JPS6277894A - Magnetic flux calculation method for induction motor - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention provides a device that calculates magnetic flux, secondary current, and slip frequency of an induction motor with high precision, and vector control of the induction motor using these calculated values. related to a device for

[Conventional technology]

Detecting the slip frequency is necessary for vector control of induction motors.

Conventionally, detection using a tachometer generator or a pulse generator has been common, but research is being conducted to calculate the slip frequency without using these detectors.

As shown in equation +11, the slip angular frequency ω5 is expressed by the secondary magnetic flux (amplitude) φ2 and the secondary current (amplitude) shi2.

ω,=R2shi2/φ2−・−・−・−・・−・−・
-(Formula 11, where R2 is a secondary resistance.

[Problem that the invention seeks to solve]

However, the calculation of the secondary magnetic flux φ2 and the secondary current E2 has the following problems, making it difficult to calculate the slip frequency with high accuracy.

1) Problems with magnetic flux calculation ・ Conventionally, the amplitude of the secondary magnetic flux of an induction motor (hereinafter abbreviated as motor) is 1
The internal induced voltage was obtained by subtracting the voltage drop due to the secondary resistance and leakage inductance, and was obtained by integrating over time.

This calculation formula is shown in equation (2).

φz= l f(u+ R+, LI j!'at −
LI) dtl=1f(bi+R+LI) dt-
1, l+ l −・−・Formula (2), where φ2 is the amplitude of the secondary magnetic flux, H, is the motor 1 child voltage vector, A is the motor primary current vector, R1 is the primary resistance value, and l is the Total leakage inductance.

However, the secondary magnetic flux obtained by this calculation has the following problems and lacks practicality.

a) Due to drift and offset, it is not possible to create an integrator that can integrate accurately down to low frequencies.

b) Since the integrator transiently causes a transient phenomenon in its integral value, errors also occur in the obtained magnetic flux.

c) If there is a difference between the set value and the actual value of the primary resistance, low IJ
There is a problem that the calculation accuracy of magnetic flux decreases significantly in the wave region.

Equation (3) shows the calculation formula for the secondary magnetic flux when the set values and actual values of the negative-order resistance and leakage inductance are different.

t.
f((el +R1,L++″i′fence,)-ma, top,
−i” −JJal dt lt =l f(e−ΔR+ LI −Δ′ LL+l ”
l=1. /'(e-ΔR+J1)dt-Δn,z+1-
−−−−・−−−−−−−−+31 formula % formula % f2: Secondary magnetic flux obtained by calculation R″I + RI′ Setting value and actual value of primary resistance respectively ff
i'', f: set value and actual value of total leakage inductance, e: internal induced voltage vector Expression (3) is expressed as a complex expression (4).

tz = l -A-(e-ΔR+j, +l-Δ1k1
1j ω1 = 1φ. +jAR+j-Δl-Work11-・(4) Expression. : True secondary magnetic flux vector ω1 : Primary angular frequency j : Imaginary unit From this, if there is a difference between the set value and the actual value of the primary resistance,
It can be seen that the calculation accuracy of the secondary magnetic flux decreases in the low frequency range. Furthermore, since the primary resistance value varies greatly depending on the motor temperature, it is actually difficult to match the set value of the primary resistance with the actual value.

2) Problems with secondary current calculation The secondary current J2 of the motor is expressed by equation [5].

it =φ2×upper, /1φ, 1−・・・・・−・・−・
...Equation (5) where φ2: Secondary magnetic flux vector, LI:
Primary Current (Vector) Since the secondary magnetic flux required to calculate the secondary current 12 includes the items shown in the above-mentioned problems with magnetic flux calculation, the secondary current cannot be calculated with high accuracy either.

In view of these conventional problems, the present invention eliminates the influence of primary resistance by directly calculating from the voltage and current of the motor without using an integral calculator, and thereby calculates the slip frequency. The purpose is to improve accuracy and controllability of the electric motor.

Means for Solving Problem C] The present invention calculates active power and reactive power from the terminal voltage and current of an induction motor, calculates magnetic flux and secondary current from these, and further calculates the calculated magnetic flux and secondary current from the calculated magnetic flux and secondary current. This is a control device for an induction motor, characterized in that it includes a slip frequency calculation device that calculates a slip frequency.

The present invention will be explained in detail below.

