CN106549399B - A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms - Google Patents
A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms Download PDFInfo
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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
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
- H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
- H02J3/1835—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control
- H02J3/1842—Arrangements 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
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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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- 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
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- 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
- Y02E40/20—Active power filtering [APF]
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Abstract
A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms.This method uses synchronous rotating angle first, establishes the lower order system model of dq coordinate systems；Then the sliding formwork switching function of DC voltage is determined according to sliding-mode surface selection principle；The control parameter output function of PI controllers is finally designed according to the switching function of sliding-mode surface.The control method improves the steady-state behaviour and response speed of DC voltage, while effectively reducing voltage fluctuation；APF control systems in parallel based on sliding formwork PI complex control algorithms have good robust performance and dynamic property.A kind of APF DC side voltage control methods in parallel of sliding formwork PI complex control algorithms of the present invention, PI controller parameters are determined by sliding mode controller, the stable state accuracy and response speed when load sudden change and reference voltage saltus step are improved, reduces DC side power attenuation to ensure the compensation ability of parallel active filter.
Description
Technical field
The invention belongs to active filter control field, specifically a kind of parallel connection based on sliding formwork PI complex control algorithms
APF DC side voltage control methods.
Background technology
Shunt (Active Power Filter, APF) is as a kind of solution harmonic pollution in electric power net
Effective means, it can realize harmonic wave, negative-sequence current existing for network system and reactive power accurate, effective in real time mend
It repays.The output compensation characteristic of active filter depends primarily on the control method to Current Voltage, and used converter plant
Main circuit topological structure.It is most of using tradition three at present to the research of active filter topological structure comparative maturity
Phase PWM converter structure, thus Shunt compensation performance raising depend on used control method,
In the control algolithm to electric current and voltage, to the algorithm of current detecting and current control comparative maturity, and DC side is electric
Press control algolithm relatively fewer.However in entire APF control systems, the quality of DC voltage control performance directly influences
Therefore the quality of active filter compensation performance controls the fast accurate of DC voltage the compensation performance to active filter
It is of great significance, is studied herein primarily directed to the DC voltage of three-phase three-wire system parallel active filter.
The primary method of control for being presently used for APF DC voltages has conventional PI control algorithm, fuzzy controller, adaptive
Control methods should be waited.When conventional PI control device is used for DC voltage control, though it can finally meet DC voltage stability, electricity
The response speed of pressure is slow, and there are overshoot, cannot be satisfied needs in load sudden change and when reference voltage saltus step.Fuzzy control
Device does not depend on system, and convenient for transplanting, robust performance is stronger；However its control accuracy is poor, DC voltage fluctuation causes to damage greatly
Consumption increases and reduces the compensation performance of APF.It is complex based on the realization of voltage adaptive control method, in control algolithm operation
Occupancy Resources on Chip is more, and DC voltage dynamic property is undesirable.
Invention content
For the above deficiency, the present invention provides a kind of APF DC voltages in parallel based on sliding formwork PI complex control algorithms
Control method, this method use synchronous rotating angle, establish the lower order system model of dq coordinate systems first；Then according to cunning
Die face selection principle determines the sliding formwork switching function of DC voltage；PI controllers are finally designed according to the switching function of sliding-mode surface
Control parameter output function.The control method improves the steady-state behaviour and response speed of DC voltage, effectively reduces simultaneously
Voltage fluctuation；APF control systems in parallel based on sliding formwork PI complex control algorithms have good robust performance and dynamic
Energy.
The technical solution adopted in the present invention is：
A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms, include the following steps：
Step 1：Lower order system models of the foundation parallel connection APF in dq coordinate systems；
usk(k=a, b, c) is three-phase access point voltage；ufk(k=a, b, c) is each bridge arm midpoint potential of three-phase；
is(a,b,c)、if(a,b,c)、is(a,b,c)Respectively mains input current, load current and compensation electric current；R be circuit and inductance etc.
