CN102280888A - Direct current side voltage control method of three-phase four-leg active power filter - Google Patents

Abstract

The invention discloses a direct current side voltage control method of a three-phase four-leg active power filter. The method comprises the following steps: establishing a state space model of the three-phase four-leg active power filter under dq0 coordinates, using a d-axis control quantity to control direct current side voltage, using q-axis and 0-axis control quantities to control alternating current output current and selecting q-axis and 0-axis output current and the direct current side voltage as system output; defining an error vector, selecting the sliding mode surface and deriving a d-axis current command value; adding the d-axis current command value to output of a harmonic wave detection circuit and taking the sum as total d-axis reference current; and introducing an integral term into the sliding mode surface so as to improve the control precision. When voltage or load of a power grid is unbalanced, two filters are increased, one is a wave trap for filtering out second harmonic waves in voltage at a common connection point, the other one is a low-pass filter for filtering out the harmonic waves contained in a voltage measured value on the direct current side and then accurate compensation of the active power filter can be realized. By adopting the method, the problem of poor effects of conventional PI (proportional and integral) control is solved, and the method further has the advantages of fast response, strong robustness, capability of removing adverse effects of an outer ring on an inner ring and the like.

Description

A kind of DC side voltage control method of three-phase four-arm Active Power Filter-APF

Technical field

The present invention relates to a kind of voltage control method, specifically, relate to a kind of voltage control method of three-phase four-arm Active Power Filter-APF.

Background technology

Three-phase four-wire system extensive use in industry and civilian power system, the main load of system is the little single-phase load of power, but because quantity is more and more, the harmonic wave that they cause, current in middle wire and three-phase imbalance problem are serious day by day, cause various accidents.Therefore the above-mentioned distortion in the three-phase four-wire system is compensated and have important and practical meanings.Active Power Filter-APF (APF) is a kind of novel electric power electric device that is used for dynamically suppressing harmonic wave, compensating power, can the humorous reactive power that involves that big or small and frequency all change be compensated, it is a kind of important way of administering power quality problems such as harmonic wave, various distortion that can fast and flexible ground compensates electric system.The Active Power Filter-APF that is applicable to three-phase four-wire system has various topological structures, studies show that the three-phase four-arm structure obtains using comparatively widely because of possessing plurality of advantages.

Three-phase four-arm APF adopts the dicyclo control system usually, i.e. outer voltage and current inner loop.The reference value of outer voltage control inverter dc voltage for setting, it is output as current inner loop simultaneously provides current reference value.So the stable and good transient performance of outer loop voltag is the basis of the normal operation of APF, the design of voltage controller is the important component part in the design of APF device.Outer loop voltag one with proportional integral (PI) controller, this control strategy exists some shortcomings, start and time that transient process is required longer.In addition, for three-phase four-wire system, multiple reasons such as a large amount of uses of threephase load imbalance, large capacity single phase load, unbalanced fault all can cause unbalanced source voltage; Even line voltage balance, nonlinear load can make electric current contain zero-sequence component equally.This just requires three-phase four-arm APF not only to possess the ability of compensation harmonic simultaneously, idle, negative phase-sequence, zero-sequence current, also should avoid of the influence of these current distortion components, but also not have a kind of control method can satisfy requirement recited above at present the DC side controller.

Summary of the invention

At the problems referred to above, the DC side voltage control method that the purpose of this invention is to provide a kind of three-phase four-arm Active Power Filter-APF, it can solve conventional PI and be controlled at not good problem on the control effect, also has the advantages such as harmful effect that response is fast, robustness is strong, can remove the internal ring of outer shroud.

