CN104467001A - Control method for DC side voltage of doubly-fed induction wind generator when power grid voltage is unbalanced - Google Patents

Abstract

The invention discloses a control method for DC side voltage of a doubly-fed induction wind generator when power grid voltage is unbalanced. The method is characterized in that when the power grid voltage is unbalanced, a mathematic model of a grid-side converter of the doubly-fed induction wind generator under a positive and negative sequence synchronous rotating coordinate system with active power fluctuation of a grid connection electric reactor taken into consideration is established, and the control method for eliminating 2-doubling fluctuation of the DC side voltage is proposed according to the corresponding relation of the DC side voltage in the model and the active power output by an AC side port of the grid-side converter. The control method effectively eliminates the 2-doubling fluctuation of the DC side voltage of the doubly-fed induction wind generator when the power grid voltage is unbalanced, prolongs the service life of a DC side capacitor, restricts current harmonic component fed into a power grid at the same time, and is especially suitable for the control filed of the doubly-fed induction wind generator when the power grid voltage is unbalanced.

Description

The control method of double-fed wind power generator group DC voltage during a kind of unbalanced source voltage

Technical field

The present invention relates to a kind of control method of double-fed wind power generator group DC voltage, the control method of double-fed wind power generator group DC voltage when particularly relating to a kind of unbalanced source voltage.

Background technology

Along with the quick raising of installed capacity of wind-driven power, influencing each other between Wind turbines and electrical network is increasingly outstanding, and the wind energy turbine set access electric power network technique that State Grid Corporation of China promulgates specifies to require that Wind turbines can bear the unbalanced electric grid voltage of voltage unbalance factor maximum 4%.Double-fed wind power generator group is as the Wind turbines type of current main flow, and the research of double-fed unit when unbalanced source voltage is just receiving increasing concern, needs the control method of double-fed unit when seeking a kind of unbalanced source voltage.

The factor such as unbalanced grid faults or asymmetrically placed load all can cause the imbalance of line voltage, the negative sequence component of the voltage and current produced during unbalanced source voltage can cause 2 double-frequency fluctuation of DC voltage, and then produce 3 subharmonic currents injection electrical networks at the AC of the grid side converter of double-fed unit, 2 double-frequency fluctuation of DC voltage can cause DC bus capacitor discharge and recharge frequently simultaneously, very large stress is brought to capacitor, reduce the useful life of capacitor, time serious, even can affect the stable operation of whole converter.Industry experience shows, the method suppressing DC voltage to fluctuate by simply increasing DC bus capacitor value greatly reduces the tracking performance of system economy and DC voltage, therefore needs the pulsation-free stable control method of DC voltage during a kind of more actual and effective unbalanced source voltage badly.

Through retrieving domestic and international patent and relevant technical document, not yet finding the patent similar with content of the present invention and bibliographical information at present, but mainly containing with the immediate scientific and technical literature of the present invention:

Hu Sheng, woods the new year, Kang Yong, Zou Xudong, the improvement control strategy of a kind of double-fed wind power generator under unbalanced source voltage condition, " electrotechnics journal ", 7 phases in 2011, P.21-29.

This article proposes the improvement control strategy of a kind of double-fed wind power generator under unbalanced electric grid voltage condition, and it according to the difference of control objectives, can realize the suppression of stator and rotor current, active reactive power and electromagnetic torque pulsation; But the control method of this article does not consider 2 double-frequency fluctuation of the active power that grid-connected reactor absorbs when line voltage is asymmetric, therefore can not eliminate 2 double-frequency fluctuation of DC voltage in actual motion.

In engineering practice, when line voltage uneven, for alleviating the stress to DC bus capacitor, eliminate the adverse effect to converter stable operation, the ripple disable stability contorting ability of DC voltage under unbalanced source voltage condition need be strengthened, need the control method of double-fed wind power generator group DC voltage when proposing a kind of unbalanced source voltage badly.

Summary of the invention

The object of the invention is for the deficiencies in the prior art, and the control method of double-fed wind power generator group DC voltage during a kind of unbalanced source voltage provided.This controlling party ratio juris is: when unbalanced source voltage, the grid side converter setting up a kind of double-fed wind power generator group considers the Mathematical Modeling of grid-connected reactor active power fluctuation under positive and negative sequence synchronous rotating frame, and the corresponding relation of the active power exported according to the DC voltage in this model and grid side converter AC port and a kind of control method eliminating DC voltage 2 double-frequency fluctuation proposed.

