RU2491559C1 - Method to determine resistance and inductance of scattering of primary winding of voltage transformer - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: in the available method of measurement of inductance of scattering of the primary winding of the voltage transformer as product of the time constant of the transition process τ and active resistance of the oscillographed R_c, circuit L_σ2bh=τ·R₁₁, consisting in measurement of parameters of the second section of the transition process of current as output voltage jumps on one of phases, according to the invention the secondary winding of the same phase is shorted, the voltage surge is sent from the voltage source with negligible resistance to the primary winding, inductance of scattering is determined, as well as resistance of the primary winding of the voltage transformer, the transition process is considered in the form of three exponents, in accordance with the expression $$i_1\left(t\right)=U_1\left(\frac{1}{2R_m}\left(1-e^{\frac{-t}{{\tau }_1}}\right)+\left(\frac{1}{2R_a}-\frac{1}{R_m}\right)\left(1-e^{\frac{-t}{{\tau }_2}}\right)+\left(\frac{1}{2R_a}+\frac{1}{2R_m}\right)\left(1-e^{\frac{-t}{{\tau }_3}}\right)\right).$$

EFFECT: possibility to determine both inductance of scattering of a pair of voltage transformer windings and resistance of a pair of voltage transformer windings, at the same time the transition process is considered in the form of three exponents, which helps to more accurately determine transformer parameters.

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Description

The invention relates to measuring technique and can be used to determine the resistance and leakage inductance of the primary winding of a voltage transformer. The invention can be used to diagnose transformers.

For a voltage transformer, the measurement time of the resistance of the primary winding on direct current with an open secondary winding is tens of minutes. Meanwhile, in industry, the measurement time is undesirable to have more than 30 s. [Oleh W. Iwansiw, P. Eng. "The art and science of measuring the winding resistance of power transformers.", October 29, 2011, <http://www.eltelindustries.com/webadmin/PDFs/22042009104706100.pdf>]. To reduce the time of measuring the resistance of the primary winding, it was proposed to test the transformer with a jump in the input signal and idling at the output [GuanGen-zhi, LiuKai, HuangHai-kun, ZhaoLai-hong. "A New Quick Measuring Method of DC Resistance of Transformer's Windings." Gaoyadianqi, HighVoltageAppar., 40, No. 1, p.50-52, 2004. China, rez. Eng.], When the steady-state value of the input current and the resistance of the primary DC winding is found by extrapolation. The time constant in this measurement is proportional to the magnetization inductance. Depending on the current, it can vary by 2-3 times. When measuring only at the beginning of the exponent, achieving a sufficiently high accuracy is difficult both due to a change in the scattering inductance and due to instrumental errors. If the measurement interval is used at several time constants, then the nonlinearity and instrumental errors affect less, but the measurement time is less than 30 s.

Closest to the proposed method for determining the leakage inductance of the primary winding of a voltage transformer is the determination of the leakage inductance of the high voltage (primary) winding L _σBH as the product of the transient time constant (τ) and the resistance of the oscillographic circuit (R _c ):

L _σBH = τ * R _c (patent No. 2377586).

The essence of the method is that the primary winding of one of the phases is alternately supplied with a DC voltage and a zero signal, the primary windings of the other two phases are shorted through resistors, and all secondary windings are open. The measurement of the leakage inductance of the primary winding is made by calculating the transient time constant when the input signal is reset to zero. The resistance of the oscilloscope circuit must be measured in some other way that is not discussed in the application. The speed of determining the time constant is quite high compared to the previous method. The disadvantage of this method is the lack of measurement of active resistance. This method is not applicable for single phase transformers. This method takes into account only one exponent in the transition process, which makes it insufficiently accurate.

The technical problem solved by the invention is to expand the measured parameters and increase the accuracy of the measurement.

The technical result obtained by the invention consists in supplying a voltage jump with a negligible output resistance to the primary winding of the transformer when the secondary winding is short-circuited. In this case, it is possible to determine not only the leakage inductance of the pair of voltage transformer windings, but also the resistance of the pair of voltage transformer windings, the transient is considered in the form of three exponentials, which contributes to a more accurate determination of the parameters of the transformer.

