CN102420434B - Method for analyzing sub-synchronous resonance of alternating-current system - Google Patents

Abstract

The invention discloses a method for analyzing the sub-synchronous resonance of an alternating-current system in the technical field of running and control of a power system. The method comprises the following steps of: calculating the natural frequency of each decoupling modal of a multi-mass-block model of a generator shaft system, and scanning the frequency of a power transmission system to be researched by using a frequency scanning method to acquire the resonance frequency feA of an asynchronous generator effect and the resonance frequency feC of a transient torque amplification function; if the feA and/or the feC accords with a condition shown in the specifications, determining that f0(i) is partial main resonance frequency of the sub-synchronous resonance, calculating a line series compensation degree KS according to the feA and the feC and determining the minimum value KSmin of the line series compensation degree; establishing a full system equation, and calculating a curve of each modal electric damp which is changed with the series compensation degree in a range of between 0 and KSmin by using a characteristic value method; and further obtaining all the main resonance frequencies of the sub-synchronous resonance and a secure series compensation region. By the method, a characteristic of quickness of the frequency scanning method and a characteristic of the precision of characteristic value method are combined, the shortcoming of low precision of the frequency scanning method and the shortcoming of large calculation quantity of the characteristic value method are overcome, and the obtained secure series compensation region has a great significance for engineering practice.

Description

A kind of AC system subsynchronous resonance analytical method

Technical field

The invention belongs to power system operation and control technology field, relate in particular to a kind of AC system subsynchronous resonance analytical method.

Background technology

Along with the quickening of transferring electricity from the west to the east strategy implementation and national interconnected network paces, remote big capacity send electricity imperative.In China's power industry, thermal power generation is occupied an leading position, and generator inserts and adopts the mode of series capacitor compensation to improve the circuit transmission power in the transmission line of big system mostly, increases the transient stability performance.But series capacitor compensation can be provided with improperly at string benefit degree and cause subsynchronous resonance under the situation, and infringement even damage turbonator shafting cause very big loss to system stable operation.From 1970, subsynchronous resonance took place and begun in U.S. Mohave power plant, and is more and more to the research of subsynchronous resonance and sub-synchronous oscillation.Therefore adopt string to mend the Study on Technology background one after another at the extensive fired power generating unit transmission line of China, the research of mending the subsynchronous resonance problem that causes for string is very urgent.

Along with putting into operation of many high voltage direct current transmission projects, China will form in the world the most complicated many feed-ins alternating current-direct current hybrid system.For the alternating current-direct current hybrid system, still occupy an leading position in the sub-synchronous oscillation electrical damping characteristic of decision whole system in transmission line of alternation current with serial compensation capacitance, so the bonding analysis method that this paper proposes also has certain meaning for analyzing alternating current-direct current hybrid system sub-synchronous oscillation problem.

The method of research subsynchronous resonance has frequency sweep method and method of characteristic at present.The frequency sweep method computational speed is fast, and operation is convenient, and usually as the prefered method of studying the subsynchronous resonance problem, but this method accuracy is not enough.Method of characteristic has strict Fundamentals of Mathematics, sets up the system linearity model at operating point, and the system features value is found the solution.This method amount of calculation is bigger, all will form sytem matrix again for each string benefit degree, and find the solution characteristic value, for comparatively complicated system, is all having difficulties aspect the formation sytem matrix.And the new model of subsynchronous resonance problem is analyzed in this paper proposes frequency sweep method is combined with method of characteristic, it is quick to combine frequency sweep method, method of characteristic is characteristics accurately, have reduced the amount of calculation of method of characteristic when having overcome frequency sweep method precision deficiency.Output in use characteristic value method that the machine end is meritorious and idle is decided to be normal value.

Summary of the invention

Not high at the method precision of mentioning existing detection subsynchronous resonance in the above-mentioned background technology, the big deficiency that waits of amount of calculation the present invention proposes a kind of AC system subsynchronous resonance analytical method.