In order to realize foregoing invention object, technical scheme of the present invention is achieved like this:

1) DC bus capacitor power balance equation

$C\frac{{\mathrm{du}}_{\mathrm{dc}}}{\mathrm{dt}}+P_r=P_c$

P _c＝P _g+P _l

Wherein: C is DC bus capacitor value; u _dcfor DC capacitor voltage; P _rfor double-fed wind power generator rotor side exports instantaneous active power; P _cfor grid side converter AC port instantaneous active power; P _gfor the instantaneous active power of grid side converter feed-in electrical network; P _lfor the instantaneous active power that grid-connected reactor absorbs.

2) each active power equation under positive-negative sequence synchronization rotational coordinate ax system

$\left[\begin{array}{c}{P}_{g0}\\ P_{\mathrm{gc}2}\\ P_{\mathrm{gs}2}\\ P_{l0}\\ P_{\mathrm{lc}2}\\ P_{\mathrm{ls}2}\end{array}\right]=\left[\begin{array}{cccc}{u_{\mathrm{gd}}}^p& {u_{\mathrm{gq}}}^p& {u_{\mathrm{gd}}}^n& {u_{\mathrm{gq}}}^n\\ {u_{\mathrm{gd}}}^n& {u_{\mathrm{gq}}}^n& {u_{\mathrm{gd}}}^p& {u_{\mathrm{gq}}}^p\\ {u_{\mathrm{gq}}}^n& -{u_{\mathrm{gd}}}^n& -{u_{\mathrm{gq}}}^p& {u_{\mathrm{gd}}}^p\\ R_g{i_{\mathrm{gd}}}^p& R_g{i_{\mathrm{gq}}}^p& R_g{i_{\mathrm{gd}}}^n& R_g{i_{\mathrm{gq}}}^n\\ {2\mathrm{\ωL}}_g{i_{\mathrm{gq}}}^n& -{2\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^n& {2R}_g{i_{\mathrm{gd}}}^p& {2R}_g{i_{\mathrm{gq}}}^p\\ -{2\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^n& -{2\mathrm{\ωL}}_g{i_{\mathrm{gq}}}^n& {-2R}_g{i_{\mathrm{gq}}}^p& {2R}_g{i_{\mathrm{gd}}}^p\end{array}\right]\left[\begin{array}{c}{i_{\mathrm{gd}}}^p\\ {i_{\mathrm{gq}}}^p\\ {i_{\mathrm{gd}}}^n\\ {i_{\mathrm{gq}}}^n\end{array}\right]$

Wherein: P _g0for the DC component of the active power of grid side converter feed-in electrical network; P _gc2, P _gs2for more than active power, sinusoidal 2 times of mains frequency wave components; P _l0for the DC component of the active power that grid-connected reactor absorbs; P _lc2, P _ls2for more than the active power that grid-connected reactor absorbs, sinusoidal 2 times of mains frequency wave components; u _gd ^p, u _gq ^pfor positive sequence line voltage d, q axle component; u _gd ⁿ, u _gq ⁿfor negative phase-sequence line voltage d, q axle component; i _gd ^p, i _gq ^pfor positive sequence power network current d, q axle component; i _gd ⁿ, i _gq ⁿfor d, q axle component of negative phase-sequence power network current; R _g, L _gfor grid-connected reactor resistance and inductance; ω is mains frequency.

3) negative phase-sequence d, q shaft current command value accounting equation

From 1) the DC bus capacitor power balance equation that obtains, for controlling DC voltage without 2 harmonics, need to control the active-power P that grid side converter AC port exports _cwithout 2 harmonics, namely meet following formula:

$\left\{\begin{array}{c}{P}_{\mathrm{gc}2}+P_{\mathrm{lc}2}=0\\ P_{\mathrm{gs}2}+P_{\mathrm{ls}2}=0\end{array}\right.$

