CN103728506A - Method for judging saturated harmonic instability of HVDC system converter transformer iron core - Google Patents

Abstract

The invention discloses a method for judging the saturated harmonic instability of an HVDC system converter transformer iron core. The method comprises the steps of S1, establishing a voltage current switching function according to power frequency voltage of a known conversion bus, direct current component of direct current and a trigger instruction angle and calculating a power frequency sequence component amplitude value of the voltage current switching function; S2, calculating a secondary equivalent harmonic impedance Zac2 of an alternating current system and a primary equivalent harmonic impedance Zac1 of a direct current system according to a alternating current/direct current equivalent circuit; S3, calculating a saturated harmonic unstable saturation stability factor lambda of a harmonic converter transformer; S4, finding that disturbance increases with the time and the system is unstable when the lambda is larger than 1, and the disturbance decreased with the time and the system finally tends to stability when the lambda is smaller than 1. In the method, the theoretical basis concept is clear, a computation expression is simple, parameters are easy to obtain, and the degree of the saturated harmonic instability of the converter transformer can be quantitatively accessed.

Description

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

Technical field

The present invention relates to protecting electrical power system technical field, be specifically related to a kind of method that HVDC system converter power transformer core sataration type harmonic instability is judged.

Background technology

In current high voltage direct current (HVDC) engineering, may there is harmonic instability in the harmonic interactions between ac and dc systems under some specific condition, i.e. near disturbance current conversion station causes harmonic wave because resonance is difficult for the phenomenon that decay is even amplified.Harmonic instability will cause the serious distortion of change of current busbar voltage, and then may cause the even locking of straight-flow system operation difficulty, and the stable operation of ac and dc systems is brought and had a strong impact on.The mechanism of direct current transportation harmonic instability is very complicated, causes harmonic instability factor not unique, and the harmonic instability producing by phase firing control is a kind of in harmonic instability type.As saturatedly in converter power transformer can cause harmonic instability equally, it is so-called core sataration type harmonic instability, even and the harmonic instability of this type adopts uniformly-spaced trigger pulse control mode also to occur in the same old way, make one of its focus that becomes current direct current transportation harmonic instability research.

In high voltage direct current (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 instability 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 instability 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 transverter both sides harmonic relationships matrix and converter power transformer saturation characteristic can obtain respectively saturated stable factor criterion and the impedance conditions of converter power transformer saturation type harmonic instability, but characterize the matrix parameter dyscalculia of transverter both sides harmonic relationships, generally need to ask for by simulation method, and utilize the matrix parameter that simulation method obtains to be unfavorable for theoretically the influence factor of harmonic instability being analyzed, also have the converter power transformer core sataration unstable analysis > > (author: Yang little Bing of document < < based on modulation theory, Li Xingyuan, gold Xiao Ming etc., source: < < electric power network technique > > 2009) modulation theory is introduced to harmonic instability analysis, proposed based on DC current harmonic wave phase angle

harmonic instability decision method, although this method without asking for relational matrix, harmonic wave phase angle

theory calculate still very complicatedly, can only obtain by the method for emulation equally.

Different from above-mentioned prior art scheme thinking, the inventive method is based on following thinking: first to transverter both sides and converter transformer DC magnetic bias, the harmonic wave progress of disease characteristic under saturated is analyzed, disclose the closed loop positive feedback mechanism that converter power transformer saturation type harmonic instability forms, then obtain on this basis the saturated stable factor of converter power transformer saturation type harmonic instability, propose thus a kind of method that converter power transformer saturation type harmonic instability based on the transmission gain of disturbing signal closed loop is judged.Further introduce the principle of the method below:

According to modulation theory, the DC voltage of transverter can be regarded the modulation of transverter to alternating voltage as, and the ac-side current of transverter can be regarded the modulation of transverter to DC current as.Figure 2 shows that the structural representation of HVDC rectifier.Under normal circumstances, each converter valve is by numbering conducting successively in figure, and the relation of its alternating current-direct current both sides voltage and current can be expressed as:

u _dr=u _ars _ua+u _brs _ub+u _crs _uc

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

In formula, subscript " r " represents rectifier, s _ua, s _uband s _ucbe respectively abc three-phase voltage switch function; s _ia, s _iband s _icbe respectively three-phase current switch function.

