CN107846041A - A kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system - Google Patents

A kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system Download PDF

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CN107846041A
CN107846041A CN201711122161.8A CN201711122161A CN107846041A CN 107846041 A CN107846041 A CN 107846041A CN 201711122161 A CN201711122161 A CN 201711122161A CN 107846041 A CN107846041 A CN 107846041A
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CN107846041B (en
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王环
曾国强
戴瑜兴
吴烈
李理敏
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Wenzhou University
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    • H02J3/386—
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The present invention discloses a kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system, using the controlling electric energy structure of back-to-back total power unsteady flow, pusher side converter control system and the state-space model of net side current transformer control system are established respectively, and by the pusher side Variable flow control module in direct-drive permanent magnetism synchronous wind generating system, the weighted superposition of the absolute value of the tracking error of net side Variable flow control module and the sum of products system output voltage waveform total harmonic distortion factor of time is as the fitness function for assessing control performance, design the difference optimal control method based on real coding, realize the optimization of PI controller parameters in direct-drive permanent magnetism synchronous wind generating system.The control method of the present invention can effectively improve direct-drive permanent magnetism synchronous wind generating system operating efficiency and power generating quality, energy conversion efficiency, the operational reliability of Wind turbines, and ensure that direct-drive permanent magnetism synchronous wind generating system stabilization time is shorter when power network disturbs, steady-state error is smaller, and robustness is stronger.

Description

A kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system
Technical field
The present invention relates to grid-connected power generation system field intelligent control technology, and in particular to a kind of direct-drive permanent-magnet synchronous wind-force The difference optimal control method of electricity generation system.
Background technology
Direct-drive permanent magnetism synchronous wind generating system (Directly-driven Permanent Magnet Synchronous Generator, hereinafter referred to as D-PMSG) complicated mechanical transmission mechanism is saved, by using total power unsteady flow controlling electric energy, drop The low loss of wind power generating set, improve the energy conversion efficiency and operational reliability of Wind turbines.Full power convertor Operation characteristic and electric energy output quality of the controlling electric energy strategy to D-PMSG has very crucial influence.Hold in wind power integration power network The background to increase sharply, the failure defensive ability/resistance ability that grid-connected directly driven wind-powered unit must be stronger are measured, and is had when power network disturbs There are stronger robustness and certain antijamming capability.Therefore, effective D-PMSG total power grid-connected converter control how is designed System processed has important engineering application value.
D-PMSG total power grid-connected converter control strategy is common at present to have the uncontrollable rectifier of pusher side to connect net side IGCT The uncontrollable rectification of inversion control strategy, pusher side connects net side PWM voltage source type inversion control strategy, the uncontrollable rectification of pusher side connects Boost boostings connect PWM voltage source inversion control strategy and back-to-back total power Variable flow control strategy etc..Back-to-back total power becomes Flow control policy regulates and controls by using pusher side PWM commutation systems to the rotating speed and reactive power of permanent magnet synchronous motor, real Now wind energy optimal power is tracked；Stablize by using the stable middle dc voltage of net side PWM inversion systems and regulate and control injection electricity The reactive power of net.For back-to-back total power Variable flow control strategy because both-end is PWM converter systems, control is more flexible, but Also increase the complexity and uncertainty of system optimization control.Difference optimal control is as a kind of theoretical based on swarm intelligence New system optimizing control, the application study in power system are started late, and are concentrated mainly on Electric Power Network Planning, load economy point Match somebody with somebody, optimal load flow calculate etc..How by setting multiple target weighting function, the back-to-back total powers of design D-PMSG become for research The DE optimal control methods of device electric energy control system are flowed, to lift work of the wind power system under complex working condition and uncertain factor Make efficiency and power generating quality, be the generally acknowledged problem in a domestic and international academia and engineer applied field.
