CN104375083A - Noise testing method for multi-phase alternating-current permanent magnet motor with even number of units - Google Patents

Abstract

The invention discloses a noise testing method for a multi-phase alternating-current permanent magnet motor with an even number of units, and belongs to the technical field of motor testing. The noise testing method aims to solve the problem that accurate testing of noise of a motor system is affected due to the fact that load equipment needs to be additionally arranged when noise of the multi-phase permanent magnet synchronous motor with the even number of units is tested. When the noise of the motor is tested, one half of the N independently running units of the motor runs electrically to serve as an input power end, the other half of the N independently running units of the motor runs in a power-generating mode to serve as a power output end, and therefore on the condition of simulating the load of the motor, it is guaranteed that all the units of the motor run. The noise of the motor in a certain load state is tested equivalently by testing the noise of the motor and relevant motor parameters in the state and the noise of the motor in any output power state can be tested equivalently by simply changing load resistance of a power generating unit. The noise testing method is used for testing the noise of the multi-phase alternating-current permanent magnet motor with the even number of units.

Description

Heterogeneous even location AC magnetoelectric machine noise testing method

Technical field

The invention belongs to Motor Measuring Technology field.

Background technology

At present, the method for testing for permagnetic synchronous motor noise mainly contains sound-pressure-level measurement, sound intersity measurement, vibration-testing method these three kinds.These three kinds of method of testings test environment as requested and appointed condition, can measure the noise of motor comparatively preparatively, but also there are some problems for the noise testing of heavy-duty motor.Generally, the torque of testing of electric motors needs additional dynamometer machine or mechanical load device as load, this adds increased the appointed condition needed for test.For this running speed of high-power low-speed permagnetic synchronous motor lower (being generally no more than 200rpm), torque very large treat for measured motor, need very jumbo direct current generator and utility appliance thereof as load, some laboratory or research institute do not possess hundreds of kilowatts even the direct current generator load test condition of MW class, can not be completed this test.And after adding load, proving installation will be connected by motor and torque sensor, become motor, load and torque sensor series connection, add axial length, too increase the part of system, will affect the accurate test of electric system noise simultaneously.

Summary of the invention

When the object of the invention is to solve the noise testing heterogeneous even location permagnetic synchronous motor, need applied load equipment, and affect the accurate test problem of electric system noise, the invention provides a kind of heterogeneous even location AC magnetoelectric machine noise testing method.

Heterogeneous even location AC magnetoelectric machine noise testing method of the present invention,

The stator winding of described motor has N number of stand-alone unit, and each stand-alone unit is 3 symmetrical interchange windings, and the number of phases of described motor is 3N, wherein N be greater than 3 even number; Described method comprises the steps:

Step one: measure in the electric cycle, the curve that the self-induction of stator winding and mutual inductance change with rotor-position;

Step 2: utilize empty load of motor described in motor run to move to constant rotational speed, measures described motor winding wire back-emf now, and then carries air gap flux density by the waveshape clearancen of the line back-emf obtained;

Step 3:

The unloaded air gap flux density that the curve utilizing the three-phase current of described motor, step one to obtain and step 2 obtain, the motor gas-gap magnetic obtained under desired operation is close;

By N ₁individual stand-alone unit is used as generator unit, meanwhile, by remaining N ₂individual stand-alone unit is used as electrodynamic element, described generator unit generator operation, described electrodynamic element electric operation, the unloaded air gap flux density that the curve utilizing the three-phase current of the three-phase current of generator unit, electrodynamic element, step one to obtain and step 2 obtain, the motor gas-gap magnetic obtained under now running status is close;

According to motor produce the acoustical power of noise and the relation of air gap flux density, the acoustical power that motor under associated ideal running status produces noise therewith time running status under motor to produce the acoustical power of noise equal, and then obtain when electric machine phase current phase effective value is I, electrodynamic element phase current values effective value is I ' ₁, the phase current effective value of generator unit is I ' ₂;

Step 4: by described N ₁individual stand-alone unit all accesses pull-up resistor; Meanwhile, by described N ₂individual stand-alone unit connects driver, wherein, and N ₁=N ₂, N ₁+ N ₂=N;

Step 5: control and drive system brings into operation, by regulating load resistance, makes electrodynamic element phase current values be I ' ₁, the phase current values I ' of generator unit ₂;

Step 6: being that sound meter is placed at 1m place apart from the axis centre radius of described motor, utilize described sound meter to measure the noise of multiple measuring points that surrounding motors spacing is 1m; The mean value of the noise of described multiple measuring point is N number of stand-alone unit electric operation in loaded situation outside of motor, and noise of motor when electric machine phase current is I;

Step 7: change electric machine phase current phase effective value I according to demand, proceed to step 3.

