RU2696365C1 - Method of measuring resistance to direct current - Google Patents

Abstract

FIELD: metrology.SUBSTANCE: invention relates to measurement equipment, and namely to the field of electrical measurements of resistance to direct current of two-terminal devices having high inductance. Method of measuring resistance to direct current of windings of electrical equipment consists in the fact that through serially connected winding and reference resistor passing constant stabilized current generated by current controller, voltage drops on the winding and the reference resistor are measured and their ratio is calculated, on the basis of which the required resistance of the winding is obtained. Further, when the current in the winding increases to a predetermined value, winding current and voltage are measured on it, based on the results of which the current controller transmission coefficient is calculated, after the current rise to the value close to the preset value, the control error signal is multiplied. At that, after the measuring current increases to a value close to the predetermined value, the control error signal is further integrated, current controller integrating element transfer coefficient is set in compliance with parameters of analyzed winding to be calculated on the basis of measurements made during current rise.EFFECT: technical result is higher measurement accuracy.1 cl, 2 dwg

Description

Technical field

The invention relates to measuring equipment, namely to the field of electrical measurements of DC resistance of two-terminal devices having a large inductance, for example, windings of transformers, reactors and electrical machines.

GOST 3484.1-88 recommends a method for measuring the direct current resistance of the windings of power transformers, which consists in passing direct current from a constant voltage source through a winding and an ammeter, and characterized by a measuring transient process in which the current in the winding and the voltage on it change simultaneously according to a nonlinear law. Measurement of current and voltage to calculate the resistance in the winding is possible only after the establishment time t _{mouth of} their values: t _mouth ≈ 4.6τ when setting the current and voltage with an error of δ = 1% and t _mouth ≈ 6.9τ at δ = 0, 1%, where τ is the transformer winding time constant equal to: τ = L _rpm / R _rpm . Due to the long measurement time by this method, most modern devices of this purpose do not use voltage sources, but current sources - compensating type DC stabilizers with current feedback. Regulation of the measuring current in the transformer windings is a difficult task, since the parameters of the windings (inductance L _rm and resistance R _rm ) of different transformers can vary very much. In particular, the time constants τ of the winding circuit of transformers of various types can vary thousands of times. Therefore, the bandwidth of the controller (and, consequently, its speed) can also vary by a thousand times. In addition, the static gain of the current control loop changes, which depends on the value of the measured resistance, which affects the accuracy of regulation and the stability of the measuring current.

State of the art

The known method described in the invention "Method for measuring the DC resistance of the windings of electrical equipment" (RF patent No. 2531850, CL G01R 27/08, published in Bull. No. 30, 2014).

The method consists in the fact that at the first stage, a constant constant current is passed through the winding and the reference resistor in series, the value of which is calculated based on a preliminary measurement of the resistance of the winding. The voltage drops across the winding and the reference resistor are measured and their ratio is calculated, based on which the desired winding resistance is obtained. Moreover, during the increase in the current in the winding to the calculated current, the voltage of the current stabilizer is maximized, and in the second stage after the current is set equal to the calculated one, this voltage is reduced, which leads to a decrease in the rate of change of current by a factor of many and, as a result, to a reduction in duration second stage.

The disadvantage of this method is the relatively large time to establish current in the second stage.

As a prototype closest to the claimed one, the method described in the invention, “Method for measuring direct current resistance" (RF patent No. 2653173, CL G01R 27/08, published in Bull. No. 13, 05/07/2018) was selected

The specified method consists in the fact that a constant constant current produced by the current regulator is passed through a winding and a reference resistor in series, voltage drops across the winding and the reference resistor are measured, and their ratio is calculated, based on which the desired winding resistance is obtained, and during the current rise in the winding to a predetermined value, measurements of the current of the winding and the voltage on it are carried out and the parameters of the winding are evaluated, and after increasing the current to a value close to the specified d, set the transfer coefficient of the current regulator, the value of which is calculated on the basis of measurements made during the rise of current.

