CN103728506B - The method that HVDC system converter power transformer core sataration type harmonic instability judges - Google Patents

Abstract

The invention discloses a kind of method that HVDC system converter power transformer core sataration type harmonic instability judges, its step: S1, according to the known power-frequency voltage of change of current bus, the DC component of DC current and triggering command angle, set up voltage x current switch function, obtain the power frequency order components amplitude of the switch function of voltage x current；S2, obtain AC system secondary equivalent harmonic wave impedance Z according to alternating current-direct current equivalent circuit_ac2With equivalent harmonic wave impedance Z of straight-flow system_dc1；S3, saturated stable factor λ of calculating harmonic wave converter power transformer saturation type harmonic instability；S4, when λ is more than 1, disturbance will increase over time, and system occurs unstable；When λ is less than 1, disturbance will decay over time, and system finally tends towards stability.The inventive method theoretical foundation clear thinking, calculation expression is simple, and parameter is easy to get, and the degree that can occur with qualitative assessment converter power transformer saturation type harmonic instability.

Description

The method that HVDC system converter power transformer core sataration type harmonic instability judges

Technical field

The present invention relates to technical field of electric system protection, be specifically related to a kind of HVDC system converter power transformer core sataration The method that type harmonic instability judges.

Background technology

In current HVDC (HVDC) engineering, the harmonic interactions between ac and dc systems may be specific at some Under the conditions of occur the disturbance near harmonic instability, i.e. current conversion station to cause harmonic wave to be difficult to due to resonance to decay showing of even amplifying As.Harmonic instability will result in the Severe distortion of change of current busbar voltage, and then straight-flow system operation difficulty may be caused even to close Lock, brings the stable operation of ac and dc systems and has a strong impact on.The mechanism of direct current transportation harmonic instability is sufficiently complex, causes humorous Ripple unstable factor is not unique, and harmonic instability as produced by phase firing control is in harmonic instability type A kind of.The harmonic instability that can cause equally as saturated in converter power transformer, the most so-called core sataration type harmonic instability, and should Even if the harmonic instability of type uses triggering pulse control mode at equal intervals to occur so that it becomes current direct current the most in the same old way One of focus of transmission of electricity harmonic instability research.

In HVDC (HVDC) system converter power transformer core sataration type harmonic instability decision technology field, there is document 《HVDC converter transformer core saturation instability:a frequency domain Analysis " (" the saturated unstability of high voltage direct current converter transformer core: frequency-domain analysis ", author: S.Chen, A.R.Wood, J.Arrillaga, source: IEE Proceedings, 1996) and " Prediction of core saturation Instability at an HVDC converter " (" core sataration unstability prediction in high voltage direct current converter ", author: BURTON R S, FUCHSHUBER C, WOODFORD D A, et al, source: IEEE Trans on Power Delivery, 1996) propose, utilize inverter both sides harmonic relationships matrix and converter power transformer saturated characteristic can respectively obtain change of current transformation The saturated stable factor criterion of device saturation type harmonic instability and impedance conditions, but characterize the square of inverter both sides harmonic relationships Battle array parameter dyscalculia, it is generally required to asked for by simulation method, and the matrix parameter utilizing simulation method to obtain is unfavorable for from theory On the influence factor of harmonic instability is analyzed；" converter power transformer core sataration based on modulation theory is not to also have document Stability analysis " (author: Yang little Bing, Li Xingyuan, gold Xiao Ming etc., source: " electric power network technique " 2009) introduce harmonic wave modulation theory Unstable analysis, it is proposed that based on DC current harmonic wave phase angleHarmonic instability decision method, although this method without Ask for relational matrix, but harmonic wave phase angleTheoretical Calculation the most sufficiently complex, equally can only by emulation method obtain.

Different from above-mentioned prior art thinking, the inventive method is based on following thinking: first to inverter both sides with And converter transformer DC magnetic bias saturated under harmonic wave Transfer characteristic be analyzed, disclose converter power transformer saturation type harmonic wave not The stable closed loop positive feedback mechanism formed, obtain the most on this basis converter power transformer saturation type harmonic instability saturated surely Determining cause, thus proposes what a kind of converter power transformer saturation type harmonic instability based on disturbing signal closed loop transmission gain judged Method.The principle of the method be described further below:

According to modulation theory, the DC voltage of inverter is considered as the inverter modulation to alternating voltage, inverter Ac-side current be considered as the inverter modulation to DC current.Fig. 2 show the structural representation of HVDC commutator.? Under normal circumstances, each converter valve is sequentially turned on by numbering in figure, then the relation of its alternating current-direct current both sides voltage and current is represented by:

u_dr=u_ars_ua+u_brs_ub+u_crs_uc

$\left\{\begin{array}{c}{i}_{ar}=i_{dr}{s}_{ia}\\ i_{br}=i_{dr}{s}_{ib}\\ i_{cr}=i_{dr}{s}_{ic}\end{array}\right.---\left(1\right)$

In formula, subscript " r " represents commutator, s_ua、s_ubAnd s_ucIt is respectively abc three-phase voltage switch function；s_ia、s_ibAnd s_ic It is respectively three-phase current switch function.

Theoretical and the phasor product natures according to Dynamic Phasors, can obtain (because DC voltage is not affected by AC zero sequence voltage, Therefore analysis below does not the most consider zero-sequence component):

${\stackrel{\·}{U}}_{d\left(m\right)}=\underset{n}{\Σ}{\stackrel{\·}{S}}_{u(m-n)}{T}_1{\stackrel{\·}{U}}_{\left(n\right)}^{(\±)}=\underset{n}{\Σ}({\stackrel{\·}{S}}_{u(m-n)}^{+}{\stackrel{\·}{U}}_{\left(n\right)}^{+}+{\stackrel{\·}{S}}_{u(m-n)}^{-}{\stackrel{\·}{U}}_{\left(n\right)}^{-})---\left(2\right)$

${\stackrel{\·}{I}}_{\left(n\right)}^{(\±)}=T_2\underset{m}{\Σ}{\stackrel{\·}{S}}_{i(n-m)}{\stackrel{\·}{I}}_{d\left(m\right)}=\underset{m}{\Σ}{\stackrel{\·}{S}}_{i(n-m)}^{(\±)}{\stackrel{\·}{I}}_{d\left(m\right)}---\left(3\right)$

In formula:M-n the phasor for three-phase voltage switch function；For Positive and negative sequence component；N-m the phasor for three-phase current switch function；ForPositive and negative sequence component；WithFor DC voltage and m phasor of electric current；N for inverter commutation voltage Secondary positive and negative sequence component；N positive and negative sequence component of AC system electric current is injected for inverter；M=0,1,2,3 ...；N=1, 2,3…； $a=e^{j2\mathrm{\π}/3};T_1=\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right];T_2=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\end{array}\right].$

DC current inflow transformer winding can make transformator generation D.C. magnetic biasing effect, cause transformer core saturated and Each low-order harmonic composition that converter power transformer is injected to AC system dramatically increases.Core sataration degree is the highest, and direct current is inclined Exciting current distortion under magnetic is the most serious, and harmonic content is the biggest.Positive sequence second harmonic current and the unidirectional current of injection valve side winding Relation between stream is substantially linear.Experience conversion formula can be used to describe, the unidirectional current that valve side winding is injected by this formula Stream and line side positive sequence second harmonic current connect:

In formula,It it is the positive sequence second harmonic only considering to flow into when transformer core is saturated converter power transformer AC winding Electric current；I_a0、I_b0And I_c0It is to inject valve winding in converter transformer three-phase dc electric current, to flow into converter transformer valve-side respectively Winding is positive direction；N is positive sequence second harmonic current and the ratio system of transformator valve side winding injection direct current of transformator generation Number, the factor such as this coefficient and the architectural characteristic of transformator, AC excitation situation is relevant；e^i180°Characterize the conversion positive sequence to line side Phase angle difference π is there is between second harmonic current and DC current；1/3[1 e^i(-120°) e^i120°] it is that three-phase dc electric current is changed Transformation matrix for positive sequence second harmonic.

In the case of converter power transformer core sataration, harmonic wave is at alternating current-direct current both sides and the transmittance process of converter power transformer both sides As shown in Figure 3.

According to Fig. 3, the harmonic propagation relation in the case of converter power transformer core sataration can be briefly described as follows: if changed There is second harmonic voltage disturbance in stream device AC, this disturbance voltage, through inverter on-off action, can cause work at DC side Frequently voltage, thus produce industrial frequency harmonic electric current at DC side；The power current of direct current will produce at AC after inverter is modulated Raw positive sequence second harmonic current component and negative phase-sequence direct-current component；And DC current flows through converter power transformer and makes transformer core Saturated, produce substantial amounts of individual harmonic current, including positive sequence second harmonic current；If above-mentioned second harmonic current acts on jointly In positive sequence second harmonic voltage magnitude produced by AC second harmonic impedance more than original Secondary Disturbance harmonic voltage, then This closed loop positive feedback will cause harmonic instability to occur.

