CN101834437B - Determination method of high voltage direct current converter commutation overlap angle - Google Patents

Abstract

The invention discloses a determination method of a high voltage direct current converter commutation overlap angle, aiming to solve the problem that a traditional method for calculating a commutation overlap angle can not take nonideal factors including background harmonics into consider to cause poor design performance of a wave filter. The method comprises the following steps of dividing the working period of a converter into six commutation sections and six non-commutation sections; establishing a differential equation to each commutation section by considering factors such as background harmonic interference, asymmetric fundamental voltage, asymmetric converter trigger angle distances, commutation impedance deviation and the like; and accurately calculating the commutation overlap angle. The invention efficiently enhances the calculation efficiency when ensuring the accuracy and can enhance the design quality of an alternating current converter.

Description

Definite method at a kind of high voltage direct current converter commutation overlap angle

Technical field

The present invention relates to the high voltage direct current transmission project technical field, relate in particular to definite method at a kind of high voltage direct current converter commutation overlap angle.

Background technology

HVDC transmission system converting plant structural representation in tradition two ends is as shown in Figure 1; The transformer that is connected with YD through YY is with the alternating current step-down on the current conversion station ac bus (being referred to as to net side or AC side); Become the lower valve side alternating current of voltage; Two bridge commutation voltages provide the phase difference of 30 degree about being simultaneously; The three-phase alternating current of the converter that rectification circuit is contained in inside after with step-down converts the direct current of DC side to, through flat ripple reactance and DC filtering system elimination harmonic wave wherein, is transported to the Inverter Station that is positioned at load center through hvdc transmission line again.

Fig. 2 is the sketch map of six pulsation full bridge rectifier unit of the converter shown in Fig. 1 frame of broken lines; Under the perfect condition, triphasic potential voltage peak occurs successively with the order of a phase-b phase-c phase-a phase, the phase place of front and back two phases always be separated by 120 the degree; Be referred to as positive sequence, its waveform is as shown in Figure 3.If the order that the crest voltage on the three-phase occurs is a phase-c phase-b phase-a phase, be referred to as negative phase-sequence; The Phase synchronization of three-phase is called zero sequence.But exist voltage distortion on the actual ac bus, the no longer level and smooth and adjacent two phase phase differences of waveform no longer are 120 degree, but periodic non-sinusoidal waveform.Decompose but carry out phase sequence through symmetrical component method, can ac bus voltage be decomposed into positive sequence, negative phase-sequence, zero sequence three group components, every group component is formed by stacking the harmonic wave of different frequency.Simultaneously, all there is leakage inductance in transformer on a, b, c three-phase, in Fig. 2, uses L respectively _a, L _b, L _cExpression because the electric current at inductance two ends can not suddenly change, makes thyristor (V in the converter ₁～V ₆) electric current can not suddenly change, thyristor needs the regular hour from beginning to be triggered to complete conducting (perhaps fully by), this time period is referred to as commutation, the time period of commutation, pairing electrical degree was referred to as the commutation overlap angle.The existence of commutation process will make the first-harmonic that calculates under the instantaneous commutation condition and the size and the phase place of each harmonic electric current change, and what can embody a concentrated reflection of this influence is the commutation overlap angle.In harmonic current calculates, the calculated relationship at commutation overlap angle finding the solution to the AC side voltage transitions to dc voltage, and follow-up DC side current conversion is to the calculating of ac-side current.

In DC transmission engineering; It is for alternating current filter design the each harmonic current source data under various operating modes and the various load level to be provided that the AC side harmonic current calculates; Its result will directly influence choosing of filter type selecting and parameter selection and component ratings; If the calculating of harmonic wave is bigger than normal, not only can causes the serious waste of Design of Filter, and will cause a series of difficulties such as idle control; If Harmonics Calculation is less than normal, possibly causes that index of correlation such as performance of filter definite value exceeds standard, even produce the security of operation problem.Simultaneously because DC engineering scheduling and the flexibility regulated, need to consider and the operating condition of checking very many, amount of calculation is big, so harmonic wave is carried out not only accurately but also fast analyzing and calculating has crucial meaning.The accurate Calculation at commutation overlap angle can improve the design schedule of alternating current filter, promotes its filtering performance, has great economic worth.