In step one, measure in the electric cycle, the method for the curve that the self-induction of stator winding and mutual inductance change with rotor-position is:

Direct current is added in a stand-alone unit, motor is made to be in optional position, add the sinusoidal AC voltage signal with direct current biasing at phase winding two ends of described stand-alone unit, the component of voltage of direct current biasing is equal with the voltage of this phase winding under running status to be measured;

Measure the electric current of described phase winding and the electric current of other phase windings, thus the stator winding self-induction obtained when motor is in described position and the mutual inductance with other stator winding, change and add direct current vector in electric unit, make motor be in other positions, thus measure the curve that the self-induction of an electric cycle inner stator winding and mutual inductance change with rotor-position.

In step 3, the acoustical power that motor under desired operation produces noise therewith time running status under motor produce equal being embodied as of acoustical power of noise:

$\underset{i=1...n}{\mathrm{\Σ}}{\left({B^{\′}}_{i(\mathrm{\θ},t)}\right)}^4=\underset{i=1...n}{\mathrm{\Σ}}{B}_{i(\mathrm{\θ},t)}^4$

Wherein, B ' _{i (θ, t)}the air gap flux density on i-th stator tooth surface of motor time for this reason under running status, B _{i (θ, t)}for the air gap flux density on i-th stator tooth surface of the motor under desired operation; N is the stator number of teeth, and θ is the Space Angle angle value that distance first runs separate unit winding axis, and t is current time;

Motor gas-gap magnetic under described acquisition desired operation is close is:

$\begin{array}{c}{B}_{(\mathrm{\θ},t)}\·N_z\·S=B_{0\left(\mathrm{\θ}\right)}\·N_z\·S+i_{a\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}+\\ i_{b\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}+i_{c\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\end{array},$ Wherein, N _zfor each coil turn, S is each stator tooth area, B _{0 (θ)}for unloaded air gap flux density, i _{a (t)}, i _{b (t)}and i _{c (t)}be respectively the three-phase current of described motor, L _{am (θ)}, L _{bm (θ)}and L _{cm (θ)}be respectively the self-induction between each stand-alone unit three-phase windings or mutual inductance; A, b and c represent the three-phase of stand-alone unit respectively;

The motor gas-gap magnetic of described acquisition now under running status is close is:

$\begin{array}{c}{B^{\′}}_{(\mathrm{\θ},t)}\·N_z\·S=B_{0\left(\mathrm{\θ}\right)}\·N_z\·S+i_{a\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}\\ +i_{b\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}+i_{c\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\\ +i_{a\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}+i_{b\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}\\ +i_{c\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\end{array}$

Wherein, with for the three-phase current of generator unit, for the three-phase current of electrodynamic element.

Beneficial effect of the present invention is, the present invention utilizes the winding construction feature of heterogeneous even location permagnetic synchronous motor even location when testing of electric motors noise, part stand-alone unit electric operation can be utilized as power input end, part stand-alone unit generator operation is as output power end, thus when simulated machine in load, ensure that all unit of motor runs.Noise of motor under a certain load condition is tested out by testing noise of motor under this state and associated motor parameter equivalent, equivalence can test out noise under any output power state of motor by the pull-up resistor changing generator unit, thus not only equivalence tested out the noise of motor but also had eliminated additional load device.

Adopt the inventive method to realize in the test process of heterogeneous even location noise of motor, the casing of motor and shaft extension all need not specially be fixed, and also do not need load equipment.The series of advantages such as have that structure is simple, stable performance, data are reliable, can meet the needs of general permagnetic synchronous motor machine noise testing.

Accompanying drawing explanation

Fig. 1 is method testing principle schematic of the present invention.

Fig. 2 is the principle schematic of step 4 in embodiment one.