The DC side voltage control method of a kind of three-phase four-arm Active Power Filter-APF provided by the invention, adopt following technical scheme:

1) during the line voltage balance, for the simplification problem, ignore the loss of APF AC side inductance and the various losses that current transformer self produces, then the AC side instantaneous power equates with the DC side instantaneous power.Set up the state-space model of three-phase four-arm APF under the dq0 coordinate in view of the above

Wherein A and B are coefficient matrix, and x is by 3 offset current i under the dq0 coordinate _Cd, i _Cq, i _C0And APF dc voltage u _DcThe state vector that constitutes, u is the dominant vector under the dq0 coordinate.

2) with d axle controlled quentity controlled variable control dc voltage u _Dc, q axle and 0 controlled quentity controlled variable control ac output current i _Cd, i _Cq, i _C0, choose q axle output current i _Cq, 0 spool output current i _C0With dc voltage u _DcBe system's output.

3) definition error vector e=[e ₁, e ₂, e ₃, e ₄], e wherein ₃And e ₄Be respectively dc voltage u _DcAnd derivative

Error.

4), select sliding-mode surface S according to sliding mode control theory ₁, S ₂, S ₃, S wherein ₃=e ₃+ β e ₄=0, β releases the command value of d shaft current greater than 0 constant

5) under the dq0 coordinate, the d axle offset current i of APF _CdDC component represent the fundamental positive sequence active current, die and derived In with q axle and 0 relevant amount, obtain new d axle instruction current

Draw with harmonics detection circuit Addition is as total d axle reference current.

6) in order further to reduce the direct voltage static difference, at sliding-mode surface S ₃The middle integral of introducing.

The present invention can also do following improvement: when line voltage or laod unbalance, the controller of above-mentioned steps design is made amendment, increase by two filters on former controller basis.The one, for filtering

In the trapper of 2 subharmonic, trap frequency is taken as 100Hz; Another is filtering dc voltage u _DcThe low pass filter of the contained harmonic wave of measured value, its cut-off frequency is taken as 40Hz.

Compared with prior art, beneficial effect of the present invention is:

1) the present invention inherits the advantage of Sliding-Mode Control Based, and voltage controller has characteristics such as response is fast, robustness is stronger.

2) the present invention does not relate to complex calculation, is easy to realize fast operation with digital signal processor.

APF DC side current i when 3) the present invention can avoid line voltage or laod unbalance _Dc6 integral multiple characteristic harmonics and 2,4,8 of contained 6,12,18 grades, the non-feature subharmonic of 10 grades are to the output of voltage controller

Influence.Negative sequence component contained when particularly avoiding unbalanced source voltage is at d axle PCC voltage

2 subharmonic of middle performance cause

Distortion.

Description of drawings

Fig. 1 is the topological structure of parallel connection type three-phase four-arm Active Power Filter-APF.

DC voltage control block diagram when Fig. 2 is line voltage and load balance.

DC voltage control block diagram when Fig. 3 is line voltage or laod unbalance.

Embodiment

Below in conjunction with accompanying drawing patent of the present invention is described further, but does not constitute any limitation of the invention.

Embodiment 1

U among Fig. 1 _sBe grid side voltage, L _s, R _sBe electrical network inductance and resistance, i _sBe current on line side, i _LBe load current, 8 electronic power switches constitute three-phase four-arm APF, L and L _nBe interface inductance, i _cBe the offset current of APF output,

Be points of common connection (PCC) voltage, C is a dc bus capacitor, u _DcBe dc voltage.

Four brachium pontis APF are typical multiple-input and multiple-output coupling nonlinear systems, contain the product of state variable and control variables.For the simplification problem, ignore the loss of AC side inductance and the own loss of four brachium pontis current transformers, then the AC side instantaneous power equates with the DC side instantaneous power, that is:

$u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0}=u_{\mathrm{dc}}C\frac{d{u}_{\mathrm{dc}}}{\mathrm{dt}}---\left(1\right)$

Wherein

Be the PCC voltage under the dq0 coordinate, i _Cd, i _Cq, i _C0Be the APF offset current under the dq0 coordinate.According to Fig. 1 and convolution (1), can write out the state-space model of three-phase four-arm APF:

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{cd}}\\ {\stackrel{\·}{i}}_{\mathrm{cq}}\\ {\stackrel{\·}{i}}_{c0}\\ {\stackrel{\·}{u}}_{\mathrm{dc}}\end{array}\right]=\left[\begin{array}{cccc}-\frac{R}{L}& \mathrm{\ω}& 0& \frac{d_d}{L}\\ -\mathrm{\ω}& -\frac{R}{L}& 0& \frac{d_q}{L}\\ 0& 0& -\frac{R+3R_n}{L+3L_n}& \frac{d_0}{L+3L_n}\\ \frac{u_{\mathrm{sd}}}{{\mathrm{Cu}}_{\mathrm{dc}}}& \frac{u_{\mathrm{sq}}}{{\mathrm{Cu}}_{\mathrm{dc}}}& \frac{u_{s0}}{{\mathrm{Cu}}_{\mathrm{dc}}}& 0\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{cd}}\\ i_{\mathrm{cq}}\\ i_{c0}\\ u_{\mathrm{dc}}\end{array}\right]+\left[\begin{array}{cccc}-\frac{1}{L}& 0& 0& 0\\ 0& -\frac{1}{L}& 0& 0\\ 0& 0& -\frac{1}{L+3L_n}& 0\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{sd}}^{\′}\\ u_{\mathrm{sq}}^{\′}\\ u_{s0}^{\′}\\ 0\end{array}\right]---\left(2\right)$

From formula (2) as can be seen, there are 3 controlled quentity controlled variables, d in system _dOne is used for controlling dc voltage u _Dc, d _qAnd d ₀Be used for controlling output current, so choose i _Cq, i _C0, u _DcBe system's output.According to the definition on relative rank, because i _CqAnd i _C0First derivative contained input variable d _qAnd d ₀So their relative rank are 1; And u _DcSecond dervative just contain input variable d _d, its relative rank are 2.The total relative rank of system are 4, equal system's exponent number, so system equation formula (2) can be rewritten as formula (3) once more.

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{cq}}\\ {\stackrel{\·}{i}}_{c0}\\ {\stackrel{\·}{u}}_{\mathrm{dc}}\\ {\stackrel{\·\·}{u}}_{\mathrm{cd}}\end{array}\right]=\left[\begin{array}{c}-\mathrm{\ω}{i}_{\mathrm{cd}}-\frac{R}{L}{i}_{\mathrm{cq}}+\frac{d_q}{L}{u}_{\mathrm{dc}}-\frac{u_{\mathrm{sq}}^{\′}}{L}\\ -\frac{R+3R_n}{L+3L_n}{i}_{c0}+\frac{d_0}{L+3L_n}{u}_{\mathrm{dc}}-\frac{u_{s0}^{\′}}{L+3L_n}\\ \frac{u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0}}{{\mathrm{Cu}}_{\mathrm{dc}}}\\ -\frac{{(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})}^2}{C^2{u}_{\mathrm{dc}}^3}-\\ \frac{R{(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}})}^2+{\left(u_{\mathrm{sd}}^{\′}\right)}^2+{\left(u_{\mathrm{sq}}^{\′}\right)}^2-\mathrm{\ωL}(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cq}}-u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cd}})}{L{\mathrm{Cu}}_{\mathrm{dc}}}\\ \frac{(R+3R_n)u_{s0}^{\′}{i}_{c0}+{\left(u_{s0}^{\′}\right)}^2}{(L+3L_n){\mathrm{Cu}}_{\mathrm{dc}}}+\frac{u_{\mathrm{sd}}^{\′}{d}_d+u_{\mathrm{sq}}^{\′}{d}_q}{\mathrm{LC}}+\frac{u_{s0}^{\′}{d}_0}{(L+3L_n)C}\end{array}\right]---\left(3\right)$

