CN103762921A - Multi-objective control method for DFIG under unbalanced power grid based on particle swarm optimization - Google Patents

Abstract

The invention discloses a multi-objective control method for a DFIG under an unbalanced power grid based on particle swarm optimization. Consideration is given to output three-phase stator currents, output active power and output reactive power of the DFIG, so that multi-objective optimization control over control performance of the output three-phase stator currents, the output active power and the output reactive power is achieved at the same time, according to the adopted particle swarm optimization, codes are simplified, calculation time is short, which helps real-time calculation to be achieved, operation control performance of the DFIG can be effectively improved under unbalanced power grid voltage conditions, and electric energy quality and stability and safety of a power system are ensured. Meanwhile, a vector proportional integral adjustment or proportional integral resonance adjustment technology is adopted, and angular frequency can restrain adverse effects caused by negative sequence components in power grid voltage for vector proportional integral adjustment or resonance adjustment of double fundamental frequency.

Description

A kind of multi objective control method of DFIG under uneven electrical network based on particle cluster algorithm

Technical field

The invention belongs to electric machines control technology field, be specifically related to the multi objective control method of DFIG under a kind of uneven electrical network based on particle cluster algorithm.

Background technology

Now, DFIG(double-fed wind power generator) due to its variable speed constant frequency four quadrant running ability, and required Converter Capacity is compared capacity motor compared with the advantage such as little and becomes a kind of main flow wind driven generators.Yet, because DFIG motor stator winding is directly connected with electrical network, so when electrical network generation three-phase unbalanced fault, DFIG unit will correspondingly produce runnability to be worsened: as DFIG stator output three-phase current unbalance, output is meritorious, reactive power 100Hz shakes etc.Above-mentioned performance index deterioration will cause the three-phase current of wind power system injection electrical network asymmetric, and input grid power concussion etc. harmful effect, will threaten the reliable and stable operation of electrical network.Therefore, inquire into and to run on the DFIG control technology under unbalanced electric grid voltage condition, to eliminating stator output three-phase current unbalance, and the harmful effect such as power output concussion has very positive effect.

Under unbalanced electric grid voltage condition, Jiabing Hu and Yikang He are Modeling and enhanced control of DFIG under unbalanced grid voltage conditions(Electric Power Systems Research at title, vol.79, no.2, pp.273-281 just, a kind of vector oriented control method of extracting based on negative sequence component has been proposed in document Feb.2009), the core concept of the method is that the positive sequence in line voltage and negative sequence component are extracted respectively, and this is extracted to result as calculating the different foundations of controlling the rotor current reference value under target, and control target and can be chosen as symmetrical output threephase stator electric current, or active power of output stably, or output reactive power stably, it by selecting one in three targets, take the rotor current reference value of Mathematical Modeling under the current control target of basic calculation, effective work of passing ratio integration resonant regulator, make the reference value that actual rotor current tracking is given, finally reach control target.Yet from the Mathematical Modeling of DFIG, three control targets in traditional control strategy are conflicting, cannot improve threephase stator electric current, active power of output and the reactive power of DFIG simultaneously.That is to say, when reaching a certain control target, will cause all the other two deteriorations of controlling target capabilities, as when threephase stator electric current keeps balance, active power of output and reactive power will produce 100Hz big ups and downs, be unfavorable for the reliable and stable operation of electrical network; In like manner, when eliminating active power of output or reactive power 100Hz fluctuation, by causing injecting the imbalance of the DFIG stator current of electrical network, be unfavorable for equally the reliable and stable operation of electrical network.Therefore, under uneven electrical network, DFIG tradition control strategy only can be paid close attention to three and control one of target, and cannot take into account three, thus make when reaching a certain control target and all the other target capabilities are greatly worsened, be finally unfavorable for the reliable and stable operation of electrical network.

Summary of the invention

For the existing above-mentioned technical problem of prior art, the invention provides the multi objective control method of DFIG under a kind of uneven electrical network based on particle cluster algorithm, can take into account DFIG output threephase stator electric current simultaneously, the runnability of active power of output and output reactive power, guarantee that three runnabilities are in electrical network tolerance interval, and then guarantee the reliable and stable operation of electrical network.

Under uneven electrical network based on particle cluster algorithm, a multi objective control method of DFIG, comprises the steps:

(1) gather the threephase stator voltage U of DFIG _sa～U _sc, three-phase rotor current I _ra～I _rc, threephase stator electric current I _sa～I _sc, rotational speed omega _rand rotor position angle θ _r, and utilize phase-locked loop to extract threephase stator voltage U _sa～U _scangular frequency and phase theta;

(2) utilize phase theta respectively to threephase stator voltage U _sa～U _scwith threephase stator electric current I _sa～I _sccarry out dq conversion, obtain the stator voltage synthetic vector that comprises positive-negative sequence component under forward synchronous speed coordinate system stator current synthetic vector

and the stator voltage synthetic vector that comprises positive-negative sequence component under reverse sync speed coordinate system

utilize rotor position angle θ _rto three-phase rotor current I _ra～I _rccarry out dq conversion, obtain the rotor current synthetic vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

And then from stator voltage synthetic vector

the positive sequence component that middle extraction is corresponding

from stator voltage synthetic vector

the negative sequence component that middle extraction is corresponding

(3) utilize particle cluster algorithm to calculate reverse sync speed coordinate system lower rotor part electric current negative phase-sequence reference component

and then to rotor current negative phase-sequence reference component

carry out Rotating Transition of Coordinate and obtain forward synchronous speed coordinate system lower rotor part electric current negative phase-sequence reference component

make given rotor current positive sequence reference component

with rotor current negative phase-sequence reference component corresponding stack obtains the rotor current reference vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

(4) according to described rotor current synthetic vector and rotor current reference vector

by regulating error decoupling compensation algorithm, obtain modulation signal

(5) to modulation signal

carry out Park inverse transformation and obtain the modulation signal under the static alpha-beta coordinate system of rotor orientation

and then by SVPWM(space vector pulse width modulation) technical construction obtains one group of pwm signal so that DFIG is controlled.

