CN103825522A - Method for online computing motor optimal operating point - Google Patents

Abstract

The invention discloses a method for online computing a motor optimal operating point. Online computing on the optimal operating point of an asynchronous motor is completed through optimal slip frequency corresponding to the optimal operating point of the asynchronous motor. The optimal slip frequency w2_max is obtained by the following formula, Rs represents stator resistance, Rr represents rotor resistance, and Lm represents mutual inductance. The method has the advantages of being high in real-time performance, high in precision, good in system stability, strong in anti-interference capacity and the like.

Description

A kind of motor best operating point on-line calculation method

Technical field

The present invention is mainly concerned with the control technology field of motor, refers in particular to a kind of best operating point on-line calculation method that is applicable to asynchronous machine.

Background technology

Asynchronous machine is operated in different working points, and its operational efficiency is not quite similar, and for making the long-term work of motor energy on the working point of efficiency optimization, must make machine operation at best operating point.Due to the impact that the parameter of electric machine can be changed by operating temperature, therefore best operating point can change, and therefore needs accurate calculating.

At present, the online account form of best operating point probably can be classified as three classes: the optimal exciting control strategy based on loss model, the minimum control strategy of input power and the minimum control strategy of stator current.Efficiency optimization control based on loss model is to derive the minimum or optimal exciting magnetic linkage when most effective of the loss of electric machine by the mathematics loss model of motor.The minimum control strategy of input power, exports under the constant prerequisite of operating mode at motor, by on-line search algorithm, progressively reduces rotor flux, changes the iron loss of motor and the distribution of copper loss, finally reduces power input to a machine, implementation efficiency optimization.Minimum stator current control is controlled and is realized the minimum conduct control of stator current target by breakdown torque/ampere, reaches with this object that system effectiveness is optimized.The amount of calculation of above-mentioned various traditional calculations modes is large, it is complicated to realize, and becomes while being limited to the parameter of electric machine, and performance is difficult to reach requirement.

Summary of the invention

The technical problem to be solved in the present invention is just: the technical problem existing for prior art, the invention provides a kind of real-time, precision is high, the stability of a system good, interference rejection ability is strong a kind of motor best operating point on-line calculation method.

For solving the problems of the technologies described above, the present invention by the following technical solutions:

A kind of motor best operating point on-line calculation method, while being in best operating point by asynchronous machine corresponding optimum slip frequency complete asynchronous machine best operating point in line computation; Described optimum slip frequency w _{2_max}obtained by following formula:

$w_{2\_\max }=\frac{R_r}{L_m}\sqrt{\frac{R_s}{R_r+R_s}}$

Wherein, R represents resistance, and L represents inductance, and subscript s and r represent respectively stator and rotor;

Meanwhile, in motor actual moving process, must meet:

$\sqrt{(\frac{L_{\mathrm{\σ}}^2{L}_r^2{w}_{\mathrm{\σ}}^2}{R_r^2}+L_s^2)\frac{T_e{R}_r}{1.5p{L}_m^2{w}_2}}\≤{\mathrm{\Ψ}}_{\max }$

$\sqrt{[1+{\left(\frac{L_r{w}_2}{R_r}\right)}^2]\frac{T_e{R}_r}{1.5p{L}_m^2{w}_2}}\≤I_{\max }$

Wherein, $w_2=\frac{R_r}{L_r}\frac{i_{\mathrm{qs}}}{i_{\mathrm{ds}}},L_{\mathrm{\σ}}=\frac{L_r{L}_r-L_m^2}{L_r},T_e=1.5p\frac{L_m}{L_r}{\mathrm{\Ψ}}_{\mathrm{dr}}{i}_{\mathrm{qs}},$ ψ _dr=L _ri _dr+ L _mi _ds, the number of pole-pairs that p is motor, i represents electric current, and ψ represents magnetic linkage, and subscript s and r represent respectively stator and rotor, and subscript d and q represent respectively d and q coordinate system.