The definition error vector

I wherein _Cq ^*, i _C0 ^*, u _Dc ^*Be respectively the command value of q shaft current, 0 shaft current, dc voltage.Obvious e ₁And e ₂Rank are 1 relatively, e ₃Rank are 2 relatively, according to sliding mode control theory, can select sliding-mode surface to be:

S ₁＝k ₁e ₁＝0 (4)

S ₂＝k ₂e ₂＝0 (5)

S ₃＝k ₃e ₃+k ₄e ₄＝e ₃+βe ₄＝0 (6)

β＞0 wherein.With the 4th formula substitution formula (6) of formula (2):

$S_3=(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})-\mathrm{\β}{\stackrel{\·}{u}}_{\mathrm{dc}}^{*}=0---\left(7\right)$

Further can be write as:

$S_3=\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}[(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})-\mathrm{\β}{\stackrel{\·}{u}}_{\mathrm{dc}}^{*}]+i_{\mathrm{cd}}=0---\left(8\right)$

If definition:

$i_{\mathrm{cd}}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}[(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})-\mathrm{\β}{\stackrel{\·}{u}}_{\mathrm{dc}}^{*}]---\left(9\right)$

Wherein

Be the command value of dc voltage, be constant, its derivative

Be 0, so following formula can be reduced to:

$i_{\mathrm{cd}}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}[(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})]---\left(10\right)$

In APF, dc voltage comprises DC component

And alternating current component

The mean value of expression dc voltage in a power frequency period, because the APF system can produce active loss,

Can fluctuate, this fluctuation has reflected the meritorious of APF and electrical network exchange, so should add first-harmonic gain merit and compensate active loss in direct current.Under the dq0 coordinate, APF offset current i _CdDC component represent the fundamental positive sequence active current, so should remove q axle and 0 relevant amount in the formula (10), and be rewritten as:

$i_{\mathrm{cd}1}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})---\left(11\right)$

Following formula is the control law of Voltage loop, its output

Draw with harmonics detection circuit

Addition, common reference current as the d axle.

In order further to reduce the static difference of direct voltage, at sliding-mode surface S ₃The middle integral of introducing, its expression formula becomes:

S ₃＝β ₁∫e ₃dt+e ₃+β ₂e ₄＝0 (12)

β wherein ₁And β ₂All greater than 0. Expression formula also becomes:

$i_{\mathrm{cd}1}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{{\mathrm{\β}}_2{u}_{\mathrm{sd}}^{\′}}[{\mathrm{\β}}_1\∫(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})\mathrm{dt}+(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})]---\left(13\right)$

In this up-to-date style

If also balance of load, then the control block diagram of Voltage loop as shown in Figure 2, the amplitude limit link among the figure is exported when APF starts

Excessive.

Embodiment 2

U among Fig. 1 _sBe grid side voltage, L _s, R _sBe electrical network inductance and resistance, i _sBe current on line side, i _LBe load current, 8 electronic power switches constitute three-phase four-arm APF, L and L _nBe interface inductance, i _cBe the offset current of APF output, Be points of common connection (PCC) voltage, C is a dc bus capacitor, u _DcBe dc voltage.

Four brachium pontis APF are typical multiple-input and multiple-output coupling nonlinear systems, contain the product of state variable and control variables.For the simplification problem, ignore the loss of AC side inductance and the own loss of four brachium pontis current transformers, then the AC side instantaneous power equates with the DC side instantaneous power, that is:

$u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0}=u_{\mathrm{dc}}C\frac{{\mathrm{du}}_{\mathrm{dc}}}{\mathrm{dt}}---\left(1\right)$

Wherein

Be the PCC voltage under the dq0 coordinate, i _Cd, i _Cq, i _C0Be the APF offset current under the dq0 coordinate.According to Fig. 1 and convolution (1), can write out the state-space model of three-phase four-arm APF:

