CN107332261A - A kind of micro-capacitance sensor quality of power supply distributed coordination administering method - Google Patents

A kind of micro-capacitance sensor quality of power supply distributed coordination administering method Download PDF

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CN107332261A
CN107332261A CN201710687070.2A CN201710687070A CN107332261A CN 107332261 A CN107332261 A CN 107332261A CN 201710687070 A CN201710687070 A CN 201710687070A CN 107332261 A CN107332261 A CN 107332261A
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msubsup
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voltage
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吴丽珍
雷艾虎
郝晓弘
蒋力波
王晓婷
刘腾飞
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Lanzhou University of Technology
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Lanzhou University of Technology
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/26Arrangements for eliminating or reducing asymmetry in polyphase networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01Arrangements for reducing harmonics or ripples
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • H02J3/1835Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control
    • H02J3/1842Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control wherein at least one reactive element is actively controlled by a bridge converter, e.g. active filters
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381Dispersed generators
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30Reactive power compensation
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40Arrangements for reducing harmonics
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/50Arrangements for eliminating or reducing asymmetry in polyphase networks

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Inverter Devices (AREA)

Abstract

The invention discloses a kind of micro-capacitance sensor quality of power supply distributed coordination administering method, this method coordinates compensation point of common coupling PCC voltages using APF and DG, realized by two key-courses, key-course contains DG local controller, including power calculation, droop control, voltage x current control ring, virtual impedance ring and compensation capacity regulator etc., linear quadratic control layer includes distributed secondary controller, sampling computing module is acquired to PCC point voltages and extracts the positive and negative order components of its fundamental wave and the positive and negative order components of each harmonic, the PCC point component of voltages under dq coordinate systems are transmitted into each distributed secondary controller by low bandwidth communication, distributed secondary controller is substantially carried out calculating and the generation compensation reference of voltage harmonic distortion, then reference value is sent in local controller and carries out Voltage unbalance compensation harmonic suppression, the present invention is able to maintain that the three-phase equilibrium of micro-capacitance sensor PCC voltages, ensure DG output voltage quality simultaneously.

Description

A kind of micro-capacitance sensor quality of power supply distributed coordination administering method
Technical field
The invention belongs to electricity field, more particularly to a kind of micro-capacitance sensor quality of power supply distributed coordination administering method.
Background technology
Micro-capacitance sensor (Microgrid, MG) is effective as distributed power source (Distributed Generators, DGs) Carrier, is mainly made up of multiple renewable energy sources, energy storage device, local load and monitoring and protecting device.Micro-capacitance sensor technology Development, provide effective approach for on-site elimination regenerative resource, a variety of distributed power sources, energy storage etc. be combined together Formed one it is small-sized be transported to electric system, can run on grid-connected and isolated island both of which, greatly improve regenerative resource Utilization rate and power supply reliability, are the most effective modes for playing regenerative resource benefit.
In the micro-capacitance sensor being made up of the micro- source of three-phase inversion type, as point of common coupling (Point of Common Coupling, PCC) on connect three-phase imbalance load when, it will cause micro-capacitance sensor support voltage there is three-phase imbalance, cause Stability and the reliability reduction of micro-grid system.When micro-capacitance sensor PCC points voltage has serious imbalance, or even sense can be influenceed Answer the normal work of motor, Technics of Power Electronic Conversion device etc..In International Electrotechnical Commission (IEC) regulation power system, PCC points are just Normal voltage unbalance factor permissible value is 2%, in short-term no more than 4%;And each user on common bus is connected to, causing the point just Normal voltage unbalance factor permissible value is generally 1.3%.Therefore, micro-capacitance sensor voltage imbalance compensation is of crucial importance.In addition, except injustice Weighing apparatus load is outer, and harmonic problem caused by nonlinear load brings huge challenge to the power quality controlling of micro-capacitance sensor.
The power quality problem brought is normally run to micro-grid system in order to solve above-mentioned non-linear unbalanced load, it is existing There is Voltage unbalance compensation mainly by electric energy regulator of connecting, to inject negative sequence voltage to realize to circuit.And use Although the above method can improve the quality of power supply of micro-capacitance sensor PCC points, the output voltage of distributed power source can produce serious Distortion, and PCC point current harmonics can not effectively be administered.Therefore, it can realize that point of common coupling Voltage unbalance is compensated, The output voltage quality of distributed power source is taken into account simultaneously, will be a kind of significantly solution.