When calculating the commutation overlap angle of converter, adopt some Utopian assumed conditions usually, be regarded as three symmetrical first-harmonic, positive sequence voltages, do not contain any harmonic component such as voltage with AC side with classical way; The three-phase structure symmetry of converter transformer, each phase parameter is identical; In same current conversion station, each converter valve triggers with the pulse of constant duration successively, and trigger angle keeps constant; The electric current of converter DC side is not for containing the Constant Direct Current electric current of any harmonic component, and this reactance that is equivalent to suppose smoothing reactor is for infinitely great.And in the real system owing to there are non-ideal factors such as negative phase-sequence fundamental voltage, background harmonics voltage, converter trigger angle (the pass angle of rupture) are asymmetric at interval, change of current impedance deviation, change of current no-load voltage ratio deviation; Make that the commutation of each valve will be no longer identical with the non-commutation duration; Conventional method based on ideal conditions obviously can't be taken into account influencing each other of above-mentioned various factors; Reduce precision thereby cause harmonic current to calculate, possibly cause under some bad working environments that safety problem appears in filter configuration.So it is one of key that improves the Harmonics Calculation precision that accurate Calculation is carried out at the commutation overlap angle, has important engineering application value.

Summary of the invention

The invention provides definite method at a kind of high voltage direct current converter commutation overlap angle; Consider that background harmonics disturbs in the actual high-voltage DC transmission system, the YY connection is connected factors such as transformer voltage ratio is inconsistent, the converter trigger angle is asymmetric at interval, commutating impedance deviation with YD; The commutation overlap angle under the various working conditions can be accurately and efficiently calculated, alternating current filter accuracy of designs and convenience can be effectively improved.

Definite method at a kind of high voltage direct current converter commutation overlap of the present invention angle comprises:

(1) triggers sequencing constantly according to six thyristors in the six pulsation rectifier circuits, work period of six pulsation rectifier circuits is divided into 6 commutation sections and 6 corresponding non-commutation sections, and confirms the commutation mode of each commutation section;

The moment (t=0) with a phase positive sequence first-harmonic zero crossing is a starting point, and the trigger sequence of six thyristors in one-period in the converter is followed successively by V ₁, V ₂, V ₃, V ₄, V ₅, V ₆, as shown in Figure 2, the triggering of each valve pairing electrical degree constantly is expressed as α ₁, α ₂, α ₃, α ₄, α ₅, α ₆, corresponding commutation overlap angle is expressed as μ ₁, μ ₂, μ ₃, μ ₄, μ ₅, μ ₆, according to triggering constantly and the commutation overlap angle, a work period is divided into 6 commutation sections and 6 corresponding non-commutation sections, as shown in Figure 4.At the initial moment of commutation section 1, i.e. α ₁The pairing triggering moment is to thyristor V ₁Apply trigger impulse, V ₁The beginning conducting, simultaneously, thyristor V ₅Owing to the voltage difference of its positive and negative end is that negative value begins to end; To the termination moment of commutation section 1, i.e. α ₁+ μ ₁Moment corresponding, V ₁Conducting fully, V ₅End fully.This time period is referred to as the commutation time, pairing electrical degree μ ₁It promptly is the commutation overlap angle of commutation section 1.

Because in different commutation processes and non-commutation process; The equivalent electric circuit topological structure of six pulsation rectifier bridges is identical; For for simplicity; Be illustrated in k (k is the natural number between 1～6) commutation section by phase with p, be illustrated in this commutation section by being conducting to the phase of ending, be illustrated in q and do not participate in commutation in this commutation section and keep the phase of conducting with r by the end of conducting.For example, in commutation section 1, promptly at [α ₁, α ₁+ μ ₁] during in by being a phase, then p=a mutually by the end of conducting; By being conducting to what end is c phase, then r=c mutually; That keep conducting is b phase, then q=b mutually.Promptly in commutation section 1, to a phase, in back to back non-commutation section 1, a phase and b are conducted by the c phase transformation in system, and c ends mutually.Commutation section and non-commutation section to other are analyzed, and can obtain commutation table as shown in the table:

Operation interval	p	r	q	The commutation mode
					Commutation section 1 [α 1，α 1+μ 1]	a	c	b	c→a
Commutation section 2 [α 2，α 2+μ 2]	c	b	a	b→c
					Commutation section 3 [α 3，α 3+μ 3]	b	a	c	a→b
Commutation section 4 [α 4，α 4+μ 4]	a	c	b	c→a
					Commutation section 5 [α 5，α 5+μ 5]	c	b	a	b→c
Commutation section 6 [α 6，α 6+μ 6]	b	a	c	a→b

(2), set up corresponding differential equation and boundary condition according to the equivalent electric circuit of each commutation section;

From beginning of the initial moment (t=0), as t=α _kThe moment of/ω (ω is the first-harmonic angular frequency) is to valve V _kTrigger, begun electric current by the commutation process of r phase transformation to the p phase.In this course, the phase current i that goes up mutually of p _pIncrease gradually by zero beginning, and the phase current i that r goes up mutually _rBy I _dBeginning reduces gradually, until i _pIncrease to I _d, i _rBe reduced to zero, commutation process finishes, and the change in current process is as shown in Figure 7, wherein I _dBe the direct current of converter DC side, it does not contain any harmonic component, promptly ignores harmonic current; Because during the converter actual motion; After flat ripple reactance and DC filtering system, the ratio of the relative direct current amplitude of harmonic current amplitude is very little, can not impact commutation process.

