CN107248744A - Double feedback electric engine is based on pusher side and grid side converter coordinated passivity control method - Google Patents
Double feedback electric engine is based on pusher side and grid side converter coordinated passivity control method Download PDFInfo
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Classifications
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- 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
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/01—Arrangements for reducing harmonics or ripples
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- H02J3/386—
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- 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]
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- 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
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- 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
- Y02E40/40—Arrangements for reducing harmonics
Abstract
Pusher side and grid side converter coordinated passivity control method are based on the present invention relates to a kind of double feedback electric engine, increase a series transformer and a series connection grid side converter SGSC in fan stator side, series transformer secondary tandem is between fan stator and power network, SGSC input termination parallel-connection network side converter PGSC inputs, it is primary that SGSC output ends connect series transformer by inductance L, Passive Shape Control strategy is based on using series connection grid side converter structure, PGSC two multiplied frequency harmonics can be offset using the harmonic wave of SGSC generations, stator voltage is easily controllable, so as to realize the suppression to the double-frequency fluctuation of system gross output two, reducing influence of the unbalanced electric grid voltage to rotor side converter RSC system, that improves RSC system unbalanced electric grid voltage realizes the global stability of system while passing through service ability.Compared with prior art, the present invention has the advantages that theoretical advanced, rapid dynamic response speed, strong robustness.
Description
Technical field
It is more particularly to a kind of to be based in the case of unbalanced source voltage the present invention relates to a kind of distributed power generation control technology
The pusher side of doubly fed induction generator, net side current transformer use coordinated passivity control method.
Background technology
The increase influenceed with Wind turbines on stability of power system, it is ensured that the wind-powered electricity generation when line voltage occurs uneven
Off-grid operation is not particularly important unit.Dual-feed asynchronous wind power generator (the Doubly Fed in numerous wind-driven generators
Induction Generator, DFIG) it is used widely with the cost of its relative moderate.DFIG rotor uses two
Pwm converter, i.e. rotor side converter (Rotor-Side Converter, RSC) and grid side converter (Grid-Side
Converter, GSC).Because two converters are connected by middle dc bus with bulky capacitor, it therefore, it can by net
Side converter realizes the uneoupled control of net side independence, obtains its control targe, improves control quality.4th phase in 2014《Power train
System automation》In《PCHD modelings and the IDA-PB of double-fed wind power generator net side current transformer are controlled》One text is proposed according to duplex feeding
The physical model of machine introduces dissipation Hamilton (the Port-Controlled Hamilton with based on Port-Controlled
Dissipation, PCHD) model Passive Shape Control (Passivity-based Control, PBC) method, this method have ring
Answer that speed is fast, strong robustness, system architecture are simple, explicit physical meaning, the advantages of be easily achieved.However, Passive Shape Control be
Ignore inductance in circuit, resistance parameter perturbation, rectifier exist it is interior disturb and set up in the case of disturbing outside, therefore merely mutual
Connection and damping configuration Passive Shape Control strategy can be affected to the control effect people of grid side converter.
The content of the invention
A kind of the problem of existing the present invention be directed to dual-feed asynchronous wind power generator Passive Shape Control, it is proposed that double feedback electric engine base
In pusher side and grid side converter coordinated passivity control method, using series connection grid side converter and Passive Shape Control strategy, it can utilize
The harmonic wave that series connection grid side converter (SGSC) is produced offsets two multiplied frequency harmonics of parallel-connection network side converter (PGSC), stator voltage
It is easily controllable, so as to realize the suppression to the double-frequency fluctuation of system gross output two, reducing unbalanced electric grid voltage to RSC systems
The influence of system, improve RSC system unbalanced electric grid voltage realize the global stability of system while passing through service ability.