Technical scheme of the present invention is that a kind of AC system subsynchronous resonance analytical method is characterized in that this method may further comprise the steps:

Step 1: the calculating generator axle is each decoupling zero mode natural frequency of many matter block models

Wherein, i=1,2 ... N, N are the matter piece sum of many matter of generator block models;

Step 2: the frequency of utilization scanning method is treated the research transmission system and is carried out frequency scanning, obtains asynchronous generator effect resonance frequency f _EAWith transient state moment amplification resonance frequency f _EC

Step 3: if f _EASatisfy

Or f _ECSatisfy

Then should

Be the master oscillator frequenc of subsynchronous resonance, execution in step 4; Otherwise synchronous resonant does not take place, process ends;

Step 4: on the basis of step 3 by f _EAAnd f _ECTry to achieve circuit string benefit degree K _SAnd the minimum value K of definite circuit string benefit degree _Smin

Step 5: set up the total system equation, with method of characteristic interval [0, K _Smin] on try to achieve the curve of each mode electrical damping with the variation of string benefits degree; When string benefit degree is K _SminThe time, the mode electrical damping is the master oscillator frequenc of subsynchronous resonance for negative natural frequency of oscillation; The mode electrical damping interval [0, K _Smin] be that the safety string is mended interval upward for the interval of timing correspondence.

Described natural frequency

Computing formula be:

$f_0^{\left(i\right)}=\frac{\sqrt{T^{\left(i\right)}/{2M}^{\left(i\right)}}}{2\mathrm{\π}}$

Wherein:

It is the natural frequency of i mode;

T ⁽ⁱ⁾It is the coefficient of elasticity of i mode;

M ⁽ⁱ⁾It is the quality constant of i mode.

Described T ⁽ⁱ⁾And M ⁽ⁱ⁾Computing formula be:

M ⁽ⁱ⁾＝Q ^TMQ

T ⁽ⁱ⁾＝Q ^TTQ

Wherein:

M is the quality coefficient matrix of matter piece;

T is an elastic coefficient matrix;

Q is the characteristic vector battle array, Q=M ^-1T.

The computing formula of described M and T is:

$M=\left(\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000118234300000012.png,HDA0000118234300000043.png"\; state="\{\{state\}\}">M</figure-callout>}}_1& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA0000118234300000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& M_N\end{array}\right)$

$T=\left(\begin{array}{cccc}{T}_{12}& -T_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ -T_{12}& T_{12}+T_{23}& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& T_{(N-2)(N-1)}+T_{(N-1)N}& -T_{(N-1)N}\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& -T_{(N-1)N}& T_{(N-1)N}\end{array}\right)$

Wherein:

M _NQuality coefficient for the matter piece;

T _{(N-1) N}Coefficient of elasticity for matter piece N-1 confrontation piece N.

Described circuit string benefit degree K _SComputing formula be:

$K_S={\left(\frac{f_e}{f_0}\right)}^2$

Wherein:

f _eBe asynchronous generator effect resonance frequency f _EAOr transient state moment amplification resonance frequency f _EC

f ₀Be power frequency.

Described total system equation is:

${\stackrel{\&CenterDot;}{X}}_{\mathrm{SYS}}=A_{\mathrm{SYS}}{X}_{\mathrm{SYS}}$

Wherein:

X _SYSBe the total system state variable;

A _SYSBe sytem matrix;

Be X _SYSIn each element first derivation.

Effect of the present invention is, combines the quick and method of characteristic advantage of high precision of frequency sweep method, has overcome the not accurate enough and big shortcoming of method of characteristic amount of calculation of frequency sweep method, can also find out the safety string benefit degree interval of system simultaneously, is easy to realization.General features value method need be set string benefit degree interval and be each mode electrical damping on [0,1], and our rule has utilized frequency sweep method to find out mode nature frequency of oscillation and string benefit degree K that a part becomes the subsynchronous resonance master oscillator frequenc fast _i, only need afterwards to calculate string benefit degree interval [0, K _Smin] on each mode electrical damping of not found out by frequency sweep method just can find out the mode nature frequency of oscillation that residue all can become the subsynchronous resonance master oscillator frequenc.Do the formation number of times that has significantly reduced sytem matrix like this, calculation times, thereby reduce number of characteristics value method amount of calculation.Simultaneously, the shortcoming of frequency sweep method precision deficiency has also obtained remedying.In addition, this method can also interval [0, K _Smin] on find out safety string and mend intervally, instruct the capacitance of safe series compensation to select.