Imitate resistance；L is flat wave inductance；C is DC bus capacitor；Capacitance both end voltage is udc。
To simplify the design of parallel connection APF control systems, if switch is in perfect condition, ignore the influence of switch parameter；Together
Close coupling high order system model under abc coordinate systems is transformed to the low order of dq coordinate systems by Shi Caiyong synchronous rotating angles
System model.If under dq coordinate systems, access point voltage is usd、usq, APF bridge arm voltages in parallel are ufd、ufq, APF compensation electricity in parallel
Stream is ifd、ifq, then the mathematical model of parallel connection APF be：
Step 2:Detect DC capacitor voltage udc, by itself and DC side reference voltage level udcrefIt makes comparisons, obtains error
Signal, this error signal obtain the current reference value i of current inner loop by sliding formwork PI controllersfd_ref, by checking in electric current
The current actual value i of ringfd, by ifd_refWith ifdIt makes comparisons and obtains error signal, this error signal passes through the controls such as d shaft currents control
U is maded。
udc(s) it is the Lars form of capacitance both end voltage；id(s) it is Laplce's form of d shaft currents；RdcFor DC side
Resistance；C is DC bus capacitor.
The stability contorting of DC voltage is one of the key technology for ensureing active filter compensation performance, currently available technology
It is fairly simple about introducing for DC voltage PI controllers, it often directly gives PI controllers and does not introduce PI controllers in frequency
The tuning process in domain, the present invention derive DC voltage PI controllers in frequency domain.Harmonic wave electricity is compensated only in APF normal operating conditions
Stream and reactive current, to simplify derivation, it is zero to enable q shaft currents, then d shaft currents is utilized to derive active filter DC side electricity
The transmission function of pressure is：
B=1/C, a=1/R in formula (2)dcC, a are resistance RdcWith the inverse of capacitance C products, b is the inverse of capacitance C, and C is
DC bus capacitor, s are the Laplace variable factor.
According to the mentality of designing of current transformer tradition double-closed-loop control device, it is φ to enable current closed-loop transmission functionc(s), direct current
Side voltage PI control block diagrams are as shown in Figure 3.It, will be in electric current since outer voltage response speed is much smaller than current inner loop response speed
Ring is replaced to simplify the design process of DC voltage PI controllers, then obtaining outer voltage open loop Transmission Function with constant
For：
T in formula (3)v=RdcC, PI (s) are the control function of outer voltage, φc(s) it is current closed-loop transmission function, Gv1
(s) it is the transmission function of active filter DC voltage, RdcFor direct current side resistance, C is DC bus capacitor, and s is Laplce
Variable Factors, KpFor outer voltage control parameter.
The system is a typical second-order system, and the design for eliminating zero pole point simplify control device obtains closed loop transmission letter
Number：
τ=C/K in formulap, Gv1oFor outer voltage open loop Transmission Function, KpFor outer voltage control parameter, C is DC side electricity
Hold.
The realization of conventional PI control device is fairly simple, but control parameter is fixed；Change in load sudden change and with reference to given voltage
When, PI controllers cannot meet requirement of the system to steady-state behaviour and dynamic property, and DC voltage cannot timely stability contorting
The problems such as compensation effect of active filter can be caused to reduce.
DC voltage uses novel sliding formwork PI controllers, and control principle is similar to conventional PI control, the difference is that：
The control parameter of sliding formwork PI controllers with system change, the control parameter of PI controllers by sliding mode controller come positive definite, in this way
Do to adjust PI control parameters according to the variation of DC side in real time, to meet system to DC voltage dynamic and stable state
The requirement of performance.Current reference value i of the output of sliding formwork PI controllers as current inner loopfd_ref, next main to study sliding formwork
PI controllers, the accessibility of main design and sliding mode controller including sliding-mode surface.