At the first stage, the maximum output voltage of the source is applied to the winding and the current rises to a certain fraction, for example, to (95 - 99)% of the set current. In this case, at the time of increasing current, current and voltage measurements are made to determine the estimates of resistance R _rm and inductance L _rm .

The dependence of the voltage on the transformer winding on the current passing through it is determined by the equation:

u _rm = i (t) · R _rm + L _rm · di / dt. (one)

Integrating equation (1) over the interval from t _k-1 to t _k by the trapezoidal method, we obtain:

L _rm · (i _k - i _k-1 ) + T · (i _k + i _k-1 ) · R _rm / 2 = T · (u _k + u _k-1 ) / 2, (2)

where T = t _k - t _k-1 is the time interval between samples.

In combination with the measurement results in the previous step, we obtain a system of equations in a vector-matrix form

U = IZ, (3)

where Z = [R_sw L_sw]^T- vector of winding parameters; I is a matrix of samples of currents with a dimension of 2 × 2, and the components of the matrix are:

i _{11 (k)} = i _{11 (k -1)} + T · i _k ;

i _{12 (k)} = i _{12 (k -1)} + T · i _{11 (k)} ;

i _{21 (k)} = i _{11 (k-1)} ;

i _{22 (k)} = i _{12 (k-1)} ;

U is a vector of stress samples of dimension 2 × 1, and the components of the vector:

u_{1 (k)}= u_{1 (k-1)}+ u^* _(k)· T;

u _{2 (k)} = u _{1 (k-1)} ;

u ^* _(k) = u ^* _(k-1) + u _(k)

Then the solution of equation (3):

Z = U ⁻¹ · I. (four)

In the prototype, a proportional regulator is used as a current regulator. The parameters of the proportional current controller are the transmission coefficient K _p and the setpoint current. The set current is defined as the value of the output current at which the mismatch between the adjustable and set values is zero. Under the influence of disturbing influences, a deviation of the controlled quantity occurs.

The transfer coefficient of the current regulator K _p and the static error of the current regulation δ is as follows.

Transfer function of the current regulator control loop:

W (s) = A / (1 + s · τ), (5)

Where

A = K _p ⋅K _s / (R _rm + R _p ),

τ = L _rpm / (R _rm + R _p ), (6)

R _p is the resistance of the conductors connecting the winding to the device, K _with is the transfer coefficient of the current measuring circuit (in the simplest case, it is equal to the resistance of the reference resistor in the feedback of the current source).

When using a microcontroller as a current regulator, to strictly describe the processes in the current control loop, one should use the mathematical apparatus of z-conversion. In this case, the discrete transfer function of the first-order link with the zero-order storage element has the form (see, for example, Rotach V.Ya. Theory of automatic control. - M .: MPEI, 2008, p. 291):

W ^* (z) = [(z - 1) / z] · Z {W (s) / s} = A · (1 - d) / (z - d), (7)

where d = exp (–T / τ), T is the sampling period of the analog-to-digital converter (ADC) of the microcontroller.

If the cutoff frequency of the open system of the current regulator is significantly less than the sampling frequency, you can replace the discrete representation of the system with a continuous one without significant loss of accuracy. Then the transfer function of the current control loop will have the form (5).

Let the selected cutoff frequency of the system

f _c << 1 / T. (eight)

Then the condition is satisfied:

| W (j2πf _c τ) | = 1,

and the required transfer coefficient of the current regulator, taking into account (5), is approximately equal

. (9)

. (9)

Static current control error

δ = 1 / (1 + W (0)), (10)

taking into account (5) and (9), approximately

δ ≈ 1 / 2πf _c τ, (11)

or as a percentage

δ _% ≈ 15.9 / f _c τ%. (12)

Current establishment time in the second stage with an accuracy of 0.1%

T _per = 6.9τ (R _rm + R _p ) / (K _p ⋅K _s + R _rm + R _p ). (13)

When condition (8) is satisfied, approximately

T _lane ≈ 1.1 / f _c . (14)

The disadvantage of this method is that with a small constant winding time τ, the error in the stabilization of the measuring current can be large, which will lead to an increase in the error in measuring the resistance of the winding.