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{cd}}\\ {\stackrel{\·}{i}}_{\mathrm{cq}}\\ {\stackrel{\·}{i}}_{c0}\\ {\stackrel{\·}{u}}_{\mathrm{dc}}\end{array}\right]=\left[\begin{array}{cccc}-\frac{R}{L}& \mathrm{\ω}& 0& \frac{d_d}{L}\\ -\mathrm{\ω}& -\frac{R}{L}& 0& \frac{d_q}{L}\\ 0& 0& -\frac{R+3R_n}{L+3L_n}& \frac{d_0}{L+3L_n}\\ \frac{u_{\mathrm{sd}}}{{\mathrm{Cu}}_{\mathrm{dc}}}& \frac{u_{\mathrm{sq}}}{{\mathrm{Cu}}_{\mathrm{dc}}}& \frac{u_{s0}}{{\mathrm{Cu}}_{\mathrm{dc}}}& 0\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{cd}}\\ i_{\mathrm{cq}}\\ i_{c0}\\ u_{\mathrm{dc}}\end{array}\right]+\left[\begin{array}{cccc}-\frac{1}{L}& 0& 0& 0\\ 0& -\frac{1}{L}& 0& 0\\ 0& 0& -\frac{1}{L+3L_n}& 0\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{sd}}^{\′}\\ u_{\mathrm{sq}}^{\′}\\ u_{s0}^{\′}\\ 0\end{array}\right]---\left(2\right)$

From formula (2) as can be seen, there are 3 controlled quentity controlled variables, d in system _dOne is used for controlling dc voltage u _Dc, d _qAnd d ₀Be used for controlling output current, so choose i _Cq, i _C0, u _DcBe system's output.According to the definition on relative rank, because i _CqAnd i _C0First derivative contained input variable d _qAnd d ₀So their relative rank are 1; And u _DcSecond dervative just contain input variable d _d, its relative rank are 2.The total relative rank of system are 4, equal system's exponent number, so system equation formula (2) can be rewritten as formula (3) once more.

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{cq}}\\ {\stackrel{\·}{i}}_{c0}\\ {\stackrel{\·}{u}}_{\mathrm{dc}}\\ {\stackrel{\·\·}{u}}_{\mathrm{cd}}\end{array}\right]=\left[\begin{array}{c}-\mathrm{\ω}{i}_{\mathrm{cd}}-\frac{R}{L}{i}_{\mathrm{cq}}+\frac{d_q}{L}{u}_{\mathrm{dc}}-\frac{u_{\mathrm{sq}}^{\′}}{L}\\ -\frac{R+3R_n}{L+3L_n}{i}_{c0}+\frac{d_0}{L+3L_n}{u}_{\mathrm{dc}}-\frac{u_{s0}^{\′}}{L+3L_n}\\ \frac{u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0}}{{\mathrm{Cu}}_{\mathrm{dc}}}\\ -\frac{{(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})}^2}{C^2{u}_{\mathrm{dc}}^3}-\\ \frac{R{(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}})}^2+{\left(u_{\mathrm{sd}}^{\′}\right)}^2+{\left(u_{\mathrm{sq}}^{\′}\right)}^2-\mathrm{\ωL}(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cq}}-u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cd}})}{L{\mathrm{Cu}}_{\mathrm{dc}}}\\ \frac{(R+3R_n)u_{s0}^{\′}{i}_{c0}+{\left(u_{s0}^{\′}\right)}^2}{(L+3L_n){\mathrm{Cu}}_{\mathrm{dc}}}+\frac{u_{\mathrm{sd}}^{\′}{d}_d+u_{\mathrm{sq}}^{\′}{d}_q}{\mathrm{LC}}+\frac{u_{s0}^{\′}{d}_0}{(L+3L_n)C}\end{array}\right]---\left(3\right)$