At present, content related with the present patent application mainly has in the prior art:Chinese patent literature CN104836258 is public A kind of micro-capacitance sensor multi-inverter control method for having Voltage unbalance compensation harmonic suppression concurrently is opened.This method is controlled by concentrating Device processed is acquired to common bus voltage and calculates its unbalance factor vector and the compensation of harmonics component positive-negative sequence Reference vector, and then voltage-regulation reference vector is produced, realize that common bus voltage is uneven by contravarianter voltage current control Weighing apparatus compensation harmonic suppresses.But, when micro-capacitance sensor PCC points voltage is serious uneven, compensation ability requirement of this method to DG Higher, after being compensated to PCC point voltages, the quality of voltage at DG ends is relatively low.Chinese patent literature CN103715704A is disclosed A kind of micro-capacitance sensor common bus Voltage unbalance suppressing method, this method is directly mended to micro-capacitance sensor common bus negative sequence voltage Repay, however, can produce substantial amounts of harmonic wave when micro-capacitance sensor is connected with non-linear unbalanced load, this method can not be very to harmonic wave Good suppression, is not suitable for while being connected to the micro-grid system of three-phase imbalance load and nonlinear load in this way.In State patent document CN103368191B discloses a kind of micro-capacitance sensor multi-inverter parallel Voltage unbalance compensation method.This method bag Power droop control, voltage x current ring and the part of imbalance compensation ring three are included, can be realized active and reactive accurate between each DG Distribution.However, this method can not directly express the running environment on common bus, therefore, this method also needs to further change Enter and perfect.In addition, this method does not consider the harmonic problem produced during the load of micro-grid system connected nonlinearity.
In summary, in the prior art not thoroughly solve take into account micro-capacitance sensor point of common coupling Voltage unbalance compensation and The technical barrier of inverter output voltage quality.
The content of the invention
While the technical problems to be solved by the invention are to provide a kind of point voltage compensation to PCC, it is ensured that inverter is defeated Going out voltage has the micro-capacitance sensor quality of power supply distributed coordination administering method of high voltage quality.
To solve the above problems, a kind of micro-capacitance sensor quality of power supply distributed coordination administering method of the present invention, including Following steps:
A kind of micro-capacitance sensor quality of power supply distributed coordination administering method, it is characterised in that:Including how inverse distributed electricity Source isolated island micro-grid system in parallel, many inverse distributed powers isolated island micro-grid system in parallel includes several points Cloth generator unit, Active Power Filter-APF APF, distributed secondary controller, sampling computing module, DG buses, public coupling Point PCC, non-linear unbalanced load, linear load;It is connected in parallel between some distributed generation units, described some points Cloth generator unit connects the DG buses, the APF, the sampling computing module, the non-linear imbalance by feeder line Load and the linear load are connected between the DG buses and the point of common coupling PCC, the distributed linear quadratic control Device be connected with the sampling computing module, and the distributed generation unit is inverse including the micro- source of direct current that is sequentially connected, three phase full bridge Become circuit, LC filter circuits, feeder line, the distributed generation unit also includes local controller, driving protection module, the LC Filter circuit is connected with the local controller;
The sampling computing module carries out sampling processing and calculating to the PCC points voltage, and output quantity is passed through into low strap Wide communications are into the distributed secondary controller, and the distributed secondary controller transmits the compensation reference of generation Into the local controller, the local controller output quantity is by driving protection module to drive the three phase full bridge inversion electricity Power tube in road being opened and turning off, and specific steps include:
(1) sampling computing module is to point of common coupling PCC voltages vabcSampling calculating and dq coordinate transforms are carried out, is obtained PCC point fundamental positive sequence voltages under dq coordinate systemsFundamental wave negative sequence voltageAnd h subharmonic voltagesAnd pass through low strap Width communication LBC is sent in distributed secondary controller;Wherein, vabc=[va,vb,vc]T, h be harmonic wave number of times, h=3,5, 7;
(2) by PCC point fundamental positive sequence voltagesFundamental wave negative sequence voltageH subharmonic voltagesPass through dq → α β coordinates Conversion and virtual value computing module can obtain the fundamental positive sequence voltage under α β coordinate systemsFundamental wave negative sequence voltageh Subharmonic voltage
(3) voltage for obtaining above-mentioned calculatingPass through the Voltage unbalance factor and harmonic distortion Computing module can be obtainedThen by VUF, HDhReference value VUF corresponding with its* It is compared, difference can obtain compensation reference after proportional integration PI controllersFinally again by compensation referencePass Transport in local controller and compensate;Wherein, the calculation formula of compensation reference is shown below:
(4) in local controller, the filter capacitor voltage vector v of LC filter circuits is detected in real timeoabc, filter inductance electric current Vectorial iLabcAnd feeder current vector ioabc, its expression formula is shown below:
voabc=[voa,vob,voc]T
iLabc=[iLa,iLb,iLc]T
ioabc=[ioa,iob,ioc]T