Description of drawings

Fig. 1 is an IEEE FIRST BENCHMARK MODEL FOR SSR resolution chart;

Fig. 2 is six matter block models for generator shaft;

Fig. 3 is frequency sweep method scanning result figure;

Fig. 3 a figure is that equivalent resistance is with frequency variation curve; Fig. 3 b is that equivalent reactance is with frequency change figure; Fig. 3 c is the partial enlarged drawing of Fig. 3 b;

Fig. 4 is each mode electrical damping figure;

Fig. 5 is subsynchronous resonance time domain frequency analysis figure;

Fig. 6 is subsynchronous resonance time-domain-simulation figure (K=0.27);

Fig. 7 is subsynchronous resonance time-domain-simulation figure (K=0.24);

Fig. 8 is subsynchronous resonance energy maximum amplitude figure (K=0～0.24);

Fig. 9 mends greater than 1 each mode electrical damping figure of back for string;

Figure 10 is a flow chart of the present invention.

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 at first operating frequency scanning method axle of finding out a part and become the subsynchronous resonance master oscillator frequenc is mode nature frequency of oscillation and string benefit degree, be applied in the method for characteristic calculating with this string benefit degree, value between the string benefit degree test section when dwindling conventional use characteristic value method, thus the amount of calculation that has reduced method of characteristic in a large number guarantees accuracy simultaneously.

Technical scheme of the present invention is that a kind of frequency sweep method is combined with method of characteristic analyzed the method for being mended the AC system subsynchronous resonance problem that causes by string, comprises the following steps:

Step 1: the calculating generator axle is each decoupling zero mode natural frequency of many matter block models

I=1 wherein, 2 ... N, N are the matter piece sum of many matter of generator block models;

Step 2: the frequency of utilization scanning method is treated the research transmission system and is carried out frequency scanning.Draw the asynchronous generator effect resonance frequency f that frequency sweep method is analyzed _EA, dynamo-electric torsional oscillation resonance frequency f _EBAnd transient state moment amplification resonance frequency f _ECF wherein _EAWith f _ECCan be on principle "

" find out.If a certain resonance frequency satisfies mentioned above principle, be that the axle of power frequency is that mode nature frequency of oscillation will become one of master oscillator frequenc of subsynchronous resonance with this resonance frequency sum so.Because dynamo-electric torsional oscillation function analysis needs a large amount of measured datas, also relation is arranged simultaneously with generator self mechanical damping size, analytic process extremely bothers.Therefore in the actual analysis, only analyze f _EAWith f _EC, this part work of dynamo-electric torsional oscillation can replace with the work of method of characteristic analysis.

Step 3: by the resonance frequency f of gained in the step 2 _e, determine circuit string benefit degree K this moment _SFor a transmission line following formula is arranged:

$\left\{\begin{array}{c}j{X}_L-j{X}_C=0\\ K_S=\frac{X_C}{X_L}=\frac{1}{{\mathrm{\&omega;}}_0^2\mathrm{LC}}\\ X_C=\frac{1}{{\mathrm{\&omega;}}_{e}C}\\ X_L={\mathrm{\&omega;}}_{e}L\end{array}\right.$

In the formula:

ω _eWith ω ₀Represent resonance point angular speed and power frequency angular speed respectively, unit: radian per second;

L and C represent to be connected inductance value and the capacitance in the circuit of generator and system respectively, and unit is respectively prosperous (H) and method (F);

X _LWith X _CBe respectively inductive reactance value and condensance value in the circuit, unit: Ω.

Can draw thus

Resonance frequency wherein

The Hz of unit; Power frequency

The Hz of unit.So far set up the f that draws in the step 2 _eWith K _SCorresponding relation, determined K _SSet K _Smin=min{K _S.

Step 4: setting string benefit interval [0, K _Smin] and step delta K, use characteristic value method is calculated each mode electrical damping of waiting the system of studying, can obtain the interval [0, K _Smin] go up the curve of each mode electrical damping with the variation of string benefits degree.At string benefit degree is K _SminThe time, which mode electrical damping is for negative, and the natural frequency of oscillation of which mode will become one of subsynchronous resonance master oscillator frequenc.Each mode electrical damping interval [0, K _Smin] on be positive string and mend the zone and mend interval for the safety string.On this interval, go here and there to mend and to guarantee that system avoids the threat of subsynchronous resonance problem.

