, carries out computing and obtains d axle electrical time constant, thus solve d axle inductance by sampling d shaft current and voltage.The method of this measurement d-axis inductance needs to sample before electric current stable state, measure accuracy not only with detect voltage and current precision about and also relevant with the measured value of the accuracy that the d axle of motor is located and stator resistance, affect the many factors of its accuracy.

Summary of the invention

Technical problem to be solved by this invention is to overcome the deficiencies in the prior art, provides one do not need d-axis to locate and additionally add measuring equipment, is easy to operation, the d-axis inductance measurement method of the permagnetic synchronous motor that accuracy of measurement is higher.

The present invention solves the problems of the technologies described above by the following technical solutions:

The d-axis inductance measurement method of permagnetic synchronous motor, is characterized in that, comprise the following steps:

Step 1, utilize same control method to drive permagnetic synchronous motor to realize unloaded steady operation at twice, the amplitude of the drive singal under twice unloaded steady-state operating condition is different, and frequency is the identical frequencies omega being less than described permagnetic synchronous motor fundamental frequency _r;

Step 2, calculate the d-axis inductance L of described permagnetic synchronous motor according to any one in following two formulas _sd:

$L_{\mathrm{sd}}=\frac{\sqrt{{U_2}^2-{R_s}^2{i_{\mathrm{sd}2}}^2}-\sqrt{{U_1}^2-{R_s}^2{i_{\mathrm{sd}1}}^2}}{(i_{\mathrm{sd}2}-i_{\mathrm{sd}1}){\mathrm{\ω}}_r},$

$L_{\mathrm{sd}}=\frac{U_1\sin {\mathrm{\θ}}_1-U_2\sin {\mathrm{\θ}}_2}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})},$

Wherein, R _sfor stator resistance; U ₁, U ₂be respectively the three-phase steady state voltage modulus value of drive singal under d-q coordinate system under twice unloaded steady-state operating condition; i _sd1, i _sd2be respectively the three-phase steady-state current modulus value of drive singal under d-q coordinate system under twice unloaded steady-state operating condition; θ ₁, θ ₂be respectively the angle between the voltage vector of the drive singal under twice unloaded steady-state operating condition and current phasor.

Compared to existing technology, the present invention has following beneficial effect:

The present invention is identical by twice frequency, voltage or the different empty load of motor steady operation of electric current, the d-axis inductance of synchronous machine can be solved by calculating according to voltage during twice unloaded stable state and electricity value, the inventive method can record the d-axis inductance of permagnetic synchronous motor more exactly, synchronous machine d-axis is not needed to locate, and the method is simple to operate, strong robustness.

Accompanying drawing explanation

Fig. 1 is the principle schematic of one embodiment of the invention;

Fig. 2 is three-phase current waveform when adopting the inventive method to carry out the linkage coefficient identification of 3KW synchronous machine;

Fig. 3 is voltage waveform when adopting the inventive method to carry out the linkage coefficient identification of 3KW synchronous machine.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in detail:

The linkage coefficient discrimination method of permagnetic synchronous motor of the present invention, comprises the following steps:

Step 1, utilize same control method to drive permagnetic synchronous motor to realize unloaded steady operation at twice, the amplitude of the drive singal under twice unloaded steady-state operating condition is different, and frequency is the identical frequencies omega being less than described permagnetic synchronous motor fundamental frequency _r;

Step 2, calculate the d-axis inductance L of described permagnetic synchronous motor according to any one in following two formulas _sd:

$L_{\mathrm{sd}}=\frac{\sqrt{{U_2}^2-{R_s}^2{i_{\mathrm{sd}2}}^2}-\sqrt{{U_1}^2-{R_s}^2{i_{\mathrm{sd}1}}^2}}{(i_{\mathrm{sd}2}-i_{\mathrm{sd}1}){\mathrm{\ω}}_r},$

$L_{\mathrm{sd}}=\frac{U_1\sin {\mathrm{\θ}}_1-U_2\sin {\mathrm{\θ}}_2}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})},$

Wherein, R _sfor stator resistance; U ₁, U ₂be respectively the three-phase steady state voltage modulus value of drive singal under d-q coordinate system under twice unloaded steady-state operating condition; i _sd1, i _sd2be respectively the three-phase steady-state current modulus value of drive singal under d-q coordinate system under twice unloaded steady-state operating condition; θ ₁, θ ₂be respectively the angle between the voltage vector of the drive singal under twice unloaded steady-state operating condition and current phasor.

Described control method preferably adopts voltage open-loop control method or closed-loop current control method.

