CN103368443B - A kind of neural network internal model control method of megawatt three-phase current transformer - Google Patents

Abstract

The invention discloses a kind of neural network internal model control method of megawatt three-phase current transformer, neural net is applied in internal model control, for the feature of MW class current transformer under rotation alpha β coordinate system, propose a kind of control program based on neural Networks Internal Model principle, 3-phase power converter model will be balanced after 3S/2S coordinate transform, be equivalent to two separate single-phase converters.Therefore, only need two identical single-phase controllers to control with β phase α phase respectively, just can realize the control to whole MW class current transformer.Method of the present invention can overcome the impact that system parameters perturbs or external disturbance causes system, makes system have good robustness and vulnerability to jamming.

Description

A kind of neural network internal model control method of megawatt three-phase current transformer

Technical field

The present invention relates to power electronics intelligent control technology, particularly a kind of neural network internal model control method of megawatt three-phase current transformer.

Background technology

The considerable control problem of present industrial control field can control to solve with simple PID.But under the impact of the condition such as noise, disturbance, process model parameter even structure all can change, regulatory PID control is adopted to be difficult to obtain satisfied effect.Internal model control, as a kind of novel control method, has that structure is simple, parameter tuning is simple and clear, on-line tuning is easy, for the advantage such as improvement successful of robust and vulnerability to jamming, but requires accurate internal model.And neural net can approximating function and have self-learning capability arbitrarily, makes internal model control have better adaptive ability, can strengthen the scope of the controlled device of internal model control by the self study of neural net.

Summary of the invention

Technical problem to be solved by this invention is, not enough for prior art, a kind of neural network internal model control method of megawatt three-phase current transformer is provided, overcomes the impact that system parameters perturbs or external disturbance causes system, make system have good robustness and vulnerability to jamming.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of neural network internal model control method of megawatt three-phase current transformer, comprise MW class 3-phase power converter, described MW class 3-phase power converter comprises IGBT inversion module, and described IGBT inversion module connects load by LC filter circuit; Described IGBT inversion module comprises DC bus capacitor and three brachium pontis in parallel, and described DC bus capacitor is in parallel with described brachium pontis, and described brachium pontis is composed in series by two IGBT, and the method is:

1) Mathematical Modeling of MW class current transformer under static abc coordinate is calculated:

$\left[\begin{array}{cc}{A}^T& 0\\ 0& A\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_u\\ {\stackrel{\·}{I}}_l\end{array}\right]=\left[\begin{array}{cc}0& (1/C)\·I_3\\ (-1/L)\·I_3& (-r/L)\·A\end{array}\right]\left[\begin{array}{c}{u}_u\\ I_l\end{array}\right]$

$+\left[\begin{array}{cc}0& (-1/C)\·I_3\\ (1/L)\·A& 0\end{array}\right]\left[\begin{array}{c}{U}_i\\ I_{\mathrm{oph}}\end{array}\right],$

Wherein, $A=\left[\begin{array}{ccc}1& -1& 0\\ 0& 1& -1\\ -1& 0& 1\end{array}\right],$ I ₃be three rank unit matrixs, u _u=[u _abu _bcu _ca] ^tfor LC filtering circuit capacitor voltage, I _l=[I _ai _bi _c] ^tfor LC filter circuit inductive current, I _oph=[I _oai _obi _oc] ^tfor LC filter circuit output current, r is LC filter circuit inductor loss, and C is LC filter circuit filtering capacitance, and L is LC filter circuit inductance value, U _ifor IGBT inversion module three-phase output voltage, i=A, B, C;

2) coordinate transform is carried out to described Mathematical Modeling, obtains:

$\left[\begin{array}{cc}0& (-1/C)\·T_{2S/3S}\\ (U_d/L)\·{\mathrm{AT}}_{2S/3S}& 0\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{\α\β}}\\ {\stackrel{\·}{i}}_{\mathrm{\α\β}}\end{array}\right]=\left[\begin{array}{cc}0& (1/C)\·T_{2S/3S}\\ (-1/L)\·{\mathrm{AT}}_{2S/3S}& (-r/L)\·{\mathrm{AT}}_{2S/3S}\end{array}\right],$

$+\left[\begin{array}{cc}0& (-1/C)\·T_{2S/3S}\\ (U_d/L)\·{\mathrm{AT}}_{2S/3S}& 0\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{\α},\mathrm{\β}}\\ I_{\mathrm{\α},\mathrm{\β}}\end{array}\right]$

Wherein, $T_{2S/3S}=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right];$ for IGBT inversion module three-phase output voltage under α β coordinate system; for IGBT inversion module three-phase output current under α β coordinate system; S _{α, β}for IGBT inversion module on off state under α β coordinate system; I _{α, β}for LC filter circuit output current under α β coordinate system;