The equivalent electric circuit of commutation period is as shown in Figure 5, L _p, L _r, L _qBe transformer in each leakage inductance that goes up mutually, promptly only consider commutating reactance, ignore commutating resistance.Because commutating resistance is very little with respect to commutating reactance, can not impact commutation process.In commutation process, p, r, all conductings of q three-phase, commutation finishes, and r ends mutually, and equivalent electric circuit is converted into Fig. 6 by Fig. 5.

Can derive the balance of voltage equation of corresponding circuit by circuit diagram shown in Figure 5, this is a Nonhomogeneous Linear Differential:

$L_p\frac{d}{\mathrm{dt}}{i}_p\left(t\right)-L_r\frac{d}{\mathrm{dt}}[{(-1)}^{k+1}{I}_d-i_p\left(t\right)]=u_p\left(t\right)-u_r\left(t\right)---\left(1\right)$

U in the formula _p(t), u _r(t) be the phase voltage that net side phase voltage process transformer is transformed into the valve side afterwards, because zero-sequence current can not flow to the valve side, then they only comprise the component of positive sequence and negative phase-sequence, can be written as:

$\left\{\begin{array}{c}{u}_a\left(t\right)=\underset{n=1}{\overset{h}{\mathrm{\Σ}}}{U}_{\left(n\right)}\sin (\mathrm{n\ωt}+{\mathrm{\θ}}_{a\left(n\right)})+\underset{n=1}{\overset{h}{\mathrm{\Σ}}}{U}_{(-n)}\sin (\mathrm{n\ωt}+{\mathrm{\θ}}_{a(-n)})\\ u_b\left(t\right)=\underset{n=1}{\overset{h}{\mathrm{\Σ}}}{U}_{\left(n\right)}\sin (\mathrm{n\ωt}+{\mathrm{\θ}}_{b\left(n\right)})+\underset{n=1}{\overset{h}{\mathrm{\Σ}}}{U}_{(-n)}\sin (\mathrm{n\ωt}+{\mathrm{\θ}}_{b(-n)})\\ u_c\left(t\right)=\underset{n=1}{\overset{h}{\mathrm{\Σ}}}{U}_{\left(n\right)}\sin (\mathrm{n\ωt}+{\mathrm{\θ}}_{c\left(n\right)})+\underset{n=1}{\overset{h}{\mathrm{\Σ}}}{U}_{(-n)}\sin (\mathrm{n\ωt}+{\mathrm{\θ}}_{c(-n)})\end{array}\right.---\left(2\right)$

Wherein n is a harmonic number, and the high order harmonic component number of times of h for considering only considered 50 times usually.U _(n)Be the positive sequence each harmonic phase voltage amplitude of valve side, U _(-n)Be the negative phase-sequence each harmonic phase voltage amplitude of valve side, θ _{A (n)}, θ _{B (n)}, θ _{C (n)}Be the starting phase angle of each phase each harmonic, selecting a is benchmark mutually, and they satisfy following relation:

θ _b(n)＝θ _a(n)-2π/3

θ _c(n)＝θ _a(n)+2π/3

θ _b(-n)＝θ _a(-n)+2π/3 (3)

θ _c(-n)＝θ _a(-n)-2π/3

Can find out by Fig. 7, as t=α _kThe moment of/ω, the phase current i that p goes up mutually _pBe 0; As t=α _k/ ω+μ _kThe moment of/ω, the phase current i that p goes up mutually _pBe (1) ^K+1I _d, then the boundary condition of formula (1) can be written as:

$i_p\left(\frac{{\mathrm{\α}}_k}{\mathrm{\ω}}\right)=0---\left(4\right)$

$i_p\left(\frac{{\mathrm{\α}}_k+{\mathrm{\μ}}_k}{\mathrm{\ω}}\right)={(-1)}^{k+1}{I}_d---\left(5\right)$

(3) with the commutation overlap angle of positive sequence fundametal compoment as initial value, utilize alternative manner constantly to revise, obtain the commutation overlap angle under the various non-ideal factor situation;

By the boundary condition shown in formula (4), (5), can write out the general solution of formula (1):