In described step (3), utilize particle cluster algorithm to calculate reverse sync speed coordinate system lower rotor part electric current negative phase-sequence reference component

method as follows:

A1. initialization population under plane coordinate system, described population is comprised of a plurality of particles, and each particle is expressed as 2 * 2 vector of following form, and each element value under initial condition in this vector is given at random;

$P_i=\left[\begin{array}{cc}{z}_{i1}& z_{i2}\\ v_{i1}& v_{i2}\end{array}\right]$

Wherein: P _ifor the i particle in population, z _i1and z _i2for P _iposition attribution value and corresponding P _iabscissa under plane coordinate system and ordinate, vi ₁and v _i2for P _ispeed property value;

A2. according to following formula, calculate the comprehensive adaptive value of each particle in population, get particle and the more comprehensive adaptive value of current optimal particle of comprehensive adaptive value minimum, make particle that comprehensive adaptive value the is less optimal particle that is as the criterion;

GF _i＝weight ₁OF _i1+weight ₂OF _i2+weight ₃OF _i3

Wherein: GF _ifor particle P _icomprehensive adaptive value, OF _i1for particle P _iactive power of output wave component, OF _i2for particle P _ioutput reactive power fluctuation component, OF _i3for particle P _ithreephase stator electric current negative sequence component, weight ₁, weight ₂and weight ₃be weight coefficient;

A3. first, under plane coordinate system, centered by quasi-optimal particle, descend on the four direction of left and right newly-built four to be the position attribution value of disturbance particle the deterministic disturbances particle of L with its distance thereon, and then calculate the comprehensive adaptive value of four disturbance particles; Described disturbance particle is not included in population, and L is default disturbance displacement;

Then, relatively the comprehensive adaptive value of quasi-optimal particle and four disturbance particles, is updated to optimal particle by the particle of comprehensive adaptive value minimum;

A4. according to following formula, each particle in population is carried out after iteration renewal, return to execution step A2;

$P_{i=}^{\′}\left[\begin{array}{cc}{z}_{i1}^{\′}& z_{i2}^{\′}\\ v_{i1}^{\′}& v_{i2}^{\′}\end{array}\right]$

$v_{i1}^{\′}={\mathrm{wv}}_{i1}+c_1{r}_1(z_{g1}-z_{i1})$

$v_{i2}^{\′}={\mathrm{wv}}_{i2}+c_1{r}_1(z_{g2}-z_{i2})$

$\begin{array}{c}{z}_{i1}^{\′}=z_{i1}+v_{i1}^{\′}\\ z_{i2}^{\′}=z_{i2}+v_{i2}^{\′}\end{array}$

Wherein:

for the particle P after iteration renewal _i, w is inertia coeffeicent, r ₁for random parameter, c ₁for learning coefficient, z _g1and z _g2for the position attribution value of optimal particle and corresponding its abscissa and ordinate under plane coordinate system;

Two position attribution value z of optimal particle in each iteration renewal process _g1and z _g2corresponding to the required rotor current negative phase-sequence reference component of each control

Described active power of output wave component OFi ₁calculation expression as follows:

${\mathrm{OF}}_{i1}={\left(P_{s\cos 2}\right)}^2+{\left(P_{s\sin 2}\right)}^2$

${\mathrm{<figure-callout\; id="2"\; label="P\; s\; cos"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_{s\cos }=\frac{3}{2\mathrm{\&omega;}{L}_S}(-U_{\mathrm{sd}-}^{-}{U}_{\mathrm{sq}+}^{+}+U_{\mathrm{sq}-}^{-}{U}_{\mathrm{sd}+}^{+}+U_{\mathrm{sd}+}^{+}{U}_{\mathrm{sp}-}^{-}-U_{\mathrm{sq}+}^{+}{U}_{\mathrm{sd}-}^{-})+\frac{3L_m}{2L_S}(U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rd}+}^{+*}+U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sd}+}^{+}{z}_{i1}+U_{\mathrm{sq}+}^{+}{z}_{i2})$

${\mathrm{<figure-callout\; id="2"\; label="P\; s\; sin"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_{s\sin }=\frac{3}{2\mathrm{\&omega;}{L}_S}(-U_{\mathrm{sq}-}^{-}{U}_{\mathrm{sq}+}^{+}+U_{\mathrm{sd}-}^{-}{U}_{\mathrm{sd}+}^{+}+U_{\mathrm{sq}+}^{+}{U}_{\mathrm{sp}-}^{-}-U_{\mathrm{sd}+}^{+}{U}_{\mathrm{sd}-}^{-})+\frac{3L_m}{2L_S}(U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rd}+}^{+*}+U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sq}+}^{+}{z}_{i1}+U_{\mathrm{sd}+}^{+}{z}_{i2})$

Described output reactive power fluctuation component OFi ₂calculation expression as follows:

${\mathrm{OF}}_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">i</figure-callout>}2}={\left(Q_{s\cos 2}\right)}^2+{\left(Q_{s\sin 2}\right)}^2$

${\mathrm{<figure-callout\; id="2"\; label="Q\; s\; cos"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{s\cos }=\frac{3L_m}{2L_S}(U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rd}+}^{+*}-U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sq}+}^{+}{z}_{i1}-U_{\mathrm{sd}+}^{+}{z}_{i2})$

$Q_{s\sin 2}=\frac{3L_m}{2L_S}(U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rd}+}^{+*}-U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sd}+}^{+}{z}_{i1}-U_{\mathrm{sq}+}^{+}{z}_{i2})$

Described threephase stator electric current negative sequence component OFi ₃calculation expression as follows:

${\mathrm{OF}}_{\mathrm{<figure-callout\; id="3"\; label="i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">i</figure-callout>}3}={\left(I_{\mathrm{sd}-}^{-}\right)}^2+{\left(I_{\mathrm{sq}-}^{-}\right)}^2$

$I_{\mathrm{sd}-}^{-}=\frac{1}{L_S}(\frac{U_{\mathrm{sq}-}^{-}}{\mathrm{\&omega;}}-L_m{z}_{i1})$

Wherein: L _sfor the stator inductance of DFIG, L _mrotor mutual inductance for DFIG.

