CN106026821A - Delta connection PMSM (permanent magnet synchronous motor) stator winding resistive unbalance fault diagnosis method - Google Patents

Abstract

The invention discloses a delta connection PMSM (permanent magnet synchronous motor) stator winding resistive unbalance fault diagnosis method, and the method comprises the following steps: S1, building the relation between zero sequence currents and a resistance deviation and the relation between phase currents and the resistance deviation, deducing the relation formula of the mean value of the zero sequence currents and the resistance deviation and the relation formula of the phase currents and the resistance deviation; S2, injecting three different DC signals into a direct-axis reference current in a two-phase rotating coordinate system, and recording the phase current and zero sequence current of a PMSM after each injection of the signals; S3, respectively calculating the mean values of phase currents and zero sequence currents recorded at three times, and estimating the deviations of stator winding resistance: delta Ra, delta Rb and delta Rc; S4, judging whether there is a resistive unbalance fault or not: judging that the A phase of the PMSM has the resistive unbalance fault if delta Ra is greater than zero; judging that the B phase of the PMSM has the resistive unbalance fault if delta Rb is greater than zero; judging that the C phase of the PMSM has the resistive unbalance fault if delta Rc is greater than zero.

Description

The unbalance fault of permanent-magnetic synchronous motor stator winding resistance that a kind of triangle connects is examined Disconnected method

Technical field

The present invention relates to fault diagnosis technology field, particularly relate to a kind of triangle connect permanent-magnetic synchronous motor stator around Group resistive imbalance fault diagnosis method.

Background technology

Permagnetic synchronous motor (Permanent magnet synchronous machine, PMSM) has power density The advantages such as high, efficiency is high, big, the speed-regulating range width of torque ratio of inertias.In recent years, high-power in wind-power electricity generation, elevator drives etc. And electric automobile and Digit Control Machine Tool etc. high-new can application scenario get the attention and use.

In permanent-magnetic synchronous motor stator winding failure, stator winding resistance is unbalance is a kind of common fault.When sending out When giving birth to unbalance fault in early days, motor still can continue to run with, if but can not detect in time and the aggravation of the causing trouble order of severity, Motor speed etc. can be caused to produce concussion, if this fault is not detected in the early stage, fault will increase the weight of, and makes motor Temperature is continuously increased, and finally results in motor and damages completely.Accordingly, it would be desirable to diagnose the stator winding event of permagnetic synchronous motor in time Barrier.

At present, it has been proposed that it is unbalance that certain methods diagnoses permanent-magnetic synchronous motor stator winding resistance, as fixed in utilized Triple-frequency harmonics method in electron current and residual voltage method etc..But existing method exists certain deficiency, it is on the one hand existing side Method mostly for the permagnetic synchronous motor of star-like connection, is poorly suited for the permagnetic synchronous motor that triangle connects；On the other hand In the case of heterogeneous breaking down, existing method mostly can not judge fault phase and the fault journey of the unbalance fault of resistive Degree.

Summary of the invention

The technical problem existed based on background technology, the permagnetic synchronous motor that the present invention proposes the connection of a kind of triangle is fixed Sub-winding resistance imbalance fault diagnosis method.

The permanent-magnetic synchronous motor stator winding resistance imbalance fault diagnosis method that the triangle that the present invention proposes connects, bag Include following steps:

S1, the relation set up between zero-sequence current and resistance shift amount, phase current and resistance shift amount, derive further Mathematic(al) representation between the meansigma methods of zero-sequence current and resistance shift amount, the meansigma methods of phase current and resistance shift amount；

S2, d-axis reference current injects in biphase rotating coordinate system three different direct current signals, and record every The phase current of the permagnetic synchronous motor after secondary Injection Signal and zero-sequence current；

S3, the meansigma methods of phase current calculating three records respectively and the meansigma methods of zero-sequence current, and substituted into S1 and push away In the mathematic(al) representation led, estimate offset Δ R of stator winding resistance_a、ΔR_b、ΔR_c；

