CN106059433A - Train set traction converter non-beat frequency control strategy - Google Patents

Abstract

The invention provides a train set traction converter non-beat frequency control strategy. Through carrying out mathematical modeling on a transmission system, a relationship between a motor beat frequency torque and motor beat frequency current and pulsating DC voltage is obtained, and on the basis, a train set traction converter non-beat frequency control strategy is provided. Through adding a compensation link, a non-beat frequency controller is arranged, the motor rotating-speed difference frequency is corrected according to the pulsating DC voltage, and the motor beat frequency torque and the beat frequency current caused by the pulsating DC voltage are eliminated. The control performance of the controller in a digital system depends on a discretization method. Discretization processing is carried out on the controller, and the optimal discretization method is obtained.

Description

A kind of traction converter of motor train unit is without beat frequency control strategy

Technical field

The present invention relates to motor train unit traction system, particularly relate to a kind of traction converter of motor train unit without beat frequency control strategy.

Background technology

Traction convertor is the core of motor train unit transmission system system, is the power resources of EMUs vehicle.At motor train unit train In, owing to using single phase ac contact net 1 powering mode, traction drive many employings Single-phase PWM Rectifier 2 and three-phase PWM The topology of inverter 4, as shown in Figure 1.Due to the introducing of single-phase four-quadrant rectifier 2, there are two frequency multiplication pulsation electricity in dc bus Pressure component, this pulsating volage can cause the pulsation of motor side torque and electric current, i.e. beat frequency phenomenon.

In tradition traction converter of motor train unit, eliminate by increasing bulky bis-resonance filters 3 of hardware LC Two frequency multiplication pulsating volage components, which increase weight and the cost of trailer system, and the introducing of non-linear element simultaneously also brings Unstable factor.In order to cancel bulky hardware filter, the present invention passes through a kind of traction converter of motor train unit without beat frequency Beat frequency phenomenon is suppressed by control strategy.

Summary of the invention

The present invention provides a kind of traction converter of motor train unit without beat frequency control strategy, reaches to suppress the purpose of beat frequency phenomenon, To remove hardware resonance filter, reduce weight and the cost, beneficially light-weight design of traction convertor.

For achieving the above object, the technical solution used in the present invention is:

On the basis of summing up former achievements, traction drive is carried out mathematical modeling, under frequency domain, it is entered Row is analyzed, and proposes to be applicable to the control strategy without beat frequency of rotor flux-orientation vector control system.The method is with DC voltage arteries and veins Dynamic component is input, and the sampling precision of DC voltage ripple component directly affects compensation effect, and therefore the present invention is first to employing Traditional pulsating volage sampling that backward Euler is discrete is optimized accurately to obtain flutter component, then carries out discrete to controller Change processes, and carries out detailed comparisons from discrete precision, control performance and Digital Implementation complexity, draws for controller of the present invention Grid optimization method.

A kind of traction converter of motor train unit, without beat frequency control strategy, comprises the following steps:

(1) it is derived by pulsating dc voltage expression formula according to commutator input-output power balance:

$u_{dc}^{\mathrm{\Δ}}=\frac{I_{dc}sin(2{\mathrm{\ω}}_{grid}t+\mathrm{\φ})}{2{\mathrm{\ω}}_{grid}C\cos \mathrm{\φ}}---\left(1\right)$

Wherein, I_dcFor DC side steady-state current component, C is DC bus capacitor,For pulsating dc voltage, ω_gridFor electricity Net angular frequency, φ is rectifier power factor angle, and t is time variable.

It will be seen that pulsating dc voltage frequency is mains frequency 2 times, amplitude and traction power, DC capacitor size And rectifier power factor is relevant.

Use series connection high and low pass filter that pulsating dc voltage is filtered obtaining flutter component, and apply amplitude, Phase compensation and discretization error compensate accurately samples to pulsating dc voltage.