(5) by abc → α β coordinate transforms by filter capacitor voltage vector voabc, filter inductance current vector iLabcAnd Feeder current vector ioabcIt is transformed to the filter capacitor voltage vector v under the static mark systems of α βoαβ, filter inductance current vector iLαβWith And feeder current vector ioαβ, its expression formula is shown below:
voαβ=[v,v]T
iLαβ=[i,i]T
ioαβ=[i,i]T
(6) two-phase fundamental voltage v is extracted respectivelyoαβ, two-phase fundamental current ioαβFundamental positive sequence voltage under α β coordinate systems VectorFundamental positive sequence current vectorIts expression formula is shown below:
(7) Theory of Instantaneous Reactive Power of Three-Phase Circuits is based on, the fundamental positive sequence active-power P of inverter output is calculated+, Fundamental positive sequence reactive power Q+It is shown below:
(8) according to the fundamental positive sequence voltage vector of said extractedFundamental positive sequence electric currentIt can obtain by virtually hindering The voltage vector v that anti-ring is producedVαβ=[v,v]TIt is shown below:
Wherein:RvFor virtual resistance, LvFor virtual inductor;
(9) according to power droop control characteristic, three-phase inverter output reference voltage E is respectively obtained*With refer to angular frequency ω*, its formula is shown below:
ω*n-kpP+
E*=En-kqQ+
Wherein:kpFor sagging active proportionality coefficient, kqFor sagging idle proportionality coefficient, ω*To refer to angular frequency, ωnFor volume Determine angular frequency, E*For reference voltage amplitude, EnFor rated voltage amplitude;
(10) angular frequency is referred to according to three-phase inverter output voltage*With reference voltage amplitude E*, calculate three-phase fundamental wave Positive sequence voltage reference vectorAnd abc → α β coordinate transforms are done, obtain the reference voltage under α β coordinate systemsWherein,
(11) in APF and DG coordination compensation process, the total harmonic distortion factor THD of all DG nodes is calculated firstN(i) And with total harmonic distortion factor reference value THDrefCompare, if actual THDN(i)More than reference value, then by Ti h±,1-Pass through low strap Width communication LBC is sent in corresponding DG local controller, synthesizes the reference voltage level of each DG nodes, therefore, by n DG Ti h±,1-Summation, then averaged, can obtain total coordination cancellation ratio and are shown below:
Wherein:Th±,1-For chief coordinator's cancellation ratio, Ti h±,1-For DGiCoordination cancellation ratio, adjusted by integral controller Section, in the range of between 0-1, n is DG number, as can be seen from the above equation, when DG separate compensations PCC point voltages,Then, by above-mentioned chief coordinator's cancellation ratio Th±,1-It is sent to by low bandwidth communication in APF compensating controllers;
(12) in APF and DG coordination compensation process, APF output current iAPFIt is larger on coordinating compensation effect influence, iAPFIt can be calculated and obtained by following formula:
Wherein:For load end fundamental wave negative sequence, harmonic wave positive-negative sequence current,It is positive and negative for DG ends fundamental wave negative sequence, harmonic wave Sequence electric current;
(13) in Active Power Filter-APF APF, the positive and negative order components of each harmonic component, fundamental wave are calculated by measurement module And each harmonic aberration rate, each harmonic aberration rate is compared with percent harmonic distortion reference value, and difference passes through proportional integration PI controllers obtain each electric conductivity valueByAnd vabcIt can obtain reference currentIt is shown below:
Wherein:H is overtone order,For each electric conductivity value, vabcFor PCC point voltages;
(14) reference current obtained according to above-mentioned calculatingAnd PCC point voltages vabcWith electric current iabc, produced by APF Reference offset voltage valueIt is shown below:
Wherein:LiFor APF inductance, Δ T is the sampling period;
(15) the reference offset voltage value obtained according to above-mentioned calculatingα β are can obtain by abc → α β coordinate transforms to sit Reference voltage under mark systemWherein,
(16) reference voltage obtained using above-mentioned calculatingWithAfter summation, v is subtractedVαβObtain outer voltage control Reference voltageWithSubtract the filter capacitor voltage v that actual measurement is obtainedoαβ, its difference is sent to how quasi- ratio resonance In PR controllers, the reference value i of electric current loop is obtainedref
(17) by reference value irefWith actually measuring obtained inductive current iLαβSubtract each other and obtain current error, this error is sent It is controlled toward current inner loop, obtains the driving pulse of each bridge arm of three-phase full-bridge inverting circuit, control the open-minded of each power tube With disconnection.
Dq → α β coordinate transform formula in the step (2) are:
Wherein:θ is the anglec of rotation;
Abc → α β coordinate transform formula in the step (5) are:
How quasi- ratio resonance PR controller transfer functions in the step (16) are:
In formula:kpV、kpIRespectively voltage, current control coefficient, krV、krIRespectively resonance gain, ωcV、ωcIRespectively Cut-off angular frequency, ω0For controller resonance angular frequency, k is to specify subharmonic number of times.
Compared with prior art, the present invention has advantages below:Distributed linear quadratic control method of the present invention with Centerized fusion method is compared, and system is relatively low to communication bandwidth requirement, and the reliability of system is relatively strong and is easy to extension, easily realizes and divides The plug and play of cloth power supply, can independently, fast and efficiently realize data transfer and control, be suitable for large-scale micro- electricity Net is incorporated to bulk power grid.In addition, for being connect on many inverse distributed powers isolated island micro-grid system point of common coupling PCC in parallel When having three-phase imbalance load and nonlinear load, the method that the present invention is carried coordinates distribution using Active Power Filter-APF APF Formula power supply DG compensates PCC point voltages, while suppress Current harmonic distortion, and DG quality of voltage is higher, and power output is accurately divided Match somebody with somebody.