As a further improvement on the present invention: in described method, stator resistance obtains by following formula:

$\hat{A}=\left(\begin{array}{cc}-(\frac{{\hat{R}}_s}{L_s^{\′}}+\frac{1}{L_s^{\′}}{\left(\frac{L_m}{L_r}\right)}^2{R}_r)I& -\frac{L_m}{L_m^{\′}{L}_r}(\frac{1}{T_r}I-w_{r}J)\\ \frac{L_m}{T_r}I& -\frac{1}{T_r}I+w_{r}J\end{array}\right)$

Wherein, I is unit matrix, and J is j matrix,

for stator resistance estimation value, L _mfor mutual inductance, L _sfor stator inductance, L _rfor inductor rotor, T _rfor rotor time constant, w _rfor rotating speed, L' _sfor stator side equivalent inductance .

As a further improvement on the present invention: in described method, Stator resistance identification adaptive rate obtains by following formula:

${\hat{R}}_s=-(K_p+\frac{K_i}{p})[(i_D-{\hat{i}}_D){\hat{i}}_D+(i_Q-{\hat{i}}_Q){\hat{i}}_Q]$

Wherein,

for stator resistance estimation value, i _dfor actual D shaft current,

for the D shaft current of observer output, i _qfor actual Q shaft current,

for the Q shaft current of observer output, K _pfor proportionality coefficient, K _ifor integral coefficient.

As a further improvement on the present invention: described method rotor resistance obtains by following formula:

${\hat{T}}_s=T_{s0}+\frac{{\hat{R}}_s-R_{s0}}{{\mathrm{\α}}_1{R}_{s0}}$

${\hat{R}}_r=R_{r0}+{\mathrm{\α}}_2{R}_{r0}({\hat{T}}_s-T_{s0})$

Wherein,

for the estimated value of Current Temperatures, T _s0for the initial value of temperature,

for current rotor resistance estimation value,

for current stator resistance estimation value, R _s0for stator resistance initial value, α ₁for stator resistance temperature coefficient, α ₂for rotor resistance temperature coefficient.

Compared with prior art, the invention has the advantages that:

1, a kind of motor best operating point on-line calculation method of the present invention, the optimum corresponding slip of computational efficiency in real time, real-time.

2, a kind of motor best operating point on-line calculation method of the present invention, by the real-time identification parameter of electric machine, guarantees to control the real-time matching of parameter and actual parameter, meets high-precision requirement.

3, a kind of motor best operating point on-line calculation method of the present invention, identification algorithm has self adaptation feature, and the stability of a system is good, and interference rejection ability is strong.

4, the present invention utilizes the optimum slip frequency that motor best operating point is corresponding to carry out implementation efficiency optimal control, passes through the set up optimum slip computational methods based on motor model prediction, the impact that can avoid performance changed by the parameter of electric machine, and system suitability is good.

Accompanying drawing explanation

Fig. 1 is the control system block diagram forming in concrete application example according to the inventive method.

Embodiment

Below with reference to Figure of description and specific embodiment, the present invention is described in further details.

A kind of motor best operating point on-line calculation method of the present invention, has merged efficiency optimization control thought and minimum stator current control thought based on model loss, corresponding slip frequency when having obtained asynchronous machine and being in best operating point; And the feature becoming during for the parameter of electric machine set up a set of optimum slip frequency computational methods based on motor model prediction, form the on-line calculation method of a set of complete asynchronous machine best operating point.

The derivation of corresponding slip frequency when asynchronous machine is in best operating point in the present invention (optimum slip frequency) is:

By in rotor field-oriented synchronous rotating frame, asynchronous machine Mathematical Modeling is as follows:

$V_{\mathrm{qs}}=R_i{i}_{\mathrm{qs}}+\frac{d{\mathrm{\Ψ}}_{\mathrm{qs}}}{\mathrm{dt}}+w_1{\mathrm{\Ψ}}_{\mathrm{ds}}---\left(1\right)$

