CN106549399A - A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms - Google Patents

Abstract

A kind of APF DC side voltage control methods in parallel based on sliding formwork PI complex control algorithms.The method sets up the lower order system model of dq coordinate systems initially with synchronous rotating angle；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 designed finally 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 pulsation；Good robust performance and dynamic property are had based on the APF control systems in parallel of sliding formwork PI complex control algorithms.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, stable state accuracy and response speed when raising load changing and reference voltage saltus step, reduces DC side power attenuation to ensure the compensation ability of parallel active filter.

Description

A kind of APF DC voltage controls in parallel based on sliding formwork PI complex control algorithms Method

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 used as a kind of solution harmonic pollution in electric power net Effective means, it can realize effectively mending accurately, in real time to harmonic wave, negative-sequence current and reactive power that network system is present Repay.The output compensation characteristic of active filter depends primarily on the control method to current/voltage, and adopted converter plant Main circuit topological structure.At present to the research of active filter topological structure comparative maturity, great majority are using tradition three Phase PWM converter structure, is improved by this Shunt compensation performance and depends on the control method for adopting, 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 Pressure control algolithm is relatively fewer.But in whole APF control systems, the quality of DC voltage control performance is directly influenced Active filter compensates the quality of performance, therefore, the compensation performance to active filter is controlled to the fast accurate of DC voltage Significant, the DC voltage for being primarily directed to three-phase three-wire system parallel active filter herein is studied.

The primary method of control for being presently used for APF DC voltages has conventional PI control algorithm, fuzzy controller, adaptive Control method should be waited.When conventional PI control device is used for DC voltage control, though can finally meet DC voltage stability, electricity The response speed of pressure is slow, and there is overshoot, cannot meet needs in load changing and during reference voltage saltus step.Fuzzy control Device is independent of system, is easy to transplanting, and its robust performance is stronger；But its control accuracy is poor, DC voltage fluctuation causes greatly to damage Consumption increases and the compensation performance of reduction APF.Realized based on voltage adaptive control method it is complex, in control algolithm computing Occupancy Resources on Chip is more, and its DC voltage dynamic property is undesirable.

The content of the invention

Not enough for more than, the present invention provides a kind of APF DC voltages in parallel based on sliding formwork PI complex control algorithms Control method, the method set up the lower order system model of dq coordinate systems initially with synchronous rotating angle；Then according to cunning Die face selection principle determines the sliding formwork switching function of DC voltage；Finally according to the switching function design PI controllers of sliding-mode surface Control parameter output function.The control method improves the steady-state behaviour and response speed of DC voltage, while effectively reducing Voltage pulsation；Good robust performance and dynamic are had based on the APF control systems in parallel of sliding formwork PI complex control algorithms 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, comprise the following steps：

Step 1：Set up lower order system models of the parallel connection APF in dq coordinate systems；

u_sk(k=a, b, c) accesses point voltage for three-phase；u_fk(k=a, b, c) is each bridge arm midpoint potential of three-phase； i_s(a,b,c)、i_f(a,b,c)、i_s(a,b,c)Respectively mains input current, load current and compensation electric current；R be circuit and inductance etc. Effect resistance；L is flat ripple inductance；C is DC bus capacitor；Electric capacity both end voltage is u_dc。

To simplify the design of parallel connection APF control systems, if switch ignores the impact of switch parameter in perfect condition；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 u_sd、u_sq, APF bridge arm voltages in parallel are u_fd、u_fq, APF compensation electricity in parallel Flow for i_fd、i_fq, then the mathematical model of parallel connection APF be：

Step 2:Detection DC capacitor voltage u_dc, by itself and DC side reference voltage level u_dcrefMake comparisons, draw error Signal, this error signal obtain current reference value i of current inner loop through sliding formwork PI controllers_{fd_ref}, by checking in electric current The current actual value i of ring_fd, by i_{fd_ref}With i_fdMake comparisons and draw error signal, this error signal is by controls such as d shaft currents controls U is obtained_d。

u_dcThe Lars form of (s) for electric capacity both end voltage；i_dThe Laplce's form of (s) for d shaft currents；R_dcFor DC side Resistance；C is DC bus capacitor.

