CN101340121A - Transient simulation simplified model for internal fault of generator, modeling method and application thereof - Google Patents

Abstract

The invention discloses a fault transient simulation model inside motors, a modeling method and the application thereof, and relates to a fault transient simulation model inside the motor. The model is as follows: the stator of the motor is three phases a, b, and c, each phase is respectively equivalent to the serial form of an inductance and a resistance; an equation is written to get a mathematic model with the form of differential equations according to the voltage and magnetic linkage relation of the stator and rotator circuits, and through solving the differential equations, the values of transient current and voltage of a motor stator winding can be got; for the damper winding of the motor rotator, only the damper winding under the pole face of odd rotators is counted and the damper winding under the pole face of each odd rotator is equivalent to the form of two damper sticks. The invention greatly simplifies the structure of the damper winding so as to greatly reduce the order of written differential equations used for the fault simulation models inside the motor and shorten the simulation calculation time, and is applicable to the fault simulation analysis inside the motor and the main protection design field of hydro-generators.

Description

A kind of transient simulation simplified model for internal fault of generator and modeling method thereof and application

Technical field

The present invention relates to a kind of internal fault of electric generator transient emulation model, relate in particular to a kind of internal fault of electric generator transient emulation model and modeling method and application of damping circuit under the rotor pole faces of odd-numbered being simplified equivalence.

Background technology

In order deeply to inquire into the electrical characteristic under the internal fault of electric generator situation so that generator protection is carried out researching and analysing of system and quantification, since the middle of last century, scholars have carried out broad research [document 1,2] to generator internal short circuit fault computational problem, be limited to the level of understanding at that time, research work mainly is based on symmetrical component method and launches; Found afterwards, generator takes place under the inner asymmetric short trouble situation, air-gap field exists very strong branch several and higher harmonic components [document 3], at this moment, between each preface amount that symmetrical component method produces dependence has been arranged, made traditional symmetrical component method and Parker conversion all no longer be applicable to the evaluation work of internal fault of electric generator.

The proposition of the multi-loop analysis method [document 3] of the inner rotor loop equation of generator, the calculating to air gap harmonic wave under generator unit stator winding construction form and the internal fault situation provides solution theoretically.[document 3] is elementary cell with stator single-turn circular coil and each damping mesh of rotor, computational methods to inductance parameters between multiloop theory and each winding elaborate, and the electromagnetic relationship that [document 4,5] write between the inner rotor of generator loop by row in conjunction with external constraint has been set up corresponding simulation model.

But above-mentioned this class internal fault of electric generator simulation model is with rotor damping circuit individual processing; when in large-sized water turbine generator, taking into account the amortisseur bar under each pole-face; the order of simulation model is quite high; the emulation [document 6 of growing very much consuming time when so just making model be used for transient state to find the solution; 7]; and large-sized water turbine generator main protection optimal design need of work carries out simulation analysis [document 8] to thousands of fault; like this; emulation long problem consuming time during being used for transient state and calculating based on complete multiloop simulation model of this class routine makes this model can't satisfy the engineering application request.

With Dadu River, Sichuan waterfall ditch 600MW large-sized water turbine generator is example, the every phase of this generator unit stator 6 branches, and rotor 48 utmost points, wherein every utmost point comprises 6 amortisseur bars, and the order of internal short circuit fault situation drag can reach 307 rank when generator connecting in parallel with system moves.Studies show that, (adopt the CPU of Pentium2.4GHz dominant frequency, the 512M internal memory) more than the transient emulation that a kind of internal short circuit fault situation of this generator is carried out 5 cycles needs half an hour; Existing document [document 7] has proposed the Model Simplification Method based on the two amortisseur bars of the every pole-face of rotor; this method for simplifying also reaches (can be longer to large-scale rotor number of poles greater power generation machine simulation times such as Three Gorges) about 7 minutes to 5 cycle times of internal fault emulation of waterfall ditch generator; and when research generator main protection configuration scheme, need carry out simulation calculation to thousands of fault, carrying out once in batches to this waterfall ditch generator, the simulation time of fault will reach more than 20 day in [document 7].Therefore, on the transient emulation of the large batch of internal fault of electric generator of this class calculated, it was found the solution and consuming timely is difficult to satisfy the engineering application requirements, and order is too high also causes producing bigger accumulated error in solution procedure easily.