3) utilize step 2) formula, obtain MW class current transformer Mathematical Modeling under α β coordinate system:

$\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{\α}}\\ {\stackrel{\·}{u}}_{\mathrm{\β}}\end{array}\right]=\frac{1}{3C}\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]-\frac{1}{3C}\left[\begin{array}{c}{I}_{\mathrm{o\α}}\\ I_{\mathrm{o\β}}\end{array}\right],$

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{\α}}\\ {\stackrel{\·}{i}}_{\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}-r/L& 0\\ 0& -r/L\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]-\frac{1}{L}\left[\begin{array}{c}{u}_{\mathrm{\α}}\\ u_{\mathrm{\β}}\end{array}\right]+\frac{1}{L}\left[\begin{array}{c}{U}_{\mathrm{\α}}\\ U_{\mathrm{\β}}\end{array}\right],$

Wherein,

I _α, i _βfor MW class output current of converter, U under α β coordinate system _α, U _βfor IGBT inversion module output voltage, u under α β coordinate system _α, u _βfor MW class current transformer output voltage under α β coordinate system;

4) under utilizing α β coordinate system, α phase MW class current transformer output voltage sets up neural Networks Internal Model Control device model:

y _α(k)=h ₁u _α(k-1)+h ₂u _α(k-2)-g ₁y _α(k-1)-g ₂y _α(k-2)，

Wherein, y _αk () is the centrifugal pump of α phase MW class current transformer output voltage, h ₁, h ₂, g ₁, g ₂be d axle current transformer transfer-function coefficient; u _αk () is neural network contrary modeling;

5) by above-mentioned y _α(k), u _αk (), as the input of neural net internal model, obtains neural net internal model expression formula:

y _α(k+1)=f[y _α(k)，…，y _α(k-n+1)，u _α(k)，…，u _α(k-m+1)]+d _α(k)，

Wherein d _αk () is d axle interference noise; F0 is the Function Mapping relation between the input of neural net hidden layer and hidden layer export;

6) suppose that exporting zero deflection follows the tracks of input, then y _α(k) ≈ r _α(k) ..., y _α(k-n+1) ≈ r _α(k-n+1) neural network contrary modeling expression formula, is obtained:

u _α(k)=f ^-1[r _α(k)，…，r _α(k-n+1)，u _α(k-1)，…，u _α(k-m+1)，e _f(k)]，

Wherein, e _fk () is e _fthe centrifugal pump of (s), e _f(s)=G _f(s) e _m(s)=G _f(s) [y _α(s)-y _m(s)], G _fs () is feedback function, y _αs () is y _αthe continuous function of (k), y _ms () is neural net output layer output y _mthe continuous function of (k), v _ik () is the network weight between neural net hidden node and output node, z _ik () is the output of neural net hidden layer, r _αk () is current time α phase MW class current transformer reference input voltage;

7) defining J (k) is neural network learning target function, then neural metwork training performance index function J is:

$J=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}J\left(k\right)=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\frac{{[r_{\mathrm{\α}}\left(k\right)-u_{\mathrm{\α}}\left(k\right)]}^2}{2}=\frac{1}{2}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{e}_c^2\left(k\right)\≤{\mathrm{\ϵ}}_2,$

Wherein, ε ₂>0; N is the length that neural net inputs or outputs sample;

8) ask the minimum value of neural metwork training performance index function J, determine u _α(k), thus try to achieve y _αk (), makes y _αk () follows the tracks of input signal r well _α(k).

In described step 5), the Function Mapping between the input of neural net hidden layer and hidden layer export is closed and is

$f\left(x\right)=\frac{1}{1+e^{-n_i\left(k\right)}},$ $x=[y_{\mathrm{\α}}\left(k\right),\·\·\·,y_{\mathrm{\α}}(k-n+1),u_{\mathrm{\α}}\left(k\right),\·\·\·,u_{\mathrm{\α}}(k-m+1)].$

Compared with prior art, the beneficial effect that the present invention has is: the present invention is directed to the feature of MW class current transformer under rotation alpha β coordinate system, propose a kind of control program based on neural Networks Internal Model principle, 3-phase power converter model will be balanced after 3S/2S coordinate transform, two separate single-phase converters can be equivalent to.Therefore, two identical single-phase controllers are only needed to control with β phase α phase respectively, just can realize the control to whole MW class current transformer, control method of the present invention can overcome the impact that system parameters perturbs or external disturbance causes converter system, makes system have good robustness and vulnerability to jamming.

