JP3345990B2 - Calculation method and display method of secondary current of induction motor - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a secondary current generated in a rotor winding of an induction motor, and more particularly to an induction motor for calculating a secondary current by numerically analyzing an in-machine magnetic field of the induction motor. The present invention relates to a secondary current calculation method and a display method.

[0002]

2. Description of the Related Art As an example of calculating a secondary current in an induction motor as an induction current by numerically analyzing an in-machine magnetic field at each minute time step, an example of an induction motor is described as "Induction Mo."
tor Analysis by Time-Stepping Techniques, IEEE Tra
ns. on Magnetics, Vol. 24, No. 1 (1988) "," Analysis of Magnetic Fields and Characteristics of Single-Phase Induction Motors by Finite Element Method, IEEJ Transactions D, Vol. 107, pp. 1236 (1987) " is there. These methods employ a technique of numerically analyzing the in-machine magnetic field by a finite element method, and further performing an unsteady analysis of a secondary current based on a time difference between vector potentials calculated for each minute time step.

[0003]

In the above prior art, when calculating the waveform over one cycle of the secondary current, the former requires an enormous amount of computer processing time and data as described by the author himself in the article. It requires memory to store and computer usage costs. This is because the time period of the secondary current in the induction motor becomes several tens to several hundred times the primary current period, and the number of minute time steps required for the magnetic field analysis becomes enormous. On the other hand, in the latter, the secondary current is calculated by setting the time interval of the minute time step longer than in the former, but relatively higher-order harmonics generated by the influence of the phase arrangement of the stator winding and the slot opening are used. Since the components cannot be considered, the accuracy is insufficient. In particular, there is a problem that the application becomes inapplicable when a harmonic component is a problem.

The present invention has been made in view of the above points, and by calculating one cycle of the secondary current from the result of the calculation of the secondary current by the magnetic field analysis of the secondary current time cycle or less,
It is an object of the present invention to provide a method for calculating a secondary current of an induction motor and a method for displaying the same with high accuracy, taking into account even higher harmonic components, while making the calculation time and memory much smaller than in the past.

[0005]

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for calculating and displaying a secondary current flowing through a secondary winding of an induction motor, in which a movement of an object is considered in a field where an eddy current occurs and a moving boundary condition. Magnetic field analyzing means, means for extracting the secondary current from the magnetic field analyzing means, and time, position and phase from each secondary current flowing through each of the secondary windings extracted by the secondary current extracting means. A secondary current calculation method comprising a means for calculating the secondary current taking into account, and a secondary current display method for an induction motor, characterized in that time and a secondary current amount are displayed from the calculation method, Moreover,
This is achieved by harmonic analysis and display of the calculated amount of secondary current.

In the above-mentioned means, in the secondary current calculation method and the display method of the induction motor for discretely calculating the secondary current of the induction motor as an eddy current, that is, an induction current, the slip s of the rotor in the magnetic field analysis is calculated. , A multiple of the primary current time period n _s (n _s : integer), the number of rotor slots N _{s2 (2p)} per two poles of the machine to be analyzed (N _{s2 (2p)} : integer), and the primary current time times n _s The number of rotor slots N _2tl (N _2tl) rotated behind the synchronous speed of the magnetic field generated by the stator winding during the cycle.
Integer), s = represents _{N 2tl / (n s · N} s2 (2p)) becomes the relationship, to set the amount of time between the magnetic field analysis time so that n _s times of at least the primary current time period, the Each of the secondary currents generated in each of the rotor windings during the analysis time is synthesized in time series in accordance with the moving state of the rotor slot, and one cycle of the secondary current is calculated and displayed. do it.

[0007]

As described above, the magnetic field analyzing means, the means for extracting the secondary current from the magnetic field analyzing means, and the secondary current flowing through each of the secondary windings extracted by the secondary current extracting means are used. By means for calculating the secondary current in consideration of time, position and phase, it is possible to calculate the secondary current of the induction motor in a much shorter time and with higher accuracy than in the past. Further, by displaying the calculation result of the secondary current obtained by the calculation method with respect to the time and the amount of the secondary current, it is possible to accurately confirm the calculation result of the secondary current. In addition, by performing harmonic analysis on the secondary current calculation result, the secondary current calculation result can be evaluated with higher accuracy.

