JP3136667B2 - Characteristic calculation method for linear 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 method for calculating characteristics of a linear induction motor.

[0002]

2. Description of the Related Art An equivalent circuit of a linear induction motor can be handled in the same manner as a rotary induction motor. The equivalent circuit of the induction motor is represented by, for example, a T-type equivalent circuit shown in FIG.

In order to calculate various characteristics of an induction machine from this equivalent circuit, it is necessary to determine the constant value of the equivalent circuit. For example, the standard JEC-37 requires resistance measurement, no-load test, and constraint test. By doing so, each constant value is obtained.

[0004] Among these, resistance measurement by the conversion to the reference winding temperature by measuring the inter-primary winding terminals resistance r _1, the no-load test is the primary voltage V when the no-load operation at rated voltage and rated frequency ₁ , the primary current I ₁ , and the primary input W are measured. In the restraint test, a rated voltage and a low voltage are applied while the rotor is restrained, and the primary voltage V ₁ , the primary current I ₁ , and the primary input W at full load current are applied. Is measured.

When the above-described test method for a rotary induction machine is used for a linear induction motor, the linear induction motor performs a linear motion unlike a rotary machine, so that a no-load test cannot be performed. Therefore, a test machine as shown in FIG. 10 is prepared as a no-load test device for a linear induction motor.
A voltage / frequency of a no-load test is supplied to a primary stator 31 composed of a winding and a yoke, and a secondary rotating disk 32 is rotatably held by a support plate 33 and a shaft 34 by a shaft 35.
The load absorbing device 36 and the tachometer 37 connected to the shaft 34 of the rotating disk 32 are used for measuring the dynamic thrust of the motor and for measuring the speed characteristics.

[0006]

In the conventional characteristic calculation method, various constants of an equivalent circuit are calculated by a no-load test or a constraint test, similarly to the case of a rotary induction machine. Therefore, there is a problem that a large-scale test machine is required for the no-load test.

In the restraint test, the rotor is restrained. The linear induction motor is equivalent to a rotary induction machine because the sum of the air gap and the thickness of the secondary conductor becomes an equivalent air gap. The air gap increases. further,
The operating frequency is low for low-speed machines. From these, linear induction motor has a small excitation reactance X _m, the exciting current is abundant in current during restraint test, there is a problem that can not be accurately tested.

SUMMARY OF THE INVENTION An object of the present invention is to provide a characteristic calculation method in which a characteristic is calculated only by resistance measurement and a constraint test, and which is accurate and easy.

[0009]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems, the present invention provides a resistance measuring means for measuring a primary resistance of a linear induction motor, a primary current and a voltage at different frequencies depending on a constraint test of the motor. A T-type equivalent circuit including primary leakage reactance of the motor as a secondary leakage reactance and an equivalent secondary impedance including an exciting reactance from the measurement results obtained by the two means. Assuming an approximate expression expressing the secondary-side impedance of the equivalent circuit as a function of the slip S and the frequency f, each coefficient of the approximate expression is calculated from the equivalent secondary impedance obtained from the measurement result and the simultaneous equation of the approximate expression. Calculated and calculated from the approximate expression
The characteristic of the motor is calculated by obtaining each constant of the equivalent circuit .

[0010]

[Action equivalent circuit shown in FIG. 1 is obtained by erasing the primary leakage reactance X ₁ in FIG. 9 by the equivalent conversion, starting from π shape equivalent circuit of a so-called induction machine. The introduction of this equivalent circuit is described in, for example, Transactions of the Institute of Electrical Engineers of Japan, Vol. 87
-1, No. 940, pages 173 to 180, "Constant determination method for calculating characteristics of induction motor".

Since the equivalent circuit of FIG. 1 performs equivalent conversion, it electrically represents the same circuit as the π-type equivalent circuit, and each constant represents the excitation reactance X _m and the primary reactance in the π-type equivalent circuit. X ₁ = x ₁ + X _m (x ₁ : primary leakage reactance), and the secondary reactance is X ₂ = x ₂ + X _m
(X ₂ : secondary leakage reactance), assuming a secondary resistance R ₂ ,

[0012]

(Equation 1)

## EQU1 ## That is, X _m 'is the same as X ₁ in FIG. Therefore, in the equivalent circuit of FIG. 1, it is not necessary to separate the primary and secondary leakage reactances, and the calculation of the constant becomes easy.