The content of the invention
In view of the shortcomings of the prior art, the present invention provides a kind of difference optimization control of direct-drive permanent magnetism synchronous wind generating system Method processed, this method can effectively improve D-PMSG operating efficiency and the energy conversion efficiency of power generating quality and Wind turbines And operational reliability, and ensuring that D-PMSG stabilization times are shorter when power network disturbs, steady-state error is smaller, and robustness is more By force.Concrete technical scheme is as follows：
A kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system, it is characterised in that the system uses Back-to-back full power convertor controlling electric energy structure, wherein pusher side current transformer control generator speed and power output, net side become Flow device stable DC busbar voltage, active power, the reactive power of control electricity generation system output；This method comprises the following steps：
(1) modeling method described by using duty cycle functions establishes the state-space model of net side current transformer system：
Wherein, L is filter inductance, and R is the equivalent resistance of filter inductance, C filter capacitors, ekFor three phase network electromotive force, ik For three-phase output current, dkFor dutycycle, udcFor DC bus-bar voltage, edFor dc bus side direct electromotive force., RdIt is female for direct current Line side equivalent resistance；
(2) formula (1) is subjected to d, q synchronous rotating angle so that the state-space model of net side current transformer system It is adjusted to：
Wherein, ed、eqFor d, q axis component under three phase network electromotive force two-phase synchronous rotating frame, id、iqFor net side D, q axis component under converter system output current two-phase synchronous rotating frame, dd、dqIt is synchronised for equivalent switch function two D, q axis component under rotating coordinate system；ω is three-phase power grid voltage angular frequency.
(3) by being modeled under two-phase synchronous rotating frame to pusher side converter system, the electricity of threephase stator winding can be obtained Press equation：
Wherein usa、usb、usc- stator three-phase voltage, isa、isb、isc- stator three-phase current.RsThe winding electricity of-stator Resistance, ψa、ψb、ψc- stator is as follows per phase winding magnetic linkage, its expression formula：
Wherein Laa、Lbb、LccBe stator per phase winding inductance, Mab=Mba、Mbc=Mcb、Mac=McaBetween every phase winding Mutual inductance, ψfa、ψfb、ψfcIt is expressed as each pole permanent magnet flux linkage of three-phase windings：
Wherein, ψfFor permanent magnet excitation magnetic linkage；
(4) obtaining pusher side converter system state space equation according to formula (3), (4) and (5) is：
Wherein, p is differential operator, LsFor the winding inductance of stator.In three-phase system,
isa+isb+isc=0 (7)
Formula (4)-(7) are merged, pusher side converter system state space equation is further transformed to：
Wherein, ωeFor the angular rate of rotor；
(5) formula (8) is subjected to d, q synchronous rotating angle, the state-space model of final pusher side converter system It is adjusted to：
Wherein, usd、usqFor d, q axis component under stator three-phase voltage two-phase synchronous rotating frame, isd、isqStator three D, q axis component under phase current two-phase synchronous rotating frame, ψd、ψqGenerator magnetic linkage d, q axis component, Ld、LqStator winding D, q axis component of inductance, ωsFor generator angular speed.
(6) PI controllers are combined using formula (2), (9), (10), obtained in direct-drive permanent magnetism synchronous wind generating system Back-to-back full power convertor electric energy control system；
(7) start to carry out difference optimization to the system obtained in step (6), the parameter value for setting difference to optimize：Variation because Sub- F, intersect factor CR, population size M, maximum iteration G；
(8) in the direct-drive permanent magnetism synchronous wind generating for randomly generating a real coding for meeting formula (11) constraints Initial population P={ the x of the electric energy control system PI controller variables of back-to-back total power unsteady flow1,x2,…,xp, wherein i-th Body xiRepresent controlling increment sequence { K to be optimizedp1i,Ki1i,Kp2i,Ki2i,Kp3i,Ki3i,Kp4i,Ki4i, it is specific to produce process such as Under：
xij=Δ umin+randij(Δumax-Δumin), i=1,2 ..., p；J=1,2 ..., 8 (11)
Wherein, Δ uminWith Δ umaxThe lower and upper limit of controlling increment sequence, rand are represented respectivelyijOne group is represented in 0 and 1 Between caused random number；
(9) according to formula (11) to each individual x in population Pi, i=1,2 ..., p carries out object function fiCalculating is commented Valency, it is specific as shown in formula (13), and current minimum target function value in population is arranged to fbest, corresponding individual is set It is set to and currently preferably solves Sbest；