According to Dynamic Phasors theory and phasor product natures, can obtain (because AC zero sequence voltage is on not impact of DC voltage, therefore following analysis all do not considered zero-sequence component):

${\stackrel{\&CenterDot;}{U}}_{d\left(m\right)}=\underset{n}{\mathrm{\&Sigma;}}{\stackrel{\&CenterDot;}{S}}_{u(m-n)}{T}_1{\stackrel{\&CenterDot;}{U}}_{\left(n\right)}^{(\&PlusMinus;)}=\underset{n}{\mathrm{\&Sigma;}}({\stackrel{\&CenterDot;}{S}}_{u(m-n)}^{+}{\stackrel{\&CenterDot;}{U}}_{\left(n\right)}^{+}+{\stackrel{\&CenterDot;}{S}}_{u(m-n)}^{-}{\stackrel{\&CenterDot;}{U}}_{\left(n\right)}^{-})---\left(2\right)$

${\stackrel{\&CenterDot;}{I}}_{\left(n\right)}^{(\&PlusMinus;)}={\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000407843030000031.png,HDA0000407843030000032.png"\; state="\{\{state\}\}">T</figure-callout>}}_2\underset{m}{\mathrm{\&Sigma;}}{\stackrel{\&CenterDot;}{S}}_{i(n-m)}{\stackrel{\&CenterDot;}{I}}_{d\left(m\right)}=\underset{m}{\mathrm{\&Sigma;}}{\stackrel{\&CenterDot;}{S}}_{i(n-m)}^{(\&PlusMinus;)}{\stackrel{\&CenterDot;}{I}}_{d\left(m\right)}---\left(3\right)$

In formula:

for the m of three-phase voltage switch function n phasor;

for

positive and negative sequence component;

for the n of three-phase current switch function m phasor;

for

positive and negative sequence component;

with

m the phasor for DC voltage and electric current;

n the positive and negative sequence component for transverter commutation voltage; n the positive and negative sequence component for transverter injection AC system electric current; M=0,1,2,3 N=1,2,3

$a={\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000407843030000031.png,HDA0000407843030000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^j;{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA0000407843030000032.png,HDA0000407843030000034.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right];{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000407843030000031.png,HDA0000407843030000032.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\end{array}\right].$

DC current inflow transformer winding can make transformer generation DC magnetic biasing effect, causes that each low-order harmonic composition that transformer core is saturated and converter power transformer is injected to AC system significantly increases.Core sataration degree is higher, and the exciting current distortion under DC magnetic biasing is more serious, and harmonic content is larger.Relation between the DC current of positive sequence second harmonic current and fillup valve side winding is linear substantially.Can adopt experience conversion formula to describe, DC current and line side positive sequence second harmonic current that this formula injects valve side winding connect:

In formula, it is the positive sequence second harmonic current of only considering to flow into when transformer core is saturated converter power transformer AC winding; I _a0, I _b0and I _c0be respectively to inject valve winding in converter transformer three-phase dc electric current, take and flow into valve winding in converter transformer as positive dirction; The ratio coefficient that N is the positive sequence second harmonic current that produces of transformer and transformer valve side winding injects direct current, the factors such as the architectural characteristic of this coefficient and transformer, AC excitation situation are relevant; e ^{i180 °}characterize conversion and have phase angle difference π between the positive sequence second harmonic current in line side and DC current; 1/3[1 e ^{i(-120 °)}e ^{i120 °}] be to be the transformation matrix of positive sequence second harmonic by three-phase dc current conversion.

In converter power transformer core sataration situation harmonic wave in 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, harmonic propagation relation in converter power transformer core sataration situation can be briefly described as follows: if there is second harmonic voltage disturbance at transverter AC, this disturbance voltage is through transverter on-off action, can cause power-frequency voltage in DC side, thereby produce industrial frequency harmonic electric current in DC side; The power current of direct current will produce positive sequence second harmonic current component and negative phase-sequence direct-current component at AC after transverter modulation; And DC current flows through converter power transformer, make transformer core saturated, produce a large amount of individual harmonic currents, comprise positive sequence second harmonic current; If the positive sequence second harmonic voltage magnitude that above-mentioned second harmonic current acting in conjunction produces in the impedance of AC second harmonic is greater than original Secondary Disturbance harmonic voltage, this closed loop positive feedback will cause that harmonic instability occurs.