In order to obtain the electric current and voltage data of fault in batches, once once adopting the way that differential equation of higher order is converted into algebraic equation in the practical engineering application; Algebraic equation solving is fast, but resulting be the stable state electric parameters of fault, be the transient state fault characteristic data of electric parameters and relaying protection needs; Therefore, can not satisfy the requirement of large-sized water turbine generator relaying protection research and engineering application based on the way of finding the solution algebraic equation.

To obtain the transient state electrical data of fault in batches fast; to be used for the engineering reality of generator main protection design; just must carry out depression of order to existing simulation model method for building up simplifies; therefore, seek suitable internal fault of electric generator transient emulation modeling method is generator main protection research and problem that presses for solution of engineering application always.

Summary of the invention

When purpose of the present invention just is to overcome existing high-rating generator internal fault simulation model based on loop equation and is used for the internal fault of electric generator transient emulation and calculates, dimension height, length consuming time, can not obtain the difficult problem of the Temporal Data of thousands of failure modes fast, a kind of internal fault of electric generator transient emulation model and modeling method and application based on odd number rotor pole faces equivalent damping loop is provided.

The object of the present invention is achieved like this:

With aforementioned Sichuan waterfall ditch 600MW large-sized water turbine generator is example, this generator unit stator divides 3 phases, every phase 6 branches, rotor 48 utmost points, wherein every utmost point comprises 6 amortisseur bars, the order of internal short circuit fault situation drag can reach 307 rank and (comprises when generator connecting in parallel with system moves, damping circuit 48 * 6=288, excitation winding 1, stator winding free variable 3 * 6-1=17, stator short-circuited conducting sleeve 1; 288+1+17+1=307).

After the model that the present invention proposes is simplified equivalence with damping winding, 24 equivalent down damper bars of odd-numbered pole-face add up to 48, the order of internal short circuit fault situation drag only was that 67 rank (comprise when this moment, generator connecting in parallel with system moved, damping circuit 48, excitation winding 1, stator winding free variable 3 * * 6-1=17, stator short-circuited conducting sleeve 1; 48+1+17+1=67).

To rotor number of poles and every damper bar greater power generation machine that extremely descends, the effect that the present invention simplifies differential equation exponent number is more obvious, and this also makes thousands of batch fault is carried out simulation calculation, and draws the fault transient characteristic fast and become possibility.

One, based on the internal fault of electric generator transient emulation model in odd number rotor pole faces equivalent damping loop

This structure of models

The stator of generator is a, b, c three-phase, and the series connection form of equivalence for inductance and resistance all distinguished by each branch of every phase, as shown in Figure 4.

The damping winding of generator amature by the equivalent structure shown in thick line among Fig. 3, is promptly only taken into account the damping winding under the odd number rotor pole faces, and, be the form of 2 damper bars with damping winding equivalence under each odd number rotor pole faces.

The operation principle of this model

With stator coil and equivalent damping mesh is elementary cell, and row are write the magnetic linkage and the voltage equation of each winding of stator and rotor, set up the internal fault of electric generator simulation model;

The reason of the damping mesh being carried out equivalence and simplifying is in order to solve based on actual damping mesh modeling, the simulation model dimension height that causes, calculates length consuming time, can not carry out the difficult problem of the simulation calculation of fault in batches fast.

Two, the modeling method of internal fault of electric generator transient emulation model

Comprise the following steps:

1. according to rotor and damper bar structure thereof, determine the damper bar parameter and the spacing of equivalence, be listed as the basis of writing as the damping mesh;

2. row are write the voltage equation of each branch of stator, rotor-exciting winding;

3. row are write the voltage equation in each equivalent damping cage modle loop of rotor;

4. with the arrangement of stator, rotor-side voltage equation, get final product the differential equation of the inner Simulation Calculation of generator.

The present invention has following advantage and good effect:

1. this invention is simplified damping winding structure in a large number, makes the listed differential equation order of writing (dimension) that is used for the internal fault of electric generator simulation model greatly reduce, and the simulation calculation time shortens.

2. in the large-sized water turbine generator main protection scheme optimal design process, need calculate thousands of fault.Overcome traditional model that damping circuit is not simplified and under the active computer level, carried out batch calculating, consuming time long, do not satisfy the difficult problem that engineering is used.

3. the present invention is applicable to internal fault of electric generator simulation analysis and hydraulic generator main protection design field.