In order to verify the validity of institute's extracting method of the present invention, two points in Matlab/Simulink emulation platform buildings Micro-grid system simulation model in parallel cloth power supply DG, institute's loading is three-phase imbalance load and nonlinear load.Two Distributed power source DG control system is identical with main circuit parameter, and the switching frequency of inverter is 10kHz, DG main circuit and control The simulation parameter of system processed is as shown in table 1, table 2.
The main circuit parameter of table 1
The control system parameter of table 2
The output voltage of front and rear DG1, DG2 and PCC point of compensation and the current simulations ripple of PCC points are extracted in implementation process Shape, it can be seen that effective and feasible using method proposed by the invention.Specific emulation is described as follows:
(1) the output voltage simulation waveform of DG1, DG2 and PCC point is as shown in Fig. 7,8,9 before and after compensating, its compensation process For:It is uncompensated before 1.05s, compensated during 1.05~1.15s for DG, APF collaborations DG compensation after 1.15s.Can from simulation waveform To find out, preferably, PCC point voltages are due to the access of three-phase imbalance nonlinear load, its electricity for the quality of voltage at DG ends before compensation Pressure is second-rate;And DG compensation is added in t=1.05s, due to DG compensating actions so that the quality of voltage of PCC points has bright It is aobvious to improve, but DG itself compensation ability and finite capacity, PCC points quality of voltage is also in the presence of slightly voltage distortion and injustice Weighing apparatus;Therefore, APF coordinations DG is added after t=1.15s to compensate, it can be seen that the output voltage of PCC points has been obtained completely Compensation, effect is obvious;And DG in t=1.05s due to compensate for the output voltages of PCC points, its output voltage there occurs abnormal Become and uneven, and PCC point voltages are compensated because APF coordinates DG in t=1.15s, the output voltage at DG ends is also obtained Recovery is arrived.
(2) Figure 10 show simulation waveform before and after PCC point current compensations, it can be seen that compensation before due to by To the influence of non-linear unbalanced load, PCC point current waveform Severe distortions and imbalance;DG is added in t=1.05s to mend Repay, and because DG compensation is PCC point voltage compensations, it is smaller to the compensating action of electric current, therefore, it can be seen that current waveform has slightly Perhaps improvement;And APF coordinations DG is added in t=1.15s and is compensated, it can be seen that due to APF compensating action so that The electric current of PCC points has obtained complete compensation, and effect is obvious.
Brief description of the drawings
The embodiment to the present invention is described in further detail below in conjunction with the accompanying drawings.
Fig. 1 is isolated island micro-capacitance sensor multi-inverter parallel system architecture schematic diagram of the present invention.
Fig. 2 is distributed power source DG compensation reference schematic diagram calculations of the present invention.
Fig. 3 is Active Power Filter-APF APF collocation structure schematic diagrams of the present invention.
Fig. 4 is Active Power Filter-APF APF current compensation schematic diagram calculations of the present invention.
Fig. 5 is Active Power Filter-APF APF of the present invention and distributed power source DG collaboration compensation principle figures.
Fig. 6 is emulation experiment test schematic diagram of the present invention.
Fig. 7 is simulation waveform before and after DG1 output voltage compensations of the present invention.
Fig. 8 is simulation waveform before and after DG2 output voltage compensations of the present invention.
Fig. 9 is simulation waveform before and after PCC points output voltage compensation of the present invention.
Figure 10 is simulation waveform before and after PCC points output current of the present invention compensation.