The equivalent electrical circuit of ac and dc systems as shown in Figure 4.In figure: for the equivalent power supply of AC system; Z _sfor system impedance; Z _lbequivalent impedance for wave filter and reactive power compensator; H is transformer voltage ratio; Z _dcmexpression from transverter to straight-flow system, see into m equivalent harmonic impedance of straight-flow system, comprise the m subharmonic impedance of DC filter, smoothing reactor, DC line and offside transverter; Z _acnexpression from transverter to AC system, see into n equivalent harmonic impedance of AC system, its expression formula is:

Z _acn＝Z _sn||Z _lbn+Z _Tn (5)

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

${\stackrel{\&CenterDot;}{U}}_{\mathrm{<figure-callout\; id="2"\; label="ac"\; filenames="HDA0000407843030000031.png,HDA0000407843030000032.png"\; state="\{\{state\}\}">ac</figure-callout>}2}^{+}=U_{\mathrm{ac}2}\&angle;\mathrm{\&theta;}---\left(6\right)$

In formula, U _ac2be respectively amplitude and the phase angle of this disturbance with θ.

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

In formula

represent

conjugation.

The power frequency impedance of note DC side is Z _dc1, have:

Now according to formula (3), known

the change of current become harmonic current that AC produces into:

In formula:

for

the positive sequence second harmonic current of transverter AC after transverter modulation, I _a0, I _b0and I _c0for

after transverter modulation in the generation three-phase negative/positive DC current of transverter AC.

According to formula (4), I _a0, I _b0and I _c0the change of current become second harmonic current that AC produces into:

For the change of current, become the secondary positive sequence harmonic voltage disturbance of AC through transverter and converter power transformer, in AC and DC both sides, transmit after conversion, its change of current become second harmonic current that AC produces into:

In formula

expression is converted to the second harmonic current of net side by the second harmonic current of converter transformer valve side,

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

Therefore, harmonic voltage

through the converter power transformer under transverter and saturated conditions, after the progress 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., from formula (13), when λ is greater than 1, disturbance will increase along with the time, and system occurs unstable; When λ is less than 1, disturbance will decay along with the time, and system finally tends towards stability.

From above-mentioned principles illustrated, the method theoretical foundation clear thinking, calculation expression is simple, parameter is easy to get, and the degree can qualitative assessment converter power transformer saturation type harmonic instability occurring, so can be applied to more efficiently risk assessment and the inhibition field of HVDC (High Voltage Direct Current) transmission system harmonic instability.

Summary of the invention

The object of the invention is in order to solve the defect of above-mentioned prior art, a kind of method that provides HVDC system converter power transformer core sataration type harmonic instability to judge, the method theoretical foundation clear thinking, calculation expression is simple, parameter is easy to get, and the degree can qualitative assessment converter power transformer saturation type harmonic instability occurring, for the unsettled risk assessment of HVDC system harmonics and braking measure etc. provide theoretical foundation.

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

S1, according to the power-frequency voltage of known change of current bus

with

the DC component I of DC current _dc0and triggering command angle α ₀, set up electric current and voltage switch function, obtain the power frequency order component amplitude S of the switch function of electric current and voltage _u1and S _i1;

S2, according to alternating current-direct current equivalent electrical circuit, obtain AC system secondary equivalent harmonic wave impedance Z _ac2with equivalent harmonic wave impedance Z of straight-flow system _dc1;

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

In formula (14), Z _ac2and Z _dc1be respectively an equivalent harmonic wave impedance of the equivalent harmonic wave impedance of AC system secondary and straight-flow system; S _u1and S _i1be respectively voltage switch power frequency negative sequence component and current switch function power frequency positive-sequence component; H is the no-load voltage ratio of converter power transformer, i.e. the ratio of original edge voltage and secondary voltage; N is the positive sequence second harmonic current of transformer generation and the ratio coefficient that transformer valve side winding injects direct current;

for power-factor angle;

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

More specifically, S in step S1 _u1and S _i1calculation procedure as follows:

S11, according to the power-frequency voltage of known change of current bus

with

the DC component I of DC current _dc0and triggering command angle α ₀, the skew of calculating synchronizing voltage phase place;

If

with

the α component and the β component that represent respectively commutation voltage, calculate by following formula:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{U}}_{\mathrm{\&alpha;}}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{\&beta;}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{U}}_{\mathrm{ca}1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{ab}1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{bc}1}\end{array}\right]---\left(15\right)$

