Method for determining the short-circuit inductance of an asynchronous machine

Method for determining the short-circuit inductance of an asynchronous machine

The present invention relates to a method for determining the short-circuit inductance of an asynchronous machine, in which method the short-circuit inductance is determined by means of a stator voltage and a stator current derivative.

In the control of an asynchronous machine, the goal is usually to make the torque generated by the machine behave as desired when the current and voltage supplied to the machine are known. In this case, the aim is to influence the electrical torque, the relative value of which as a function of the stator flux and current is:

T = (ψ₃^χϊ₅), (1) where T = electrical torque, = stator flux and = stator current.

Controlled torque control therefore requires that the current i be known_s in addition, the stator flux of the machine or a proportional variable (such as rotor or air gap flux).

The stator flux calculation methods are based on the well-known differential and current equations of the stator and rotor of an asynchronous machine, which are in the stator coordinate system:

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<img file="FI89415B_D0003.tif" />

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<td>R i +</td><td></td>

<td>rr</td><td>dt</td>

<td>^LÄ ⁺</td><td>LJ:</td>

<td>^LÄ ⁺</td><td></td>

S ⁹

<img file="FI89415B_D0008.tif" />

<img file="FI89415B_D0009.tif" />

(2) (3) (4) (5)

9 415

<td>where ψ_Γ</td><td>= rotor flow, = rotor current,</td>

<td>ΰ_β^Rr</td><td>= stator voltage, = stator resistance, = rotor resistance, = stator inductance, = rotor inductance = main inductance and</td>

<td> %</td><td>mechanical rotation speed</td>

The goal is to calculate the stator flux using the measured stator current and voltage, so the rotor flux and current must be eliminated from the above equations. Using Equations 4 and 5, we first solve the rotor flux and current as a function of stator flux and current:

ψ_Γ = --- (ψ_Β - oL_ei_B) (6)

L_m i_r = - (Ψ, - L_ei_B) · (⁷)

K ^Lm where σ = 1 - --- = scatter factor and

LL or oL_b = short circuit inductance.

Using Equations 6 and 7, Equation 2 and the following form are now obtained:

^dB'_{s =} dt ^UB -

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(Θ) ₌ dt

<img file="FI89415B_D0011.tif" />

dt - (Ψ, - L, i.)⁺j^w»J.W.. -θν.) / (9)

8941 5 where τ_Γ = - = rotor time constant.

R_r

Most known stator flux calculation methods utilize either Equation 8 or Equation 9 or both equations. When using Equation 8 alone, it is not possible to implement functional control at very low frequencies, so the best methods always use either Equation 9 or both equations.

One very central required parameter in Equation 9 is the short circuit inductance. In order to derive one of its calculation methods, we first consider the derivative of the rotor flux, which according to Equations 2 and 6 is dif_r L_r , άψ_β di. L_r (_ _dl

----- = —-- ol_b --- = — | ^U_e-R₈i - '° L_B --- (10) dt L dt dt 'Ldt mm

Placing Equation 10 in Equation 3 gives:

^dIe __ _be---- = u_a+ u₀ , (11) dt where u₀ is the voltage depending on the state of the machine:

K ^u0 = - (Vr - ίωχ) - R_Bi₈(12)

At the start of the asynchronous machine (denoted by t₀) and the stator and rotor currents and flows are zero, so that is approx_o(t_o) = O and it follows from Equation 11 that «VUt») = u_B(t₀), (13) where i '(t₀) is the derivative of the stator current at time t₀.

Thus, the stator current starts to increase with the stator

9 415 in the direction of the volume with a slope u, (t₀) / oL ,, when a certain voltage u, (t₀). The situation is illustrated in Figure 1, which shows the voltage u, and the current i, as a function of time in a start-up situation as described.

Indeed, one known method of determining aL, is based on measuring the stator voltage of the machine and the derivative of the stator current at the time of start-up, whereby the short-circuit inductance can be calculated directly in relation to these:

u. (t₀) oL_b = ₌---- (14) is (to)

The weakness of the method described above is that aL_sis determined only at startup, after which it is assumed to remain constant. In reality, the short-circuit inductance, like other machine inductances, can vary considerably during operation due to variations in the saturation state of the stator or rotor magnetic flux as the operating point of the machine varies.

It is an object of the present invention to provide a method for determining an estimate of short-circuit inductance which does not involve the above-mentioned limitations and problems and which can also be applied while the machine is running. This is achieved by a method according to the invention, characterized in that the method comprises the steps of causing a stepwise change in the stator voltage, measuring both the stator voltage and the stator current derivative both before and after said step change of the stator voltage, determining the differences between the measured stator voltages and the derivatives of the measured stator currents, respectively, and determining the quotient of the difference between the stator voltages and the derivatives of the stator currents to obtain a short-circuit inductance.

9 41 5

The method eliminates the unknown voltage component u in equation 11, which normally deviates from zero while the machine is running.₀ thus, instead of the derivative value of a single stator current, its change under the influence of the step change of the stator voltage is examined.