The equivalent circuit of ac and dc systems is as shown in Figure 4.In figure:For AC system equivalence power supply；Z_sFor system impedance； Z_lbFor wave filter and the equivalent impedance of reactive power compensator；H is transformer voltage ratio；Z_dcmRepresent from inverter in terms of straight-flow system M equivalent harmonic impedance of the straight-flow system entered, including DC filter, smoothing reactor, DC line and offside inverter M subharmonic impedance；Z_acnRepresent from inverter to n equivalence harmonic impedance of the AC system entered in terms of AC system, its expression formula For:

Z_acn=Z_sn||Z_lbn+Z_Tn (5)

Assume that the change of current becomes AC and contains secondary positive sequence harmonic voltage disturbance:

${\stackrel{\·}{U}}_{ac2}^{+}=U_{ac2}\∠\mathrm{\θ}---\left(6\right)$

In formula, U_ac2With amplitude and the phase angle that θ is respectively this disturbance.

According to formula (2), the power-frequency voltage component of DC side be (equally using the phase place of change of current bus power frequency positive sequence voltage as Fixed phase):

In formulaRepresentConjugation.

The power frequency impedance of note DC side is Z_dc1, then have:

Now according to formula (3), it is known thatThe change of current become AC produce harmonic current into:

In formula:ForThe positive sequence second harmonic current of inverter AC, I after inverter is modulated_a0、I_b0And I_c0ForAt the generation three-phase negative/positive DC current of inverter AC after inverter is modulated.

According to formula (4), I_a0、I_b0And I_c0The change of current become AC produce second harmonic current into:

Then the change of current is become to the secondary positive sequence harmonic voltage disturbance of ACHanding over through inverter and converter power transformer Stream and direct current both sides transmission conversion after, its change of current become AC produce second harmonic current into:

In formulaRepresent the second harmonic current being converted to net side by the second harmonic current of converter transformer valve side, i.e.

Now, the second harmonic voltage that this electric current produces in AC system impedance is:

Therefore, harmonic voltageAfter the converter power transformer under inverter and saturated conditions is in the change of disease of alternating current-direct current both sides, its Amplitude gain λ is:

Note λ is the saturated stable factor of converter power transformer saturation type harmonic instability.Then from formula (13), when λ is more than 1 Time, disturbance will increase over time, and instability occurs in system；When λ is less than 1, disturbance will decay over time, and system is Tend towards stability eventually.

From above-mentioned principles illustrated, the method theoretical foundation clear thinking, calculation expression is simple, and parameter is easy to get, and The degree that can occur with qualitative assessment converter power transformer saturation type harmonic instability, it is possible to more efficient is applied to high straightening The risk assessment of stream transmission system harmonic instability and suppression field.

Summary of the invention

The invention aims to solve the defect of above-mentioned prior art, it is provided that a kind of HVDC system converter power transformer ferrum The method that core saturation type harmonic instability judges, the method theoretical foundation clear thinking, calculation expression is simple, and parameter is easy to get, And the degree that can occur with qualitative assessment converter power transformer saturation type harmonic instability, for the risk that HVDC system harmonics is unstable Assessment and braking measure etc. provide theoretical foundation.

In order to achieve the above object, the technical solution used in the present invention is, a kind of HVDC system converter power transformer iron core is satisfied The method judged with type harmonic instability, comprises the following steps:

S1, power-frequency voltage according to known change of current busWithDC component I of DC current_dc0With And triggering command angle α₀, set up voltage x current switch function, obtain power frequency order components amplitude S of the switch function of voltage x current_u1 And S_i1；

S2, obtain AC system secondary equivalent harmonic wave impedance Z according to alternating current-direct current equivalent circuit_ac2Inferior with straight-flow system one Value harmonic impedance Z_dc1；

S3, saturated stable factor λ of calculating harmonic wave converter power transformer saturation type harmonic instability, calculation expression is as follows:

In formula (14), Z_ac2And Z_dc1It is respectively AC system secondary equivalent harmonic wave impedance and equivalent harmonic wave of straight-flow system Impedance；S_u1And S_i1It is respectively voltage switch function power frequency negative sequence component and current switch function power frequency positive-sequence component；H is the change of current The no-load voltage ratio of transformator, i.e. original edge voltage and the ratio of secondary voltage；N is positive sequence second harmonic current and the transformation of transformator generation Device valve side winding injects the ratio coefficient of direct current；For power-factor angle；

S4, when λ is more than 1, disturbance will increase over time, and system occurs unstable；When λ is less than 1, disturbance will be with The time and decay, system finally tends towards stability.The schematic flow sheet of the inventive method is as shown in Figure 1.