$i_p\left(t\right)=\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{r\left(n\right)}}{n(X_p+X_r)}\cos (\mathrm{n\ωt}+{\mathrm{\θ}}_{r\left(n\right)})+\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{r(-n)}}{n(X_p+X_r)}\cos (\mathrm{n\ωt}+{\mathrm{\θ}}_{r(-n)})$

$-\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{p\left(n\right)}}{n(X_p+X_r)}\cos (\mathrm{n\ωt}+{\mathrm{\θ}}_{p\left(n\right)})-\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{p(-n)}}{n(X_p+X_r)}\cos (\mathrm{n\ωt}+{\mathrm{\θ}}_{p(-n)})+C---\left(6\right)$

In the formula, X _p=ω L _pX _q=ω L _qX _r=ω L _r

$C=\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{p\left(n\right)}}{n(X_p+X_r)}\cos (n{\mathrm{\α}}_k+{\mathrm{\θ}}_{p\left(n\right)})+\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{p(-n)}}{n(X_p+X_r)}\cos (n{\mathrm{\α}}_k+{\mathrm{\θ}}_{p(-n)})---\left(7\right)$

$-\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{r\left(n\right)}}{n(X_p+X_r)}\cos (n{\mathrm{\α}}_k+{\mathrm{\θ}}_{r\left(n\right)})-\underset{n=1}{\overset{h}{\mathrm{\Σ}}}\frac{U_{r(-n)}}{n(X_p+X_r)}\cos (n{\mathrm{\α}}_k+{\mathrm{\θ}}_{r(-n)})$

Only consider the positive sequence fundametal compoment, ignore positive sequence harmonic voltage and negative phase-sequence fundamental voltage, then formula (6), (7) are reduced to following form:

$i_p\left(t\right)=\frac{U_{\left(1\right)}}{X_p+X_r}\cos (\mathrm{\ωt}+{\mathrm{\θ}}_{r\left(1\right)})-\frac{U_{\left(1\right)}}{X_p+X_r}\cos (\mathrm{\ωt}+{\mathrm{\θ}}_{p\left(1\right)})+C^{\′}---\left(8\right)$

Wherein

$C^{\′}=-\frac{U_{\left(1\right)}}{X_p+X_r}\cos ({\mathrm{\α}}_1+{\mathrm{\θ}}_{r\left(1\right)})+\frac{U_{\left(1\right)}}{X_p+X_r}\cos ({\mathrm{\α}}_1+{\mathrm{\θ}}_{p\left(1\right)})---\left(9\right)$

Formula (8), (9) substitution formula (5) are obtained:

$\frac{U_{\left(1\right)}}{X_p+X_r}\cos ({\mathrm{\α}}_1+{\mathrm{\μ}}_1+{\mathrm{\θ}}_{r\left(1\right)})-\frac{U_{\left(1\right)}}{X_p+X_r}\cos ({\mathrm{\α}}_1+{\mathrm{\μ}}_1+{\mathrm{\θ}}_{p\left(1\right)})+C^{\′}=I_d---\left(10\right)$

Thus, the commutation overlap angle in the time of can obtaining the positive sequence fundametal compoment:

${\mathrm{\μ}}_k^{\left(0\right)}={\cos }^{-1}\left((\cos ({\mathrm{\α}}_{\left(k\right)}-\frac{{\mathrm{\θ}}_{p\left(1\right)}+{\mathrm{\θ}}_{r\left(1\right)}}{2})-\frac{(X_p+X_r)I_d}{\sqrt{3}{U}_{\left(1\right)}})\right)-{\mathrm{\α}}_k+\frac{{\mathrm{\θ}}_{p\left(1\right)}+{\mathrm{\θ}}_{r\left(1\right)}}{2}---\left(11\right)$

As iterative initial value, write out the l+1 time iterative equation according to formula (7):

${\mathrm{\μ}}_k^{(l+1)}={\cos }^{-1}(\left(\frac{X_p+X_r}{U_{\left(1\right)}}\right)\×\left(\begin{array}{c}{(-1)}^{k+1}{I}_d-i_p\left(\frac{{\mathrm{\α}}_k+{\mathrm{\μ}}_k^{\left(l\right)}}{\mathrm{\ω}}\right)\\ +\frac{U_{\left(1\right)}}{X_p+X_r}\cos ({\mathrm{\α}}_k+{\mathrm{\μ}}_k^{\left(l\right)}+{\mathrm{\θ}}_{r\left(1\right)})\end{array}\right))-{\mathrm{\α}}_k-{\mathrm{\θ}}_{r\left(1\right)}---\left(12\right)$