S4, judge whether the unbalance fault of resistive: if Δ R_a> 0, show that permagnetic synchronous motor exists resistive unbalance Fault, and occur in A phase, and according to phase resistance deviation delta R_aEstimation fault degree；If Δ R_b> 0, show that permagnetic synchronous motor is deposited In the unbalance fault of resistive, and occur in B phase, and according to phase resistance deviation delta R_bEstimation fault degree；If Δ R_c> 0, show forever There is the unbalance fault of resistive in magnetic-synchro motor, and occurs in C phase, and according to phase resistance deviation delta R_cEstimation fault degree.

Preferably, the meansigma methods of derivation zero-sequence current and resistance shift amount, phase current meansigma methods and resistance shift amount it Between the method for mathematic(al) representation be:

Under abc coordinate system, the voltage equation of the magneto that triangle connects is represented by

$\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right]=\left[\begin{array}{ccc}{R}_a& 0& 0\\ 0& R_b& 0\\ 0& 0& R_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{ccc}L& M& M\\ M& L& M\\ M& M& L\end{array}\right]\frac{d}{dt}\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\mathrm{\λ}}_{PM,a}\\ {\mathrm{\λ}}_{PM,b}\\ {\mathrm{\λ}}_{PM,c}\end{array}\right]---\left(1\right)$

In formula: u_a、u_b、u_cFor threephase stator voltage, i_a、i_b、i_cFor threephase stator electric current, L is stator winding self-induction, and M is Stator winding mutual inductance；R_a、R_b、R_cFor threephase stator resistance, when there is not the unbalance fault of stator winding resistance in magneto, R_a、R_b、R_cIt is equal；When the unbalance fault of stator winding resistance occurs, R_a、R_b、R_cThe most equal；λ_PM,a、λ_PM,b、λ_PM,c Being the permanent magnet flux linkage of threephase stator winding, it is expressed as

$\left\{\begin{array}{c}{\mathrm{\λ}}_{PM,a}={\mathrm{\λ}}_{PM,1}\cos \left(\mathrm{\θ}\right)+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v)\\ {\mathrm{\λ}}_{PM,b}={\mathrm{\λ}}_{PM,1}\cos (\mathrm{\θ}-\frac{2\mathrm{\π}}{3})+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v-2v\frac{\mathrm{\π}}{3})\\ {\mathrm{\λ}}_{PM,c}={\mathrm{\λ}}_{PM,1}\cos (\mathrm{\θ}+\frac{2\mathrm{\π}}{3})+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v+2v\frac{\mathrm{\π}}{3})\end{array}\right.---\left(2\right)$

In formula: λ_PM,1Being the amplitude of first-harmonic magnetic linkage, v is overtone order, λ_PM,vBeing the amplitude of v subharmonic magnetic linkage, θ is rotor Electrical angle, θ_vIt it is the angle between v subharmonic magnetic linkage and first-harmonic magnetic linkage；

Every phase stator resistance is regarded as two parts constitute, be represented by

$\begin{array}{cc}\left\{\begin{array}{c}{R}_a=R_m+{\mathrm{\ΔR}}_a\\ R_b=R_m+{\mathrm{\ΔR}}_b\\ R_c=R_m+{\mathrm{\ΔR}}_c\end{array}\right.& R_m=\min \{R_a,R_b,R_c\}\end{array}---\left(3\right)$

According to Kirchhoff's second law, in the magneto that triangle connects, following equalities perseverance is set up

u_a+u_b+u_c=0 (4)

Formula (1) substituted into formula (4) and considers formula (3), can obtain

$R_m(i_a+i_b+i_c)+(L+2M)\frac{d(i_a+i_b+i_c)}{dt}+{\mathrm{\ΔR}}_a{i}_a+{\mathrm{\ΔR}}_b{i}_b+{\mathrm{\ΔR}}_c{i}_c+\frac{{\mathrm{d\λ}}_{PM,0}}{dt}=0---\left(5\right)$

In formula:

Definition zero-sequence current is

i_zsc=i_a+i_b+i_c (6)

Ignoring higher hamonic wave in stator current, stator current is represented by

$\left\{\begin{array}{c}{i}_a=I_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a)\\ i_b=I_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b)\\ i_c=I_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c)\end{array}\right.---\left(7\right)$

In formula: I_jAnd θ_j(j=a, b c) are respectively stator current i_jThe amplitude of middle first-harmonic and starting phase angle.