In described step (4), by regulating error decoupling compensation algorithm, obtain modulation signal

concrete grammar as follows:

First, make rotor current reference vector deduct respectively rotor current synthetic vector

obtain rotor current error vector

Then, to rotor current error vector

carry out vector ratio integral adjustment or proportional integral resonance and regulate, obtain voltage-regulation vector

Finally, according to following formula to voltage-regulation vector

carry out decoupling compensation, obtain modulation signal

$U_{\mathrm{cd}}^{+}=\mathrm{\&sigma;}{L}_r{V}_{\mathrm{cd}}^{+}+E_{\mathrm{rd}}^{+}$

$U_{\mathrm{cq}}^{+}=\mathrm{\&sigma;}{L}_r{V}_{\mathrm{cq}}^{+}+E_{\mathrm{rq}}^{+}$

$E_{\mathrm{rd}}^{+}=(R_r{I}_{\mathrm{rd}}^{+}-(\mathrm{\&omega;}-{\mathrm{\&omega;}}_r)\mathrm{\&sigma;}{L}_r{I}_{\mathrm{rq}}^{+})+L_m(U_{\mathrm{sd}}^{+}-R_S{I}_{\mathrm{sd}}^{+}+{\mathrm{\&omega;}}_r{\mathrm{\&psi;}}_{\mathrm{sq}}^{+})/L_S$

$E_{\mathrm{rq}}^{+}=(R_r{I}_{\mathrm{rq}}^{+}-(\mathrm{\&omega;}-{\mathrm{\&omega;}}_r)\mathrm{\&sigma;}{L}_r{I}_{\mathrm{rd}}^{+})+L_m(U_{\mathrm{sq}}^{+}-R_S{I}_{\mathrm{sq}}^{+}+{\mathrm{\&omega;}}_r{\mathrm{\&psi;}}_{\mathrm{sd}}^{+})/L_S$

Wherein: L _rand L _sbe respectively inductor rotor and the stator inductance of DFIG, R _rand R _sbe respectively rotor resistance and the stator resistance of DFIG, L _mfor the rotor mutual inductance of DFIG,

be respectively d axle component and the q axle component of stator magnetic linkage under forward synchronous speed coordinate system, the magnetic leakage factor that σ is DFIG.

The d axle component of described stator magnetic linkage with q axle component

$\begin{array}{c}{\mathrm{\&psi;}}_{\mathrm{sd}}^{+}=L_S{I}_{\mathrm{sd}}^{+}{L}_m{I}_{\mathrm{rd}}^{+}\\ {\mathrm{\&psi;}}_{\mathrm{sq}}^{+}=L_S{I}_{\mathrm{sq}}^{+}+L_m{I}_{\mathrm{rq}}^{+}\end{array}.$

According to following formula to rotor current error vector

carry out vector ratio integral adjustment:

$\begin{array}{c}{V}_{\mathrm{cd}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rd}}^{+}\\ V_{\mathrm{cq}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rq}}^{+}\end{array}$ $C_{\mathrm{VPI}}\left(s\right)=K_p+\frac{K_i}{s}+\frac{{\mathrm{<figure-callout\; id="2"\; label="K\; pr\; s"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{pr}}{s}^{}{}^2+K_{\mathrm{ir}}\mathrm{<figure-callout\; id="2"\; label="s\; s"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">s</figure-callout>}}{s^{}}$

Wherein: C _vPI(s) be the transfer function of vector ratio integral adjustment, K _pand K _prbe proportionality coefficient, K _iand K _irbe integral coefficient, ω _cfor resonant bandwidth coefficient, s is Laplacian.

According to following formula to rotor current error vector

carry out the adjusting of proportional integral resonance:

$\begin{array}{c}{V}_{\mathrm{cd}}^{+}=C_{\mathrm{PIR}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rd}}^{+}\\ V_{\mathrm{cq}}^{+}=C_{\mathrm{PIR}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rq}}^{+}\end{array}$ $C_{\mathrm{PIR}}\left(s\right)=K_p+\frac{K_i}{s}+\frac{{\mathrm{<figure-callout\; id="2"\; label="K\; pr\; s"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">K</figure-callout>}}_{\mathrm{pr}}{s}^{}{}^2+K_{\mathrm{ir}}\mathrm{<figure-callout\; id="2"\; label="s\; s"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">s</figure-callout>}}{s^{}}$

Wherein: C _pIR(s) transfer function regulating for proportional integral resonance, K _pfor proportionality coefficient, K _ifor integral coefficient, K _rfor resonance coefficient, ω _cfor resonant bandwidth coefficient, s is Laplacian.