(2) according to motor beat frequency small-signal model, it is derived by beat frequency current increment under d-q coordinate system and increases with beat frequency voltage Amount and the relation of slip frequency increment:

$\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\\ I_{rd}^{\mathrm{\Δ}}\\ I_{rq}^{\mathrm{\Δ}}\end{array}\right]={\[Z\left(s\right)\]}^{-1}B\left[\begin{array}{c}{V}_{sd}^{\mathrm{\Δ}}\\ V_{sq}^{\mathrm{\Δ}}\end{array}\right]---\left(2\right)$

$\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\\ I_{rd}^{\mathrm{\Δ}}\\ I_{rq}^{\mathrm{\Δ}}\end{array}\right]=2\mathrm{\π}{\[Z\left(s\right)\]}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]f_{sl}^{\mathrm{\Δ}}---\left(3\right)$

Its Chinese style (2) is the relation of beat frequency current increment and beat frequency voltage increment, and formula (3) is beat frequency current increment and slip The relation of frequency increment.

WhereinWithFor motor stator d, q shaft current flutter component, I_sd0And I_sq0For motor stator d, q shaft current stable state Component, whereinWithFor rotor d, q shaft current flutter component, I_rd0And I_rq0Divide for rotor d, q shaft current stable state Amount,WithFor motor stator d, q shaft voltage flutter component,For motor slip frequency flutter component, Z (s) and B is square Battle array；

(3) beat frequency phenomenon is modeled:

According to motor torque expression formula (23) and beat frequency small-signal model, obtain beat frequency torque about pulsating dc voltage Transmission function expression:

$G_{T_{e}u}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=\frac{3m}{\mathrm{\π}}{\mathrm{pL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T{\[Z\left(s\right)\]}^{-1}B\left[\begin{array}{c}cos\mathrm{\φ}\\ sin\mathrm{\φ}\end{array}\right]---\left(4\right)$

Wherein m is modulation depth, and p is motor number of pole-pairs, L_mFor magnetizing inductance.

Expressed formula (24) and beat frequency small-signal model by current of electric, obtain the beat frequency electric current biography about pulsating dc voltage Delivery function expression formula:

$G_{Iu}\left(s\right)=\frac{I^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=\frac{2m}{{\mathrm{\πI}}_0}{\left[\begin{array}{c}{I}_{sd0}\\ I_{sq0}\end{array}\right]}^T{\[Z\left(s\right)\]}_{2\×4}^{-1}B\left[\begin{array}{c}cos\mathrm{\φ}\\ sin\mathrm{\φ}\end{array}\right]---\left(5\right)$

(4) to step (3) institute established model at ripple frequency point ω_ripplePlace carries out spectrum analysis, obtains amplitude/phase characteristic curves (as shown in Figures 2 and 3).It is analyzed amplitude/phase characteristic curves obtaining, when system operating frequency is at ripple frequency point ω_ripple Time, beat frequency torque and beat frequency current amplitude gain all reach maximum.

(5) beat frequency torque and beat frequency electric current are as follows about the transmission function of slip frequency increment:

$G_{T_{e}f}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{f_{el}^{\mathrm{\Δ}}}=3{\mathrm{\πpL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T{\[Z\left(s\right)\]}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]---\left(6\right)$

$G_{If}\left(s\right)=\frac{I^{\mathrm{\Δ}}}{f_{sl}^{\mathrm{\Δ}}}=\frac{2\mathrm{\π}}{I_0}{\left[\begin{array}{c}{I}_{sd0}\\ I_{sq0}\end{array}\right]}^T{\[Z\left(s\right)\]}_{2\×4}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]---\left(7\right)$

Its Chinese style (6) is the transmission function of beat frequency torque and slip frequency increment, and formula (7) is beat frequency electric current and slip frequency The transmission function of increment.

(6) according to shown in Fig. 4 without beat frequency control block diagram, after overcompensation, beat frequency torque and beat frequency electric current are about arteries and veins The transmission function expression of dynamic DC voltage becomes:

$G_{T_e}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=G_c\left(s\right)G_{T_{e}f}\left(s\right)+G_{T_{e}u}\left(s\right)---\left(8\right)$

$G_I\left(s\right)=\frac{I^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=G_c\left(s\right)G_{If}\left(s\right)+G_{Iu}\left(s\right)---\left(9\right)$

Its Chinese style (8) is the transmission function of beat frequency torque and DC pulse moving voltage, and formula (9) is beat frequency electric current and DC pulse The transmission function of voltage.