Description of drawings

Fig. 1 is the Pareto diagram (is example with following 6 damper bars of every pole-face) of original damper bar under the rotor pole faces;

Fig. 2 is the Pareto diagram (wherein thick line is the simplification to the damper bar of odd-numbered rotor pole) that damper bar is simplified under the rotor pole faces;

Fig. 3 simplifies in the simulation model damper bar and is connected lead bar schematic diagram;

Fig. 4 is the equivalent circuit diagram of stator winding in the simulation model.

Wherein:

1-the 1st rotor pole;

2-the 2nd rotor pole;

3-the 3rd rotor pole;

4-the 4th rotor pole;

......

N-n rotor pole;

The number of poles of rotor is different and different according to generator, is 80 utmost points as Three Gorges left bank ALSTOM generator, and Three Gorges right bank ALSTOM generator is 84 utmost points, and Sichuan waterfall ditch DFEM generator is 48 utmost points;

4 rotor pole faces wherein of only having drawn among Fig. 1,2,3 are as example.

Embodiment

Describe in detail below in conjunction with drawings and Examples:

One, structure of models

To the equivalent structure of generator unit stator winding and rotor damping winding respectively as Fig. 4 and Fig. 3;

Promptly according to the voltage and the magnetic linkage relation in stator, each loop of rotor, row are write equation to the process of setting up of model, finally obtain following differential equation group form; By finding the solution this differential equation group, can obtain generator unit stator winding transient current and voltage value.

$\left[\begin{array}{cc}{M}_{11}& M_{12}\\ M_{21}& M_{22}\end{array}\right]\left[\begin{array}{c}p{I}_s^{\′}\\ p{I}_r\end{array}\right]+\left[\begin{array}{cc}{N}_{11}& N_{12}\\ N_{21}& N_{22}\end{array}\right]\left[\begin{array}{c}{I}_s^{\′}\\ I_r\end{array}\right]=\left[\begin{array}{c}{U_s}^{\′}\\ U_r\end{array}\right]$

Wherein, Is ' and Us ' are the electric current and the voltages of branches of stator;

Ir and Ur are the electric current and the voltages in each loop of rotor;

P represents derivative, i.e. differential operator;

M and N are the coefficient matrixes of this differential equation group.

Two, modeling method

Supposing that generator unit stator is every is composed in parallel by m branch, is the series connection of resistance and inductance with each stator branch equivalence, and its equivalent electric circuit as shown in Figure 4.

The equation of rotor-side damping winding is write by the equivalent circuit row of this method for simplifying, and the situation of following 2 amortisseur bars of odd number pole-face as shown in Figure 3.When the rotor number of poles was 2P, the rotor damping circuit of equivalence add up to d _n=P * 2.

Adopt positive current to produce positive magnetic linkage rule, then each branch's voltage equation of stator can be expressed as among Fig. 4:

$\frac{{\mathrm{d\ψ}}_{a1}}{\mathrm{dt}}+{\mathrm{ri}}_{a1}=-u_a$

.

.

.

$\frac{{\mathrm{d\ψ}}_{\mathrm{am}}}{\mathrm{dt}}+{\mathrm{ri}}_{\mathrm{am}}=-u_a$

$\frac{{\mathrm{d\&psi;}}_{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">b</figure-callout>}1}}{\mathrm{dt}}+{\mathrm{<figure-callout\; id="1"\; label="ri\; b"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">ri</figure-callout>}}_b=-u_b$

.

. (1)

.

$\frac{{\mathrm{d\&psi;}}_{\mathrm{bm}}}{\mathrm{dt}}{+\mathrm{ri}}_{\mathrm{bm}}=-u_b$

$\frac{{\mathrm{d\&psi;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">c</figure-callout>}1}}{\mathrm{dt}}{+\mathrm{<figure-callout\; id="1"\; label="ri\; c"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">ri</figure-callout>}}_c=-u_c$

.

.

.