The present invention takes into account the output threephase stator electric current of DFIG, active power of output and output reactive power, make this three's control performance can obtain multiobjective optimal control simultaneously, and the particle cluster algorithm code adopting is simplified, computing time is shorter, be conducive to the realization aspect calculating in real time, can effectively improve the operation control performance of DFIG under unbalanced electric grid voltage condition, guarantee stability and the safety of the quality of power supply and electric power system.Simultaneously the present invention adopts vector ratio integral adjustment or proportional integral resonance regulation technology, and wherein angular frequency is that the vector ratio integral adjustment of two times of fundamental frequencies or resonance regulate and can suppress negative sequence component adverse effect in line voltage.

Therefore compare traditional control method, the inventive method can be taken into account DFIG output threephase stator electric current simultaneously, active power of output and output reactive power, therefore can avoid occurring only taking a certain control target into account in traditional control method and cause all the other to control the greatly deterioration of targets, the feature of comprehensively taking into account a plurality of control targets makes the inventive method strengthen the runnability of DFIG under unbalanced electric grid voltage condition, is conducive to the reliable and stable operation of electrical network.

Accompanying drawing explanation

Fig. 1 is the principle process schematic diagram of control method of the present invention.

Fig. 2 is for adopting the simulation waveform figure of DFIG under control method of the present invention.

Embodiment

In order more specifically to describe the present invention, below in conjunction with the drawings and the specific embodiments, DFIG control method of the present invention is elaborated.

As shown in Figure 1, under a kind of uneven electrical network based on particle cluster algorithm, the multi objective control method of DFIG, comprises the steps:

(1) utilize three-phase voltage Hall element 2 to gather the threephase stator voltage U of DFIG _sa～U _sc, utilize three-phase current Hall element 3 to gather three-phase rotor current I _ra～I _rc, utilize orthogonal encoder 1 to gather rotational speed omega _rand rotor position angle θ _r, utilize phase-locked loop 4 to extract threephase stator voltage U _sa～U _scline voltage angular frequency and electric network voltage phase θ;

(2) according to electric network voltage phase θ, utilize 5 pairs of threephase stator voltage U of dq coordinate transformation module _sa～U _sccarry out dq conversion, correspondence obtains the stator voltage synthetic vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

and the stator voltage synthetic vector that comprises positive-negative sequence component under reverse sync speed coordinate system

with

according to rotor position angle θ _rutilize 5 couples of three-phase rotor current I of dq coordinate transformation module _ra～I _rccarry out dq conversion, obtain the rotor current synthetic vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

And then utilize positive-negative sequence component extraction module 6 from stator voltage synthetic vector middle extraction stator voltage positive sequence component

from stator voltage synthetic vector

middle extraction stator voltage negative sequence component

(3) utilize particle cluster algorithm module 7 to calculate reverse sync speed coordinate system lower rotor part electric current negative phase-sequence reference component

A. initialization population under plane coordinate system, population is comprised of a plurality of particles, and each particle is expressed as 2 * 2 vector of following form, and each element value under initial condition in this vector is given at random;

$P_i=\left[\begin{array}{cc}{z}_{i1}& z_{i2}\\ v_{i1}& {\mathrm{<figure-callout\; id="2"\; label="v\; i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">v</figure-callout>}}_i\end{array}\right]$

Wherein: P _ifor the i particle in population, z _i1and z _i2for P _iposition attribution value and corresponding P _iabscissa under plane coordinate system and ordinate, vi ₁and v _i2for P _ispeed property value;

B. according to following formula, calculate the comprehensive adaptive value of each particle in population, get particle and the more comprehensive adaptive value of current optimal particle of comprehensive adaptive value minimum, make particle that comprehensive adaptive value the is less optimal particle that is as the criterion;

GF _i=weight ₁OF _i1+weight ₂OF _i2+weight ₃OF _i3

${\mathrm{OF}}_{i1}={\left(P_{s\cos 2}\right)}^2+{\left(P_{s\sin 2}\right)}^2$

$P_{s\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">cos</figure-callout>}2}=\frac{3}{2\mathrm{\&omega;}{L}_S}(-U_{\mathrm{sd}-}^{-}{U}_{\mathrm{sq}+}^{+}+U_{\mathrm{sq}-}^{-}{U}_{\mathrm{sd}+}^{+}+U_{\mathrm{sd}+}^{+}{U}_{\mathrm{sp}-}^{-}-U_{\mathrm{sq}+}^{+}{U}_{\mathrm{sd}-}^{-})+\frac{3L_m}{2L_S}(U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rd}+}^{+*}+U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sd}+}^{+}{z}_{i1}+U_{\mathrm{sq}+}^{+}{z}_{i2})$

$P_{s\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">sin</figure-callout>}2}=\frac{3}{2\mathrm{\&omega;}{L}_S}(-U_{\mathrm{sq}-}^{-}{U}_{\mathrm{sq}+}^{+}+U_{\mathrm{sd}-}^{-}{U}_{\mathrm{sd}+}^{+}+U_{\mathrm{sq}+}^{+}{U}_{\mathrm{sp}-}^{-}-U_{\mathrm{sd}+}^{+}{U}_{\mathrm{sd}-}^{-})+\frac{3L_m}{2L_S}(U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rd}+}^{+*}+U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sq}+}^{+}{z}_{i1}+U_{\mathrm{sd}+}^{+}{z}_{i2})$

${\mathrm{OF}}_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">i</figure-callout>}2}={\left(Q_{s\cos 2}\right)}^2+{\left(Q_{s\sin 2}\right)}^2$

$Q_{s\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">cos</figure-callout>}2}=\frac{3L_m}{2L_S}(U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rd}+}^{+*}-U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sq}+}^{+}{z}_{i1}-U_{\mathrm{sd}+}^{+}{z}_{i2})$

$Q_{s\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">sin</figure-callout>}2}=\frac{3L_m}{2L_S}(U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rd}+}^{+*}-U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sd}+}^{+}{z}_{i1}-U_{\mathrm{sq}+}^{+}{z}_{i2})$