Mainly there are two purposes for the design of sliding formwork PI controllers：(1) in load sudden change and reference voltage saltus step, DC side
Voltage can keep enough response speeds；(2) there can be good robust performance in DC-side Voltage Stabilization control.APF
The controller of DC side is mainly used for the stability contorting of voltage, and control freedom degree variable uses Direct Variable DC voltage
udc, directly controlled quentity controlled variable can be controlled in this way；According to the principle for choosing sliding-mode surface, the sliding formwork control of DC voltage can define
Face S processed is：
K is normal number, u in formula (5)dc_refFor the reference value of DC voltage, udcFor the actual value of DC voltage.
For determining PI controller parameters, form is similar with conventional PI control device for the output of sliding mode controller, based on upper
One trifle can immediately arrive at the PI controllers based on sliding formwork control about the introduction of conventional PI control device：
K in formula (6)sp, ksiFor the parameter of PI controllers, they are by sliding mode controller according to designed sliding-mode surface (5)
It determines the size of its value, is mainly characterized by obtaining appropriate PI control parameters according to the variation of system.It utilizes formula (2)
(6) the Dynamic Closed Loop function of DC voltage can be obtained：
B=1/C, a=1/R in formula (7)dcC, a 1/RdcThe representative letter of C, b is the inverse of capacitance, and s is Laplce
Variable Factors, ksp, ksiFor the parameter of PI controllers.
To ensure the stability contorting of DC voltage, relational expression once can be obtained according to formula (7)：
B=1/C, a=1/R in formula (8)dcC, a 1/RdcThe representative letter of C, b is the inverse of capacitance, and s is Laplce
Variable Factors, ksp, ksiFor the parameter of PI controllers.
It is set up for formula (8), the control parameter output function of PI controllers is designed according to sliding-mode surface (5)：
Control parameter k in formula (9)p+、kp-、ki+、ki-All it is positive number, these control parameters are to meet PI control output spies
Adjusting as a result, they can be adjusted according to the method for standard PI controllers, for example, by using root-locus technique etc. under property；Together
When the DC voltage fluctuation that is generated near sliding formwork control face for elimination system, respectively in the differential and integral parameter of PI controllers
In addition positive parameter kav_p、kav_i, the fluctuation problem for causing DC voltage is buffeted by sliding-mode surface from eliminating.Wherein sgn (s) is full
And function：
In the sliding-mode surface neighborhood of sliding mode controller, the system based on sliding mode controller will reach switching in finite time
Face then means that sliding formwork mode exists, and sliding mode is in the presence of the premise for being Sliding Mode Controller application, Lee usually chosen
Ya Punuofu functions are：
In formula (11)For DC voltage square-error, V (edc) it is about DC voltage square-errorLetter
Number.
And time derivation is obtained：
K is normal number in formula (12),Derivative for DC voltage error about the time, edcIt is missed for DC voltage
Difference, andMore than zero, formula (12) is less than the stability that zero permanent establishment then demonstrates designed sliding mode controller.
Buffeting of the sliding mode controller in sliding-mode surface field is difficult to avoid that, to eliminate system in sliding formwork control face field
The DC voltage fluctuation of generation adds positive parameter k in the differential and integral parameter of PI controllers respectivelyav_p、kav_i, from eliminate by
Sliding-mode surface buffets the fluctuation problem for causing DC voltage.Work as S>When 0, ksp=2kp++kav_p, ksi=2ki++kav_i；Work as S<0
When, ksp=2kp-+kav_p, ksi=2ki-+kav_i。
Step 3:The load current i of detection at this timeLHarmonic component iLh, stablize fortune if load current at this time does not have harmonic wave
Row, otherwise return to step 2, repeat step 2.
A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms of the present invention, advantageous effect
It is as follows：
1：For Active Power Filter-APF, the present invention proposes a kind of APF DC sides in parallel of sliding formwork PI complex control algorithms
Voltage control method determines PI controller parameters by sliding mode controller, when improving load sudden change and reference voltage saltus step
Stable state accuracy and response speed reduce DC side power attenuation to ensure the compensation ability of parallel active filter.
