CN101834446B - Sub-synchronous oscillation suppression method based on controlled series compensation - Google Patents

Abstract

The invention relates to a sub-synchronous oscillation suppression method based on controlled series compensation, which is based on the concept of damping torque, adopts a design method of phase compensation, and carries out proper amplification and phase shift processing on speed signal delta omega to generate an additional control signal to modulate a TCSC (Thyristor Controlled Series Capacitor) trigger angle. Therefore, equivalent reactance of the TCSC is changed, the TCSC can provide positive electrical damping in the entire sub-synchronous frequency range, and the problem of SSR (Sub-Synchronous Resonance) caused by series compensation capacitors can be thoroughly eliminated.

Description

A kind of sub-synchronous oscillation suppression method based on controlled series compensation

Technical field

The present invention proposes a kind of sub-synchronous oscillation suppression method of the series capacitor (being controlled series compensation) based on thyristor control, belongs to the innovative technology of electric power system control.

Background technology

Transmission line adds series capacitor compensation can improve ability to transmit electricity, has therefore worldwide obtained using widely.But the fixed series capacitor compensation of high series compensatnig degree may cause the subsynchronous resonance of electric power system, and then causes the axle system of turbo generator to damage, and has a strong impact on the safe operation of electric power system.

Along with the development of power electronic device, because of having the higher system response speed, more and more coming into one's own aspect the inhibition subsynchronous resonance in recent years based on the series capacitor (TCSC) of thyristor control.The basic module of TCSC is composed in parallel by the reactance L of a series capacitors C and a thyristor control, and its structure is as shown in Figure 1, T among the figure ₁, T ₂It is the thyristor of two parallel connected in reverse phase.As with capacitance voltage u _CBecome the trigger angle that positive zero passage begins to calculate the forward thyristor constantly by bearing, then for the C and the L of given parameter, the stable state first-harmonic equiva lent impedance of TCSC is determined by trigger angle α.Shown in (1):

$X_{\mathrm{TCSC}}=X_c-\frac{K^2{X}_c}{\mathrm{\π}(K^2-1)}[2\·(\mathrm{\π}-\mathrm{\α})+\sin 2(\mathrm{\π}-\mathrm{\α})]+$

$\frac{4K^2{X}_c{\cos }^2(\mathrm{\π}-\mathrm{\α})}{\mathrm{\π}(K^2-1)}[K\tan K(\mathrm{\π}-\mathrm{\α})-\tan (\mathrm{\π}-\mathrm{\α})]---\left(1\right)$

$K=\sqrt{X_C/X_L}$

In the formula, X _LBe the fundamental frequency reactance of variable reactor, X _CCapacitor value for capacitor under the fundamental frequency.K is the characteristic parameter of TCSC major loop, a plurality of resonance points occur for avoiding TCSC, and the value of K is usually less than 3.0.

From the consideration of cost, TCSC is not used for series compensation usually separately, can be used with fixing series capacitance.Though can reduce cost like this, slow down sub-synchronous oscillation to a certain extent, often can not thoroughly suppress the generation of sub-synchronous oscillation.

Summary of the invention

The present invention is based on the notion of damping torque; Adopt the method for designing of phase compensation; On the TCSC open-cycle controller, design an additional SSR damping controller, can in whole subsynchronous frequency range, positive electrical damping be provided, thereby thoroughly eliminated the SSR problem that causes by serial compensation capacitance.

A kind of method of the inhibition subsynchronous oscillation of electrical power system based on controlled series compensation is handled through generator speed signal delta ω being carried out suitable amplification and phase shift, generates additional control signal the TCSC trigger angle is modulated, thereby change the equivalent reactance X of TCSC _Eff, the electrical damping of raising system.The practical implementation process is as shown in Figure 2, comprises the steps:

(1) gather the speed discrepancy signal delta ω of generators in power systems (if among the present invention no specified otherwise, described generator refers to that all needs pass through that generator that the inventive method is protected), the speed discrepancy signal is meant actual speed and rated speed poor of generator;

(2) speed discrepancy signal delta ω is carried out Filtering Processing, filters low signal and high order harmonic component obtain the generator torsion frequency signal in the subsynchronous frequency range.The band pass filter that is adopted, its band connection frequency are 10Hz～55Hz.So filter cutoff frequency is ω _C1=55Hz, ω _C2=10Hz, its transfer function can be expressed as:

$H\left(s\right)=\frac{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^4}{s^4+2.613{\mathrm{\&omega;}}_{c1}{s}^3+3.414{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^2{s}^2+{2.613\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{3}s+{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^4}$

$\&CenterDot;\frac{s^4}{s^4+2.613{\mathrm{\&omega;}}_{c2}{s}^3+3.414{\mathrm{\&omega;}}_{c2}^2{s}^2+2.613{\mathrm{\&omega;}}_{c2}^{3}s+{\mathrm{\&omega;}}_{c2}^4}---\left(2\right)$

(3) signal that filtering is obtained amplify with phase compensation after, obtain the be added to benchmark trigger angle α of TCSC of additional signal Δ α ₀On.