1) Calculation of magnetic flux In the equivalent circuit of the motor shown in Fig. 2, the magnitude of reactive power IP, 1 of the motor is determined by the vector product of voltage and current, and is expressed by equation (6).

IP--:=lbi,×work,I =l(e+R++jωIffJz)XjJ+l=l e
X LI"j" ll-J+21-(61 formula 11:1
Amplitude of the secondary current As mentioned above, Equation (6) has no term that depends on the primary resistance (and only includes an inductance component that is unrelated to the motor temperature. From this, if magnetic flux is induced, 1 It is expected that magnetic flux that is not affected by the following resistance can be detected.

Here, 6 = j (Ll l M , from Lm, (
Equation 6) can be further transformed into equation (7).

l Pre l = l j ω+M, j, 1llx
Ll+3(r)+1 j+21= l j ω+M j
,”+jω, l L+” l=1ωIl (M s2
+1 j, + 2)...-+71 formula where, L,:
Excitation current vector, ヱ: amplitude of excitation current, M: mutual inductance (7) From 2, the secondary magnetic flux is obtained by removing the component due to leakage reactance from the reactive power as shown in equation (8).

φ2 = M This equation (8) shows that magnetic flux can be detected that is not affected by the primary resistance component and is not affected by temperature.

2) Calculation of secondary current Next, a method for calculating the secondary current will be described.

In the equivalent circuit of the electric motor shown in FIG. 2, equation (9).

Equation 00) and Equation 00 hold true.

Here, vd: d-axis primary voltage, v9: q-axis primary voltage, e: secondary induced voltage, v: primary voltage.

R,: Primary resistance value, l: Leakage inductance.

1 = excitation current, j, z: secondary current, ω1: primary angular frequency In the 001 formula, e = ω, Mt, I, so the 00 formula can be transformed into the ω formula.

vq = R+ i z + (L/M) e
−−−−−−−+1B formula where M: excitation inductance, L=M+β Also, there is a relationship of the aj formula between the secondary electromotive force e, the secondary power P2, and the secondary current J2.

Sit = PK/e ・・・−・−・・−・−
・−・−・−・−・−・−−−−−・α [exist] expression a
From the formula 031, the secondary current Lt is expressed as 0432.

-P t R+-4z+(L/M)ee
vQ L R,L.

=”-・I P2+ Pa+ IIMe =”-・(Pz + R+ Jz”I qM −・・−・−m−−−・・−・−・・・α4J formula Also, secondary input P2 and An αω expression is established between the primary input P1 and the primary input P1.

P2=PI IR+j+2 =P IR+ -Lm" R+ Lz" ---1
By substituting the 51 formula α5) into the α ship formula, the α0 formula is derived.

−・−・−−−１−−−−−・−・・−−−１−−・−
Further modification of the αe formula Q61 formula yields the α9 formula.

Here, from formula 00, vQ = vI 8ba lower 2 1l-il
It is. Also, normally v, <<v9. -! −・Noue soil 2<<
1, M Vq , the OD equation can be approximated to the 0ω equation.

In the α0 formula, the secondary current 12 can be measured simply by detecting the primary quantity, which can be easily and accurately measured, thus enabling highly accurate calculations.

From the above, it has been shown that magnetic flux and secondary current can be detected without being affected by resistance components.

From these, the slip angular frequency ω5 is expressed by equation 111.

ωyo-Rzzz/φ −・−・・−−１−−・・・−・
-------------------------Embodiments of the present invention will be described below. Figure 1 shows an arithmetic circuit implementing the present invention, in which 1 is a power supply, 2 is an induction motor, 3.4 is a current detector, 5 is a voltage detector, and 6.7 is a 3-phase to 2-phase converter. , 8-15 are multipliers, 16 is an absolute value circuit, 17-19
is a divider, 20.21 is a square rooter, 22 to 25 are amplifiers,
26 is a setting device, and 27 to 32 are adders and subtracters.

In this figure, a three-phase to two-phase converter 6 converts current into two-phase alternating currents of Loc and Lβ according to equation (2).

Further, the three-phase to two-phase converter 7 is a three-phase to two-phase converter that converts the terminal voltage (phase voltage) into two-phase AC voltages of V, X, and Vβ according to equation (21).

Next, the operation of the circuit shown in FIG. 1 will be explained.

