CN101726660B - Identification method of transformer internal faults based on leakage magnetic field model - Google Patents

Abstract

The invention discloses an identification method of transformer internal faults based on a leakage magnetic field model, belonging to the technical field of the major equipment relaying protection of electric systems. The identification method of transformer internal faults comprises the following steps of: calculating the difference of active power winding resistance consuming power infused to the leakage magnetic field model; forming protection criterion by combining with a threshold value; and identifying whether a transformer generates internal faults or not. The transformer internal fault identification method has small calculated amount without being influenced by a wiring mode, is adapted to various operation conditions of the transformer and has reliability, sensitivity, high redundancy rate and property obviously superior to the traditional power differential protection.

Description

A kind of power transformer interior fault recognition methods based on the stray field model

Technical field

The invention belongs to the power system main equipment technical field of relay protection, relate in particular to a kind of power transformer interior fault recognition methods based on the stray field model.

Background technology

No matter be traditional analog protection, the still at present digital protecting that generally adopts is one of main protection of power transformer based on the transformer differential protection of Kirchhoff's current law (KCL) always.Though differential protection is applied to tranformer protection certain defective is arranged on principle, have irreplaceability as the main protection of operating transformer.Therefore, the important content of studying for transformer differential protection at present is reliability and the sensitivity that how to improve the protection action.Transformer differential protection is subjected to the influence of unfavorable factors such as the matching error, load tap changer, CT progress of disease error, high resistance ground single-phase short circuit, small turn number turn-to-turn short circuit, excitation surge current of current transformer ratio.Wherein the first five some unfavorable factor can be solved by the differential protection self-characteristic, and excitation surge current then needs additionally to increase the locking link and prevents malfunction.Therefore, transformer differential protection most critical, the most difficult problem are exactly the differential protection misoperation that how to prevent that transformer excitation flow from causing.

In recent years, Chinese scholars is devoted to the research of tranformer protection new principle always, has proposed the new principle and the new method of many differentiation excitation surge currents.These principles and method can be divided into two classes substantially: a class is only to rely on the magnitude of current to differentiate, and is main foundation with the identification Current Waveform Characteristics; Another kind of is to utilize the voltage and the magnitude of current to differentiate simultaneously.Traditional recognition technology can't be avoided the problem of excitation surge current; therefore many scholars have proposed to utilize the tranformer protection new principle of voltage, the magnitude of current; as magnetic flux characteristic principle, equivalent circuit parameter differential method, based on the method for transformer circuit equation, based on the differential method of method, the power of instant excitation inductance.Particularly study more deeply based on the criterion of power differential principle, yet, this scheme still has following 3 problems to need to be resolved hurrily: (1) can't avoid the adverse effect that excitation surge current brings, and the charging process in the 1st cycle in the time of need avoiding shoving causes differentiating time-delay; Copper loss is difficult to accurate Calculation when (2) shoving, and iron loss increases, and is not easy to adjust; (3) to the transformer of Y/ Δ wiring,, cause copper loss to determine, reduced the sensitivity of protection because Δ side winding internal current can't obtain.

Summary of the invention

The objective of the invention is the problem that exists at the present tranformer protection described in the background technology, proposed a kind of power transformer interior fault recognition methods based on the stray field model.It is characterized in that, may further comprise the steps:

Step 1: start protection according to current break:

Calculate the sudden change amount Δ i of each phase current _k=|| i _k-i _K-N|-| i _K-N-i _K-2N||, wherein k is the sampled point sequence number, N is weekly the sampling number of phase;

When the sudden change amount of certain phase current satisfies Δ i _k＞0.2I _eThe time, after then full one-period data are adopted in time-delay through 20ms, start protection and carry out the calculating of stray field model injecting power, wherein I _eRated current for transformer;

Step 2: form the stray field model:

Judge the transformer connection form, to the same side, the equivalent loop balance equation that cancellation mutual inductance parametric configuration is new makes up only relevant with leakage inductance and winding resistance stray field model by equivalent loop balance equation with the equal reduction of each winding parameter of transformer;

Step 3: the injection active power of calculating the stray field model:

The instantaneous power that the stray field model absorbs is: s _g(t)=u _Ab(t) * i _Da(t), resolve into s _g(t)=s _g+ s ' _g(t) form, wherein, DC component s _gActive power for the absorption of stray field model;

Step 4: the difference P between the active power that the injection active power of calculating stray field model and normal winding resistance consume;

Step 5: differentiate transformer fault and non-malfunction, differentiating transformer troubles inside the sample space and external area error may further comprise the steps:

1) sets threshold values ξ;

2) the power difference P that calculates by step 4 _iAnd threshold values ξ formation protection criterion, when any one group of P satisfies criterion P _i＞ξ then judges transformer generation internal fault;

3) each the phase power difference P that calculates when step 4 satisfies criterion P simultaneously _iDuring＜ξ, judge that then transformer does not break down.