In setting accuracy, can obtain needed commutation overlap angle according to the alternative manner shown in the formula (12).Because background harmonics is less for the positive sequence first-harmonic usually, more approaching by commutation overlap angle and actual commutation overlap angle that the positive sequence first-harmonic obtains, as iterative initial value, convergence rate is very fast with this, and general iteration promptly can converge to 10 1～2 time ^-6In, so this method has computational speed faster.The invention provides definite method at a kind of high voltage direct current converter commutation overlap angle; Commutation overlap angle computational methods to traditional in the high-voltage dc transmission electric network can not be considered non-ideal factors such as background harmonics; Cause problem to the Design of Filter poor-performing; System duty cycle is divided into six commutation sections and six corresponding non-commutation sections, considers factors such as background harmonics disturbs in the actual high-voltage DC transmission system, fundamental voltage is asymmetric, the converter trigger angle is asymmetric at interval, commutating impedance deviation, accurately calculate the commutation overlap angle; When guaranteeing accuracy; Mention computational efficiency, thereby optimized Filter Design, can effectively improve the performance of high-voltage dc transmission electric network median filter.

Description of drawings

Fig. 1 is common high voltage direct current transmission schematic network structure;

Fig. 2 is the sketch map of six pulsation full bridge rectifier unit;

Fig. 3 is the oscillogram of six pulsation work periods of full bridge rectifier under the perfect condition;

Fig. 4 is the division figure of the present invention to six pulsation work periods of full bridge rectifier;

Fig. 5 is the equivalent circuit diagram of converter in a commutation section;

Fig. 6 is the equivalent circuit diagram of converter in a non-commutation section;

Fig. 7 is that converter DC side electric current changes sketch map in the commutation section;

Fig. 8 is the test system structure sketch map that the present invention adopts.

Embodiment

Because the unlimitedness of operational mode; The limited operational mode of normal calculating in the actual engineering; To a kind of definite throughput direction, definite system's connected mode, brownout operation whether; From the operate power of minimum (be generally rated power 10%) to overload (be generally rated power 120%), a certain percentage (representative value is 2% or 5%) of getting rated power is as increment, and one group of harmonic current is calculated in pointwise.Following examples adopt different load levels.

Embodiment 1

Adopting the test operating mode in this example is one pole single valve group (12 pulsation) the metallic(return) circuit mode of connection, and as shown in Figure 8, transmission power is 1250MW, and load level is 100%, and direct current is rated value 3.125kA, and definite method at its commutation overlap angle is following:

(1) triggers sequencing constantly according to six thyristors in the six pulsation rectifier circuits, work period of six pulsation rectifier circuits is divided into 6 commutation sections and 6 corresponding non-commutation sections, and confirms the commutation mode of each commutation section;

The YY bridge can Equivalent Decoupling become six pulsation full-wave rectification unit through the no-load voltage ratio conversion with star-triangular transformation with the YD bridge, because YY bridge and YD bridge have similitude on circuit structure, the equivalent electric circuit after its decoupling zero is identical, and is as shown in Figure 2.

In a work period, the trigger sequence of YY bridge internal valve is V ₁, V ₂, V ₃, V ₄, V ₅, V ₆, corresponding trigger impulse pairing electrical degree constantly is followed successively by α ₁, α ₂, α ₃, α ₄, α ₅, α ₆, corresponding commutation overlap angle is followed successively by μ ₁, μ ₂, μ ₃, μ ₄, μ ₅, μ ₆The trigger sequence of YD bridge internal valve does

Corresponding trigger impulse pairing electrical degree constantly is followed successively by

Corresponding commutation overlap angle is followed successively by

According to triggering constantly and the commutation overlap angle, a work period is divided into 6 commutation sections and 6 corresponding non-commutation sections, the YY bridge is identical with the dividing mode of YD bridge work period, and all available following table is represented:

Table 1 work period is divided table

Active section	Operation interval	The commutation mode
			Commutation section 1	[α 1，α 1+μ 1]	c→a
Non-commutation section 1	[α 1+μ 1，α 2]
			Commutation section 2	[α 2，α 2+μ 2]	b→c

Non-commutation section 2	[α 2+μ 2，α 3]
			Commutation section 3	[α 3，α 3+μ 3]	a→b
Non-commutation section 3	[α 3+μ 3，α 4]
			Commutation section 4	[α 4，α 4+μ 4]	c→a
Non-commutation section 4	[α 4+μ 4，α 5]
			Commutation section 5	[α 5，α 5+μ 5]	b→c
Non-commutation section 5	[α 5+μ 5，α 6]
			Commutation section 6	[α 6，α 6+μ 6]	a→b
Non-commutation section 6	[α 6+μ 6，2π+α 1]

For the converter of actual motion, because operating condition can not be desirable, so can produce various uncharacteristic harmonics, especially the low order uncharacteristic harmonics has material impact to Design of Filter, configuration and operation.Non-ideal factor mainly comprises: have harmonic wave in the alternating voltage; The interchange fundamental voltage is asymmetric, promptly has negative sequence voltage; Converter transformer impedance differences; The incomplete equidistance of trigger impulse; Because it is not equal that converter transformer no-load voltage ratio difference causes YY connection transformer to be connected the transformer commutation voltage with YD.