$\frac{{\mathrm{d\&psi;}}_{\mathrm{cm}}}{\mathrm{dt}}+{\mathrm{ri}}_{\mathrm{cm}}=-u_c$

Rotor-exciting winding voltage equation can be written as:

$\frac{{\mathrm{d\&psi;}}_f}{\mathrm{dt}}+r_f{i}_f=u_f---\left(2\right)$

To rotor damping mesh, establish r _DiBe d _iThe loop resitance of equivalent damping mesh, r _MdBe every equivalent damping rod resistance, then the voltage equation in each equivalent damping cage modle loop can be written as:

$\frac{{\mathrm{d\&psi;}}_{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">d</figure-callout>}1}}{\mathrm{dt}}+r_{d1}{i}_{d1}-r_{\mathrm{md}}(i_{\mathrm{dn}}+i_{d2})=0$

$\frac{{\mathrm{d\&psi;}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">d</figure-callout>}2}}{\mathrm{dt}}+r_{d2}{i}_{d2}-r_{\mathrm{md}}({\mathrm{<figure-callout\; id="1"\; label="i\; d"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">i</figure-callout>}}_d+i_{d3})=0$

.

. (3)

.

$\frac{{\mathrm{d\&psi;}}_{d(n-1)}}{\mathrm{dt}}+r_{d(n-1)}{i}_{d(n-1)}-r_{\mathrm{md}}(i_{d(n-2)}+i_{\mathrm{dn}})=0$

$\frac{{\mathrm{d\&psi;}}_{\mathrm{dn}}}{\mathrm{dt}}+r_{\mathrm{dn}}{i}_{\mathrm{dn}}-r_{\mathrm{md}}(i_{d(n-1)}+i_{d1})=0$

Formula (1) (2) (3) can be written as:

$\left[\begin{array}{c}\frac{{\mathrm{d\&psi;}}_s}{\mathrm{dt}}\\ \frac{{\mathrm{d\&psi;}}_r}{\mathrm{dt}}\end{array}\right]+\left[\begin{array}{cc}{R}_s& 0\\ 0& R_r\end{array}\right]\left[\begin{array}{c}{I}_s\\ I_r\end{array}\right]\text{=}\left[\begin{array}{c}{U}_s\\ U_r\end{array}\right]---\left(4\right)$

' s ' expression stator amount in the formula, ' r ' expression rotor amount, the stator and rotor magnetic linkage is respectively

ψ _s＝[ψ _a1，ψ _a2，…ψ _am，ψ _b1，ψ _b2，…ψ _bm，ψ _c1，ψ _c2，…ψ _cm] ^T(3m×1)，

ψ _r＝[ψ _f，ψ _d1，…，ψ _dn] ^T，

The stator and rotor voltage vector is respectively:

U _s＝[-u _a…-u _a-u _b…-u _b-u _c…-u _c] ^T，U _r＝[u _f0 _d1…0 _dn] ^T

The stator and rotor current vector is respectively:

$I_s=[I_{a1}...I_{\mathrm{am}},I_{b1}...I_{\mathrm{bm}},I_{c1}...I_{\mathrm{cm}}{]}^T,I_r=[i_f,i_{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A20081004899000122.png,A20081004899000123.png"\; state="\{\{state\}\}">d</figure-callout>}}_1},...i_{\mathrm{dn}}{]}^T$

In each electric weight of rotor: u _f, i _fBe the excitation winding electric current and voltage;

i _DkBe k equivalent damping winding loop electric current.

In the formula 4, the stator resistance matrix $R_s={\left[\begin{array}{cccc}{r}_s& 0& ...& 0\\ 0& r_s& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ 0& 0& ...& r_s\end{array}\right]}_{(3m\&times;3m)},$

The rotor resistance matrix $R_r={\left[\begin{array}{ccccccccc}{r}_f& 0& 0& 0& 0& ...& 0& 0& 0\\ 0& r_{d1}& {-r}_{\mathrm{md}}& 0& 0& ...& 0& 0& {-r}_{\mathrm{md}}\\ 0& {-r}_{\mathrm{md}}& r_{d2}& {-r}_{\mathrm{md}}& 0& ...& 0& 0& 0\\ 0& 0& {-r}_{\mathrm{md}}& r_{d3}& {-r}_{\mathrm{md}}& ...& 0& 0& 0\\ .& .& .& .& .& .& .& .& .\\ .& .& .& .& .& .& .& .& .\\ .& .& .& .& .& .& .& .& .\\ 0& 0& 0& 0& 0& ...& {-r}_{\mathrm{md}}& r_{d(n-1)}& {-r}_{\mathrm{md}}\\ 0& {-r}_{\mathrm{md}}& 0& 0& 0& ...& 0& {-r}_{\mathrm{md}}& r_{\mathrm{dn}}\end{array}\right]}_{(n+1)\&times;(n+1)}$

Formula (1) distortion has:

$\frac{d}{\mathrm{dt}}({\mathrm{\&psi;}}_{a1}-{\mathrm{\&psi;}}_{a2})+r_s(i_{a1}-i_{a2})=0$

.