2：Sliding formwork PI complex control algorithms are proposed, for improving DC voltage in load sudden change and reference voltage saltus step
Stable state accuracy and response speed, reduce DC side power attenuation to ensure the compensation ability of parallel active filter.It is loading
When mutation and when reference voltage saltus step occurs, sliding formwork PI composite control methods utilize the spy of sliding mode controller rapid dynamic response speed
Property, the control parameter as PI algorithms is output it, the method for this variable PI parameter control can effectively improve DC voltage
Dynamic and steady-state characteristic.In addition, to weaken the buffeting of sliding mode controller, boundary value is set for voltage error, in boundary value
Outer sliding mode controller can improve the dynamic responding speed of DC voltage, and the tracking that system is can effectively improve in boundary layer is steady
State property energy.
3：The method of the present invention uses synchronous rotating angle first, establishes the lower order system model of dq coordinate systems；Then
The sliding formwork switching function of DC voltage is determined according to sliding-mode surface selection principle；PI is finally designed according to the switching function of sliding-mode surface
The control parameter output function of controller.The control method improves the steady-state behaviour and response speed of DC voltage, has simultaneously
Effect reduces voltage fluctuation；APF control systems in parallel based on sliding formwork PI complex control algorithms have good robust performance and
Dynamic property.
Description of the drawings
Fig. 1 is the APF DC voltage controls flow diagram in parallel based on sliding formwork PI complex control algorithms.
Fig. 2 is the basic functional principle of three-phase three-wire system parallel active filter.
Fig. 3 is phase three-wire three parallel connection type APF main circuit structures.
Fig. 4 is the sliding formwork PI complex controll figures of DC voltage.
Fig. 5 is the double-closed-loop control figure of parallel active filter.
When Fig. 6 uprushes for DC reference voltage, the DC voltage oscillogram of PI control and sliding formwork PI complex controlls.
When Fig. 7 is that load reduces, the DC voltage oscillogram of PI control and sliding formwork PI complex controlls.
Specific implementation mode
With reference to embodiment and attached drawing, the present invention is done and is further described in detail, but embodiments of the present invention are not
It is limited to this.
Fig. 1 is the APF DC voltage controls block diagram in parallel based on sliding formwork PI complex control algorithms, compound based on sliding formwork PI
The specific steps of the APF DC side voltage control methods in parallel of control algolithm：
(1) lower order system models of the foundation parallel connection APF in dq coordinate systems；
(2) detection DC capacitor voltage udc, by itself and DC side reference voltage level udcrefIt makes comparisons, show that error is believed
Number, this error signal obtains the current reference value i of current inner loop by sliding formwork PI controllersfd_ref, by checking current inner loop
Current actual value ifd, by ifd_refWith ifdIt makes comparisons and obtains error signal, this error signal passes through the controls such as d shaft currents control
Obtain Ud
The stability contorting of DC voltage is one of the key technology for ensureing active filter compensation performance, currently available technology
In it is fairly simple about introducing for DC voltage PI controllers, often directly give PI controllers and do not introduce PI controllers and exist
The tuning process of frequency domain, the present invention derive DC voltage PI controllers in frequency domain.Harmonic wave is compensated only in APF normal operating conditions
Electric current and reactive current, to simplify derivation, it is zero to enable q shaft currents, then utilizes d shaft currents to derive active filter DC side
The transmission function of voltage is：
B=1/C in above formula, a=1/RdcC。
DC bus capacitor C=4000 μ F, load resistance Rdc=10 Ω, then：