Fig. 3 is the structural representation of heterogeneous even location permagnetic synchronous motor of the present invention, and in figure, 1A, 1B and 1C represent that 3 of first stand-alone unit symmetrically exchange winding respectively; 2A, 2B and 2C represent that 3 of second stand-alone unit symmetrically exchange winding respectively; 3A, 3B and 3C represent that 3 of the 3rd stand-alone unit symmetrically exchange winding respectively; NA, NB and NC represent 3 of the N number of stand-alone unit symmetrical windings that exchange respectively; E represents motor stator, and f represents rotor, and g represents permanent magnet.

Embodiment

Embodiment one: composition graphs 1 to Fig. 3 illustrates present embodiment, heterogeneous even location AC magnetoelectric machine noise testing method described in present embodiment, the stator winding of described motor has N number of stand-alone unit, each stand-alone unit is 3 symmetrical interchange windings, the number of phases of described motor is 3N, wherein N be greater than 3 even number; Described method comprises the steps:

Step one: measure in the electric cycle, the curve that the self-induction of stator winding and mutual inductance change with rotor-position;

Step 2: utilize empty load of motor described in motor run to move to constant rotational speed, measures described motor winding wire back-emf now, and then carries air gap flux density by the waveshape clearancen of the line back-emf obtained;

Step 3:

The unloaded air gap flux density that the curve utilizing the three-phase current of described motor, step one to obtain and step 2 obtain, the motor gas-gap magnetic obtained under desired operation is close;

By N ₁individual stand-alone unit is used as generator unit, meanwhile, by remaining N ₂individual stand-alone unit is used as electrodynamic element, described generator unit generator operation, described electrodynamic element electric operation, the unloaded air gap flux density that the curve utilizing the three-phase current of the three-phase current of generator unit, electrodynamic element, step one to obtain and step 2 obtain, the motor gas-gap magnetic obtained under now running status is close;

According to motor produce the acoustical power of noise and the relation of air gap flux density, the acoustical power that motor under associated ideal running status produces noise therewith time running status under motor to produce the acoustical power of noise equal, and then obtain when electric machine phase current phase effective value is I, electrodynamic element phase current values effective value is I ' ₁, the phase current effective value of generator unit is I ' ₂;

Step 4: by described N ₁individual stand-alone unit all accesses pull-up resistor; Meanwhile, by described N ₂individual stand-alone unit connects driver, wherein, and N ₁=N ₂, N ₁+ N ₂=N;

Step 5: control and drive system brings into operation, by regulating load resistance, makes electrodynamic element phase current values be I ' ₁, the phase current values I ' of generator unit ₂;

Step 6: being that sound meter is placed at 1m place apart from the axis centre radius of described motor, utilize described sound meter to measure the noise of multiple measuring points that surrounding motors spacing is 1m; The mean value of the noise of described multiple measuring point is N number of stand-alone unit electric operation in loaded situation outside of motor, and noise of motor when electric machine phase current is I;

Step 7: change electric machine phase current phase effective value I according to demand, proceed to step 3.

The step 3 of present embodiment is the unloaded air gap flux density that the curve that utilizes the three-phase current of motor, step one to obtain and step 2 obtain, and the motor gas-gap magnetic under the state calculating motor gas-gap magnetic under a certain running status close and a part of unit generator operation and a part of unit electric operation is respectively close.The close motor three-phase current of rear a kind of motor gas-gap magnetic is variable, and the acoustical power under two states is equal, instead can release the electric current of each stand-alone unit under mechanical loading condition.Can realize motor at a part of unit generator operation by regulating load resistance, the electric current that under the state of a part of unit electric operation, unit motor passes into reaches the object of equivalent testing of electric motors noise.

Embodiment two: present embodiment is the further restriction to the heterogeneous even location AC magnetoelectric machine noise testing method described in embodiment one, in step, measure in the electric cycle, the method for the curve that the self-induction of stator winding and mutual inductance change with rotor-position is:

Direct current is added in a stand-alone unit, motor is made to be in optional position, add the sinusoidal AC voltage signal with direct current biasing at phase winding two ends of described stand-alone unit, the component of voltage of direct current biasing is equal with the voltage of this phase winding under running status to be measured;

Measure the electric current of described phase winding and the electric current of other phase windings, thus the stator winding self-induction obtained when motor is in described position and the mutual inductance with other stator winding, change and add direct current vector in electric unit, make motor be in other positions, thus measure the curve that the self-induction of an electric cycle inner stator winding and mutual inductance change with rotor-position.