The specified technical result is achieved by the fact that in the known method for measuring the scattering inductance of the primary winding of a voltage transformer as the product of the transient time constant τ by the active resistance of the oscillogram R _{c of the} circuit L _σBH = τ * R _c , consisting in measuring the parameters of the second portion of the current transient during the jump input voltage at one of the phases, according to the invention, the secondary winding of the same phase is short-circuited, a voltage surge is supplied from a voltage source with a negligible resistance by gravitating to the primary winding, the scattering inductance and the resistance of the primary winding of the voltage transformer are determined, the transient is considered in the form of three exponentials, in accordance with the expression

,

,

,where τ ₁ is the time constant of the first exponent of the transient, taken equal to the ratio $$\frac{L_a}{2R_m}$$

,

,τ ₂ is the time constant of the second exponent of the transient, taken equal to the ratio $$\frac{L_a}{R_a}$$

,

,τ ₃ - time constant of the third exponent of the transition process, taken equal to the ratio $$\frac{2L_m}{R_a}$$

,

i ₁ - input current,

U ₁ - voltage surge at the input of the transformer,

R _m is the magnetization resistance,

L _m - magnetization inductance,

L _a - leakage inductance of the primary winding, taken equal to the leakage inductance of the secondary winding reduced to the primary winding,

R _a is the resistance of the primary winding, taken equal to the resistance of the secondary winding, reduced to the primary winding;

the time interval in which the third exponent is linear and the time interval in which the first exponent has already been established and the second exponent is linear are considered in turn; the influence of the currents of the first and third exponents on the transformer transient is taken into account, after their exclusion a new transient is obtained and the time constant of the second exponent τ ₂ is determined, and then the resistance R _a and the leakage inductance L _{a of the} primary winding of the voltage transformer.

Figure 1. The equivalent circuit of the voltage transformer.

Figure 2. Transient process for a power transformer (a special case of a voltage transformer with a power above 1 MW) with typical parameters U ₁ = 1 B, L _a = 2.89 H, R _a = 45.56 Ohm, L _m = 1,033 kH, R _m = 1.21 megohms.

Figa. The transient process for a power transformer (a special case of a voltage transformer with a power above 1 MW) with typical parameters U ₁ = 1 V, L _a = 2.89 H, R _a = 45.560 m, L _m = 1.033 kH, R _m = 1, 21 megohms, excluding the influence of the third exponent.

Fig.2b. The transient process for a power transformer (a special case of a voltage transformer with a power above 1 MW) with typical parameters U ₁ = 1 V, L _a = 2.89 H, R _a = 45.560 m, L _m = 1.033 kH, R _m = 1, 21 megohms, excluding the influence of the third and first exponents.

Figure 3. A device that supplies a voltage jump to the input of a voltage transformer with a negligible resistance.

The input current of the voltage transformer, represented by the equivalent circuit in Fig. 1, when applying a voltage jump with a negligible output resistance to the primary winding of the voltage transformer during a short circuit of the secondary winding, is shown in Fig. 2 and can be written up to a fraction of a percent as:

,

,

,where τ ₁ is the time constant of the first exponent of the transient, taken equal to the ratio $$\frac{L_a}{2R_m}$$

,

,τ ₂ is the time constant of the second exponent of the transient, taken equal to the ratio $$\frac{L_a}{R_a}$$

,

,τ ₃ - time constant of the third exponent of the transition process, taken equal to the ratio $$\frac{2L_m}{R_a}$$

,

U ₁ - voltage surge at the input of the transformer,

R _m is the magnetization resistance,

L _m - magnetization inductance,

L _a - leakage inductance of the primary winding, taken equal to the leakage inductance of the secondary winding, reduced to the primary winding;

R _a is the resistance of the primary winding, taken equal to the resistance of the secondary winding reduced to the primary winding.

The scattering inductance of a pair of windings is calculated as L _volt = 2L _a . The resistance of a pair of windings is found as R _rm = 2R _a .

The values of the parameters L _a and R _a are found from the instantaneous values of the transient current.

To determine the leakage inductance of a pair of windings of a voltage transformer, we study the transient process for a voltage transformer with a voltage jump at the input and a short circuit of the output windings.

The recommended algorithm for calculating the desired parameters is given below for U ₁ = 1 V and typical parameters of a voltage transformer: L _a = 2.89 Gh, R _a = 45.560 m, L _m = 1.033 kH, R _m = 1.21 MΩ.