Embodiment
A kind of micro-capacitance sensor quality of power supply distributed coordination administering method, it is characterised in that:Including how inverse distributed electricity Source isolated island micro-grid system in parallel, many inverse distributed powers isolated island micro-grid system in parallel includes several points Cloth generator unit, Active Power Filter-APF APF, distributed secondary controller, sampling computing module, DG buses, public coupling Point PCC, non-linear unbalanced load, linear load;It is connected in parallel between some distributed generation units, described some points Cloth generator unit connects the DG buses, the APF, the sampling computing module, the non-linear imbalance by feeder line Load and the linear load are connected between the DG buses and the point of common coupling PCC, the distributed linear quadratic control Device be connected with the sampling computing module, and the distributed generation unit is inverse including the micro- source of direct current that is sequentially connected, three phase full bridge Become circuit, LC filter circuits, feeder line, the distributed generation unit also includes local controller, driving protection module, the LC Filter circuit is connected with the local controller;
The sampling computing module carries out sampling processing and calculating to the PCC points voltage, and output quantity is passed through into low strap Wide communications are into the distributed secondary controller, and the distributed secondary controller transmits the compensation reference of generation Into the local controller, the local controller output quantity is by driving protection module to drive the three phase full bridge inversion electricity Power tube in road being opened and turning off, and specific steps include:
(1) sampling computing module is to point of common coupling PCC voltages vabcSampling calculating and dq coordinate transforms are carried out, is obtained PCC point fundamental positive sequence voltages under dq coordinate systemsFundamental wave negative sequence voltageAnd h subharmonic voltagesAnd pass through low strap Width communication LBC is sent in distributed secondary controller;Wherein, vabc=[va,vb,vc]T, h be harmonic wave number of times, h=3,5, 7;
(2) by PCC point fundamental positive sequence voltagesFundamental wave negative sequence voltageH subharmonic voltagesPass through dq → α β coordinates Conversion and virtual value computing module can obtain the fundamental positive sequence voltage under α β coordinate systemsFundamental wave negative sequence voltageh Subharmonic voltage
(3) voltage for obtaining above-mentioned calculatingPass through the Voltage unbalance factor and harmonic distortion Computing module can be obtainedThen by VUF, HDhReference value VUF corresponding with its* It is compared, difference can obtain compensation reference after proportional integration PI controllersFinally again by compensation referencePass Transport in local controller and compensate;Wherein, the calculation formula of compensation reference is shown below:
(4) in local controller, the filter capacitor voltage vector v of LC filter circuits is detected in real timeoabc, filter inductance electric current Vectorial iLabcAnd feeder current vector ioabc, its expression formula is shown below:
voabc=[voa,vob,voc]T
iLabc=[iLa,iLb,iLc]T
ioabc=[ioa,iob,ioc]T
(5) by abc → α β coordinate transforms by filter capacitor voltage vector voabc, filter inductance current vector iLabcAnd Feeder current vector ioabcIt is transformed to the filter capacitor voltage vector v under the static mark systems of α βoαβ, filter inductance current vector iLαβWith And feeder current vector ioαβ, its expression formula is shown below:
voαβ=[v,v]T
iLαβ=[i,i]T
ioαβ=[i,i]T
(6) two-phase fundamental voltage v is extracted respectivelyoαβ, two-phase fundamental current ioαβFundamental positive sequence voltage under α β coordinate systems VectorFundamental positive sequence current vectorIts expression formula is shown below:
(7) Theory of Instantaneous Reactive Power of Three-Phase Circuits is based on, the fundamental positive sequence active-power P of inverter output is calculated+, Fundamental positive sequence reactive power Q+It is shown below:
(8) according to the fundamental positive sequence voltage vector of said extractedFundamental positive sequence electric currentIt can obtain by virtually hindering The voltage vector v that anti-ring is producedVαβ=[v,v]TIt is shown below:
Wherein:RvFor virtual resistance, LvFor virtual inductor;
(9) according to power droop control characteristic, three-phase inverter output reference voltage E is respectively obtained*With refer to angular frequency ω*, its formula is shown below:
ω*n-kpP+
E*=En-kqQ+
Wherein:kpFor sagging active proportionality coefficient, kqFor sagging idle proportionality coefficient, ω*To refer to angular frequency, ωnFor volume Determine angular frequency, E*For reference voltage amplitude, EnFor rated voltage amplitude;
(10) angular frequency is referred to according to three-phase inverter output voltage*With reference voltage amplitude E*, calculate three-phase fundamental wave Positive sequence voltage reference vectorAnd abc → α β coordinate transforms are done, obtain the reference voltage under α β coordinate systemsWherein,
(11) in APF and DG coordination compensation process, the total harmonic distortion factor THD of all DG nodes is calculated firstN(i) And with total harmonic distortion factor reference value THDrefCompare, if actual THDN(i)More than reference value, then willPass through low bandwidth Communication LBC is sent in corresponding DG local controller, the reference voltage level of each DG nodes is synthesized, therefore, by n DG 'sSummation, then averaged, can obtain total coordination cancellation ratio and are shown below:
Wherein:Th±,1-For chief coordinator's cancellation ratio, Ti h±,1-For DGiCoordination cancellation ratio, adjusted by integral controller Section, in the range of between 0-1, n is DG number, as can be seen from the above equation, when DG separate compensations PCC point voltages,Then, by above-mentioned chief coordinator's cancellation ratio Th±,1-It is sent to by low bandwidth communication in APF compensating controllers;
(12) in APF and DG coordination compensation process, APF output current iAPFIt is larger on coordinating compensation effect influence, iAPFIt can be calculated and obtained by following formula:
Wherein:For load end fundamental wave negative sequence, harmonic wave positive-negative sequence current,It is positive and negative for DG ends fundamental wave negative sequence, harmonic wave Sequence electric current;
(13) in Active Power Filter-APF APF, the positive and negative order components of each harmonic component, fundamental wave are calculated by measurement module And each harmonic aberration rate, each harmonic aberration rate is compared with percent harmonic distortion reference value, and difference passes through proportional integration PI controllers obtain each electric conductivity valueByAnd vabcIt can obtain reference currentIt is shown below:
Wherein:H is overtone order,For each electric conductivity value, vabcFor PCC point voltages;
(14) reference current obtained according to above-mentioned calculatingAnd PCC point voltages vabcWith electric current iabc, produced by APF Reference offset voltage valueIt is shown below:
Wherein:LiFor APF inductance, Δ T is the sampling period;
(15) the reference offset voltage value obtained according to above-mentioned calculatingα β are can obtain by abc → α β coordinate transforms to sit Reference voltage under mark systemWherein,
(16) reference voltage obtained using above-mentioned calculatingWithAfter summation, v is subtractedVαβObtain outer voltage control Reference voltageWithSubtract the filter capacitor voltage v that actual measurement is obtainedoαβ, its difference is sent to how quasi- ratio resonance In PR controllers, the reference value i of electric current loop is obtainedref
(17) by reference value irefWith actually measuring obtained inductive current iLαβSubtract each other and obtain current error, this error is sent It is controlled toward current inner loop, obtains the driving pulse of each bridge arm of three-phase full-bridge inverting circuit, control the open-minded of each power tube With disconnection.
