CN104101805A - Excitation system negative damping detection method based on oscillation energy injection - Google Patents

Abstract

The invention discloses an excitation system negative damping detection method based on oscillation energy injection and relates to the technical field of power system dynamic stability. The method includes calculating the excitation system oscillation energy injection through a formula of Wex=integral (t2, t1) delta mu f (t) delta i f (t) d t; only extracting the oscillation component of the concerned oscillation frequency through an identification algorithm for calculation; determining the negative and positive of the damping of the excitation system according to the positive and negative of the oscillation energy injection. The excitation system damping is detected through the directly measured generator excitation voltage mu f and excitation current i f for avoiding the reconstruction of generator internal variables, so that the calculation is simple; the generator internal parameters are not used for avoiding errors caused by inaccurate generator parameters, so that the calculation is accurate. The excitation voltage and the excitation current during oscillation can be extracted from a generator monitoring system database for being used for the analysis of excitation system damping characteristics; the method can also be programmed as a subroutine to be integrated into the generator monitoring system for application.

Description

A kind of excitation system negative damping detection method of injecting based on oscillation energy

Technical field

The present invention relates to power system dynamic stability technical field, especially a kind of excitation system negative damping detection method of injecting based on oscillation energy.

Background technology

In modern power systems, the use with the faster exciter of high-amplification-factor is the one of the main reasons that causes low-frequency oscillation.Excitation unit may may make to produce a negative damping torque on generator amature under special operating condition, causes hunting of generator.

On the other hand, excitation system is also to suppress the key point of low-frequency oscillation.Just installing power system stabilizer, PSS (Power System Stabilizer additional in excitation system, PSS), by reaction generator rotating speed, machine end frequency or generator power, through processing such as filtering, amplification, phase compensations, generate an additional excitation reference signal, act on excitation unit, change field voltage, so that it produces a positive damping torque on generator amature, can play the effect that suppresses hunting of generator.

When the PSS improper negative damping that also may produce of adjusting.As inappropriate phase compensation parameter, excessive or too small enlargement factor, all likely causes PSS to produce negative damping.Also may provide positive damping for generator a frequency range, and provide negative damping in another frequency range for generator.

Existing excitation system negative damping detection method has several as follows through retrieval:

Method 1: detect index ∫ Δ i _fΔ ω dt judge excitation system whether produce negative damping (river is kept burning day and night for Wang Maohai, Guo Dengfeng. excitation system damping characteristic analysis method [J] in low-frequency oscillation process. Automation of Electric Systems, 2013,37 (04): 47-50).

Method 2: detect index judge excitation system whether produce negative damping (Li Ying, Shen Chen, Liu Feng. the power system oscillation source device level location [J] of realizing based on Hamilton. Automation of Electric Systems, 2012,36 (23): 6-11.).

Method 3: detect index ∫ Δ E ' _qΔ ω dt judges whether excitation system produces negative damping, (Li Wenfeng, Li Ying, Zhou Xiaoxin, Deng. the Power Systems analysis of the oscillation based on WAMS and oscillation source location (2) moment decomposition method [J]. Proceedings of the CSEE, 2013,33 (25): 47-53.).

The defect map of said method is present: method 1, and the derivation of this method relies on engineering experience, lacks strict Mathematics Proof;

Method 2: two variable i of detection _dwith can not directly measure, need to carry out reconstruct by the amount that can measure, this makes to calculate comparatively complicated; Reconstruct variable need to be used some generator parameter, if the parameter that device fabrication business provides is inaccurate, or parameter changes in operational process, may cause detection error;

Method 3: similar with the shortcoming of method 2, variable Δ E ' _qcan not directly measure, need to carry out reconstruct by the amount that can measure, this makes to calculate comparatively complicated; Reconstruct variable need to be used some generator parameter, if the parameter that device fabrication business provides is inaccurate, or parameter changes in operational process, may cause detection error.

Summary of the invention

Object of the present invention overcomes above-mentioned technological deficiency with not enough, adopts direct measurement generator excitation voltage and exciting current to detect excitation system damping, calculates simple; Can not bring the error of calculation because generator parameter changes, calculate accurately; Detect excitation system and whether produced negative damping, a kind of excitation system negative damping detection method of injecting based on oscillation energy is provided.

Excitation system negative damping is to cause the main cause of low-frequency oscillation of electric power system.The problem to be solved in the present invention is to detect excitation system whether to have produced negative damping.