The stability contorting of DC voltage is to ensure one of key technology of active filter compensation performance, currently available technology It is fairly simple with regard to introducing for DC voltage PI controllers, often directly give PI controllers PI controllers are not introduced 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, are to simplify derivation, make q shaft currents be zero, then derive active filter DC side electricity using d shaft currents The transmission function of pressure is：

B=1/C, a=1/R in formula (2)_dcC, a are resistance R_dcWith the inverse of electric capacity C products, inverses of the b for electric capacity C, C is DC bus capacitor, s are the Laplace variable factor.

According to the mentality of designing of current transformer traditional double closed loop controller, current closed-loop transmission function is made to be φ_c(s), direct current Side voltage PI control block diagrams are as shown in Figure 3.As outer voltage response speed is much smaller than current inner loop response speed, by electric current Ring constant replaces so as to the design process of simplified DC voltage PI controllers, then obtain outer voltage open loop Transmission Function For：

T in formula (3)_v=R_dcThe control function of C, PI (s) for outer voltage, φ_cS () is current closed-loop transmission function, G_v1 The transmission function of (s) for active filter DC voltage, R_dcFor direct current side resistance, C is DC bus capacitor, and s is Laplce Variable Factors, K_pFor 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 formula_p, G_v1oFor outer voltage open loop Transmission Function, K_pFor outer voltage control parameter, C is DC side electricity Hold.

Conventional PI control device is realized fairly simple, but control parameter fixes；In load changing and with reference to given change in voltage When, PI controllers can not meet requirement of the system to steady-state behaviour and dynamic property, and DC voltage can not stability contorting in time The problems such as compensation effect of active filter can be caused reducing.

DC voltage adopts new sliding formwork PI controllers, and its control principle is similar to conventional PI control, and difference is： The control parameter of sliding formwork PI controllers carrys out positive definite by sliding mode controller with system change, the control parameter of PI controllers, so Do and PI control parameters can be adjusted according to the change of DC side in real time, so that system is met 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 loop_{fd_ref}, it is next main to study sliding formwork The accessibility of PI controllers, the main design for including sliding-mode surface and sliding mode controller.

The design of sliding formwork PI controllers mainly has two purposes：(1) in load changing 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 its control freedom degree variable adopts Direct Variable DC voltage u_dc, so directly controlled quentity controlled variable can be controlled；According to the principle for choosing sliding-mode surface, the sliding formwork control of definable DC voltage Face S processed is：

In formula (5) k be normal number, u_{dc_ref}For the reference value of DC voltage, u_dcFor the actual value of DC voltage.

The output of sliding mode controller is used to determine PI controller parameters that its form to be similar with conventional PI control device, based on upper One trifle can immediately arrive at the PI controllers based on sliding formwork control with regard to the introduction of conventional PI control device：

K in formula (6)_sp, k_siFor the parameter of PI controllers, they are according to designed sliding-mode surface (5) by sliding mode controller To determine the size of its value, which is mainly characterized by obtaining appropriate PI control parameters according to the change of system.Using 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 are 1/R_dcThe representative letter of C, inverses of the b for electric capacity, s is Laplce Variable Factors, k_sp, k_siFor 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 are 1/R_dcThe representative letter of C, inverses of the b for electric capacity, s is Laplce Variable Factors, k_sp, k_siFor the parameter of PI controllers.

To set up 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+、k_p-、k_i+、k_i-All it is positive number, these control parameters are to meet PI controlled outputs spy Result of adjusting under property, they can be adjusted according to the method for standard PI controller, for example with root-locus technique etc.；Together When be DC voltage fluctuation that elimination system is produced near sliding formwork control face, respectively in the differential and integral parameter of PI controllers Plus positive parameter k_{av_p}、k_{av_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 mean that sliding formwork mode is present, and sliding mode presence is the premise of Sliding Mode Controller application, generally Lee of selection Ya Punuofu functions are：

In formula (11)For DC voltage square-error, V (e_dc) it is with regard to DC voltage square-errorLetter Number.

And time derivation is obtained：

In formula (12), k is normal number,For DC voltage error with regard to the time derivative, e_dcMiss for DC voltage Difference, andMore than zero, formula (12) is permanent less than zero to set up the stability for then demonstrating designed sliding mode controller.

