CN105259425A - Method for testing relative dielectric constant of oil gap of transformer under low-frequency sine excitation - Google Patents

Abstract

The invention discloses a method for testing the relative dielectric constant of the oil gap of a transformer under low-frequency sine excitation. First, the direct-current conductivity Sigma0 of the oil gap of a transformer, the ion mobility Mu in the oil gap of the transformer, the thickness L of the oil gap of the transformer and the angular frequency Omega for applying low-frequency sine excitation are tested at the temperature T; then, the tested data is substituted in a relevant formula and processed; and finally, the relative dielectric constant of the oil gap of the transformer under low-frequency sine excitation is obtained. By adopting the method of the invention, on the basis of effectively working out the relative dielectric constant of the oil gap of the transformer under low-frequency sine excitation, the electrode polarization parameters of the oil gap of the transformer under low-frequency sine excitation can be reflected.

Description

The method of testing of the lower transformer oil clearance relative dielectric constant of low frequency sinusoidal excitation

Technical field

The invention belongs to transformer insulation state detection field, be specifically related to the method for testing of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation.

Background technology

Oil-filled transformer is the unique selection of main-transformer in current UHV (ultra-high voltage), extra-high voltage electric transmission and transformation system, the operational reliability of oil-filled transformer is directly connected to the safety and stability of associate power system, oil-filled transformer is the nucleus equipment in electric system, paper oil insulation state is one of key factor determining oil-filled transformer insulation life, and frequency domain dielectric response method is can one of the accepted method of efficient diagnosis paper oil insulation moisture and ageing state thereof.Oil-filled transformer Oil-Paper Insulation is made up of transformer oil clearance, paper web pressing plate and stay etc., and transformer oil clearance is the important component part of Oil-Paper Insulation.

When Oil-Paper Insulation carries out the test of frequency domain dielectric response, executing sinusoidal excitation voltage outward carries out by frequency sweep test by high frequency to low frequency, when low-frequency test, the dielectric response characteristic of transformer oil clearance is one of principal element determining Oil-Paper Insulation overall dielectric characteristic, and the dielectric response characteristic major effect mechanism of transformer oil clearance is the conductance for alternating current caused that polarized by transformer oil clearance internal electrode, therefore in order to can more comprehensively study, characterize the dielectric response characteristic of the lower Oil-Paper Insulation of low frequency sinusoidal excitation, can better dielectric spectroscopy method be applied in Practical Project, be badly in need of a kind of relative dielectric constant that can either calculate the lower transformer oil clearance of low frequency sinusoidal excitation, the method of the lower transformer oil clearance electrode polarization parameter of low frequency sinusoidal excitation can be characterized again simultaneously.

Summary of the invention

In order to the relative dielectric constant of the lower transformer oil clearance of low frequency sinusoidal excitation can be calculated, the lower transformer oil clearance electrode polarization parameter of low frequency sinusoidal excitation can be characterized again simultaneously, the invention provides the method for testing of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation.

The method of testing of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation, relative dielectric constant and the oil clearance electrode polarization parameter of the lower transformer oil clearance of low frequency sinusoidal excitation is obtained in the test of Oil-Paper Insulation frequency domain dielectric response, it is characterized in that, comprise following steps:

1.1 import following data into by the sensor be arranged in experimental provision under probe temperature T: the DC conductivity σ of transformer oil clearance ₀, transformer oil clearance intermediate ion mobility [mu], the thickness L of transformer oil clearance; Measure the angular frequency obtaining applying low frequency sinusoidal excitation;

The data that above-mentioned test obtains to be input in the model (1) in computing unit by 1.2, obtain the relative dielectric constant of the lower transformer oil clearance of low frequency sinusoidal excitation:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_r^{\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′}+\frac{{\mathrm{\ϵ}}_{r}L{({\mathrm{q\σ}}_0^3\mathrm{\μ}kT/2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_0)}^{1/2}-2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\\ {\mathrm{\ϵ}}_r^{\′\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′\′}+\frac{{\mathrm{\σ}}_0{\mathrm{\ωL}}^2{\mathrm{q\ϵ}}_r/2-{\mathrm{\ϵ}}_r\mathrm{\ω}L{\left(2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r{\mathrm{\ϵ}}_{0}q\right)}^{1/2}}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\end{array}\right.---\left(1\right)$

In formula, q is unit electric charge carried charge, k=1.38 × 10 ^-23j/K is Boltzmann constant, ε _r=2.2 is transformer oil power frequency relative dielectric constant, ε 0=8.85 × 10 ^-12f/m is permittivity of vacuum, ε ' _f, ε " _fbe respectively relative dielectric constant real part, the relative dielectric constant imaginary part of transformer oil clearance when applying the frequency f=0.1Hz of sinusoidal excitation, ε ' _r(ω), ε " _r(ω) relative dielectric constant real part, relative dielectric constant imaginary part that angular frequency is the lower transformer oil clearance of low frequency sinusoidal excitation of ω is respectively;