The technical solution that realizes the object of the invention is as follows: a kind of excitation system negative damping detection method of injecting based on oscillation energy, comprises the steps:

1) select field voltage and the exciting current of duration of oscillation generator to be detected to analyze;

2) utilize identification algorithm to measure obtain field voltage and exciting current carry out identification, pick out respectively oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of field voltage and exciting current in selected time window

3) select mode of oscillation to be analyzed, according to field voltage and exciting current reconstruction formula and corresponding oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of oscillation frequency that will analyze in time domain, difference reconstruct field voltage oscillating component and exciting current oscillating component, obtain Δ u _fand Δ i (t) _f(t);

4) excitation system to the oscillation energy injecting in generator is:

$W_{\mathrm{ex}}={\∫}_{t_1}^{t_2}\mathrm{\Δ}{u}_f\left(t\right)\mathrm{\Δ}{i}_f\left(t\right)\mathrm{dt}---\left(16\right)$

In formula: Δ u _ffor the main oscillations mode component of field voltage, Δ i _ffor exciting current mode of oscillation component to be analyzed;

5) by formula (16) discretize, obtain formula (22)

$W_{\mathrm{ex}}\left(k\right)=\underset{j=1}{\overset{k}{\mathrm{\Σ}}}\mathrm{\Δ}{u}_f\left(j\right)\mathrm{\Δ}{i}_f\left(j\right)\mathrm{\Δt}---\left(22\right)$

The oscillation energy computing formula that is recursion by further formula (22) abbreviation:

W _ex(0)＝0

(23)

W _ex(k)＝W _ex(k-1)+Δu _f(k)Δi _f(k)Δt?(k＞0)

Calculate according to oscillation energy computing formula (23) oscillation energy that mode of oscillation to be analyzed is injected, form excitation system and inject energy flow curve W _ex;

6) computer-made decision, if excitation system is injected energy flow curve W _exrate of curve is for just, and excitation system presents negative damping, and excitation system reduces the damping ratio of electric system mode of oscillation to be analyzed; Can flow curve W if injected _exrate of curve is for negative, and this system presents positive damping, and excitation system increases electric system mode of oscillation damping ratio to be analyzed.

Further, described a kind of excitation system negative damping detection method of injecting based on oscillation energy, step 6) described computer-made decision, its concrete steps are as follows:

2.1), select the time period that will analyze, input field voltage and exciting current in this time period;

2.2), input sample cycle Δ t, identification program exponent number P, counts m oscillation period roughly;

2.3), estimation main oscillation frequency section, main oscillation frequency meets f _min≤ f _i≤ f _maxwherein

2.4), start identification program, pick out oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of field voltage and exciting current in this time period

2.5), select mode of oscillation to be analyzed, according to field voltage reconstruction formula:

in time domain, reconstruct field voltage mode of oscillation oscillating component to be analyzed, obtains Δ u _f(t);

2.6), according to exciting current reconstruction formula:

in time domain, reconstruct exciting current mode of oscillation oscillating component to be analyzed, obtains Δ i _f(t);

2.7), the corresponding relation of computing time and sampled point is: t (k)=Δ tk;

2.8), calculate oscillation energy stream according to the oscillation energy computing formula of recursion:

W _ex(0)＝0

W _ex(k)＝W _ex(k-1)+Δu _f(k)Δi _f(k)Δt?(k＞0)

Calculate the oscillation energy that excitation system is injected;

2.9), print curve W _ex(t), judgment curves W _exdoes is (t) slope greater than 0? if so, excitation system presents negative damping, and excitation system reduces electric system mode of oscillation damping ratio to be analyzed; If not, excitation system presents positive damping, and excitation system increases electric system mode of oscillation damping ratio to be analyzed.

Further, the described excitation system negative damping detection method of injecting based on oscillation energy, described identification program comprises any one identification program in Prony algorithm or TLS-Esprit algorithm.

Excitation system oscillation energy of the present invention injects the principle of calculating theoretical foundation, is below the strict Mathematics Proof that oscillation energy calculates.

According to generator third-order model:

$\begin{array}{c}{\stackrel{\·}{\mathrm{\δ}}}_i=\mathrm{\Δ}{\mathrm{\ω}}_i\\ M_i{\stackrel{\·}{\mathrm{\ω}}}_i=P_{\mathrm{Mi}}-P_{\mathrm{ei}}-D_i\mathrm{\Δ}{\mathrm{\ω}}_i\\ T_{d0i}^{\′}{E}_{\mathrm{qi}}^{\′}=E_{\mathrm{Fi}}-E_{\mathrm{qi}}^{\′}-(x_{\mathrm{di}}-x_{\mathrm{di}}^{\′})i_{\mathrm{di}}\end{array}---\left(1\right);$

And Tsolas-Arapostathis-Varaiya model transient energy function (referred to as TAV model):