Detailed process is as follows:

Calculating generator axle in the step 1 is that natural mode of vibration frequency process is as follows:

According to generator shaft is parameter, i.e. each matter piece quality coefficient M ₁, M ₂M _NWith coefficient of elasticity T ₁₂, T ₂₃T _{(N-1) N}, set up matter piece quality coefficient matrix M and elastic coefficient matrix T:

$M=\left(\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000118234300000012.png,HDA0000118234300000043.png"\; state="\{\{state\}\}">M</figure-callout>}}_1& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA0000118234300000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& M_N\end{array}\right);$

$T=\left(\begin{array}{cccc}{T}_{12}& -T_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ -T_{12}& T_{12}+T_{23}& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& T_{(N-2)(N-1)}+T_{(N-1)N}& -T_{(N-1)N}\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& -T_{(N-1)N}& T_{(N-1)N}\end{array}\right).$

Make Q=M ^-1T is the characteristic vector battle array, then after the decoupling zero M is arranged ⁽ⁱ⁾=Q ^TMQ, T ⁽ⁱ⁾=Q ^TTQ.

Wherein:

M ⁽ⁱ⁾It is the quality constant of i mode;

T ⁽ⁱ⁾It is the coefficient of elasticity of i mode;

Q ^TTransposed matrix for the Q battle array.

Again according to formula Can draw the natural frequency of oscillation of each mode after the decoupling zero

In the step 2, from the generator amature lateral system side direction of looking, injected frequency is changed to the continuous sinusoidal variations electric current of three-phase of 1-50Hz, record voltage, voltage and current ratio are a complex impedance value, can obtain equivalent resistance like this with the curve of frequency change and the equivalent reactance curve with frequency change.Asynchronous machine resonance frequency f _EAMust satisfy: 1. equivalent reactance is 0 o'clock a frequency; 2. equivalent resistance is negative frequency; 3. be power frequency with a certain mode nature frequency of oscillation sum.Transient state moment is amplified resonance frequency f _ECMust satisfy: the frequency when 1. the equivalent reactance curve reaches minimum; 2. be power frequency with a certain mode nature frequency of oscillation sum.

In the step 3, may there be a plurality of resonance frequency f _e, therefore may have a plurality of K _SSituation.Be difficult for taking place subsynchronous resonance because low string is mended the zone, therefore set K _Smin=min{K _S.In addition, from formula

In as can be seen, work as K _S＞1 o'clock, f _e＞f ₀, system measures inhibitory action for the overclocking branch that surpasses power frequency, therefore when string benefits degree greater than 1 the time, it is regional safety string benefit also may to occur.But in the actual engineering, can not remove to pay the utmost attention to too high string and mend.Therefore, and in the interval [0, K _Smin] in find out safety string and mend interval getting final product.

In the step 4, be the example introduction, when use characteristic value method, at first will set up the total system equation with IEEE FIRST BENCHMARK MOEDEL FOR SSR:

${\stackrel{\&CenterDot;}{X}}_{\mathrm{SYS}}=A_{\mathrm{SYS}}{X}_{\mathrm{SYS}}$

Wherein:

X _SYSBe the total system state variable;

A _SYSBe sytem matrix;

Be X _SYSIn each element first derivation.

When setting up the total system equation, system need be divided into mechanical subsystem and electrical subsystem two parts, by electromagnetic torque increment Delta T _eTwo subsystems are merged into the total system equation.Generator shaft system adopts six matter block models.Six matter pieces are high-pressure cylinder (HP), intermediate cylinder (IP), low-pressure cylinder A (LPA), low-pressure cylinder B (LPB), generator module (G) and excitation system (EXC).If not below indicate and to be perunit value.

1. tool subsystem:

In the formula:

Δ δ _H-XIt is the angular displacement increment of six matter pieces;

Δ ω _H-XIt is the angular speed increment of six matter pieces;

M _GQuality coefficient for generator matter piece;

Δ T _eBe the electromagnetic torque increment;

A battle array and D battle array are the null matrix of 6*6.

$B=\left(\begin{array}{cccccc}{\mathrm{\&omega;}}_0& 0& 0& 0& 0& 0\\ 0& {\mathrm{\&omega;}}_0& 0& 0& 0& 0\\ 0& 0& {\mathrm{\&omega;}}_0& 0& 0& 0\\ 0& 0& 0& {\mathrm{\&omega;}}_0& 0& 0\\ 0& 0& 0& 0& {\mathrm{\&omega;}}_0& 0\\ 0& 0& 0& 0& 0& {\mathrm{\&omega;}}_0\end{array}\right)---\left(2\right)$