According to 2) the active power equation that obtains, then have

$\left\{\begin{array}{c}({u_{\mathrm{gd}}}^n{i_{\mathrm{gd}}}^p+{u_{\mathrm{gq}}}^n{i_{\mathrm{gq}}}^p+{u_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{u_{\mathrm{gq}}}^p{i_{\mathrm{gq}}}^n)\\ +2[R_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{i_{\mathrm{gq}}}^p{i_{\mathrm{gq}}}^n)+{\mathrm{\ωL}}_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n-{i_{\mathrm{gq}}}^p{i_{\mathrm{gd}}}^n)]=0\\ ({u_{\mathrm{gq}}}^n{i_{\mathrm{gd}}}^p-{u_{\mathrm{gd}}}^n{i_{\mathrm{gq}}}^p-{u_{\mathrm{gq}}}^p{i_{\mathrm{gd}}}^n+{u_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n)\\ +2[R_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n-{i_{\mathrm{gq}}}^p{i_{\mathrm{gd}}}^n)-{\mathrm{\ωL}}_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{i_{\mathrm{gq}}}^p{i_{\mathrm{gq}}}^n)]=0\end{array}\right.$

D axle under positive sequence rotating coordinate system is by positive sequence grid voltage orientation, and simplifying above formula is

$\left\{\begin{array}{c}{u_{\mathrm{gd}}}^n{i_{\mathrm{gd}}}^p+{u_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+2(R_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n)=0\\ {u_{\mathrm{gq}}}^n{i_{\mathrm{gd}}}^p+{u_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n+2(R_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n-{\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n)=0\end{array}\right.$

Calculate negative current instructions value by above formula, namely have

$\left\{\begin{array}{c}{i_{\mathrm{gd}}}^{n^{*}}=-\frac{{u_{\mathrm{gd}}}^p{u_{\mathrm{gd}}}^n{i_{\mathrm{gd}}}^p-2{\left({i_{\mathrm{gd}}}^p\right)}^2(R_g{u_{\mathrm{gd}}}^n-{\mathrm{\ωL}}_g{u_{\mathrm{gq}}}^n)}{{\left({u_{\mathrm{gd}}}^p\right)}^2+{4R}_g{i_{\mathrm{gd}}}^p({u_{\mathrm{gd}}}^p+R_g{i_{\mathrm{gd}}}^p)+{\left({2\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^p\right)}^2}\\ {i_{\mathrm{gq}}}^{n^{*}}=-\frac{{u_{\mathrm{gd}}}^p{u_{\mathrm{gq}}}^n{i_{\mathrm{gd}}}^p+2{\left({i_{\mathrm{gd}}}^p\right)}^2(R_g{u_{\mathrm{gq}}}^n+{\mathrm{\ωL}}_g{u_{\mathrm{gd}}}^n)}{{\left({u_{\mathrm{gd}}}^p\right)}^2+{4R}_g{i_{\mathrm{gd}}}^p({u_{\mathrm{gd}}}^p+R_g{i_{\mathrm{gd}}}^p)+{\left({2\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^p\right)}^2}\end{array}\right.$

Above formula shows, under positive-negative sequence synchronous rotary axle system, the calculating of grid side converter negative current instructions value only needs simple algebraic operation, avoids inverse the solving of complicated high level matrix.

4) detection of the positive and negative sequence component of line voltage and electric current

Adopt T/4 time expander method (T is grid cycle): by the three-phase electricity magnitude transform under three phase static ABC axle system under two-phase static α β axle system, obtain the value after time delay T/4 simultaneously; Utilize this two class value carry out algebraic operation obtain α β coordinate system under each positive and negative sequence component; Utilize the coordinate transform of α β-dq, obtain each component value under positive and negative sequence dq coordinate system.

Positive and negative sequence component under line voltage α β coordinate system

$\left[\begin{array}{c}{u_{\mathrm{g\α}}}^p\left(t\right)\\ {u_{\mathrm{g\β}}}^p\left(t\right)\\ {u_{\mathrm{g\α}}}^n\left(t\right)\\ {u_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}1& 0& 0& -1\\ 0& 1& 1& 0\\ 1& 0& 0& 1\\ 0& 1& -1& 0\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{g\α}}\left(t\right)\\ u_{\mathrm{g\β}}\left(t\right)\\ u_{\mathrm{g\α}}(t-T/4)\\ u_{\mathrm{g\β}}(t-T/4)\end{array}\right]$

Positive and negative sequence component under line voltage α β coordinate system