${\mathrm{OF}}_{\mathrm{<figure-callout\; id="3"\; label="i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">i</figure-callout>}3}={\left(I_{\mathrm{sd}-}^{-}\right)}^2+{\left(I_{\mathrm{sq}-}^{-}\right)}^2$

$I_{\mathrm{sd}-}^{-}=\frac{1}{L_S}(\frac{U_{\mathrm{sq}-}^{-}}{\mathrm{\&omega;}}-L_m{z}_{i1})$ $I_{\mathrm{sq}-}^{-}=\frac{1}{L_S}(\frac{U_{\mathrm{sd}-}^{-}}{-\mathrm{\&omega;}}-L_m{z}_{i2})$

Wherein: GF _ifor particle P _icomprehensive adaptive value, OF _i1for particle P _iactive power of output wave component, OF _i2for particle P _ioutput reactive power fluctuation component, OF _i3for particle P _ithreephase stator electric current negative sequence component, weight ₁, weight ₂and weight ₃be weight coefficient; In present embodiment, weight ₁=0.3, weight ₂=0.4, weight ₃=0.3;

C. first, under plane coordinate system, centered by quasi-optimal particle, descend on the four direction of left and right newly-built four to be the position attribution value of disturbance particle the deterministic disturbances particle of L with its distance thereon, and then calculate the comprehensive adaptive value of four disturbance particles; Disturbance particle is not included in population, and L is default disturbance displacement, L=0.00001 in present embodiment;

Then, relatively the comprehensive adaptive value of quasi-optimal particle and four disturbance particles, is updated to optimal particle by the particle of comprehensive adaptive value minimum;

D. according to following formula, each particle in population is carried out after iteration renewal, return to execution step B;

$P_{i=}^{\&prime;}\left[\begin{array}{cc}{z}_{i1}^{\&prime;}& {\mathrm{<figure-callout\; id="2"\; label="z\; i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">z</figure-callout>}}_i^2\\ v_{i1}^{\&prime;}& v_{i2}^{\&prime;}\end{array}\right]$

$v_{i1}^{\&prime;}={\mathrm{wv}}_{i1}+c_1{r}_1(z_{g1}-z_{i1})$

$v_{i2}^{\&prime;}={\mathrm{<figure-callout\; id="2"\; label="wv\; i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">wv</figure-callout>}}_i+c_1{r}_1(z_{g2}-z_{i2})$

$\begin{array}{c}{z}_{i1}^{\&prime;}=z_{i1}+v_{i1}^{\&prime;}\\ {\mathrm{<figure-callout\; id="2"\; label="z\; i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">z</figure-callout>}}_i^2={\mathrm{<figure-callout\; id="2"\; label="z\; i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">z</figure-callout>}}_i+{\mathrm{<figure-callout\; id="2"\; label="v\; i"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">v</figure-callout>}}_i^2\end{array}$

Wherein:

for the particle P after iteration renewal _i, w is inertia coeffeicent, r ₁for random parameter, c ₁for learning coefficient, z _g1and z _g2for the position attribution value of optimal particle and corresponding its abscissa and ordinate under plane coordinate system; In present embodiment, w=0.8, c ₁=1;

Two position attribution value z of optimal particle in each iteration renewal process _g1and z _g2as the each fast coordinate system lower rotor part of required reverse sync electric current negative phase-sequence reference component of controlling

Obtain rotor current negative phase-sequence reference component

after, utilize 8 conversion of rotation of coordinate module to obtain forward synchronous speed coordinate system lower rotor part electric current negative phase-sequence reference component

by rotor current positive sequence reference component

with

with negative phase-sequence reference component corresponding stack obtains the rotor current reference vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

in present embodiment,

(4) according to rotor current synthetic vector

and rotor current reference vector

by regulating error decoupling compensation algorithm, obtain modulation signal

First, make rotor current reference vector

deduct respectively rotor current synthetic vector

obtain rotor current error vector

Then, utilize the following formula of vector proportional and integral controller 9 basis to rotor current error vector

with

carry out vector ratio integral adjustment, obtain voltage-regulation vector

$\begin{array}{c}{V}_{\mathrm{cd}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rd}}^{+}\\ V_{\mathrm{cq}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rq}}^{+}\end{array}$ $C_{\mathrm{VPI}}\left(s\right)=K_p+\frac{K_i}{s}+\frac{K_{\mathrm{pr}}{s}^2+K_{\mathrm{ir}}s}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000439824640000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+{\mathrm{\&omega;}}_{c}s+{\left(2\mathrm{\&omega;}\right)}^2}$

Wherein: C _vPI(s) be the transfer function of vector ratio integral adjustment, K _pand K _prbe proportionality coefficient, K _iand K _irbe integral coefficient, ω _cfor resonant bandwidth coefficient, s is Laplacian; In present embodiment, K _p=1.5, K _i=0.5, K _pr=1, K _ir=700, ω _c=15rad/s;

Finally, utilize the following formula of feedback compensation decoupling module 10 basis to voltage-regulation vector carry out decoupling compensation, obtain modulation signal

$U_{\mathrm{cd}}^{+}=\mathrm{\&sigma;}{L}_r{V}_{\mathrm{cd}}^{+}+E_{\mathrm{rd}}^{+}$

$U_{\mathrm{cq}}^{+}=\mathrm{\&sigma;}{L}_r{V}_{\mathrm{cq}}^{+}+E_{\mathrm{rq}}^{+}$

