CN105259467A - Single-phase fault analysis method considering star-triangle transformation - Google Patents

Abstract

The invention discloses a single-phase fault analysis method considering star-triangle transformation. According to the single-phase fault analysis method, a transformer wiring mode is Y,d11; when a fault occurs at the exterior of the Y side of a transformer, the triangle-side winding voltage of the transformer is obtained through utilizing the electromagnetic induction law and Kirchhoff's law; triangle-side line-to-line voltage is obtained according to the triangle-side winding voltage; and triangle-side phase voltage is obtained according to the triangle-side line-to-line voltage and the triangle centroid theorem. According to the single-phase fault analysis method of the invention, the electromagnetic induction law is utilized to analyze fault characteristics of a high voltage and a low voltage side when a single-phase fault occurs on the exterior of the transformer, and therefore, physical meaning is clear, and the method is more approximate to practical engineering application. With the single-phase fault analysis method of the invention adopted, the neutral point of a system is determined according to the triangle centroid theorem under the situation that the voltage of a line is known, so that the phase voltage can be calculated, and therefore, physical meaning is clear, and the method is more approximate to practical engineering application, and a new idea is provided for fault calculation.

Description

A kind of single-phase fault analytical approach considering star triangular transformation

Technical field

The present invention relates to a kind of single-phase fault analytical approach considering star triangular transformation, belong to power system automation technology field.

Background technology

In electric system research, the identification of failure message, disposal and utilization are the bases of Protection Technology, and fault signature is the imbody of failure message, extract the prerequisite that correct fault signature is relay protection correct operation.Transformer is one of electrical equipment important in electric system, and it is the principle according to electromagnetic induction, the alternating voltage of a certain grade and electric current is converted to another voltage gradation of same frequency and the equipment of electric current, as shown in Figure 1.Whole from generating plant to user, defeated, join, with in process, transformer plays and raises and reduce voltage, transmits the effect of electric energy.In ideal transformer, magnetic flux all concentrates in iron core, and transformer does not have energy loss, and power input equals output power.The critical piece of transformer is an iron core and two windings be enclosed within iron core.Two windings only have magnetic coupling not have electrical communication.In a winding, add alternating voltage, produce the alternating flux of interlinkage first and second winding, difference induction electromotive force e in two windings ₁, e ₂.According to the known induction electromotive force e of the law of electromagnetic induction ₁, e ₂as follows:

$e_1=-N_1\frac{d\mathrm{\Φ}}{dt}$

$e_2=-N_2\frac{d\mathrm{\Φ}}{dt}$

Wherein, N ₁, N ₂be respectively the coil turn of two windings, Φ is magnetic flux, and t is the time; Negligible resistance pressure drop, can be similar to and think u ₁≈ e ₁, u ₂≈ e ₂, u ₁be the terminal voltage of a winding, u ₂for the terminal voltage of Secondary Winding.

In practical power systems, transformer adopts Y usually, the d11 mode of connection.When single-phase fault occurs in transformer outside, because of the difference of transformer winding and the Secondary Winding mode of connection, cause both sides electric current not corresponding, fault signature is also inconsistent.At present the general symmetrical component method that adopts carries out unbalanced fault analysis, need carry out angular transition respectively when star triangular transformation to positive-sequence component, negative sequence component, zero-sequence component, loaded down with trivial details and easily make mistakes.

Summary of the invention

In order to solve the problems of the technologies described above, the invention provides a kind of single-phase fault analytical approach considering star triangular transformation.

In order to achieve the above object, the technical solution adopted in the present invention is:

A kind of single-phase fault analytical approach considering star triangular transformation, described unidirectional fault analytical approach for transformer connection mode be Y, d11, when there is single-phase fault in outside, transformer Y side, the law of electromagnetic induction and Kirchhoff's law is first utilized to obtain transformer triangle side winding voltage, obtain triangle side voltage between lines according to triangle side winding voltage, then obtain triangle side phase voltage according to triangle side voltage between lines and triangle core theorem.