According to the mentality of designing of current transformer tradition double-closed-loop control device, it is φ to enable current closed-loop transmission functionc(s), direct current
The sliding formwork PI complex controll block diagrams of side voltage are as shown in Figure 3.Since outer voltage response speed is much smaller than current inner loop response speed
Current inner loop is replaced to simplify the design process of DC voltage PI controllers, then obtaining outer voltage and opening by degree with constant
Ring Transmission Function is：
T in above formulav=RdcC, the system are a typical second-order systems, eliminate being designed for zero pole point simplify control device
To closed loop transfer function,：
τ=C/K in formulap。
Current loop control parameter is kp=55, ki=10, outer shroud control parameter is kp=1.5, ki=3, switching frequencyDC bus capacitor C=4000 μ F, load resistance Rdc=10 Ω, then：
For determining PI controller parameters, form is similar with conventional PI control device for the output of sliding mode controller, based on upper
One trifle can immediately arrive at the PI controllers based on sliding formwork control about the introduction of conventional PI control device：
K in above formulasp, ksiFor the parameter of PI controllers, they are determined according to designed sliding-mode surface by sliding mode controller
The size of its fixed value, is mainly characterized by obtaining appropriate PI control parameters according to the variation of system.Utilize DC side electricity
The transmission function of pressure and PI controllers based on sliding formwork control can obtain the Dynamic Closed Loop function of DC voltage：
To ensure the stability contorting of DC voltage, a ShiShimonoseki can be obtained according to the Dynamic Closed Loop function of DC voltage
It is formula：
To make above formula set up, the control parameter output function of PI controllers is designed according to sliding-mode surface：
Control parameter based on sliding formwork PI Compound Control Strategies is k=100, kp+=0.035, kp-=0.027, ki+=
3.125 ki-=0.92, kav_p=0.23, kav_i=3.25, then：
Fig. 2 is the basic functional principle figure of parallel active filter.Its component part includes referential current detection and operation
Module etc. occurs for module and compensation electric current；Basic functional principle is analyzed as follows, and the load current that current detection module measures is
iL, using corresponding detection algorithm by iLIn fundamental wave iLfWith harmonic wave iLhSeparation, extraction harmonic wave is negated, by harmonic wave of the inverted
As instruction current if_ref, parallel inverter device generates the compensation electric current, the electric current and harmonic current iLhDirection phase equal in magnitude
Instead, to eliminate electric power outputting current isHarmonic wave, so that the system that nonlinear load and APF are constituted is absorbed into from power grid and be free of
The electric current of harmonic wave achievees the purpose that eliminate mains by harmonics.
Fig. 3 is three-phase three-wire system parallel connection type APF main circuit structure figures.Three-phase three-wire system parallel connection type APF main circuit structures are such as
Shown in Fig. 3.U in figuresa、usb、uscFor three-phase access point voltage, ufa、ufb、ufcFor each bridge arm midpoint potential of three-phase, is(a,b,c)、
il(a,b,c)、if(a,b,c)Respectively mains input current, load current and compensation electric current, R are the equivalent electricity of circuit and inductance
Resistance, L are flat wave inductance, and C is DC bus capacitor, and capacitance both end voltage is udc。
To simplify the design of parallel connection APF control systems, if switch is in perfect condition, ignore the influence of switch parameter；Together
Close coupling high order system model under abc coordinate systems is transformed to the low order of dq coordinate systems by Shi Caiyong synchronous rotating angles
System model.If under dq coordinate systems, access point voltage is usd、usq, APF bridge arm voltages in parallel are ufd、ufq, APF compensation electricity in parallel
Stream is ifd、ifq, then the mathematical model of parallel connection APF be：
Fig. 4 is the sliding formwork PI complex controll block diagrams of DC voltage.