The motor terminal voltage (phase voltage) detected by the voltage detector 5 is converted into two-phase alternating current voltages Vp and Vp by a three-phase to two-phase converter 7.

The primary current detected by the voltage detector 3.4 is converted into a two-phase alternating current 1tx, ip by a three-phase to two-phase converter 6.

In the following, calculation of magnetic flux and calculation of secondary current will be explained separately.

○ Calculation of magnetic flux Calculation of equation (22) is performed by multiplier 8.9 and adder/subtractor 28 to obtain reactive power Pr1l.

P ra-vat t9 'I seat -------
--- Equation (22) In addition, the two-phase current sh α and Jl are multiplier 1
2, 13, the adder/subtractor 27 calculates the equation (23), and the square C of the primary current amplitude calculates the equation (24) using the absolute value circuit 16, the divider 17, the adder/subtractor 31, the amplifier 22, 24, This is performed using a flattener 20 to obtain the secondary magnetic flux φ2.

(29)
By calculating the equation, electric power a and primary human power P are obtained.

P + ”V(X J(z + vβt p ---
−−−−−−−−Equation (25) Also, two-phase voltage V. (,V
ll is multipliers 14, 15, adder/subtractor 30, and switch 21
Equation (26) is calculated by
, l are obtained.

IV, l = ψ4ryo7 hit go・・・−・・・・−−−−
------- Equation (26) Next, the motor current l at no load,
(primary copper at no load) determined by the primary resistance value R1) JIR,
The adder/subtracter 32 subtracts the power P' from the primary input P1, which is the output of the adder/subtracter 29, to obtain the power P'.

The above power P' is divided by the primary voltage amplitude value IV, l, which is the output of the square rooter 21, using the divider 18, and then multiplied by L'/M by the amplifier 23 to obtain the secondary current 12. It will be done.

In addition, in order to obtain the primary power and primary voltage amplification values, the phase current and phase voltage were converted to α phase and β phase, but the primary input and primary voltage amplitude values were calculated without converting to α and β phases. Of course, it is possible to calculate .

From the secondary magnetic flux and secondary current obtained above, the calculation of equation (19) is performed by the amplifier 25 and the divider 19 to obtain the slip frequency.

FIG. 3 is a block diagram of a vector control device using the slip frequency calculation device of the present invention.

In the figure, 41 is a speed control amplifier, 42 is a frequency control amplifier, 43 is a magnetic flux control amplifier, 44 is a current control amplifier, 45
is a vector calculator, 46 is a secondary current-secondary magnetic flux calculation device, 47 is a vector multiplier, 4B is an integrator, 49 is a current detector, 50 is a voltage detector, 51 is a voltage filter, 52.5
3 is a divider, 54 is an amplifier, 55 to 60 are adders/subtractors, 6
1 is a power source, 62 is an impark, and 63 is an induction motor.

First, the operation of each part will be explained.

The speed control amplifier 41 outputs a predetermined torque command 2- so that the speed command value ω7* and the estimated speed value i match.

The frequency control amplifier 42 outputs a torque command and a magnetic flux command φ"
The frequency is controlled so that the ratio t2*/φ'' and the ratio 'j:z/l between the calculated secondary current value 2° and the calculated magnetic flux value t match.

The magnetic field control amplifier 43 controls the excitation current command φ2 so that the magnetic flux command φ2 and the magnetic flux calculation value F match.

The current control amplifier 44 controls the output current of the inverter so that the current command vector L1* and the actual current vector match.

The vector calculator 45 calculates the torque command j? according to equation (27). and excitation current command i, *, output the primary current command amplitude 1, and calculate and output the phase ψ1 according to equation (28).

” l*= J-8 lower “Otsu d...−1−−−−−
--...(27) Formula % Formula % (28) The secondary current-magnetic flux calculation device 46 calculates the above, voltage HI, secondary current 2□ and magnetic flux V according to the calculation method described above. It is used to calculate.

The vector multiplier 47 vector multiplies the phase ψ4+01, which is the output of the adder/subtractor 19, for each primary current command amplitude ホ,
It outputs a primary current command vector.

The voltage filter 51 extracts only the fundamental wave component from the voltage detected by the voltage detector 50.

The current control type inverter 62 controls the inverter output current according to the output signal of the current control amplifier 44.