$E_{\mathrm{rd}}^{+}=(R_r{I}_{\mathrm{rd}}^{+}-(\mathrm{\&omega;}-{\mathrm{\&omega;}}_r)\mathrm{\&sigma;}{L}_r{I}_{\mathrm{rq}}^{+})+L_m(U_{\mathrm{sd}}^{+}-R_S{I}_{\mathrm{sd}}^{+}+{\mathrm{\&omega;}}_r{\mathrm{\&psi;}}_{\mathrm{sq}}^{+})/L_S$

$E_{\mathrm{rq}}^{+}=(R_r{I}_{\mathrm{rq}}^{+}-(\mathrm{\&omega;}-{\mathrm{\&omega;}}_r)\mathrm{\&sigma;}{L}_r{I}_{\mathrm{rd}}^{+})+L_m(U_{\mathrm{sq}}^{+}-R_S{I}_{\mathrm{sq}}^{+}+{\mathrm{\&omega;}}_r{\mathrm{\&psi;}}_{\mathrm{sd}}^{+})/L_S$

$\begin{array}{c}{\mathrm{\&psi;}}_{\mathrm{sd}}^{+}=L_S{I}_{\mathrm{sd}}^{+}{L}_m{I}_{\mathrm{rd}}^{+}\\ {\mathrm{\&psi;}}_{\mathrm{sq}}^{+}=L_S{I}_{\mathrm{sq}}^{+}+L_m{I}_{\mathrm{rq}}^{+}\end{array}.$

Wherein: L _rand L _sbe respectively inductor rotor and the stator inductance of DFIG, R _rand R _sbe respectively rotor resistance and the stator resistance of DFIG, L _mfor the rotor mutual inductance of DFIG, the magnetic leakage factor that σ is DFIG.

(5) utilize 11 pairs of modulation signals of anti-Park coordinate transformation module

carry out Park inverse transformation and obtain the modulation signal under the static alpha-beta coordinate system of rotor orientation

$\left[\begin{array}{c}{U}_{\mathrm{c\&alpha;}}^{+}\\ U_{\mathrm{c\&beta;}}^{+}\end{array}\right]=\left[\begin{array}{cc}\cos (\mathrm{\&theta;}-{\mathrm{\&theta;}}_r)& -\sin (\mathrm{\&theta;}-{\mathrm{\&theta;}}_r)\\ \sin (\mathrm{\&theta;}-{\mathrm{\&theta;}}_r)& \cos (\mathrm{\&theta;}-{\mathrm{\&theta;}}_r)\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{cd}}^{+}\\ U_{\mathrm{cq}}^{+}\end{array}\right]$

And then, utilize pulse width modulation module 12 to obtain one group of pwm signal S by SVPWM technical construction _a～S _cwith the IGBT in DFIG converter 13, carry out switch control.

We,, to adopting the DFIG under present embodiment control to carry out emulation experiment, in having four simulation time sections altogether, adopt respectively the following 4 groups of weight coefficients by user's appointment below, and the simulation waveform of system as shown in Figure 2.

1.weight ₁=1.0，weight ₂=0.0，weight ₃=0.0；

2.weight ₁=0.0，weight ₂=1.0，weigh _t3=0.0；

3.weight ₁=0.0，weight ₂=0.0，weight ₃=1.0；

4.weight ₁=0.3，weight ₂=0.2，weight ₃=0.5。

From simulation result, the performance of DFIG system is steady by the active power of output of first stage gradually, the output reactive power that transits to second stage is steady, three-phase output stator electric current to the phase III is symmetrical, in fourth stage, comprehensively take into account three and controlled target, make three-phase output stator current asymmetry degree, active power of output and reactive power fluctuation are all within the acceptable scope of electrical network.

As can be seen here, after adopting present embodiment, the three-phase output stator electric current of DFIG system under uneven electrical network, active power of output and output reactive power can be realized different DFIG systems and show by setting different weight coefficients by user, are conducive to this reliable and stable operation under unbalanced electric grid voltage condition of electrical network and DFIG.

Claims (9)

1. a multi objective control method of DFIG under the uneven electrical network based on particle cluster algorithm, comprises the steps:

(1) gather the threephase stator voltage U of DFIG _sa～U _sc, three-phase rotor current I _ra～I _rc, threephase stator electric current I _sa～I _sc, rotational speed omega _rand rotor position angle θ _r, and utilize phase-locked loop to extract threephase stator voltage U _sa～U _scangular frequency and phase theta;

(2) utilize phase theta respectively to threephase stator voltage U _sa～U _scwith threephase stator electric current I _sa～I _sccarry out dq conversion, obtain the stator voltage synthetic vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

stator current synthetic vector

and the stator voltage synthetic vector that comprises positive-negative sequence component under reverse sync speed coordinate system

utilize rotor position angle θ _rto three-phase rotor current I _ra～I _rccarry out dq conversion, obtain the rotor current synthetic vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

And then from stator voltage synthetic vector the positive sequence component that middle extraction is corresponding

from stator voltage synthetic vector

the negative sequence component that middle extraction is corresponding

(3) utilize particle cluster algorithm to calculate reverse sync speed coordinate system lower rotor part electric current negative phase-sequence reference component and then to rotor current negative phase-sequence reference component

carry out Rotating Transition of Coordinate and obtain forward synchronous speed coordinate system lower rotor part electric current negative phase-sequence reference component

make given rotor current positive sequence reference component with rotor current negative phase-sequence reference component

corresponding stack obtains the rotor current reference vector that comprises positive-negative sequence component under forward synchronous speed coordinate system

(4) according to described rotor current synthetic vector and rotor current reference vector

by regulating error decoupling compensation algorithm, obtain modulation signal

(5) to modulation signal

carry out Park inverse transformation and obtain the modulation signal under the static alpha-beta coordinate system of rotor orientation

and then obtain one group of pwm signal so that DFIG is controlled by SVPWM technical construction.