1.3 by the model of 1.2 the data obtaineds in computing unit (2), and the data obtained substitute into the relaxation time τ that following formula then can obtain the lower transformer oil clearance electrode polarization of low frequency sinusoidal excitation _ePwith electrode polarization polarization layer thickness L _d:

$\left\{\begin{array}{c}{\mathrm{\τ}}_{EP}=L{\left(\frac{{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}{2{\mathrm{\σ}}_0\mathrm{\μ}kT}\right)}^{1/2}\\ L_D={\left(\frac{2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}kT\mathrm{\μ}}{{\mathrm{q\σ}}_0}\right)}^{1/2}\end{array}\right.---\left(2\right);$

1.4 export 1.2 and 1.3 step gained to subsequent processing units or result display unit.

The formulation process of method of testing of the present invention is as follows:

When transformer oil clearance does not apply outside sinusoidal excitation, have when the transformer oil in transformer oil clearance reaches thermal equilibrium:

$n_{+}=n_{-}=n_0=\frac{{\mathrm{\σ}}_0}{2q\mathrm{\μ}}---\left(3\right)$

In formula, n ₊, n _-be respectively negative ion concentrations in transformer oil clearance, when transformer oil clearance reaches thermal equilibrium, the concentration of negative ions is equal is n ₀, σ ₀for the DC conductivity of transformer oil clearance, q is electric charge institute of unit carried charge.When applying low frequency sinusoidal driving voltage, transformer oil clearance internal electrode polarization process can complete and transformer oil clearance inner ion concentration balances required relaxation time τ again _ePfor:

${\mathrm{\τ}}_{EP}=\frac{L}{2\mathrm{\μ}}{\left(\frac{{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_0}{n_{0}kT}\right)}^{1/2}---\left(4\right)$

In formula, k=1.38 × 10 ^-23j/K is Boltzmann constant, ε _r=2.2 is transformer oil power frequency relative dielectric constant, ε ₀=8.85 × 10 ^-12f/m is permittivity of vacuum, and T is the temperature of transformer oil clearance.Now, at the polarization layer thickness L that ate electrode produces _dfor:

$L_D=\frac{1}{q}{\left(\frac{{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}kT}{n_0}\right)}^{1/2}---\left(5\right)$

Formula (3) substitution formula (4), formula (5) can be obtained:

$\left\{\begin{array}{c}{\mathrm{\τ}}_{EP}=L{\left(\frac{{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}{2{\mathrm{\σ}}_0\mathrm{\μ}kT}\right)}^{1/2}\\ L_D={\left(\frac{2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}kT\mathrm{\μ}}{{\mathrm{q\σ}}_0}\right)}^{1/2}\end{array}\right.---\left(6\right)$

Electrode polarization parameter shown in formula (6) is updated in Debye relaxation model, transformer oil relative dielectric constant can be obtained and express equation:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_r^{\′}\left(\mathrm{\ω}\right)={\mathrm{\ϵ}}_r+\frac{{\mathrm{\Δ\ϵ}}_{EP}}{1+{\mathrm{\ω}}^2{\mathrm{\τ}}_{EP}^2}\\ {\mathrm{\ϵ}}_r^{\′\′}\left(\mathrm{\ω}\right)=\frac{{\mathrm{\Δ\ϵ}}_{EP}{\mathrm{\ω\τ}}_{EP}}{1+{\mathrm{\ω}}^2{\mathrm{\τ}}_{EP}^2}\end{array}\right.---\left(7\right)$

In formula, ω is applied voltage angular frequency, Δ ε _ePexpression formula is:

Δε _EP＝(L/2L _D-1)ε _r(8)

Formula (6) is substituted into formula (7) can obtain

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_r^{\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′}+\frac{{\mathrm{\ϵ}}_{r}L{({\mathrm{q\σ}}_0^3\mathrm{\μ}kT/2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_0)}^{1/2}-2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\\ {\mathrm{\ϵ}}_r^{\′\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′\′}+\frac{{\mathrm{\σ}}_0{\mathrm{\ωL}}^2{\mathrm{q\ϵ}}_r/2-{\mathrm{\ϵ}}_r\mathrm{\ω}L{\left(2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r{\mathrm{\ϵ}}_{0}q\right)}^{1/2}}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\end{array}\right.---\left(9\right)$