More specifically, S in step S1_u1And S_i1Calculation procedure as follows:

S11, power-frequency voltage according to known change of current busWithDC component I of DC current_dc0 And triggering command angle α₀, calculate the skew of synchronizing voltage phase place；

IfWithRepresent α component and the β component of commutation voltage respectively, calculated by following formula:

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{\mathrm{\α}}\\ {\stackrel{\·}{U}}_{\mathrm{\β}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{ca1}\\ {\stackrel{\·}{U}}_{ab1}\\ {\stackrel{\·}{U}}_{bc1}\end{array}\right]---\left(15\right)$

Utilize the α component of commutation voltageβ component with commutation voltageCalculated by following formula The phase place of DC control system synchronizing voltage

In formula (16), U_αAnd U_βIt is respectively α component and the amplitude of β component of commutation voltage；WithIt is respectively commutation electricity The α component of pressure and the phase angle of β component；

If subscript m n=ab, bc, ca in formula, wherein a, b, c represent the phase in three-phase respectively；

According toPhase placePhase placePhase placeThe phase place calculating synchronizing voltage respectively is inclined Move

In formula (17),For the phase offset of ca phase Yu synchronizing voltage,Inclined with the phase place of synchronizing voltage for ab phase Move,Phase offset for bc phase Yu synchronizing voltage；

S12, calculating converter valve turn on delay angle θ_mn, actual Trigger Angle α_mnWith actual angle of overlap μ_mn；

Turn on delay angle θ_mnComputing formula be:

Actual Trigger Angle α_mnComputing formula be:

In formula (18) and (19), all angles are with delayed for just, and advanced is negative；

If μ_mnAngle of overlap during commutation biphase for mn, the computing formula of angle of overlap is:

${\mathrm{\μ}}_{mn}={\cos }^{-1}({\mathrm{cos\α}}_{mn}-2X_r{I}_{dc0}/{\stackrel{\·}{U}}_{mn1})-{\mathrm{\α}}_{mn}---\left(20\right)$

In formula (20)For the commutation voltage of concrete mn phase, X_rFor commutating impedance, by converter power transformer parameter according to

FormulaTry to achieve, wherein z^*For transformator leakage reactance perunit value, U is primary voltage of transformer, and S is that transformator holds Amount；

S13, according to θ_mn、α_mnAnd μ_mnMake three-phase voltage current switching waveform, utilized by this three-phase voltage current waveform Fourier space derives each order component of voltage x current switch function:

$\left\{\begin{array}{c}{\stackrel{\·}{S}}_{uak}=\frac{1}{T}{\∫}_0^T{s}_{ua}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{ubk}=\frac{1}{T}{\∫}_0^T{s}_{ub}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{uck}=\frac{1}{T}{\∫}_0^T{s}_{uc}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\end{array}\right.---\left(21\right)$

$\left\{\begin{array}{c}{\stackrel{\·}{S}}_{iak}=\frac{1}{T}{\∫}_0^T{s}_{ia}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{ibk}=\frac{1}{T}{\∫}_0^T{s}_{ib}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{ick}=\frac{1}{T}{\∫}_0^T{s}_{ic}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\end{array}\right.---\left(22\right)$

Taking k=1, the power frequency order components then obtaining voltage x current switch function after symmetry transformation is as follows:

${\stackrel{\·}{S}}_{u1}^{\±}=\[\begin{array}{ccc}{\stackrel{\·}{S}}_{ua1}& {\stackrel{\·}{S}}_{ub1}& {\stackrel{\·}{S}}_{uc1}\end{array}\]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]---\left(23\right)$

${\stackrel{\·}{S}}_{i1}^{\±}=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{S}}_{ia1}\\ {\stackrel{\·}{S}}_{ib1}\\ {\stackrel{\·}{S}}_{ic1}\end{array}\right]---\left(24\right)$