(7) based on analyzing above, beat frequency phenomenon is at ripple frequency point ω_ripplePlace is the most serious, so that ripple frequency Point ω_rippleBeat frequency torque and the beat frequency electric current at place are the least, arrange without beat frequency controller G_cS the expression formula of () is:

$G_c\left(s\right)=K\frac{{\mathrm{s\ω}}_{ripple}}{{(s+{\mathrm{\ω}}_{ripple})}^2}---\left(10\right)$

Determine that the parameter without beat frequency controller, the ideal values of penalty coefficient K should make beat frequency torque and beat frequency electric current Transmission function amplitude gain all minimizes, and is compensated coefficient, level angle and the increasing of beat frequency torque amplitude through simulation calculation The relation of benefit, and the relation (see Fig. 5 and Fig. 6) of penalty coefficient, level angle and beat frequency current amplitude gain, determine compensation system Number K=0.134.

(8) controller control performance in digital display circuit depends on discretization method；By discretization method is carried out Analyze, select discretization precision high, and be prone to the Bilinear transformation method TUS discretization method as controller of Digital Implementation, Controller is carried out sliding-model control.

On the basis of such scheme, the matrix B described in step (2) is:

$B=\left[\begin{array}{cc}\frac{1}{L_s\mathrm{\σ}}& 0\\ 0& \frac{1}{L_s\mathrm{\σ}}\\ -\frac{L_m}{L_r{L}_s\mathrm{\σ}}& 0\\ 0& -\frac{L_m}{L_r{L}_s\mathrm{\σ}}\end{array}\right]---\left(19\right)$

On the basis of such scheme, matrix Z (s) described in step (2) is:

$Z\left(s\right)=\left[\begin{array}{cccc}s+\frac{R_s}{L_s\mathrm{\σ}}& -\frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}-{\mathrm{\ω}}_{sl}& -\frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}\\ \frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& s+\frac{R_s}{L_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}& -\frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}\\ -\frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& s+\frac{R_r}{L_r\mathrm{\σ}}& \frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}-{\mathrm{\ω}}_{sl}\\ -\frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& -\frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& s+\frac{R_r}{L_r\mathrm{\σ}}\end{array}\right]---\left(21\right)$

On the basis of such scheme, the motor torque expression formula described in step (3) is:

$T_e^{\mathrm{\Δ}}=\frac{3}{2}{\mathrm{pL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T\left[\begin{array}{c}{i}_{sd}^{\mathrm{\Δ}}\\ i_{sq}^{\mathrm{\Δ}}\\ i_{rd}^{\mathrm{\Δ}}\\ i_{rq}^{\mathrm{\Δ}}\end{array}\right]---\left(23\right)$

On the basis of such scheme as, current of electric being write the form of steady-state component and flutter component, both sides square are again Carry out abbreviation and obtain current of electric described in step (3) and express formula be:

I=I₀+I^△ (24)

Compared with prior art, one traction converter of motor train unit of the present invention is without beat frequency control strategy, and had is useful Effect is:

The present invention provides a kind of traction converter of motor train unit without beat frequency control strategy, utilizes software approach to reach to suppress beat frequency The purpose of phenomenon, to remove hardware resonance filter, reduces current transformer weight and cost, beneficially light-weight design.

Accompanying drawing explanation

Fig. 1 is EMUs traction drive canonical topologies；

The beat frequency torque that Fig. 2 provides for the present invention is about the amplitude/phase characteristic curves of pulsating dc voltage；

The beat frequency electric current that Fig. 3 provides for the present invention is about the amplitude/phase characteristic curves of pulsating dc voltage；

The control block diagram without beat frequency that Fig. 4 provides for the present invention；

The relation of penalty coefficient that Fig. 5 provides for the present invention and level angle and beat frequency torque amplitude gain；

The relation of penalty coefficient that Fig. 6 provides for the present invention and level angle and beat frequency current amplitude gain；

After the compensation that Fig. 7 provides for the present invention, beat frequency torque is about the amplitude-versus-frequency curve of pulsating dc voltage；

After the compensation that Fig. 8 provides for the present invention, beat frequency electric current is about the amplitude-versus-frequency curve of pulsating dc voltage.

Detailed description of the invention

The present invention is described further below in conjunction with the accompanying drawings.