The main interest for us is the second exponent of the transition process (Figure 2), the time constant τ _{2 of} which is determined by the desired parameters. It is impossible to wait long for the process to be established, since as the third exponent approaches the end, the influence of nonlinearity increases. To exclude the third exponent, we consider the interval from 10τ ₂ to 0.1τ ₃ , because the nonlinearity in this section is relatively small, and the measurement time usually does not exceed 30 seconds. In this interval, the third exponent has the linear form a + bt, i.e. we can take into account the introduced change of this exponential on the transient process in the interval from zero to 0.1τ ₃ if we find bt. The value of and b can be found by solving a system of two equations:

, $$\{\begin{array}{l}{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="00000017.png"\; state="\{\{state\}\}">i</figure-callout>}}_{\mathrm{3,1}}=a+b{t}_{\mathrm{one}}\\ i_{3.2}=a+\mathrm{<figure-callout\; id="2"\; label="b\; t"\; filenames="00000018.png"\; state="\{\{state\}\}">b\; </figure-callout>}{t}_{}{}_2\end{array}$$

,

Where

t ₁ = 10τ ₂ ,

t ₂ = 0,1τ ₃ ,

i _3,1 - current at time t ₁ ,

i _3,2 is the current at time t ₂ .

Solving the system of equations, we find a = 0.0109809 A and b = 2.28813 · 10 ^-4 A / s. Subtract from all current values bt, thereby we obtain a new graph (Fig.2A).

Next, get rid of the first exponent. For this, we consider the interval from 10τ ₁ to 0.1τ ₂ , because in this section, the first exponent is established and the second exponent has the linear form c + dt. The value of c and d can be found by solving a system of two equations:

, $$\{\begin{array}{l}{i}_{2.1}=c+b{t}_3\\ i_{2.2}=c+b{t}_{\mathrm{four}}\end{array}$$

,

Where

t ₁ = 10τ ₂ ,

t ₂ = 0,1τ ₃ ,

i _2,1 - the current at time t ₃ ,

i _2.2 is the current at timev.

Solving the system of equations, we find c = 5.13137 · 10 ^-7 A and d = 0.164626 A / s. Subtracting from all current values in the interval from 10τ ₁ to 10τ _{2 the} value of s, we obtain the adjusted graph of the transition process of the input current (Fig.2b).

On the resulting graph, we consider the interval from 10τ ₁ to 10τ ₂ . Take a few points and calculate the inductance of the dissipation of the voltage transformer according to the formula L _a = τ ₂ · R _a .

First point: t = 0.1 s, the current value i = 0,00870660 A.

The second point: t = 0.001 s, the current value i = 0.000171554 A.

The resulting exponent (figb) is described by the formula:

, $$i_{n\mathrm{about}\mathrm{at}}=I_{\mathrm{at}\mathrm{from}t2}\left(\mathrm{one}-e^{\frac{-t}{{\tau }_2}}\right)$$

,

where i _new is the current value at time t in the interval from 10τ ₁ to 10τ ₂ ,

- установившееся значение тока. $$I_{\mathrm{at}\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="00000018.png"\; state="\{\{state\}\}">t</figure-callout>}2}=\frac{U_{\mathrm{one}}}{2R_a}-\frac{U_{\mathrm{one}}}{R_m}$$

- steady-state current value.

The magnetization resistance R _m can be found by the formula:

, $$R_m=\frac{\mathrm{one}}{2c}$$

,

where c is the steady-state current value of the first exponent found earlier.

The steady-state current of the second exponent is determined by the following formula:

I _mouth2 = a-s,

where a is the sum of the steady-state current values of the first and second exponent, found earlier.

For a three-phase transformer, the resistance and leakage inductance of the primary winding of the voltage transformer are alternately found for each phase.

The resistance of the primary winding of the voltage transformer R _a is found by the following formula:

. $$R_a=\frac{U_{\mathrm{one}}}{2(I_{\mathrm{at}\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="00000018.png"\; state="\{\{state\}\}">t</figure-callout>}2}+\frac{U_{\mathrm{one}}}{R_m})}$$

.

We find the value of the time constant by the formula:

.

.

The scattering inductance of the primary winding of a voltage transformer is defined as the product of the time constant of the second exponent τ ₂ and the resistance of the primary winding R _a : L _a = τ ₂ R _a ,

where τ ₂ - corresponds to τ from the prototype after the exclusion of the first and third exponent,

R _a - corresponds to R _c from the prototype when using a voltage surge feed device with a negligible resistance.

According to the calculations, the resistance of the primary winding is 45.5313 Ohms, the scattering inductance of the primary winding for the first point is 2.8915 H, and for the second - 2.8914 H. The nominal resistance of the primary winding is 45.560 m, and the nominal leakage inductance of the primary winding is 2.89 GN. The relative error in determining the resistance of the primary winding or a pair of windings is - 0.063%. The relative error in determining the leakage inductance of the primary winding or a pair of windings in the first case is 0.052%, in the second case it is 0.048%. The obtained errors in determining the resistance and inductance of the primary winding are significantly lower than those given in the literature, including in patent No. 2377586.