.

.

$\frac{d}{\mathrm{dt}}({\mathrm{\&psi;}}_{\mathrm{am}}-{\mathrm{\&psi;}}_{b1})+r_s(i_{\mathrm{am}}-i_{b1})={-u}_{\mathrm{ab}}$

$\frac{d}{\mathrm{dt}}({\mathrm{\&psi;}}_{b1}-{\mathrm{\&psi;}}_{b2})+r_s(i_{b1}-i_{b2})=0---\left(5\right)$

.

.

.

$\frac{d}{\mathrm{dt}}({\mathrm{\&psi;}}_{\mathrm{bm}}-{\mathrm{\&psi;}}_{c1})+r_s(i_{\mathrm{bm}}-i_{c1})={-u}_{\mathrm{bc}}$

.

.

.

$\frac{d}{\mathrm{dt}}({\mathrm{\&psi;}}_{\mathrm{cm}-1}-{\mathrm{\&psi;}}_{\mathrm{cm}})+r_s(i_{\mathrm{cm}-1}-i_{\mathrm{cm}})=0$

If ψ _S1=[ψ _A1, ψ _A2... ψ _Am, ψ _B1, ψ _B2... ψ _Bm, ψ _C1, ψ _C2... ψ _Cm-1] ^T(3m-1) * 1

ψs ₂＝[ψ _a2，ψ _a3，…ψ _am，ψ _b1，ψ _b2，…ψ _bm，ψ _c1，ψ _c2，…ψ _cm] ^T(3m-1)×1

Then formula 5 magnetic linkage correlated variabless can be rewritten as:

$\frac{d({\mathrm{\&psi;}}_{s1}-{\mathrm{\&psi;}}_{s2})}{\mathrm{dt}}=\frac{{\mathrm{d\&psi;}}_{s1}}{\mathrm{dt}}-\frac{{\mathrm{d\&psi;}}_{s2}}{\mathrm{dt}}=E_r\frac{{\mathrm{d\&psi;}}_s}{\mathrm{dt}}---\left(6\right)$

E wherein _rBe (3m-1) * 3m matrix,

$E_r={\left[\begin{array}{cccccc}1& -1& 0& ...& 0& 0\\ 0& 1& -1& ...& 0& 0\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ 0& 0& 0& ...& 1& -1\end{array}\right]}_{(3m-1)\&times;3m}$

Earth-free or constraints arranged when big grounding through resistance when generator neutral point:

i _a1+i _a2+…+i _am+i _b1+i _b2+…+i _bm+i _c1+i _c2+…+i _cm＝0 (7)

Order: I _s=[i _A1, i _A2..., i _Am, i _B1, i _B2..., i _Bm, i _C1, i _C2I _Cm] ^T, I ' _s=[i _A1... i _Am, i _B1..., i _Bm, i _C1..., i _Cm-1] ^T

Then have: I _s=D _rI ' _sIn the formula $D_r={\left[\begin{array}{ccccc}1& 0& ...& 0& 0\\ 0& 1& ...& 0& 0\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ 0& 0& ...& 1& 0\\ -1& -1& ...& -1& -1\end{array}\right]}_{3m\&times;(3m-1)}$

Order:

Simultaneous formula (5) and formula (6) have:

$E_r\frac{{\mathrm{d\&psi;}}_s}{\mathrm{dt}}+r_s{E}_r{I}_s=E_r\frac{{\mathrm{d\&psi;}}_s}{\mathrm{dt}}+r_s{E}_r{D}_r{I}_s^{\&prime;}=U_s^{\&prime;}---\left(8\right)$

On the other hand, the magnetic linkage equation of stator and rotor is:

$\left[\begin{array}{c}{\mathrm{\&psi;}}_s\\ {\mathrm{\&psi;}}_r\end{array}\right]=\left[\begin{array}{cc}{L}_{\mathrm{ss}}& L_{\mathrm{sr}}\\ L_{\mathrm{rs}}& L_{\mathrm{rr}}\end{array}\right]\left[\begin{array}{c}{I}_s\\ I_r\end{array}\right]---\left(9\right)$

Wherein, L _SsBe 3m * 3m rank stator inductance matrix, stator and rotor mutual inductance matrix L _Sr, L _RsOrder be respectively 3m * (n+1) and (n+1) * 3m.