The definition error vector I wherein _Cq ^*, i _C0 ^*, u _Dc ^*Be respectively the command value of q shaft current, 0 shaft current, dc voltage.Obvious e ₁And e ₂Rank are 1 relatively, e ₃Rank are 2 relatively, according to sliding mode control theory, can select sliding-mode surface to be:

S ₁＝k ₁e ₁＝0 (4)

S ₂＝k ₂e ₂＝0 (5)

S ₃＝k ₃e ₃+k ₄e ₄＝e ₃+βe ₄＝0 (6)

β＞0 wherein.With the 4th formula substitution formula (6) of formula (2):

$S_3=(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sd}}^{\′}{i}_{\mathrm{cd}}+u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})-\mathrm{\β}{\stackrel{\·}{u}}_{\mathrm{dc}}^{*}=0---\left(7\right)$

Further can be write as:

$S_3=\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}[(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})-\mathrm{\β}{\stackrel{\·}{u}}_{\mathrm{dc}}^{*}]+i_{\mathrm{cd}}=0---\left(8\right)$

If definition:

$i_{\mathrm{cd}}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}[(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})-\mathrm{\β}{\stackrel{\·}{u}}_{\mathrm{dc}}^{*}]---\left(9\right)$

Wherein

Be the command value of dc voltage, be constant, its derivative

Be 0, so following formula can be reduced to:

$i_{\mathrm{cd}}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}[(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})+\frac{\mathrm{\β}}{{\mathrm{Cu}}_{\mathrm{dc}}}(u_{\mathrm{sq}}^{\′}{i}_{\mathrm{cq}}+u_{s0}^{\′}{i}_{c0})]---\left(10\right)$

In APF, dc voltage comprises DC component

And alternating current component

The mean value of expression dc voltage in a power frequency period, because the APF system can produce active loss,

Can fluctuate, this fluctuation has reflected the meritorious of APF and electrical network exchange, so should add first-harmonic gain merit and compensate active loss in direct current.Under the dq0 coordinate, APF offset current i _CdDC component represent the fundamental positive sequence active current, so should remove q axle and 0 relevant amount in the formula (10), and be rewritten as:

$i_{\mathrm{cd}1}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{\mathrm{\β}{u}_{\mathrm{sd}}^{\′}}(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})---\left(11\right)$

Following formula is the control law of Voltage loop, its output

Draw with harmonics detection circuit

Addition, common reference current as the d axle.

In order further to reduce the static difference of direct voltage, at sliding-mode surface S ₃The middle integral of introducing, its expression formula becomes:

S ₃＝β ₁∫e ₃dt+e ₃+β ₂e ₄＝0 (12)

β wherein ₁And β ₂All greater than 0.

Expression formula also becomes:

$i_{\mathrm{cd}1}^{*}=-\frac{{\mathrm{Cu}}_{\mathrm{dc}}}{{\mathrm{\β}}_2{u}_{\mathrm{sd}}^{\′}}[{\mathrm{\β}}_1\∫(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})\mathrm{dt}+(u_{\mathrm{dc}}-u_{\mathrm{dc}}^{*})]---\left(13\right)$

In this up-to-date style

If also balance of load, then the control block diagram of Voltage loop as shown in Figure 2, the amplitude limit link among the figure is exported when APF starts

Excessive.

If only consider positive and negative, the zero sequence fundametal compoment of line voltage, the DC side current i _DcCan turn to:

$i_{\mathrm{dc}}\left(t\right)=\frac{\left[C_{23}R\left(\mathrm{\θ}\right)\left[\begin{array}{c}{u}_{\mathrm{sd}}^{\′}\\ u_{\mathrm{sq}}^{\′}\end{array}\right]\right]\left[\underset{m\≠0}{\overset{\∞}{\underset{m=-\∞}{\mathrm{\Σ}}}}{C}_{23}R\left(\mathrm{m\θ}\right)\left[\begin{array}{c}{i}_{\mathrm{cd}}\left(m\right)\\ i_{\mathrm{cq}}\left(m\right)\end{array}\right]\right]+\frac{1}{2}{u}_{s0}^{\′}\underset{m=1}{\overset{\∞}{\mathrm{\Σ}}}{i}_{c0}\left(m\right)}{u_{\mathrm{dc}}}---\left(14\right)$