The described formation stray field of step 2 model is for three-phase three winding connection forms, as Δ/Y/Y ₀Wiring, the equal reduction of the parameter of transformer is to the Δ side, wherein:

$\left\{\begin{array}{c}{i}_{\mathrm{da}}=i_{\mathrm{La}1}+i_{a2}-{\mathrm{<figure-callout\; id="2"\; label="i\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_b+i_{a3}-i_{b3}\\ i_{\mathrm{db}}=i_{\mathrm{<figure-callout\; id="1"\; label="Lb"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">Lb</figure-callout>}1}+i_{b2}-{\mathrm{<figure-callout\; id="2"\; label="i\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_c+i_{b3}-i_{c3}\\ i_{\mathrm{dc}}=i_{\mathrm{<figure-callout\; id="1"\; label="Lc"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">Lc</figure-callout>}1}+i_{c2}-{\mathrm{<figure-callout\; id="2"\; label="i\; a"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_a+i_{c3}-i_{a3}\end{array}\right.$ $\left\{\begin{array}{c}{x}_1=\mathrm{\&omega;}(L_1-m_{12}-{\mathrm{<figure-callout\; id="13"\; label="m"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">m</figure-callout>}}_{13}+m_{23})\\ x_2=\mathrm{\&omega;}(L_2-m_{12}-m_{23}+m_{13})\\ x_3=\mathrm{\&omega;}(L_3-m_{13}-m_{23}+m_{12})\end{array}\right.$

Mutual inductance magnetic linkage and Δ side winding current in the cancellation winding voltage loop equation respectively differ stream, the equivalent loop balance equation when deriving transformer internal fault not taking place in conjunction with definition:

$\left\{\begin{array}{c}{u}_{\mathrm{ab}12}=u_{b2}-u_{a2}+u_{a1}-{\mathrm{<figure-callout\; id="1"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+(i_{a2}-i_{b2})({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{a2}-i_{b2})}{\mathrm{dt}}+(i_{a3}-i_{b3}){\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{a3}-i_{b3})}{\mathrm{dt}}=i_{\mathrm{da}}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+(L_1-m_{12})\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{<figure-callout\; id="12"\; label="bc"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">bc</figure-callout>}12}=u_{c2}-{\mathrm{<figure-callout\; id="2"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+u_{b1}-{\mathrm{<figure-callout\; id="1"\; label="u\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_c+(i_{b2}-i_{c2})({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{b2}-i_{c2})}{\mathrm{dt}}+(i_{b3}-i_{c3}){\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{b3}-i_{c3})}{\mathrm{dt}}={\mathrm{<figure-callout\; id="1"\; label="i\; db\; r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_{\mathrm{db}}{r}_{}{}_1+(L_1-m_{12})\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{<figure-callout\; id="12"\; label="ca"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">ca</figure-callout>}12}=u_{a2}-{\mathrm{<figure-callout\; id="2"\; label="u\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_c+u_{c1}-{\mathrm{<figure-callout\; id="1"\; label="u\; a"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_a+(i_{c2}-i_{a2})({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{c2}-i_{a2})}{\mathrm{dt}}+(i_{c3}-i_{a3}){\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{c3}-i_{a3})}{\mathrm{dt}}={\mathrm{<figure-callout\; id="1"\; label="i\; dc\; r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_{\mathrm{dc}}{r}_{}{}_1+(L_1-m_{12})\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\\ u_{\mathrm{ab}23}=u_{b3}-{\mathrm{<figure-callout\; id="3"\; label="u\; a"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_a+u_{a2}-{\mathrm{<figure-callout\; id="2"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+(i_{a3}-i_{b3})({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+r_3)+\frac{x_2+x_3}{\mathrm{\&omega;}}\frac{d(i_{a3}-i_{b3})}{\mathrm{dt}}+i_{\mathrm{La}1}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+\frac{x_2}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{La}1}}{\mathrm{dt}}=i_{\mathrm{da}}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+(L_2-m_{23})\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}23}=u_{c3}-{\mathrm{<figure-callout\; id="3"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+u_{b2}-{\mathrm{<figure-callout\; id="2"\; label="u\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_c+(i_{b3}-i_{c3})({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+r_3)+\frac{x_2+x_3}{\mathrm{\&omega;}}\frac{d(i_{b3}-i_{c3})}{\mathrm{dt}}+i_{\mathrm{Lb}1}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+\frac{x_2}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{<figure-callout\; id="1"\; label="Lb"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">Lb</figure-callout>}1}}{\mathrm{dt}}={\mathrm{<figure-callout\; id="2"\; label="i\; db\; r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_{\mathrm{db}}{r}_{}{}_2+(L_2-m_{23})\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}23}=u_{a3}-{\mathrm{<figure-callout\; id="3"\; label="u\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_c+u_{c2}-u_{a2}+(i_{c3}-i_{a3})({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+r_3)+\frac{x_2+x_3}{\mathrm{\&omega;}}\frac{d(i_{c3}-i_{a3})}{\mathrm{dt}}+i_{\mathrm{Lc}1}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+\frac{x_2}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{<figure-callout\; id="1"\; label="Lc"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">Lc</figure-callout>}1}}{\mathrm{dt}}={\mathrm{<figure-callout\; id="2"\; label="i\; dc\; r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_{\mathrm{dc}}{r}_{}{}_2+(L_2-m_{23})\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\\ u_{\mathrm{ab}31}=u_{b1}-u_{a1}+u_{a3}-{\mathrm{<figure-callout\; id="3"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+i_{\mathrm{La}1}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_3)+\frac{x_1+x_3}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{La}1}}{\mathrm{dt}}+(i_{a2}-i_{b2}){\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_3+\frac{x_3}{\mathrm{\&omega;}}\frac{d(i_{a2}-i_{b2})}{\mathrm{dt}}=i_{\mathrm{da}}{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_3+(L_1-m_{13})\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}31}=u_{c1}-{\mathrm{<figure-callout\; id="1"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+u_{b3}-{\mathrm{<figure-callout\; id="3"\; label="u\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_c+i_{\mathrm{Lb}1}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_3)+\frac{x_1+x_3}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{<figure-callout\; id="1"\; label="Lb"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">Lb</figure-callout>}1}}{\mathrm{dt}}+(i_{b2}-i_{c2}){\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_3+\frac{x_3}{\mathrm{\&omega;}}\frac{d(i_{b2}-i_{c2})}{\mathrm{dt}}=i_{\mathrm{<figure-callout\; id="3"\; label="db\; r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">db</figure-callout>}}{r}_{}{}_3+(L_1-m_{13})\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}31}=u_{a1}-{\mathrm{<figure-callout\; id="1"\; label="u\; c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_c+u_{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">c</figure-callout>}3}+u_{a3}+i_{\mathrm{Lc}1}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_3)+\frac{x_1+x_3}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{<figure-callout\; id="1"\; label="Lc"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">Lc</figure-callout>}1}}{\mathrm{dt}}+(i_{c2}-i_{a2}){\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_3+\frac{x_3}{\mathrm{\&omega;}}\frac{d(i_{c2}-i_{a2})}{\mathrm{dt}}={\mathrm{<figure-callout\; id="3"\; label="i\; dc\; r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">i</figure-callout>}}_{\mathrm{dc}}{r}_{}{}_3+(L_1-m_{13})\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\end{array}\right.$