Accompanying drawing explanation

Fig. 1 is MW class main circuit of converter schematic diagram;

Fig. 2 is the neural Networks Internal Model Control structured flowchart of one embodiment of the invention MW class current transformer;

Fig. 3 is one embodiment of the invention d axle current transformer neural network predicting meter BP network configuration.

Embodiment

MW class main circuit of converter is shown in Fig. 1, and Ud is DC bus-bar voltage; S1-S6 is ideal power switching device IGBT module; Assuming that three-phase output filtering unit is symmetrical, filter capacitor is C, and filter inductance is the gross effect that L, r represent that inductor loss, line impedance and switch turn on and off loss, and R is system load.

The Mathematical Modeling of this MW class current transformer under static abc coordinate can be obtained by Fig. 1:

$\left[\begin{array}{cccccc}1& 0& -1& 0& 0& 0\\ -1& 1& 0& 0& 0& 0\\ 0& -1& 1& 0& 0& 0\\ 0& 0& 0& 1& -1& 0\\ 0& 0& 0& 0& 1& -1\\ 0& 0& 0& -1& 0& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{ab}}\\ {\stackrel{\·}{u}}_{\mathrm{bc}}\\ {\stackrel{\·}{u}}_{\mathrm{ca}}\\ {\stackrel{\·}{I}}_a\\ {\stackrel{\·}{I}}_b\\ {\stackrel{\·}{I}}_c\end{array}\right]=\left[\begin{array}{cccccc}0& 0& 0& 1/C& 0& 0\\ 0& 0& 0& 0& 1/C& 0\\ 0& 0& 0& 0& 0& 1/C\\ -1/L& 0& 0& -r/L& r/L& 0\\ 0& -1/L& 0& 0& -r/L& r/L\\ 0& 0& -1/L& r/L& 0& -r/L\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{ab}}\\ u_{\mathrm{bc}}\\ u_{\mathrm{ca}}\\ I_a\\ I_b\\ I_c\end{array}\right]---\left(1\right)$

$+\left[\begin{array}{cccccc}0& 0& 0& -1/C& 0& 0\\ 0& 0& 0& 0& -1/C& 0\\ 0& 0& 0& 0& 0& -1/C\\ 1/L& -1/L& 0& 0& 0& 0\\ 0& 1/L& -1/L& 0& 0& 0\\ -1/L& 0& 1/L& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{U}_A\\ U_B\\ U_C\\ I_{\mathrm{oa}}\\ I_{\mathrm{ob}}\\ I_{\mathrm{oc}}\end{array}\right]$

Can be expressed as

$\left[\begin{array}{cc}{A}^T& 0\\ 0& A\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_u\\ {\stackrel{\·}{I}}_l\end{array}\right]=\left[\begin{array}{cc}0& (1/C)\·I_3\\ (-1/L)\·I_3& (-r/L)\·A\end{array}\right]\left[\begin{array}{c}{u}_u\\ I_l\end{array}\right]$ (2)

$+\left[\begin{array}{cc}0& (-1/C)\·I_3\\ (1/L)\·A& 0\end{array}\right]\left[\begin{array}{c}{U}_i\\ I_{\mathrm{oph}}\end{array}\right]$

In formula: $A=\left[\begin{array}{ccc}1& -1& 0\\ 0& 1& -1\\ -1& 0& 1\end{array}\right],$ I ₃be three rank unit matrix,

i=A,B,C；

U _u=[u _abu _bcu _ca] ^tfor three-phase inversion output filtering cell capacitance voltage;

I _l=[I _ai _bi _c] ^tfor three-phase inversion output filtering unit inductive current;

I _oph=[I _oai _obi _oc] ^tfor three-phase inversion output filtering unit loads electric current.

Simplify the design of controller for the coupling eliminated between each phase, after being phase voltage by line voltage transitions, by formula (3), coordinate transform is carried out to formula (2).

$\left[\begin{array}{c}{x}_{\mathrm{\α}}\\ x_{\mathrm{\β}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{x}_A\\ x_B\\ x_C\end{array}\right]=T_{3S/2S}\left[\begin{array}{c}{x}_A\\ x_B\\ x_C\end{array}\right]---\left(3\right)$

Can obtain:

$\left[\begin{array}{cc}0& (-1/C)\·T_{2S/3S}\\ (U_d/L)\·{\mathrm{AT}}_{2S/3S}& 0\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{\α\β}}\\ {\stackrel{\·}{i}}_{\mathrm{\α\β}}\end{array}\right]=\left[\begin{array}{cc}0& (1/C)\·T_{2S/3S}\\ (-1/L)\·{\mathrm{AT}}_{2S/3S}& (-r/L)\·{\mathrm{AT}}_{2S/3S}\end{array}\right]---\left(4\right)$