The technical scheme is that：A kind of double feedback electric engine is based on pusher side and grid side converter coordinated passivity control method,
Dual-feed asynchronous wind power generator DFIG rotor using two pwm converters, i.e. rotor side converter RSC and therewith parallel connection and
Networked side converter PGSC, and two converters are connected by middle dc bus with bulky capacitor, in the increase of fan stator side
One series transformer and a series connection grid side converter SGSC, series transformer secondary tandem fan stator and power network it
Between, SGSC input termination PGSC inputs, SGSC output ends connect series transformer primary, unbalanced source voltage by inductance L
In the case of DFIG pusher side and grid side converter coordination control comprise the following steps that：S1：According to unbalanced source voltage situation
The lower coordination control based on Passive Shape Control strategy using series connection grid side converter, sets up its positive-negative sequence model, and calculate series connection net
Current on line side reference value under the control targe of side converter and different control targes：SGSC control targe is：DFIG stators
The positive-sequence component u of side voltages+With line voltage positive-sequence component ug+All the time it is consistent, control stator side voltage negative sequence component us-Make it
It is zero, i.e.,：Power network transports to parallel-connection network side converter PGSC instantaneous power S under Voltage unbalance, is organized into
Matrix form is：In formula：Subscript p, n are represented respectively
Positive and negative sequence component, subscript d, q represents dq axis components ,+,-the forward and backward direction of reference axis is represented, such as：
WithRespectively positive-sequence component is exchanged in rotating forward coordinate system d axles with the voltage on line side component on q axles, GSC
Side component of voltage, current on line side component；WithTurn to sit negative for negative sequence component
Voltage on line side component, GSC ACs component of voltage, current on line side component on mark system d axles and q axles；(1) target 1：Net side is inputted
Electric current be free of negative sequence component, i.e.,
In formula：* net side command current value is represented；Subscript g_av, g_sin2, g_cos2 represent parallel-connection network side converter respectively
The DC component of power, 2 frequency multiplication sinusoidal components, 2 frequency multiplication cosine components；Subscript series_av, series_sin2, series_
Cos2 represents the series connection DC component of grid side converter, 2 frequency multiplication sinusoidal components, 2 frequency multiplication cosine components respectively；P is active power,
Q is reactive power；
(2) target 2：Net side input active power comprises only DC component, i.e.,
Pg_sin2-Pseries_sin2=0, Pg_cos2-Pseries_cos2=0：
(3) target 3：DC bus-bar voltage is without two frequencys multiplication sine, cosine component, i.e. udc_sin2=udc_cos2=0：
(4) target 4：The reactive power of net side input comprises only DC component, i.e.,
Qg_sin2-Qseries_sin2=0, Qg_cos2-Qseries_cos2=0：
S2：SGSC adoption rate integral resonance PIR controllers realize effective control to SGSC top-cross flow component, and it is passed
Delivery function is represented by：
In formula：kpAnd kiRespectively ratio, integral coefficient；krFor the resonance coefficient of resonant regulator, ωcFor cut-off frequency；
S3：Dissipation Hamilton PCHD models based on Port-Controlled, using interconnection and assignment of damping passive coherent locating IDA-PBC methods,
PGSC Passive Shape Control devices are designed, its precondition is：
1) parallel-connection network side converter positive sequence system capacity increases summation and always had less than system capacity dissipation summation, i.e. system
There is dissipativeness；
2) parallel-connection network side converter positive sequence system is to dissipate, and meets input Strictly passive control and output Strictly passive control, then
System is Strictly passive control；
Define net side current transformer mathematical modeling be：
Lgpqgp+Cgpqgp+Rgqgp=ugp
Wherein,
Take the energy function H of systemgpFor：
TakeWith
The PCHD models that DFIG net side positive sequences can be obtained are：
In formula：JgpFor interconnection matrix,For antisymmetric matrix；For dissipative matrix,
For the symmetrical matrix of positive definite；
Similarly, can obtain the negative PCHD models for turning negative sequence component under synchronous rotating frame is：
Due to new and old interconnection matrix structure conservation, the new interconnection matrix J of injection is takengpaAnd damping matrixRespectively
For：
Wherein, can be according to being on the basis of system Strictly passive control is ensured
The arbitrary constant that structure of uniting is chosen,
S4：RSC is using the inner ring Passive Shape Control as PGSC, the vector strategy of outer shroud PI controls.
The beneficial effects of the present invention are：Double feedback electric engine of the present invention is based on pusher side and grid side converter coordinated passivity controlling party
Method, offsets PGSC two multiplied frequency harmonics, stator voltage is easily controllable using the harmonic wave of grid side converter of connecting (SGSC) generation,
So as to realize the suppression to the double-frequency fluctuation of system gross output two；Meanwhile, the complete of system is realized with Passive Shape Control theory
Office's stability.For RSC, because structure special grid-connected DFIG, even if under the conditions of unbalanced power supply, DFIG set end voltages are still
All the time it is symmetrical, therefore the vector strategy that RSC is controlled using the inner ring Passive Shape Control similar with PGSC, outer shroud PI here.With it is existing
Technology is compared, and the present invention has the advantages that theoretical advanced, rapid dynamic response speed, strong robustness.