Formula (6) and (7) are substituted into formula (5), owing to only considering the first-harmonic composition in zero-sequence current, for simplifying the analysis, neglects Slightly λ_PM,0Differential, can obtain

$R_m{i}_{zsc}+(L+2M)\frac{{\mathrm{di}}_{zsc}}{dt}=-{\mathrm{\ΔR}}_a{I}_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a)-{\mathrm{\ΔR}}_b{I}_{b}sin(\mathrm{\θ}+{\mathrm{\θ}}_b)-{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c)---\left(8\right)$

Formula (8) is transformed to

$R_m{i}_{zsc}+{\mathrm{\ω}}_e(L+2M)\frac{{\mathrm{di}}_{zsc}}{d\mathrm{\θ}}=-{\mathrm{\ΔR}}_a{I}_a\sin (\mathrm{\θ}+{\mathrm{\θ}}_a)-{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b)-{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c)---\left(9\right)$

In formula: ω_e=d θ/dt is rotor angular rate.

In formula (9), if θ to be regarded as independent variable, i_zscSee that dependent variable, formula (9) are exactly the nonhomogeneous line of single order constant coefficient The property differential equation.Therefore, i_zscCan be calculated

$\begin{array}{c}{i}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}\left({\mathrm{\ΔR}}_a{I}_{a}sin\right(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})+{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ +{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ}))++{\mathrm{Ce}}^{\frac{-R_s}{{\mathrm{\ω}}_e(L+2M)}\mathrm{\θ}}\end{array}---\left(10\right)$

In formula: C is arbitrary constant, γ is expressed as

γ=tan^-1(-ω_e(L+2M)/R_s) (11)

When θ trends towards infinity, and last on the right of formula (11) equal sign is close to zero；Therefore, formula (11) is reduced to

$\begin{array}{c}{i}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}\left({\mathrm{\ΔR}}_a{I}_{a}sin\right(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})+{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ +{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ}))\end{array}---\left(12\right)$

For convenience of calculation, formula (12) can be transformed to

$i_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}({\mathrm{\ΔR}}_a{i}_a^{\′}+{\mathrm{\ΔR}}_b{i}_b^{\′}+{\mathrm{\ΔR}}_c{i}_c^{\′})---\left(13\right)$

In formula:

$\left\{\begin{array}{c}{i}_a^{\′}=I_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})\\ i_b^{\′}=I_{b}sin(\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ i_c^{\′}=I_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ})\end{array}\right.---\left(14\right)$

The meansigma methods of zero-sequence current can be expressed as

${\stackrel{\‾}{i}}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}({\mathrm{\ΔR}}_a{\stackrel{\‾}{i}}_a^{\′}+{\mathrm{\ΔR}}_b{\stackrel{\‾}{i}}_b^{\′}+{\mathrm{\ΔR}}_c{\stackrel{\‾}{i}}_c^{\′})$

The resistive imbalance fault diagnosis method that the present invention proposes, the most respectively d-axis reference electricity in biphase rotating coordinate system Stream injects three different direct current signals, and calculates the meansigma methods of the phase current of three records and the average of zero-sequence current respectively Being worth, then simultaneous formula sets up ternary linear function group, estimates the side-play amount of resistance, the side-play amount judgement finally according to resistance is No there is the unbalance fault of resistive, and estimate fault degree.The method that the present invention proposes is applicable to the permanent magnetism that triangle connects Synchronous motor, overcome the diagnostic method of fault unbalance to resistive in prior art mostly just for star-like connection permanent magnetism with The drawback of step motor；And method disclosed by the invention can heterogeneous break down simultaneously time, remain to judge resistive unbalance therefore The fault phase of barrier and estimate fault degree, and the present invention is without increasing extra detection equipment, has saved production cost Meanwhile, improve the specific aim to permanent-magnetic synchronous motor stator winding resistance imbalance fault diagnosis and reliability.