Utilize the α component of commutation voltage β component with commutation voltage

by following formula, calculated the phase place of DC control system synchronizing voltage

In formula (16), U _αand U _βbe respectively the amplitude of α component and the β component of commutation voltage;

with

be respectively the α component of commutation voltage and the phase angle of β component;

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

According to

phase place phase place

phase place

calculate respectively the phase deviation of synchronizing voltage

In formula (17),

for the phase deviation of ca phase and synchronizing voltage,

for the phase deviation of ab phase and synchronizing voltage, phase deviation for bc phase and 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 to lag behind as just, leading for negative;

If μ _mnangle of overlap during for the commutation of mn two-phase, computing formula is:

${\mathrm{\&mu;}}_{\mathrm{mn}}={\cos }^{-1}({\cos \mathrm{\&alpha;}}_{\mathrm{mn}}-2X_{\mathrm{<figure-callout\; id="0"\; label="r\; I\; dc"\; filenames="HDA0000407843030000031.png,HDA0000407843030000032.png"\; state="\{\{state\}\}">r</figure-callout>}}{I}_{\mathrm{dc}}{0}_{}/{\stackrel{\&CenterDot;}{U}}_{\mathrm{mn}1})-{\mathrm{\&alpha;}}_{\mathrm{mn}}---\left(20\right)$

X in formula (20) _rfor commutating impedance, by converter power transformer parameter according to formula

try to achieve, wherein z ^*for transformer leakage reactance perunit value, U is transformer primary polygonal voltage, and S is transformer capacity;

S13, according to θ _mn, α _mnand μ _mnmake three-phase voltage current switching waveform, by this three-phase voltage current waveform, utilize Fourier series to derive each order component of electric current and voltage switch function:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{S}}_{\mathrm{uak}}=\frac{1}{T}{\&Integral;}_0^T{s}_{\mathrm{ua}}{e}^{-\mathrm{jk\&omega;\&tau;}}\mathrm{d\&tau;}\\ {\stackrel{\&CenterDot;}{S}}_{\mathrm{ubk}}=\frac{1}{T}{\&Integral;}_0^T{s}_{\mathrm{ub}}{e}^{-\mathrm{jk\&omega;\&tau;}}\mathrm{d\&tau;}\\ {\stackrel{\&CenterDot;}{S}}_{\mathrm{uck}}=\frac{1}{T}{\&Integral;}_0^T{s}_{\mathrm{uc}}{e}^{-\mathrm{jk\&omega;\&tau;}}\mathrm{d\&tau;}\end{array}\right.---\left(21\right)$

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{S}}_{\mathrm{iak}}=\frac{1}{T}{\&Integral;}_0^T{s}_{\mathrm{ia}}{e}^{-\mathrm{jk\&omega;\&tau;}}\mathrm{d\&tau;}\\ {\stackrel{\&CenterDot;}{S}}_{\mathrm{ibk}}=\frac{1}{T}{\&Integral;}_0^T{s}_{\mathrm{ib}}{e}^{-\mathrm{jk\&omega;\&tau;}}\mathrm{d\&tau;}\\ {\stackrel{\&CenterDot;}{S}}_{\mathrm{ick}}=\frac{1}{T}{\&Integral;}_0^T{s}_{\mathrm{ic}}{e}^{-\mathrm{jk\&omega;\&tau;}}\mathrm{d\&tau;}\end{array}\right.---\left(22\right)$

Get k=1, the power frequency order component that then obtains electric current and voltage switch function after symmetry transformation is as follows:

${\stackrel{\&CenterDot;}{S}}_{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000407843030000032.png,HDA0000407843030000034.png"\; state="\{\{state\}\}">u</figure-callout>}1}^{\&PlusMinus;}=\left[\begin{array}{ccc}{\stackrel{\&CenterDot;}{S}}_{\mathrm{uak}}& {\stackrel{\&CenterDot;}{S}}_{\mathrm{ubk}}& {\stackrel{\&CenterDot;}{S}}_{\mathrm{<figure-callout\; id="1"\; label="uck"\; filenames="HDA0000407843030000032.png,HDA0000407843030000034.png"\; state="\{\{state\}\}">uck</figure-callout>}}\end{array}\right]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]---\left(23\right)$