Brief description of the drawings
Fig. 1 is the DFIG system topology figures using SGSC；
Fig. 2 is the structured flowchart of grid side converter；
Fig. 3 is that the DFIG based on SGSC coordinates control block diagram；
Rotor current simulation result figure when Fig. 4 (a) is net side selection control targe 1-4, rotor-side selection control targe 4；
Stator side Simulation of SAR power image result when Fig. 4 (b) is net side selection control targe 1-4, rotor-side selection control targe 4
Figure；
Electromagnetic torque simulation result figure when Fig. 4 (c) net sides selection control targe 1-4, rotor-side selection control targe 4；Fig. 5
It is DC bus-bar voltage waveform under 3 kinds of control strategies；
Fig. 6 (a) is the network side current waveform figure that SGSC+PID is controlled；
Fig. 6 (b) is the current on line side ripple figure that PBC is controlled；
Fig. 6 (c) is SGSC+PBC control strategy network side current waveform figures；
Fig. 7 (a) is net side active power oscillogram under 3 kinds of control methods；
Fig. 7 (b) is net side reactive power oscillogram under 3 kinds of control methods.
Embodiment
As shown in figure 1, compared with classical double-fed blower fan system, the system topological structure has more one in fan stator side
Series transformer and a series connection grid side converter SGSC.Series transformer secondary tandem is between fan stator and power network, string
Side converter SGSC inputs of networking terminate parallel-connection network side converter PGSC inputs, and series connection grid side converter SGSC output ends pass through
Inductance L connects series transformer primary, and the SGSC of addition can either inject appropriate series compensating voltage support by stator loop
Disappear stator negative sequence voltage, injects a positive sequence compensation voltage vector to eliminate series-transformer to stator loop while also can control it
Influence of the device leakage impedance pressure drop to DFIG stator voltages, so as to ensure DFIG stator voltage positive-sequence component us+ with line voltage just
Order components ug+ is identical.SGSC output control voltage vector is under unbalanced source voltage：
useries=ucom+-ug-
In formula：useriesFor the output voltage of series transformer, ucom+The positive sequence voltage vector compensated for needed for SGSC, ug-
Line voltage negative sequence component.
The structured flowchart of grid side converter as shown in Figure 2, one kind that the embodiment of the present invention is provided is based on line voltage not
Under balance in the coordination control strategy of the pusher side of double feedback electric engine, grid side converter, figure, ua、ub、ucFor line voltage, va、
vb、vcFor GSC AC voltages, RgFor line impedance and inductance equivalent series resistance summation, LgFor GSC output end filter inductances,
ia、ib、icFor GSC input currents, C is the electric capacity of dc bus, udcFor the voltage of dc bus, iloadFlow to RSC's for net side
Electric current.Comprise the following steps that：
Step S1：Passive Shape Control strategy is based on according to series connection grid side converter structure is used in the case of unbalanced source voltage
Coordination control, set up its positive-negative sequence model, and calculate under the control targe and different control targes of series connection grid side converter
Current on line side reference value.
SGSC control targe is：The positive-sequence component u of DFIG stator side voltagess+With line voltage positive-sequence component ug+All the time
Unanimously, control stator side voltage negative sequence component us-Zero is, i.e.,：
Power network transports to parallel-connection network side converter PGSC instantaneous power S under Voltage unbalance, is organized into matrix form and is：
In formula：Subscript p, n represent positive and negative sequence component respectively, and subscript d, q represents dq axis components ,+,-represent reference axis
Forward and backward direction, such as：WithRespectively positive-sequence component is rotating forward coordinate system d
Voltage on line side component, GSC ACs component of voltage, current on line side component on axle and q axles；WithIt is negative sequence component in negative voltage on line side component, the GSC AC voltages turned on coordinate system d axles and q axles
Component, current on line side component.
(1) target 1：The electric current of net side input is free of negative sequence component, i.e.,
In formula：* net side command current value is represented；Subscript g_av, g_sin2, g_cos2 represent parallel-connection network side converter respectively
The DC component (mean power) of power, 2 frequency multiplication sinusoidal components, 2 frequency multiplication cosine components；Subscript series_av, series_
Sin2, series_cos2 represent the series connection DC component of grid side converter, 2 frequency multiplication sinusoidal components, 2 frequency multiplication cosine components respectively；
P is active power, and Q is reactive power.