Parameter U ₁, U ₂, i _sd1, i _sd2and θ ₁, θ ₂various existing method can be adopted to obtain, such as, U ₁, U ₂pass through three-phase voltage U _{abc_1}, U _{abc_2}obtained by coordinate transform, three-phase voltage U _{abc_1}, U _{abc_2}directly can be obtained by sampling, also can be calculated by voltage acquisition unit mentioned in this article and obtain; i _sd1, i _sd2, the three-phase current I to be exported by motor _{abc_1}, I _{abc_2}obtained by coordinate transform, I _{abc_1}, I _{abc_2}acquisition directly can measure and obtain, θ ₁, θ ₂the angle of electric current and voltage when being stable state, is by carrying out the calculating of DFT discrete Fourier to electric current and voltage, trying to achieve the phase angle of electric current and voltage, carries out by their phase angle the angle that mathematic interpolation obtains Two Variables.

For the ease of public understanding technical scheme of the present invention, with the permagnetic synchronous motor frequency converter control system based on PWM shown in Fig. 1, the inventive method is described in detail below.As shown in Figure 1, net side three-phase alternating-current supply and provide constant DC bus-bar voltage U through rectifier to dc-link capacitance _dc, inverter connects dc-link capacitance, control unit by control inverter threephase switch state, to voltage vector or the current phasor of motor output frequency and voltage or controlled current flow, to drive synchronous machine to run, ω _rfor the electric frequency of synchronous electric motor rotor.Current sampling unit measures A, B, C three-phase current i of synchronous machine _a, i _b, i _c.Voltage acquisition unit obtains busbar voltage by measurement, and according to brachium pontis duty ratio T on the three-phase of control unit output _a, T _b, T _c, obtain three-phase voltage by the computational methods mentioned in literary composition, so-called duty ratio T _a, T _b, T _cthe i.e. ratio of switch device conductive time and carrier cycle in a carrier wave.PWM is pwm unit, accepts the Duty ratio control instruction of the output of control unit, calculates on off state instruction in the output inverter cycle by pulse-width modulation, on off state instruction is 1 or 0,1 is conducting, and 0 for closing, and PWM unit is to the symbol description of inverter input switch instruction: S _a, S _b, S _cfor brachium pontis switch command on A, B, C three-phase; S _a, S _b, S _cfor brachium pontis switch command under A, B, C three-phase.Parameter calculation unit is the computing unit of parameter identification method in the present invention, passes through can be calculated DC inductance L according to the three-phase voltage obtained and three-phase current _dwith permanent magnet flux linkage coefficient ψ _r.

When empty load of motor, send twice different amplitude by control unit according to closed-loop current control (or voltage open loop control mode), frequency is ω _r(ω _rlower than the fundamental frequency of this synchronous machine, about being preferably the half of fundamental frequency) three-phase alternating current control signal, by the SVPWM module first backward motor injection drive singal of inverter, drive motors realizes unloaded stable operation, and the control voltage of no-load running is increasing magnetic direction.When motor to be synchronized operates in stable state, the current peak I of alternating current drive signal A, B, C phase under twice unloaded steady operational status of being sampled respectively by current sampling unit _{abc_1}, I _{abc_2}, obtained the steady state voltage U under twice unloaded steady operational status by voltage acquisition unit simultaneously _{abc_1}, U _{abc_2}.

Suppose that adopted voltage open loop control mode is constant voltage constant frequency control, i.e. the electric machine speed regulation control mode of V/f control, V is output voltage values, f=ω _r/ 2 π, the implementation procedure of this control mode is: make V/ ω _r=k, k are constant value, ω _rfor motor target frequency, control unit is according to target frequency ω _routput voltage amplitude is k* ω _raC voltage control signal, injecting amplitude by the SVPWM module of inverter to motor is k* ω _rfrequency be ω _rthree-phase alternating voltage.As adopted closed-loop current control mode as the speed-regulating controling mode of motor, then its implementation procedure is: after the current amplitude of the electric current of given amplitude and feedback is done deviation, calculate the amplitude providing output voltage through PI controller, inject this amplitude and given frequencies omega by the SVPWM module of inverter to motor _rthree-phase alternating voltage.