Wherein,It is respectively the voltage switch function power frequency component of a, b, c three-phase, It is respectively the current switch function power frequency component of a, b, c three-phase, a=e^j2π/3。

S14, try to achieve voltage x current switch function power frequency order components amplitude S of each 6 pulse conversion device_u1、S_i1。

More specifically, AC system secondary equivalent harmonic wave impedance Z in step S2_ac2With equivalent harmonic wave resistance of straight-flow system Anti-Z_dc1Computational methods are as follows:

The equivalent circuit of ac and dc systems as shown in Figure 4, wherein:For AC system equivalence power supply；Z_sFor system impedance； Z_lbFor wave filter and the equivalent impedance of reactive power compensator；H is the ratio of transformer voltage ratio, i.e. original edge voltage and secondary voltage； Z_dcmRepresent from inverter to m equivalent harmonic impedance of the straight-flow system entered in terms of straight-flow system, electric including DC filter, flat ripple The m subharmonic impedance of anti-device, DC line and offside inverter；Z_acnRepresent from inverter to the exchange entered in terms of AC system N equivalent harmonic impedance of system, its expression formula is:

Z_acn=Z_sn||Z_lbn+Z_Tn。

More specifically, power-factor angle in step S3Can be byTrying to achieve, wherein α is triggering command angle；μ is commutation Angle, can be according to the formula seeking angle of overlapTry to achieve, whereinFor commutation voltage, X_rFor commutation Impedance, by converter power transformer parameter according to formulaTry to achieve, wherein z^*For transformator leakage reactance perunit value, U is transformer primary Polygonal voltage, S is transformer capacity.

More specifically, in step S3, N is positive sequence second harmonic current and the injection of transformator valve side winding of transformator generation The ratio coefficient of direct current, this coefficient is relevant with factors such as the architectural characteristic of transformator, AC excitation situations；Its calculation procedure:

S31, converter transformer valve-side is inputted 10 groups of DC current I_a0、I_b0And I_c0(in view of transformator overcurrent because of Element, input current is not preferably greater than 100A), record the positive sequence second harmonic current of corresponding converter power transformer net sideWherein,It is Only consider to flow into when transformer core is saturated the positive sequence second harmonic current of converter power transformer AC winding, I_a0、I_b0And I_c0Point It not to inject valve winding in converter transformer three-phase dc electric current, to flow into valve winding in converter transformer as positive direction；

S32, according to formula:

Try to achieve 10 M values of correspondence；

S33, fitting coefficient N are the arithmetic mean of instantaneous value of 10 M values.

The present invention has a following beneficial effect relative to prior art:

The inventive method theoretical foundation clear thinking, calculation expression is simple, and parameter is easy to get, and can be with the qualitative assessment change of current The degree that transformator saturation type harmonic instability occurs, it is possible to more efficient is applied to HVDC transmission system harmonic wave not Stable risk assessment and suppression field.

Accompanying drawing explanation

Fig. 1 is the flow process signal of the method that HVDC system converter power transformer core sataration type harmonic instability of the present invention judges Figure.

Fig. 2 is the HVDC system equivalent simplified circuit of the present invention.

Fig. 3 is the harmonic propagation graph of a relation during converter power transformer core sataration of the present invention.

Fig. 4 is the equivalent circuit of the ac and dc systems of the present invention.

Fig. 5 is the equivalent circuit of ac and dc systems in the embodiment of the present invention.

Fig. 6 is the DC line current waveform of saturated stable factor λ=3.5 correspondence in the embodiment of the present invention 1.

Fig. 7 (a) is transformator a phase exciting current during λ=3.5 in the embodiment of the present invention 1.

Fig. 7 (b) is transformator b phase exciting current during λ=3.5 in the embodiment of the present invention 1.

Fig. 7 (c) is transformator c phase exciting current during λ=3.5 in the embodiment of the present invention 1.

Fig. 8 is the DC line current waveform of saturated stable factor λ=1.23 correspondence in the embodiment of the present invention 2.

Fig. 9 is the DC line current waveform of saturated stable factor λ=0.86 correspondence in the embodiment of the present invention 3.

Figure 10 (a) is transformator a phase exciting current during λ=0.86 in the embodiment of the present invention 3.

Figure 10 (b) is transformator b phase exciting current during λ=0.86 in the embodiment of the present invention 3.

Figure 10 (c) is transformator c phase exciting current during λ=0.86 in the embodiment of the present invention 3.