2. multi objective control method according to claim 1, is characterized in that: in described step (3), utilize particle cluster algorithm to calculate reverse sync speed coordinate system lower rotor part electric current negative phase-sequence reference component

with

A1. initialization population under plane coordinate system, described population is comprised of a plurality of particles, and each particle is expressed as 2 * 2 vector of following form, and each element value under initial condition in this vector is given at random;

$P_i=\left[\begin{array}{cc}{z}_{i1}& z_{i2}\\ v_{i1}& v_{i2}\end{array}\right]$

Wherein: P _ifor the i particle in population, z _i1and z _i2for P _iposition attribution value and corresponding P _iabscissa under plane coordinate system and ordinate, vi ₁and v _i2for P _ispeed property value;

A2. according to following formula, calculate the comprehensive adaptive value of each particle in population, get particle and the more comprehensive adaptive value of current optimal particle of comprehensive adaptive value minimum, make particle that comprehensive adaptive value the is less optimal particle that is as the criterion;

GF _i＝weight ₁OF _i1+weight ₂OF _i2+weight ₃OF _i3

Wherein: GF _ifor particle P _icomprehensive adaptive value, OF _i1for particle P _iactive power of output wave component, OF _i2for particle P _ioutput reactive power fluctuation component, OF _i3for particle P _ithreephase stator electric current negative sequence component, weight ₁, weight ₂and weight ₃be weight coefficient;

A3. first, under plane coordinate system, centered by quasi-optimal particle, descend on the four direction of left and right newly-built four to be the position attribution value of disturbance particle the deterministic disturbances particle of L with its distance thereon, and then calculate the comprehensive adaptive value of four disturbance particles; Described disturbance particle is not included in population, and L is default disturbance displacement;

Then, relatively the comprehensive adaptive value of quasi-optimal particle and four disturbance particles, is updated to optimal particle by the particle of comprehensive adaptive value minimum;

A4. according to following formula, each particle in population is carried out after iteration renewal, return to execution step A2;

$v_{i1}^{\&prime;}={\mathrm{wv}}_{i1}+c_1{r}_1(z_{g1}-z_{i1})$ $P_{i=}^{\&prime;}\left[\begin{array}{cc}{z}_{i1}^{\&prime;}& z_{i2}^{\&prime;}\\ v_{i1}^{\&prime;}& v_{i2}^{\&prime;}\end{array}\right]$ $v_{i2}^{\&prime;}={\mathrm{wv}}_{i2}+c_1{r}_1(z_{g2}-z_{i2})$ $\begin{array}{c}{z}_{i1}^{\&prime;}=z_{i1}+v_{i1}^{\&prime;}\\ z_{i2}^{\&prime;}=z_{i2}+v_{i2}^{\&prime;}\end{array}$

Wherein:

for the particle P after iteration renewal _i, w is inertia coeffeicent, r ₁for random parameter, c ₁for learning coefficient, z _g1and z _g2for the position attribution value of optimal particle and corresponding its abscissa and ordinate under plane coordinate system;

Two position attribution value z of optimal particle in each iteration renewal process _g1and z _g2corresponding to the required rotor current negative phase-sequence reference component of each control

3. multi objective control method according to claim 2, is characterized in that: described active power of output wave component OFi ₁calculation expression as follows:

${\mathrm{OF}}_{i1}={\left(P_{s\cos 2}\right)}^2+{\left(P_{s\sin 2}\right)}^2$

$P_{s\cos 2}=\frac{3}{2\mathrm{\&omega;}{L}_S}(-U_{\mathrm{sd}-}^{-}{U}_{\mathrm{sq}+}^{+}+U_{\mathrm{sq}-}^{-}{U}_{\mathrm{sd}+}^{+}+U_{\mathrm{sd}+}^{+}{U}_{\mathrm{sp}-}^{-}-U_{\mathrm{sq}+}^{+}{U}_{\mathrm{sd}-}^{-})+\frac{3L_m}{2L_S}(U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rd}+}^{+*}+U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sd}+}^{+}{z}_{i1}+U_{\mathrm{sq}+}^{+}{z}_{i2})$

$P_{s\sin 2}=\frac{3}{2\mathrm{\&omega;}{L}_S}(-U_{\mathrm{sq}-}^{-}{U}_{\mathrm{sq}+}^{+}+U_{\mathrm{sd}-}^{-}{U}_{\mathrm{sd}+}^{+}+U_{\mathrm{sq}+}^{+}{U}_{\mathrm{sp}-}^{-}-U_{\mathrm{sd}+}^{+}{U}_{\mathrm{sd}-}^{-})+\frac{3L_m}{2L_S}(U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rd}+}^{+*}+U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sq}+}^{+}{z}_{i1}+U_{\mathrm{sd}+}^{+}{z}_{i2})$

Wherein: L _sfor the stator inductance of DFIG, L _mrotor mutual inductance for DFIG.

4. multi objective control method according to claim 2, is characterized in that: described output reactive power fluctuation component OFi ₂calculation expression as follows:

${\mathrm{OF}}_{i2}={\left(Q_{s\cos 2}\right)}^2+{\left(Q_{s\sin 2}\right)}^2$

$Q_{s\cos 2}=\frac{3L_m}{2L_S}(U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rd}+}^{+*}-U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sq}+}^{+}{z}_{i1}-U_{\mathrm{sd}+}^{+}{z}_{i2})$

$Q_{s\sin 2}=\frac{3L_m}{2L_S}(U_{\mathrm{sd}-}^{-}{I}_{\mathrm{rd}+}^{+*}-U_{\mathrm{sq}-}^{-}{I}_{\mathrm{rq}+}^{+*}+U_{\mathrm{sd}+}^{+}{z}_{i1}-U_{\mathrm{sq}+}^{+}{z}_{i2})$

Wherein: L _sfor the stator inductance of DFIG, L _mrotor mutual inductance for DFIG.