Consider before galvanic polarization, due to the effect of the dipole pilot polarization etc. of transformer oil clearance inside, its dielectric parameter has changed, and the time scale of ion thermal motion, then formula (9) should be rewritten as:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_r^{\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′}+\frac{{\mathrm{\ϵ}}_{r}L{({\mathrm{q\σ}}_0^3\mathrm{\μ}kT/2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_0)}^{1/2}-2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\\ {\mathrm{\ϵ}}_r^{\′\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′\′}+\frac{{\mathrm{\σ}}_0{\mathrm{\ωL}}^2{\mathrm{q\ϵ}}_r/2-{\mathrm{\ϵ}}_r\mathrm{\ω}L{\left(2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r{\mathrm{\ϵ}}_{0}q\right)}^{1/2}}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\end{array}\right.---\left(10\right)$

In formula, ε ' _f, ε " _fbe respectively relative dielectric constant real part, the relative dielectric constant imaginary part of transformer oil clearance during the frequency f=0.1Hz applying excitation.

The present invention can calculate the relative dielectric constant of the lower transformer oil clearance of low frequency sinusoidal excitation, the lower transformer oil clearance electrode polarization parameter of low frequency sinusoidal excitation can be characterized again simultaneously, contribute to the dielectric response characteristic more comprehensively studying, characterize the lower transformer oil clearance of low frequency sinusoidal excitation, can dielectric spectroscopy method be applied in Practical Project better.

Accompanying drawing explanation

The method of testing process flow diagram of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation of Fig. 1

The method of testing example of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation of Fig. 2

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described:

Figure 1 shows that the method for testing process flow diagram of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation.As can be seen from the figure the method for testing of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation mainly comprises the following steps:

1.1 tests obtain the temperature T of transformer oil clearance;

Under 1.2 probe temperature T, the DC conductivity σ of transformer oil clearance ₀, transformer oil clearance intermediate ion mobility [mu];

The thickness L of 1.3 measuring transformer oil clearances;

1.4 measure the angular frequency applying low frequency sinusoidal excitation;

1.5 data above-mentioned test obtained substitute into following formula, obtain the relative dielectric constant of the lower transformer oil clearance of low frequency sinusoidal excitation:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_r^{\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′}+\frac{{\mathrm{\ϵ}}_{r}L{({\mathrm{q\σ}}_0^3\mathrm{\μ}kT/2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_0)}^{1/2}-2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\\ {\mathrm{\ϵ}}_r^{\′\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′\′}+\frac{{\mathrm{\σ}}_0{\mathrm{\ωL}}^2{\mathrm{q\ϵ}}_r/2-{\mathrm{\ϵ}}_r\mathrm{\ω}L{\left(2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r{\mathrm{\ϵ}}_{0}q\right)}^{1/2}}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\end{array}\right.$

In formula, q is unit electric charge carried charge, k=1.38 × 10 ^-23j/K is Boltzmann constant, ε _r=2.2 is transformer oil power frequency relative dielectric constant, ε ₀=8.85 × 10 ^-12f/m is permittivity of vacuum, ε ' _f, ε " _fbe respectively relative dielectric constant real part, the relative dielectric constant imaginary part of transformer oil clearance during the frequency f=0.1Hz applying excitation, ε ' _r(ω), ε " _r(ω) relative dielectric constant real part, relative dielectric constant imaginary part that angular frequency is the lower transformer oil clearance of low frequency sinusoidal excitation of ω is respectively.

Calculating the parameter that can obtain the polarization of low frequency sinusoidal excitation bottom electrode under low frequency sinusoidal excitation while transformer oil clearance relative dielectric constant, the data obtained by above-mentioned test substitute into the relaxation time τ that following formula then can obtain the lower transformer oil clearance electrode polarization of low frequency sinusoidal excitation _ePwith electrode polarization polarization layer thickness L _d:

$\left\{\begin{array}{c}{\mathrm{\τ}}_{EP}=L{\left(\frac{{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}{2{\mathrm{\σ}}_0\mathrm{\μ}kT}\right)}^{1/2}\\ L_D={\left(\frac{2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}kT\mathrm{\μ}}{{\mathrm{q\σ}}_0}\right)}^{1/2}\end{array}\right.$

Figure 2 shows that the method for testing example of the lower transformer oil clearance relative dielectric constant of a kind of low frequency sinusoidal excitation.Recording transformer oil clearance temperature is 30 DEG C, and at recording 30 DEG C, transformer oil clearance DC conductivity is 7.23 × 10 ^-13s/m, at 30 DEG C, transformer oil clearance intermediate ion mobility is 1.73 × 10 ^-10m ²/ Vs, the thickness 0.5mm of oil clearance, execute recording transformer oil clearance relative dielectric constant when driving voltage frequency is 0.1Hz and be outward: ε ' _f=3.86, ε " _f=0.8.The lower transformer oil clearance relative permittivity value of low frequency sinusoidal excitation adopting the inventive method to calculate as shown in Figure 2 can preferably and experiment test value meet, calculated value and measured value error are in 5%, in tolerance interval, in computation process can under environment described in example transformer oil clearance electrode polarization parameter be: the relaxation time τ of electrode polarization simultaneously _ePfor 824s, polarization layer thickness is about 0.018mm.Then illustrate that the inventive method can obtain the lower transformer oil clearance relative permittivity value of low frequency sinusoidal excitation effectively, the parameter characterizing the lower transformer oil clearance electrode polarization of low frequency sinusoidal excitation can be obtained again simultaneously.