Buffeting of the sliding mode controller in sliding-mode surface field be difficult to avoid that, is elimination system in sliding formwork control face field The DC voltage fluctuation of generation, respectively PI controllers differential and integral parameter add positive parameter k_{av_p}、k_{av_i}, from eliminate by Sliding-mode surface buffets the fluctuation problem for causing DC voltage.Work as S>When 0, k_sp=2k_p++k_{av_p}, k_si=2k_i++k_{av_i}；Work as S<0 When, k_sp=2k_p-+k_{av_p}, k_si=2k_i-+k_{av_i}。

Step 3:Detection load current i now_LHarmonic component i_Lh, stably transport if now load current does not have harmonic wave OK, 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, beneficial 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 raising load changing 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 changing and reference voltage saltus step Stable state accuracy and response speed, reduce DC side power attenuation ensureing the compensation ability of parallel active filter.In load During mutation and when reference voltage saltus step occurs, spy of the sliding formwork PI composite control methods using 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, the buffeting to weaken sliding mode controller, sets boundary value for voltage error, in boundary value Outer sliding mode controller can improve the dynamic responding speed of DC voltage, and the tracking that system can be effectively improved in boundary region is steady State property energy.

3：The inventive method sets up the lower order system model of dq coordinate systems initially with synchronous rotating angle；Then The sliding formwork switching function of DC voltage is determined according to sliding-mode surface selection principle；Finally according to the switching function design PI 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, while having Effect reduces voltage pulsation；Based on the APF control systems in parallel of 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 FB(flow block) in parallel based on sliding formwork PI complex control algorithms.

Basic functional principles of the Fig. 2 for three-phase three-wire system parallel active filter.

Fig. 3 is phase three-wire three parallel connection type APF main circuit structures.

Sliding formwork PI complex controll figures of the Fig. 4 for DC voltage.

Double-closed-loop control figures of the Fig. 5 for parallel active filter.

When Fig. 6 uprushes for DC reference voltage, the DC voltage oscillogram of PI controls and sliding formwork PI complex controlls.

When Fig. 7 reduces for load, the DC voltage oscillogram of PI controls and sliding formwork PI complex controlls.

Specific embodiment

With reference to embodiment and accompanying 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 concrete steps of the APF DC side voltage control methods in parallel of control algolithm：

(1) set up lower order system models of the parallel connection APF in dq coordinate systems；

(2) detect DC capacitor voltage u_dc, by itself and DC side reference voltage level u_dcrefMake comparisons, show that error is believed Number, this error signal obtains current reference value i of current inner loop through sliding formwork PI controllers_{fd_ref}, by checking current inner loop Current actual value i_fd, by i_{fd_ref}With i_fdMake comparisons and draw error signal, this error signal is by controls such as d shaft currents controls Obtain U_d

The stability contorting of DC voltage is to ensure one of key technology of active filter compensation performance, currently available technology In it is fairly simple with regard to 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, are to simplify derivation, make q shaft currents be zero, then derive active filter DC side using d shaft currents The transmission function of voltage is：

B=1/C in above formula, a=1/R_dcC。

DC bus capacitor C=4000 μ F, load resistance R_dc=10 Ω, then：

According to the mentality of designing of current transformer traditional double closed loop controller, current closed-loop transmission function is made to be φ_c(s), direct current The sliding formwork PI complex controll block diagrams of side voltage are as shown in Figure 3.As outer voltage response speed is much smaller than current inner loop response speed Degree, current inner loop is replaced so as to the design process of simplified DC voltage PI controllers, then obtaining outer voltage and opening with constant Ring Transmission Function is：

T in above formula_v=R_dcC, the system are a typical second-order systems, eliminate being designed to for zero pole point simplify control device To closed loop transfer function：

τ=C/K in formula_p。

Current loop control parameter is k_p=55, k_i=10, outer shroud control parameter is k_p=1.5, k_i=3, switching frequencyDC bus capacitor C=4000 μ F, load resistance R_dc=10 Ω, then：

The output of sliding mode controller is used to determine PI controller parameters that its form to be similar with conventional PI control device, based on upper One trifle can immediately arrive at the PI controllers based on sliding formwork control with regard to the introduction of conventional PI control device：

K in above formula_sp, k_siFor the parameter of PI controllers, they are determining by sliding mode controller according to designed sliding-mode surface The size of fixed its value, which is mainly characterized by obtaining appropriate PI control parameters according to the change of system.Using DC side electricity The transmission function of pressure and the Dynamic Closed Loop function of DC voltage can be obtained based on the PI controllers of sliding formwork control：