Accompanying drawing explanation

Fig. 1 is the frame of a kind of permanent-magnetic synchronous motor stator winding resistance imbalance fault diagnosis method that triangle connects Figure.

Detailed description of the invention

As it is shown in figure 1, the permanent-magnetic synchronous motor stator winding resistance that a kind of triangle that Fig. 1 is the present invention to be proposed connects Imbalance fault diagnosis method.

With reference to Fig. 1, the unbalance fault of permanent-magnetic synchronous motor stator winding resistance that the triangle that the present invention proposes connects is examined Disconnected method, comprises the following steps:

S1, the relation set up between zero-sequence current and resistance shift amount, phase current and resistance shift amount, derive further Mathematic(al) representation between the meansigma methods of zero-sequence current and resistance shift amount, the meansigma methods of phase current and resistance shift amount；

S2, d-axis reference current injects in biphase rotating coordinate system three different direct current signals, and record every The phase current of the permagnetic synchronous motor after secondary Injection Signal and zero-sequence current；

S3, the meansigma methods of phase current calculating three records respectively and the meansigma methods of zero-sequence current, and substituted into S1 and push away In the mathematic(al) representation led, estimate offset Δ R of stator winding resistance_a、ΔR_b、ΔR_c；

S4, judge whether the unbalance fault of resistive: if Δ R_a> 0, show that permagnetic synchronous motor exists resistive unbalance Fault, and occur in A phase, and according to phase resistance deviation delta R_aEstimation fault degree；If Δ R_b> 0, show that permagnetic synchronous motor is deposited In the unbalance fault of resistive, and occur in B phase, and according to phase resistance deviation delta R_bEstimation fault degree；If Δ R_c> 0, show forever There is the unbalance fault of resistive in magnetic-synchro motor, and occurs in C phase, and according to phase resistance deviation delta R_cEstimation fault degree.

The invention will be further described below:

According to Fig. 1, under abc coordinate system, the voltage equation of the magneto that triangle connects is represented by

$\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right]=\left[\begin{array}{ccc}{R}_a& 0& 0\\ 0& R_b& 0\\ 0& 0& R_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{ccc}L& M& M\\ M& L& M\\ M& M& L\end{array}\right]\frac{d}{dt}\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\mathrm{\λ}}_{PM,a}\\ {\mathrm{\λ}}_{PM,b}\\ {\mathrm{\λ}}_{PM,c}\end{array}\right]---\left(1\right)$

In formula: u_a、u_b、u_cFor threephase stator voltage, i_a、i_b、i_cFor threephase stator electric current, L is stator winding self-induction, and M is Stator winding mutual inductance.R_a、R_b、R_cFor threephase stator resistance, when magneto is health, R_a、R_b、R_cIt is equal；Work as stator When fault that winding resistance is unbalance occurs, R_a、R_b、R_cThe most equal.λ_PM,a、λ_PM,b、λ_PM,cIt it is the permanent-magnet magnetic of threephase stator winding Chain, it is expressed as

$\left\{\begin{array}{c}{\mathrm{\λ}}_{PM,a}={\mathrm{\λ}}_{PM,1}\cos \left(\mathrm{\θ}\right)+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v)\\ {\mathrm{\λ}}_{PM,b}={\mathrm{\λ}}_{PM,1}\cos (\mathrm{\θ}-\frac{2\mathrm{\π}}{3})+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v-2v\frac{\mathrm{\π}}{3})\\ {\mathrm{\λ}}_{PM,c}={\mathrm{\λ}}_{PM,1}\cos (\mathrm{\θ}+\frac{2\mathrm{\π}}{3})+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v+2v\frac{\mathrm{\π}}{3})\end{array}\right.---\left(2\right)$