The data owner that engineering design is adopted will comprise converter transformer no-load voltage ratio, nominal impedance and impedance deviation, the specified trigger angle of converter valve, current conversion station bus fundamental voltage and each harmonic voltage, shown in table 2, table 3.The distribution of converter uneven symmetrical factor in service is difficult to prediction, usually adopts worst system condition to design in the engineering, to guarantee system safety operation.According to engineering experience and theoretical research in the past, obtain the maximum deviation combination, as shown in table 4.

Table 2 major loop stable state parameter

Net side line voltage effective value/kV	525
		Rated direct current/kA	3.125
Specified trigger angle/°	15
		Rating system frequency/Hz	50
No-load voltage ratio (secondary side/one time side line voltage)	169.85/525
		Commutation inductance/mH	22.5

Table 3 background harmonics and negative phase-sequence first-harmonic

Harmonic number	Ratio with respect to positive sequence fundamental voltage amplitude	Starting phase angle
			-1	0.010	0
3	0.005	0
			5	0.005	0

7	0.004	0
			9	0.007	0
11	0.006	0

The undesirable factor of table 4

Usually; The specified trigger angle α that major loop parameter provides (being generally 15 °) is a corresponding electrical degree of a time period, and the present invention is a reference point with a phase positive sequence fundamental voltage zero crossing, then needs trigger angle deviation in the associative list 4; Obtain each thyristor and trigger corresponding constantly electrical degree; Its corresponding corresponding relation is following, and wherein YY connects transformer and connects transformer leading 30 degree on phase place than YD, then has:

Can confirm each commutation section boundary according to table 1 like this, wherein the commutation overlap angle of each valve is amount to be asked.

Because YY connects than YD and connects leading 30 ° of commutation voltage phase place, according to star-triangular transformation, can obtain YY according to table 2 and table 3 and be connected transformer and be connected respectively each second phase voltage magnitude and phase angle of phase of transformer with YD, as shown in the table:

Table 5 each phase voltage amplitude and phase angle

Generally, the listed each harmonic of table 5 is bigger to systematic influence, and other subharmonic are less to the influence of system, can ignore.Obtain the rated angular velocity of equipment operation according to system's rated frequency:

ω＝2πf＝314.15926rad/s (15)

Combine the nominal value and the deviation of converter transformer equivalent commutation inductance under this operating condition then, obtain following result:

X _a＝ω(L _a+ΔL _a)＝7.068583

X _b＝ω(L _b+ΔL _b)＝7.225663

X _c＝ω(L _c+ΔL _c)＝6.911504

$X_a^{\′}=\mathrm{\ω}(L_a^{\′}+\mathrm{\Δ}{L}_a^{\′})=7.068583---\left(16\right)$

$X_b^{\′}=\mathrm{\ω}(L_b^{\′}+\mathrm{\Δ}{L}_b^{\′})=7.225663$

$X_c^{\′}=\mathrm{\ω}(L_c^{\′}+\mathrm{\Δ}{L}_c^{\′})=6.911504$

L in the formula _a, L _b, L _c,

Be the commutation inductance in the table 2, Δ L _a, Δ L _b, Δ L _c,

Value take from table 4.

(2), set up corresponding differential equation and boundary condition according to the equivalent electric circuit of each commutation section;

With commutation section 1 is YY bridge valve V ₅To valve V ₁Commutation is an example, its equivalent electric circuit such as Fig. 5, and corresponding differential equation is:

${L^{\′\′}}_a\frac{d}{\mathrm{dt}}{i}_a\left(t\right)-{L^{\′\′}}_c\frac{d}{\mathrm{dt}}[{(-1)}^{k+1}{I}_d-i_a\left(t\right)]=u_a\left(t\right)-u_c\left(t\right)---\left(17\right)$