Therefore, stator magnetic linkage:

${\mathrm{\&psi;}}_s=\left[\begin{array}{cc}{L}_{\mathrm{ss}}& L_{\mathrm{sr}}\end{array}\right]\left[\begin{array}{c}{I}_s\\ I_r\end{array}\right]=L_{\mathrm{ss}}{I}_s+L_{\mathrm{sr}}{I}_r=L_{\mathrm{ss}}{D}_r{I}_s^{\&prime;}+L_{\mathrm{sr}}{I}_r---\left(10\right)$

Formula (10) substitution formula (8) arrangement can be got

$\left[\begin{array}{cc}{E}_{r}p{L}_{\mathrm{ss}}{D}_r+r_s{E}_r{D}_r& E_{r}p{L}_{\mathrm{sr}}\end{array}\right]\left[\begin{array}{c}{I}_s^{\&prime;}\\ I_r\end{array}\right]+\left[\begin{array}{cc}{E}_r{L}_{\mathrm{ss}}{D}_r& E_r{L}_{\mathrm{sr}}\end{array}\right]\left[\begin{array}{c}{\mathrm{pI}}_s^{\&prime;}\\ {\mathrm{pI}}_r\end{array}\right]=U_s^{\&prime;}---\left(11\right)$

In the formula, make M ₁₁=E _rL _SsD _r, M ₁₂=E _rL _Sr, N ₁₁=(E _rPL _SsD _r+ r _sE _rD _r), N ₁₂=E _rPL _SrWherein p is a differential operator, M ₁₁, N ₁₁Be (3m-1) * (3m-1) matrix, M ₁₂, N ₁₂Be (3m-1) * (n+1) matrix.

Then (11) formula can be rewritten as:

$\left(\begin{array}{cc}{M}_{11}& M_{12}\end{array}\right)\left[\begin{array}{c}{\mathrm{pI}}_s^{\&prime;}\\ {\mathrm{pI}}_r\end{array}\right]+\left(\begin{array}{cc}{N}_{11}& N_{12}\end{array}\right)\left(\begin{array}{c}{I}_s^{\&prime;}\\ I_r\end{array}\right)=U_s^{\&prime;}---\left(12\right)$

Can get the rotor loop voltage equation with reason formula (4) is:

$\frac{{\mathrm{d\&psi;}}_r}{\mathrm{dt}}{+R}_r{I}_r=U_r---\left(13\right)$

Rotor flux wherein

${\mathrm{\&psi;}}_r=\left[\begin{array}{cc}{L}_{\mathrm{rs}}& L_{\mathrm{rr}}\end{array}\right]\left[\begin{array}{c}{I}_s\\ I_r\end{array}\right]=L_{\mathrm{rs}}{I}_s+L_{\mathrm{rr}}{I}_r=L_{\mathrm{rs}}{D}_r{I_s}^{\&prime;}\text{+}{L}_{\mathrm{rr}}{I}_r---\left(14\right)$

L in the formula _Rs, L _RrBe respectively (n+1) * 3m, (n+1) * (n+1) matrix, formula (14) substitution formula (13) can be put in order:

$\left[\begin{array}{cc}{L}_{\mathrm{rs}}{D}_r& L_{\mathrm{rr}}\end{array}\right]\left[\begin{array}{c}{\mathrm{pI}}_s^{\&prime;}\\ {\mathrm{pI}}_r\end{array}\right]+\left[\begin{array}{cc}{\mathrm{pL}}_{\mathrm{rs}}{D}_r& R_r\end{array}\right]\left[\begin{array}{c}{I}_s^{\&prime;}\\ I_r\end{array}\right]=U_r---\left(15\right)$

Order: M ₂₁=L _RsD _r, M ₂₂=L _Rr, N ₂₁=pL _RsD _r, N ₂₂=R _r

Wherein: M ₂₁, N ₂₁Be (n+1) * (3m-1) matrix, M ₂₂, N ₂₂Be (n+1) * (n+1) matrix.Simultaneous formula (12) and formula (15) can get under the non-failure condition of following large-scale multiple-limb hydraulic generator the simulation model mathematic(al) representation.