[0008]

An embodiment of the present invention will be described below with reference to the drawings.

[0009] In general, machine magnetic field analysis of the induction motor, the analysis start time and the analysis end time analysis period determined by the T _a of magnetic field analysis (in seconds), the number of rotor slots per two poles N _{s2 ( 2p)} and the rotor is 2π / N in electrical angle.
Assuming that the rotation is n _r times _{s2 (2p)} (one slot pitch expressed in electrical angle), the following relational expression holds.

2π (1−s) T _a = n _r · 2π / N _{s2 (2p) (Equation} 1) From this, the slip s that can be analyzed is determined by the analysis cycle _Ta and the rotation multiple n _r , and is fixed. The time period until the magnetic state in the child coordinate system becomes strictly equal (until the symmetry of the magnetic field appears) is one period of the magnetic field analysis. The symmetry of the magnetic field appears at every 1 bar pitch in the cage rotor, and at every phase band pitch of the winding in the wound rotor. Therefore, _Ta and _{nr in the} expression (1) can be only integers. Here, the slip s of the rotor in the magnetic field analysis is represented by the primary current time period T
a multiple of _s (unit: second) n _s , the number of rotor slots per two poles of the machine to be analyzed N _{s2 (2p)} , and a synchronization of the magnetic field generated by the stator winding during the primary current time period of _ns times When _rewritten from the number N _{2tl of} rotor slots rotated with a delay from the speed, the following equation can be obtained.

S = N _2tl / (n _s · N _{s2 (2p)} ) (Equation 2) By using the relationship of Equation 2, one cycle of the slip frequency, which is the fundamental wave component of the secondary current, is applied to the magnetic field. without setting the analysis time period, in a short analysis time period set as n _s times the primary current time period T _s, can analyze the slip frequency one period. This is shown in the example of FIG.

FIG. 2 is an explanatory view of a process of calculating a secondary current of an induction motor according to an embodiment of the present invention. The cross section of the induction motor to be analyzed is modeled in two dimensions, and the in-machine magnetic field is determined by a finite element method. A case is shown in which a secondary current is calculated by performing a numerical analysis and considering the movement of the rotor. The figure shows 4
Rotor at the pole of the cage form machine (count bar: 16) show the asynchronous operating condition that rotates with a delay by one Bapitchi every cycle T _s of the primary current. Assuming that the periodicity of the space region is satisfied by the modeling of the 断面 section in the magnetic field analysis for this operation state, the slip s is given by
/8=12.5%. So, from this magnetic field analysis,
Consider a case where a waveform over one cycle of the slip frequency of the bar current (secondary current) is obtained.

First, when the time t is t = 0, the spatial distribution of each bar current can be obtained discretely as shown in FIG. Here, each rotor bar 12 in FIG.
Numbers are assigned from 0 to 2π in the direction of 1 → 8, 1 ′ → 8 ′, respectively. Then, if attention to # 1 of the bar 12 at t = 0 → T _s, # 1 is to a position where there is # 8 when t = 0 with a delay of one Bapitchi from the synchronization state at time t = T _s Move (Fig. 2 (2)). T = 0 at the time of further t = 2T _s
It moves to the position where # 7 was at the time of (FIG. 2 (3)). The same applies to the other bars 12, the absolute position for each T _s is gradually delayed by 1 Bapitchi. Hereinafter, bars 12 is one period of the slip frequency to return to the position of t = 0 through some multiple of the primary current time period T _s.

By the way, # 1 of the bar 12 is t = 0 → T _s
When moving to the position where # 8 at t = 0 was,
Since the relative positional relationship between the stator and the rotor is equal at the two points in time, the in-plane magnetic field is exactly the same. From this, t =
# 8 of bar 12 at 0 and bar 12 at t = T _s
It can be said that the current value # 1 is equal. This is the same for the other bars 12.