${\stackrel{\&CenterDot;}{S}}_{i1}^{\&PlusMinus;}=\frac{1}{3}\left[\begin{array}{ccc}1& a& a^2\\ 1& a^2& a\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{S}}_{\mathrm{ia}1}\\ {\stackrel{\&CenterDot;}{S}}_{\mathrm{ib}1}\\ {\stackrel{\&CenterDot;}{S}}_{\mathrm{ic}1}\end{array}\right]---\left(24\right)$

S14, try to achieve the electric current and voltage switch function power frequency order component 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 impedance Z of straight-flow system _dc1computing method are as follows:

The equivalent electrical circuit of ac and dc systems as shown in Figure 4, wherein:

for the equivalent power supply of AC system; Z _sfor system impedance; Z _lbequivalent impedance for wave filter and reactive power compensator; H is transformer voltage ratio, i.e. the ratio of original edge voltage and secondary voltage; Z _dcmexpression from transverter to straight-flow system, see into m equivalent harmonic impedance of straight-flow system, comprise the m subharmonic impedance of DC filter, smoothing reactor, DC line and offside transverter; Z _acnexpression from transverter to AC system, see into n equivalent harmonic impedance of AC system, its expression formula is:

Z _acn＝Z _sn||Z _lbn+Z _Tn。

More specifically, power-factor angle in step S3

can be by try to achieve, wherein α is triggering command angle; μ is angle of overlap, can basis

try to achieve, wherein X _rfor commutating impedance, by converter power transformer parameter according to formula

try to achieve, wherein z ^*for transformer leakage reactance perunit value, U is transformer primary polygonal voltage, and S is transformer capacity.

More specifically, the ratio coefficient that in step S3, N is the positive sequence second harmonic current that produces of transformer and transformer valve side winding injects direct current, the factors such as the architectural characteristic of this coefficient and transformer, AC excitation situation are relevant; Its calculation procedure:

S31, converter transformer valve-side is inputted to 10 groups of DC current I _a0, I _b0and I _c0(the excess current factor of considering transformer, input current should not be greater than 100A), records the positive sequence second harmonic current of corresponding converter power transformer net side

wherein,

the positive sequence second harmonic current of only considering to flow into when transformer core is saturated converter power transformer AC winding, I _a0, I _b0and I _c0be respectively to inject valve winding in converter transformer three-phase dc electric current, take and flow into valve winding in converter transformer as positive dirction;

S32, according to formula:

Try to achieve 10 corresponding M values;

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

The present invention has following beneficial effect with respect to prior art:

The inventive method theoretical foundation clear thinking, calculation expression is simple, parameter is easy to get, and the degree can qualitative assessment converter power transformer saturation type harmonic instability occurring, so can be applied to more efficiently risk assessment and the inhibition field of HVDC (High Voltage Direct Current) transmission system harmonic instability.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the method for HVDC system converter power transformer core sataration type harmonic instability judgement of the present invention.

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

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

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

Fig. 5 is the equivalent electrical 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 the transformer a phase exciting current of λ=3.5 o'clock in the embodiment of the present invention 1.

Fig. 7 (b) is the transformer b phase exciting current of λ=3.5 o'clock in the embodiment of the present invention 1.

Fig. 7 (c) is the transformer c phase exciting current of λ=3.5 o'clock 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 the transformer a phase exciting current of λ=0.86 o'clock in the embodiment of the present invention 3.

Figure 10 (b) is the transformer b phase exciting current of λ=0.86 o'clock in the embodiment of the present invention 3.

Figure 10 (c) is the transformer c phase exciting current of λ=0.86 o'clock in the embodiment of the present invention 3.

Embodiment

Below in conjunction with drawings and Examples, further illustrate the present invention, but the scope of protection of present invention is not limited to the scope of embodiment statement.The other changes and modifications that those skilled in the art is made in the situation that not deviating from spirit of the present invention and protection domain, are still included in the scope of claims protection.

In high voltage direct current (HVDC) system, the equivalent electrical circuit of ac and dc systems as shown in Figure 4, is set up the emulation test system of core sataration type harmonic instability, as shown in Figure 5 based on PSCAD/EMTDC.In this test macro: 12 pulsation rectifiers adopt determines trigger angle control, Trigger Angle α ₀it is 18 °; Owing to only analyzing the core sataration type harmonic instability of rectification side generation, inversion side adopts a current source equivalence; DC line rated current I _dc0for 1kA, alternating-current voltage source effective value 100kV; Converter power transformer parameter is in Table 1.