$\left[\begin{array}{c}{u_{\mathrm{gd}}}^p\left(t\right)\\ {u_{\mathrm{gq}}}^p\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}{u_{\mathrm{g\α}}}^p\left(t\right)\\ {u_{\mathrm{g\β}}}^p\left(t\right)\end{array}\right]$ $\left[\begin{array}{c}{u_{\mathrm{gd}}}^n\left(t\right)\\ {u_{\mathrm{gq}}}^n\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos (-\mathrm{\θ})& \sin (-\mathrm{\θ})\\ -\sin (-\mathrm{\θ})& \cos (-\mathrm{\θ})\end{array}\right]\left[\begin{array}{c}{u_{\mathrm{g\α}}}^n\left(t\right)\\ {u_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]$

Positive and negative sequence component under power network current α β coordinate system

$\left[\begin{array}{c}{i_{\mathrm{g\α}}}^p\left(t\right)\\ {i_{\mathrm{g\β}}}^p\left(t\right)\\ {i_{\mathrm{g\α}}}^n\left(t\right)\\ {i_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}1& 0& 0& -1\\ 0& 1& 1& 0\\ 1& 0& 0& 1\\ 0& 1& -1& 0\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{g\α}}\left(t\right)\\ i_{\mathrm{g\β}}\left(t\right)\\ i_{\mathrm{g\α}}(t-T/4)\\ i_{\mathrm{g\β}}(t-T/4)\end{array}\right]$

Positive and negative sequence component under power network current α β coordinate system

$\left[\begin{array}{c}{i_{\mathrm{gd}}}^p\left(t\right)\\ {i_{\mathrm{gq}}}^p\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}{i_{\mathrm{g\α}}}^p\left(t\right)\\ {i_{\mathrm{g\β}}}^p\left(t\right)\end{array}\right]$ $\left[\begin{array}{c}{i_{\mathrm{gd}}}^n\left(t\right)\\ {i_{\mathrm{gq}}}^n\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos (-\mathrm{\θ})& \sin (-\mathrm{\θ})\\ -\sin (-\mathrm{\θ})& \cos (-\mathrm{\θ})\end{array}\right]\left[\begin{array}{c}{i_{\mathrm{g\α}}}^n\left(t\right)\\ {i_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]$

5) positive-negative sequence current governing equation

D axle under positive sequence rotating coordinate system by the governing equation of the forward-order current after positive sequence grid voltage orientation is

$\left\{\begin{array}{c}{u_{\mathrm{cd}}}^p={u_{\mathrm{gd}}}^p-R_g{i_{\mathrm{gd}}}^p+{\mathrm{\ωL}}_g{i_{\mathrm{gq}}}^p-\mathrm{PI}({i_{\mathrm{gd}}}^{p^{*}}-{i_{\mathrm{gd}}}^p)\\ {u_{\mathrm{cq}}}^p=-R_g{i_{\mathrm{gq}}}^p-{\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^p-\mathrm{PI}({i_{\mathrm{gq}}}^{p^{*}}-{i_{\mathrm{gq}}}^p)\end{array}\right.$

The governing equation of negative-sequence current is

$\left\{\begin{array}{c}{u_{\mathrm{cd}}}^n={u_{\mathrm{gd}}}^n-R_g{i_{\mathrm{gd}}}^n-{\mathrm{\ωL}}_g{i_{\mathrm{gq}}}^n-\mathrm{PI}({i_{\mathrm{gd}}}^{n^{*}}-{i_{\mathrm{gd}}}^n)\\ {u_{\mathrm{cq}}}^n={u_{\mathrm{gq}}}^n-R_g{i_{\mathrm{gq}}}^n+{\mathrm{\ωL}}_g{i_{\mathrm{gd}}}^n-\mathrm{PI}({i_{\mathrm{gq}}}^{n^{*}}-{i_{\mathrm{gq}}}^n)\end{array}\right.$

The control method of double-fed wind power generator group DC voltage during a kind of unbalanced source voltage that the present invention proposes, it can solve following key technical problem:

1. the waveform by reference to the accompanying drawings 5, in accompanying drawing 6: the active power that when adopting traditional control method, not only grid side converter exports electrical network to has 2 certain double-frequency fluctuation, also there are significant 2 double-frequency fluctuation in DC voltage, the voltage fluctuation of this 2 frequencys multiplication will cause DC bus capacitor discharge and recharge frequently, greatly reduce the useful life of electric capacity; And the control method of the DC voltage that the present invention proposes, the active power exported by Controling network side converter AC port is without 2 harmonics, 2 double-frequency fluctuation of DC voltage can be eliminated, thus be conducive to the useful life of improving electric capacity, 2 double-frequency fluctuation that simultaneously grid side converter exports the active power of electrical network to also reduce relatively, and its fluctuation amplitude is worth identical with the active power fluctuation on grid-connected reactor.