(1) derivation to pulsating dc voltage.Fig. 1 is EMUs traction drive canonical topologies, defines impulse commutation Device 2 instantaneous input voltage, electric current are as follows:

$u_s=\sqrt{2}{U}_{s}cos\left({\mathrm{\ω}}_{grid}t\right)---\left(11\right)$

$i_s=\sqrt{2}{I}_{s}cos({\mathrm{\ω}}_{grid}t+\mathrm{\φ})---\left(12\right)$

Utilize trigonometric function simplification of a formula can obtain commutator input power:

P_i=u_si_s=U_sI_scosφ+U_sI_scos(2ω_gridt+φ) (13)

Wherein, U_sAnd I_sIt is respectively input voltage, current effective value, ω_gridFor electrical network angular frequency, φ is rectifier power Factor angle.

Definition commutator output:

$P_o=U_{dc}{I}_{dc}+{\mathrm{CU}}_{dc}\frac{{\mathrm{du}}_{dc}^{\mathrm{\Δ}}}{dt}---\left(14\right)$

Wherein, U_dcAnd I_dcFor DC side steady state voltage, current component, C is DC bus capacitor,For pulsating dc voltage. In order to obtain pulsating dc voltage expression formula, it is assumed that commutator input-output power is equal, i.e. formula (13) and (14) are equal, push away Lead and obtain:

$u_{dc}^{\mathrm{\Δ}}=\frac{I_{dc}sin(2{\mathrm{\ω}}_{grid}t+\mathrm{\φ})}{2{\mathrm{\ω}}_{grid}C\cos \mathrm{\φ}}---\left(1\right)$

It will be seen that pulsating dc voltage frequency is mains frequency 2 times, amplitude and traction power, DC capacitor size And rectifier power factor is relevant.

(2) motor beat frequency small-signal model is derived.

Can be obtained by the electric moter voltage under biphase rotating coordinate system and flux linkage equations:

$\left[\begin{array}{c}{V}_{sd}\\ V_{sq}\\ 0\\ 0\end{array}\right]=\[Z_1\left(s\right)\]\left[\begin{array}{c}{I}_{sd}\\ I_{sq}\\ I_{rd}\\ I_{rq}\end{array}\right]---\left(15\right)$

Wherein,

$Z_1\left(s\right)=\left[\begin{array}{cccc}{R}_s+{\mathrm{sL}}_s& -{\mathrm{\ω}}_e{L}_s& {\mathrm{sL}}_m& -{\mathrm{\ω}}_e{L}_m\\ {\mathrm{\ω}}_e{L}_s& R_S+{\mathrm{sL}}_s& {\mathrm{\ω}}_e{L}_m& {\mathrm{sL}}_m\\ {\mathrm{sL}}_m& -{\mathrm{\ω}}_{sl}{L}_m& R_r+{\mathrm{sL}}_r& -{\mathrm{\ω}}_{sl}{L}_r\\ {\mathrm{\ω}}_{sl}{L}_m& {\mathrm{sL}}_m& {\mathrm{\ω}}_{sl}{L}_r& R_r+{\mathrm{sL}}_r\end{array}\right]---\left(16\right)$

R_sAnd R_rIt is respectively fixed rotor resistance, L_sAnd L_rIt is respectively rotor inductance, L_mFor magnetizing inductance, ω_eFor stator angle Frequency, ω_slFor slip angular frequency, I_sdAnd I_sqFor motor stator d, q shaft current, I_rdAnd I_rqFor rotor d, q shaft current.

By Z in formula (16)₁Battle array splits into containing differential term with without two parts of differential term, and carries out abbreviation and obtain:

$s\left[\begin{array}{c}{I}_{sd}\\ I_{sq}\\ I_{rd}\\ I_{rq}\end{array}\right]=A\left[\begin{array}{c}{I}_{sd}\\ I_{sq}\\ I_{rd}\\ I_{rq}\end{array}\right]+B\left[\begin{array}{c}{V}_{sd}\\ V_{sq}\end{array}\right]---\left(17\right)$

Wherein,

$A=\left[\begin{array}{cccc}-\frac{R_s}{L_s\mathrm{\σ}}& \frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& \frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}\\ -\frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}-{\mathrm{\ω}}_{sl}& -\frac{R_s}{L_s\mathrm{\σ}}& -\frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}& \frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}\\ \frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& -\frac{R_r}{L_r\mathrm{\σ}}& -\frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}+{\mathrm{\ω}}_{sl}\\ \frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& \frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& \frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}-{\mathrm{\ω}}_{sl}& -\frac{R_r}{L_r\mathrm{\σ}}\end{array}\right]---\left(18\right)$