[0015] Thus, the slip frequency one period over current waveform in # 1 of the bar 12, as shown in FIG. 2 (4), the current waveform in # 1 of the bar 12 over t = 0 → T _s as the initial value, the current value at t = 0 → T _s of each bar 12 # 1 → # becomes 8 → # 7 → ... → # 2 strictly obtained that if # traces the first transfer process synthesis.

FIG. 1 shows an algorithm for calculating a secondary current of an induction motor according to one embodiment of the present invention, and shows a generalized calculation process of the secondary current shown in FIG. In this algorithm, the element division data of the machine to be analyzed is input in step 1, and in step 2, the slip of the rotor for performing the magnetic field analysis on the element division data is determined by equation (2). Next, in step 3, an analysis time period that is n _s times the primary current time period T _s that satisfies the periodicity of the in-machine magnetic field described in the description of FIG. 2 is set to an analysis end time TEND (unit: second).
Set as In this case, the analysis start time TSTART (unit: second) is set in advance to be 0. Here, TSTART does not necessarily have to be 0. And t
The number of analysis time steps between = 0 and TEND, that is, an analysis end step SEND is set. Step 4 represents a calculation loop in which the element division data input in step 1 is repeated for the analysis time and the analysis steps set in step 3, and the processing is changed to step 7 after predetermined repetition processing is performed. . Step 5 in the calculation loop of Step 4 is a processing portion for calculating a vector potential by numerical analysis for each node constituting a minute element of the element division data input in Step 1. Step 6 is a part for calculating the secondary current generated in the rotor winding from the vector potential calculated in step 5 and the vector potential one analysis step before from the time difference of the vector potential. Steps 1-6 above
Is an outline of the magnetic field analysis means.

If it is determined in step 4 that the magnetic field analysis has been performed for a predetermined number of analysis steps, the processing is changed to step 7. This step 7 is a part for extracting and outputting the rotor potential, which is the vector potential and the secondary current, for each analyzed step to an output device such as a magnetic disk.

In step 8 based on the above calculation results,
The movement process of the rotor slot as shown in FIG. 2 determined by N _2tl in the equation is calculated, and finally in step 9 the secondary current waveform of each rotor winding is calculated based on the calculation result in step 8. In time series. Then, although not shown, the synthesized secondary current data is transferred to and displayed on a display unit for displaying time and a secondary current amount. On the other hand, means for performing harmonic analysis on the obtained secondary current waveform may be executed after step 9 is completed.

FIG. 3 shows a calculation result, that is, a display result of the secondary current waveform according to one embodiment of the present invention. The figure shows three-phase four
Poles, output 55kW, number of rotor slots N per two poles
_The analysis is for a cage machine with _{s2 (2p)} of 19, and shows two cycles of the secondary current waveform when the primary current frequency is 50 Hz and the rotor slip is 1.75%. Rotor slip 1.
75% of the primary current time period T _s is 3
In this case, the rotor movement is delayed by one slot pitch. The time period of the secondary current in this state is shown in FIG.
Is 1.14 seconds, but the secondary current calculation by actual magnetic field analysis is 0.019, which is 1/19 of 1.14 seconds.
Only go for seconds. As shown in the figure, the calculated waveform has no discontinuous portion, and is calculated in a form superimposed on higher-order harmonic components as in an actual secondary current waveform.

FIG. 4 shows the results of analyzing the harmonic components of the secondary current waveform of FIG. 3 calculated according to the embodiment of the present invention and the actually measured secondary current waveform, respectively. It can be seen that the calculated values according to the present invention and the measured values show good agreement. Therefore, according to the present invention, from the slip frequency component, which is the fundamental component of the secondary current, to the stator winding phase band harmonic component and the stator slot ripple component generated by the influence of the stator slot opening. It can be seen that the analysis has been completed sufficiently.
Therefore, according to the secondary current calculation method and the display method according to the present invention, the computer processing time can be remarkably shortened, the secondary current can be calculated with high accuracy, and the result can be accurately grasped as compared with the conventional magnetic field analysis. It turns out that it can be confirmed.