Wherein, e1And e2The tracking error of pusher side Variable flow control module and net side Variable flow control module is represented respectively, and t is represented System operation moment value, TminAnd TmaxThe initial time of three-phase inversion system operation is represented respectively and terminates the time, and THD represents straight The voltage waveform percent harmonic distortion of drive permanent magnetism synchronous wind generating system output, w1And w2Weight coefficient is represented, and meets w1+w2 =1；
(10) mutation operation is carried out to population, 3 individual x is randomly choosed from colonyp1, xp2, xp3, and i, p1, p2, p3 are mutual Unequal, specific mutation operation is as follows：
hij(t+1)=xp1j(t)+F·(xp2j(t)-xp3j(t)) (13)
Wherein, hij(t+1) it is intermediate variable individual after temporary variation；
(11) in order to increase the diversity of interference parameter vector, carry out crossover operation again to the population after mutation operation, have Gymnastics is made as follows：
Wherein, randlijRepresent one group of caused random number between zero and one, vij(t+1) to be individual after temporary intersect Intermediate variable；
(12) in order to determine xi(t) follow-on member can be turned into, experiment vector v is obtained using formula (12)i(t+1) With object vector xi(t) value of evaluation function, and it is compared, concrete operations are as follows：
(13) repeat step (9)~(12) obtain the optimal change of PI controllers until system operation to maximum iteration G Amount, so as to be controlled to the electric energy control system of back-to-back total power unsteady flow in direct-drive permanent magnetism synchronous wind generating.
Compared with prior art, beneficial effects of the present invention are as follows：
Using the difference optimal control method of the back-to-back total power converter systems of D-PMSG of the present invention, can effectively improve D-PMSG operating efficiency and power generating quality, the energy conversion efficiency and operational reliability of Wind turbines, and disturbed in power network Ensure that D-PMSG stabilization times are shorter when dynamic, steady-state error is smaller, and robustness is stronger.
Brief description of the drawings
Fig. 1 is a direct-drive permanent magnetism synchronous wind generating system architecture diagram and DE optimal control principle schematics；
Fig. 2 is the implementation process flow chart of the control method of the present invention；
Fig. 3 is the target function value optimization process curve map after the control method of the present invention is implemented；
Fig. 4 is three-phase electricity output voltage waveforms of the D-PMSG after the present invention is implemented in RT-LAB electric power real-time simulation platforms Figure.
Embodiment
Representational embodiment specifically describes present disclosure below, but these embodiments are not used in limitation this paper institutes Belong to the scope of invention.
As illustrated in fig. 1 and 2, a kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system, the system are adopted With back-to-back full power convertor controlling electric energy structure, wherein pusher side current transformer control generator speed and power output, net side Current transformer stable DC busbar voltage, active power, the reactive power of control electricity generation system output；This method includes following step Suddenly：
A kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system, it is characterised in that the system uses Back-to-back full power convertor controlling electric energy structure, wherein pusher side current transformer control generator speed and power output, net side become Flow device stable DC busbar voltage, active power, the reactive power of control electricity generation system output；This method comprises the following steps：
(1) modeling method described by using duty cycle functions establishes the state-space model of net side current transformer system：
Wherein, L is filter inductance, and R is the equivalent resistance of filter inductance, C filter capacitors, ekFor three phase network electromotive force, ik For three-phase output current, dkFor dutycycle, udcFor DC bus-bar voltage, edFor dc bus side direct electromotive force., RdIt is female for direct current Line side equivalent resistance；
(2) formula (1) is subjected to d, q synchronous rotating angle so that the state-space model of net side current transformer system It is adjusted to：
Wherein, ed、eqFor d, q axis component under three phase network electromotive force two-phase synchronous rotating frame, id、iqFor net side D, q axis component under converter system output current two-phase synchronous rotating frame, dd、dqIt is synchronised for equivalent switch function two D, q axis component under rotating coordinate system；ω is three-phase power grid voltage angular frequency.