$B=\left[\begin{array}{cc}\frac{1}{L_s\mathrm{\σ}}& 0\\ 0& \frac{1}{L_s\mathrm{\σ}}\\ -\frac{L_m}{L_r{L}_s\mathrm{\σ}}& 0\\ 0& -\frac{L_m}{L_r{L}_s\mathrm{\σ}}\end{array}\right]---\left(19\right)$

$\mathrm{\σ}=1-\frac{L_m^2}{L_r{L}_s}---\left(20\right)$

Variable in formula (18) is write as the form of steady-state component and flutter component sum, and abbreviation further, is obtained d-q Beat frequency current increment and beat frequency voltage increment and the relation of slip frequency increment under coordinate system

$\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\\ I_{rd}^{\mathrm{\Δ}}\\ I_{rq}^{\mathrm{\Δ}}\end{array}\right]={\[Z\left(s\right)\]}^{-1}B\left[\begin{array}{c}{V}_{sd}^{\mathrm{\Δ}}\\ V_{sq}^{\mathrm{\Δ}}\end{array}\right]---\left(2\right)$

$\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\\ I_{rd}^{\mathrm{\Δ}}\\ I_{rq}^{\mathrm{\Δ}}\end{array}\right]=2\mathrm{\π}{\[Z\left(s\right)\]}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]f_{sl}^{\mathrm{\Δ}}---\left(3\right)$

Wherein,

$Z\left(s\right)=\left[\begin{array}{cccc}s+\frac{R_s}{L_s\mathrm{\σ}}& -\frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}-{\mathrm{\ω}}_{sl}& -\frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}\\ \frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& s+\frac{R_s}{L_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}& -\frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}\\ -\frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& s+\frac{R_r}{L_r\mathrm{\σ}}& \frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}-{\mathrm{\ω}}_{sl}\\ -\frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& -\frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& s+\frac{R_r}{L_r\mathrm{\σ}}\end{array}\right]---\left(21\right)$

(3) beat frequency phenomenon is modeled.Motor torque expression formula under biphase rotating coordinate system:

$T_e=\frac{3}{2}{\mathrm{pL}}_m(i_{sq}{i}_{rd}-i_{sd}{i}_{rq})---\left(22\right)$

Write as the form of matrix multiple

$T_e^{\mathrm{\Δ}}=\frac{3}{2}{\mathrm{pL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T\left[\begin{array}{c}{i}_{sd}^{\mathrm{\Δ}}\\ i_{sq}^{\mathrm{\Δ}}\\ i_{rd}^{\mathrm{\Δ}}\\ i_{rq}^{\mathrm{\Δ}}\end{array}\right]---\left(23\right)$

Can obtain the beat frequency torque transmission function expression about pulsating dc voltage:

$G_{T_{e}u}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=\frac{3m}{\mathrm{\π}}{\mathrm{pL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T{\[Z\left(s\right)\]}^{-1}B\left[\begin{array}{c}cos\mathrm{\φ}\\ \sin \mathrm{\φ}\end{array}\right]---\left(4\right)$

Current of electric is write as the form of steady-state component and flutter component, and both sides square carry out abbreviation again:

I=I₀+I^△ (24)

Ignore fluctuating signal quadrantal component, then beat frequency current expression can be changed into:

$I^{\mathrm{\Δ}}=\frac{I_{sd0}{I}_{sd}^{\mathrm{\Δ}}+I_{sq0}{I}_{sq}^{\mathrm{\Δ}}}{I_0}---\left(25\right)$

Write as the form of matrix multiple:

$I^{\mathrm{\Δ}}=\frac{1}{I_0}{\left[\begin{array}{c}{I}_{sd0}\\ I_{sq0}\end{array}\right]}^T\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\end{array}\right]---\left(26\right)$

Can obtain the beat frequency electric current transmission function expression about pulsating dc voltage:

$G_{Iu}\left(s\right)=\frac{I^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=\frac{2m}{{\mathrm{\πI}}_0}{\left[\begin{array}{c}{I}_{sd0}\\ I_{sq0}\end{array}\right]}^T{\[Z\left(s\right)\]}_{2\×4}^{-1}B\left[\begin{array}{c}cos\mathrm{\φ}\\ sin\mathrm{\φ}\end{array}\right]---\left(5\right)$

(4) control block diagram without beat frequency provided according to Fig. 4, obtain after overcompensation beat frequency torque and beat frequency electric current about The transmission function of pulsating dc voltage, beat frequency phenomenon is at ripple frequency point ω_ripplePlace is the most serious, so that ripple frequency Beat frequency torque and beat frequency electric current at Dian are the least, arrange without beat frequency controller G_c(s).Respectively to beat frequency torque and beat frequency electricity Stream is analyzed, and obtains the optimum K value of correspondence, and carries out compromise selection.