As described above, the present embodiment has described in detail the method of calculating the secondary current of the induction motor and the method of displaying the same. However, the present invention can be applied to a case where another rotating electric machine is operating asynchronously with slipping of the rotor. Of course, it is applicable. Further, it goes without saying that the present invention can be applied to the secondary magnetic flux and all other secondary physical quantities.

[0022]

As described in detail above, according to the present invention,
The secondary current of the induction motor can be calculated in a much shorter time and more accurately than in the past, and the result can be accurately grasped and confirmed.

[Brief description of the drawings]

FIG. 1 shows an algorithm for calculating a secondary current of an induction motor according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram of a secondary current calculation process showing one embodiment of the present invention.

FIG. 3 is a calculation result of a secondary current waveform according to an embodiment of the present invention.

FIG. 4 is a harmonic analysis result of a secondary current waveform and an actually measured waveform calculated according to an embodiment of the present invention.

[Explanation of symbols]

 10 ... stator, 11 ... rotor, 12 ... rotor bar.

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Satoshi Kikuchi 7-1-1, Omikacho, Hitachi City, Ibaraki Prefecture Within Hitachi Research Laboratory, Hitachi, Ltd. (72) Inventor Mika Takahashi 7-1 Omikacho, Hitachi City, Ibaraki Prefecture No. 1 Hitachi, Ltd. Hitachi Research Laboratory (58) Field surveyed (Int. Cl. ⁷ , DB name) G01R 31/34 H02K 17/02 H02P 7/36 302

Claims (7)