$V_{\mathrm{ds}}=R_s{i}_{\mathrm{ds}}+\frac{d{\mathrm{\Ψ}}_{\mathrm{ds}}}{\mathrm{dt}}-w_1{\mathrm{\Ψ}}_{\mathrm{qs}}---\left(2\right)$

$V_{\mathrm{qr}}=R_r{i}_{\mathrm{qr}}+\frac{d{\mathrm{\Ψ}}_{\mathrm{qr}}}{\mathrm{dt}}+w_2{\mathrm{\Ψ}}_{\mathrm{dr}}---\left(3\right)$

$V_{\mathrm{dr}}=R_r{i}_{\mathrm{dr}}+\frac{d{\mathrm{\Ψ}}_{\mathrm{dr}}}{\mathrm{dt}}-w_2{\mathrm{\Ψ}}_{\mathrm{qr}}---\left(2\right)$

$T_e=1.5p\frac{L_m}{L_r}{\mathrm{\Ψ}}_{\mathrm{dr}}{i}_{\mathrm{qs}}---\left(5\right)$

ψ _qs=L _si _qs+L _mi _qr (6)

ψ _ds=L _si _ds+L _mi _dr (7)

ψ _qr=L _ri _qr+L _mi _qs (8)

ψ _dr=L _ri _dr+L _mi _ds (9)

Wherein V represents voltage, and i represents electric current, and ψ represents magnetic linkage, and R represents resistance, and L represents inductance, and subscript s and r represent respectively stator and rotor, and subscript d and q represent respectively d and q coordinate system, the number of pole-pairs that p is motor, w ₁and w ₂represent respectively stator angular frequency and slip frequency, motor mathematics model of stable state can be by following expression:

V _qs=R _si _qs+w ₁L _si _ds (10)

V _ds=R _si _ds-w ₁L _σi _qs (11)

$T_e=1.5p\frac{L_m^2}{L_r}{\mathrm{\Ψ}}_{\mathrm{ds}}{i}_{\mathrm{qs}}---\left(12\right)$

$w_2=\frac{R_r}{L_r}\frac{i_{\mathrm{qs}}}{i_{\mathrm{ds}}}---\left(13\right)$

Wherein

when steady operation, its motor operational efficiency can be expressed as

wherein P _in=1.5 (V _dsi _ds+ V _qsi _qs), be the active power that motor stator side is inputted.By formula (1)-(13) substitution, the expression formula that just can obtain η is:

$\mathrm{\η}=\frac{T_e{w}_r}{P_{\mathrm{in}}}=\frac{p{L}_m^2{w}_r{R}_r{w}_2}{(R_s{L}_r^2+R_r{L}_m^2)w_2^2+L_m^2{R}_{r}p{w}_r{w}_2+R_s{R}_r^2}---\left(14\right)$

W in formula _rfor the mechanical rotation angular frequency of rotor.Work as w _rwhen fixing, along with w ₂increase, electric efficiency exist a maximum.Solve

shown in the calculating formula (15) of optimum slip frequency:

$w_{2\_\max }=\frac{R_r}{L_m}\sqrt{\frac{R_s}{R_r+R_s}}---\left(15\right)$

In motor actual moving process, following two conditions must meet:

$\begin{array}{cc}\sqrt{{\mathrm{\Ψ}}_{\mathrm{sd}}^2+{\mathrm{\Ψ}}_{\mathrm{sq}}^2}\≤{\mathrm{\Ψ}}_{\max }& \sqrt{i_{\mathrm{sd}}^2+i_{\mathrm{sq}}^3}\≤I_{\max }\end{array}$

Simultaneous formula (6)-(9), can be converted into above-mentioned restrictive condition following formula (16), (17):

$\sqrt{(\frac{L_{\mathrm{\σ}}^2{L}_r^2{w}_{\mathrm{\σ}}^2}{R_r^2}+L_s^2)\frac{T_e{R}_r}{1.5p{L}_m^2{w}_2}}\≤{\mathrm{\Ψ}}_{\max }---\left(16\right)$

$\sqrt{[1+{\left(\frac{L_r{w}_2}{R_r}\right)}^2]\frac{T_e{R}_r}{1.5p{L}_m^2{w}_2}}\≤I_{\max }---\left(17\right)$

Simultaneous above formula (15), (16), (17) three formulas form optimum slip computing.