$\left[\begin{array}{cc}{M}_{11}& M_{12}\\ M_{21}& M_{22}\end{array}\right]\left[\begin{array}{c}p{I}_s^{\&prime;}\\ p{I}_r\end{array}\right]+\left[\begin{array}{cc}{N}_{11}& N_{12}\\ N_{21}& N_{22}\end{array}\right]\left[\begin{array}{c}{I}_s^{\&prime;}\\ I_r\end{array}\right]=\left[\begin{array}{c}{U_s}^{\&prime;}\\ U_r\end{array}\right]---\left(16\right)$

In the formula, in M and the N matrix except M ₂₂And N ₂₂Outward, become when other coefficient all is, can obtain each electric parameters characteristic in the generator operation process by finding the solution this variable coefficient differential equation group.

Three, application of the present invention

Based on model proposed by the invention and modeling method thereof, can calculate fast generator large batch of in Each electric parameters of section's failure mode (electric current, voltage) transient fault data, these fault datas can be used for generating The research of machine relay protective plan, and the engineering of the optimal design work of main protection scheme is used.

Literature index

[document 1] He Yangzan, the synchronous generator internal short circuit fault calculates, Huazhong Institute of Technology journal, 1979 (1): 140-151

[document 2] Hou Xuguang, Yang Shunyi, Stator Coil is snapped the computational analysis of fault, power station equipment automation, 1981 (3): 6-8

[document 3] Gao Jingde, Wang Xianghang, Li Fahai, the analysis of alternating current machine and system thereof, Beijing, publishing house of Tsing-Hua University, 1993

[document 4] Zhang Longzhao, the research [D] of synchronous motor stator winding asymmetrical state, Beijing, Tsing-Hua University, 1989

[document 5] slaughters dawn, the research of Stator Winding internal fault analytical method and application thereof [D], Nanjing, Southeast China University, 1999

[document 6] Sun Yuguang, Wang Xianghang, Guilin etc., Three Gorges generator unit stator Winding Internal Faults Transient Simulation is calculated, Automation of Electric Systems, 2002,26 (16), 56-61

[document 7] Xia Yongjun, Yin Xianggen, Chen Deshu, etc., large-sized water turbine generator internal fault transient emulation simplified models and simulating, verifying Automation of Electric Systems thereof, 2006,30 (12)

[document 8] yellow of heap of stone, Yin Xianggen, Xia Yongjun, a kind of super-huge hydraulic generator stator failure mode is analyzed and the searching algorithm design, relay, 2005,33 (15): 1-4

Claims (2)

1, a kind of damping winding under the odd-numbered rotor pole faces is simplified the internal fault of electric generator transient emulation model of equivalence, the stator of generator is a, b, c three-phase, and the series connection form that equivalence is inductance and resistance all distinguish by each branch of every phase; According to the voltage and the magnetic linkage relation in stator, each loop of rotor, row are write equation, obtain the differential equation group form of mathematical model

$\left[\begin{array}{cc}{M}_{11}& M_{12}\\ M_{21}& M_{22}\end{array}\right]\left[\begin{array}{c}p{I}_s^{\&prime;}\\ p{I}_r\end{array}\right]+\left[\begin{array}{cc}{N}_{11}& N_{12}\\ N_{21}& N_{22}\end{array}\right]\left[\begin{array}{c}{I}_s^{\&prime;}\\ I_r\end{array}\right]=\left[\begin{array}{c}{U_s}^{\&prime;}\\ U_r\end{array}\right]$

By finding the solution differential equation group, can obtain generator unit stator winding transient current and voltage value;

Wherein, Is ' and Us ' are the electric current and the voltages of branches of stator,

Ir and Ur are the electric current and the voltages in each loop of rotor,

P represents derivative, i.e. differential operator,

M and N are the coefficient matrixes of this differential equation group;

It is characterized in that:

In the processing to the damping winding of generator amature, only take into account the damping winding under the odd-numbered rotor pole faces, and be the form of 2 damper bars damping winding equivalence under each odd-numbered rotor pole faces.

2, by the modeling method of the described simulation model of claim 1, it is characterized in that comprising the following steps:

1. according to rotor and damper bar structure thereof, determine the damper bar parameter and the spacing of equivalence, be listed as the basis of writing as the damping mesh;

2. row are write the voltage equation of each branch of stator, rotor-exciting winding;

3. row are write the voltage equation in each equivalent damping cage modle loop of rotor;

4. with the arrangement of stator, rotor-side voltage equation, get final product the differential equation of the inner Simulation Calculation of generator.

Images