$C=\left(\begin{array}{cccccc}-\frac{T_{12}}{M_1}& \frac{T_{12}}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000118234300000012.png,HDA0000118234300000043.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}& 0& 0& 0& 0\\ \frac{T_{12}}{M_1}& -\frac{T_{12}+T_{23}}{M_2}& \frac{T_{23}}{{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA0000118234300000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_2}& 0& 0& 0\\ 0& \frac{T_{23}}{M_3}& -\frac{T_{23}+T_{34}}{M_3}& \frac{T_{34}}{{\mathrm{<figure-callout\; id="3"\; label="M"\; filenames="HDA0000118234300000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_3}& 0& 0\\ 0& 0& \frac{T_{34}}{M_4}& -\frac{T_{34}+T_{45}}{M_4}& \frac{T_{45}}{{\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="HDA0000118234300000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_4}& 0\\ 0& 0& 0& \frac{T_{45}}{M_5}& -\frac{T_{45}+T_{56}}{M_5}& \frac{T_{56}}{{\mathrm{<figure-callout\; id="5"\; label="M"\; filenames="HDA0000118234300000012.png"\; state="\{\{state\}\}">M</figure-callout>}}_5}\\ 0& 0& 0& 0& \frac{T_{56}}{M_6}& -\frac{T_{56}}{M_6}\end{array}\right)---\left(5\right)$

ω in the B battle array ₀Be fundamental frequency rotating speed, ω ₀=314.16 radian per seconds.

2. electrical subsystem: use 6 rank Park equations, supposing has damping winding S on the q axle, damping winding D and F (excitation winding) are arranged on the d axle like this, and damping winding Q and S are arranged on the q axle.

$\frac{1}{{\mathrm{\&omega;}}_0}E\&CenterDot;\left(\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{i_d}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{i_q}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{i_F}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{i_D}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{i_Q}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{i_S}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{e_d}\\ \mathrm{\&Delta;}{\stackrel{\&CenterDot;}{e}}_q\end{array}\right)=F\&CenterDot;\left(\begin{array}{c}\mathrm{\&Delta;}{i}_d\\ \mathrm{\&Delta;}{i}_q\\ \mathrm{\&Delta;}{i}_F\\ \mathrm{\&Delta;}{i}_D\\ \mathrm{\&Delta;}{i}_Q\\ \mathrm{\&Delta;}{i}_S\\ \mathrm{\&Delta;}{e}_d\\ \mathrm{\&Delta;}{e}_q\end{array}\right)+G\&CenterDot;\left(\begin{array}{c}\mathrm{\&Delta;}{\mathrm{\&delta;}}_G\\ \mathrm{\&Delta;}{\mathrm{\&omega;}}_G\end{array}\right)---\left(4\right)$

In the formula (4):

Δ i _dWith Δ i _qBe d axle and q shaft current increment;

Δ i _FΔ i _SBe respectively excitation winding, D damping winding, Q damping winding and S damping winding current increment;

Δ e _dWith Δ e _qBe d axle and the q axle component after the decomposition of serial compensation capacitance voltage Parker;

$E=\left(\begin{array}{cccccccc}-(X_d+X_T+X_L)& 0& X_{\mathrm{md}}& X_{\mathrm{md}}& 0& 0& 0& 0\\ 0& -(X_d+X_T+X_L)& 0& 0& X_{\mathrm{mq}}& X_{\mathrm{mq}}& 0& 0\\ X_{\mathrm{md}}& 0& X_F& X_{\mathrm{md}}& 0& 0& 0& 0\\ X_{\mathrm{md}}& 0& X_{\mathrm{md}}& X_D& 0& 0& 0& 0\\ 0& X_{\mathrm{mq}}& 0& 0& X_Q& X_{\mathrm{mq}}& 0& 0\\ 0& X_{\mathrm{mq}}& 0& 0& X_{\mathrm{mq}}& X_S& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right)---\left(5\right)$

In the formula (5):

X _dBe the reactance of generator d axle;

X _TBe transformer reactance;

X _LBe the transmission line reactance;

X _MdAnd X _MqBe respectively reaction reactance of d armature axis and q armature axis reaction reactance;

X _FBe the excitation winding reactance;

X _DBe the reactance of D damping winding;

X _QBe the reactance of Q damping winding;

X _SBe the reactance of S damping winding.