For the transformer of two winding connection forms, form following equivalent loop balance equation:

$\left\{\begin{array}{c}{u}_{\mathrm{ab}1}=u_a-u_b-u_A+u_B+(i_A-i_B)r_k+\frac{x_k}{\mathrm{\&omega;}}\frac{d(i_A-i_B)}{\mathrm{dt}}=i_{\mathrm{da}}r+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{<figure-callout\; id="1"\; label="bc"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">bc</figure-callout>}1}=u_b-u_c-u_B+u_C+(i_B-i_C)r_k+\frac{x_k}{\mathrm{\&omega;}}\frac{d(i_B-i_C)}{\mathrm{dt}}=i_{\mathrm{db}}r+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{<figure-callout\; id="1"\; label="ca"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">ca</figure-callout>}1}=u_c-u_a-u_C+u_A+(i_C-i_A)r_k+\frac{x_k}{\mathrm{\&omega;}}\frac{d(i_C-i_A)}{\mathrm{dt}}=i_{\mathrm{dc}}r+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\\ u_{\mathrm{ab}2}=u_b-u_a+u_A-u_B+i_{\mathrm{La}}{r}_k+\frac{x_k}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{La}}}{\mathrm{dt}}=i_{\mathrm{da}}R+{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{<figure-callout\; id="2"\; label="bc"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">bc</figure-callout>}2}=u_c-u_b+u_B-u_C+i_{\mathrm{Lb}}{r}_k+\frac{x_k}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lb}}}{\mathrm{dt}}=i_{\mathrm{db}}R+{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{<figure-callout\; id="2"\; label="ca"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">ca</figure-callout>}2}=u_a-u_c+u_C-u_A+i_{\mathrm{Lc}}{r}_k+\frac{x_k}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lc}}}{\mathrm{dt}}=i_{\mathrm{dc}}R+{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\end{array}\right.$

Wherein,

$\left\{\begin{array}{c}{i}_{\mathrm{dA}}=i_{\mathrm{La}}+i_A-i_B\\ i_{\mathrm{dB}}=i_{\mathrm{Lb}}+i_B-i_C\\ i_{\mathrm{dC}}=i_{\mathrm{Lc}}+i_C-i_A\end{array}\right.$ $\left\{\begin{array}{c}{r}_k={\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2\\ x_k=\mathrm{\&omega;}({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2)\end{array}\right..$

The stray field model that only contains leakage inductance and winding resistance by equivalent loop balance equation structure.