In the practical application,, realize phase compensation than wide-angle through adopting a plurality of lead-lag links to carrying out phase compensation through amplifying signal.

The transfer function of described lead-lag link can be expressed as the form of

, wherein:

T _a, T _bBe the time constant of lead-lag link,

n＝T _b/T _a＝(1-sinφ)/(1+sinφ)

$T_a=1/\left({\mathrm{\&omega;}}_x\sqrt{n}\right)$

T _b＝nT _a

ω _xBe selected phase compensation frequency; φ is ω _xThe pairing lagging phase angle that needs compensation.

When confirming to need the lagging phase angle φ of compensation, referring to formula (3)

$D_e=\mathrm{Re}\left(\frac{\mathrm{\&Delta;}{T}_e}{\mathrm{\&Delta;\&omega;}}\right)---\left(3\right)$

Δ T in the formula (3) _eBe the torque deviation of generator, speed discrepancy signal, the D that Δ ω is generator _eElectrical damping for electric power system;

Can draw by formula (3), as Δ T _eAnd the phase angle difference between the Δ ω is in the time of-90 ° to+90 °, the electrical damping D of electric power system _eWill be for just.As Δ T _eWith the same phase time of Δ ω, system can provide maximum electrical damping.Need make Δ T _eWith the Δ ω homophase of trying one's best, thereby maximum electrical damping is provided for suppressing SSR.

For the lagging phase angle φ that the needs that obtain confirming compensate, can utilize the time domain frequency sweep method to try to achieve the additional control signal Δ α of TCSC to generator additional electromagnetic torque Δ T _eBetween the phase characteristic of transfer function G (s), making generator speed increment Delta ω to generator electromagnetic torque increment Delta T _eBetween phase characteristic under the principle within ± 90 °, confirm to need the lagging phase angle φ of compensation, make the electrical damping that TCSC can both be positive in whole subsynchronous frequency range.

Concrete steps are:

(a) at benchmark trigger angle α ₀On apply a string 10Hz of comprising～55Hz, frequency interval is the swept-frequency signal of the subsynchronous frequency of 0.2Hz.

(b) apply swept-frequency signal after, until electric power system gets into stable state, the generator electromagnetic torque T on common period of intercepting once more _eWith the TCSC trigger angle α that applies after the swept-frequency signal _m

(c) T that step (b) is obtained _eAnd α _mCarry out Fourier and decompose, try to achieve TCSC trigger angle increment Delta α _mTo generator electromagnetic torque increment Delta T _eBetween the phase characteristic of transfer function G (s).

(d) definite then lagging phase angle φ that needs compensation makes that generator speed increment Delta ω is to generator electromagnetic torque increment Delta T in the subsynchronous frequency range of whole 10Hz～55Hz _eBetween phase characteristic within ± 90 °.

The inventive method makes TCSC positive electrical damping is provided in whole subsynchronous frequency range through the additional control of TCSC trigger angle, thereby reaches the purpose of eliminating SSR, in practical engineering application, has great reference value.

Description of drawings

Fig. 1 TCSC basic structure sketch map;

Fig. 2 adopts the TCSC control system block diagram of the inventive method;

Test macro winding diagram among Fig. 3 embodiment;

Before Fig. 4 compensates and compensation back G (s) phase-frequency characteristic;

Fig. 5 adopts system electrical damping after the inventive method;

Moment of torsion on former each shaft part of test macro generator of Fig. 6;

Fig. 7 adopts the moment of torsion on each shaft part of generator after the inventive method.

Embodiment

Describe embodiment of the present invention in detail below in conjunction with accompanying drawing and embodiment, but the present invention is not limit by said specific embodiment.