$F=\left(\begin{array}{cccccccc}{r}_a+R_T+R_L& -(X_q+X_T+X_L)& 0& 0& X_{\mathrm{<figure-callout\; id="1"\; label="mq\; X\; mq"\; filenames="HDA0000118234300000012.png,HDA0000118234300000043.png"\; state="\{\{state\}\}">mq</figure-callout>}}& X_{\mathrm{mq}}{}_{}& 1& 0\\ X_d+X_T+X_L& r_a+R_T+R_L& -X_{\mathrm{md}}& -X_{\mathrm{md}}& 0& 0& 0& 1\\ 0& 0& -r_F& 0& 0& 0& 0& 0\\ 0& 0& 0& -r_D& 0& 0& 0& 0\\ 0& 0& 0& 0& -r_Q& 0& 0& 0\\ 0& 0& 0& 0& 0& -r_S& 0& 0\\ X_C& 0& 0& 0& 0& 0& 0& 1\\ 0& X_C& 0& 0& 0& 0& -1& 0\end{array}\right)---\left(6\right)$

In the formula (6):

r _aBe generator resistance;

R _TBe transformer resistance;

R _LBe transmission line resistance;

X _qBe the reactance of q axle;

r _F-SBe respectively excitation winding, D damping winding, Q damping winding and S damping winding resistance;

X _CBe the serial compensation capacitance reactance.

$G=\left(\begin{array}{cc}{V}_{\&infin;q0}& {\mathrm{\&psi;}}_{q0}-(X_T+X_L)i_{q0}\\ -V_{\&infin;d0}& {\mathrm{\&psi;}}_{d0}+(X_T+X_L)i_{d0}\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\end{array}\right)---\left(7\right)$

In the formula (7):

V _{∞ d0}And V _{∞ q0}Be respectively d axle and q shaft voltage component after the infinite busbar steady state voltage decomposes;

ψ _D0And ψ _Q0Be respectively d axle and q axle magnetic linkage under the stable state;

i _D0And i _Q0Be respectively d axle and q shaft current value under the stable state;

e _Cd0And e _Cq0Be respectively d axle and q axle component after serial compensation capacitance voltage decomposes under the stable state.

3. electromagnetic torque increment:

ΔT _e＝-(X _d-X _q)i _q0Δi _d+(X _mdi _F0-(X _d-X _q)i _d0)Δi _q+X _mdi _q0Δi _F+X _mdi _q0Δi _D-X _mqi _d0Δi _Q-X _mqi _d0Δi _S(8)

Through type (1)-(8) can merge the total system equation

Wherein:

X _SYS＝(Δδ _H?Δδ _I?Δδ _A?Δδ _B?Δδ _G?Δδ _X?Δω _H?Δω _I?Δω _A?Δω _B?Δω _G?Δω _X?Δi _d?Δi _q?Δi _F?Δi _D?Δi _Q?Δi _S?Δe _d?Δe _q) ^T

Know and how to form the total system matrix A _SYSAfter, carry out following steps:

1) sets original string benefit degree K ₀=0.

2) according to string benefit degree K _i, i=0,1 ... set up sytem matrix A _SYSAnd computation of characteristic values, be expressed as σ _i+ j ξ _iBy

Find out the conjugate character root of the model frequency that is not scanned out, and calculate corresponding mode electrical damping

3) change string benefit degree K _I+1=K _i+ Δ K; If K _i=K _Smin, carry out step 4); If K _i＜K _Smin, repeating step 2) and-3).

Draw each modal damping with string benefit degree change curve according to result of calculation.For arbitrary string benefit degree, if having the damping of negative norm attitude, then this model frequency

Be master oscillator frequenc; If there is not the damping of negative norm attitude, should string benefit degree be safety string benefit degree then.

The method that test the present invention proposes adopts IEEE FIRST BENCHMARK MODEL FOR SSR (as Fig. 1), because Chinese electrical network characteristic changes the parameter relevant with fundamental frequency into 50Hz, generator shaft system adopts six matter block models (as Fig. 2).

The natural mode of vibration frequency of calculating generator axle system at first, owing to be six matter block models, N=6 also has six mode nature frequencies of oscillation so after the decoupling zero.Table 1 is six matter piece quality coefficients of generator shaft system, and table 2 is six matter piece coefficient of elasticity of generator shaft system, and table 3 is a result of calculation.