(3) by being modeled under two-phase synchronous rotating frame to pusher side converter system, the electricity of threephase stator winding can be obtained Press equation：
Wherein usa、usb、usc- stator three-phase voltage, isa、isb、isc- stator three-phase current.RsThe winding electricity of-stator Resistance, ψa、ψb、ψc- stator is as follows per phase winding magnetic linkage, its expression formula：
Wherein Laa、Lbb、LccBe stator per phase winding inductance, Mab=Mba、Mbc=Mcb、Mac=McaBetween every phase winding Mutual inductance, ψfa、ψfb、ψfcIt is expressed as each pole permanent magnet flux linkage of three-phase windings：
Wherein, ψfFor permanent magnet excitation magnetic linkage；
(4) obtaining pusher side converter system state space equation according to formula (3), (4) and (5) is：
Wherein, p is differential operator, LsFor the winding inductance of stator.In three-phase system,
isa+isb+isc=0 (7)
Formula (4)-(7) are merged, pusher side converter system state space equation is further transformed to：
Wherein, ωeFor the angular rate of rotor；
(5) formula (8) is subjected to d, q synchronous rotating angle, the state-space model of final pusher side converter system It is adjusted to：
Wherein, usd、usqFor d, q axis component under stator three-phase voltage two-phase synchronous rotating frame, isd、isqStator three D, q axis component under phase current two-phase synchronous rotating frame, ψd、ψqGenerator magnetic linkage d, q axis component, Ld、LqStator winding D, q axis component of inductance, ωsFor generator angular speed.
(6) PI controllers are combined using formula (2), (9), (10), obtained in direct-drive permanent magnetism synchronous wind generating system Back-to-back full power convertor electric energy control system；
(7) start to carry out difference optimization to the system obtained in step (6), the parameter value for setting difference to optimize：Variation because Sub- F, intersect factor CR, population size M, maximum iteration G；
(8) in the direct-drive permanent magnetism synchronous wind generating for randomly generating a real coding for meeting formula (11) constraints Initial population P={ the x of the electric energy control system PI controller variables of back-to-back total power unsteady flow1,x2,…,xp, wherein i-th Body xiRepresent controlling increment sequence { K to be optimizedp1i,Ki1i,Kp2i,Ki2i,Kp3i,Ki3i,Kp4i,Ki4i, it is specific to produce process such as Under：
xij=Δ umin+randij(Δumax-Δumin), i=1,2 ..., p；J=1,2 ..., 8 (11)
Wherein, Δ uminWith Δ umaxThe lower and upper limit of controlling increment sequence, rand are represented respectivelyijOne group is represented in 0 and 1 Between caused random number；
(9) according to formula (11) to each individual x in population Pi, i=1,2 ..., p carries out object function fiCalculating is commented Valency, it is specific as shown in formula (13), and current minimum target function value in population is arranged to fbest, corresponding individual is set It is set to and currently preferably solves Sbest；
Wherein, e1And e2The tracking error of pusher side Variable flow control module and net side Variable flow control module is represented respectively, and t is represented System operation moment value, TminAnd TmaxThe initial time of three-phase inversion system operation is represented respectively and terminates the time, and THD represents straight The voltage waveform percent harmonic distortion of drive permanent magnetism synchronous wind generating system output, w1And w2Weight coefficient is represented, and meets w1+w2 =1；
(10) mutation operation is carried out to population, 3 individual x is randomly choosed from colonyp1, xp2, xp3, and i, p1, p2, p3 are mutual Unequal, specific mutation operation is as follows：
hij(t+1)=xp1j(t)+F·(xp2j(t)-xp3j(t)) (13)
Wherein, hij(t+1) it is intermediate variable individual after temporary variation；
(11) in order to increase the diversity of interference parameter vector, carry out crossover operation again to the population after mutation operation, have Gymnastics is made as follows：
Wherein, randlijRepresent one group of caused random number between zero and one, vij(t+1) to be individual after temporary intersect Intermediate variable；
(12) in order to determine xi(t) follow-on member can be turned into, experiment vector v is obtained using formula (12)i(t+1) With object vector xi(t) value of evaluation function, and it is compared, concrete operations are as follows：
(13) repeat step (9)~(12) obtain the optimal change of PI controllers until system operation to maximum iteration G Amount, so as to be controlled to the electric energy control system of back-to-back total power unsteady flow in direct-drive permanent magnetism synchronous wind generating.