The process utilizing the law of electromagnetic induction and Kirchhoff's law to obtain transformer triangle side winding voltage is,

There is A phase earth fault, i.e. A phase voltage U in outside, definition transformer Y side _a=0;

According to the law of electromagnetic induction, in the winding of triangle side, three-phase induction electromotive force is respectively E _a, E _b, E _c, wherein E _a=0;

Triangle side winding voltage U is can be calculated by Kirchhoff's law _sa, U _sb, U _sc;

$U_{sa}=-\frac{E_b+E_c}{3};---\left(1\right)$

$U_{sb}=\frac{2E_b-E_c}{3};---\left(2\right)$

$U_{sc}=\frac{2E_c-E_b}{3}.---\left(3\right)$

Definition triangle side voltage between lines is U _ab, U _bc, U _ca, computing formula is,

$U_{ab}=-U_{sb}=\frac{E_c-2E_b}{3};---\left(4\right)$

$U_{bc}=-U_{sc}=\frac{E_b-2E_c}{3};---\left(5\right)$

$U_{ca}=-U_{sa}=\frac{E_b+E_c}{3}.---\left(6\right)$

Definition triangle side phase voltage is U _oa, U _ob, U _oc, computing formula is,

$U_{oa}=\frac{2}{3}(U_{sb}+\frac{1}{2}{U}_{sc})=\frac{E_b}{3};---\left(7\right)$

$U_{ob}=\frac{2}{3}(U_{sc}+\frac{1}{2}{U}_{sa})=\frac{E_c-E_b}{3};---\left(8\right)$

$U_{oc}=\frac{2}{3}(U_{sa}+\frac{1}{2}{U}_{sb})=-\frac{E_c}{3}.---\left(9\right)$

The beneficial effect that the present invention reaches: the fault signature of high and low pressure side when 1, the present invention utilizes the law of electromagnetic induction to analyze transformer outside single-phase fault, not only explicit physical meaning, and more press close to practical implementation; 2, the present invention is when known line voltage, determines the neutral point of system, then calculates phase voltage, not only explicit physical meaning, and press close to practical implementation according to triangle core theorem, for calculation of fault provides new thinking.

Accompanying drawing explanation

Fig. 1 is the basic functional principle figure of transformer.

Fig. 2 is process flow diagram of the present invention.

Fig. 3 is the wiring system figure of transformer.

Fig. 4 is transformer equivalent circuit figure.

Fig. 5 is voltage phasor-diagram between triangle side line.

Fig. 6 is triangle theorem schematic diagram.

Fig. 7 is triangle side phase voltage phasor graph.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.Following examples only for technical scheme of the present invention is clearly described, and can not limit the scope of the invention with this.

As shown in Figure 2, a kind of single-phase fault analytical approach considering star triangular transformation, this unidirectional fault analytical approach for transformer connection mode be Y, d11, when there is single-phase fault in outside, transformer Y side, first utilize the law of electromagnetic induction and Kirchhoff's law to obtain transformer triangle side winding voltage, obtain triangle side voltage between lines according to triangle side winding voltage, then obtain triangle side phase voltage according to triangle side voltage between lines and triangle core theorem.

The law of electromagnetic induction and Kirchhoff's law is utilized to obtain transformer triangle side winding voltage.In definition Fig. 3 there is A phase earth fault in the outside K1 point in transformer Y side, is namely equivalent to A phase voltage U in Fig. 4 _a=0, according to the law of electromagnetic induction, in the winding of triangle side, three-phase induction electromotive force is respectively E _a, E _b, E _c, wherein E _a=0, can be calculated triangle side winding voltage U by Kirchhoff's law _sa, U _sb, U _sc, as shown in formula (1), (2) and (3):

$U_{sa}=-\frac{E_b+E_c}{j*3x}*jx=-\frac{E_b+E_c}{3};---\left(1\right)$

$U_{sb}=E_b-\frac{E_b+E_c}{3}=\frac{2E_b-E_c}{3};---\left(2\right)$

$U_{sc}=E_c-\frac{E_b+E_c}{3}=\frac{2E_c-E_b}{3};---\left(3\right)$

Wherein, in above formula, x is the winding reactance of triangle side.