C wherein ₂₃Be the static coordinate transformation matrix, R (θ) and R (m θ) are positive sequence rotational coordinates matrix.Formula (14) illustrates that when three phase network or laod unbalance, the integral multiple characteristic harmonics and 2,4,8 of 6,12,18 grades 6, the uncharacteristic harmonics of 10 grades can appear in the DC side of APF, make dc voltage also contain harmonic wave.The harmonic wave of DC side can make the output of voltage controller

Contain harmonic wave, thereby influence the waveform of APF output current.2 subharmonic voltages in the dc voltage can produce 3 subharmonic currents in output current.Further, DC side nth harmonic voltage can produce the n+1 subharmonic current.

According to above-mentioned analysis,, then can make the current compensation deleterious if when electrical network or laod unbalance, still adopt the voltage controller of Fig. 2.

In order to obtain perfect compensation effect when the imbalance, voltage controller is made amendment, on former controller basis, increase by two filters.The one, for filtering

In the trapper of 2 subharmonic, trap frequency is taken as 100Hz; Another is filtering dc voltage u _DcThe low pass filter of the contained harmonic wave of measured value, its cut-off frequency is taken as 40Hz.As shown in Figure 3.Will

With tested u _DcIn harmonic filtration after, though u _DcStill contain than multiple-harmonic, but Distortion very little, making the current on line side after the APF compensation is desirable sine wave.

The above embodiments only are the preferred embodiments of the present invention, can not limit interest field of the present invention with this, and therefore, the equivalent variations according to the present patent application claim is done still belongs to the scope that the present invention is contained.

Claims (2)

1. the DC side voltage control method of a three-phase four-arm Active Power Filter-APF is characterized in that, in turn includes the following steps:

1) during the line voltage balance, ignore the loss of APF AC side inductance and the various losses that current transformer self produces, then the AC side instantaneous power equates with the DC side instantaneous power; Set up the state-space model of three-phase four-arm APF under the dq0 coordinate in view of the above

Wherein A and B are coefficient matrix, and x is by 3 offset current i under the dq0 coordinate _Cd, i _Cq, i _C0And APF dc voltage u _DcThe state vector that constitutes, u is the dominant vector under the dq0 coordinate;

2) with d axle controlled quentity controlled variable control dc voltage u _Dc, q axle and 0 controlled quentity controlled variable control ac output current i _Cd, i _Cq, i _C0, choose q axle output current i _Cq, 0 spool output current i _C0With dc voltage u _DcBe system's output;

3) definition error vector e=[e ₁, e ₂, e ₃, e ₄], e wherein ₃And e ₄Be respectively dc voltage u _DcAnd derivative

Error;

4), select sliding-mode surface S according to sliding mode control theory ₁, S ₂, S ₃, S wherein ₃=e ₃+ β e ₄=0, β releases the command value of d shaft current greater than 0 constant

5) under the dq0 coordinate, the d axle offset current i of APF _CdDC component represent the fundamental positive sequence active current, die and derived

In with q axle and 0 relevant amount, obtain new d axle instruction current

Draw with harmonics detection circuit

Addition is as total d axle reference current;

6) at sliding-mode surface S ₃The middle integral of introducing.

2. the DC side voltage control method of a kind of three-phase four-arm Active Power Filter-APF according to claim 1 is characterized in that: when line voltage or laod unbalance, increase by two filters on former controller basis; One is for filtering

In the trapper of 2 subharmonic, trap frequency is taken as 100Hz; Another is filtering dc voltage u _DcThe low pass filter of the contained harmonic wave of measured value, its cut-off frequency is taken as 40Hz.

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