Table 1 generator inertia mass constant M

The elastic constant T of table 2 generator matter interblock

Table 3 generator natural frequency

Then adopt frequency sweep method that system is carried out frequency scanning, the result as shown in Figure 3.Among Fig. 3 (a) figure be equivalent resistance with frequency variation curve, as can be seen its value always near 0, (b) be equivalent reactance with frequency change figure, (c) be the partial enlarged drawing of (b) figure, the resonance frequency that therefrom corresponding as can be seen asynchronous motor effect causes

And K _Smin=0.53, the 5th mode in the correspondence table 3.(b) minimum occurs as can be seen when 23.5Hz from Fig. 3, as shown in Table 3, in interval (20.5,26.5) not with the resonance frequency of model frequency complementation, so resonance frequency that does not have transient state moment amplification to cause in this system.This example generator model mechanical damping is zero, does not consider the resonance frequency that is interacted and produced by mechanical torsional.We have obtained the 5th mode nature frequency of oscillation like this will become one of subsynchronous resonance master oscillator frequenc, and this moment, circuit string benefit degree was 0.53.

Then use characteristic value method is set up the sytem matrix process and seen formula (1)-(8), if not parameter is indicated, is perunit value, and is as follows:

Table 4 generator parameter table

Set original string benefit degree K=0, the computing system matrix exgenvalue, (step 4) changes string benefit degree K=K+ Δ K, repeats above calculating until K=K to calculate each mode electrical damping value again _Smin, the electrical damping that we have just obtained each mode interval [0, K _Smin] the last curve that changes.In the Practical Calculation, be 10-40Hz because the subsynchronous resonance frequency takes place, the 1st in this example, 6 mode do not need to calculate, and can ignore.If in order to determine master oscillator frequenc, the 5th mode is found out by frequency sweep method in this example merely, do not need to calculate yet, but, still consider the electrical damping of the 2nd, 3,4 and 5 mode during this example is calculated for mending interval consideration to seeking the safety string.Result of calculation as shown in Figure 4.

From Fig. 4, can obviously find out, at string benefit degree is 0.53 o'clock, the 3rd mode will become master oscillator frequenc, the 2nd modal damping is little about 10 times than the 3rd modal damping, consideration based on the error of calculation, the 2nd mode can not become master oscillator frequenc, even subsynchronous resonance takes place, its energy is also than little many of the 3rd mode.The 4th modal damping be on the occasion of, can not become master oscillator frequenc.In addition, when string benefit degree interval was [0,0.25] as can be seen, each mode electrical damping value just was, and should the interval be that the safety string is mended the interval therefore.

Through the analysis of this method, the 3rd, 5 mode nature frequency of oscillation will become the subsynchronous resonance master oscillator frequenc, and interval [0,0.25] is that the safety string is mended interval.

System is carried out time-domain-simulation, and the result is frequency analysis such as Fig. 5 to vibration, can clearly find out that the natural frequency of oscillation of the 3rd, 5 mode becomes the master oscillator frequenc of subsynchronous resonance.By comparison diagram 6 and Fig. 7, can find out obviously that subsynchronous resonance conditions is obviously improved after string benefit degree enters interval [0,0.25], the consideration of mechanical damping in the reality in addition can be thought the threat of having eliminated subsynchronous resonance.Fig. 8 has provided string and has mended intervally when 0～0.24 changes, and subsynchronous resonance ceiling capacity amplitude is with the curve that string benefits degree changes, and finds out that obviously oscillation energy progressively reduces along with going here and there the reducing of benefit degree.

Fig. 9 has provided string and has mended interval each modal damping figure greater than 1 o'clock, and after string benefits degree was greater than 1.2, the positive damping value all appearred in each mode as can be seen, and this has illustrated that also it is correct also having the saying in safety string benefit interval for string benefits degree greater than 1 o'clock in the step 3.But in the actual engineering, too high string is mended and is meaned bigger investment, sometimes may not be economical, therefore pay the utmost attention to the interval [0, K _Smin] interior analysis.

The contrast of table 5 analytical method

Table 5 has provided the precision when using method of the present invention with separately frequency of utilization scanning method and method of characteristic and the contrast of amount of calculation.Can clearly find out that the method that the present invention proposes has reduced a large amount of amount of calculation of method of characteristic when having guaranteed precision.Δ K=0.01 herein, K _Smin=0.53, amount of calculation has reduced 47 times, 50% when being about independent use characteristic value method.For complication system, adopt method provided herein, obtain K _SminAfter, rational Δ K is set, the amount of calculation that can reduce is appreciable.