Difference P between the described active power of step 4, for three-winding transformer, can calculate by following formula:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_1=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}12}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)r_1)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_2=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}12}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)r_1)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_3=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}12}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)r_1)\mathrm{dt}\right|\end{array}\right.,$ $\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="4"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_4=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}23}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)r_2)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="5"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_5=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}23}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)r_2)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="6"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_6=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}23}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)r_2)\mathrm{dt}\right|\end{array}\right.,$ $\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="7"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_7=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}31}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)r_3)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="8"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_8=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}31}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)r_3)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="9"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_9=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}31}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)r_3)\mathrm{dt}\right|\end{array}\right.$

For two-winding transformer, then calculate by following formula:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_1=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}2}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)R)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_2=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}2}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)R)\mathrm{dt}\right|\\ {\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">P</figure-callout>}}_3=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}2}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)R)\mathrm{dt}\right|\end{array}\right.$

Wherein, T is the sampling period.

The described threshold values of step 5 is taken as ξ=0.05P in power transformer interior fault identification ₀, P wherein ₀Open circuit loss for this transformer.

The present invention utilizes the measured current of transformer to construct only relevant with leakage inductance and winding resistance stray field model, by the injection active power of calculating the stray field model and the active power difference that normal winding resistance consumes, has proposed the criterion of tranformer protection.Thoroughly broken away from the adverse effect that transformer iron loss and copper loss are brought; Be adapted to multiple connection types such as single transformer, three-phase two-winding transformer, three-phase three-winding transformer; Calculated amount is little, is not subjected to the influence of the Y/ Δ mode of connection, need not know the leakage inductance parameter of transformer; Be applicable to the various operating conditions of transformer, on performance, obviously be better than present differential protection principle.

Description of drawings

Fig. 1: three-phase three-winding transformer wiring diagram;

Fig. 2: three-phase three-winding transformer stray field illustraton of model;

Fig. 3: three-phase two-winding transformer wiring diagram;

Fig. 4: three-phase two-winding transformer stray field illustraton of model;

Fig. 5: the transformer operation wiring figure in the present embodiment;

Fig. 6-a: the former limit of the transformer internal fault tapping location drawing;

Fig. 6-b: the transformer secondary internal fault tapping location drawing;

Fig. 7: the difference change curve of three-phase difference current oscillogram and three phases active power under the situation of the normal air-drop of transformer;

Fig. 8: transformer drops the oscillogram of three-phase difference current under the situation of Y side B phase earth fault and the difference change curve of three phases active power;

Fig. 9: transformer drops the oscillogram of three-phase difference current under the situation of little turn ratio fault and the difference change curve of three phases active power;

Figure 10: the oscillogram of three-phase difference current and the difference change curve of three phases active power under the normal generation Y side B phase ground fault condition in service of transformer;

Figure 11: the oscillogram of three-phase difference current and the difference change curve of three phases active power under the situation of the little turn ratio fault of the normal generation in service of transformer;

Figure 12: existing power differential principle and based on the dynamic model experiment result of calculation figure of the power transformer interior fault recognition methods of stray field model under the various operating conditions;

Figure 13: the program flow diagram of protection scheme in the present embodiment.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.

The present invention proposes power transformer interior fault recognition methods based on the stray field model.Gordian technique is to construct and only contains the stray field model relevant with leakage inductance, the winding resistance of monolateral winding; the injection active power of utilizing the stray field model and the power difference of normal winding resistance consumption have constituted the criterion of tranformer protection, judge whether transformer internal fault takes place.

Figure 1 shows that Δ/Y/Y ₀The three-winding transformer of wiring, all parameters all reduction to the Δ side.Wherein, u _A1, u _B1, u _C1Voltage for each phase of Δ side winding; u _A2, u _B2, u _C2And u _A3, u _B3, u _C3Be respectively Y and Y ₀The voltage of each phase of side winding; r ₁, r ₂, r ₃Be Δ, Y, Y ₀The resistance value of side winding; L ₁, L ₂, L ₃Be leakage inductance from the leakage flux correspondence; m ₁₂, m ₁₃, m ₂₁, m ₂₃, m ₃₁, m ₃₂Leakage inductance for mutual leakage flux correspondence.All mainly pass through air or transformer oil closure from leakage flux and mutual leakage flux, corresponding leakage reactance is constant, and m ₁₂=m ₂₁, m ₁₃=m ₃₁, m ₂₃=m ₃₂

Fig. 2 is the synoptic diagram that certain stray field model of three-phase three-winding transformer structure is arranged, and the terminal voltage of this stray field model is:

$u_{\mathrm{ab}12}=u_{b2}-u_{a2}+u_{a1}-{\mathrm{<figure-callout\; id="1"\; label="u\; b"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">u</figure-callout>}}_b+(i_{a2}-i_{b2})({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{a2}-i_{b2})}{\mathrm{dt}}+(i_{a3}-i_{b3}){\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2009102435717E00061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{a3}-i_{b3})}{\mathrm{dt}}$