Dq → α β coordinate transform formula in the step (2) are:
Wherein:θ is the anglec of rotation;
Abc → α β coordinate transform formula in the step (5) are:
How quasi- ratio resonance PR controller transfer functions in the step (16) are:
In formula:kpV、kpIRespectively voltage, current control coefficient, krV、krIRespectively resonance gain, ωcV、ωcIRespectively Cut-off angular frequency, ω0For controller resonance angular frequency, k is to specify subharmonic number of times.
More than, it is only the present invention preferably embodiment, but protection scope of the present invention is not limited thereto, and it is any Those familiar with the art the invention discloses technical scope in, technique according to the invention scheme and its invention Design is subject to equivalent substitution or change, should all be included within the scope of the present invention.

Claims (5)

1. a kind of micro-capacitance sensor quality of power supply distributed coordination administering method, it is characterised in that:Using including how inverse distributed The isolated island micro-grid system of power sources in parallel;Wherein many inverse distributed powers isolated island micro-grid system in parallel includes several Distributed generation unit, Active Power Filter-APF APF, distributed secondary controller, sampling computing module, DG buses, public coupling Chalaza PCC, non-linear unbalanced load, linear load;It is connected in parallel between some distributed generation units;It is described some Distributed generation unit connects the DG buses by feeder line;The APF, the sampling computing module, the non-linear injustice Weighing apparatus load and the linear load are connected between the DG buses and the point of common coupling PCC;Distributed two secondary control Device processed is connected with the sampling computing module;The distributed generation unit includes the micro- source of direct current, the three phase full bridge being sequentially connected Inverter circuit, LC filter circuits, feeder line, the distributed generation unit also include local controller, driving protection module, described LC filter circuits are connected with the local controller;
The sampling computing module carries out sampling processing and calculating to the PCC points voltage, and output quantity is led to by low bandwidth Letter is transmitted into the distributed secondary controller, and the compensation reference of generation is sent to institute by the distributed secondary controller State in local controller, the local controller output quantity is by driving protection module to drive in the three-phase full-bridge inverting circuit Power tube opening and turn off.
2. a kind of micro-capacitance sensor quality of power supply distributed coordination administering method according to claim 1, it is characterised in that adopted It is with many inverse distributed powers isolated island micro-grid system operating method in parallel:
(1) sampling computing module is to point of common coupling PCC voltages vabcSampling calculating and dq coordinate transforms are carried out, dq seats are obtained PCC point fundamental positive sequence voltages under mark systemFundamental wave negative sequence voltageAnd h subharmonic voltagesAnd it is logical by low bandwidth Letter LBC is sent in distributed secondary controller;Wherein, vabc=[va,vb,vc]T, h is the number of times of harmonic wave, h=3,5,7;
(2) by PCC point fundamental positive sequence voltagesFundamental wave negative sequence voltageH subharmonic voltagesPass through dq → α β coordinate transforms And virtual value computing module can obtain the fundamental positive sequence voltage under α β coordinate systemsFundamental wave negative sequence voltageH times humorous Wave voltage
(3) voltage for obtaining above-mentioned calculatingCalculated by the Voltage unbalance factor and harmonic distortion Module can be obtainedThen by VUF, HDhReference value VUF corresponding with its*Compared Compared with difference can obtain compensation reference after proportional integration PI controllersFinally again by compensation referenceTransmit to this Compensated in ground controller;Wherein, the calculation formula of compensation reference is shown below:
<mrow> <msubsup> <mi>C</mi> <mrow> <mi>d</mi> <mi>q</mi> </mrow> <mn>1</mn> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msup> <mi>VUF</mi> <mo>*</mo> </msup> <mo>-</mo> <mi>V</mi> <mi>U</mi> <mi>F</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>P</mi> <mi>I</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msubsup> <mi>v</mi> <mrow> <mi>d</mi> <mi>q</mi> </mrow> <mrow> <mn>1</mn> <mo>-</mo> </mrow> </msubsup> <mo>;</mo> </mrow>
<mrow> <msubsup> <mi>C</mi> <mrow> <mi>d</mi> <mi>q</mi> </mrow> <mi>h</mi> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>HD</mi> <mi>h</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>HD</mi> <mi>h</mi> </msub> <mo>)</mo> </mrow> <mi>P</mi> <mi>I</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msubsup> <mi>v</mi> <mrow> <mi>d</mi> <mi>q</mi> </mrow> <mi>h</mi> </msubsup> <mo>;</mo> </mrow>
(4) in local controller, the filter capacitor voltage vector v of LC filter circuits is detected in real timeoabc, filter inductance current vector iLabcAnd feeder current vector ioabc, its expression formula is shown below:
voabc=[voa,vob,voc]T
iLabc=[iLa,iLb,iLc]T
ioabc=[ioa,iob,ioc]T
(5) by abc → α β coordinate transforms by filter capacitor voltage vector voabc, filter inductance current vector iLabcAnd feeder line Current vector ioabcIt is transformed to the filter capacitor voltage vector v under the static mark systems of α βoαβ, filter inductance current vector iLαβAnd feedback Line current vector ioαβ, its expression formula is shown below:
voαβ=[v,v]T
iLαβ=[i,i]T
ioαβ=[i,i]T
(6) two-phase fundamental voltage v is extracted respectivelyoαβ, two-phase fundamental current ioαβFundamental positive sequence voltage vector under α β coordinate systemsFundamental positive sequence current vectorIts expression formula is shown below:
<mrow> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <mo>,</mo> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow>
<mrow> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <mo>,</mo> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow>
(7) Theory of Instantaneous Reactive Power of Three-Phase Circuits is based on, the fundamental positive sequence active-power P of inverter output is calculated+, fundamental wave Positive sequence reactive power Q+It is shown below:
<mrow> <msup> <mi>P</mi> <mo>+</mo> </msup> <mo>=</mo> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <mo>+</mo> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>;</mo> </mrow>
<mrow> <msup> <mi>Q</mi> <mo>+</mo> </msup> <mo>=</mo> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <mo>;</mo> </mrow>
(8) according to the fundamental positive sequence voltage vector of said extractedFundamental positive sequence electric currentIt can obtain by virtual impedance ring The voltage vector v of generationVαβ=[v,v]TIt is shown below:
<mrow> <msub> <mi>v</mi> <mrow> <mi>V</mi> <mi>&amp;alpha;</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>v</mi> </msub> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <mo>-</mo> <msub> <mi>L</mi> <mi>v</mi> </msub> <msubsup> <mi>&amp;omega;i</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>;</mo> </mrow>
<mrow> <msub> <mi>v</mi> <mrow> <mi>V</mi> <mi>&amp;beta;</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>v</mi> </msub> <msubsup> <mi>i</mi> <mrow> <mi>o</mi> <mi>&amp;beta;</mi> </mrow> <mo>+</mo> </msubsup> <mo>+</mo> <msub> <mi>L</mi> <mi>v</mi> </msub> <msubsup> <mi>&amp;omega;i</mi> <mrow> <mi>o</mi> <mi>&amp;alpha;</mi> </mrow> <mo>+</mo> </msubsup> <mo>;</mo> </mrow>
Wherein:RvFor virtual resistance, LvFor virtual inductor;
(9) according to power droop control characteristic, three-phase inverter output reference voltage E is respectively obtained*With refer to angular frequency*, its Formula is shown below:
ω*n-kpP+
E*=En-kqQ+
Wherein:kpFor sagging active proportionality coefficient, kqFor sagging idle proportionality coefficient, ω*To refer to angular frequency, ωnFor specified angle Frequency, E*For reference voltage amplitude, EnFor rated voltage amplitude;
(10) angular frequency is referred to according to three-phase inverter output voltage*With reference voltage amplitude E*, calculate three-phase fundamental positive sequence Voltage Reference vectorAnd abc → α β coordinate transforms are done, obtain the reference voltage under α β coordinate systemsWherein,
(11) in APF and DG coordination compensation process, the total harmonic distortion factor THD of all DG nodes is calculated firstN(i)And with it is total Percent harmonic distortion reference value THDrefCompare, if actual THDN(i)More than reference value, then by Ti h±,1-Pass through low bandwidth communication LBC is sent in corresponding DG local controller, is synthesized the reference voltage level of each DG nodes, therefore, is passed through the T to n DGi h ±,1-Summation, then averaged, can obtain total coordination cancellation ratio and are shown below:
<mrow> <msup> <mi>T</mi> <mrow> <mi>h</mi> <mo>&amp;PlusMinus;</mo> <mo>,</mo> <mn>1</mn> <mo>-</mo> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msubsup> <mi>T</mi> <mi>i</mi> <mrow> <mi>h</mi> <mo>&amp;PlusMinus;</mo> <mo>,</mo> <mn>1</mn> <mo>-</mo> </mrow> </msubsup> </mrow> <mi>n</mi> </mfrac> <mo>;</mo> </mrow>
Wherein:Th±,1-For chief coordinator's cancellation ratio, Ti h±,1-For DGiCoordination cancellation ratio, be adjusted by integral controller, its Scope be 0-1 between, n be DG number, as can be seen from the above equation, when DG separate compensations PCC point voltages,Then, by above-mentioned chief coordinator's cancellation ratio Th±,1-It is sent to by low bandwidth communication in APF compensating controllers;
(12) in APF and DG coordination compensation process, APF output current iAPFLarger, i is influenceed on coordinating compensation effectAPF It can be calculated and obtained by following formula:
<mrow> <msub> <mi>i</mi> <mrow> <mi>A</mi> <mi>P</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>i</mi> <mi>L</mi> <mrow> <mi>h</mi> <mo>&amp;PlusMinus;</mo> <mo>,</mo> <mn>1</mn> <mo>-</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>i</mi> <mi>s</mi> <mrow> <mi>h</mi> <mo>&amp;PlusMinus;</mo> <mo>,</mo> <mn>1</mn> <mo>-</mo> </mrow> </msubsup> <mo>;</mo> </mrow>