In the present embodiment, voltage acquisition unit calculates three-phase voltage according to the inverter three-phase service time of measuring busbar voltage and the control unit output obtained, and circular is:

$u_A=U_{\mathrm{dc}}(\frac{2}{3}{T}_a-\frac{1}{3}{T}_b-\frac{1}{3}{T}_c);u_B=U_{\mathrm{dc}}(\frac{2}{3}{T}_b-\frac{1}{3}{T}_a-\frac{1}{3}{T}_c);u_C=U_{\mathrm{dc}}(\frac{2}{3}{T}_c-\frac{1}{3}{T}_a-\frac{1}{3}{T}_b)$

U _dc: busbar voltage; T _a: A phase service time; T _b: B phase service time; T _c: C phase service time.

According to A, B, C three-phase current under twice unloaded steady-state operating condition that the three-phase voltage under twice unloaded steady-state operating condition that voltage acquisition unit obtains and current sampling unit obtain, the three-phase current peak I of twice unloaded steady-state operating condition down-sampling drive singal can be obtained _{abc_1}, I _{abc_2}with three-phase voltage peak value U _{abc_1}, U _{abc_2}, then to I _{abc_1}, I _{abc_2}, U _{abc_1}, U _{abc_2}carry out coordinate transform, the three-phase steady state voltage modulus value U of drive singal under d-q coordinate system under twice unloaded steady-state operating condition can be obtained ₁, U ₂and three-phase steady-state current modulus value i _sd1, i _sd2.By U ₁, U ₂, i _sd1, i _sd2and synchronous motor stator resistance R _ssubstitute into the d-axis inductance L that following formula can obtain permagnetic synchronous motor _sd:

$L_{\mathrm{sd}}=\frac{\sqrt{{U_2}^2-{R_s}^2{i_{\mathrm{sd}2}}^2}-\sqrt{{U_1}^2-{R_s}^2{i_{\mathrm{sd}1}}^2}}{(i_{\mathrm{sd}2}-i_{\mathrm{sd}1}){\mathrm{\ω}}_r}$

Or, by U ₁, U ₂, i _sd1, i _sd2and the angle theta between the voltage vector of drive singal under twice unloaded steady-state operating condition and current phasor ₁, θ ₂substitute into following formula, also can obtain the d-axis inductance L of permagnetic synchronous motor _sd:

$L_{\mathrm{sd}}=\frac{U_1\sin {\mathrm{\θ}}_1-U_2\sin {\mathrm{\θ}}_2}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})}$

θ ₁, θ ₂calculate the phase angle of electric current and voltage by the electric current of twice unloaded steady-state operating condition down-sampling and voltage through DFT (discrete Fourier transform (DFT)), electric current and voltage phase angle are subtracted each other the angle theta that can obtain electric current and voltage ₁, θ ₂.Wherein said DFT (discrete Fourier transform (DFT)) belongs to known technology, " power network harmonic wave management and reactive power compensation technology and equipment " of seeing that Luo An in 2006 writes.

In order to make the public more fully understand, below general principle of the present invention is described in detail.

When no-load running, the dynamic mathematical models of permagnetic synchronous motor under d-q coordinate system are:

$\left\{\begin{array}{c}{u}_{\mathrm{sd}}=R_s{i}_{\mathrm{sd}}+L_{\mathrm{sd}}{\mathrm{pi}}_{\mathrm{sd}}-{\mathrm{\ω}}_r{L}_{\mathrm{sq}}{i}_{\mathrm{sq}}\\ u_{\mathrm{sq}}={\mathrm{\ω}}_r{L}_{\mathrm{sd}}{i}_{\mathrm{sd}}+R_s{i}_{\mathrm{sq}}+L_{\mathrm{sq}}{\mathrm{pi}}_{\mathrm{sq}}+{\mathrm{\ω}}_r{\mathrm{\ψ}}_r\end{array}\right.---\left(1\right)$

Wherein, u _sd, u _sqd, q shaft voltage, i _sd, i _sqd, q shaft current, L _sd, L _sqd-axis, quadrature axis inductance, ω _rrotor speed, R _sstator resistance, ψ _rit is the linkage coefficient under d-q coordinate system.

During due to empty load of motor operation stable state, the differential term of electric current is zero, i.e. i _sq=0, then the synchronous machine dynamic mathematical models that represent of formula (1), can be reduced to:

$\left\{\begin{array}{c}{u}_{\mathrm{sd}}=R_s{i}_{\mathrm{sd}}\\ u_{\mathrm{sq}}={\mathrm{\ω}}_r{L}_{\mathrm{sd}}{i}_{\mathrm{sd}}+{\mathrm{\ω}}_r{\mathrm{\ψ}}_r\end{array}\right.---\left(2\right)$