If the equivalent circuit of the linear induction motor is shown in FIG. 1, the equivalent circuit in the restrained state (slip S = 1) can be represented as shown in FIG. Now, subjected to restraint test at the rated frequency f _n, the phase voltage V _L, the current I _L, the input W _L and the thrust T _L
The measure can be determined assuming that measured immediately after termination one phase winding resistance R _1, the constant of each component in a restraint state when taking the phase voltage reference vector according to the following procedure, the voltage and current .

[0015]

(Equation 2)

Here, the equivalent secondary current is the sum of the exciting current and the secondary current, and the equivalent secondary impedance is the total impedance on the secondary side including X _m '.

Meanwhile, determined from the equivalent circuit of FIG. 1 the equivalent secondary impedance at any slip S, a resistor-R _2E
(S) and the reactance component as X _2E (s), the quadratic constants R ₂ ′ and x ₂ ′ are obtained from the relationship between the two equations.

[0018]

(Equation 3)

## EQU1 ##

Therefore, by substituting the calculation results of the above equations (12) and (13) with S = 1, the quadratic constant at the time of constraint can be calculated, but X _m 'is unknown at this stage. Therefore, the second order constant cannot be determined.

As a method of determining X _m ′ without performing a no-load test, a primary current, a primary voltage and an input at a reference frequency f ₁ and an arbitrary frequency f ₂ are measured in a constraint test of a linear induction motor, respectively, as shown in FIG. The secondary resistance and the leakage reactance are obtained for the frequencies f ₁ and f ₂ from the equivalent circuit of the following formula, and the ratio of the secondary resistance to the secondary reactance and the ratio α of the frequencies f ₁ and f ₂ are α
The applicant of the present application has already proposed a characteristic calculation method for obtaining X _m 'from the formula (Japanese Patent Application No. 3-48528).

However, the above-mentioned method has problems that the number of measurement points increases and that drawing is required. In the present invention,
Approximate expressions for the operating frequency and slip of the equivalent secondary impedance including X _m 'are derived to calculate X _m ' and the second order constant, thereby obtaining the characteristic calculation.

(A) Approximate Expression of Equivalent Secondary Impedance Generally, the secondary current of a linear induction motor is an eddy current and flows with an infinite degree of freedom. Therefore, if this phenomenon is expressed using an infinite number of secondary circuits, the equivalent circuits on the secondary side can be converted as shown in FIG. 3 using fixed constants. Where r ₁ , r ₂ , r ₃ ,... And x ₁ ,
x _2, x _3, ... represent the resistance and leakage reactance of each circuit.

From FIG. 5, the equivalent secondary impedance is obtained and expressed as a function of the slip S and the frequency f.

[0025]

(Equation 4)

## EQU1 ## Where the coefficients a ₁ , a ₂ , a ₃ ,.
_{b 1, b 2, b 3} , ..., c 1, c 2, c 3, ... is a constant determined by the circuit constants of Fig.

Here, since an actual constant can be determined as an actual approximation expression and it is sufficient if a certain degree of accuracy is ensured, the second expression of the numerator and denominator of the expressions (16) and (17) is sufficient.
Take up section, the following (18) further molecules, by dividing the denominator in b _1, can represent the resistance and reactance of the equivalent secondary impedance in the form of (19).

[0028]

(Equation 5)

Even if this approximation formula is adopted, practically sufficient characteristics can be calculated as will be described later. In the present invention, the coefficient of the approximation formula is determined from the result of the constraint test.

(B) Determination of Equivalent Secondary Impedance In determining the coefficients of the above equations (18) and (19), since there are five coefficients in total, they cannot be determined by a constraint test at a single frequency. . Therefore, in addition to the rated frequency f _n ,
A constraint test is performed at the ２ frequency and the ４ frequency, and the equivalent secondary impedance at each frequency is determined.