Embodiment three: present embodiment is the further restriction to the heterogeneous even location AC magnetoelectric machine noise testing method described in embodiment one, in step 3, the acoustical power that motor under desired operation produces noise therewith time running status under motor produce equal being embodied as of acoustical power of noise:

$\underset{i=1...n}{\mathrm{\Σ}}{\left({B^{\′}}_{i(\mathrm{\θ},t)}\right)}^4=\underset{i=1...n}{\mathrm{\Σ}}{B}_{i(\mathrm{\θ},t)}^4$

Wherein, B ' _{i (θ, t)}the air gap flux density on i-th stator tooth surface of motor time for this reason under running status, B _{i (θ, t)}for the air gap flux density on i-th stator tooth surface of the motor under desired operation; N is the stator number of teeth, and θ is the Space Angle angle value that distance first runs separate unit winding axis, and t is current time;

Motor gas-gap magnetic under described acquisition desired operation is close is:

$\begin{array}{c}{B}_{(\mathrm{\θ},t)}\·N_z\·S=B_{0\left(\mathrm{\θ}\right)}\·N_z\·S+i_{a\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}+\\ i_{b\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}+i_{c\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\end{array},$ Wherein, N _zfor each coil turn, S is each stator tooth area, B _{0 (θ)}for unloaded air gap flux density, i _{a (t)}, i _{b (t)}and i _{c (t)}be respectively the three-phase current of described motor, L _{am (θ)}, L _{bm (θ)}and L _{cm (θ)}be respectively the self-induction between each stand-alone unit three-phase windings or mutual inductance; A, b and c represent the three-phase of stand-alone unit respectively;

The motor gas-gap magnetic of described acquisition now under running status is close is:

$\begin{array}{c}{B^{\′}}_{(\mathrm{\θ},t)}\·N_z\·S=B_{0\left(\mathrm{\θ}\right)}\·N_z\·S+i_{a\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}\\ +i_{b\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}+i_{c\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\\ +i_{a\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}+i_{b\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}\\ +i_{c\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\end{array}$

Wherein, with for the three-phase current of generator unit, for the three-phase current of electrodynamic element.

In present embodiment, motor produces the acoustical power of noise and the close relation following formula of motor gas-gap magnetic:

$L_{\mathrm{cy}}\∝\underset{i=1...n}{\mathrm{\Σ}}{B}_{i(\mathrm{\θ},t)}^4$

Wherein, L _cyfor the acoustical power of motor.

Claims (3)

1. heterogeneous even location AC magnetoelectric machine noise testing method, the stator winding of described motor has N number of stand-alone unit, and each stand-alone unit is 3 symmetrical interchange windings, and the number of phases of described motor is 3N, wherein N be greater than 3 even number; It is characterized in that, described method comprises the steps:

Step one: measure in the electric cycle, the curve that the self-induction of stator winding and mutual inductance change with rotor-position;

Step 2: utilize empty load of motor described in motor run to move to constant rotational speed, measures described motor winding wire back-emf now, and then carries air gap flux density by the waveshape clearancen of the line back-emf obtained;

Step 3:

The unloaded air gap flux density that the curve utilizing the three-phase current of described motor, step one to obtain and step 2 obtain, the motor gas-gap magnetic obtained under desired operation is close;

By N ₁individual stand-alone unit is used as generator unit, meanwhile, by remaining N ₂individual stand-alone unit is used as electrodynamic element, described generator unit generator operation, described electrodynamic element electric operation, the unloaded air gap flux density that the curve utilizing the three-phase current of the three-phase current of generator unit, electrodynamic element, step one to obtain and step 2 obtain, the motor gas-gap magnetic obtained under now running status is close;

According to motor produce the acoustical power of noise and the relation of air gap flux density, the acoustical power that motor under associated ideal running status produces noise therewith time running status under motor to produce the acoustical power of noise equal, and then obtain when electric machine phase current phase effective value is I, electrodynamic element phase current values effective value is I ₁', the phase current effective value of generator unit is I ₂';

Step 4: by described N ₁individual stand-alone unit all accesses pull-up resistor; Meanwhile, by described N ₂individual stand-alone unit connects driver, wherein, and N ₁=N ₂, N ₁+ N ₂=N;

Step 5: control and drive system brings into operation, by regulating load resistance, makes electrodynamic element phase current values be I ₁', the phase current values I of generator unit ₂';

Step 6: being that sound meter is placed at 1m place apart from the axis centre radius of described motor, utilize described sound meter to measure the noise of multiple measuring points that surrounding motors spacing is 1m; The mean value of the noise of described multiple measuring point is N number of stand-alone unit electric operation in loaded situation outside of motor, and noise of motor when electric machine phase current is I;

Step 7: change electric machine phase current phase effective value I according to demand, proceed to step 3.