Because under the static ABC coordinate when opened loop control of curtage can only obtain no-load running, the amplitude of phase current and the amplitude of voltage then can be obtained by formula (2)

u _sd ²+u _sq ²＝R _s ²i _sd ²+ω _r ²(L _sdi _sd+ψ _r) ²，

Due to U ²=u _sd ²+ u _sq ² the relational expression of phase voltage amplitude and phase current magnitude and magnetic linkage and d-axis inductance can be obtained:

U ²＝i _sd ²*R _s ²+ω _r ²(L _sdi _sd+ψ _r) ²(3)

If carry out closed-loop current control or the voltage opened loop control of twice same frequency, following equation can be obtained:

$\left\{\begin{array}{c}{U_1}^2={i_{\mathrm{sd}1}}^2*{R_s}^2+{{\mathrm{\ω}}_r}^2{(L_{\mathrm{sd}}{i}_{\mathrm{sd}1}+{\mathrm{\ψ}}_r)}^2\\ {U_2}^2={i_{\mathrm{sd}2}}^2*{R_s}^2+{{\mathrm{\ω}}_r}^2{(L_{\mathrm{sd}}{i}_{\mathrm{sd}2}+{\mathrm{\ψ}}_r)}^2\end{array}\right.---\left(4\right)$

Separate this equation and can try to achieve d-axis inductance and linkage coefficient expression formula, respectively such as formula shown in (5), formula (6):

$L_{\mathrm{sd}}=\frac{\sqrt{{U_2}^2-{R_s}^2{i_{\mathrm{sd}2}}^2}-\sqrt{{U_1}^2-{R_s}^2{i_{\mathrm{sd}1}}^2}}{(i_{\mathrm{sd}2}-i_{\mathrm{sd}1}){\mathrm{\ω}}_r}---\left(5\right)$

${\mathrm{\ψ}}_r=\frac{i_{\mathrm{sd}1}\sqrt{{U_2}^2-{i_{\mathrm{sd}2}}^2*{R_s}^2}-i_{\mathrm{sd}2}\sqrt{{U_2}^2-{i_{\mathrm{sd}1}}^2*{R_s}^2}}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})}---\left(6\right)$

Wherein, U ₁, U ₂, I _sd1, I _sd2for the voltage and current modulus value under twice unloaded steady-state operating condition under d-q coordinate, the I that this class value can record according to twice no-load test above _{abc_1}, I _{abc_2}, U _{abc_1}, U _{abc_2}, carry out obtaining after coordinate transform through parameter calculation unit; Because rotor speed during synchronous machine stable state is equal with stator rotating speed, stator rotating speed can be obtained and be the rotational speed omega that current-order provides _rcomputing unit obtains the phase voltage of phase current and the voltage acquisition unit recorded by current sampling unit, row-coordinate of going forward side by side conversion obtains calculating the required electric current of d-q coordinate and the amplitude of voltage, can calculate d-axis inductance and linkage coefficient according to formula (5) and formula (6).

Be by stator resistance as known quantity in formula (5) and formula (6), if do not obtain the measured value of stator resistance, so, the solution formula calculating linkage coefficient and d-axis inductance also can be:

$L_{\mathrm{sd}}=\frac{U_1\sin {\mathrm{\θ}}_1-U_2\sin {\mathrm{\θ}}_2}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})}---\left(7\right)$

${\mathrm{\ψ}}_r=\frac{i_{\mathrm{sd}1}{U}_2\sin {\mathrm{\θ}}_2-i_{\mathrm{sd}2}{U}_1\sin {\mathrm{\θ}}_1}{{\mathrm{\ω}}_r}---\left(8\right)$

Wherein θ ₁, θ ₂the angle of the voltage vector that the electric current of sampling when being twice unloaded stable state and voltage are tried to achieve through DFT computing (discrete Fourier calculating) and current phasor.

In order to verify the effect of the inventive method, utilize the inventive method to carry out the measurement of d-axis inductance, linkage coefficient to 3kw synchronous machine, and compare with instrument measurement method and anti-result of dragging experiment measuring method to obtain.Synchronous machine with certain frequency No Load Start, treat motor stabilizing after-current sampling unit obtain unloaded phase current and, voltage acquisition unit obtains phase voltage, and the three-phase current waveform obtained, voltage waveform are respectively as shown in Figure 2 and Figure 3; In the constant situation of frequency, change Current Control instruction, after motor stabilizing runs, current sampling unit obtains electric machine phase current, and voltage acquisition unit obtains phase voltage; The unloaded phase voltage of twice measurement and phase current, give parameter calculation unit and try to achieve linkage coefficient and d-axis inductance.