The ideal values of penalty coefficient K should make the transmission function amplitude gain of beat frequency torque and beat frequency electric current all reach Little.The transmission function amplitude gain of beat frequency torque has with included angle and modulation depth m of d axle with penalty coefficient K, voltage vector Relation, and beat frequency torque amplitude gain increases with the increase of modulation depth m.In order to seek penalty coefficient and angle to beat frequency The impact of torque amplitude, fixed modulation depth is 1, calculates beat frequency torque amplitude.

Result of calculation is as it is shown in figure 5, X-axis is voltage vector angle, and Y-axis is penalty coefficient, and Z axis is that beat frequency torque amplitude increases Benefit.As seen from the figure, beat frequency torque is unrelated with voltage vector angle, is two sections of curves with penalty coefficient relation, and along with K value increases Greatly, beat frequency torque amplitude first reduces and increases afterwards, and obtains minima at two sections of intersections of complex curve.Can according to Matlab result of calculation Bosom friend's point is (0.136 ,-14.4dB), and when i.e. penalty coefficient K is 0.136, the compensation effect of beat frequency torque is best.

Same method obtains beat frequency current amplitude and penalty coefficient and the relation of level angle, as shown in Figure 6.Same reason Figure understands, and beat frequency current amplitude gain is unrelated with level angle, first reduces with penalty coefficient K and increases afterwards, i.e. there is a K value and makes Obtain beat frequency current amplitude gain minimum.Be (0.132 ,-28.5dB) according to this point of Matlab result of calculation, i.e. penalty coefficient K is When 0.132, the compensation effect of beat frequency electric current is best.

Take into account torque and current compensation effect, take the two optimal compensation coefficient compromise point, i.e. K=0.134.

Can be seen that from Fig. 7 with Fig. 8 after overcompensation, eliminate the motor beat frequency torque that pulsating dc voltage causes With beat frequency electric current.

Controller control performance in digital display circuit depends on discretization method；By discretization method being carried out point Analysis, selects discretization precision high, and is prone to the Bilinear transformation method TUS discretization method as controller of Digital Implementation, right Controller carries out sliding-model control.

In the present embodiment, eliminate hardware secondary filtering circuit 3, use and eliminate DC side secondary without beat frequency control algolithm The pulsating volage impact on current transformer outlet side, alleviates weight, reduces cost.

Last it is noted that above example is only in order to illustrate technical scheme, it is not intended to limit；Although With reference to previous embodiment, the present invention is described in detail, it will be understood by those within the art that: it still may be used So that the technical scheme described in foregoing embodiments to be modified, or wherein portion of techniques feature is carried out equivalent； And these amendments or replacement, do not make the essence of appropriate technical solution depart from the scope of various embodiments of the present invention technical scheme.

Claims (5)

1. a traction converter of motor train unit is without beat frequency control strategy, it is characterised in that comprise the following steps:

(1) it is derived by pulsating dc voltage expression formula according to commutator input-output power balance:

$u_{dc}^{\mathrm{\Δ}}=\frac{I_{dc}sin(2{\mathrm{\ω}}_{grid}t+\mathrm{\φ})}{2{\mathrm{\ω}}_{grid}C\cos \mathrm{\φ}}---\left(1\right)$

Wherein, I_dcFor DC side steady-state current component, C is DC bus capacitor,For pulsating dc voltage, ω_gridFor electrical network angle Frequency, φ is rectifier power factor angle, and t is time variable；

And use series connection high and low pass filter that pulsating dc voltage is filtered obtaining flutter component, and apply amplitude, phase Position compensates and discretization error compensates and accurately samples pulsating dc voltage；