(2) target 2：Net side input active power comprises only DC component, i.e.,
Pg_sin2-Pseries_sin2=0, Pg_cos2-Pseries_cos2=0：
(3) target 3：DC bus-bar voltage is without two frequencys multiplication sine, cosine component, i.e. udc_sin2=udc_cos2=0：
(4) target 4：The reactive power of net side input comprises only DC component, i.e.,
Qg_sin2-Qseries_sin2=0, Qg_cos2-Qseries_cos2=0：
Step S2：Adopted here because considering that traditional PI control strategies have a definite limitation to the bandwidth of adjuster SGSC sides
Effective control to SGSC top-cross flow component is realized with proportional integration resonance (PIR) controller, without the separation of phase sequence, so that
Add the transient performance of system.Its transmission function is represented by：
In formula：kpAnd kiRespectively ratio, integral coefficient；krFor the resonance coefficient of resonant regulator, ωcFor cut-off frequency.
Step S3：Dissipation Hamilton (PCHD) model based on Port-Controlled, using interconnection and assignment of damping passivity control
(IDA-PBC) method of system, designs PGSC Passive Shape Control devices, its precondition is：
1) parallel-connection network side converter positive sequence system capacity increases summation and always had less than system capacity dissipation summation, i.e. system
There is dissipativeness；
2) parallel-connection network side converter positive sequence system is to dissipate, and meets input Strictly passive control and output Strictly passive control, then
System is Strictly passive control.
Define net side current transformer mathematical modeling be：
Lgpqgp+Cgpqgp+Rgqgp=ugp
Wherein,
Take the energy function H of systemgpFor：
TakeWith
The PCHD models that DFIG net side positive sequences can be obtained are：
In formula：JgpFor interconnection matrix,For antisymmetric matrix；For dissipative matrix,
For the symmetrical matrix of positive definite.
Similarly, can obtain the negative PCHD models for turning negative sequence component under synchronous rotating frame is：
Due to new and old interconnection matrix structure conservation, the new interconnection matrix J of injection is takengpaAnd damping matrixRespectively
For：
Wherein, can be according to being on the basis of system Strictly passive control is ensured
The arbitrary constant that structure of uniting is chosen.
Step S4：Fig. 3 is DFIG pusher sides and the coordination control block diagram of net side based on SGSC.In figure, 3s/2r is that three-phase is quiet
Only arrive the computing of two-phase rotation.For RSC, because structure special grid-connected DFIG, even if under the conditions of unbalanced power supply, DFIG
Set end voltage is still symmetrical all the time, therefore the vector plan that RSC is controlled using the inner ring Passive Shape Control similar with PGSC, outer shroud PI here
Slightly, about RSC vector control strategy, here is omitted.
In MATLAB/Simulink emulation platforms to set forth herein the DFIG control that is combined of use SGSC and PBC
The feasibility of method processed has carried out simulation study with validity.The given unbalanced source voltage degree of system is 15%, duplex feeding
The main simulation parameter value of machine is shown in Table 1；PIR control parameter is as shown in table 2 in SGSC and PGSC Voltage loop；To meet system
The Strictly passive control of system, controller architecture simplifies enough, chooses the damped coefficient of electric current loop and interconnection coefficient point in RSC and PGSC
It is not：
Table 1
Table 2
In order to illustrate the superiority for the control method that the use SGSC and PBC that propose are combined, herein respectively to institute in text
Control is proposed, control is combined with PI only with SGSC and carries out simulation comparison only with PBC 3 kinds of methods.In t=0~0.4s phases
Between, realized and run under unbalanced power supply using 3 kinds of control strategies, and realize in different periods 4 kinds of different control targes,
I.e.：1) t=0~0.1s：Control targe 1 is selected, to eliminate current on line side negative sequence component；2) t=0.1~0.2s：According to control
2 times operations of target, to eliminate the frequency multiplication of net side active power 2；3) t=0.2~0.3s：According to 3 times operations of control targe, to eliminate
The frequency multiplication of DC bus-bar voltage 2；4) t=0.3~0.4s：Control targe 4, to eliminate the frequency multiplication of net side reactive power 2.In addition, rotor
Side selects control targe：Constant electromagnetic torque, reduces the mechanical load to wind system axle.