Detailed description of the invention

Further illustrate the present invention below in conjunction with the accompanying drawings with embodiment, but the scope of protection of present invention is not limited to reality Execute the scope of example statement.Those skilled in the art is made in the case of without departing substantially from the spirit and scope of the present invention Other changes and modifications, are included in the range of claims protection.

In HVDC (HVDC) system, the equivalent circuit of ac and dc systems as shown in Figure 4, is built based on PSCAD/EMTDC The emulation test system of vertical core sataration type harmonic instability, as shown in Figure 5.In this test system: 12 pulsation commutators use Determine trigger angle control, Trigger Angle α₀It it is 18 °；Owing to only analyzing the core sataration type harmonic instability that rectification side occurs, inverter side Use a current source equivalence；DC line rated current I_dc0For 1kA, alternating-current voltage source virtual value 100kV；Converter power transformer is joined Number is shown in Table 1.

Table 1 converter power transformer parameter

Parameter according to table 1 converter power transformer sets up test model, and valve winding in converter transformer inputs 10 groups of differences Three-phase dc electric current I_a0、I_b0And I_c0, record the positive sequence second harmonic current of 10 converter power transformer net sidesAccording to formula (25) 10 M values of correspondence are tried to achieve, as shown in table 2.

When three-phase dc electric current is injected in table 2 valve side, the amplitude of line side positive sequence second harmonic and phase angle and corresponding M value table

Then final fitting coefficient N=0.71 is tried to achieve by the arithmetic mean of instantaneous value of 10 M values.

Embodiment 1～embodiment 3 parameter are arranged as shown in table 3.

Table 3 embodiment parameter is arranged

Parameter	R1/Ω	C1/μF	R2/Ω	L2/mH	C2/μF	L3/mH	C3/μF	Trigger Angle (α0)	λ	Zac2	Zdc1
												Embodiment 1	100	1000	993.72	0.005	509.8	0.70	15.70	18°	3.50	446.86	17.2 1
Embodiment 2	100	1000	993.72	0.005	509.8	0.6	11.3	18°	1.23	446.86	100. 00
												Embodiment 3	80	500	393.72	0.005	509.8	0.6	11.3	18°	0.86	309.93	100. 00

Embodiment 1:

The present embodiment, a kind of method that HVDC system converter power transformer core sataration type harmonic instability judges, described height In straightening stream (HVDC) system, the equivalent circuit of ac and dc systems as shown in Figure 4, the emulation test system of foundation as it is shown in figure 5, Each parameter value is as it has been described above, step is as follows:

S1-1, power-frequency voltage according to known change of current bus WithDC component I of DC current_dc0And triggering command angle α₀, set up voltage x current switch letter Number, obtains power frequency order components amplitude S of the switch function of voltage x current_u1And S_i1, it is specifically divided into following four step:

S11-1, power-frequency voltage according to known change of current busWithThe DC component of DC current I_dc0And triggering command angle α₀, calculate the skew of synchronizing voltage phase place.Synchronizing voltage is calculated according to formula (15)～(17) Phase offsetIt is 0；

S12-1, calculating converter valve turn on delay angle θ_mn, actual Trigger Angle α_mnWith actual angle of overlap μ_mn.Count in conjunction with S11 Calculate result, try to achieve θ according to formula (18)～(20)_mn=0, α_mn=18 °, μ_mn=19.1285 °；

S13-1, according to θ_mn、α_mnAnd μ_mnMake three-phase voltage current switching waveform, in conjunction with formula (21)～(22), take k= 1, try to achieve

Then the power frequency order components obtaining voltage x current switch function after symmetry transformation is as follows:

S14-1, try to achieve voltage x current switch function power frequency order components amplitude S of each 6 pulse conversion device_u1=1.6479, S_i1=0.5493；

S2-1, the parameter provided according to Fig. 5 alternating current-direct current equivalent circuit and table 3 obtain the resistance of AC system secondary equivalent harmonic wave Anti-Z_ac2=446.86 and equivalent harmonic wave impedance Z of straight-flow system_dc1=17.21, as shown in table 3；

S3-1, saturated stable factor λ of calculating harmonic wave converter power transformer saturation type harmonic instability, calculation expression is such as Under:

Power-factor angleCan be byTrying to achieve, wherein α is 18 ° of triggering command angle；μ is angle of overlap, in S12-1 Through obtaining μ=19.1285 °；Can obtain according to table 1Fitting coefficient N=0.71；Result of calculation λ is 3.5；

S4-1, now λ are more than 1, and disturbance will increase over time, it is determined that instability occurs in system；It is corresponding straight Flow Line current waveform as shown in Figure 6, after knowing disturbance disappearance, do not restrain, changing when Fig. 7 then gives λ=3.5 by direct current harmonic wave Convertor transformer three-phase excitation current waveform, after disturbance disappears as seen from the figure, transformator is still in saturation.