The stability contorting of DC voltage is one of the key technology for ensureing active filter compensation performance, currently available technology
It is fairly simple about introducing for DC voltage PI controllers, it often directly gives PI controllers and does not introduce PI controllers in frequency
The tuning process in domain, the present invention derive DC voltage PI controllers in frequency domain.Harmonic wave electricity is compensated only in APF normal operating conditions
Stream and reactive current, to simplify derivation, it is zero to enable q shaft currents, then d shaft currents is utilized to derive active filter DC side electricity
The transmission function of pressure is：
According to the mentality of designing of current transformer tradition double-closed-loop control device, it is φ to enable current closed-loop transmission functionc(s), direct current
Side voltage PI control block diagrams are as shown in Figure 4.It, will be in electric current since outer voltage response speed is much smaller than current inner loop response speed
Ring is replaced to simplify the design process of DC voltage PI controllers, then obtaining outer voltage open loop Transmission Function with constant
For：
T in above formulav=RdcC, the system are a typical second-order systems, eliminate being designed for zero pole point simplify control device
To closed loop transfer function,：
τ=C/K in formulap。
The realization of conventional PI control device is fairly simple, but control parameter is fixed；Change in load sudden change and with reference to given voltage
When, PI controllers cannot meet requirement of the system to steady-state behaviour and dynamic property, and DC voltage cannot timely stability contorting
The problems such as compensation effect of active filter can be caused to reduce.
Fig. 5 is the double-closed-loop control block diagram of parallel active filter.Fig. 5 is that parallel connection APF is based on the compound controls of voltage sliding formwork PI
The double closed-loop control system of system, DC voltage use novel sliding formwork PI controllers, and control principle is similar to conventional PI control, no
It is with place：The control parameter of sliding formwork PI controllers is with system change, and the control parameter of PI controllers is by sliding mode controller
Carry out positive definite, do so to adjust PI control parameters according to the variation of DC side in real time, to meet system to DC side electricity
Press the requirement of state and steady-state behaviour.Current reference value i of the output of sliding formwork PI controllers as current inner loopfd_ref, about electricity
It flows inner ring control and has lot of documents introduction, repeats no more herein, next main research sliding formwork PI controllers, and main includes sliding
The design of die face and the accessibility of sliding mode controller.
Fig. 6 is respectively DC voltage oscillogram when the DC side reference voltage under PI and sliding formwork PI control methods increases.
DC voltage waveform based on PI sliding formwork controls meets the feature that sliding mode controller switches in sliding-mode surface field, and rapidity wants excellent
In PI control methods, show that sliding formwork PI control strategies advantage in terms of rapidity and stability is obvious from Fig. 6, sliding formwork PI
Control only about needs 0.11s just to reach stable state, and PI controls take around 0.3s and just tend towards stability value.
When Fig. 7 loads reduce, the DC voltage oscillogram of PI control and sliding formwork PI complex controlls.In t=12s,
It loads 20 Ω of parallel connection on 10 Ω and jumps to 6.67 Ω；From Fig. 7 it is observed that sliding formwork PI control strategy voltage waveform overshoot is small, and
Fast response time.The response speed that DC voltage control is improved based on sliding formwork PI control methods is demonstrated by the above comparison of wave shape
The convergence process of degree and acceleration system, to make system quickly reach stable state.