In the formula, L " _a=L _a+ Δ L _a, L " _c=L _c+ Δ L _c,

According to table 5 and formula (2), u _a(t), u _c(t) can be written as:

u _a(t)＝169.85sin(ωt)+1.6985sin(-ωt)+0.84925sin(3ωt)+0.84925sin(5ωt)

+0.6794sin(7ωt)+1.18895sin(9ωt)+1.0191sin(11ωt)

u _c(t)＝169.85sin(ωt-240°)+1.6985sin(-ωt-120°)+0.84925sin(3ωt-240°)

+0.84925sin(5ωt-240°)+0.6794sin(7ωt-240°)+1.18895sin(9ωt-240°)+1.0191sin(11ωt-240°)

Its boundary condition is:

$i_a\left(\frac{{\mathrm{\α}}_1}{\mathrm{\ω}}\right)=0---\left(18\right)$

$i_a\left(\frac{{\mathrm{\α}}_1+{\mathrm{\μ}}_1}{\mathrm{\ω}}\right)=I_d---\left(19\right)$

Similarly, can set up equivalent electric circuit, the differential equation and the boundary condition of other commutation sections.

(3) according to above-mentioned data, substitution formula (8)～(12) respectively as initial value, utilize alternative manner constantly to revise with the commutation overlap angle of positive sequence fundametal compoment, obtain the commutation overlap angle under the various non-ideal factor situation, and are as shown in table 6.

In order to verify the precision of the inventive method, in the PSCAD/EMTDC of electrical power system transient simulation software, build identical model, be normative reference check the inventive method with its simulation result, the result is as shown in the table:

Table 6 commutation overlap angle result (100% load level)

The commutation overlap angle	PSCAD/EMTDC	The inventive method	Relative error
				μ 1	23.059°	23.042°	0.077％

Adopt conventional method to calculate ideal conditions, promptly do not consider the commutation overlap angle of various asymmetric factors, computational methods are following:

$\mathrm{\μ}=-\mathrm{\α}+{\cos }^{-1}(\cos \mathrm{\α}-\frac{2X_{\mathrm{\μ}}{I}_d}{\sqrt{3}U})---\left(20\right)$

Wherein μ is the commutation overlap angle, and α is a trigger angle, and U is for converting valve side positive sequence first-harmonic phase voltage amplitude, I _dBe DC side electric current, X _μFor converter transformer is converted the single-phase equiva lent impedance of valve side, i.e. commutation inductance in the table 2, the commutation overlap angle μ that obtains=23.556 °.The commutation overlap angle maximum deviation of calculating with PSCAD/EMTDC reaches 0.618 °, and relative deviation is 2.56%, and maximum relative deviation of the present invention is merely 0.091%, and visible the present invention compares conventional method has sizable improvement.

Embodiment 2

Present embodiment testing load level is 10% of a rated power, and direct current is 0.3125kA, and other conditions are said consistent with embodiment 1, then according to the step of embodiment 1 result as follows:

Table 7 commutation overlap angle result (10% load level)

Can find out that through table 7 the maximum relative deviation of the inventive method and PSCAD/EMTDC simulation result is 0.654% under the low load levels, maximum absolute deviation is 0.023 °, still has very high precision; If adopt conventional method calculate the result be μ=3.642 °, with the maximum absolute deviation of PSCAD/EMTDC be 0.403 °, relative deviation is near 10%, this error itself is big than trigger angle deviation (± 0.2 °).

Usually above contrast can be found out; Conventional method is calculated the commutation overlap angle can't satisfy various operating modes in the actual engineering; Especially the required precision under the low load levels, and then commutation section and non-commutation section are confirmed to occur to influence the Harmonics Calculation result than mistake when causing harmonic current to calculate; Finally influence Design of Filter and configuration, even safety problem possibly occur.

Though and PSCAD/EMTDC emulation is accurate, The model carries out the transition to harmonic wave stable state required time from initial condition and is no less than 1.8s, if will carry out the Design of Filter of an engineering, needs to calculate above 15000 operational modes, needs 7.5 hours at least.And use the inventive method that the time that 1 operational mode calculating commutation overlap angle needs is less than 0.01s; The whole service time can not surpass 0.1s yet in the harmonic current computational methods even be embedded into; Once can not surpass 20 minutes to all operating condition that need check traversals, have very high efficient.