The direction of arrow is the direction of voltage drop; The electric current that injects the stray field model is: i _Da=i _La1+ i _A2-i _B2+ i _A3-i _B3During idle-loaded switching-on, the terminal voltage u of stray field model _Ab12=u _B1-u _A1+ u _A2-u _B2, the electric current that injects the stray field model is: i _Da=i _A2-i _B2

The three-phase two-winding transformer wiring diagram of Y/ Δ shown in Figure 3 wiring, the reduction of all parameters is to the Y side.Wherein, i _a, i _b, i _cBe the electric current in the Δ winding, i _A, i _B, i _CBe the electric current in the Y winding, u _a, u _b, u _cBe the voltage in the Δ winding, u _A, u _B, u _CBe the voltage in the Y winding, i _La, i _Lb, i _LcBe the outer A of Δ winding, B, the electric current of C three-phase, L _A, L _B, L _CBe the leakage inductance in the Y winding, L _a, L _b, L _cBe the leakage inductance in the Δ winding, R is the resistance in the Y winding, and r is the resistance in the Δ winding.

Fig. 4 is the synoptic diagram of a certain group of Y side leakage magnetic field model of three-phase two-winding transformer structure, and the terminal voltage of this stray field model is:

The direction of arrow is the direction of voltage drop; The electric current that injects the stray field model is: i _DA=i _La+ i _A-i _BDuring idle-loaded switching-on, the terminal voltage of stray field model is: u _Ab2=u _b-u _a+ u _A-u _B, the electric current that injects the stray field model is: i _DA=i _A-i _B

Fig. 5 is the transformer operation wiring figure in the present embodiment, and by the three-phase transformer that three single-phase DMB-10 type transformers are formed, wiring group is Yn, d11.Correlation parameter is: (1) capacity: 10kVA; (2) low-pressure side rated voltage: 380V; (3) low-pressure side rated current: 25.3A; (4) high-pressure side rated voltage: 1000V; (5) high-pressure side rated current: 10A; (6) no-load current: 1.45%; (7) open circuit loss: 100W; (8) short circuit loss: 0.35%; (9) short-circuit voltage: 9%-15%.The inductance summation of (10) windings and Secondary Winding (reduction is to primary side): 0.0038H; The resistance summation of (11) windings and Secondary Winding (reduction is to primary side): 0.16610 Ω.

Fig. 6 is the former and deputy limit of the transformer internal fault tapping location drawing, according to the condition simulation of experimental system the various running statuses of transformer, comprise normal operation, idle-loaded switching-on, internal ground fault, inner turn-to-turn fault, drop, drop in inner turn-to-turn fault etc. in internal ground fault.Taken into full account the influence of the different moment, different separate and different faults position, every kind of fault type has been carried out repeatedly experiment.

Fig. 7 is the situation of the normal air-drop of transformer, each the phase difference current i during idle-loaded switching-on generation excitation surge current _DA, i _DBAnd i _DCOscillogram (a) shown in, represent with two line, solid line and dot-and-dash line respectively.Figure (b) has provided the change curve of each phase stray field model injection active power with normal winding resistance consumed power difference.Transformer normally drops, because the estimation error of winding resistance and the measuring error of voltage transformer (VT) summation current transformer, the wattful power rate variance can not be zero yet, by figure (b) as can be seen, and maximum active power difference P _Imax=1.98W.ξ=0.05P that the present invention sets ₀=5W, promptly each phase power difference P satisfies P simultaneously _iThe criterion of＜ξ, tranformer protection locking, reliably not malfunction.

Fig. 8 drops in Y side B phase ground fault condition, each phase difference current i for transformer _DA, i _DBAnd i _DCOscillogram (a) shown in, represent with two line, solid line and dot-and-dash line respectively.Figure (b) has provided the change curve of each phase stray field model injection active power with normal winding resistance consumed power difference.When transformer generation internal fault, because series reaction such as arc discharge heating increase the wattful power rate variance of fault phase.By scheming (b) P as can be seen _Imax=668.6W, P ₁＞ξ, P ₂＞ξ has two groups of difference powers to satisfy P _i＞ξ is judged to be power transformer interior fault, the fast and reliable action.

Fig. 9 drops in the situation of little turn ratio fault for transformer: the turn-to-turn fault of 2.4% turn ratio has taken place in Y side A mutually before closing a floodgate.Each phase difference current i _DA, i _DBAnd i _DCOscillogram (a) shown in, represent with two line, solid line and dot-and-dash line respectively.Figure (b) has provided the change curve of each phase stray field model injection active power with normal winding resistance consumed power difference.When little turn ratio fault took place, the electric current of Magnetic Leakage Field of Transformer model changed very little, but the electric current in the short circuit circle alters a great deal.The short circuit part can break down for transformer the 3rd winding in equivalence, and the numerical value of power difference will be very big, by scheming (b) P as can be seen _Imax=35.3W, P ₁＞ξ, P ₃＞ξ has two groups of power differences to satisfy P _i＞ξ is judged to be power transformer interior fault, the fast and reliable action.What deserves to be mentioned is that figure (a) shows that second harmonic content accounts for fundametal compoment in the three-phase current number percent all above 36%, is 15% (accepted value) if get secondary harmonic brake ratio, will bring the time-delay of long period to protection.