$\begin{array}{c}W=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{1}{2}{M}_i\mathrm{\Δ}{\mathrm{\ω}}_i^2-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_{\mathrm{Mi}}{\mathrm{\δ}}_i-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{E_{\mathrm{Fi}}{E}_{\mathrm{qi}}^{\′}}{x_{\mathrm{di}}-x_{\mathrm{di}}^{\′}}+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[\frac{E_{\mathrm{qi}}^{\′2}}{2(x_{\mathrm{di}}-x_{\mathrm{di}}^{\′})}+\frac{E_{\mathrm{qi}}^{\′2}}{2x_{\mathrm{di}}^{\′}}]\\ -\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{E_{\mathrm{qi}}^{\′}{V}_i\cos ({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)}{x_{\mathrm{di}}^{\′}}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{V_i}^2\cos \left[2({\mathrm{\δ}}_i-{\mathrm{\θ}}_i)\right](x_{\mathrm{di}}^{\′}-x_{\mathrm{qi}})}{4x_{\mathrm{di}}^{\′}{x}_{\mathrm{qi}}}+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{x_{\mathrm{di}}^{\′}+x_{\mathrm{qi}}}{4x_{\mathrm{di}}^{\′}{x}_{\mathrm{qi}}}{V_i}^2\\ -\frac{1}{2}\underset{i=1}{\overset{n+1}{\mathrm{\Σ}}}\underset{j\≠i}{\overset{n+1}{\underset{j=1}{\mathrm{\Σ}}}}{B}_{\mathrm{ij}}{V}_i{V}_j\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-\underset{i=1}{\overset{n+1}{\mathrm{\Σ}}}\underset{k=n+2}{\overset{n+m+1}{\mathrm{\Σ}}}{B}_{\mathrm{ik}}{V}_i{V}_k\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_k)-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{B}_{\mathrm{ii}}{V_i}^2\\ +\underset{k=n+2}{\overset{n+m+1}{\mathrm{\Σ}}}{P_k}^d{\mathrm{\θ}}_k+\underset{k=n+2}{\overset{n+m+1}{\mathrm{\Σ}}}\∫\frac{Q_k^d}{V_k}d{V}_k-\frac{1}{2}\underset{k=n+2}{\overset{n+m+1}{\mathrm{\Σ}}}\underset{l\≠k}{\overset{n+m+1}{\underset{l=n+2}{\mathrm{\Σ}}}}{B}_{\mathrm{kl}}{V}_k{V}_l\cos ({\mathrm{\θ}}_k-{\mathrm{\θ}}_l)-\frac{1}{2}\underset{k=n+2}{\overset{n+m+1}{\mathrm{\Σ}}}{B}_{\mathrm{kk}}{V_k}^2\end{array}---\left(2\right);$

The power that can calculate the transient state energy dissipation of generator i is:

$-\frac{\∂W}{\∂{\mathrm{\δ}}_i}\·\frac{d{\mathrm{\δ}}_i}{\mathrm{dt}}=D_i\mathrm{\Δ}{\mathrm{\ω}}_i^2=P_{\mathrm{Mi}}\mathrm{\Δ}{\mathrm{\ω}}_i-P_{\mathrm{ei}}\mathrm{\Δ}{\mathrm{\ω}}_i-M_i\mathrm{\Δ}{\stackrel{\·}{\mathrm{\ω}}}_i\mathrm{\Δ}{\mathrm{\ω}}_i---\left(3\right);$

$-\frac{\∂W}{\∂E_{\mathrm{qi}}^{\′}}\·\frac{d{E}_{\mathrm{qi}}^{\′}}{\mathrm{dt}}=\frac{T_{d0}^{\′}}{x_{\mathrm{di}}-x_{\mathrm{di}}^{\′}}{\stackrel{\·}{E}}_{\mathrm{qi}}^{\′2}=\frac{E_{\mathrm{Fi}}}{x_{\mathrm{di}}-x_{\mathrm{di}}^{\′}}{\stackrel{\·}{E}}_{\mathrm{qi}}^{\′}-\frac{E_{\mathrm{qi}}^{\′}}{x_{\mathrm{di}}-x_{\mathrm{di}}^{\′}}{\stackrel{\·}{E}}_{\mathrm{qi}}^{\′}-i_{\mathrm{di}}{\stackrel{\·}{E}}_{\mathrm{qi}}^{\′}---\left(4\right);$