Specific experiment effect is：
Rotor current, stator side when Fig. 4 (a)-(c) is net side selection control targe 1-4, rotor-side selection control targe 4
The simulation result figure of power and electromagnetic torque.In Fig. 4 (a), it is seen that the requirement for eliminating current on line side negative sequence component can be reached,
Represented in Fig. 4 (b) and (c), can also realize the mesh for the harmonic wave for eliminating double feedback electric engine electromagnetic torque and stator output reactive power
Mark.
Fig. 5 is DC bus-bar voltage waveform under 3 kinds of control strategies.As can be seen that under the conditions of identical Voltage unbalance,
When selecting control targe 1, DC bus-bar voltage 20ms moment under SGSC+PID control strategies reaches stationary value 700V, and makes
With PBC and this paper control strategy, just stablize at the 3ms moment.When selecting control targe 2-4, this paper control strategies are compared with first two
Under control strategy, its concussion is smaller, and waveform is smoother.Therefore, the control strategy that this patent is proposed can increase bandwidth and accelerate sound
Speed is answered, the antijamming capability of system can be improved again.
Comparing the current waveform of net side under Fig. 6 (a), 6 (b), and 6 (c) 3 kinds of control strategies can obtain, under control targe 1,
Using SGSC+PID control strategies, current on line side value overshoot in 0~0.06s is larger, is easily caused converter saturation, and uses
PBC strategies and this paper control strategy non-overshoots；Under control targe 2 and 3, the influence of 3 kinds of control strategies is similar.Selection control mesh
When marking 4, under the first control strategy, relative equilibrium, Passive Shape Control and the control plan put forward herein are reached during current on line side 0.35s
Just balanced when slightly descending 0.3s, but individually two-phase drop current is respectively 15.2A, 15.8A in PBC strategies, and for as herein
Control strategy equally reaches complete equipilibrium.Therefore, this patent control strategy is either in dynamic responding speed or stability side
Face is respectively provided with clear superiority.
Table 3 be when 3 kinds of control strategies are used under 3 kinds of different control targes active and reactive 2 multiplied frequency harmonic flutter component with
The ratio table of mean power.Fig. 7 (a) is net side active power oscillogram under 3 kinds of control methods；Fig. 7 (b) is 3 kinds of control methods
Lower net side reactive power oscillogram.Can by Fig. 7 (a), 7 (b) and the lower 3 kinds of control of the different control targes of table 3 operation result contrast
See, under control targe 1-4, controlled compared to SGSC+PID controls, PBC, it is active and reactive under the control strategy carried herein
Regulating time, overshoot harmonic content it is smaller.Therefore, this patent proposes the net side power of control strategy in control performance
It is upper to be better than first two control strategy.
Table 3
Claims (1)
1. a kind of double feedback electric engine is based on pusher side and grid side converter coordinated passivity control method, dual-feed asynchronous wind power generator DFIG
Rotor using two pwm converters, i.e. the parallel-connection network side converter PGSC of rotor side converter RSC and therewith parallel connection, two
Converter is connected by middle dc bus with bulky capacitor, it is characterised in that is increased a series connection in fan stator side and is become
Depressor and a series connection grid side converter SGSC, series transformer secondary tandem is between fan stator and power network, SGSC inputs
Terminate PGSC inputs, SGSC output ends connect that series transformer is primary by inductance L, DFIG in the case of unbalanced source voltage
The coordination control of pusher side and grid side converter is comprised the following steps that：
S1：According in the case of unbalanced source voltage using series connection grid side converter based on Passive Shape Control strategy coordination control,
Its positive-negative sequence model is set up, and calculates the current on line side reference under the control targe and different control targes of series connection grid side converter
Value：
SGSC control targe is：The positive-sequence component u of DFIG stator side voltagess+With line voltage positive-sequence component ug+It is all the time consistent,
Control stator side voltage negative sequence component us-Zero is, i.e.,：
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Power network transports to parallel-connection network side converter PGSC instantaneous power S under Voltage unbalance, is organized into matrix form and is：
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<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
In formula：Subscript p, n represent positive and negative sequence component respectively, and subscript d, q represents dq axis components ,+,-represent the positive and negative of reference axis
Turn direction, such as：WithRespectively positive-sequence component is rotating forward coordinate system d axles and q
Voltage on line side component, GSC ACs component of voltage, current on line side component on axle；WithIt is negative sequence component in negative voltage on line side component, the GSC AC voltages turned on coordinate system d axles and q axles
Component, current on line side component；
(1) target 1：The electric current of net side input is free of negative sequence component, i.e.,