Claims (1)

1. the method for testing of the lower transformer oil clearance relative dielectric constant of low frequency sinusoidal excitation, relative dielectric constant and the oil clearance electrode polarization parameter of the lower transformer oil clearance of low frequency sinusoidal excitation is obtained in the test of Oil-Paper Insulation frequency domain dielectric response, it is characterized in that, comprise following steps:

1.1 import following data into by the sensor be arranged in experimental provision under probe temperature T: the DC conductivity σ of transformer oil clearance ₀, transformer oil clearance intermediate ion mobility [mu], the thickness L of transformer oil clearance; Measure the angular frequency obtaining applying low frequency sinusoidal excitation;

The data that above-mentioned test obtains to be input in the model (1) in computing unit by 1.2, obtain the relative dielectric constant of the lower transformer oil clearance of low frequency sinusoidal excitation:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_r^{\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′}+\frac{{\mathrm{\ϵ}}_{r}L{({\mathrm{q\σ}}_0^3\mathrm{\μ}kT/2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_0)}^{1/2}-2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\\ {\mathrm{\ϵ}}_r^{\′\′}\left(\mathrm{\ω}\right)={{\mathrm{\ϵ}}_f}^{\′\′}+\frac{{\mathrm{\σ}}_0{\mathrm{\ωL}}^2{\mathrm{q\ϵ}}_r/2-{\mathrm{\ϵ}}_r\mathrm{\ω}L{\left(2{\mathrm{\σ}}_0{\mathrm{\μkT\ϵ}}_r{\mathrm{\ϵ}}_{0}q\right)}^{1/2}}{2{\mathrm{\σ}}_0\mathrm{\μ}kT+{\mathrm{\ω}}^2{L}^2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}\end{array}\right.---\left(1\right)$

In formula, q is unit electric charge carried charge, k=1.38 × 10 ^-23j/K is Boltzmann constant, ε _r=2.2 is transformer oil power frequency relative dielectric constant, ε ₀=8.85 × 10 ^-12f/m is permittivity of vacuum, ε ' _f, ε " _fbe respectively relative dielectric constant real part, the relative dielectric constant imaginary part of transformer oil clearance when applying the frequency f=0.1Hz of sinusoidal excitation, ε ' _r(ω), ε " _r(ω) be respectively relative dielectric constant real part, relative dielectric constant imaginary part that angular frequency is the lower transformer oil clearance of low frequency sinusoidal excitation of ω, T is probe temperature, σ ₀for the DC conductivity of transformer oil clearance, μ is transformer oil clearance intermediate ion mobility, and L is the thickness of transformer oil clearance, and ω is the angular frequency applying low frequency sinusoidal excitation;

1.3 by the model of 1.2 the data obtaineds in computing unit (2), and the data obtained substitute into the relaxation time τ that following formula then can obtain the lower transformer oil clearance electrode polarization of low frequency sinusoidal excitation _ePwith electrode polarization polarization layer thickness L _d:

$\left\{\begin{array}{c}{\mathrm{\τ}}_{EP}=L{\left(\frac{{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}q}{2{\mathrm{\σ}}_0\mathrm{\μ}kT}\right)}^{1/2}\\ L_D={\left(\frac{2{\mathrm{\ϵ}}_r{\mathrm{\ϵ}}_{0}kT\mathrm{\μ}}{{\mathrm{q\σ}}_0}\right)}^{1/2}\end{array}\right.---\left(2\right);$

In formula, q is unit electric charge carried charge, k=1.38 × 10 ^-23j/K is Boltzmann constant, ε _r=2.2 is transformer oil power frequency relative dielectric constant, ε ₀=8.85 × 10 ^-12f/m is permittivity of vacuum, and T is probe temperature, σ ₀for the DC conductivity of transformer oil clearance, μ is transformer oil clearance intermediate ion mobility, and L is the thickness of transformer oil clearance, and ω is the angular frequency applying low frequency sinusoidal excitation

1.4 export 1.2 and 1.3 step gained to subsequent processing units or result display unit.