Magnetic linkage attenuation equation in comparison expression (4) and formula (1) is known, and formula (4) is to be multiplied by magnetic linkage attenuation equation two ends simultaneously obtain.Formula (4) has represented that excitation system transient state energy injects generator, and the process that transforms in generator, dissipates, propagates.Wherein represent the transient state energy power of excitation system injection generator, represent the power of the transient state energy of generator electromagnetic system storage, represent the transient state energy power that generator electromagnetic system dissipates, represent the transient state energy power of generator electromagnetic system to external communication.Without loss of generality, in explanation below, omit subscript i.Generator d, q shaft voltage equation are:

u _d＝x _qi _q

(5)

u _q＝E′ _q-x′ _di _d

Time differential is asked in formula (5) two ends simultaneously, obtain formula (6)

$\begin{array}{c}{\stackrel{\·}{u}}_d=p{x}_q{i}_q\\ {\stackrel{\·}{u}}_q={\stackrel{\·}{E}}_q^{\′}-p{x}_d^{\′}{i}_d\end{array}---\left(6\right)$

In formula (6), p represents differentiating operator.By in formula (4), formula (6) with regard broad sense voltage as, i _dand i _qregard broad sense electric current as, formula (4), the represented conversion process of energy of formula (6) can be represented with the circuit diagram that a transient state energy transforms, referring to Fig. 1 (a)-Fig. 1 (b).

From Fig. 1 (a)-Fig. 1 (b), the transient state energy power being provided by generator d, q axle is respectively with according to the definition of ud and uq, Generator end d, q shaft voltage are expressed as

u _q＝Vcos(δ-θ)

(7)

u _d＝Vsin(δ-θ)

Ask formula (7) differential taking the time as variable:

$\begin{array}{c}{\stackrel{\·}{u}}_q=\stackrel{\·}{V}\cos (\mathrm{\δ}-\mathrm{\θ})-V\sin (\mathrm{\δ}-\mathrm{\θ})\stackrel{\·}{\mathrm{\δ}}+V\sin (\mathrm{\δ}-\mathrm{\θ})\stackrel{\·}{\mathrm{\θ}}\\ =\frac{u_q}{V}\stackrel{\·}{V}-u_d\stackrel{\·}{\mathrm{\δ}}+u_d\stackrel{\·}{\mathrm{\θ}}\\ {\stackrel{\·}{u}}_d=\stackrel{\·}{V}\sin (\mathrm{\δ}-\mathrm{\θ})+V\cos (\mathrm{\δ}-\mathrm{\θ})\stackrel{\·}{\mathrm{\δ}}-V\cos (\mathrm{\δ}-\mathrm{\θ})\stackrel{\·}{\mathrm{\θ}}\\ =\frac{u_d}{V}\stackrel{\·}{V}+u_q\stackrel{\·}{\mathrm{\δ}}-u_q\stackrel{\·}{\mathrm{\θ}}\end{array}---\left(8\right)$

According to formula (8), the transient state energy power that can calculate generator is provided by d axle, q axle meets

$\begin{array}{c}{\stackrel{\·}{u}}_q{i}_q-{\stackrel{\·}{u}}_d{i}_q\\ =\frac{u_q{i}_q-u_d{i}_q}{V}\stackrel{\·}{V}-(u_d{i}_d+u_q{i}_q)\stackrel{\·}{\mathrm{\δ}}+(u_d{i}_d+u_q{i}_q)\stackrel{\·}{\mathrm{\θ}}\\ =\frac{Q_e}{V}\stackrel{\·}{V}-P_e\stackrel{\·}{\mathrm{\δ}}+P_e\stackrel{\·}{\mathrm{\θ}}\\ =\frac{Q_e}{V}\stackrel{\·}{V}-P_e\mathrm{\Δ\ω}+P_e\mathrm{\Δf}\end{array}---\left(9\right)$

According to formula (9), the transient state energy that d, q axle provide adds add the transient state energy power P of Generator's Rotor Circuit _eΔ ω, equals generator and injects the transient state energy power of electric system therefore Fig. 1 (a)-Fig. 1 (b) can accurate description excitation system Implantation Energy process.If but directly used weigh excitation system Implantation Energy, exist be difficult to the problem of directly measuring.

So also will do following improvement while calculating excitation system Implantation Energy:

1, extract oscillating component and calculate oscillation energy, all adopt oscillating component in the time of calculating energy, in Fig. 1 (a)-Fig. 1 (b), broad sense voltage and broad sense electric current all represent by departure;

2, Fig. 1 (a)-Fig. 1 (b) is converted, the equivalent circuit of power unit is replaced with thevenin equivalent circuit, as shown in Fig. 2 (a)-Fig. 2 (b).