The implementation of the invention

The objective of the present invention is to reduce the error of stabilization of the measuring current and, as a consequence, to increase the accuracy of measuring the resistance of the winding to direct current.

The problem is solved by implementing the proportional-integral (PI) regulation algorithm in the microcontroller of the current controller.

In the present invention, a constant constant current generated by the current regulator is passed through the winding and the reference resistor in series, the voltage drops across the winding and the reference resistor are measured, and their ratio is calculated, based on which the desired resistance of the winding is obtained, and during the increase in current in the winding to the specified the values measure the current of the winding and the voltage on it and evaluate the parameters of the winding, and after increasing the current to a value close to the specified value, set The transmission coefficient of the current regulator is calculated, the value of which is calculated on the basis of measurements made during the rise of the current. In this case, the control error signal is additionally integrated, and the transfer coefficient of the integrating link of the current regulator is set in accordance with the values of the parameters of the studied winding, which are calculated on the basis of measurements made during the increase in current.

In the presence of an integrating link, the discrete transfer function of the current regulator control loop, taking into account formula (7), will take the form:

where K _and is the transfer coefficient of the integrating link of the PI controller.

When the condition is met

the factors (z - d) in the numerator and denominator of the transfer function (15) are reduced, and the discrete transfer function of the control loop of the current regulator will take the form:

those. the current control loop will include only an integrating link, which will provide almost zero static error and reduce the error as a whole in the regulator bandwidth. For a given cutoff frequency f _c , in the proposed method, as in the prototype, the gain K _{p is} calculated by the formula (9). Thus, the results of voltage measurements across the winding and the current through it in a first step, using the formulas (4), (6), (9) and (16) are calculated parameters of the current regulator K _p and K, _and are then used in the control algorithm current regulator in the second stage.

Brief Description of the Figures

In FIG. 1 shows a graph of the transient process of establishing the measuring current in the transformer winding using the proposed method.

In FIG. 2 shows a graph of the transient process of establishing the measuring current in the transformer winding when using the method according to patent RU No. 2653173.

Implementation example

The proposed method was tested in modeling the measurement of the resistance of the low voltage winding of the transformer TMG-630/10. Used PI controller. The voltage of the current source is 20 V, the sampling period is 100 μs. The parameters of the regulator calculated by formulas (4), (6), (9) and (16) are K _p = 113, K _and = 2.2⋅10 ^–4 . The measuring current is 10 A. A graph of the current is shown in FIG. 1. It can be seen that the transition process ends in less than 0.15 s. Small short-term initial current changes in the second stage are due to excessive accumulation of data in the regulator integrator in the first stage (current rise stage). The error in establishing the strength of the measuring current is practically absent.

In FIG. 2 shows a graph of the transient process of establishing the measuring current in the same winding of the same transformer using the method described in the prototype. It can be seen that in this case the current is set less accurately. The calculation of the error in establishing the strength of the measuring current according to the formula (12), gives the value δ _% = 0.89%.

Chelenergopribor LLC has developed and manufactured a Trom-1 milliometer designed for measuring the resistance of the windings of electric machines, including transformers (see http://limi.ru/product/milliometer_trom_1/). In the algorithm of operation of the measuring current regulator of this device, the claimed method is applied. The device passed state tests and was entered in the State Register of Measuring Instruments of the Russian Federation under No. 67448-17.

Claims (1)

A method for measuring the direct current resistance of windings of electrical equipment, which consists in passing a constant constant current produced by a current regulator through a winding and a reference resistor, measuring the voltage drop across the winding and the reference resistor and calculating their ratio, based on which the desired winding resistance is obtained moreover, during the rise of the current in the winding to a predetermined value, measurements of the current of the winding and the voltage on it are performed, based on the results the tats of which the transfer coefficient of the current regulator is calculated, by which, after the current rises to a value close to the predetermined one, the regulation error signal is multiplied, characterized in that after the measurement current rises to a value close to the predetermined one, the regulation error signal is additionally integrated, moreover, the integrating transmission coefficient the links of the current regulator are set in accordance with the values of the parameters of the studied winding, which are calculated on the basis of measurements made during the rise of current.

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