2. by reference to the accompanying drawings 7, the spectrogram of current on line side in accompanying drawing 8, the control method of the DC voltage that the present invention proposes, while elimination DC voltage 2 double-frequency fluctuation, effectively inhibit the current harmonics component of feed-in electrical network, under the unbalanced source voltage degree condition of power output 2MW and 10%, the total harmonic distortion factor of net side phase current is reduced to 2.67% by 5.62%, and wherein non-zero sequence 3 order harmonic components have decreased to 1.01% from 5.33%.

Accompanying drawing explanation

Fig. 1 be the present invention propose a kind of unbalanced source voltage time the schematic diagram of control method of double-fed wind power generator group DC voltage.

Fig. 2 is the principle schematic of the time expander method separation positive-negative sequence that the present invention adopts.

Fig. 3 is that the forward-order current that the present invention adopts controls schematic diagram.

Fig. 4 is that the negative-sequence current that the present invention adopts controls schematic diagram.

Fig. 5 is the oscillogram adopting the current on line side of control method of the present invention when unbalanced source voltage, DC voltage, active power, reactive power.

Fig. 6 is the oscillogram adopting the current on line side of traditional control method when unbalanced source voltage, DC voltage, active power, reactive power.

Fig. 7 adopts the current on line side spectrogram of control method of the present invention when unbalanced source voltage.

Fig. 8 adopts the current on line side spectrogram of traditional control method when unbalanced source voltage.

In accompanying drawing 5, accompanying drawing 6,0 ~ 1.5s line voltage is normal, and 2MW double-fed wind power generator group runs on rated condition; The unbalanced source voltage degree of 10% is there is during 1.5s; After continuing 600ms, line voltage restores balance again.

Spectrogram in accompanying drawing 7, accompanying drawing 8 is to the result that current on line side is analyzed when the unbalanced source voltage of power output 2MW and 10% is spent.

Embodiment

The control method of double-fed wind power generator group DC voltage during a kind of unbalanced source voltage proposed the present invention below in conjunction with accompanying drawing is described further.

In fig. 1, during a kind of unbalanced source voltage, the control method of the DC voltage of double-fed wind power generator group, is implemented by the following technical programs.

1) input part

Electrical network three-phase voltage U _abcinput: utilize Hall voltage transducer detectable voltage signals, sends into the AD conversion passage of controller, realizes the detection to voltage signal after modulate circuit and filter process;

Net side three-phase current I _abcinput: utilize Hall current sensor sensed current signal, sends into the AD conversion passage of controller, realizes the detection to current signal after modulate circuit and filter process.

2) positive-negative sequence electric current and voltage decouples computation part

Positive sequence line voltage frequency and angle calculation: use software PLL algorithm to extract frequency and the angle of positive sequence line voltage;

The positive-negative sequence decouples computation of line voltage: the positive-negative sequence component being separated formulae discovery line voltage according to the positive-negative sequence provided in accompanying drawing 2 and line voltage and the detection of the positive and negative sequence component of electric current;

The positive-negative sequence decouples computation of current on line side: be separated the positive-negative sequence component that the voltage magnitude of current to be substituted rear calculating current on line side by formula according to the positive-negative sequence provided in accompanying drawing 2 and line voltage and the detection of the positive and negative sequence component of electric current.

3) negative current instructions value calculating section

Negative phase-sequence dq shaft current control command value when controlling DC voltage ripple disable is obtained according to the negative current instructions value computing formula provided in negative phase-sequence d, q shaft current command value accounting equation.