In Fig. 2 (b), practical generator third-order model definition is replaced with to Park equation original definition according to the definition of practical variable in third-order model, comprise

$E_f=\frac{x_{\mathrm{ad}}}{r_f}{u}_f---\left(10\right)$

$T_{d0}^{\′}=\frac{x_f}{r_f}---\left(11\right)$

$x_d^{\′}=x_d-\frac{x_{\mathrm{ad}}^2}{x_f}---\left(12\right)$

E _q＝x _adi (13)

Therefore, the broad sense voltage of power supply in thevenin equivalent circuit

$\frac{\mathrm{\Δ}{E}_f}{x_d-x_d^{\′}}\·\frac{x_d-x_d^{\′}}{T_{d0}^{\′}}=\frac{x_{\mathrm{ad}}}{x_f}\mathrm{\Δ}{u}_f---\left(14\right)$

The broad sense electric current of voltage source output

$\frac{\mathrm{\Δ}{E}_q}{x_d-x_d^{\′}}=\frac{x_f}{x_{\mathrm{ad}}}\mathrm{\Δ}{i}_f---\left(15\right)$

Therefore,, within any one time period, excitation system to the oscillation energy injecting in generator is

$W_{\mathrm{ex}}={\∫}_{t_1}^{t_2}\mathrm{\Δ}{u}_f\left(t\right)\mathrm{\Δ}{i}_f\left(t\right)\mathrm{dt}---\left(16\right)$

The condition of work that the invention process needs comprises:

1) field voltage and the exciting current data of the generator that will detect during the low frequency oscillations by measurement mechanism measurement, wave recording device record; Because existing generator is equipped with the sensor of measuring field voltage and exciting current mostly, thus needn't be again sensor installation specially.

2) identification program, comprise any one identification program can, as Prony, TLS-Esprit etc.This class method is technology maturation in electric system, is widely used, and can pick out oscillation frequency, amplitude, decay factor, initial phase etc.The present invention selects TLS-Esprit program.

3) computing machine, field voltage and exciting current that the present invention can extract the duration of oscillation from electricity generator monitoring system database carry out excitation system damping characteristic analysis; Also able to programme as a subroutine, be integrated in electricity generator monitoring system and apply.

Compared with the prior art, the present invention has significant good effect.The present invention adopts the generator excitation voltage u of direct measurement _fwith exciting current i _fdetect excitation system damping, avoid generator variable to be reconstructed, therefore calculate simple; Owing to not needing to use generator parameter, avoid the inaccurate error causing because of generator parameter, it is more accurate therefore to calculate.

Brief description of the drawings

Fig. 1 (a)-Fig. 1 (b) is the circuit diagram that in the principle of the invention, transient state energy transforms.

Fig. 2 (a)-Fig. 2 (b) is the circuit diagram that in the principle of the invention, oscillation energy injects.

Fig. 3 is COMPUTER DETECTION program flow chart schematic diagram of the present invention.

Fig. 4 (a)-Figure 11 is the present invention's l-G simulation test effect curve schematic diagram in the time of different K values.

Terminological interpretation:

Low-frequency oscillation: low-frequency oscillation is the vibration of electric system medium frequency between 0.1～2.5Hz.In the time that low-frequency oscillation occurs, generator amature angle, rotating speed, output power, and the electric parameters generation persistent oscillation such as active power in power transmission network, reactive power, voltage, frequency.

Embodiment

Below, excitation system oscillation energy of the present invention is injected by formula calculate; By identification algorithm, only extract the oscillating component of the oscillation frequency of being concerned about and calculate; The technical scheme of the positive and negative negative, positive of judging excitation system damping injecting with oscillation energy is done specific description.

Duration of oscillation field voltage and the exciting current discrete magnitude often of the measurement mechanism record the present invention relates to, need to will calculate and inject oscillation energy after formula (16) discretize; For making energy corresponding with low-frequency oscillation mode, while extracting oscillating component, only select be concerned about component to analyze, this need to carry out identification to field voltage and exciting current, and concrete steps are as follows:

1) field voltage and the exciting current of the actual measurement of the selection duration of oscillation, selection principle is: the 1. field voltage of same same time period of generator and exciting current; If 2. vibration, by large perturbation excitation, should avoid selecting field voltage and the exciting current after disturbance has just finished; 3. data selected at least comprises 5 oscillation period.

2) calculation procedure data are inputted the 1. sampling period Δ t of input measurement data; 2. input identification program exponent number P; 3. input the roughly number of oscillation m comprising in the selected time period, error should not be greater than 2; 4. input field voltage and exciting current.