In formula: λ_PM,1Being the amplitude of first-harmonic magnetic linkage, v is overtone order, λ_PM,vBeing the amplitude of v subharmonic magnetic linkage, θ is rotor Electrical angle, θ_vIt it is the angle between v subharmonic magnetic linkage and first-harmonic magnetic linkage；

Every phase stator resistance is regarded as two parts constitute, be represented by

$\begin{array}{cc}\left\{\begin{array}{c}{R}_a=R_m+{\mathrm{\ΔR}}_a\\ R_b=R_m+{\mathrm{\ΔR}}_b\\ R_c=R_m+{\mathrm{\ΔR}}_c\end{array}\right.& R_m=\min \{R_a,R_b,R_c\}\end{array}---\left(3\right)$

According to Kirchhoff's second law, in the magneto that triangle connects, following equalities perseverance is set up

u_a+u_b+u_c=0 (4)

Formula (1) substituted into formula (4) and considers formula (3), can obtain

$R_m(i_a+i_b+i_c)+(L+2M)\frac{d(i_a+i_b+i_c)}{dt}+{\mathrm{\ΔR}}_a{i}_a+{\mathrm{\ΔR}}_b{i}_b+{\mathrm{\ΔR}}_c{i}_c+\frac{{\mathrm{d\λ}}_{PM,0}}{dt}=0---\left(5\right)$

In formula:

Definition zero-sequence current is

i_zsc=i_a+i_b+i_c (6)

Ignoring higher hamonic wave in stator current, stator current is represented by

$\left\{\begin{array}{c}{i}_a=I_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a)\\ i_b=I_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b)\\ i_c=I_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c)\end{array}\right.---\left(7\right)$

In formula: I_jAnd θ_j(j=a, b c) are respectively stator current i_jThe amplitude of middle first-harmonic and starting phase angle.By formula (6) (7) substitute into formula (5), owing to only considering the first-harmonic composition in zero-sequence current, for simplifying the analysis, ignore λ_PM,0Differential, can ?

$R_m{i}_{zsc}+(L+2M)\frac{{\mathrm{di}}_{zsc}}{dt}=-{\mathrm{\ΔR}}_a{I}_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a)-{\mathrm{\ΔR}}_b{I}_{b}sin(\mathrm{\θ}+{\mathrm{\θ}}_b)-{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c)---\left(8\right)$

Formula (8) is transformed to

$R_m{i}_{zsc}+{\mathrm{\ω}}_e(L+2M)\frac{{\mathrm{di}}_{zsc}}{d\mathrm{\θ}}=-{\mathrm{\ΔR}}_a{I}_a\sin (\mathrm{\θ}+{\mathrm{\θ}}_a)-{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b)-{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c)---\left(9\right)$

In formula: ω_e=d θ/dt is rotor angular rate.

In formula (9), if θ to be regarded as independent variable, i_zscSee that dependent variable, formula (9) are exactly the nonhomogeneous line of single order constant coefficient The property differential equation.Therefore, i_zscCan be calculated

$\begin{array}{c}{i}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}\left({\mathrm{\ΔR}}_a{I}_{a}sin\right(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})+{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ +{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ}))++{\mathrm{Ce}}^{\frac{-R_s}{{\mathrm{\ω}}_e(L+2M)}\mathrm{\θ}}\end{array}---\left(10\right)$

In formula: C is arbitrary constant, γ is expressed as

γ=tan^-1(-ω_e(L+2M)/R_s) (11)

When θ trends towards infinity, and last on the right of formula (11) equal sign is close to zero；Therefore, formula (11) is reduced to

$\begin{array}{c}{i}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}\left({\mathrm{\ΔR}}_a{I}_{a}sin\right(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})+{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ +{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ}))\end{array}---\left(12\right)$