2. heterogeneous even location AC magnetoelectric machine noise testing method according to claim 1, is characterized in that,

In step one, measure in the electric cycle, the method for the curve that the self-induction of stator winding and mutual inductance change with rotor-position is:

Direct current is added in a stand-alone unit, motor is made to be in optional position, add the sinusoidal AC voltage signal with direct current biasing at phase winding two ends of described stand-alone unit, the component of voltage of direct current biasing is equal with the voltage of this phase winding under running status to be measured;

Measure the electric current of described phase winding and the electric current of other phase windings, thus the stator winding self-induction obtained when motor is in described position and the mutual inductance with other stator winding, change and add direct current vector in electric unit, make motor be in other positions, thus measure the curve that the self-induction of an electric cycle inner stator winding and mutual inductance change with rotor-position.

3. heterogeneous even location AC magnetoelectric machine noise testing method according to claim 1, is characterized in that,

In step 3, the acoustical power that motor under desired operation produces noise therewith time running status under motor produce equal being embodied as of acoustical power of noise:

$\underset{i=1...n}{\mathrm{\Σ}}{\left({B^{\′}}_{i(\mathrm{\θ},t)}\right)}^4=\underset{i=1...n}{\mathrm{\Σ}}{B}_{i(\mathrm{\θ},t)}^4$

Wherein, B ' _{i (θ, t)}the air gap flux density on i-th stator tooth surface of motor time for this reason under running status, B _{i (θ, t)}for the air gap flux density on i-th stator tooth surface of the motor under desired operation; N is the stator number of teeth, and θ is the Space Angle angle value that distance first runs separate unit winding axis, and t is current time;

Motor gas-gap magnetic under described acquisition desired operation is close is:

$\begin{array}{c}{B}_{(\mathrm{\θ},t)}\·N_z\·S=B_{0\left(\mathrm{\θ}\right)}\·N_z\·S+i_{a\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}+\\ i_{b\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}+i_{c\left(t\right)}\·\underset{m=a,b,c,2a,2b,2c...\mathrm{Na},\mathrm{Nb},\mathrm{Nc}}{\mathrm{\Σ}}{L}_{\mathrm{cm}}\left(\mathrm{\θ}\right)\end{array},$ Wherein, N _zfor each coil turn, S is each stator tooth area, B _{0 (θ)}for unloaded air gap flux density, i _{a (t)}, i _{b (t)}and i _{c (t)}be respectively the three-phase current of described motor, L _{am (θ)}, L _{bm (θ)}and L _{cm (θ)}be respectively the self-induction between each stand-alone unit three-phase windings or mutual inductance; A, b and c represent the three-phase of stand-alone unit respectively;

The motor gas-gap magnetic of described acquisition now under running status is close is:

$\begin{array}{c}{B^{\′}}_{(\mathrm{\θ},t)}\·N_z\·S=B_{0\left(\mathrm{\θ}\right)}\·N_z\·S+i_{a\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{am}}\left(\mathrm{\θ}\right)\\ +i_{b\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{bm}\left(\mathrm{\θ}\right)}+i_{c\left(t\right)}^d\·\underset{m=a,b,c,2a,2b,2c...N_{1}a,N_{1}b,N_{1}c}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\\ +i_{a\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{3}c}{\mathrm{\Σ}}{L}_{\mathrm{am}\left(\mathrm{\θ}\right)}+i_{b\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b{,N}_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{bm}}\left(\mathrm{\θ}\right)\\ +i_{c\left(t\right)}^f\·\underset{m=a,b,c,2a,2b,2c...N_{2}a,N_{2}b,N_{2}c}{\mathrm{\Σ}}{L}_{\mathrm{cm}\left(\mathrm{\θ}\right)}\end{array}$

Wherein, with for the three-phase current of generator unit, for the three-phase current of electrodynamic element.