3) main oscillation frequency estimation, main oscillation frequency f meets f _min≤ f≤f _max, f _minand f _maxbe estimated as respectively:

$f_{\min }=\frac{m-3}{\mathrm{n\Δt}}---\left(17\right)$

$f_{\max }=\frac{m+3}{\mathrm{n\Δt}}---\left(18\right)$

Wherein n is the data amount check that input field voltage comprises.

4) respectively inputted field voltage and exciting current are carried out to identification with TLS-Esprit algorithm, pick out respectively oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of field voltage and each mode of oscillation of exciting current

5) reconstruct field voltage oscillating component.Select oscillation frequency f _imeet f _min≤ f _i≤ f _maxmode of oscillation, the oscillation amplitude A corresponding according to these mode of oscillation _i, decay factor σ _i, oscillation frequency f _iand initial phase in time domain, difference reconstruct field voltage oscillating component and exciting current oscillating component, obtain Δ u _fand Δ i (t) _f(t);

Field voltage reconstruction formula is as follows:

In formula (19), k is k sampled point in data rows, Δ u _ffor the mode of oscillation component to be analyzed of field voltage, A _uibe that i pattern field voltage is oscillation amplitude, σ _uii pattern is field voltage decay factor, f _uibe i pattern field voltage oscillation frequency, and meet f _min≤ f _i≤ f _max, i pattern is i pattern field voltage initial phase of oscillation position, and Δ t is the sampling period.

6) reconstruct exciting current oscillating component

Exciting current reconstruction formula is as follows:

Δ i _ffor this mode of exciting current is mode of oscillation component to be analyzed at the component of time domain, A _cibe that i pattern exciting current is oscillation amplitude, σ _cii pattern is exciting current decay factor, f _cibe i pattern exciting current oscillation frequency, and meet f _min≤ f _ci≤ f _max, i pattern is i pattern exciting current initial phase of oscillation position, and the corresponding relation of time and sampled point is:

t(k)＝Δt·k (21)

7) by formula (16) discretize, obtain formula (22)

$W_{\mathrm{ex}}\left(k\right)=\underset{j=1}{\overset{k}{\mathrm{\Σ}}}\mathrm{\Δ}{u}_f\left(j\right)\mathrm{\Δ}{i}_f\left(j\right)\mathrm{\Δt}---\left(22\right)$

By formula (22) the oscillation energy computing formula that further abbreviation is recursion

W _ex(0)＝0

(23)

W _ex(k)＝W _ex(k-1)+Δu _f(k)Δi _f(k)Δt?(k＞0)

8) print curve W _ex(t), if curve W _ex(t) slope is for just, and excitation system is injected oscillation energy in generator, and excitation system presents negative damping, and excitation system makes system damping than reducing; W _ex(t) rate of curve is negative, the oscillation energy in excitation system absorption system, and this system presents positive damping, and excitation system makes system damping than increasing.

Referring to Fig. 4 (a)-Figure 11, the present invention's l-G simulation test effect curve in the time of different K values has been described, prove and detected excitation system and whether produced negative damping by the method that the present invention proposes.

In one-of-a-kind system, change system damping by changing excitation system enlargement factor, emulation starts to add one at Generator end in latter 1.05 seconds, and three phase short circuit fault is to excite vibration in short-term, and after 0.1 second, fault disappears.Extract field voltage and exciting current data analysis that emulation starts latter 2.5 seconds～7.5 seconds, the present embodiment adopts TLS-Esprit Algorithm Analysis, then calculates and print oscillation energy curve W by the method for the invention _ex(t), judge excitation system damping.The sampling period Δ t=0.01 second that field voltage and exciting current are measured, identification program exponent number P=8.

Embodiment 1

K＝0

Excitation enlargement factor is 0 to mean and do not carry out adjustment of field excitation, and field voltage does not fluctuate, Δ u _f(t)=0.Excitation system does not have oscillation energy to inject in this case, does not absorb oscillation energy yet; That is to say that it is both for system provides positive damping, also not for system provides negative damping.This is dampingratioζ=0.021 of system.

K＝10

Excitation enlargement factor is K=10, and referring to Fig. 4 (a)-Fig. 4 (b), field voltage when K=10 and exciting current, provided field voltage and excitation current waveform that emulation starts 0～7.5 second.

Select the data analysis of 2.5～7.5 seconds.Within this time period, number of oscillation m=9 roughly, sampling period Δ t=0.01 second, according to formula (17), formula (18), the oscillation frequency f of main oscillations pattern meets 0.6Hz≤f≤1.2Hz.Select identification program exponent number identification program exponent number P=8, table 1, table 2 have provided respectively the TLS-Esprit analysis result of field voltage and exciting current.