At this time, the test results Z _2E , Z _2E ′, Z _2E ″
To

[0032]

(Equation 6)

Denoting the [0033], the frequency f _n, f _n in the restraint test
/ 2, f _n / 4 and slip S = 1 to (18) and (1)
9)

[0034]

(Equation 7)

Can be obtained as follows. However,

[0036]

(Equation 8)

From the above, each coefficient is obtained, and this is calculated as (1
By substituting into equations 8) and (19), any frequency,
The equivalent secondary impedance in the slip can be determined.

Further, since X _m 'is a value when the slip S = 0 of X _{2E (S)} ,

[0039]

(Equation 9)

Can be obtained as

In consideration of the rated frequency operation, f _n
Can be expressed as in equations (26) to (28).

However, equations (18) and (19) are approximations up to the second term of the numerator denominator in equations (16) and (17), and approximations taking into account the third term and above are also possible. It is. In this case, the number of coefficients in the approximate expression increases,
The number of constraint tests at different frequencies increases when determining the coefficients.

In equations (20) to (22), the frequency of the constraint test is f _n (rated frequency) f _n / 2, f _n / 4. If the constraint tests of different frequencies are performed, each coefficient is given by a simultaneous equation relating to the secondary impedance calculated from these.

[0044]

FIG. 4 is a block diagram of an apparatus showing an embodiment of the present invention. The linear induction motor is composed of a primary stator 1 and a secondary rotating roll 2, and the rotating roll 2 has a coupling 3.
As a result, it is directly connected to the induction machine 5 with the speed reducer 4. The speed of the induction machine 5 is controlled by an inverter 6 having a speed control system, and an arbitrary speed and load can be applied to the linear induction motor. In this speed control, a setting value of the speed setting device 7 is compared with a detection signal of the speed detector 7A.

The thrust of the primary stator 1 is detected by a load cell 8, and this detection signal is amplified by an amplifier 9 and taken out as a detection signal. The drive power supply is provided with an inverter 10 and a voltage and frequency setting device 1.
An alternating current according to the set values of 1 and 12 is supplied to the primary stator 1. The voltage, current and power at this time are detected by the digital power meter 13 for calculating the characteristics.

The linear induction motor is configured as a one-sided type as shown in FIG. The secondary-side rotating roll 2 has an aluminum plate serving as a secondary conductor adhered to the roll surface, and is rotatable on both sides of the roll shaft 20 by bearings 22 of columns 21. The primary stator 1 includes a bearing 2 on a roll shaft 20.
The roll 2 is suspended in the form of a pendulum by a rocking plate 25 at the tip of an arm 24 connected to the arm 3, and is formed in an arc shape with a certain gap on the peripheral surface of the roll 2. One end of the swing plate 25 is connected to the base 26 via the load cell 8. Table 1 shows the specifications of such a test apparatus.

[0047]

[Table 1]

The test apparatus of the present embodiment enables a no-load test or a load test in addition to the constraint test of the linear induction motor, and detects the thrust applied to the primary stator 1 by the load cell 8. The frequency and voltage at this time are set by setting units 11 and 12.
And the load is adjusted by the speed setting of the inverter 6. The driving inverter 10 to reduce the influence of harmonic currents, the IGBT is adopted to the switching element, the carrier frequency 10KH _Z
Then, the PWM method is used, and the current waveform is extremely close to a sine wave. In addition, digital power meter 1
3 has an improved low-frequency characteristics that can be measured stably up to about 2H _Z, to obtain a DC average effective value display to indicate the substantially fundamental component for a voltage, the current and power are measured at all effective value display.

As a constraint test using the test apparatus according to the present embodiment, as described above, R
Each coefficient is obtained by the respective values of _{2E (S = 1)} and _{X2E (S = 1)} and the above-described coefficient calculation method. Table 2 shows the results.

[0050]

[Table 2]

An approximate curve for the frequency of the equivalent secondary impedance at the time of constraint (S = 1) calculated by the above-described equations (18) and (19) using the coefficients shown in Table 2 and a constraint test at each frequency. FIG. 6 shows a comparison with the obtained measured values. From the figure, although the error between the measured value and the approximate expression slightly exists in the low-frequency region, the resistance R _2E and the reactance X _{2E of the} equivalent secondary impedance can be generally approximated well by the above-described approximate expression.

Table 2 also shows the values of X _m ′ and R _m calculated by the above equations (28) and (8).