$+\left[\begin{array}{cc}0& (-1/C)\·T_{2S/3S}\\ (U_d/L)\·{\mathrm{AT}}_{2S/3S}& 0\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{\α},\mathrm{\β}}\\ I_{\mathrm{\α},\mathrm{\β}}\end{array}\right]$

Arrange formula (4), can be balanced 3-phase power converter Mathematical Modeling under α β coordinate system is:

$\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{\α}}\\ {\stackrel{\·}{u}}_{\mathrm{\β}}\end{array}\right]=\frac{1}{3C}\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]-\frac{1}{3C}\left[\begin{array}{c}{I}_{\mathrm{o\α}}\\ I_{\mathrm{o\β}}\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{\α}}\\ {\stackrel{\·}{i}}_{\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}-r/L& 0\\ 0& -r/L\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]-\frac{1}{L}\left[\begin{array}{c}{u}_{\mathrm{\α}}\\ u_{\mathrm{\β}}\end{array}\right]+\frac{1}{L}\left[\begin{array}{c}{U}_{\mathrm{\α}}\\ U_{\mathrm{\β}}\end{array}\right]---\left(6\right)$

(u _αu _β) ^T=T _3S/2S(u _abu _bcu _ca) ^T

(I _oαI _oβ) ^T=T _3S/2S(I _oaI _obI _oc) ^T

(i _αi _β) ^T=T _3S/2S(I _aI _bI _c) ^T

State variable u as can be seen from the above equation on α axle _α, i _αwith the state variable u on β axle _β, i _βwithout any coupled relation, be mutually independent; The state equation of system on α (β) axle is consistent with the state equation of single-phase converter.Can reach a conclusion: balance 3-phase power converter model, after 3S/2S coordinate transform, can be equivalent to two separate single-phase converters.Therefore, only need two identical single-phase controllers to control with β phase α phase respectively, just can realize the control to whole MW class current transformer.

Fig. 2 is shown in by one embodiment of the invention control structure block diagram.α phase is identical with the neural Networks Internal Model Control device in β phase, therefore only introduces the design of α phase control device.In figure, NNC is neural Networks Internal Model Control device, produces the control signal u needed for current transformer work _αs (), NNM is the current transformer model of application neural network identification, and in parallel with current transformer, α phase current transformer is control object, current transformer output voltage and be the difference e that neural Networks Internal Model Control device model exports _m(s)=y _α(s)-y _ms () is used as the Modeling Error Feedback signal of NNM.Gr (s) is input filter (the simplest situation is Gr (s)=1), reduces impact during impact set point, softening control action; For feedback function, (the simplest situation is Gf (s)=1 to Gf (s); ), be used for suppressing to export concussion, obtain the dynamic characteristic and robustness expected; e _cs difference that () exports with control object for system input.E _fs () is e _ms () is by filter G _ffeedback quantity after (s).

During inversion system work, by the inputoutput data of current transformer of sampling, set up the initial model of NNC and NNM, then by determining optimal control amount u online to target function minimizing _αs (), makes control object export y _αs () can follow the tracks of input signal r well _α(s).

The process of establishing of neural net internal model (NNM) is as follows:

Controlled device 3-phase power converter is Discrete time Nonlinear Systems, definition d _αk () is d axle interference noise, y _α(k+1) be the output time series that order is n, u _αk () is sequence input time of m for order, then have:

y _α(k+1)=f[y _α(k)，…，y _α(k-n+1)，u _α(k)，…，u _α(k-m+1)]+d _α(k)（7）

Define 3 layers of neural net and be input as x _j(j=1,2, m+n-1) and, d axle practical object exports as y _α(k), then neural network input layer input can be expressed as:

$x_j\left(k\right)=\left\{\begin{array}{cc}{u}_{\mathrm{\α}}(k-j)& 0\≤j\≤m-1\\ y_{\mathrm{\α}}(k-j+m)& m\≤j\≤m+n-1\end{array}---\left(8\right)\right.$

Definition hidden layer is input as n _ik (), the network weight between network input node and hidden node is w _ij, the threshold value of input layer is θ _ik (), then have:

$n_j\left(k\right)=\underset{j=1}{\overset{v}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)x_j\left(k\right)+{\mathrm{\θ}}_i\left(k\right)---\left(9\right)$

Definition f is z _i(k) and n _ik Function Mapping relation between (), f ' is its derivative, and neural net hidden layer exports as z _i(i=l, 2, w), then hidden layer exports and is:

$z_i\left(k\right)=f\left[n_i\left(k\right)\right]=\frac{1}{{1+e}^{{-n}_i\left(k\right)}},---\left(10\right)$

$f^{\′}\left[n_i\left(k\right)\right]=z_i\left(k\right)[1-z_i\left(k\right)]$

Network weight between definition hidden node and output node is v _i(k), output layer exports and is:

$y_m\left(k\right)=\underset{i=1}{\overset{w}{\mathrm{\Σ}}}{v}_i\left(k\right)z_i\left(k\right)---\left(11\right)$

Definition E (k) is e-learning target function, and I/O sample is the error of N, ε representative setting to length, and neural metwork training performance index function is:

$E=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}E\left(k\right)=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left[\frac{{(y_{\mathrm{\α}}\left(k\right)-y_m\left(k\right))}^2}{2}\right]=\frac{1}{2}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{e}_m^2\left(k\right)\≤\mathrm{\ϵ},\mathrm{\ϵ}>0---\left(12\right)$

Network weight and threshold value correction formula are:

$w_{\mathrm{ij}}(k+1)=w_{\mathrm{ij}}\left(k\right)+\mathrm{\η}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\δ}}_i^{\left(2\right)}\left(k\right)x_j\left(k\right)+\▿[w_{\mathrm{ij}}\left(k\right)-w_{\mathrm{ij}}(k-1)]---\left(13\right)$

${\mathrm{\θ}}_i(k+1)={\mathrm{\θ}}_i\left(k\right)-\mathrm{\η}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\δ}}_i^{\left(2\right)}\left(k\right)+\▿[{\mathrm{\θ}}_i\left(k\right)-{\mathrm{\θ}}_i(k-1)]---\left(14\right)$

$v_i(k+1)=v_i\left(k\right)+\mathrm{\η}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\δ}}^{\left(3\right)}\left(k\right)z_i\left(k\right)+\▿[v_i\left(k\right)-v_i(k-1)]---\left(15\right)$

In formula: the error of hidden node is δ ⁽²⁾(k)=f'n _i(k) δ ⁽³⁾(k) v _ik (), the error of output layer node is δ ⁽³⁾(k)=y _α(k)-y _m(k), η is learning rate, for factor of momentum.

Neural Networks Internal Model Control device process of establishing is as follows:

According to current transformer model analysis, d axle current transformer transfer function can be expressed as:

$P_{\mathrm{\α}}\left(z\right)=\frac{y_{\mathrm{\α}}}{u_{\mathrm{\α}}\left(z\right)}=\frac{h_1{z}^{-1}+h_2{z}^{-2}}{1+g_1{z}^{-1}+g_2{z}^{-2}}---\left(31\right)$

H in formula ₁, h ₂, g ₁, g ₂be transfer-function coefficient, then have:

y _α(z)=h ₁u _α(z)z ^-1+h ₂u _α(z)z ^-2-g ₁y _α(z)z ^-1-g ₂y _α(z)z ^-2（32）

That is:

y _α(k)=h ₁u _α(k-1)+h ₂u _α(k-2)-g ₁y _α(k-1)-g ₂y _α(k-2)（33）

From formula (33), obvious y _α(k) and u _α(k-2), u _α(k-1), y _α(k-2), y _α(k-1) relevant, design neural net positive model is the BP network of 4-4-1 structure, neural network estimator be input as [u _α(k-1); u _α(k); y _α(k-1); y _α(k)], export as y _α(k+1).When adopting ANN Control, the network number of plies, every layer of nodal point number are more few better, can reduce operation time like this, meet the needs of Digital Implementation.Through repeatedly repetition test, determine to form hidden layer by 4 nodes, see Fig. 3, neural Networks Internal Model Control device NNC is the BP network of a 5-4-1 structure simultaneously, is input as [r _α(k-1); r _α(k); u _α(k-1); u _α(k); e _f(s)], performance index function is J=[r _α(k)-y _α(k)] ²/ 2.

Internal mode controller is the inverse of object model, can prove that the inverse of formula (7) non linear system exists.In the controls, it is desirable to export the input of zero deflection track reference, therefore have y _α(k)=r _α(k) ..., y _α(k-n+1)=r _α(k-n+1), neural network contrary modeling NNC also adopts 3 layers of BP network configuration.Then its inverse dynamic model is

u _α(k)=f ^-1[r _α(k+1)，r _α(k)，…，r _α(k-n+1)，u _α(k-1)，…，u _α(k-m+1)]（16）

In formula (16), r _α(k+1) be the reference input value of the next sampling period system in this sampling period in time series, cannot measure in this sampling period, but obtain by linearisation Forecasting Methodology, specific practice is r _α(k+1) predicted value can be passed through current time reference input sampled value r _α(k) and in the past moment reference input sampled value r _α(k-1) obtain, its expression formula is:

r _α(k+1)=2r _α(k)-r _α(k-1)（17）

The output of obvious neural Networks Internal Model Control device also with feedback quantity e _f(s)=G _f(s) e _m(s)