Table 1 converter power transformer parameter

According to the parameter of table 1 converter power transformer, set up test model, valve winding in converter transformer is inputted to 10 groups of different three-phase dc electric current I _a0, I _b0and I _c0, record the positive sequence second harmonic current of 10 converter power transformer net sides

according to formula (25), try to achieve 10 corresponding M values, as shown in table 2.

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

Then by the arithmetic mean of 10 M values, try to achieve final fitting coefficient N=0.71.

Embodiment 1～embodiment 3 parameters arrange as shown in table 3.

Table 3 embodiment parameter arranges

Parameter	R1/Ω	C1/μF	R2/Ω	L2/mH	C2/μF	L3/mH	C3/μF	Trigger Angle (α 0）	λ	Z ac2	Z dc1
												Embodiment 1	100	1000	993.72	0.005	509.8	0.70	15.70	18°	3.50	446.86	17.21
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 is judged, in described high voltage direct current (HVDC) system, the equivalent electrical circuit of ac and dc systems as shown in Figure 4, as shown in Figure 5, as mentioned above, step is as follows for each parameter value for the emulation test system of setting up:

S1 1, according to the power-frequency voltage of known change of current bus

with

the DC component I of DC current _dc0and triggering command angle α ₀, set up electric current and voltage switch function, obtain the power frequency order component amplitude S of the switch function of electric current and voltage _u1and S _i1, be specifically divided into four steps below:

S11 1, according to the power-frequency voltage of known change of current bus

with

the DC component I of DC current _dc0and triggering command angle α ₀, the skew of calculating synchronizing voltage phase place.According to formula (15)～(17), calculate the phase deviation of synchronizing voltage

be 0;

S12 1, calculate converter valve turn on delay angle θ _mn, actual Trigger Angle α _mnwith actual angle of overlap μ _mn.In conjunction with S11 result of calculation, according to formula (18)～(20), θ tries to achieve _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), get k=1, try to achieve

Then the power frequency order component that obtains electric current and voltage switch function after symmetry transformation is as follows:

S14 1, try to achieve the electric current and voltage switch function power frequency order component amplitude S of each 6 pulse conversion device _u1=1.6479, S _i1=0.5493;

S2 1, the parameter that provides according to Fig. 5 alternating current-direct current equivalent electrical circuit and table 3 obtains AC system secondary equivalent harmonic wave impedance Z _ac2=446.86 and equivalent harmonic wave impedance Z of straight-flow system _dc1=17.21, as shown in table 3;

S3 1, calculate the saturated stable factor λ of harmonic wave converter power transformer saturation type harmonic instability, calculation expression is as follows:

Power-factor angle can be by

try to achieve, wherein α is 18 °, triggering command angle; μ is angle of overlap, S12 obtained μ=19.1285 ° in 1; According to table 1, can obtain

fitting coefficient N=0.71; Result of calculation λ is 3.5;

S4 1, now λ is greater than 1, disturbance will increase along with the time, it is unstable that decision-making system occurs; Its corresponding DC line current waveform as shown in Figure 6, know disturbance disappear after direct current harmonic wave not convergence, Fig. 7 has provided the converter power transformer three-phase excitation current waveform of λ=3.5 o'clock, as seen from the figure disturbance disappear after transformer still in state of saturation.

Embodiment 2:

The present embodiment calculation procedure is with embodiment 1, and associative list 3 parameters are finally tried to achieve λ=1.23, are greater than 1, and decision-making system occurs unstable; Its corresponding DC line current waveform as shown in Figure 8, after known disturbance disappears, do not restrain by direct current harmonic wave, and transformer is still in state of saturation.

Embodiment 3:

The present embodiment calculation procedure is with embodiment 1, and associative list 3 parameters are finally tried to achieve λ=0.86, are less than 1, judges that disturbance will decay along with the time, and system finally tends towards stability; Its corresponding DC line current waveform as shown in Figure 9, Figure 10 has provided the converter power transformer three-phase excitation current waveform of λ=0.86 o'clock, along with the decay of harmonic wave, transformer magnetizing current also reduces thereupon gradually as seen from the figure, and final transformer is changed to undersaturated condition from state of saturation.