[0053]

[Table 3]

Compared with the result of the no-load test of X _m ′,
Shows a good agreement for (X ₁ equivalent). R _m
Was a small value.

That is, although there is a slight difference in the equivalent iron loss between the restraint test and the no-load test, the effect of the equivalent iron loss on the thrust and the current is small.

By substituting the coefficients shown in Table 3 into the above-mentioned equations (26) and (27) from the test results described above, the equivalent secondary impedance during the rated frequency operation can be calculated. Further, by substituting these values into the equations (14) and (15), R ₂ ′ and x ₂ ′ for an arbitrary slip can be determined. FIG. 7 shows the change of R ₂ ′ and x ₂ ′ with respect to the slip at the rated frequency. The quadratic constant of the linear induction motor changes due to slip. In general, the effect of the skin effect is such that as the frequency increases, the resistance increases and the leakage reactance tends to decrease.
The results are consistent with this trend.

Next, the characteristics of the linear induction motor are obtained from the constant calculation results based on the above-described tests and the input conditions (primary current I ₁ , voltage V ₁ ) as follows.

Primary power factor P _f = (effective current I ₁ ) / I ₁ × 100% Primary input P ₁ = (3) ^1/2 V ₁ I _{1 Pf} Secondary input P ₂ = 3 (I ₂ ) ² r ₂ / S output P _out = (1−S) P ₂ iron loss W _m = 3 (I _fe ) ² R _m thrust T = P ₂ / V ₀ efficiency η = (P _out / P ₁ ) × 100% FIG. 8 shows a constant calculation based on the present embodiment and an example of the characteristic calculation based on the constant together with the actually measured values (○, Δ), and a sufficient result was obtained as a practical characteristic calculation method.

[0059]

As described above, according to the present invention, as an equivalent circuit of a linear induction motor, an equivalent circuit including the primary leakage reactance of the T-type equivalent circuit of the induction machine on the secondary side is obtained, and the equivalent circuit is obtained by a constraint test. Since the leakage reactance, the secondary resistance, and the excitation reactance of the circuit are obtained, and the characteristic is calculated, the no-load test required for the conventional characteristic calculation is not required, and the test apparatus is not required.

In addition, since the equivalent secondary impedance obtained from the constraint test is approximated by an appropriate approximation formula, drawing is unnecessary for calculating the constant. Further, at least, if the constraint tests at three different frequencies are performed, sufficient characteristic calculation can be performed, and the number of constraint tests can be reduced.

[Brief description of the drawings]

FIG. 1 is an equivalent circuit diagram for calculating characteristics.

FIG. 2 is an equivalent circuit diagram in a restrained state.

FIG. 3 is an equivalent circuit diagram of a secondary circuit.

FIG. 4 is a configuration diagram of an apparatus according to an embodiment.

FIG. 5 is a test apparatus for a linear induction motor.

FIG. 6 is a characteristic diagram of measured values and calculated values.

FIG. 7 is a graph showing second-order constant-slip characteristics.

FIG. 8 is a diagram of a characteristic calculation example.

FIG. 9 is an equivalent circuit diagram of the induction motor.

FIG. 10 is a configuration diagram of a no-load test machine.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Primary side stator, 2 ... Secondary side rotating roll, 4 ... Reduction gear, 5 ... Induction machine, 8 ... Load cell, 13 ... Digital power meter.

──────────────────────────────────────────────────続 き Continued on front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G01R 31/34

Claims (1)

(57) [Claims] 1. A motor comprising: a resistance measuring means for measuring a primary resistance of a linear induction motor; and a constraint test means for measuring primary current, voltage, power and thrust at different frequencies by a constraint test of the motor, respectively. From the T-type equivalent circuit including the primary leakage reactance in the secondary leakage reactance and the measurement results obtained by the two means, the secondary impedance of the equivalent circuit including the excitation reactance is determined.
And assuming an approximate expression expressed as a function of the frequency f, and calculate the coefficients of the approximate expression from simultaneous equations of the approximate expression <br/> equivalent secondary impedance determined from the measurement results, given the coefficients Calculating the constants of the equivalent circuit from the approximate expression
A characteristic of the linear induction motor, wherein the characteristic of the motor is calculated by the following method.