In said method, be to utilize state observer to carry out motor model parameter prediction.State observer is a class dynamical system that draws state estimation value according to the measured value of the outside unsteady flow of system (input variable and output variable); Upstate observer carrys out state or the parameter of real-time monitored non linear system, utilizes the Mathematical Modeling of object to estimate the state of object, by the error between state estimation value and measured value, revises state estimation equation, forms closed loop state estimation.

In static ABC axle system, the induction machine state equation representing take magnetic linkage and electric current as:

$\frac{d{\mathrm{\ψ}}_r}{\mathrm{dt}}=(-\frac{1}{T_r}+j{w}_r){\mathrm{\ψ}}_r+\frac{L_m}{T_r}{i}_s---\left(18\right)$

$\frac{{\mathrm{di}}_s}{\mathrm{dt}}=-\frac{1}{T_{\mathrm{sr}}^{\′}}{i}_s-\frac{L_m}{L_s^{\′}{L}_r}(-\frac{1}{T_{\mathrm{sr}}^{\′}}+j{w}_r){\mathrm{\ψ}}_r+\frac{u_s}{L_s^{\′}}---\left(19\right)$

Wherein, T _s' _r=L' _s/ R _sr, R _sr=R _s+ (L _m/ L _r) ²r _r, its matrix form is as follows:

$\stackrel{\·}{x}=\mathrm{Ax}+\mathrm{Bu}---\left(20\right)$

In formula

x=(i _sd i _sqψ _rdψ _rq) ^T u=(u _sd u _sq) ^T $\begin{array}{cc}B={\left(\begin{array}{cc}\frac{1}{L_s^{\′}}I& 0\end{array}\right)}^T& J=\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)\end{array}$

$A=\left(\begin{array}{cc}-\frac{1}{T_{\mathrm{sr}}^{\′}}I& -\frac{L_m}{L_s^{\′}{L}_r}(\frac{1}{T_r}I-w_{r}J)\\ \frac{L_m}{T_r}I& -\frac{1}{T_r}I+w_{r}J\end{array}\right)---\left(21\right)$

Therefore the state observer that, the present invention builds is as follows:

$\frac{d\hat{x}}{\mathrm{dt}}=\hat{A}\hat{x}+\mathrm{Bu}+K(I_s-{\hat{I}}_s)---\left(22\right)$

${\hat{I}}_s=C\hat{x}---\left(23\right)$

In formula:

$\hat{A}=\left(\begin{array}{cc}-(\frac{{\hat{R}}_s}{L_s^{\′}}+\frac{1}{L_s^{\′}}{\left(\frac{L_m}{L_r}\right)}^2{R}_r)I& -\frac{L_m}{L_s^{\′}{L}_r}(\frac{1}{T_r}I-w_{r}J)\\ \frac{L_m}{T_r}I& -\frac{1}{T_r}I+w_{r}J\end{array}\right)---\left(24\right)$

$C=\left(\begin{array}{cc}{I}_s& 0\\ 0& 0\end{array}\right)---\left(25\right)$

(1), according to said method, stator resistance is predicted:

${\hat{R}}_s=-(K_p+\frac{K_i}{p})[(i_D-{\hat{i}}_D){\hat{i}}_D+(i_Q-{\hat{i}}_Q){\hat{i}}_Q]---\left(26\right)$

Wherein K _p, K _ivalue can determine according to the required pole location of matrix (A-KC).

The stator resistance of observer state matrix is set to adjustable parameter (state matrix is as follows), utilizes the error of actual stator electric current and observer stator current to proofread and correct, and utilizes the adaptive rate real-time identification stator resistance value of deriving.