Current sampling unit sampling phase current, voltage acquisition unit obtains phase voltage, and the voltage and current peak value obtained for calculating is: U ₁=205V; U ₂=225V; i _sd1=5.612A; i _sd2=9.516A; Frequency f r=20Hz; ω _r=2*3.14*20=125.6 (rad); R _s=2.1 ohm is measured the known quantity obtained.Above parameter is substituted into formula (5), (6) calculates:

$L_d=\frac{\sqrt{{U_2}^2-{R_s}^2{i_{\mathrm{sd}2}}^2}-\sqrt{{U_1}^2-{R_s}^2{i_{\mathrm{sd}1}}^2}}{(i_{\mathrm{sd}2}-i_{\mathrm{sd}1}){\mathrm{\ω}}_r}=\frac{\sqrt{{225}^2-{2.1}^2*{9.516}^2}-\sqrt{{205}^2-{2.1}^2*{5.612}^2}}{(9.516-5.612)*(20*2*3.14)}=39.7\left(\mathrm{mh}\right)$

${\mathrm{\ψ}}_r=\frac{i_{\mathrm{sd}1}\sqrt{{U_2}^2-{i_{\mathrm{sd}2}}^2*{R_s}^2}-i_{\mathrm{sd}2}\sqrt{{U_1}^2-{i_{\mathrm{sd}1}}^2*{R_s}^2}}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})}=\frac{5.612*\sqrt{{225}^2-{9.516}^2*{2.1}^2}-9.516*\sqrt{{205}^2-{5.612}^2*{2.1}^2}}{2*3.14*20*(5.612-9.516)}=1.40$

Result and instrument measurement method and the anti-Comparative result of experiment measuring that drags is calculated as shown in table 1 by said method.

Table 1

Can find out that the measurement result of d-axis inductance measured by the inventive method and instrument measurement is substantially identical according to table 1, illustrate that the inventive method is effective.And comparing instrument measurement method, the present invention does not need extra voltage checkout equipment and element, simple to operate, realizes cost lower.

Claims (3)

1. the d-axis inductance measurement method of permagnetic synchronous motor, is characterized in that, comprise the following steps:

Step 1, utilize same control method to drive permagnetic synchronous motor to realize unloaded steady operation at twice, the amplitude of the drive singal under twice unloaded steady-state operating condition is different, and frequency is the identical frequencies omega being less than described permagnetic synchronous motor fundamental frequency _r;

Step 2, calculate the d-axis inductance L of described permagnetic synchronous motor according to any one in following two formulas _sd:

$L_{\mathrm{sd}}=\frac{\sqrt{{U_2}^2-{R_s}^2{i_{\mathrm{sd}2}}^2}-\sqrt{{U_1}^2-{R_s}^2{i_{\mathrm{sd}1}}^2}}{(i_{\mathrm{sd}2}-i_{\mathrm{sd}1}){\mathrm{\ω}}_r},$

$L_{\mathrm{sd}}=\frac{U_1\sin {\mathrm{\θ}}_1-U_2\sin {\mathrm{\θ}}_2}{{\mathrm{\ω}}_r(i_{\mathrm{sd}1}-i_{\mathrm{sd}2})},$

Wherein, R _sfor stator resistance; U ₁, U ₂be respectively the three-phase steady state voltage modulus value of drive singal under d-q coordinate system under twice unloaded steady-state operating condition; i _sd1, i _sd2be respectively the three-phase steady-state current modulus value of drive singal under d-q coordinate system under twice unloaded steady-state operating condition; θ ₁, θ ₂be respectively the angle between the voltage vector of the drive singal under twice unloaded steady-state operating condition and current phasor.

2. the d-axis inductance measurement method of permagnetic synchronous motor as claimed in claim 1, it is characterized in that, described control method is voltage open-loop control method or closed-loop current control method.

3. the d-axis inductance measurement method of permagnetic synchronous motor as claimed in claim 1, is characterized in that, U ₁, U ₂, i _sd1, i _sd2obtain by the following method: the three-phase current peak I obtaining drive singal respectively under twice unloaded steady-state operating condition _{abc_1}, I _{abc_2}with three-phase voltage peak value U _{abc_1}, U _{abc_2}, then to I _{abc_1}, I _{abc_2}, U _{abc_1}, U _{abc_2}carry out coordinate transform, namely obtain the three-phase steady state voltage modulus value U of drive singal under d-q coordinate system under twice unloaded steady-state operating condition ₁, U ₂and three-phase steady-state current modulus value i _sd1, i _sd2.