Field voltage TLS-Esprit analysis result when table 1 K=10

Exciting current TLS-Esprit analysis result when table 2 K=10

Select oscillation frequency to meet the mode of oscillation of 0.6Hz≤f≤1.2Hz, press formula (19), formula (20) in time domain reconstruction field voltage and exciting current oscillating component, calculate oscillation energy, the oscillation energy that when Fig. 5 has provided K=10, excitation system was injected between 2.5～7.5 seconds by formula (23).

Referring to Fig. 5, as can be seen from the figure, excitation system is injected oscillation energy for negative, and excitation system provides positive damping for generator, and the damping ratio of system will increase when thering is no excitation control.Damping ratio is now ζ=0.026, and dampingratioζ=0.021 of contrast during without excitation control is known, excitation system damping action has been made to correct judgement by method provided by the invention.

Embodiment 2

K＝30

Excitation enlargement factor is K=30, and Fig. 6 (a)-Fig. 6 (b) has provided field voltage and the excitation current waveform that emulation starts 0～7.5 second.

Select the data analysis of 2.5～7.5 seconds.Within this time period, number of oscillation m=9 roughly, sampling period Δ t=0.01 second, according to formula (17), formula (18), the oscillation frequency f of main oscillations pattern meets 0.6Hz≤f≤1.2Hz.Select identification program exponent number identification program exponent number P=8, table 3, table 4 have provided respectively the TLS-Esprit analysis result of field voltage and exciting current.

Field voltage TLS-Esprit analysis result when table 3 K=30

Exciting current TLS-Esprit analysis result when table 4 K=30

Select oscillation frequency to meet the mode of oscillation of 0.6Hz≤f≤1.2Hz, press formula (19), formula (20) in time domain reconstruction field voltage and exciting current oscillating component, calculate oscillation energy, the oscillation energy that when Fig. 7 has provided K=30, excitation system was injected between 2.5～7.5 seconds by formula (23).

Referring to Fig. 7, as can be seen from the figure, excitation system is injected oscillation energy for just, and excitation system provides negative damping for generator, and the damping ratio of system will reduce when thering is no excitation control.Damping ratio is now ζ=0.017, and dampingratioζ=0.021 while contrasting without excitation control is known, with the invention provides method, excitation system damping action has been made to correct judgement.

Embodiment 3

K＝50

Excitation enlargement factor is K=50, and Fig. 8 (a)-Fig. 8 (b) has provided field voltage and the excitation current waveform that emulation starts 0～7.5 second.

Select the data analysis of 2.5～7.5 seconds.Within this time period, number of oscillation m=9 roughly, sampling period Δ t=0.01 second, according to formula (17), formula (18), the oscillation frequency f of main oscillations pattern meets 0.6Hz≤f≤1.2Hz.Select identification program exponent number identification program exponent number P=8, table 5, table 6 have provided respectively the TLS-Esprit analysis result of field voltage and exciting current.

Field voltage TLS-Esprit analysis result when table 5 K=50

Exciting current TLS-Esprit analysis result when table 6 K=50

Select oscillation frequency to meet the mode of oscillation of 0.6Hz≤f≤1.2Hz, press formula (19), formula (20) in time domain reconstruction field voltage and exciting current oscillating component, calculate oscillation energy, the oscillation energy that when Fig. 9 has provided K=50, excitation system was injected between 2.5～7.5 seconds by formula (23).

Referring to Fig. 9, as can be seen from the figure, excitation system is injected oscillation energy for just, and excitation system provides negative damping for generator, and the damping ratio of system will reduce when thering is no excitation control.Damping ratio is now ζ=0.003, and dampingratioζ=0.021 while contrasting without excitation control is known, with the invention provides method, excitation system damping action has been made to correct judgement.

Embodiment 4

K＝70

Excitation enlargement factor is K=70, and Figure 10 (a)-Figure 10 (b) has provided field voltage and the excitation current waveform that emulation starts 0～7.5 second.

Select the data analysis of 2.5～7.5 seconds.Within this time period, number of oscillation m=9 roughly, sampling period Δ t=0.01 second, according to formula (17), formula (18), the oscillation frequency f of main oscillations pattern meets 0.6Hz≤f≤1.2Hz.Select identification program exponent number identification program exponent number P=8, table 7, table 8 have provided respectively the TLS-Esprit analysis result of field voltage and exciting current.

Field voltage TLS-Esprit analysis result when table 7 K=70

Field voltage TLS-Esprit analysis result when table 8 K=70

Select oscillation frequency to meet the mode of oscillation of 0.6Hz≤f≤1.2Hz, press formula (19), formula (20) in time domain reconstruction field voltage and exciting current oscillating component, calculate oscillation energy, the oscillation energy that when Figure 11 has provided K=70, excitation system was injected between 2.5～7.5 seconds by formula (23).