Figure 10 is the normal generation Y side B phase ground fault condition in service of transformer, each phase difference current i _DA, i _DBAnd i _DCOscillogram (a) shown in, represent with two line, solid line and dot-and-dash line respectively.Figure (b) has provided the change curve of each phase stray field model injection active power with normal winding resistance consumed power difference.By scheming (b) P as can be seen _Imax=560.2W, P ₁＞ξ, P ₂＞ξ has two groups of difference powers to satisfy P _i＞ξ is judged to be power transformer interior fault, the fast and reliable action.Fig. 8 and Figure 10 have shown that this method can be adapted under the situation of transformer generation earth fault in idle-loaded switching-on and the normal course of operation, and criterion is accurate, the redundance height, and protection can action message.

Figure 11 is the situation of the little turn ratio fault of the normal generation in service of transformer, and the turn-to-turn fault of 2.4% turn ratio has taken place Y side A mutually.Each phase difference current i _DA, i _DBAnd i _DCOscillogram (a) shown in, represent with two line, solid line and dot-and-dash line respectively.Figure (b) has provided the change curve of each phase stray field model injection active power with normal winding resistance consumed power difference.By scheming (b) P as can be seen _Imax=29.8W, P ₁＞ξ, P ₃＞ξ has two groups of power differences to satisfy P _i＞ξ is judged to be power transformer interior fault, the fast and reliable action.Fig. 9 and Figure 11 have shown that this method is applicable to the situation that little turn ratio fault takes place in idle-loaded switching-on and the normal course of operation, dependable performance, redundance height simultaneously.

Figure 12 is existing power differential principle under the various situations and the dynamic model experiment result of calculation that the present invention is based on the power transformer interior fault recognition methods of stray field model.For existing power differential principle, if by P under the normal condition _cPeaked 1.5 times, threshold values adjusted is 2090W, and sequence number is 3,4,12,13 so, and 8 kinds of situations such as 14,15,23 and 24 can't be discerned.For purposes of the invention, P under the normal condition _mMaximal value and failure condition under P _mMinimum value differ more than 10 times, press ξ=0.05P ₀, get 5W.Figure 12 shows that this method is applicable to various operating conditions, can correctly distinguish the outer fault of inner region, and have very big redundance, and reliability and sensitivity all obviously are better than existing power differential principle.

Figure 13 is the program flow diagram of protection scheme in the present embodiment, at first obtains voltage, the magnitude of current of each side of transformer; Construct the stray field model then, calculate voltage, the electric current of stray field model; Then calculate the injection active power of stray field model and the difference of normal winding resistance consumed power, form the criterion of tranformer protection; Whether judge greater than threshold values whether transformer breaks down according to difference power at last.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and is familiar with those skilled in the art in the technical scope of the present invention's exposure; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (4)

1. the power transformer interior fault recognition methods based on the stray field model is characterized in that, may further comprise the steps:

Step 1: start protection according to current break:

Calculate the sudden change amount Δ i of each phase current _k=|| i _k-i _K-N|-| i _K-N-i _K-2N||, wherein k is the sampled point sequence number, N is weekly the sampling number of phase;

When the sudden change amount of certain phase current satisfies Δ i _k＞0.2L _eThe time, after then full one-period data are adopted in time-delay through 20ms, start protection and carry out the calculating of stray field model injecting power, wherein I _eRated current for transformer;

Step 2: form the stray field model:

Judge the transformer connection form, to the same side, the equivalent loop balance equation that cancellation mutual inductance parametric configuration is new makes up only relevant with leakage inductance and winding resistance stray field model by equivalent loop balance equation with the equal reduction of each winding parameter of transformer;

Step 3: the injection active power of calculating the stray field model:

The instantaneous power that the stray field model absorbs is: s _g(t)=u _Ab(t) * i _Da(t), resolve into

Form, wherein, DC component

Active power for the absorption of stray field model;

Step 4: the difference P between the active power that the injection active power of calculating stray field model and normal winding resistance consume _i

Step 5: differentiate transformer fault and non-malfunction, differentiating transformer troubles inside the sample space and external area error may further comprise the steps:

1) sets threshold values ξ;

2) the power difference P that calculates by step 4 _iAnd threshold values ξ formation protection criterion, as any one group of P _iSatisfy criterion P _i＞ξ then judges transformer generation internal fault;

3) each phase power difference P that calculates when step 4 _iSatisfy criterion P simultaneously _iDuring＜ξ, judge that then transformer does not break down.