To implement the supply of a signal voltage with a negligible input impedance to the transformer input with a sufficiently accurate current measurement, the circuit shown in FIG. 3 can be used.

Consider the circuit of FIG. 3 at rest. At the input of the operational amplifier A1, a zero voltage is applied. The source current I ₀ is, for example, 10 mA. We believe that the operational amplifier A1 is ideal (U _in, differential = 0, I _{in +} = I _in- = 0). From this it follows that U _{in +} = U _in = 0, that is, at the source of the field-effect transistor VT1 there will be a zero potential. No current will flow through the voltage transformer due to the lack of potential difference. So, all the current will flow through the transistor VT1. The same current will flow through a precision resistor R ₀ , the resistance of which is, for example, 10 m. The voltage drop across the resistor R ₀ will be 10 mV. Based on the specifications of field-effect transistors, it is possible to choose such that the field-effect transistor operates in an amplifying mode for any current of a voltage transformer. By connecting an analog-to-digital converter (ADC) to the potential terminals of resistor R ₀ , we can measure the current flowing through the field effect transistor VT1. Subtracting the initial current I ₀ from this current, we find the primary current i ₁ .

Consider the operation of the circuit in dynamics. The voltage jump on the primary winding of the first phase of the voltage transformer U ₃ = U _{1 is} provided by a DC voltage source using a switch. The input current of the voltage transformer is almost equal to the change in the drain current of transistor VT1. To organize the minimum delay on the voltage jump transistor VT1 is supported in the open mode using the current source I ₀ . The current i ₁ flowing through the primary winding of the voltage transformer is measured using an ADC connected to a precision resistor with a known resistance. By fixing the values of this current for different instants of time, we can find the resistance and inductance of the scattering of a pair of windings of a voltage transformer using the algorithm described above. The output resistance of the voltage source from which the voltage transformer is fed is approximately equal to the resistance of the field-effect transistor divided by the gain of the operational amplifier. With a typical field-effect transistor resistance of units of Ohms and a gain of about 10 ^{6, the} calculated output impedance of the circuit has a negligible value of the order of units of µOhm. Resistance wires and contacts can be eliminated by the well-known four-wire connection of wires. At the same time, the resistance of the reference resistor R ₀ can be selected large enough (resistors with low resistance are usually less accurate) without affecting the transformer input current of the voltage transformer. The measurement of the resistance and inductance of the dissipation of a pair of windings of a voltage transformer during a voltage surge on the primary winding and a short circuit of the secondary winding was described above. In the prototype, after the signal is established after the jump, the signal is reset and it is here that the measurement was carried out. Thus, the proposed method has an advantage over the known method and speed.

Claims (1)

A method for measuring the scattering inductance of the primary winding of a voltage transformer as a product of the transient time constant τ and the active resistance of the oscillogram R _{c of the} circuit L _σBH = τ · R _c , which consists in measuring the parameters of the second portion of the current transient when the input voltage jumps on one of the phases, characterized in that the secondary winding of the same phase is short-circuited, a voltage surge is supplied from a voltage source with a negligible resistance to the primary winding, the inductance of the Nia and resistance of the transformer pair windings transient considered as three exponentials in accordance with the expression

,
where τ ₁ is the time constant of the first exponent of the transient, taken equal to the ratio $$\frac{L_a}{2R_m}$$

,
τ ₂ - the time constant of the second exponent of the transient, taken equal to the ratio $$\frac{L_a}{R_a}$$

,
τ ₃ - time constant of the third exponent of the transient, taken equal to the ratio $$\frac{2L_m}{R_a}$$

,
i ₁ - input current,
U ₁ - voltage surge at the input of the transformer,
R _m is the magnetization resistance,
L _m - magnetization inductance,
L _a - leakage inductance of the primary winding, taken equal to the leakage inductance of the secondary winding reduced to the primary winding,
R _a is the resistance of the primary winding, taken equal to the resistance of the secondary winding, reduced to the primary winding;
considered alternately is the time interval in which the third exponent has a linear form and the time interval in which the first exponent is already established and the second exponent has a linear form;
the influence of the currents of the first and third exponents on the transformer transient is taken into account, after their exclusion a new transient is obtained and the time constant of the second exponent τ ₂ is determined, and then the resistance R _a and the leakage inductance L _{a of the} primary winding of the voltage transformer.

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