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 set up above formula, 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, k_p+=0.035, k_p-=0.027, k_i+= 3.125, k_i-=0.92, k_{av_p}=0.23, k_{av_i}=3.25, then：

Fig. 2 is the basic functional principle figure of parallel active filter.Its ingredient includes referential current detection and computing There is module etc. in module and compensation electric current；Basic functional principle is analyzed as follows, and the load current that current detection module is measured is i_L, using corresponding detection algorithm by i_LIn fundamental wave i_LfHarmonic i_LhSeparate, extract harmonic wave and negated, by harmonic wave of the inverted As instruction current i_{f_ref}, parallel inverter device produces the compensation electric current, the electric current and harmonic current i_LhDirection phase equal in magnitude Instead, so as to eliminating electric power outputting current i_sHarmonic wave, the system that nonlinear load and APF are constituted is absorbed from electrical network and do not contain The electric current of harmonic wave, reaches the purpose for eliminating 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 figure_sa、u_sb、u_scPoint voltage, u are accessed for three-phase_fa、u_fb、u_fcFor each bridge arm midpoint potential of three-phase, i_s(a,b,c)、 i_l(a,b,c)、i_f(a,b,c)Respectively mains input current, load current and compensation electric current, R is the equivalent electric of circuit and inductance Resistance, L are flat ripple inductance, and C is DC bus capacitor, and electric capacity both end voltage is u_dc。

To simplify the design of parallel connection APF control systems, if switch ignores the impact of switch parameter in perfect condition；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 u_sd、u_sq, APF bridge arm voltages in parallel are u_fd、u_fq, APF compensation electricity in parallel Flow for i_fd、i_fq, 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 to ensure one of key technology of active filter compensation performance, currently available technology It is fairly simple with regard to introducing for DC voltage PI controllers, often directly give PI controllers PI controllers are not introduced 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, are to simplify derivation, make q shaft currents be zero, then derive active filter DC side electricity using d shaft currents The transmission function of pressure is：

According to the mentality of designing of current transformer traditional double closed loop controller, current closed-loop transmission function is made to be φ_c(s), direct current Side voltage PI control block diagrams are as shown in Figure 4.As outer voltage response speed is much smaller than current inner loop response speed, by electric current Ring constant replaces so as to the design process of simplified DC voltage PI controllers, then obtain outer voltage open loop Transmission Function For：

T in above formula_v=R_dcC, the system are a typical second-order systems, eliminate being designed to for zero pole point simplify control device To closed loop transfer function：

τ=C/K in formula_p。

Conventional PI control device is realized fairly simple, but control parameter fixes；In load changing and with reference to given change in voltage When, PI controllers can not meet requirement of the system to steady-state behaviour and dynamic property, and DC voltage can not stability contorting in time The problems such as compensation effect of active filter can be caused reducing.

Fig. 5 is the double-closed-loop control block diagram of parallel active filter.Fig. 5 is parallel connection APF based on the compound controls of voltage sliding formwork PI The double closed-loop control system of system, DC voltage adopt new sliding formwork PI controllers, and its control principle is similar to conventional PI control, no With part it is：, with system change, the control parameter of PI controllers is by sliding mode controller for the control parameter of sliding formwork PI controllers Carry out positive definite, do so can adjust PI control parameters according to the change of DC side in real time, so that system is met 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 loop_{fd_ref}, with regard to electricity The existing lot of documents introduction of stream internal ring control, is repeated no more herein, and next main research sliding formwork PI controllers, main to include 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 is raised. The feature that sliding mode controller switches in sliding-mode surface field is met based on the DC voltage waveform of PI sliding formwork controls, rapidity is 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 steady statue, and PI controls take around 0.3s and just tend towards stability value.

When Fig. 7 loads reduce, the DC voltage oscillogram of PI controls and sliding formwork PI complex controlls.In t=12s, Load 20 Ω in parallel on 10 Ω and jump to 6.67 Ω；From Fig. 7 it is observed that sliding formwork PI control strategy voltage waveform overshoot is little, and Fast response time.The response speed that DC voltage control is improved based on sliding formwork PI control methods is demonstrated by above comparison of wave shape The convergence process of degree and acceleration system, so that system quickly reaches steady statue.