For convenience of calculation, formula (12) can be transformed to

$i_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}({\mathrm{\ΔR}}_a{i}_a^{\′}+{\mathrm{\ΔR}}_b{i}_b^{\′}+{\mathrm{\ΔR}}_c{i}_c^{\′})---\left(13\right)$

In formula:

$\left\{\begin{array}{c}{i}_a^{\′}=I_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})\\ i_b^{\′}=I_{b}sin(\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ i_c^{\′}=I_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ})\end{array}\right.---\left(14\right)$

The meansigma methods of zero-sequence current can be expressed as

${\stackrel{\‾}{i}}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}({\mathrm{\ΔR}}_a{\stackrel{\‾}{i}}_a^{\′}+{\mathrm{\ΔR}}_b{\stackrel{\‾}{i}}_b^{\′}+{\mathrm{\ΔR}}_c{\stackrel{\‾}{i}}_c^{\′})---\left(15\right)$

From formula (7) and (14) it can be seen that i'_a、i'_b、i'_cWith i_a、i_b、i_cSimply differ certain phase angle, therefore, In one cycle, both meansigma methodss are approximately equalised.Due to ω_e、L、M、R_mIt is all known variable, therefore, according to formula (15) have only to inject three different direct current signals knowable to, and record the zero-sequence current i in the case of three kinds_zscAnd phase current i_a、i_b、i_c, then calculate its meansigma methods, substitute into formula (15) and solve ternary linear function group, just can obtain phase resistance deviation delta R_a、ΔR_b、ΔR_c, just can complete stator winding resistance imbalance fault diagnosis, location and fault by observing phase resistance deviation The estimation of degree.Detailed process is as follows: when phase resistance deviation delta R_a> 0 time, show that permagnetic synchronous motor has the unbalance fault of resistive Occur in A phase, and according to phase resistance deviation delta R_aEstimation fault degree；When phase resistance deviation delta R_b> 0 time, show permanent magnet synchronous electric Machine has the unbalance fault of resistive to occur in B phase, and according to phase resistance deviation delta R_bEstimation fault degree；When phase resistance deviation delta R_c> When 0, show that permagnetic synchronous motor has the unbalance fault of resistive to occur in C phase, and according to phase resistance deviation delta R_cEstimation fault journey Degree；When phase resistance deviation delta R_a、ΔR_b、ΔR_cDuring no more than 0, show that permagnetic synchronous motor does not exist stator winding resistance Unbalance fault, permagnetic synchronous motor is in normal operating condition.

The above, the only present invention preferably detailed description of the invention, but protection scope of the present invention is not limited thereto, Any those familiar with the art in the technical scope that the invention discloses, according to technical scheme and Inventive concept equivalent or change in addition, all should contain within protection scope of the present invention.

Claims (2)

1. the permanent-magnetic synchronous motor stator winding resistance imbalance fault diagnosis method that a triangle connects, it is characterised in that Comprise the following steps:

S1, the relation set up between zero-sequence current and resistance shift amount, phase current and resistance shift amount, derive zero sequence further Mathematic(al) representation between the meansigma methods of electric current and resistance shift amount, the meansigma methods of phase current and resistance shift amount；

S2, d-axis reference current injects in biphase rotating coordinate system three different direct current signals, and record every time note Enter phase current and the zero-sequence current of the permagnetic synchronous motor after signal；

S3, the meansigma methods calculating the phase current of three records respectively and the meansigma methods of zero-sequence current, and substituted into what S1 derived In mathematic(al) representation, estimate offset Δ R of stator winding resistance_a、ΔR_b、ΔR_c；

S4, judge whether the unbalance fault of resistive: if Δ R_a> 0, show that permagnetic synchronous motor exists the unbalance fault of resistive, And occur in A phase, and according to phase resistance deviation delta R_aEstimation fault degree；If Δ R_b> 0, show that permagnetic synchronous motor exists resistance Property unbalance fault, and occur in B phase, and according to phase resistance deviation delta R_bEstimation fault degree；If Δ R_c> 0, show permanent-magnet synchronous There is the unbalance fault of resistive in motor, and occurs in C phase, and according to phase resistance deviation delta R_cEstimation fault degree.