4) control algolithm part

Forward-order current control algolithm part: according to control block diagram and the formula of accompanying drawing 3, DC voltage control ring is utilized to obtain positive sequence d shaft current control command value, utilize referenced reactive current value to obtain positive sequence q shaft current control command value, obtain positive sequence dq axle control voltage value by governing equation;

Negative-sequence current control algolithm part: according to obtaining negative phase-sequence dq shaft current control command value, according to control block diagram and the formula of accompanying drawing 4, obtains negative phase-sequence dq axle control voltage value by governing equation;

Master control magnitude of voltage calculates: positive-negative sequence dq axle control voltage value is added the master control magnitude of voltage namely obtained under α β axle respectively after the coordinate transform of dq-α β;

SVPWM calculates: by the control voltage under α β axle, obtain pwm control signal according to SVPWM modulation system, realize the control to grid side converter.

Claims (1)

1. the enhancing control method of double-fed wind power generator group DC voltage during unbalanced source voltage, it is characterized in that, this control method comprises the following steps:

1) DC bus capacitor power balance equation

$C\frac{{\mathrm{du}}_{\mathrm{dc}}}{\mathrm{dt}}+P_r=P_c$

P _c＝P _g+P _l

Wherein: C is DC bus capacitor value; u _dcfor DC capacitor voltage; P _rfor double-fed wind power generator rotor side exports instantaneous active power; P _cfor grid side converter AC port instantaneous active power; P _gfor the instantaneous active power of grid side converter feed-in electrical network; P _lfor the instantaneous active power that grid-connected reactor absorbs.

2) each active power equation under positive-negative sequence synchronization rotational coordinate ax system

$\left[\begin{array}{c}{P}_{g0}\\ P_{\mathrm{gc}2}\\ P_{\mathrm{gs}2}\\ P_{l0}\\ P_{\mathrm{lc}2}\\ P_{\mathrm{ls}2}\end{array}\right]=\left[\begin{array}{cccc}{u_{\mathrm{gd}}}^p& {u_{\mathrm{gq}}}^p& {u_{\mathrm{gd}}}^n& {u_{\mathrm{gq}}}^n\\ {u_{\mathrm{gd}}}^n& {u_{\mathrm{gq}}}^n& {u_{\mathrm{gd}}}^p& {u_{\mathrm{gq}}}^p\\ {u_{\mathrm{gq}}}^n& -{u_{\mathrm{gd}}}^n& -{u_{\mathrm{gq}}}^p& {u_{\mathrm{gd}}}^p\\ R_g{i_{\mathrm{gd}}}^p& R_g{i_{\mathrm{gq}}}^p& R_g{i_{\mathrm{gd}}}^n& R_g{i_{\mathrm{gq}}}^n\\ 2\mathrm{\ω}{L}_g{i_{\mathrm{gq}}}^n& -2\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^n& 2R_g{i_{\mathrm{gd}}}^p& 2R_g{i_{\mathrm{gq}}}^p\\ -2\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^n& -2\mathrm{\ω}{L}_g{i_{\mathrm{gq}}}^n& -2R_g{i_{\mathrm{gq}}}^p& 2R_g{i_{\mathrm{gd}}}^p\end{array}\right]\left[\begin{array}{c}{i_{\mathrm{gd}}}^p\\ {i_{\mathrm{gq}}}^p\\ {i_{\mathrm{gd}}}^n\\ {i_{\mathrm{gq}}}^n\end{array}\right]$

Wherein: P _g0for the DC component of the active power of grid side converter feed-in electrical network; P _gc2, P _gs2for more than active power, sinusoidal 2 times of mains frequency wave components; P _l0for the DC component of the active power that grid-connected reactor absorbs; P _lc2, P _ls2for more than the active power that grid-connected reactor absorbs, sinusoidal 2 times of mains frequency wave components; u _gd ^p, u _gq ^pfor positive sequence line voltage d, q axle component; u _gd ⁿ, u _gq ⁿfor negative phase-sequence line voltage d, q axle component; i _gd ^p, i _gq ^pfor positive sequence power network current d, q axle component; i _gd ⁿ, i _gq ⁿfor d, q axle component of negative phase-sequence power network current; R _g, L _gfor grid-connected reactor resistance and inductance; ω is mains frequency.