The test macro that adopts is based on the IEEE SSR first standard testing system, and is as shown in Figure 3.Partial fixing series compensation capacitance in the original system is replaced with controlled series compensation, and circuit is always gone here and there the benefit degree and is got 45%, wherein the reactance X of TCSC _TCSCAccount for total string and mend 20% of reactance, its reactance per unit value is seen Fig. 3.TCSC adopts the control of open loop constant-impedance, gets the main circuit characteristic parameter of TCSC

The benchmark trigger angle α of TCSC ₀It is 158.8 °.Selecting the operational mode of generator is P _G=0.9pu, power factor is 0.9 (hysteresis).The axle system of generator is made up of high pressure cylinder (HP), intermediate pressure cylinder (IP), low pressure (LP) cylinder A (LPA), low pressure (LP) cylinder B (LPB) and generator (GEN) and six lumped mass pieces of exciter (EXC).Generally speaking, there be n-1 torsional mode in the axle system that has a n mass.There are six masses in axle system in this example, so to 5 torsional modes should be arranged, be respectively: 15.7,20.2,25.6,32.3 and 47.5Hz.Because the modal damping of torsional mode 5 (47.5Hz) is very big, generally can not interact by generator net torsional oscillation, when phase compensation, will not consider the influence of pattern 5.

At first at TCSC benchmark trigger angle α ₀On apply a string 10Hz of comprising～55Hz, frequency interval is the swept-frequency signal of the subsynchronous frequency of 0.2Hz.After applying swept-frequency signal, until electric power system gets into stable state, the generator electromagnetic torque T on common period of intercepting once more _eWith the TCSC trigger angle α that applies after the swept-frequency signal _m, to the T that obtains _eAnd α _mCarry out Fourier and decompose, try to achieve TCSC trigger angle increment Delta α then _mTo generator electromagnetic torque increment Delta T _eBetween the phase characteristic of transfer function G (s), as shown in Figure 4.

The design band pass filter that subsynchronous oscillation damping controller adopted, its band connection frequency is 10Hz～55Hz.Adopt 4 rank butterworth filters, its transfer function can be expressed as:

$H\left(s\right)=\frac{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^4}{s^4+2.613{\mathrm{\&omega;}}_{c1}{s}^3+3.414{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^2{s}^2+{2.613\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{3}s+{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000057838400012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^4}$

$\&CenterDot;\frac{s^4}{s^4+2.613{\mathrm{\&omega;}}_{c2}{s}^3+3.414{\mathrm{\&omega;}}_{c2}^2{s}^2+2.613{\mathrm{\&omega;}}_{c2}^{3}s+{\mathrm{\&omega;}}_{c2}^4}---\left(4\right)$

Need to confirm the lagging phase angle φ of compensation then, make that generator speed increment Delta ω is to generator electromagnetic torque increment Delta T in the subsynchronous frequency range of whole 10Hz～55Hz _eBetween phase characteristic within ± 90 °, s is a Laplacian in the formula (4).

Utilize again shape as

The lead-lag link compensate the phase lag of G (s), make generator speed increment Delta ω to generator electromagnetic torque increment Delta T _eBetween phase characteristic within ± 90 °.Adopt following formula to confirm the time constant of compensation tache.

$a=\frac{1-\sin \mathrm{\&phi;}}{1+\sin \mathrm{\&phi;}}$

$T_a=1/\left(2\mathrm{\&pi;}{f}_x\sqrt{a}\right)---\left(5\right)$

T _b＝aT _a

In the formula, f _xFor carrying out the Frequency point of phase compensation, φ is f _xThe pairing lagging phase angle that needs compensation, T _aAnd T _bTime constant for compensation tache; S is a Laplacian.After considering the phase lag characteristic of band pass filter, each compensates-50 ° at the 15Hz place with 4 delay components, respectively compensates 40 ° at 60Hz with 3 differentiation elements.The time constant of each compensation tache is listed in table 1.

The time constant of table 1 phase compensation link

f x	15Hz	60Hz
			φ	-50°	40°
T a	3.862e-3	5.688e-3
			T b	2.915e-2	1.237e-3
n	4	3

System phase hysteresis characteristic after the compensation is shown in C among Fig. 4 (s) G (s) curve.

After having confirmed the parameter of TCSC additional controller, gather the speed discrepancy signal delta ω of generator in this test macro, utilize band pass filter that speed discrepancy signal delta ω is carried out Filtering Processing, amplify again with phase compensation after, obtain additional control signal.After additional control signal and the stack of TCSC benchmark trigger angle, TCSC is triggered control, for electric power system provides positive electrical damping with the inhibition sub-synchronous oscillation.

When carrying out effect assessment; The electrical damping of time domain frequency sweep method measuring system capable of using; The validity of checking the inventive method, when the electrical damping of gained at each torsion frequency place of generator all be on the occasion of the time, explain that then the inventive method can suppress electric power system generation sub-synchronous oscillation.