Target function value optimization process curve after the control method implementation of the present invention is as shown in figure 3, the control of the present invention Method implement after D-PMSG RT-LAB electric power real-time simulation platforms three-phase electricity output voltage waveform as shown in figure 4, from It can be seen from the figure that, difference optimization method have stronger global convergence ability and robustness, to D- after being calculated using difference optimization After back-to-back full power convertor electric energy control system optimizes control in PMSG, the three-phase electricity output of system is stable, electric energy Quality is high.

Claims (1)

1. a kind of difference optimal control method of direct-drive permanent magnetism synchronous wind generating system, it is characterised in that the system is using the back of the body Backrest full power convertor controlling electric energy structure, wherein pusher side current transformer control generator speed and power output, net side unsteady flow Device stable DC busbar voltage, active power, the reactive power of control electricity generation system output；This method comprises the following steps：
(1) modeling method described by using duty cycle functions establishes the state-space model of net side current transformer system：
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Wherein, L is filter inductance, and R is the equivalent resistance of filter inductance, C filter capacitors, ekFor three phase network electromotive force, ikFor three Phase output current, dkFor dutycycle, udcFor DC bus-bar voltage, edFor dc bus side direct electromotive force., RdFor dc bus side Equivalent resistance.
(2) formula (1) is subjected to d, q synchronous rotating angle so that the state-space model adjustment of net side current transformer system For：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>d</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <msub> <mi>d</mi> <mi>d</mi> </msub> <mo>=</mo> <msub> <mi>Ri</mi> <mi>d</mi> </msub> <mo>+</mo> <mi>L</mi> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;Li</mi> <mi>q</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mi>q</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <msub> <mi>d</mi> <mi>q</mi> </msub> <mo>=</mo> <msub> <mi>Ri</mi> <mi>q</mi> </msub> <mo>+</mo> <mi>L</mi> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;omega;Li</mi> <mi>d</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, ed、eqFor d, q axis component under three phase network electromotive force two-phase synchronous rotating frame, id、iqFor net side current transformer D, q axis component under system output current two-phase synchronous rotating frame, dd、dqSat for equivalent switch function two-phase synchronous rotary D, q axis component under mark system；ω is three-phase power grid voltage angular frequency.
(3) by being modeled under two-phase synchronous rotating frame to pusher side converter system, the voltage side of threephase stator winding can be obtained Journey：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>d&amp;psi;</mi> <mi>a</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>d&amp;psi;</mi> <mi>b</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>d&amp;psi;</mi> <mi>c</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein usa、usb、usc- stator three-phase voltage, isa、isb、isc- stator three-phase current.RsThe winding resistance of-stator, ψa、 ψb、ψc- stator is as follows per phase winding magnetic linkage, its expression formula：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mi>a</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mi>b</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mi>c</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>L</mi> <mrow> <mi>a</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>M</mi> <mrow> <mi>a</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>M</mi> <mrow> <mi>b</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>M</mi> <mrow> <mi>c</mi> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>M</mi> <mrow> <mi>c</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>L</mi> <mrow> <mi>c</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>i</mi> <mi>a</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mi>b</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mi>c</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Wherein Laa、Lbb、LccBe stator per phase winding inductance, Mab=Mba、Mbc=Mcb、Mac=McaFor the mutual inductance between every phase winding, ψfa、ψfb、ψfcIt is expressed as each pole permanent magnet flux linkage of three-phase windings：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>&amp;psi;</mi> <mi>f</mi> </msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>-</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>+</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Wherein, ψfFor permanent magnet excitation magnetic linkage；
(4) obtaining pusher side converter system state space equation according to formula (3), (4) and (5) is：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>pL</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>pL</mi> <mi>s</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>pL</mi> <mi>s</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>pL</mi> <mi>s</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>pL</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>pL</mi> <mi>s</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>pL</mi> <mi>s</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>pL</mi> <mi>s</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>pL</mi> <mi>s</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mrow> <mi>f</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Wherein, p is differential operator, LsFor the winding inductance of stator.In three-phase system,
isa+isb+isc=0 (7)
Formula (4)-(7) are merged, pusher side converter system state space equation is further transformed to：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>+</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <msub> <mi>pL</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>+</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <msub> <mi>pL</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>+</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <msub> <mi>pL</mi> <mi>s</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>a</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>b</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <msub> <mi>&amp;psi;</mi> <mi>f</mi> </msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>-</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>+</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Wherein, ωeFor the angular rate of rotor；
(5) formula (8) is subjected to d, q synchronous rotating angle, the state-space model adjustment of final pusher side converter system For：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>d</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>d&amp;psi;</mi> <mi>d</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>s</mi> </msub> <msub> <mi>&amp;psi;</mi> <mi>q</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>q</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>d&amp;psi;</mi> <mi>q</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mi>s</mi> </msub> <msub> <mi>&amp;psi;</mi> <mi>d</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;psi;</mi> <mi>d</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mi>d</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;psi;</mi> <mi>f</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;psi;</mi> <mi>q</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mi>q</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>q</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
Wherein, usd、usqFor d, q axis component under stator three-phase voltage two-phase synchronous rotating frame, isd、isqStator three-phase electricity Flow d, q axis component under two-phase synchronous rotating frame, ψd、ψqGenerator magnetic linkage d, q axis component, Ld、LqStator winding inductance D, q axis component, ωsFor generator angular speed.