(2) according to motor beat frequency small-signal model, be derived by under d-q coordinate system beat frequency current increment and beat frequency voltage increment with And the relation of slip frequency increment:

$\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\\ I_{rd}^{\mathrm{\Δ}}\\ I_{rq}^{\mathrm{\Δ}}\end{array}\right]={\[Z\left(s\right)\]}^{-1}B\left[\begin{array}{c}{V}_{sd}^{\mathrm{\Δ}}\\ V_{sq}^{\mathrm{\Δ}}\end{array}\right]---\left(2\right)$

$\left[\begin{array}{c}{I}_{sd}^{\mathrm{\Δ}}\\ I_{sq}^{\mathrm{\Δ}}\\ I_{rd}^{\mathrm{\Δ}}\\ I_{rq}^{\mathrm{\Δ}}\end{array}\right]=2\mathrm{\π}{\[Z\left(s\right)\]}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]f_{sl}^{\mathrm{\Δ}}---\left(3\right)$

Its Chinese style (2) is the relation of beat frequency current increment and beat frequency voltage increment, and formula (3) is beat frequency current increment and slip frequency The relation of increment；

WhereinWithFor motor stator d, q shaft current flutter component, I_sd0And I_sq0Divide for motor stator d, q shaft current stable state Amount, whereinWithFor rotor d, q shaft current flutter component, I_rd0And I_rq0Divide for rotor d, q shaft current stable state Amount,WithFor motor stator d, q shaft voltage flutter component,For motor slip frequency flutter component, Z (s) and B is square Battle array；

(3) beat frequency phenomenon is modeled:

According to motor torque expression formula and beat frequency small-signal model, obtain the beat frequency torque transmission function about pulsating dc voltage Expression formula:

$G_{T_{e}u}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=\frac{3m}{\mathrm{\π}}{\mathrm{pL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T{\[Z\left(s\right)\]}^{-1}B\left[\begin{array}{c}cos\mathrm{\φ}\\ sin\mathrm{\φ}\end{array}\right]---\left(4\right)$

Wherein m is modulation depth, and p is motor number of pole-pairs, L_mFor magnetizing inductance；

Expressed formula and beat frequency small-signal model by current of electric, obtain the beat frequency electric current transmission function table about pulsating dc voltage Reach formula:

$G_{Iu}\left(s\right)=\frac{I^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=\frac{2m}{{\mathrm{\πI}}_0}{\left[\begin{array}{c}{I}_{sd0}\\ I_{sq0}\end{array}\right]}^T{\[Z\left(s\right)\]}_{2\×4}^{-1}B\left[\begin{array}{c}cos\mathrm{\φ}\\ sin\mathrm{\φ}\end{array}\right]---\left(5\right)$

(4) to step (3) institute established model at ripple frequency point ω_ripplePlace carries out spectrum analysis, obtains amplitude/phase characteristic curves；Right Amplitude/phase characteristic curves is analyzed obtaining, when system operating frequency is at ripple frequency point ω_rippleTime, beat frequency torque and beat frequency electricity Stream amplitude gain all reaches maximum；

(5) beat frequency torque and beat frequency electric current are as follows about the transmission function of slip frequency increment:

$G_{T_{e}f}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{f_{sl}^{\mathrm{\Δ}}}=3{\mathrm{\πpL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T{\[Z\left(s\right)\]}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]---\left(6\right)$

$G_{If}\left(s\right)=\frac{I^{\mathrm{\Δ}}}{f_{sl}^{\mathrm{\Δ}}}=\frac{2\mathrm{\π}}{I_0}{\left[\begin{array}{c}{I}_{sd0}\\ I_{sq0}\end{array}\right]}^T{\[Z\left(s\right)\]}_{2\×4}^{-1}\left[\begin{array}{c}{I}_{sq0}\\ -I_{sd0}\\ I_{rq0}\\ -I_{rd0}\end{array}\right]---\left(7\right)$

Its Chinese style (6) is the transmission function of beat frequency torque and slip frequency increment, and formula (7) is beat frequency electric current and slip frequency increment Transmission function；

(6) after overcompensation, beat frequency torque and beat frequency electric current about the transmission function expression of pulsating dc voltage be:

$G_{T_e}\left(s\right)=\frac{T_e^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=G_c\left(s\right)G_{T_{e}f}\left(s\right)+G_{T_{e}u}\left(s\right)---\left(8\right)$