Next, the overall operation will be explained.

The deviation between the speed command value ω- and the estimated speed value b6 is outputted as a torque command 5- through the speed control amplifier 41. on the other hand,
The deviation between the magnetic flux command φ9 and the magnetic flux calculation value F is output as an excitation current command J, * through the magnetic flux control amplifier 43.

As for the frequency, it is controlled so that the l-/φ0 and 1″z/F are the same.

The estimated speed value b5 is obtained by subtracting the slip frequency command value ω- from the first-order wave number ω. Equation (29) shows an arithmetic expression for obtaining the estimated speed value ii.

Otsu, =ω−−ω−=ω−R, $J, 11/φ”
・--(29) 2 or more, calculated torque command J-2
Based on the excitation current command J,* and the primary frequency ω1, the vector calculator 45, vector multiplier 47, integrator 48, and adder/subtractor 59 output a primary current command vector LI*.

Current control amplifier 44, inverter 62, current detector 49
, a current control system including an adder/subtractor 60 supplies a predetermined current to a predetermined induction motor 63 in accordance with a primary current command vector JI*.

The feature of this speed control system is that the secondary current/magnetic flux calculation device is not affected by the motor temperature (it can perform highly accurate calculations, so that the torque determined by the magnetic flux and secondary current changes depending on the motor temperature). This is a point that is not affected.

FIG. 4 shows a comparison of torque control characteristics and speed control characteristics with respect to changes in motor temperature when a magnetic flux calculation device of a speed control system is constructed using the present calculation method and the conventional method described above. In response to a change in motor temperature of about 40°C, the torque control accuracy is 5% in the conventional method, but is 1% in the method of the present invention.
% has been improved.

Regarding speed control accuracy, the method of the present invention also uses the secondary resistance value R2 for the estimated speed value, so the accuracy decreases depending on the motor temperature, but since the torque is output as specified, the conventional method Control accuracy has not decreased.

FIG. 5 shows torque control characteristics and speed control characteristics when the set value of the secondary resistance is corrected according to the motor temperature change according to equation (30).

R2'= [1+ to θ stone/(1+sTθ)l R-・-
・Equation (30) where Kθ is the motor thermal gain, and T is the morph thermal time constant. Compared to FIG. 4, the speed control accuracy has also been improved, and an accuracy of 0.1% level has been obtained.

〔Effect of the invention〕

As described above, according to the present invention, the magnetic flux and secondary current are calculated from the terminal voltage and current of the induction motor, and the slip frequency is calculated from this, so compared to the conventional method using an integrator, the low frequency This improves the control accuracy and eliminates the influence of the primary resistance, so that it is possible to eliminate errors due to temperature changes.

[Brief explanation of drawings]

FIG. 1 is a slip frequency calculation circuit diagram according to the present invention, FIG. 2 is an equivalent circuit diagram of an induction motor, and FIG. 3 is a block diagram of a vector control device using the slip frequency calculation device of the present invention.
FIGS. 4 and 5 are explanatory diagrams comparing the control characteristics of the present invention and the conventional system, respectively, and FIG. 6 is a circuit diagram of a conventional slip frequency calculation device. l: Power supply 2: Induction motor 3.4; Current detector 5: Voltage detector 6.1: 3-phase to 2-phase converter 8-15: Multiplier 16: Absolute value 17-19: Divider 20.21: Square root unit 22 to 25: Amplifier 26: Setting device 27 to 32: Adder/subtractor 41: Speed control amplifier 42: Frequency control amplifier 43: Magnetic flux control amplifier 44: Current control amplifier 45: Hector calculator 46: Secondary current - secondary Magnetic flux calculation device 47: Vector multiplier 48: Integrator 49; Current detector 50: Voltage detector 51: Voltage filter 52, 53: Divider 54: Amplifiers 55 to 60: Adder/subtractor 61: Power supply 62: Inverter 63: Induction Electric motor

Claims (1)

[Claims] 1. A slip method in which active power and reactive power are determined from the terminal voltage and current of an induction motor, magnetic flux and secondary current are calculated from these, and a slip frequency is calculated from the calculated magnetic flux and secondary current. A control device for an induction motor, characterized by comprising a frequency calculation device. 2. The control device for an induction motor according to claim 1, characterized in that the output of the slip frequency calculating device is used to control the vector control type induction motor.