In formula：* net side command current value is represented；Subscript g_av, g_sin2, g_cos2 represent parallel-connection network side inverter power respectively
DC component, 2 frequency multiplication sinusoidal components, 2 frequency multiplication cosine components；Subscript series_av, series_sin2, series_cos2
The series connection DC component of grid side converter, 2 frequency multiplication sinusoidal components, 2 frequency multiplication cosine components are represented respectively；P is active power, and Q is
Reactive power；
(2) target 2：Net side input active power comprises only DC component, i.e.,
Pg_sin2-Pseries_sin2=0, Pg_cos2-Pseries_cos2=0：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
</msubsup>
<mo>;</mo>
</mrow>
(3) target 3：DC bus-bar voltage is without two frequencys multiplication sine, cosine component, i.e. udc_sin2=udc_cos2=0：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<msup>
<mi>p</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<msup>
<mi>n</mi>
<mo>*</mo>
</msup>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
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<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
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</mrow>
<msup>
<mi>n</mi>
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</msup>
</msubsup>
<mo>=</mo>
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<mfrac>
<mn>2</mn>
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</mfrac>
<mo>(</mo>
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<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
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<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
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<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
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</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
(4) target 4：The reactive power of net side input comprises only DC component, i.e.,
Qg_sin2-Qseries_sin2=0, Qg_cos2-Qseries_cos2=0：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
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<mi>i</mi>
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</msubsup>
<mo>=</mo>
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<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>u</mi>
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<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
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<mi>a</mi>
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</mrow>
</msub>
<mo>+</mo>
<mfrac>
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<msub>
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</msub>
</mfrac>
<msub>
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<mo>)</mo>
</mtd>
</mtr>
<mtr>
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</msubsup>
<mo>=</mo>
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<mo>(</mo>
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</mfrac>
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</mtr>
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</mfrac>
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</msub>
</mfrac>
<msub>
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</mrow>
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</mtd>
</mtr>
<mtr>
<mtd>
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</mrow>
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</msup>
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<mfrac>
<mn>2</mn>
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</mfrac>
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<mfrac>
<msubsup>
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<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>2</mn>
</msub>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>-</mo>
</mrow>
<mi>n</mi>
</msubsup>
<msub>
<mi>D</mi>
<mn>1</mn>
</msub>
</mfrac>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>e</mi>
<mi>s</mi>
<mo>_</mo>
<mi>a</mi>
<mi>v</mi>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
S2：SGSC adoption rate integral resonance PIR controllers realize effective control to SGSC top-cross flow component, and it transmits letter
Number is represented by：
<mrow>
<msub>
<mi>C</mi>
<mrow>
<mi>P</mi>
<mi>I</mi>
<mi>R</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>K</mi>
<mi>p</mi>
</msub>
<mo>+</mo>
<mfrac>
<msub>
<mi>K</mi>
<mi>i</mi>
</msub>
<mi>s</mi>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>s&omega;</mi>
<mi>c</mi>
</msub>
<msub>
<mi>K</mi>
<mi>r</mi>
</msub>
</mrow>
<mrow>
<msup>
<mi>s</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
<mi>s</mi>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mo>&PlusMinus;</mo>
<mn>2</mn>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
In formula：kpAnd kiRespectively ratio, integral coefficient；krFor the resonance coefficient of resonant regulator, ωcFor cut-off frequency；
S3：Dissipation Hamilton PCHD models based on Port-Controlled, using interconnection and assignment of damping passive coherent locating IDA-PBC side
Method, designs PGSC Passive Shape Control devices, and its precondition is：
1) parallel-connection network side converter positive sequence system capacity increases summation always has consumption less than system capacity dissipation summation, i.e. system
Dissipate property；
2) parallel-connection network side converter positive sequence system is to dissipate, and meets input Strictly passive control and output Strictly passive control, then system
It is Strictly passive control；
Define net side current transformer mathematical modeling be：
Lgpqgp+Cgpqgp+Rgqgp=ugp
Wherein,
<mrow>