=G _f(s) [y _α(s)-y _m(s)] relevant, therefore formula (16) can be expressed as:

u _α(k)=f ^-1[r _α(k)，…，r _α(k-n+1)，u _α(k-1)，L，u _α(k-m+1)，e _f(k)]（18）

The identification algorithm of neural Networks Internal Model Control device is: establish network to be input as c _j(j=1,2 ..., Ψ), then input layer is input as:

Definition hidden layer is input as o _ik (), then have:

$o_i\left(k\right)=\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{t}_{\mathrm{ij}}\left(k\right)c_j\left(k\right)---\left(20\right)$

Definition hidden layer exports g _ik (), then have:

$g_i\left(k\right)=f\left(o_i\left(k\right)\right)=\frac{1}{1+e^{{-o}_i\left(k\right)}},f^{\′}\left(o_i\left(k\right)\right)=g_i\left(k\right)(1-g_i\left(k\right))---\left(21\right)$

Definition d axle network exports as u _αk (), then have

$u_{\mathrm{\α}}\left(k\right)=f\left[o_j\left(k\right)\right]=\frac{1}{1+e^{{-o}_j\left(k\right)}}---\left(22\right)$

Definition J (k) is e-learning target function, ε ₂for the error of setting, then neural metwork training performance index function is:

$J=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}J\left(k\right)=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\frac{{[r_{\mathrm{\α}}\left(k\right)-y_{\mathrm{\α}}\left(k\right)]}^2}{2}=\frac{1}{2}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{e}_c^2\left(k\right)\≤{\mathrm{\ϵ}}_2,{\mathrm{\ϵ}}_2>0---\left(23\right)$

In formula, e _c(k)=r _α(k)-y _αk (), when the identification accuracy of neural network model changes, herein without y _mk () replaces y _αk (), can make nerve network controller identification accuracy constant.

Network weight correction formula is:

$t_{\mathrm{ij}}(k+1)=t_{\mathrm{ij}}\left(k\right)+\mathrm{\η}\frac{\∂J}{{\∂t}_{\mathrm{ij}}}+\▿[t_{\mathrm{ij}}\left(k\right)-t_{\mathrm{ij}}(k-1)]---\left(24\right)$

$b_i(k+1)=b_i\left(k\right)+\mathrm{\η}\frac{\∂J}{{\∂b}_i}+\▿[b_i\left(k\right)-b_i(k-1)]---\left(25\right)$

In formula (24) and (25), t _ijk () is the network weight correction value between network input node and hidden node; b _ik () is the network weight correction value between hidden node and output node; because neural net can approach any Nonlinear Mapping, through the study of several times, y _mk () infinitely approaches y _α(k), thus available replace , thus solve non-linear, time variation object the problem that cannot accurately obtain.

Can obtain according to the input of neural network model, output relation:

$\frac{{\∂y}_{\mathrm{\α}}}{{\∂u}_{\mathrm{\α}}}=\frac{{\∂y}_m}{{\∂u}_{\mathrm{\α}}}=\frac{{\∂y}_m}{{\∂z}_i}\frac{{\∂z}_i}{{\∂n}_i}\frac{{\∂n}_i}{{\∂x}_j}=\underset{i=1}{\overset{w}{\mathrm{\Σ}}}{v}_i\left(k\right)z_i\left(k\right)[1-z_i\left(k\right)]\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)---\left(26\right)$

If δ ⁽²⁾(k)=r _α(k)-y _α(k), δ _i ⁽¹⁾(k)=δ ⁽²⁾(k) b _i(k) g _i(k) [1-g _i(k)], then

$\frac{\∂J}{{\∂t}_{\mathrm{ij}}}=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left[{-\mathrm{\δ}}_i^{\left(1\right)}\left(k\right)c_j\left(k\right)\underset{i=1}{\overset{w}{\mathrm{\Σ}}}{v}_i\left(k\right)z_i\left(k\right)\right[1-z_i\left(k\right)\left]\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)\right]---\left(27\right)$

In like manner, following formula can be obtained:

$\frac{\∂J}{{\∂b}_i}=\frac{\∂J}{{\∂y}_{\mathrm{\α}}}\frac{{\∂y}_{\mathrm{\α}}}{{\∂u}_{\mathrm{\α}}}\frac{{\∂u}_{\mathrm{\α}}}{{\∂b}_i}=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left\{\right[y_{\mathrm{\α}}\left(k\right)-r_{\mathrm{\α}}\left(k\right)\left]g_i\left(k\right)\frac{{\∂y}_{\mathrm{\α}}}{{\∂u}_{\mathrm{\α}}}\right\}$