Claims (4)

1. definite method at a high voltage direct current converter commutation overlap angle is characterized in that, comprising:

(1) triggers sequencing constantly according to six thyristors in the six pulsation rectifier circuits, work period of six pulsation rectifier circuits is divided into 6 commutation sections and 6 corresponding non-commutation sections, and confirms the commutation mode of each commutation section;

(2), set up corresponding differential equation and boundary condition according to the equivalent electric circuit of each commutation section;

(3) with the commutation overlap angle of positive sequence fundametal compoment as initial value, utilize alternative manner constantly to revise, obtain the commutation overlap angle under the various non-ideal factor situation; Described non-ideal factor comprises: have harmonic wave in the alternating voltage; Exchange the asymmetric negative sequence voltage that promptly exists of fundamental voltage; Converter transformer impedance differences, the incomplete equidistance of trigger impulse, it is different that converter transformer no-load voltage ratio difference causes YY connection transformer to be connected the transformer commutation voltage with YD.

2. definite method at high voltage direct current converter commutation overlap according to claim 1 angle is characterized in that, the method for setting up the differential equation in the described step (2) is:

According to the commutation section of dividing in the step (1) and the commutation mode of each commutation section, confirm that transformer in the annexation of each leakage inductance that goes up mutually in equivalent electric circuit, is obtained the differential equation of commutation section equivalent electric circuit by Kirchhoff's second law:

$L_p\frac{d}{\mathrm{dt}}{i}_p\left(t\right)-L_r\frac{d}{\mathrm{dt}}[{(-1)}^{k+1}{I}_d-i_p\left(t\right)]=u_p\left(t\right)-u_r\left(t\right)$

Wherein, L _p, L _rBe the leakage inductance of each phase of transformer, u _p(t), u _r(t) for being transformed into the phase voltage of valve side, i after the net side phase voltage process transformer _p(t) be the phase current of valve side, I _dBe the direct current after six pulsation rectifier circuit rectifications, p is that k commutation section is interior by the phase by the end of conducting, and r is that k commutation section is interior by being conducting to the phase of ending, and k is the natural number between 1～6.

3. definite method at high voltage direct current converter commutation overlap according to claim 2 angle is characterized in that, the described method of setting up boundary condition is:

In the commutation section by by the phase current of going up mutually that transfers conducting in the commutation section by the I of being raised to above freezing _d, the boundary condition of commutation section zero hour is:

$i_p\left(\frac{{\mathrm{\α}}_k}{\mathrm{\ω}}\right)=0$

The boundary condition of commutation section finish time is:

$i_p\left(\frac{{\mathrm{\α}}_k+{\mathrm{\μ}}_k}{\mathrm{\ω}}\right)={(-1)}^{k+1}{I}_d$

Wherein, α _kBe the pairing electrical degree of the triggering moment of thyristor, μ _kBe six pulsation rectifier circuits at the corresponding commutation overlap angle of commutation section, ω is the first-harmonic angular frequency, I _dBe the direct current after six pulsation rectifier circuit rectifications.

4. definite method at high voltage direct current converter commutation overlap according to claim 3 angle is characterized in that described alternative manner is:

General solution according to the differential equation that obtains in the step (2); Ignore positive sequence harmonic voltage and negative phase-sequence fundamental voltage, the commutation overlap angle

that obtains under the positive sequence fundametal compoment is:

${\mathrm{\μ}}_k^{\left(0\right)}={\cos }^{-1}\left((\cos ({\mathrm{\α}}_{\left(k\right)}-\frac{{\mathrm{\θ}}_{p\left(1\right)}+{\mathrm{\θ}}_{r\left(1\right)}}{2})-\frac{(X_p+X_r)I_d}{\sqrt{3}{U}_{\left(1\right)}})\right)-{\mathrm{\α}}_k+\frac{{\mathrm{\θ}}_{p\left(1\right)}+{\mathrm{\θ}}_{r\left(1\right)}}{2}$

Wherein, X _p, X _rBe the reactance of leakage inductance each phase under first-harmonic of transformer, θ _{P (1)}, θ _{R (1)}Be each phase starting phase angle of valve side positive sequence first-harmonic, U ₍₁₎Be the positive sequence first-harmonic phase voltage amplitude of valve side, with

Be initial value,

According to following iterative formula iteration, obtain final commutation overlap angle:

${\mathrm{\μ}}_k^{(l+1)}={\cos }^{-1}(\left(\frac{X_p+X_r}{U_{\left(1\right)}}\right)\×({(-1)}^{k+1}{I}_d-i_p\left(\frac{{\mathrm{\α}}_k+{\mathrm{\μ}}_k^{\left(1\right)}}{\mathrm{\ω}}\right)+\frac{U_{\left(1\right)}}{X_p+X_r}\cos ({\mathrm{\α}}_k+{\mathrm{\μ}}_k^{\left(1\right)}+{\mathrm{\θ}}_{r\left(1\right)})))-{\mathrm{\α}}_k-{\mathrm{\θ}}_{r\left(1\right)}.$

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