2. a kind of power transformer interior fault recognition methods based on the stray field model according to claim 1 is characterized in that, the described formation stray field of step 2 model is for three-phase three winding Δ/Y/Y ₀Connection type, the equal reduction of the parameter of transformer is to the Δ side, wherein:

$\left\{\begin{array}{c}{i}_{\mathrm{da}}=i_{\mathrm{La}1}+i_{a2}-i_{b2}+i_{a3}-i_{b3}\\ i_{\mathrm{ab}}=i_{\mathrm{Lb}1}+i_{b2}-i_{c2}+i_{b3}-i_{c3}\\ i_{\mathrm{dc}}=i_{\mathrm{Lc}1}+i_{c2}-i_{a2}+i_{c3}-i_{a3}\end{array}\right.$ $\left\{\begin{array}{c}{x}_1=\mathrm{\&omega;}(L_1-m_{12}-m_{13}+m_{23})\\ x_2=\mathrm{\&omega;}(L_2-m_{12}-m_{23}+m_{13})\\ x_3=\mathrm{\&omega;}(L_3-m_{13}-m_{23}+m_{12})\end{array}\right.$

Mutual inductance magnetic linkage and Δ side winding current in the cancellation winding voltage loop equation respectively differ stream, the equivalent loop balance equation when deriving transformer internal fault not taking place in conjunction with definition:

$\left\{\begin{array}{c}{u}_{\mathrm{ab}12}=u_{b2}-u_{a2}+u_{a1}-u_{b1}+(i_{a2}-i_{b2})(r_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{a2}-i_{b2})}{\mathrm{dt}}+(i_{a3}-i_{b3})r_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{a3}-i_{b3})}{\mathrm{dt}}=i_{\mathrm{da}}{r}_1+\left(L_1-m_{12}\right)\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}12}=u_{c2}-u_{b2}+u_{b1}-u_{c1}+(i_{b2}-i_{c2})(r_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{b2}-i_{c2})}{\mathrm{dt}}+(i_{b3}-i_{c3})r_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{b3}-i_{c3})}{\mathrm{dt}}=i_{\mathrm{db}}{r}_1+(L_1-m_{12})\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}12}=u_{a2}-u_{c2}+u_{c1}-u_{a1}+(i_{c2}-i_{a2})(r_1+r_2)+\frac{x_1+x_2}{\mathrm{\&omega;}}\frac{d(i_{c2}-i_{a2})}{\mathrm{dt}}+(i_{c3}-i_{a3})r_1+\frac{x_1}{\mathrm{\&omega;}}\frac{d(i_{c3}-i_{a3})}{\mathrm{dt}}=i_{\mathrm{dc}}{r}_1+(L_1-m_{12})\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\\ u_{\mathrm{ab}23}=u_{b3}-u_{a3}+u_{a2}-u_{b2}+(i_{a3}-i_{b3})(r_2+r_3)+\frac{x_2+x_3}{\mathrm{\&omega;}}\frac{d(i_{a3}-i_{b3})}{\mathrm{dt}}+i_{\mathrm{La}1}{r}_2+\frac{x_2}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{La}1}}{\mathrm{dt}}=i_{\mathrm{da}}{r}_2+(L_2-m_{23})\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}23}=u_{c3}-u_{b3}+u_{b2}-u_{c2}+(i_{b3}-i_{c3})(r_2+r_3)+\frac{x_2+x_3}{\mathrm{\&omega;}}\frac{d(i_{b3}-i_{c3})}{\mathrm{dt}}+i_{\mathrm{Lb}1}{r}_2+\frac{x_2}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lb}1}}{\mathrm{dt}}=i_{\mathrm{db}}{r}_2+(L_2-m_{23})\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}23}=u_{a3}-u_{c3}+u_{c2}-u_{a2}+(i_{c3}-i_{a3})(r_2+r_3)+\frac{x_2+x_3}{\mathrm{\&omega;}}\frac{d(i_{c3}-i_{a3})}{\mathrm{dt}}+i_{\mathrm{Lc}1}{r}_2+\frac{x_2}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lc}1}}{\mathrm{dt}}=i_{\mathrm{dc}}{r}_2+(L_2-m_{23})\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\\ u_{\mathrm{ab}31}=u_{b1}-u_{a1}+u_{a3}-u_{b3}+i_{\mathrm{La}1}(r_1+r_3)+\frac{x_1+x_3}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{La}1}}{\mathrm{dt}}+(i_{a2}-i_{b2})r_3+\frac{x_3}{\mathrm{\&omega;}}\frac{d(i_{b2}-i_{c2})}{\mathrm{dt}}=i_{\mathrm{da}}{r}_3+(L_1-m_{13})\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}31}=u_{c1}-u_{b1}+u_{b3}-u_{c3}+i_{\mathrm{Lb}1}(r_1+r_3)+\frac{x_1+x_3}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lb}1}}{\mathrm{dt}}+(i_{b2}-i_{c2})r_3+\frac{x_3}{\mathrm{\&omega;}}\frac{d(i_{b2}-i_{c2})}{\mathrm{dt}}=i_{\mathrm{db}}{r}_3+(L_1-m_{13})\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}31}=u_{a1}-u_{c1}+u_{c3}-u_{a3}+i_{\mathrm{Lc}1}(r_1+r_3)+\frac{x_1+x_3}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lc}1}}{\mathrm{dt}}+(i_{c2}-i_{a2})r_3+\frac{x_3}{\mathrm{\&omega;}}\frac{d(i_{c2}-i_{a2})}{\mathrm{dt}}=i_{\mathrm{dc}}{r}_3+(L_1-m_{13})\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\end{array}\right.$