3) negative phase-sequence d, q shaft current command value accounting equation

From 1) the DC bus capacitor power balance equation that obtains, for controlling DC voltage without 2 harmonics, need to control the active-power P that grid side converter AC port exports _cwithout 2 harmonics, namely meet following formula:

$\left\{\begin{array}{c}{P}_{\mathrm{gc}2}+P_{\mathrm{lc}2}=0\\ P_{\mathrm{gs}2}+P_{\mathrm{ls}2}=0\end{array}\right.$

According to 2) the active power equation that obtains, then have

$\left\{\begin{array}{c}({u_{\mathrm{gd}}}^n{i_{\mathrm{gd}}}^p+{u_{\mathrm{gq}}}^n{i_{\mathrm{gq}}}^p+{u_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{u_{\mathrm{gq}}}^p{i_{\mathrm{gq}}}^n)\\ +2[R_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{i_{\mathrm{gq}}}^n{i_{\mathrm{gq}}}^n)+\mathrm{\ω}{L}_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n-{i_{\mathrm{gq}}}^p{i_{\mathrm{gd}}}^n)]=0\\ ({u_{\mathrm{gq}}}^n{i_{\mathrm{gd}}}^p-{u_{\mathrm{gd}}}^n{i_{\mathrm{gq}}}^p-{u_{\mathrm{gq}}}^p{i_{\mathrm{gd}}}^n+{u_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n)\\ +2[R_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n-{i_{\mathrm{gq}}}^p{i_{\mathrm{gd}}}^n)-\mathrm{\ω}{L}_g({i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+{i_{\mathrm{gq}}}^p{i_{\mathrm{gq}}}^n)]=0\end{array}\right.$

D axle under positive sequence rotating coordinate system is by positive sequence grid voltage orientation, and simplifying above formula is:

$\left\{\begin{array}{c}{u_{\mathrm{gd}}}^n{i_{\mathrm{gd}}}^p+{u_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+2(R_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n+\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n)=0\\ {u_{\mathrm{gq}}}^n{i_{\mathrm{gd}}}^p+{u_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n+2(R_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gq}}}^n-\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^p{i_{\mathrm{gd}}}^n)=0\end{array}\right.$

Calculate negative current instructions value by above formula, namely have

$\left\{\begin{array}{c}{i_{\mathrm{gd}}}^{n^{*}}=-\frac{{u_{\mathrm{gd}}}^p{u_{\mathrm{gd}}}^n{i_{\mathrm{gd}}}^p-2{\left({i_{\mathrm{gd}}}^p\right)}^2(R_g{u_{\mathrm{gd}}}^n-\mathrm{\ω}{L}_g{u_{\mathrm{gq}}}^n)}{{\left({u_{\mathrm{gd}}}^p\right)}^2+4R_g{i_{\mathrm{gd}}}^p({u_{\mathrm{gd}}}^p+R_g{i_{\mathrm{gd}}}^p)+{\left(2\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^p\right)}^2}\\ {i_{\mathrm{gq}}}^{n^{*}}=-\frac{{u_{\mathrm{gd}}}^p{u_{\mathrm{gq}}}^n{i_{\mathrm{gd}}}^p+2{\left({i_{\mathrm{gd}}}^p\right)}^2(R_g{u_{\mathrm{gq}}}^n+\mathrm{\ω}{L}_g{u_{\mathrm{gd}}}^n)}{{\left({u_{\mathrm{gd}}}^p\right)}^2+4R_g{i_{\mathrm{gd}}}^p({u_{\mathrm{gd}}}^p+R_g{i_{\mathrm{gd}}}^p){\left(2\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^p\right)}^2}\end{array}\right.$

Above formula shows, under positive-negative sequence synchronous rotary axle system, the calculating of grid side converter negative current instructions value only needs simple algebraic operation, avoids inverse the solving of complicated high level matrix.

4) detection of the positive and negative sequence component of line voltage and electric current

Adopt T/4 time expander method (T is grid cycle): by the three-phase electricity magnitude transform under three phase static ABC axle system under two-phase static α β axle system, obtain the value after time delay T/4 simultaneously; Utilize this two class value carry out algebraic operation obtain α β coordinate system under each positive and negative sequence component; Utilize the coordinate transform of α β-dp, obtain each component value under positive and negative sequence dp coordinate system.