Above-described embodiment is preferably embodiment of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, 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 is judged, is characterized in that, comprises the following steps:

   S1, according to the power-frequency voltage of known change of current bus

   

   with

   

   the DC component I of DC current _dc0and triggering command angle α ₀, set up electric current and voltage switch function, obtain the power frequency order component amplitude S of the switch function of electric current and voltage _u1and S _i1;

   S2, according to alternating current-direct current equivalent electrical circuit, obtain AC system secondary equivalent harmonic wave impedance Z _ac2with equivalent harmonic wave impedance Z of straight-flow system _dc1;

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

   

   wherein, Z _ac2and Z _dc1be respectively an equivalent harmonic wave impedance of the equivalent harmonic wave impedance of AC system secondary and straight-flow system; S _u1and S _i1be respectively voltage switch power frequency negative sequence component and current switch function power frequency positive-sequence component; H is the no-load voltage ratio of converter power transformer, i.e. the ratio of original edge voltage and secondary voltage; N is the positive sequence second harmonic current of transformer generation and the ratio coefficient that transformer valve side winding injects direct current;

   

   for power-factor angle;

   S4, when λ is greater than 1, disturbance will increase along with the time, it is unstable that system occurs; When λ is less than 1, disturbance will decay along with the time, and system finally tends towards stability.
2. 2. the method that HVDC system converter power transformer core sataration type harmonic instability according to claim 1 is judged, is characterized in that S in step S1 _u1and S _i1calculation procedure as follows:

   S11, according to the power-frequency voltage of known change of current bus

   

   with

   

   the DC component I of DC current _dc0and triggering command angle α ₀, the skew of calculating synchronizing voltage phase place;

   If

   

   with

   

   the α component and the β component that represent respectively commutation voltage, calculate by following formula:

   

   Utilize the α component of commutation voltage

   

   β component with commutation voltage by following formula, calculated the phase place of DC control system synchronizing voltage

   

   In formula, U _αand U _βbe respectively the amplitude of α component and the β component of commutation voltage;

   

   with be respectively the α component of commutation voltage and the phase angle of β component;

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

   According to

   

   phase place

   

   phase place

   

   phase place

   

   calculate respectively the phase deviation of synchronizing voltage

   

   

   In formula,

   

   for the phase deviation of ca phase and synchronizing voltage,

   

   for the phase deviation of ab phase and synchronizing voltage,

   

   phase deviation for bc phase and 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 to lag behind as just, leading for negative;

   If μ _mnangle of overlap during for the commutation of mn two-phase, computing formula is:

   

   X in formula _rfor commutating impedance, by converter power transformer parameter according to formula

   

   try to achieve, wherein z ^*for transformer leakage reactance perunit value, U is transformer primary polygonal voltage, and S is transformer capacity;

   S13, according to θ _mn, α _mnand μ _mnmake three-phase voltage current switching waveform, by this three-phase voltage current waveform, utilize Fourier series to derive each order component of electric current and voltage switch function:

   

   

   Get k=1, the power frequency order component that then obtains electric current and voltage switch function after symmetry transformation is as follows:

   

   

   S14, try to achieve the electric current and voltage switch function power frequency order component amplitude S of each 6 pulse conversion device _u1, S _i1.
3. 3. the method that HVDC system converter power transformer core sataration type harmonic instability according to claim 1 is judged, is characterized in that power-factor angle in step S3

   

   can be by

   

   try to achieve, wherein α is triggering command angle; μ is angle of overlap, can basis try to achieve, wherein X _rfor commutating impedance, by converter power transformer parameter according to formula try to achieve, wherein z ^*for transformer leakage reactance perunit value, U is transformer primary polygonal voltage, and S is transformer capacity.
4. 4. the method that HVDC system converter power transformer core sataration type harmonic instability according to claim 1 is judged, it is characterized in that, the ratio coefficient that in step S3, N is the positive sequence second harmonic current that produces of transformer and transformer valve side winding injects direct current, the factors such as the architectural characteristic of this coefficient and transformer, AC excitation situation are relevant; Its calculation procedure:

   S31, converter transformer valve-side is inputted to 10 groups of DC current I _a0, I _b0and I _c0, record the positive sequence second harmonic current of corresponding converter power transformer net side wherein,

   

   the positive sequence second harmonic current of only considering to flow into when transformer core is saturated converter power transformer AC winding, I _a0, I _b0and I _c0be respectively to inject valve winding in converter transformer three-phase dc electric current, take and flow into valve winding in converter transformer as positive dirction;

   S32, according to formula: try to achieve 10 corresponding M values;

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

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