<msub>
<mi>L</mi>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>L</mi>
<mi>g</mi>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>L</mi>
<mi>g</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<msub>
<mi>q</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>i</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&omega;L</mi>
<mi>g</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&omega;L</mi>
<mi>g</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>R</mi>
<mi>g</mi>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>R</mi>
<mi>g</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>v</mi>
<mrow>
<mi>g</mi>
<mi>d</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>u</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>v</mi>
<mrow>
<mi>g</mi>
<mi>q</mi>
<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Take the energy function H of systemgpFor：
<mrow>
<msub>
<mi>H</mi>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msubsup>
<mi>q</mi>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
<mi>T</mi>
</msubsup>
<msub>
<mi>Lq</mi>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
</msub>
</mrow>
TakeWith
The PCHD models that DFIG net side positive sequences can be obtained are：
In formula：JgpFor interconnection matrix,For antisymmetric matrix；For dissipative matrix,For
The symmetrical matrix of positive definite；
Similarly, can obtain the negative PCHD models for turning negative sequence component under synchronous rotating frame is：
Due to new and old interconnection matrix structure conservation, the new interconnection matrix J of injection is takengpaAnd damping matrixRespectively：
WhereinFor ensure system Strictly passive control on the basis of, can be according to system knot
The arbitrary constant that structure is chosen,
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</msubsup>
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<mn>2</mn>
</msubsup>
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<mn>1</mn>
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</mrow>
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<mi>J</mi>
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</mrow>
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</mrow>
</msubsup>
<mo>-</mo>
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<mi>i</mi>
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<mo>+</mo>
</mrow>
<mi>p</mi>
</msubsup>
<mo>)</mo>
</mrow>
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<msubsup>
<mi>J</mi>
<mn>12</mn>
<mrow>
<mi>g</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mrow>
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</mrow>
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</mrow>
</msubsup>
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</mrow>
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</msubsup>
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</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
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<mo>-</mo>
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<mi>i</mi>
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<mi>g</mi>
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</mrow>
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</msubsup>
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</mrow>
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<mi>J</mi>
<mn>12</mn>
<mrow>
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</mrow>
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</mtd>
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<mtr>
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S4：RSC is using the inner ring Passive Shape Control as PGSC, the vector strategy of outer shroud PI controls.
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Cited By (4)
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| CN108767874A (en) * | 2018-05-28 | 2018-11-06 | 国网内蒙古东部电力有限公司 | SVG based on PIR controls inhibits the practical approach of wind power plant sub-synchronous oscillation |
| CN108923443A (en) * | 2018-06-25 | 2018-11-30 | 上海电力学院 | A kind of Lyapunov control method for coordinating of the DFIG using PGSC and SGSC |
| CN109066735A (en) * | 2018-08-29 | 2018-12-21 | 国网内蒙古东部电力有限公司电力科学研究院 | Dual feedback wind power generation system and its control method under a kind of unbalanced electric grid voltage |
| CN116154845A (en) * | 2022-12-08 | 2023-05-23 | 中国石油大学(华东) | Control method of H-bridge serial-parallel switching type forced excitation converter based on DAB |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108767874A (en) * | 2018-05-28 | 2018-11-06 | 国网内蒙古东部电力有限公司 | SVG based on PIR controls inhibits the practical approach of wind power plant sub-synchronous oscillation |
| CN108923443A (en) * | 2018-06-25 | 2018-11-30 | 上海电力学院 | A kind of Lyapunov control method for coordinating of the DFIG using PGSC and SGSC |
| CN108923443B (en) * | 2018-06-25 | 2022-04-01 | 上海电力学院 | Lyapunov coordination control method for DFIG (distributed feed control group) by adopting PGSC (PGSC) and SGSC (SGSC) |
| CN109066735A (en) * | 2018-08-29 | 2018-12-21 | 国网内蒙古东部电力有限公司电力科学研究院 | Dual feedback wind power generation system and its control method under a kind of unbalanced electric grid voltage |
| CN116154845A (en) * | 2022-12-08 | 2023-05-23 | 中国石油大学(华东) | Control method of H-bridge serial-parallel switching type forced excitation converter based on DAB |
| CN116154845B (en) * | 2022-12-08 | 2023-11-21 | 中国石油大学(华东) | Control method of H-bridge serial-parallel switching type forced excitation converter based on DAB |
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