$\hat{A}=\left(\begin{array}{cc}-(\frac{{\hat{R}}_s}{L_s^{\′}}+\frac{1}{L_s^{\′}}{\left(\frac{L_m}{L_r}\right)}^2{R}_r)I& -\frac{L_m}{L_m^{\′}{L}_r}(\frac{1}{T_r}I-w_{r}J)\\ \frac{L_m}{T_r}I& -\frac{1}{T_r}I+w_{r}J\end{array}\right)$

(2), according to said method, rotor resistance is predicted:

Can estimate current temperature according to the predicted value of stator resistance and initial value:

${\hat{T}}_s=T_{s0}+\frac{{\hat{R}}_s-R_{s0}}{{\mathrm{\α}}_1{R}_{s0}}---\left(27\right)$

Wherein, T _s0for the reference temperature of stator winding, R _s0for stator resistance corresponding at this temperature, α ₁for the temperature coefficient of stator resistance.

Rotor resistance prediction is calculated by formula (28):

${\hat{R}}_r=R_{r0}+{\mathrm{\α}}_2{R}_{r0}({\hat{T}}_s-T_{s0})---\left(28\right)$

Wherein, T _s0for the reference temperature of stator winding, R _s0for stator resistance corresponding at this temperature, α ₂for the temperature coefficient of rotor resistance.

(3), according to said method, rotor flux Amplitude Estimation value is calculated by formula (29):

$\left|{\widehat{\mathrm{\Ψ}}}_r\right|=\sqrt{{\widehat{\mathrm{\ψ}}}_{\mathrm{rd}}^2+{\widehat{\mathrm{\ψ}}}_{\mathrm{rq}}^2}---\left(29\right)$

(4), according to said method, electromagnetic torque is calculated by formula (30):

$T_e=p_0\frac{L_m}{L_r}{\widehat{\mathrm{\ψ}}}_r\×i_s---\left(30\right)$

As shown in Figure 1, the control system block diagram for forming in concrete application example according to the inventive method.Wherein, the implication of each variable is: w _{r_ref}-rotary speed setting value, w _r-actual speed, T _ref-torque is given, T _e-actual torque estimated value, u _sdd shaft voltage instruction under-synchronous rotating frame, u _sqq shaft voltage instruction under-synchronous rotating frame, K _{_ status}for space voltage vector numbering, T _{_ ki}for K _{_ status}action time,

-rotor resistance identifier,

stator resistance identification value, i _aand i _bbe respectively the electric current of motor A phase and B phase.The control logic of each module comprises:

(1) rotational speed setup signal w _{r_ref}actual speed w with feedback _rafter rotating speed pi regulator as the given T of torque of permanent slip vector control module _ref;

(2) optimum slip computing module calculates real-time optimum slip according to input parameter, and its Output rusults is optimum slip w _{sl_ref}(slip as permanent slip vector control module is given), its input parameter is stator resistance rotor resistance

with actual torque T _e;

(3) motor full order observer module completes the observation of motor magnetic linkage, the parameter of electric machine and torque, and its Output rusults is stator resistance

rotor resistance

actual torque T _ewith rotor flux amplitude | ψ _r|, its input parameter is motor A phase current i _a, B phase current i _b, motor actual speed w _rand be used for carrying out the K of voltage estimate _{_ status}and T _{_ ki};

(4) constant slip frequency vector control module completes permanent slip vector control, and its Output rusults is the voltage instruction u under two-phase synchronous rotating frame _sdand u _sq(as the input of 2/3 conversion), its input parameter is the given T of torque _ref, the given w of optimum slip _{sl_ref}, motor identified parameters

actual speed w _r;

(5) 2/3 modular converters complete the conversion of voltage instruction from two-phase synchronous rotating frame to three phase static coordinate system and the function of modulating by voltage instruction, and it is output as space vector of voltage numbering and operate time thereof, and it is input as u _sdand u _sq.

Below be only the preferred embodiment of the present invention, protection scope of the present invention is also not only confined to above-described embodiment, and all technical schemes belonging under thinking of the present invention all belong to protection scope of the present invention.It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principles of the present invention, should be considered as protection scope of the present invention.