5. multi objective control method according to claim 2, is characterized in that: described threephase stator electric current negative sequence component OFi ₃calculation expression as follows:

${\mathrm{OF}}_{i3}={\left(I_{\mathrm{sd}-}^{-}\right)}^2+{\left(I_{\mathrm{sq}-}^{-}\right)}^2$

$I_{\mathrm{sd}-}^{-}=\frac{1}{L_S}(\frac{U_{\mathrm{sq}-}^{-}}{\mathrm{\&omega;}}-L_m{z}_{i1})$ $I_{\mathrm{sq}-}^{-}=\frac{1}{L_S}(\frac{U_{\mathrm{sd}-}^{-}}{-\mathrm{\&omega;}}-L_m{z}_{i2})$

Wherein: L _sfor the stator inductance of DFIG, L _mrotor mutual inductance for DFIG.

6. multi objective control method according to claim 1, is characterized in that: in described step (4), by regulating error decoupling compensation algorithm, obtain modulation signal

concrete grammar as follows:

First, make rotor current reference vector

deduct respectively rotor current synthetic vector obtain rotor current error vector

Then, to rotor current error vector

carry out vector ratio integral adjustment or proportional integral resonance and regulate, obtain voltage-regulation vector

Finally, according to following formula to voltage-regulation vector

carry out decoupling compensation, obtain modulation signal

$U_{\mathrm{cd}}^{+}=\mathrm{\&sigma;}{L}_r{V}_{\mathrm{cd}}^{+}+E_{\mathrm{rd}}^{+}$

$U_{\mathrm{cq}}^{+}=\mathrm{\&sigma;}{L}_r{V}_{\mathrm{cq}}^{+}+E_{\mathrm{rq}}^{+}$

$E_{\mathrm{rd}}^{+}=(R_r{I}_{\mathrm{rd}}^{+}-(\mathrm{\&omega;}-{\mathrm{\&omega;}}_r)\mathrm{\&sigma;}{L}_r{I}_{\mathrm{rq}}^{+})+L_m(U_{\mathrm{sd}}^{+}-R_S{I}_{\mathrm{sd}}^{+}+{\mathrm{\&omega;}}_r{\mathrm{\&psi;}}_{\mathrm{sq}}^{+})/L_S$

$E_{\mathrm{rq}}^{+}=(R_r{I}_{\mathrm{rq}}^{+}-(\mathrm{\&omega;}-{\mathrm{\&omega;}}_r)\mathrm{\&sigma;}{L}_r{I}_{\mathrm{rd}}^{+})+L_m(U_{\mathrm{sq}}^{+}-R_S{I}_{\mathrm{sq}}^{+}+{\mathrm{\&omega;}}_r{\mathrm{\&psi;}}_{\mathrm{sd}}^{+})/L_S$

Wherein: L _rand L _sbe respectively inductor rotor and the stator inductance of DFIG, R _rand R _sbe respectively rotor resistance and the stator resistance of DFIG, L _mfor the rotor mutual inductance of DFIG, be respectively d axle component and the q axle component of stator magnetic linkage under forward synchronous speed coordinate system, the magnetic leakage factor that σ is DFIG.

7. multi objective control method according to claim 6, is characterized in that: the d axle component of described stator magnetic linkage with q axle component calculation expression as follows:

$\begin{array}{c}{\mathrm{\&psi;}}_{\mathrm{sd}}^{+}=L_S{I}_{\mathrm{sd}}^{+}{L}_m{I}_{\mathrm{rd}}^{+}\\ {\mathrm{\&psi;}}_{\mathrm{sq}}^{+}=L_S{I}_{\mathrm{sq}}^{+}+L_m{I}_{\mathrm{rq}}^{+}\end{array}.$

8. multi objective control method according to claim 6, is characterized in that: according to following formula to rotor current error vector carry out vector ratio integral adjustment:

$\begin{array}{c}{V}_{\mathrm{cd}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rd}}^{+}\\ V_{\mathrm{cq}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rq}}^{+}\end{array}$ $C_{\mathrm{VPI}}\left(s\right)=K_p+\frac{K_i}{s}+\frac{K_{\mathrm{pr}}{s}^2+K_{\mathrm{ir}}s}{s^2+{\mathrm{\&omega;}}_{c}s+{\left(\mathrm{c\&omega;}\right)}^2}$

Wherein: C _vPI(s) be the transfer function of vector ratio integral adjustment, K _pand K _prbe proportionality coefficient, K _iand K _irbe integral coefficient, ω _cfor resonant bandwidth coefficient, s is Laplacian.

9. multi objective control method according to claim 6, is characterized in that: according to following formula to rotor current error vector carry out the adjusting of proportional integral resonance:

$\begin{array}{c}{V}_{\mathrm{cd}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rd}}^{+}\\ V_{\mathrm{cq}}^{+}=C_{\mathrm{VPI}}\left(s\right)\mathrm{\&Delta;}{I}_{\mathrm{rq}}^{+}\end{array}$ $C_{\mathrm{VPI}}\left(s\right)=K_p+\frac{K_i}{s}+\frac{K_{\mathrm{pr}}{s}^2+K_{\mathrm{ir}}s}{s^2+{\mathrm{\&omega;}}_{c}s+{\left(\mathrm{c\&omega;}\right)}^2}$

Wherein: C _pIR(s) transfer function regulating for proportional integral resonance, K _pfor proportionality coefficient, K _ifor integral coefficient, K _rfor resonance coefficient, ω _cfor resonant bandwidth coefficient, s is Laplacian.

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