$G_I\left(s\right)=\frac{I^{\mathrm{\Δ}}}{u_{dc}^{\mathrm{\Δ}}}=G_c\left(s\right)G_{If}\left(s\right)+G_{Iu}\left(s\right)---\left(9\right)$

Its Chinese style (8) is the transmission function of beat frequency torque and DC pulse moving voltage, and formula (9) is beat frequency electric current and DC pulse moving voltage Transmission function；

(7) based on analyzing above, beat frequency phenomenon is at ripple frequency point ω_ripplePlace is the most serious, so that ripple frequency point ω_rippleBeat frequency torque and the beat frequency electric current at place are the least, arrange without beat frequency controller G_cS the expression formula of () is:

$G_c\left(s\right)=K\frac{{\mathrm{s\ω}}_{ripple}}{{(s+{\mathrm{\ω}}_{ripple})}^2}---\left(10\right)$

Determine that the parameter without beat frequency controller, the ideal values of penalty coefficient K should make beat frequency torque and the transmission of beat frequency electric current Function amplitude gain all minimizes, and is compensated coefficient, level angle and beat frequency torque amplitude gain through simulation calculation Relation, and the relation of penalty coefficient, level angle and beat frequency current amplitude gain, determine penalty coefficient K=0.134；

(8) controller control performance in digital display circuit depends on discretization method；By discretization method is analyzed, Select discretization precision high, and be prone to the Bilinear transformation method TUS discretization method as controller of Digital Implementation, to control Device carries out sliding-model control.

2. traction converter of motor train unit as claimed in claim 1 is without beat frequency control strategy, it is characterised in that institute in step (2) The matrix B stated is:

$B=\left[\begin{array}{cc}\frac{1}{L_s\mathrm{\σ}}& 0\\ 0& \frac{1}{L_s\mathrm{\σ}}\\ -\frac{L_m}{L_r{L}_s\mathrm{\σ}}& 0\\ 0& -\frac{L_m}{L_r{L}_s\mathrm{\σ}}\end{array}\right]---\left(19\right).$

3. traction converter of motor train unit as claimed in claim 1 is without beat frequency control strategy, it is characterised in that institute in step (2) Matrix Z (s) stated is:

$Z\left(s\right)=\left[\begin{array}{cccc}s+\frac{R_s}{L_s\mathrm{\σ}}& -\frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}-{\mathrm{\ω}}_{sl}& -\frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}\\ \frac{{\mathrm{\ω}}_r}{\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& s+\frac{R_s}{L_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_s\mathrm{\σ}}& -\frac{R_r{L}_m}{L_r{L}_s\mathrm{\σ}}\\ -\frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& \frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& s+\frac{R_r}{L_r\mathrm{\σ}}& \frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}-{\mathrm{\ω}}_{sl}\\ -\frac{L_m{\mathrm{\ω}}_r}{L_r\mathrm{\σ}}& -\frac{L_m{R}_s}{L_r{L}_s\mathrm{\σ}}& -\frac{L_m^2{\mathrm{\ω}}_r}{L_r{L}_s\mathrm{\σ}}+{\mathrm{\ω}}_{sl}& s+\frac{R_r}{L_r\mathrm{\σ}}\end{array}\right]---\left(21\right).$

4. traction converter of motor train unit as claimed in claim 1 is without beat frequency control strategy, it is characterised in that institute in step (3) The motor torque expression formula stated is:

$T_e^{\mathrm{\Δ}}=\frac{3}{2}{\mathrm{pL}}_m{\left[\begin{array}{c}-i_{rq0}\\ i_{rd0}\\ i_{sq0}\\ -i_{sd0}\end{array}\right]}^T\left[\begin{array}{c}{i}_{sd}^{\mathrm{\Δ}}\\ i_{sq}^{\mathrm{\Δ}}\\ i_{rd}^{\mathrm{\Δ}}\\ i_{rq}^{\mathrm{\Δ}}\end{array}\right]---\left(23\right).$

5. traction converter of motor train unit as claimed in claim 1 is without beat frequency control strategy, it is characterised in that write as by current of electric Steady-state component and the form of flutter component, both sides square carry out abbreviation again and obtain the current of electric expression formula described in step (3) For:

I=I₀+I^△ (24)。