Embodiment 2:

The present embodiment calculation procedure, with embodiment 1, finally tries to achieve λ=1.23 in conjunction with table 3 parameter, more than 1, it is determined that system goes out Existing instability；Its corresponding DC line current waveform is as shown in Figure 8, it is known that after disturbance disappears, direct current harmonic wave is not restrained, Transformator is still in saturation.

Embodiment 3:

The present embodiment calculation procedure, with embodiment 1, finally tries to achieve λ=0.86 in conjunction with table 3 parameter, less than 1, it is determined that disturbance will Decaying over time, system finally tends towards stability；Its corresponding DC line current waveform is as it is shown in figure 9, Figure 10 is given Converter power transformer three-phase excitation current waveform during λ=0.86, as seen from the figure along with the decay of harmonic wave, transformer magnetizing current Gradually decreasing the most therewith, final transformator is changed to undersaturated condition from saturation.

Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not by above-described embodiment Limit, the change made under other any spirit without departing from the present invention and principle, modify, substitute, combine, simplify, All should be the substitute mode of equivalence, within being included in protection scope of the present invention.

Claims (4)

1. The method that 1.HVDC system converter power transformer core sataration type harmonic instability judges, it is characterised in that include following step Rapid:

   S1, power-frequency voltage according to known change of current busWithDC component I of DC current_dc0And touch Send instructions angle α₀, set up voltage x current switch function, obtain voltage switch function power frequency negative sequence component S respectively_u1And current switch Function power frequency positive-sequence component S_i1；

   S2, obtain AC system secondary equivalent harmonic wave impedance Z according to alternating current-direct current equivalent circuit_ac2The most equivalent with straight-flow system humorous Natural impedance Z_dc1；

   S3, saturated stable factor λ of calculating harmonic wave converter power transformer saturation type harmonic instability, calculation expression is as follows:Wherein, Z_ac2And Z_dc1It is respectively AC system secondary equivalent harmonic wave impedance and straight-flow system Equivalent harmonic wave impedance；S_u1And S_i1It is respectively voltage switch function power frequency negative sequence component and current switch function power frequency positive sequence Component；H is the ratio of the no-load voltage ratio of converter power transformer, i.e. original edge voltage and secondary voltage；N is that the positive sequence secondary that transformator produces is humorous Ripple electric current and transformator valve side winding inject the ratio coefficient of direct current；For power-factor angle；

   S4, when λ is more than 1, disturbance will increase over time, and system occurs unstable；When λ less than 1 time, disturbance will along with time Between and decay, system finally tends towards stability.
2. The method that HVDC system converter power transformer core sataration type harmonic instability the most according to claim 1 judges, its It is characterised by, S in step S1_u1And S_i1Calculation procedure as follows:

   S11, power-frequency voltage according to known change of current busWithDC component I of DC current_dc0And touch Send instructions angle α₀, calculate the skew of synchronizing voltage phase place；

   IfWithRepresent α component and the β component of commutation voltage respectively, calculated by following formula:

   $\left[\begin{array}{c}{\stackrel{\·}{U}}_{\mathrm{\α}}\\ {\stackrel{\·}{U}}_{\mathrm{\β}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{ca1}\\ {\stackrel{\·}{U}}_{ab1}\\ {\stackrel{\·}{U}}_{bc1}\end{array}\right]$

   Utilize the α component of commutation voltageβ component with commutation voltageDirect current control is calculated by following formula The phase place of system synchronization voltage processed

   In formula, U_αAnd U_βIt is respectively α component and the amplitude of β component of commutation voltage；WithIt is respectively the α component of commutation voltage Phase angle with β component；

   If subscript m n=ab, bc, ca in formula, wherein a, b, c represent the phase in three-phase respectively；

   According toPhase placePhase placePhase placeCalculate the phase offset of synchronizing voltage respectively

   In formula,For the phase offset of ca phase Yu synchronizing voltage,For the phase offset of ab phase Yu synchronizing voltage,For Bc phase and the phase offset of synchronizing voltage；