The concrete steps of measuring system electrical damping comprise:

(1) acceptable operating point to confirming after the system that treats gets into steady operation, applies the little value pulsating torque that a string frequency becomes integral multiple on the rotor of generator:

In the formula, λ is a constant and less than 1, T _λ,

Be respectively that frequency is λ ω ₀The amplitude and the initial phase of pulsating torque.Require T _λLess, so that Δ T _mValue be unlikely to destroy the assumed condition of system's available linearization.

(2) apply pulsating torque after, until system gets into stable state, the generator electromagnetic torque T on common period of intercepting once more _eWith the generator angular frequency.

(3) with generator electromagnetic torque T _eCarry out Fourier with the generator angular frequency and decompose, draw the Δ T under the different frequency _eWith Δ ω.

(4) basis Obtain electrical damping moment coefficient D _e

Electrical damping moment coefficient D when gained _e(being electrical damping) at each torsion frequency place all be on the occasion of the time, The controller can suppress system's generation sub-synchronous oscillation.This routine result of calculation is as shown in Figure 5, can find, after adopting the inventive method, TCSC can provide positive electrical damping in whole subsynchronous frequency band, fundamentally eliminated the danger of SSR.

For further checking the inventive method is to suppressing the validity of SSR, the use detailed model carries out the transient state time-domain-simulation.Fig. 3 system adds three-phase earth fault at the F point during t=15s after getting into stable state, and excision after 0.05 second.Fig. 6,7 are respectively former test macro and adopt the moment of torsion on each shaft part of generator after the inventive method.It is thus clear that when not using the inventive method, the moment of torsion on each shaft part of generating set is dispersed, system SSR is unstable.And after use the inventive method, the moment of torsion on each shaft part of generator is decayed gradually, and system is that SSR is stable, and the result among this and Fig. 5 coincide.

Claims (1)

1. method based on the inhibition subsynchronous oscillation of electrical power system of controlled series compensation; It is characterized in that; Handle through generator speed difference signal Δ ω being amplified, generate additional control signal the trigger angle of controlled series compensation is modulated with phase shift, thus the equivalent reactance X of change controlled series compensation _Eff, the electrical damping of raising system, the additional control signal of described generation comprises the steps:

(1) gathers the speed discrepancy signal delta ω of generators in power systems, actual speed that described speed discrepancy signal is a generator and rated speed poor;

(2) speed discrepancy signal delta ω being carried out Filtering Processing, is band pass filter filters low signal and the high order harmonic component of 10～55Hz by passband, obtains the generator torsion frequency signal in the subsynchronous frequency range; The transfer function of the band pass filter that is adopted is expressed as:

$H\left(s\right)=\frac{{\mathrm{\&omega;}}_{c1}^4}{s^4+2.613{\mathrm{\&omega;}}_{c1}{s}^3+3.414{\mathrm{\&omega;}}_{c1}^2{s}^2+2.613{\mathrm{\&omega;}}_{c1}^{3}s+{\mathrm{\&omega;}}_{c1}^4}$

$\&CenterDot;\frac{s^4}{s^4+2.613{\mathrm{\&omega;}}_{c2}{s}^3+3.414{\mathrm{\&omega;}}_{c2}^2{s}^2+2.613{\mathrm{\&omega;}}_{c2}^{3}s+{\mathrm{\&omega;}}_{c2}^4}$

In the formula, filter cutoff frequency is taken as ω _C1=55Hz, ω _C2=10Hz, s are Laplacian;

(3) signal that filtering is obtained amplify with phase compensation after, obtain additional control signal Δ α;

Wherein the signal that filtering obtains is carried out phase compensation, the transfer function of lead-lag link is

through a plurality of lead-lag links wherein:

T _a, T _bBe the time constant of lead-lag link,

n＝T _b/T _a＝(1-sinφ)/(1+sinφ)；

$T_a=1/\left({\mathrm{\&omega;}}_x\sqrt{n}\right);$

T _b＝nT _a；

ω _xFrequency for the needs compensation;

φ is ω _xThe pairing lagging phase angle that needs compensation;

Wherein utilize the time domain frequency sweep method to try to achieve the additional control signal Δ α of controlled series compensation to generator additional electromagnetic torque Δ T _eBetween the phase characteristic of transfer function, making generator speed increment Delta ω to generator electromagnetic torque increment Delta T _eBetween phase characteristic under the principle within ± 90 °, confirm to need the lagging phase angle φ of compensation.

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