Referring to Figure 11, as can be seen from the figure, excitation system is injected oscillation energy for just, and excitation system provides negative damping for generator, and the damping ratio of system will reduce when thering is no excitation control.Damping ratio is now ζ=-0.004, and dampingratioζ=0.021 while contrasting without excitation control is known, with the invention provides method, excitation system damping action has been made to correct judgement.

Claims (3)

1. an excitation system negative damping detection method of injecting based on oscillation energy, is characterized in that, comprises the steps:

1) select field voltage and the exciting current of duration of oscillation generator to be detected to analyze;

2) utilize identification algorithm to measure obtain field voltage and exciting current carry out identification, pick out respectively oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of field voltage and exciting current in selected time window

3) select mode of oscillation to be analyzed, according to field voltage and exciting current reconstruction formula and corresponding oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of oscillation frequency that will analyze in time domain, difference reconstruct field voltage oscillating component and exciting current oscillating component, obtain Δ u _fand Δ i (t) _f(t);

4) excitation system to the oscillation energy injecting in generator is:

$W_{\mathrm{ex}}={\∫}_{t_1}^{t_2}\mathrm{\Δ}{u}_f\left(t\right)\mathrm{\Δ}{i}_f\left(t\right)\mathrm{dt}---\left(16\right)$

In formula: Δ u _ffor the mode of oscillation component to be analyzed of field voltage, Δ i _ffor exciting current mode of oscillation component to be analyzed;

5) by formula (16) discretize, obtain formula (22)

$W_{\mathrm{ex}}\left(k\right)=\underset{j=1}{\overset{k}{\mathrm{\Σ}}}\mathrm{\Δ}{u}_f\left(j\right)\mathrm{\Δ}{i}_f\left(j\right)\mathrm{\Δt}---\left(22\right)$

The oscillation energy computing formula that is recursion by further formula (22) abbreviation:

W _ex(0)＝0

(23)

W _ex(k)＝W _ex(k-1)+Δu _f(k)Δi _f(k)Δt?(k＞0)

Calculate according to oscillation energy computing formula (23) oscillation energy that mode of oscillation to be analyzed is injected, form excitation system and inject energy flow curve W _ex;

6) computer-made decision, if excitation system is injected energy flow curve W _exrate of curve is for just, and excitation system presents negative damping, and excitation system reduces the damping ratio of electric system mode of oscillation to be analyzed; Can flow curve W if injected _exrate of curve is for negative, and this system presents positive damping, and excitation system increases electric system mode of oscillation damping ratio to be analyzed.

2. a kind of excitation system negative damping detection method of injecting based on oscillation energy according to claim 1, is characterized in that step 6) described computer-made decision, its concrete steps are as follows:

2.1), select the time period that will analyze, input field voltage and exciting current in this time period;

2.2), input sample cycle Δ t, identification program exponent number P, counts m oscillation period roughly;

2.3), estimation main oscillation frequency section, main oscillation frequency meets f _min≤ f _i≤ f _maxwherein $f_{\max }=\frac{m+3}{\mathrm{n\Δt}};$

2.4), start identification program, pick out oscillation amplitude A, decay factor σ, oscillation frequency f and the initial phase of field voltage and exciting current in this time period

2.5), select mode of oscillation to be analyzed, according to field voltage reconstruction formula:

in time domain, reconstruct field voltage mode of oscillation oscillating component to be analyzed, obtains Δ u _f(t);

2.6), according to exciting current reconstruction formula:

in time domain, reconstruct exciting current mode of oscillation oscillating component to be analyzed, obtains Δ i _f(t);

2.7), the corresponding relation of computing time and sampled point is: t (k)=Δ tk;

2.8), calculate oscillation energy stream according to the oscillation energy computing formula of recursion:

W _ex(0)＝0

W _ex(k)=W _ex(k-1)+Δ u _f(k) Δ i _f(k) Δ t (k > 0), calculates the oscillation energy that excitation system is injected;

2.9), print curve W _ex(t), judgment curves W _exdoes is (t) slope greater than 0? if so, excitation system presents negative damping, and excitation system reduces electric system mode of oscillation damping ratio to be analyzed; If not, excitation system presents positive damping, and excitation system increases electric system mode of oscillation damping ratio to be analyzed.

3. a kind of excitation system negative damping detection method of injecting based on oscillation energy according to claim 1, is characterized in that, described identification program comprises any one identification program in Prony algorithm or TLS-Esprit algorithm.