$=\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left\{{-\mathrm{\δ}}^{\left(2\right)}\left(k\right)g_i\left(k\right)\underset{i=1}{\overset{w}{\mathrm{\Σ}}}{v}_i\left(k\right)z_i\left(k\right)\right[1-z_i\left(k\right)\left]\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)\right\}---\left(28\right)$

Formula (27), (28) substitution formula (25), (26) can be obtained

$t_{\mathrm{ij}}(k+1)=t_{\mathrm{ij}}\left(k\right)-\mathrm{\η}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left\{{\mathrm{\δ}}_i^{\left(1\right)}\left(k\right)c_j\left(k\right)\underset{i=1}{\overset{w}{\mathrm{\Σ}}}{v}_i\left(k\right)z_i\left(k\right)\right[1-z_i\left(k\right)\left]\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)\right\}+\▿[t_{\mathrm{ij}}\left(k\right)-t_{\mathrm{ij}}(k-1)]---\left(29\right)$

$b_i(k+1)=b_i\left(k\right)-\mathrm{\η}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left\{{\mathrm{\δ}}^{\left(2\right)}\left(k\right)g_i\left(k\right)\underset{i=1}{\overset{q}{\mathrm{\Σ}}}{v}_i\left(k\right)z_i\left(k\right)\right[1-z_i\left(k\right)\left]\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}\left(k\right)\right\}+\▿[b_i\left(k\right)-b_i(k-1)]---\left(30\right)$

Claims (1)

1. a neural network internal model control method of megawatt three-phase current transformer, comprises MW class 3-phase power converter, and described MW class 3-phase power converter comprises IGBT inversion module, and described IGBT inversion module connects load by LC filter circuit; Described IGBT inversion module comprises DC bus capacitor and three brachium pontis in parallel, and described DC bus capacitor is in parallel with described brachium pontis, and described brachium pontis is composed in series by two IGBT, it is characterized in that, the method is:

1) Mathematical Modeling of MW class current transformer under static abc coordinate is calculated:

$\begin{array}{c}\left[\begin{array}{cc}{A}^T& 0\\ 0& A\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_u\\ {\stackrel{\·}{I}}_l\end{array}\right]=\left[\begin{array}{cc}0& \left(1/C\right)\·I_3\\ \left(-1/L\right)\·I_3& \left(-r/L\right)\·A\end{array}\right]\left[\begin{array}{c}{u}_u\\ I_l\end{array}\right]\\ +\left[\begin{array}{cc}0& \left(-1/C\right)\·I_3\\ \left(1/L\right)\·A& 0\end{array}\right]\left[\begin{array}{c}{U}_i\\ I_{oph}\end{array}\right]\end{array},$

Wherein, $A=\left[\begin{array}{ccc}1& -1& 0\\ 0& 1& -1\\ -1& 0& 1\end{array}\right],$ I ₃be three rank unit matrixs, u _u=[u _abu _bcu _ca] ^tfor LC filtering circuit capacitor voltage, I _l=[I _ai _bi _c] ^tfor LC filter circuit inductive current, I _oph=[I _oai _obi _oc] ^tfor LC filter circuit output current, r is LC filter circuit inductor loss, and C is LC filter circuit filtering capacitance, and L is LC filter circuit inductance value, U _ifor IGBT inversion module three-phase output voltage, i=A, B, C;

2) coordinate transform is carried out to described Mathematical Modeling, obtains:

$\begin{array}{c}\left[\begin{array}{cc}0& \left(-1/C\right)\·T_{2S/3S}\\ \left(U_d/L\right)\·{\mathrm{AT}}_{2S/3S}& 0\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{\α}\mathrm{\β}}\\ {\stackrel{\·}{i}}_{\mathrm{\α}\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}0& \left(1/C\right)\·T_{2S/3S}\\ \left(-1/L\right)\·{\mathrm{AT}}_{2S/3S}& \left(-r/L\right)\·{\mathrm{AT}}_{2S/3S}\end{array}\right],\\ +\left[\begin{array}{cc}0& \left(-1/C\right)\·T_{2S/3S}\\ \left(U_d/L\right)\·{\mathrm{AT}}_{2S/3S}& 0\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{\α},\mathrm{\β}}\\ I_{\mathrm{\α},\mathrm{\β}}\end{array}\right]\end{array}$

Wherein, $T_{3S/2S}=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right];$ for IGBT inversion module three-phase output voltage under α β coordinate system; for IGBT inversion module three-phase output current under α β coordinate system; S _{α, β}for IGBT inversion module on off state under α β coordinate system; I _{α, β}for LC filter circuit output current under α β coordinate system; U _dfor DC bus-bar voltage;

3) utilize step 2) formula, obtain MW class current transformer Mathematical Modeling under α β coordinate system:

$\left[\begin{array}{c}{\stackrel{\·}{u}}_{\mathrm{\α}}\\ {\stackrel{\·}{u}}_{\mathrm{\β}}\end{array}\right]=\frac{1}{3C}\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]-\frac{1}{3C}\left[\begin{array}{c}{I}_{o\mathrm{\α}}\\ I_{o\mathrm{\β}}\end{array}\right],$

$\left[\begin{array}{c}{\stackrel{\·}{i}}_{\mathrm{\α}}\\ {\stackrel{\·}{i}}_{\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}-r/L& 0\\ 0& -r/L\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]-\frac{1}{L}\left[\begin{array}{c}{u}_{\mathrm{\α}}\\ u_{\mathrm{\β}}\end{array}\right]+\frac{1}{L}\left[\begin{array}{c}{U}_{\mathrm{\α}}\\ U_{\mathrm{\β}}\end{array}\right],$

[u _αu _β] ^T＝T _3S/2S·[u _abu _bcu _ca] ^T,

Wherein, [I _{o α}i _{o β}] ^t=T _3S/2S[I _oai _obi _oc] ^t,

[i _αi _β] ^T＝T _3S/2S·[I _aI _bI _c] ^T,

I _α, i _βfor MW class output current of converter, U under α β coordinate system _α, U _βfor IGBT inversion module output voltage, u under α β coordinate system _α, u _βfor MW class current transformer output voltage under α β coordinate system;

4) under utilizing α β coordinate system, α phase MW class current transformer output voltage sets up neural Networks Internal Model Control device model:

y _α(k)＝h ₁u _α(k-1)+h ₂u _α(k-2)-g ₁y _α(k-1)-g ₂y _α(k-2），

Wherein, y _αk () is the centrifugal pump of α phase MW class current transformer output voltage, h ₁, h ₂, g ₁, g ₂be d axle current transformer transfer-function coefficient; u _αk () is neural network contrary modeling; _krepresent the _kmoment;

5) by above-mentioned y _α(k), u _αk (), as the input of neural net internal model, obtains neural net internal model expression formula:

y _α(k+1)＝f[y _α(k)，…，y _α(k-n+1)，u _α(k)，…，u _α(k-m+1)]+d _α(k)，

Wherein d _αk () is d axle interference noise; F (x) is the Function Mapping relation between the input of neural net hidden layer and hidden layer output;

$n_i\left(k\right)=\underset{j=1}{\overset{v}{\mathrm{\Σ}}}{w}_{ij}\left(k\right)x_j\left(k\right)+{\mathrm{\θ}}_i\left(k\right),v=m+n-1,$ W _ijfor the network weight between network input node and hidden node, θ _ik threshold value that () is input layer, $x_j\left(k\right)=\left\{\begin{array}{cc}{u}_{\mathrm{\α}}(k-j)& 0\≤j\≤m-1\\ y_{\mathrm{\α}}(k-j+m)& m\≤j\≤m+n-1\end{array}\right.;$ M is u _αthe order of (k); N is y _α(k+1) order;

6) suppose that exporting zero deflection follows the tracks of input, then y _α(k) ≈ r _α(k) ..., y _α(k-n+1) ≈ r _α(k-n+1) neural network contrary modeling expression formula, is obtained:

u _α(k)＝f ^-1[r _α(k)，…，r _α(k-n+1)，u _α(k-1)，…，u _α(k-m+1)，e _f(k)]，

Wherein, e _fk () is e _fthe centrifugal pump of (s), e _f(s)=G _f(s) e _m(s)=G _f(s) [y _α(s)-y _m(s)], G _fs () is feedback function, y _αs () is y _αthe continuous function of (k), y _ms () is neural net output layer output y _mthe continuous function of (k), v _ik () is the network weight between neural net hidden node and output node, z _ik () is the output of neural net hidden layer, r _αk () is current time α phase MW class current transformer reference input voltage; W is that neural net hidden layer exports number;

7) defining J (k) is neural network learning target function, then neural metwork training performance index function J is:

$J=\underset{k=1}{\overset{N}{\Σ}}J\left(k\right)=\underset{k=1}{\overset{N}{\Σ}}\frac{{\[r_{\mathrm{\α}}\left(k\right)-u_{\mathrm{\α}}\left(k\right)\]}^2}{2}=\frac{1}{2}\underset{k=1}{\overset{N}{\Σ}}{e}_c^2\left(k\right)\≤{\mathrm{\ϵ}}_2,$

Wherein, ε ₂>0; N is the length that neural net inputs or outputs sample;

8) ask the minimum value of neural metwork training performance index function J, determine u _α(k), thus try to achieve y _αk (), makes y _αk () follows the tracks of input signal r well _α(k).