Voltage U between triangle side line is obtained according to triangle side winding voltage _ab, U _bc, U _ca, if formula is as shown in (4), (5) and (6):

$U_{ab}=-U_{sb}=\frac{E_c-2E_b}{3};---\left(4\right)$

$U_{bc}=-U_{sc}=\frac{E_b-2E_c}{3};---\left(5\right)$

$U_{ca}=-U_{sa}=\frac{E_b+E_c}{3}.---\left(6\right)$

Between triangle side line, voltage phasor-diagram as shown in Figure 5.

As shown in Figure 6, the intersection point of Atria bar center line is called triangle core, as O point in figure.Theorem: set triangle core to be D as O, BC limit mid point, then have AO=2OD, barycentric coordinates are three apex coordinate mean values.

Triangle side voltage between lines and triangle side winding voltage equal and opposite in direction, direction are contrary, and as shown in Figure 7, the relevant equations can obtaining triangle side phase voltage according to voltage between lines and theorem of center is as follows:

U _sa＝U _oa-U _oc；

U _sb＝U _ob-U _oa；

U _sc＝U _oc-U _ob；

Can obtain triangle side phase voltage by above equation is U _oa, U _ob, U _oc, if formula is as shown in (7), (8) and (9):

$U_{oa}=\frac{2}{3}(U_{sb}+\frac{1}{2}{U}_{sc})=\frac{E_b}{3};---\left(7\right)$

$U_{ob}=\frac{2}{3}(U_{sc}+\frac{1}{2}{U}_{sa})=\frac{E_c-E_b}{3};---\left(8\right)$

$U_{oc}=\frac{2}{3}(U_{sa}+\frac{1}{2}{U}_{sb})=-\frac{E_c}{3}.---\left(9\right)$

The fault signature of high and low pressure side when above-mentioned single-phase fault analytical approach utilizes the law of electromagnetic induction to analyze transformer outside single-phase fault, not only explicit physical meaning, and more press close to practical implementation.Above-mentioned single-phase fault analytical approach, when known line voltage, is determined the neutral point of system, is then calculated phase voltage, not only explicit physical meaning, and press close to practical implementation according to triangle core theorem, for calculation of fault provides new thinking.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and distortion, these improve and distortion also should be considered as protection scope of the present invention.

Claims (4)

1. consider the single-phase fault analytical approach of star triangular transformation for one kind, it is characterized in that: described single-phase fault analytical approach for transformer connection mode be Y, d11, when there is single-phase fault in outside, transformer Y side, the law of electromagnetic induction and Kirchhoff's law is first utilized to obtain transformer triangle side winding voltage, obtain triangle side voltage between lines according to triangle side winding voltage, then obtain triangle side phase voltage according to triangle side voltage between lines and triangle core theorem.

2. a kind of single-phase fault analytical approach considering star triangular transformation according to claim 1, is characterized in that: the process utilizing the law of electromagnetic induction and Kirchhoff's law to obtain transformer triangle side winding voltage is,

There is A phase earth fault, i.e. A phase voltage U in outside, definition transformer Y side _a=0;

According to the law of electromagnetic induction, in the winding of triangle side, three-phase induction electromotive force is respectively E _a, E _b, E _c, wherein E _a=0;

Triangle side winding voltage U is can be calculated by Kirchhoff's law _sa, U _sb, U _sc;

。

3. a kind of single-phase fault analytical approach considering star triangular transformation according to claim 2, is characterized in that: definition triangle side voltage between lines is U _ab, U _bc, U _ca, computing formula is,

。

4. a kind of single-phase fault analytical approach considering star triangular transformation according to claim 3, is characterized in that: definition triangle side phase voltage is U _oa, U _ob, U _oc, computing formula is,

。