Claims (1)
1. a kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms, it is characterised in that including such as
Lower step：
Step 1：Lower order system models of the foundation parallel connection APF in dq coordinate systems:
usk(k=a, b, c) is three-phase access point voltage；ufk(k=a, b, c) is each bridge arm midpoint potential of three-phase；is(a,b,c)、
if(a,b,c)、is(a,b,c)Respectively mains input current, load current and compensation electric current；R is the equivalent resistance of circuit and inductance；L
For flat wave inductance；C is DC bus capacitor；Capacitance both end voltage is udc；
To simplify the design of parallel connection APF control systems, if switch is in perfect condition, ignore the influence of switch parameter；It adopts simultaneously
With synchronous rotating angle, the close coupling high order system model under abc coordinate systems is transformed to the lower order system of dq coordinate systems
Model, if under dq coordinate systems, access point voltage is usd、usq, APF bridge arm voltages in parallel are ufd、ufq, APF in parallel compensation electric current is
ifd、ifq, then the mathematical model of parallel connection APF be：
Step 2：Detect DC capacitor voltage udc, by itself and DC side reference voltage level udcrefIt makes comparisons, obtains error signal,
This error signal obtains the current reference value i of current inner loop by sliding formwork PI controllersfd_ref, by checking current inner loop
Current actual value ifd, by ifd_refWith ifdIt makes comparisons and obtains error signal, this error signal controls to obtain U by d shaft currentsd；
udc(s) it is the Lars form of capacitance both end voltage；id(s) it is Laplce's form of d shaft currents；RdcFor DC side electricity
Resistance；C is DC bus capacitor；
DC voltage PI controllers compensate only for harmonic current and reactive current in APF normal operating conditions, are derived for simplification
Journey, it is zero to enable q shaft currents, then the transmission function for utilizing d shaft currents to derive active filter DC voltage is：
B=1/C, a=1/R in formula (2)dcC；
According to the mentality of designing of current transformer tradition double-closed-loop control device, it is φ to enable current closed-loop transmission functionc(s), outside due to voltage
Ring response speed is much smaller than current inner loop response speed, and current inner loop is replaced with constant to simplified DC voltage PI controls
The design process of device, then obtaining outer voltage open loop Transmission Function is：
T in formula (3)v=RdcC, the system are a typical second-order systems, and the design for eliminating zero pole point simplify control device obtains
Closed loop transfer function,：
τ=C/K in formulap；
The controller of APF DC sides is mainly used for the stability contorting of voltage, and control freedom degree variable is straight using Direct Variable
Galvanic electricity presses udc, directly controlled quentity controlled variable is controlled in this way；According to the principle for choosing sliding-mode surface, the sliding formwork control of DC voltage is defined
Face processed is：
K is normal number in formula (5)；
The output of sliding mode controller is for determining PI controller parameters, the PI controllers based on sliding formwork control：
K in formula (6)sp, ksiFor the parameter of PI controllers, they are by sliding mode controller according to designed sliding formwork control face (5)
Determine the size of its value, be mainly characterized by obtaining suitable PI control parameters according to the variation of system, using formula (2) and
(6) the Dynamic Closed Loop function of DC voltage is obtained：
To ensure the stability contorting of DC voltage, relational expression once is obtained according to formula (7)：
It is set up for formula (8), the control parameter output function of PI controllers is designed according to sliding-mode surface (5)：
Control parameter k in formula (9)p+、kp-、ki+、ki-All it is positive number, these control parameters are in the case where meeting PI control output characteristics
Adjust as a result, they are adjusted according to the method for standard PI controllers；It is attached in sliding formwork control face for elimination system simultaneously
The DC voltage fluctuation closely generated adds positive parameter k in the differential and integral parameter of PI controllers respectivelyav_p、kav_i, from elimination
The fluctuation problem for causing DC voltage is buffeted by sliding-mode surface, wherein sgn (s) is saturation function：
In the sliding-mode surface neighborhood of sliding mode controller, the system based on sliding mode controller will reach diverter surface in finite time, then
Mean that sliding formwork mode exists, sliding mode is in the presence of the premise for being Sliding Mode Controller application, the Liapunov of selection
Function is：
And time derivation is obtained：
K is normal number in formula (12), andMore than zero, formula (12) is less than zero permanent establishment, then demonstrates designed sliding mode controller
Stability；
To eliminate the DC voltage fluctuation that system generates in sliding formwork control face field, join respectively in the differential of PI controllers and integral
Number adds positive parameter kav_p、kav_i, the fluctuation problem for causing DC voltage is buffeted by sliding-mode surface from eliminating, and works as S>When 0, ksp=
2kp++kav_p, ksi=2ki++kav_i；As S < 0, ksp=2kp-+kav_p, ksi=2ki-+kav_i；
Step 3：The load current i of detection at this timeLHarmonic component iLh, the stable operation if load current at this time does not have harmonic wave,
Otherwise return to step 2 repeat step 2.
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