(57) [Claims] In a method for calculating a secondary current flowing through a secondary winding of an induction motor, a magnetic field analyzing means capable of considering the movement of an object in a field where an eddy current is generated and a moving boundary condition, and means for extracting the secondary current, the secondary
Each current flowing through each of the secondary windings extracted by the current extracting means
The secondary current is defined by the angle between the secondary windings and the secondary current.
In time series as the time phase angle difference at
Therefore, analysis of the frequency period shorter than the slip frequency period
For calculating secondary current for one cycle of slip frequency
And a secondary current calculation method for an induction motor. 2. A method for calculating a secondary current flowing in a secondary winding of an induction motor, comprising: a magnetic field analyzing means capable of considering a movement of an object in a field where an eddy current is generated and a moving boundary condition; means for extracting the secondary current, the secondary
Each current flowing through each of the secondary windings extracted by the current extracting means
The secondary current is defined by the angle between the secondary windings and the secondary current.
In time series as the time phase angle difference at
Therefore, analysis of the frequency period shorter than the slip frequency period
A means for calculating a secondary current for one cycle of a slip frequency , and means for analyzing a harmonic of the result of the calculation of the secondary current. 3. A method for displaying a secondary current flowing through a secondary winding of an induction motor, comprising: a magnetic field analyzing means capable of considering movement of an object in a field where an eddy current is generated and a moving boundary condition; means for extracting the secondary current, the secondary
Each current flowing through each of the secondary windings extracted by the current extracting means
The secondary current is defined by the angle between the secondary windings and the secondary current.
In time series as the time phase angle difference at
Therefore, analysis of the frequency period shorter than the slip frequency period
For calculating secondary current for one cycle of slip frequency
And displaying a time and a secondary current amount. 2. A method for displaying a secondary current of an induction motor, comprising the steps of: 4. A method for displaying a secondary current flowing in a secondary winding of an induction motor, comprising: a magnetic field analyzing means capable of considering a movement of an object in a field where an eddy current is generated and a moving boundary condition; means for extracting the secondary current, the secondary
Each current flowing through each of the secondary windings extracted by the current extracting means
The secondary current is defined by the angle between the secondary windings and the secondary current.
In time series as the time phase angle difference at
Therefore, analysis of the frequency period shorter than the slip frequency period
Means for calculating a secondary current for one cycle of the slip frequency and means for analyzing a harmonic of the result of the calculation of the secondary current to display the harmonic order and the secondary current amount. A secondary current display method for an induction motor, comprising: 5. The structure of an induction motor having windings and slots for accommodating the windings in both a stator and a rotor is divided into minute elements, and an analysis model simulating the structure of the induction motor is used. By doing so, the rotor constituting the induction motor performs rotational movement with slip, and the induction when the magnetic field in the stator constituting the induction motor and the magnetic field in the rotor are operated in an asynchronous state. The in-machine magnetic field in the electric motor is numerically analyzed at every minute time step between analysis times determined by setting an analysis start time and an analysis end time in the magnetic field analysis, so that the rotor winding is A secondary current calculation method for an induction motor in which a flowing secondary current is discretely calculated as an induction current generated by a magnetic field generated by the stator winding for each of the minute time steps. There are, a slip s of the rotor on the magnetic field analysis, the primary current time period is a multiple n _s (n _s: integer), the number of rotor slots 2 poles per analyzed machine N _{s2 (2p) (N
s2 (2p):} integer): integer), n _s times of the primary current to rotate delayed synchronous speed of the generated magnetic field of the stator winding during the time period rotor slot number _N 2tl (N 2tl , s = represents _{n 2tl / (n s · n} s2 (2p)) becomes the relationship, to set the amount of time between the magnetic field analysis time so as to at least be n _s times of the primary current time period,
The method is characterized in that each secondary current generated in each rotor winding during the analysis time is synthesized in time series in accordance with the moving state of the rotor slot to calculate one cycle of the secondary current. The method for calculating the secondary current of the induction motor. 6. The structure of an induction motor having windings in both a stator and a rotor and having slots for accommodating the windings is divided by minute elements, and an analysis model simulating the structure of the induction motor is used. By doing so, the rotor constituting the induction motor performs rotational movement with slip, and the induction when the magnetic field in the stator constituting the induction motor and the magnetic field in the rotor are operated in an asynchronous state. The in-machine magnetic field in the electric motor is numerically analyzed at every minute time step between analysis times determined by setting an analysis start time and an analysis end time in the magnetic field analysis, so that the rotor winding is A secondary current calculation method for an induction motor in which a flowing secondary current is discretely calculated as an induction current generated by a magnetic field generated by the stator winding for each of the minute time steps. There are, a slip s of the rotor on the magnetic field analysis, the primary current time period is a multiple n _s (n _s: integer), the number of rotor slots 2 poles per analyzed machine N _{s2 (2p) (N
s2 (2p):} integer): integer), n _s times of the primary current to rotate delayed synchronous speed of the generated magnetic field of the stator winding during the time period rotor slot number _N 2tl (N 2tl , s = represents _{n 2tl / (n s · n} s2 (2p)) becomes the relationship, to set the amount of time between the magnetic field analysis time so as to at least be n _s times of the primary current time period,
Each of the secondary currents generated in each of the rotor windings during the analysis time is synthesized in a time series in accordance with the moving state of the rotor slot, one cycle of the secondary current is calculated, and time and A secondary current display method for an induction motor, wherein a secondary current amount is displayed. 7. A secondary current calculation method for an induction motor, comprising: calculating a secondary current flowing through a secondary winding of the induction motor by the following steps. (1) Input the element split data of the machine to be analyzed, (2) Set the slip of the rotor to perform magnetic field analysis on the element split data, (3) Primary current time that satisfies the periodicity of the in-machine magnetic field Period T _s
Set the analysis end time, the analysis start time, and the number of steps of the analysis time (analysis end step SEND) to the analysis time period which is n _s times of (4). (5) The vector potential calculated in step 4 and 1
The secondary current generated in the rotor winding from the vector potential before the analysis step is calculated from the time difference of the vector potential. (6) Steps 4 and 5 are repeated for the analysis time and the analysis step set in step 3, and (7) ) Store the rotor potential, which is the secondary potential, the vector potential for each analysis step analyzed above in a magnetic disk or the like, (8) calculate the movement process of the rotor slot, and (9) calculate the rotor winding The secondary current waveforms of the lines are synthesized in time series based on the calculation result of step 8.