(6) PI controllers are combined using formula (2), (9), (10), obtains leaning against in direct-drive permanent magnetism synchronous wind generating system Carry on the back full power convertor electric energy control system；
(7) start to carry out difference optimization to the system obtained in step (6), the parameter value for setting difference to optimize：Mutagenic factor F, Intersect factor CR, population size M, maximum iteration G；
(8) randomly generate and leaned against in the direct-drive permanent magnetism synchronous wind generating of a real coding for meeting formula (11) constraints Carry on the back the initial population P={ x of the electric energy control system PI controller variables of total power unsteady flow1,x2,…,xp, wherein i-th of body xi Represent controlling increment sequence { K to be optimizedp1i,Ki1i,Kp2i,Ki2i,Kp3i,Ki3i,Kp4i,Ki4i, specific generation process is as follows：
xij=Δ umin+randij(Δumax-Δumin), i=1,2 ..., p；J=1,2 ..., 8 (11)
Wherein, Δ uminWith Δ umaxThe lower and upper limit of controlling increment sequence, rand are represented respectivelyijRepresent one group between zero and one Caused random number；
(9) according to formula (11) to each individual x in population Pi, i=1,2 ..., p carries out object function fiCalculation Estimation, tool Shown in body such as formula (13), and current minimum target function value in population is arranged to fbest, corresponding individual is arranged to Currently preferably solve Sbest；
<mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>T</mi> <mi>min</mi> </msub> <msub> <mi>T</mi> <mi>max</mi> </msub> </msubsup> <mi>t</mi> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>|</mo> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <mi>T</mi> <mi>H</mi> <mi>D</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Wherein, e1And e2The tracking error of pusher side Variable flow control module and net side Variable flow control module is represented respectively, and t represents system The time of running is worth, TminAnd TmaxThe initial time of three-phase inversion system operation is represented respectively and terminates the time, and THD represents straight and driven forever The voltage waveform percent harmonic distortion of magnetic-synchro wind generator system output, w1And w2Weight coefficient is represented, and meets w1+w2=1；
(10) mutation operation is carried out to population, 3 individual x is randomly choosed from colonyp1, xp2, xp3, and the mutual not phase of i, p1, p2, p3 Deng specific mutation operation is as follows：
hij(t+1)=xp1j(t)+F·(xp2j(t)-xp3j(t)) (13)
Wherein, hij(t+1) it is intermediate variable individual after temporary variation；
(11) in order to increase the diversity of interference parameter vector, crossover operation is carried out again to the population after mutation operation, specific behaviour Make as follows：
Wherein, randlijRepresent one group of caused random number between zero and one, vij(t+1) it is middle anaplasia individual after temporary intersect Amount.
(12) in order to determine xi(t) follow-on member can be turned into, experiment vector v is obtained using formula (12)iAnd mesh (t+1) Mark vector xi(t) value of evaluation function, and it is compared, concrete operations are as follows：
<mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&lt;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
(13) repeat step (9)~(12) obtain the optimal variable of PI controllers until system operation to maximum iteration G, So as to be controlled to the electric energy control system of back-to-back total power unsteady flow in direct-drive permanent magnetism synchronous wind generating.
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