Wherein:For load end fundamental wave negative sequence, harmonic wave positive-negative sequence current,For DG ends fundamental wave negative sequence, harmonic wave positive-negative sequence electricity Stream;
(13) in Active Power Filter-APF APF, by measurement module calculate the positive and negative order components of each harmonic component, fundamental wave and Each harmonic aberration rate, each harmonic aberration rate is compared with percent harmonic distortion reference value, and difference is controlled by proportional integration PI Device processed obtains each electric conductivity valueByAnd vabcIt can obtain reference currentIt is shown below:
<mrow> <msubsup> <mi>i</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>h</mi> </munder> <msubsup> <mi>G</mi> <mi>h</mi> <mo>*</mo> </msubsup> <mo>&amp;CenterDot;</mo> <msub> <mi>v</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msub> <mo>;</mo> </mrow>
Wherein:H is overtone order,For each electric conductivity value, vabcFor PCC point voltages;
(14) reference current obtained according to above-mentioned calculatingAnd PCC point voltages vabcWith electric current iabc, the reference produced by APF Offset voltage valueIt is shown below:
<mrow> <msubsup> <mi>v</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>v</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <mfrac> <msub> <mi>L</mi> <mi>i</mi> </msub> <mrow> <mi>&amp;Delta;</mi> <mi>T</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>i</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein:LiFor APF inductance, Δ T is the sampling period;
(15) the reference offset voltage value obtained according to above-mentioned calculatingα β coordinate systems can obtain by abc → α β coordinate transforms Under reference voltageWherein,
(16) reference voltage obtained using above-mentioned calculatingWithAfter summation, v is subtractedVαβObtain the ginseng of outer voltage control Examine voltageWithSubtract the filter capacitor voltage v that actual measurement is obtainedoαβ, its difference is sent to how quasi- ratio resonance PR and controlled In device processed, the reference value i of electric current loop is obtainedref
(17) by reference value irefWith actually measuring obtained inductive current iLαβSubtract each other and obtain current error, this error is sent to electricity Stream inner ring is controlled, and obtains the driving pulse of each bridge arm of three-phase full-bridge inverting circuit, control each power tube opens through and off Open.
3. a kind of micro-capacitance sensor quality of power supply distributed coordination administering method as claimed in claim 2, it is characterised in that:The step Suddenly dq → α β coordinate transform formula in (2) are:
<mrow> <msub> <mi>f</mi> <mrow> <mi>d</mi> <mi>q</mi> <mo>&amp;RightArrow;</mo> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <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> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein:θ is the anglec of rotation;
4. a kind of micro-capacitance sensor quality of power supply distributed coordination administering method as claimed in claim 2, it is characterised in that:The step Suddenly abc → α β coordinate transform formula in (5) are:
<mrow> <msub> <mi>f</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> <mo>&amp;RightArrow;</mo> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>2</mn> </mfrac> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
5. a kind of micro-capacitance sensor quality of power supply distributed coordination administering method as claimed in claim 2, it is characterised in that:The step Suddenly the how quasi- ratio resonance PR controller transfer functions in (16) are:
<mrow> <msub> <mi>G</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mi>V</mi> </mrow> </msub> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> </mrow> </munder> <mfrac> <mrow> <mn>2</mn> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>V</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>c</mi> <mi>V</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>s</mi> </mrow> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mrow> <mi>c</mi> <mi>V</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>s</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>h&amp;omega;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow>
<mrow> <msub> <mi>G</mi> <mi>I</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mi>I</mi> </mrow> </msub> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> </mrow> </munder> <mfrac> <mrow> <mn>2</mn> <msub> <mi>k</mi> <mrow> <mi>r</mi> <mi>I</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>c</mi> <mi>I</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>s</mi> </mrow> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mrow> <mi>c</mi> <mi>I</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>s</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>h&amp;omega;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow>
In formula:kpV、kpIRespectively voltage, current control coefficient, krV、krIRespectively resonance gain, ωcV、ωcIRespectively end Angular frequency, ω0For controller resonance angular frequency, k is to specify subharmonic number of times.
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