Claims (4)

1. a motor best operating point on-line calculation method, is characterized in that, while being in best operating point by asynchronous machine corresponding optimum slip frequency complete asynchronous machine best operating point in line computation; Described optimum slip frequency w _{2_max}obtained by following formula:

$w_{2\_\max }=\frac{R_r}{L_m}\sqrt{\frac{R_s}{R_r+R_s}}$

Wherein, R _srepresent stator resistance, R _rrepresent rotor resistance, L _mrepresent mutual inductance;

Meanwhile, in motor actual moving process, must meet:

$\sqrt{(\frac{L_{\mathrm{\σ}}^2{L}_r^2{w}_{\mathrm{\σ}}^2}{R_r^2}+L_s^2)\frac{T_e{R}_r}{1.5p{L}_m^2{w}_2}}\≤{\mathrm{\Ψ}}_{\max }$

$\sqrt{[1+{\left(\frac{L_r{w}_2}{R_r}\right)}^2]\frac{T_e{R}_r}{1.5p{L}_m^2{w}_2}}\≤I_{\max }$

Wherein, $w_2=\frac{R_r}{L_r}\frac{i_{\mathrm{qs}}}{i_{\mathrm{ds}}},L_{\mathrm{\σ}}=\frac{L_r{L}_r-L_m^2}{L_r},T_e=1.5p\frac{L_m}{L_r}{\mathrm{\Ψ}}_{\mathrm{dr}}{i}_{\mathrm{qs}},$ ψ _dr=L _ri _dr+ L _mi _ds, the number of pole-pairs that p is motor, i represents electric current, and ψ represents magnetic linkage, and subscript s and r represent respectively stator and rotor, and subscript d and q represent respectively d and q coordinate system.

2. asynchronous machine best operating point on-line calculation method according to claim 1, is characterized in that, in described method, stator resistance obtains by following formula:

$\hat{A}=\left(\begin{array}{cc}-(\frac{{\hat{R}}_s}{L_s^{\′}}+\frac{1}{L_s^{\′}}{\left(\frac{L_m}{L_r}\right)}^2{R}_r)I& -\frac{L_m}{L_m^{\′}{L}_r}(\frac{1}{T_r}I-w_{r}J)\\ \frac{L_m}{T_r}I& -\frac{1}{T_r}I+w_{r}J\end{array}\right)$

Wherein, I is unit matrix, and J is j matrix, for stator resistance estimation value, L _mfor mutual inductance, L _sfor stator inductance, L _rfor inductor rotor, T _rfor rotor time constant, w _rfor rotating speed, L' _sfor stator side equivalent inductance.

3. asynchronous machine best operating point on-line calculation method according to claim 1, is characterized in that, in described method, Stator resistance identification adaptive rate obtains by following formula:

${\hat{R}}_s=-(K_p+\frac{K_i}{p})[(i_D-{\hat{i}}_D){\hat{i}}_D+(i_Q-{\hat{i}}_Q){\hat{i}}_Q]$

Wherein,

for stator resistance estimation value, i _dfor actual D shaft current, for the D shaft current of observer output, i _qfor actual Q shaft current, for the Q shaft current of observer output, K _pfor proportionality coefficient, K _ifor integral coefficient.

4. asynchronous machine best operating point on-line calculation method according to claim 1, is characterized in that, described method rotor resistance obtains by following formula:

${\hat{T}}_s=T_{s0}+\frac{{\hat{R}}_s-R_{s0}}{{\mathrm{\α}}_1{R}_{s0}}$

${\hat{R}}_r=R_{r0}+{\mathrm{\α}}_2{R}_{r0}({\hat{T}}_s-T_{s0})$

Wherein,

for the estimated value of Current Temperatures, T _s0for the initial value of temperature,

for current rotor resistance estimation value, for current stator resistance estimation value, R _s0for stator resistance initial value, α ₁for stator resistance temperature coefficient, α ₂for rotor resistance temperature coefficient.