The permanent-magnetic synchronous motor stator winding resistance imbalance fault diagnosis side that triangle the most according to claim 1 connects Method, it is characterised in that between the meansigma methods of derivation zero-sequence current and resistance shift amount, the meansigma methods of phase current and resistance shift amount The method of mathematic(al) representation be:

Under abc coordinate system, the voltage equation of the magneto that triangle connects is expressed as

$\left[\begin{array}{c}{u}_a\\ u_b\\ u_c\end{array}\right]=\left[\begin{array}{ccc}{R}_a& 0& 0\\ 0& R_b& 0\\ 0& 0& R_c\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\left[\begin{array}{ccc}L& M& M\\ M& L& M\\ M& M& L\end{array}\right]\frac{d}{dt}\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\mathrm{\λ}}_{PM,a}\\ {\mathrm{\λ}}_{PM,b}\\ {\mathrm{\λ}}_{PM,c}\end{array}\right]---\left(1\right)$

In formula: u_a、u_b、u_cFor threephase stator voltage, i_a、i_b、i_cFor threephase stator electric current, L is stator winding self-induction, and M is stator Winding mutual inductance；R_a、R_b、R_cFor threephase stator resistance, when magneto does not exist the unbalance fault of stator winding resistance, R_a、R_b、 R_cIt is equal；When the unbalance fault of stator winding resistance occurs, R_a、R_b、R_cThe most equal；λ_PM,a、λ_PM,b、λ_PM,cIt it is three-phase The permanent magnet flux linkage of stator winding, it is expressed as

$\left\{\begin{array}{c}{\mathrm{\λ}}_{PM,a}={\mathrm{\λ}}_{PM,1}\cos \left(\mathrm{\θ}\right)+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v)\\ {\mathrm{\λ}}_{PM,b}={\mathrm{\λ}}_{PM,1}\cos (\mathrm{\θ}-\frac{2\mathrm{\π}}{3})+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v-2v\frac{\mathrm{\π}}{3})\\ {\mathrm{\λ}}_{PM,c}={\mathrm{\λ}}_{PM,1}\cos (\mathrm{\θ}+\frac{2\mathrm{\π}}{3})+\underset{v=2k+1}{\Σ}{\mathrm{\λ}}_{PM,v}\cos (v\mathrm{\θ}-{\mathrm{\θ}}_v+2v\frac{\mathrm{\π}}{3})\end{array}\right.---\left(2\right)$

In formula: λ_PM,1Being the amplitude of first-harmonic magnetic linkage, v is overtone order, λ_PM,vBeing the amplitude of v subharmonic magnetic linkage, θ is rotor electric angle Degree, θ_vIt it is the angle between v subharmonic magnetic linkage and first-harmonic magnetic linkage；

Every phase stator resistance is regarded as two parts constitute, be expressed as

$\left\{\begin{array}{c}{R}_a=R_m+{\mathrm{\ΔR}}_a\\ R_b=R_m+{\mathrm{\ΔR}}_b\\ R_c=R_m+{\mathrm{\ΔR}}_c\end{array}\right.,R_m=min\{R_a,R_b,R_c\}---\left(3\right)$

According to Kirchhoff's second law, in the magneto that triangle connects, following equalities perseverance is set up

u_a+u_b+u_c=0 (4)

Formula (1) is substituted into formula (4) and considers formula (3),

$R_m(i_a+i_b+i_c)+(L+2M)\frac{d(i_a+i_b+i_c)}{dt}+{\mathrm{\ΔR}}_a{i}_a+{\mathrm{\ΔR}}_b{i}_b+{\mathrm{\ΔR}}_c{i}_c+\frac{{\mathrm{d\λ}}_{PM,0}}{dt}=0---\left(5\right)$