Positive and negative sequence component under line voltage α β coordinate system

$\left[\begin{array}{c}{u_{\mathrm{g\α}}}^p\left(t\right)\\ {u_{\mathrm{g\β}}}^p\left(t\right)\\ {u_{\mathrm{g\α}}}^n\left(t\right)\\ {u_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}1& 0& 0& -1\\ 0& 1& 1& 0\\ 1& 0& 0& 1\\ 0& 1& -1& 0\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{g\α}}\left(t\right)\\ u_{\mathrm{g\β}}\left(t\right)\\ u_{\mathrm{g\α}}(t-T/4)\\ u_{\mathrm{g\β}}(t-T/4)\end{array}\right]$

Positive and negative sequence component under line voltage α β coordinate system

$\begin{array}{cc}\left[\begin{array}{c}{u_{\mathrm{gd}}}^p\left(t\right)\\ {u_{\mathrm{gq}}}^p\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}{u_{\mathrm{g\α}}}^p\left(t\right)\\ {u_{\mathrm{g\β}}}^p\left(t\right)\end{array}\right]& \left[\begin{array}{c}{u_{\mathrm{gd}}}^n\left(t\right)\\ {u_{\mathrm{gq}}}^n\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos (-\mathrm{\θ})& \sin (-\mathrm{\θ})\\ -\sin (-\mathrm{\θ})& \cos (-\mathrm{\θ})\end{array}\right]\left[\begin{array}{c}{u_{\mathrm{g\α}}}^n\left(t\right)\\ {u_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]\end{array}$

Positive and negative sequence component under power network current α β coordinate system

$\left[\begin{array}{c}{i_{\mathrm{g\α}}}^p\left(t\right)\\ {i_{\mathrm{g\β}}}^p\left(t\right)\\ {i_{\mathrm{g\α}}}^n\left(t\right)\\ {i_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}1& 0& 0& -1\\ 0& 1& 1& 0\\ 1& 0& 0& 1\\ 0& 1& -1& 0\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{g\α}}\left(t\right)\\ i_{\mathrm{g\β}}\left(t\right)\\ i_{\mathrm{g\α}}(t-T/4)\\ i_{\mathrm{g\β}}(t-T/4)\end{array}\right]$

Positive and negative sequence component under power network current α β coordinate system

$\begin{array}{cc}\left[\begin{array}{c}{i_{\mathrm{gd}}}^p\left(t\right)\\ {i_{\mathrm{gq}}}^p\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}{i_{\mathrm{g\α}}}^p\left(t\right)\\ {i_{\mathrm{g\β}}}^p\left(t\right)\end{array}\right]& \left[\begin{array}{c}{i_{\mathrm{gd}}}^n\left(t\right)\\ {i_{\mathrm{gq}}}^n\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos (-\mathrm{\θ})& \sin (-\mathrm{\θ})\\ -\sin (-\mathrm{\θ})& \cos (-\mathrm{\θ})\end{array}\right]\left[\begin{array}{c}{i_{\mathrm{g\α}}}^n\left(t\right)\\ {i_{\mathrm{g\β}}}^n\left(t\right)\end{array}\right]\end{array}$

5) positive-negative sequence current governing equation

D axle under positive sequence rotating coordinate system by the governing equation of the forward-order current after positive sequence grid voltage orientation is

$\left\{\begin{array}{c}{u_{\mathrm{cd}}}^p={u_{\mathrm{gd}}}^p-R_g{i_{\mathrm{gd}}}^p+\mathrm{\ω}{L}_g{i_{\mathrm{gq}}}^p-\mathrm{PI}({i_{\mathrm{gd}}}^{p^{*}}-{i_{\mathrm{gd}}}^p)\\ {u_{\mathrm{cq}}}^p=-R_g{i_{\mathrm{gq}}}^p-\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^p-\mathrm{PI}({i_{\mathrm{gq}}}^{p^{*}}-{i_{\mathrm{gq}}}^p)\end{array}\right.$

The governing equation of negative-sequence current is

$\left\{\begin{array}{c}{u_{\mathrm{cd}}}^n={u_{\mathrm{gd}}}^n-R_g{i_{\mathrm{gd}}}^n-\mathrm{\ω}{L}_g{i_{\mathrm{gq}}}^n-\mathrm{PI}({i_{\mathrm{gd}}}^{n^{*}}-{i_{\mathrm{gd}}}^n)\\ {u_{\mathrm{cq}}}^n={u_{\mathrm{gq}}}^n-R_g{i_{\mathrm{gq}}}^n+\mathrm{\ω}{L}_g{i_{\mathrm{gd}}}^n-\mathrm{PI}({i_{\mathrm{gq}}}^{n^{*}}-{i_{\mathrm{gq}}}^n)\end{array}\right.$