The invention will now be described in more detail with reference to the accompanying drawings, in which Figures 1a and Ib show examples of the absolute values ​​of stator voltage and stator current, respectively, as a function of time when the stator voltage of an unmagnetized machine is changed stepwise at time t.₀, Figures 2a and 2b show examples of the absolute values ​​of the stator voltage and the stator current, respectively, as a function of time when the stator voltage of a magnetized rotating machine is changed stepwise at time t_c, Fig. 3 shows a flow chart illustrating an asynchronous machine short-circuit inductance estimation method according to the invention, and Fig. 4 shows an application of an asynchronous machine short-circuit inductance estimation method according to the invention in an asynchronous machine torque control method.

Assume that the stator voltage of a magnetized rotary asynchronous machine changes stepwise at time t_c, and that the stator voltage and the stator current derivative have been measured shortly before this change at time t₂ as well as shortly after the change at time t_x (Figure 2). Since Equation 11 is valid for both at time t_x that t₂, the following dependencies are obtained for said measured quantities s oLj ^ tJ = ujtj + u₀(t_x) (15)

0L_eI (t₂) = u „(t₂) + u₀(t₂) (16)

In practice, the currents and currents of an asynchronous machine cannot change stepwise, so according to Equation 12, the voltage6

9 415 components u₀ is a time-continuous function for which lim {u holds₀(t)} = lim {u₀(t)} = u₀(t_c) (17) t -1; t -1 *

When the measurement moments t_x and t₂ placed very close to the moment of change t_c, then it follows from Equation 17 that

UoitJ «u₀(t₂)(18)

The derivative values ​​of the stator current must therefore be measured just before and immediately after the change in stator voltage. In practice, this means that the stator current derivatives are determined, for example, about 100 μ3 before and after the stator voltage change in a machine with a rotor time constant of about 100 ms. In general, it is conceivable that the measurement moments are set at a time distance from the moment of the stator voltage change, which is at most one thousandth of the rotor time constant of the machine.

When Equation 16 is partially subtracted from Equation 15 and the approximate Equation 18 is applied, oL, (i; (tj-i; (t₂)) = u_e(t₁) -u_e(t₂) + U₀(t₁) -u₀(t₂) «» U_1&gt;(t₁) -u_e(t₂) (19)

It is observed that when the stator voltage changes stepwise, the corresponding change in the stator current derivative depends not only on the short-circuit inductance but only on the magnitude of the voltage change in question. The individual current derivative depends on both the stator voltage and the voltage u₀ (Equation 11), which, however, shrinks in Equation 19, since in the short term u₀(t) is constant despite fluctuations in the supply voltage.

By solving the equation for 19 oL, we find that

9415 that the short-circuit inductance estimate can be calculated by dividing the instantaneous change in stator voltage by the corresponding change in the stator current derivative:

u '(t_x) -U (t₂) oL_s = ------------- ₍20) i'Ctj-iutJ

The method according to the invention is shown as a flow chart in Figure 3, in which the symbol τ has been used to describe the measurement moments t_x and t₂ time difference between:

t_x-t₂ = τ (21)

In blocks 3 and 5, a delay operator D is used, which is defined as follows:

D (x) f (t) = f (t — x), (22) where f is an arbitrary function of t that is delayed by τ: η when multiplied by D (x).

In addition, the method of Figure 3 requires that the stator voltage change stepwise at times t_x and t₂between. This condition does not cause any problems in practice, as typical asynchronous machine drives where parameter identification is required are usually based on frequency converters that control the stator voltage stepwise. The question is only oL_Bsynchronizing the estimation of so that the changes in the stator voltage occur at times t_x and t₂ between.

In Figure 3, at time t_x the stator current i of the asynchronous machine 1 obtained by measuring (t_x) is first derived in block 2 from the derivative ij (t_x). In block 3 Ij (t_x) is delayed by x, so the output of the block in question is i '(t₂). Block 4 is an adder in which the latter delayed derivative is subtracted from the former and whose output corresponds to: / 9415 denominator in Equation 20. Correspondingly at time t_x the stator voltage u.itj obtained by measuring is first delayed by τ; η in block 5 u, (t₂) to obtain. Thereafter, the latter delayed voltage is subtracted from the former in block 6, the output of which corresponds to the numerator in Equation 20. Finally, in block 7, the output of block 6 is divided by the output of block 4 to obtain an estimate of short circuit inductance based on Equation 20.

Figure 4 shows a flow chart of the application of the method according to the invention in an asynchronous machine torque control method. The stator current and voltage of the asynchronous machine 1 obtained by measuring are input quantities to block 8, which corresponds to the short-circuit inductance estimation method according to Fig. 3. The oL obtained as the output of block 8_B, as well as Ϊ. and u_B as well as the presumed parameters R_B, L_B, x_r and (¾ are the input variables for block 9, the output of which is the stator flux estimate that implements Equation 9 as accurately as possible. The flux estimate obtained from block 9 and the measured stator current are input variables for block 10, where the torque estimate T is calculated using the cross input. T_Ref to obtain the control variable μ. Block 12 is a controller in which, on the basis of said control variable, the torque-increasing effect, if μ &lt;0, and the torque-reducing effect, if μ&gt; 0, are obtained by changing the current or voltage supplied to the machine.