In formula:

Definition zero-sequence current is

i_zsc=i_a+i_b+i_c (6)

Ignoring higher hamonic wave in stator current, stator current is expressed as

$\left\{\begin{array}{c}{i}_a=I_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a)\\ i_b=I_{b}sin(\mathrm{\θ}+{\mathrm{\θ}}_b)\\ i_c=I_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c)\end{array}\right.---\left(7\right)$

In formula: I_jAnd θ_j(j=a, b c) are respectively stator current i_jThe amplitude of middle first-harmonic and starting phase angle；

Formula (6) and (7) are substituted into formula (5), only considers the first-harmonic composition in zero-sequence current, ignore λ_PM,0Differential,

$R_m{i}_{zsc}+(L+2M)\frac{{\mathrm{di}}_{zsc}}{dt}=-{\mathrm{\ΔR}}_a{I}_a\sin (\mathrm{\θ}+{\mathrm{\θ}}_a)-{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b)-{\mathrm{\ΔR}}_c{I}_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c)---\left(8\right)$

Formula (8) is transformed to

$R_m{i}_{zsc}+{\mathrm{\ω}}_e(L+2M)\frac{{\mathrm{di}}_{zsc}}{d\mathrm{\θ}}=-{\mathrm{\ΔR}}_a{I}_a\sin (\mathrm{\θ}+{\mathrm{\θ}}_a)-{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b)-{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c)---\left(9\right)$

In formula: ω_e=d θ/dt is rotor angular rate.

In formula (9) as, θ is regarded independent variable, i_zscSee dependent variable, obtain:

$\begin{array}{c}{i}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}\left({\mathrm{\ΔR}}_a{I}_a\sin \right(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})+{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ +{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ}))++{\mathrm{Ce}}^{\frac{-R_s}{{\mathrm{\ω}}_e(L+2M)}\mathrm{\θ}}\end{array}---\left(10\right)$

In formula: C is arbitrary constant, γ is expressed as

γ=tan^-1(-ω_e(L+2M)/R_s) (11)

Making θ trend towards infinity, formula (11) is reduced to

$\begin{array}{c}{i}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}\left({\mathrm{\ΔR}}_a{I}_a\sin \right(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})+{\mathrm{\ΔR}}_b{I}_b\sin (\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ +{\mathrm{\ΔR}}_c{I}_c\sin (\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ}))\end{array}---\left(12\right)$

For convenience of calculation, formula (12) is transformed to

$i_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}({\mathrm{\ΔR}}_a{i}_a^{\′}+{\mathrm{\ΔR}}_b{i}_b^{\′}+{\mathrm{\ΔR}}_c{i}_c^{\′})---\left(13\right)$

In formula:

$\left\{\begin{array}{c}{i}_a^{\′}=I_{a}sin(\mathrm{\θ}+{\mathrm{\θ}}_a+\mathrm{\π}+\mathrm{\γ})\\ i_b^{\′}=I_{b}sin(\mathrm{\θ}+{\mathrm{\θ}}_b+\mathrm{\π}+\mathrm{\γ})\\ i_c^{\′}=I_{c}sin(\mathrm{\θ}+{\mathrm{\θ}}_c+\mathrm{\π}+\mathrm{\γ})\end{array}\right.---\left(14\right)$

The meansigma methods of zero-sequence current is expressed as

${\stackrel{\‾}{i}}_{zsc}=\frac{1}{\sqrt{{\left({\mathrm{\ω}}_e\right(L+2M\left)\right)}^2+{R_m}^2}}({\mathrm{\ΔR}}_a{\stackrel{\‾}{i}}_a^{\′}+{\mathrm{\ΔR}}_b{\stackrel{\‾}{i}}_b^{\′}+{\mathrm{\ΔR}}_c{\stackrel{\‾}{i}}_c^{\′}).$