   S12, calculating converter valve turn on delay angle θ_mn, actual Trigger Angle α_mnWith actual angle of overlap μ_mn；

   Turn on delay angle θ_mnComputing formula be:

   Actual Trigger Angle α_mnComputing formula be:

   In formula, all angles are with delayed for just, and advanced is negative；

   If μ_mnAngle of overlap during commutation biphase for mn, the computing formula of angle of overlap is:

   ${\mathrm{\μ}}_{mn}={\cos }^{-1}({\mathrm{cos\α}}_{mn}-2X_r{I}_{dc0}/{\stackrel{\·}{U}}_{mn1})-{\mathrm{\α}}_{mn}$

   In formulaFor the commutation voltage of concrete mn phase, X_rFor commutating impedance, by converter power transformer parameter according to formulaAsk , wherein z^*For transformator leakage reactance perunit value, U is primary voltage of transformer, and S is transformer capacity；

   S13, according to θ_mn、α_mnAnd μ_mnMake three-phase voltage current switching waveform, utilized in Fu by this three-phase voltage current waveform Leaf-size class number derives each order component of voltage x current switch function:

   $\left\{\begin{array}{c}{\stackrel{\·}{S}}_{uak}=\frac{1}{T}{\∫}_0^T{s}_{ua}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{ubk}=\frac{1}{T}{\∫}_0^T{s}_{ub}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{uck}=\frac{1}{T}{\∫}_0^T{s}_{uc}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\end{array}\right.$

   $\left\{\begin{array}{c}{\stackrel{\·}{S}}_{iak}=\frac{1}{T}{\∫}_0^T{s}_{ia}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{ibk}=\frac{1}{T}{\∫}_0^T{s}_{ib}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\\ {\stackrel{\·}{S}}_{ick}=\frac{1}{T}{\∫}_0^T{s}_{ic}{e}^{-jk\mathrm{\ω}\mathrm{\τ}}d\mathrm{\τ}\end{array}\right.$

   Taking k=1, the power frequency order components then obtaining voltage x current switch function after symmetry transformation is as follows:

   ${\stackrel{\·}{S}}_{u1}^{\±}=\left[\begin{array}{ccc}{\stackrel{\·}{S}}_{ua1}& {\stackrel{\·}{S}}_{ub1}& {\stackrel{\·}{S}}_{uc1}\end{array}\right]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]$

   ${\stackrel{\·}{S}}_{i1}^{\±}=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{S}}_{ia1}\\ {\stackrel{\·}{S}}_{ib1}\\ {\stackrel{\·}{S}}_{ic1}\end{array}\right]$

   Wherein, a=e^j2π/3；It is respectively the voltage switch function power frequency component of a, b, c three-phase,It is respectively the current switch function power frequency component of a, b, c three-phase；

   S14, try to achieve voltage x current switch function power frequency order components amplitude S of each 6 pulse conversion device_u1、S_i1。
3. The method that HVDC system converter power transformer core sataration type harmonic instability the most according to claim 1 judges, its It is characterised by, power-factor angle in step S3Can be byTrying to achieve, wherein α is triggering command angle；μ is angle of overlap, can root According to the formula seeking angle of overlapTry to achieve, whereinFor commutation voltage, X_rFor commutating impedance, by Converter power transformer parameter is according to formulaTry to achieve, wherein z^*For transformator leakage reactance perunit value, U is primary voltage of transformer, S For transformer capacity.
4. The method that HVDC system converter power transformer core sataration type harmonic instability the most according to claim 1 judges, its Being characterised by, in step S3, N is positive sequence second harmonic current and the ratio of transformator valve side winding injection direct current of transformator generation Value coefficient, this coefficient is relevant with factors such as the architectural characteristic of transformator, AC excitation situations；Its calculation procedure:

   S31, converter transformer valve-side is inputted 10 groups of DC current I_a0、I_b0And I_c0, just recording corresponding converter power transformer net side Sequence second harmonic currentWherein,It is only to consider just flowing into converter power transformer AC winding when transformer core is saturated Sequence second harmonic current, I_a0、I_b0And I_c0It is to inject valve winding in converter transformer three-phase dc electric current, to flow into the change of current respectively Transformator valve side winding is positive direction；

   S32, according to formula:Try to achieve 10 M values of correspondence；

   S33, fitting coefficient N are the arithmetic mean of instantaneous value of 10 M values.