For the transformer of two winding connection forms, form following equivalent loop balance equation:

$\left\{\begin{array}{c}{u}_{\mathrm{ab}1}=u_a-u_b-u_A+u_B+(i_A-i_B)r_k+\frac{x_k}{\mathrm{\&omega;}}\frac{d(i_A-i_B)}{\mathrm{dt}}=i_{\mathrm{da}}r+L_1\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}1}=u_b-u_c-u_B+u_C+(i_B-i_C)r_k+\frac{x_k}{\mathrm{\&omega;}}\frac{d(i_B-i_C)}{\mathrm{dt}}=i_{\mathrm{db}}r+L_1\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}1}=u_c-u_a-u_C+u_A+(i_C-i_A)r_k+\frac{x_k}{\mathrm{\&omega;}}\frac{d(i_C-i_A)}{\mathrm{dt}}=i_{\mathrm{dc}}r+L_1\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\\ u_{\mathrm{ab}2}=u_b-u_a+u_A-u_B+i_{\mathrm{La}}{r}_k+\frac{x_k}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{La}}}{\mathrm{dt}}=i_{\mathrm{da}}R+L_2\frac{{\mathrm{di}}_{\mathrm{da}}}{\mathrm{dt}}\\ u_{\mathrm{bc}2}=u_c-u_b+u_B-u_C+i_{\mathrm{Lb}}{r}_k+\frac{x_k}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lb}}}{\mathrm{dt}}=i_{\mathrm{db}}R+L_2\frac{{\mathrm{di}}_{\mathrm{db}}}{\mathrm{dt}}\\ u_{\mathrm{ca}2}=u_a-u_c+u_C-u_A+i_{\mathrm{Lc}}{r}_k+\frac{x_k}{\mathrm{\&omega;}}\frac{{\mathrm{di}}_{\mathrm{Lc}}}{\mathrm{dt}}=i_{\mathrm{dc}}R+L_2\frac{{\mathrm{di}}_{\mathrm{dc}}}{\mathrm{dt}}\end{array}\right.$

Wherein,

$\left\{\begin{array}{c}{i}_{\mathrm{da}}=i_{\mathrm{La}}+i_A-i_B\\ i_{\mathrm{db}}=i_{\mathrm{Lb}}+i_B-i_C\\ i_{\mathrm{dc}}=i_{\mathrm{Lc}}+i_C-i_A\end{array}\right.$ $\left\{\begin{array}{c}{r}_k=r_1+r_2\\ x_k=\mathrm{\&omega;}(L_1+L_2)\end{array}\right.;$

The stray field model that only contains leakage inductance and winding resistance by equivalent loop balance equation structure.

3. a kind of power transformer interior fault recognition methods based on the stray field model according to claim 1 is characterized in that the difference P between the described active power _i, for three-winding transformer, calculate by following formula:

$\left\{\begin{array}{c}{P}_1=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}12}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)r_1)\mathrm{dt}\right|\\ P_2=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}12}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)r_1)\mathrm{dt}\right|\\ P_3=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}12}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)r_1)\mathrm{dt}\right|\end{array}\right.,\left\{\begin{array}{c}{P}_4=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}23}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)r_2)\mathrm{dt}\right|\\ P_5=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}23}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)r_2)\mathrm{dt}\right|\\ P_6=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}23}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)r_2)\mathrm{dt}\right|\end{array}\right.=,\left\{\begin{array}{c}{P}_7=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}31}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)r_3)\mathrm{dt}\right|\\ P_8=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}31}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)r_3)\mathrm{dt}\right|\\ P_9=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}31}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)r_3)\mathrm{dt}\right|\end{array}\right.$

For two-winding transformer, then calculate by following formula:

$\left\{\begin{array}{c}{P}_1=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ab}2}\left(t\right)i_{\mathrm{da}}\left(t\right)-i_{\mathrm{da}}^2\left(t\right)R)\mathrm{dt}\right|\\ P_2=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{bc}2}\left(t\right)i_{\mathrm{db}}\left(t\right)-i_{\mathrm{db}}^2\left(t\right)R)\mathrm{dt}\right|\\ P_3=\frac{1}{T}\left|{\&Integral;}_0^T(u_{\mathrm{ca}2}\left(t\right)i_{\mathrm{dc}}\left(t\right)-i_{\mathrm{dc}}^2\left(t\right)R)\mathrm{dt}\right|\end{array}\right.$

Wherein, T is the sampling period.

4. a kind of power transformer interior fault recognition methods based on the stray field model according to claim 1 is characterized in that, described threshold values is taken as ξ=0.05P in power transformer interior fault identification ₀, P wherein ₀Open circuit loss for this transformer.

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