The above has verified that fully the present invention when the analysis string is mended the subsynchronous resonance problem that causes, combines the accurate advantage of the quick and method of characteristic of frequency sweep method, overcomes the amount of calculation that frequency sweep method precision deficiency has reduced method of characteristic simultaneously.In addition, method of the present invention can also be mended the interval for system provides safe string.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; 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 range of claim.

Claims (6)

1. AC system subsynchronous resonance analytical method is characterized in that this method may further comprise the steps:

Step 1: the calculating generator axle is each decoupling zero mode natural frequency of many matter block models

Wherein, i=1,2 ... N, N are the matter piece sum of many matter of generator block models;

Step 2: the frequency of utilization scanning method is treated the research transmission system and is carried out frequency scanning, obtains asynchronous generator effect resonance frequency f _EAWith transient state moment amplification resonance frequency f _EC

Step 3: if f _EASatisfy

Or f _ECSatisfy

Then should

Be the master oscillator frequenc of subsynchronous resonance, execution in step 4; Otherwise subsynchronous resonance does not take place, process ends;

Step 4: on the basis of step 3 by f _EAAnd f _ECTry to achieve circuit string benefit degree K _SAnd the minimum value K of definite circuit string benefit degree _Smin

Step 5: set up the total system equation, with method of characteristic interval [0, K _Smin] on try to achieve the curve of each mode electrical damping with the variation of string benefits degree; When string benefit degree is K _SminThe time, the mode electrical damping is the master oscillator frequenc of subsynchronous resonance for negative natural frequency of oscillation; The mode electrical damping interval [0, K _Smin] be that the safety string is mended interval upward for the interval of timing correspondence.

2. a kind of AC system subsynchronous resonance analytical method according to claim 1 is characterized in that described natural frequency

Computing formula be:

$f_0^{\left(i\right)}=\frac{\sqrt{T^{\left(i\right)}/2M^{\left(i\right)}}}{2\mathrm{\&pi;}}$

Wherein:

It is the natural frequency of i mode;

T ⁽ⁱ⁾It is the coefficient of elasticity of i mode;

M ⁽ⁱ⁾It is the quality constant of i mode.

3. a kind of AC system subsynchronous resonance analytical method according to claim 2 is characterized in that described T ⁽ⁱ⁾And M ⁽ⁱ⁾Computing formula be:

M ⁽ⁱ⁾=Q ^TMQ

T ⁽ⁱ⁾=Q ^TTQ

Wherein:

M is the quality coefficient matrix of matter piece;

T is an elastic coefficient matrix;

Q is the characteristic vector battle array, Q=M ^-1T.

4. a kind of AC system subsynchronous resonance analytical method according to claim 3 is characterized in that the computing formula of described M and T is:

$M=\left(\begin{array}{cccc}{M}_1& 0& ...& 0\\ 0& M_2& ...& 0\\ ...& ...& ...& ...\\ 0& ...& 0& M_N\end{array}\right)$

$T=\left(\begin{array}{cccc}{T}_{12}& -T_{12}& ...& 0\\ -T_{12}& T_{12}+T_{23}& ...& 0\\ ...& ...& ...& ...\\ 0& ...& T_{(N-2)(N-1)}+T_{(N-1)N}& -T_{(N-1)N}\\ 0& ...& -T_{(N-1)N}& T_{(N-1)N}\end{array}\right)$

Wherein:

M _NQuality coefficient for the matter piece;

T _{(N-1) N}Coefficient of elasticity for matter piece N-1 confrontation piece N.

5. a kind of AC system subsynchronous resonance analytical method according to claim 1 is characterized in that described circuit string benefit degree K _SComputing formula be:

$K_S={\left(\frac{f_e}{f_0}\right)}^2$

Wherein:

f _eBe asynchronous generator effect resonance frequency f _EAOr transient state moment amplification resonance frequency f _EC

f ₀Be power frequency.

6. a kind of AC system subsynchronous resonance analytical method according to claim 1 is characterized in that described total system equation is:

${\stackrel{\&CenterDot;}{X}}_{\mathrm{SYS}}=A_{\mathrm{SYS}}{X}_{\mathrm{SYS}}$

Wherein:

X _SYSBe the total system state variable;

A _SYSBe sytem matrix;

Be X _SYSIn each element first derivation.

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