Claims (6)

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 include as Lower step：

Step 1：Set up lower order system models of the parallel connection APF in dq coordinate systems；

Step 2：Detection DC capacitor voltage u_dc, by itself and DC side reference voltage level u_dcrefMake comparisons, draw error signal, This error signal obtains current reference value i of current inner loop through sliding formwork PI controllers_{fd_ref}, by checking current inner loop Current actual value i_fd, by i_{fd_ref}With i_fdMake comparisons and draw error signal, this error signal is controlled by d shaft currents control etc. To U_d；

Step 3：Detection load current i now_LHarmonic component i_Lh, the stable operation if now load current does not have harmonic wave, Otherwise return to step 2, repeat step 2.

2. APF DC side voltage control methods in parallel of a kind of sliding formwork PI complex control algorithms according to claim 1, its It is characterised by：In step 1, u_sk(k=a, b, c) accesses point voltage for three-phase；u_fk(k=a, b, c) is each bridge arm midpoint electricity of three-phase Position；i_s(a,b,c)、i_f(a,b,c)、i_s(a,b,c)Respectively mains input current, load current and compensation electric current；R is circuit and inductance Equivalent resistance；L is flat ripple inductance；C is DC bus capacitor；Electric capacity both end voltage is u_dc。

3. APF DC side voltage control methods in parallel of a kind of sliding formwork PI complex control algorithms according to claim 1, its It is characterised by：In step 1, it is the design for simplifying parallel connection APF control systems, if switch ignores switch parameter in perfect condition Impact；Adopt synchronous rotating angle simultaneously, the close coupling high order system model under abc coordinate systems is transformed to into dq coordinates The lower order system model of system, if under dq coordinate systems, access point voltage is u_sd、u_sq, APF bridge arm voltages in parallel are u_fd、u_fq, it is in parallel APF compensation electric currents are i_fd、i_fq, then the mathematical model of parallel connection APF be：

$\left\{\begin{array}{c}L\frac{{\mathrm{di}}_{fd}}{dt}=u_{sd}-u_{fd}+{\mathrm{L\&omega;i}}_{fq}-{\mathrm{Ri}}_{fd}\\ L\frac{{\mathrm{di}}_{fq}}{dt}=u_{sq}-u_{fq}-{\mathrm{L\&omega;i}}_{fd}-{\mathrm{Ri}}_{fq}\\ C\frac{{\mathrm{du}}_{dc}}{dt}=i_{fd}+i_{fq}-\frac{u_{dc}}{R_{dc}}\end{array}\right.---\left(1\right).$

4. APF DC side voltage control methods in parallel of a kind of sliding formwork PI complex control algorithms according to claim 1, its It is characterised by：In step (2), u_dcThe Lars form of (s) for electric capacity both end voltage；i_dThe Laplce's shape of (s) for d shaft currents Formula；R_dcFor direct current side resistance；C is DC bus capacitor.

5. APF DC side voltage control methods in parallel of a kind of sliding formwork PI complex control algorithms according to claim 1, its It is characterised by：In step (2), DC voltage PI controllers compensate only for harmonic current and idle electricity in APF normal operating conditions Stream, is to simplify derivation, makes q shaft currents be zero, then the transmission letter of active filter DC voltage is derived using d shaft currents Number is：

$G_{dc}\left(s\right)=\frac{u_{dc}\left(s\right)}{i_d\left(s\right)}=\frac{1/C}{S+1/R_{dc}C}=\frac{b}{S+a}---\left(2\right)$

B=1/C, a=1/R in formula (2)_dcC；

According to the mentality of designing of current transformer traditional double closed loop controller, current closed-loop transmission function is made to be φ_c(s), due to voltage outside Ring response speed is much smaller than current inner loop response speed, and current inner loop is replaced with constant so as to simplify DC voltage PI controls The design process of device, then obtaining outer voltage open loop Transmission Function is：

$G_{vlo}=PI\left(s\right){\mathrm{\&phi;}}_c\left(s\right)G_{vl}\left(s\right)=\frac{K_p(T_{v}s+1)R_{dc}}{T_{v}s(R_{dc}Cs+1)}---\left(3\right)$

T in formula (3)_v=R_dcC, the system are a typical second-order systems, and the design for eliminating zero pole point simplify control device is obtained Closed loop transfer function：

$G_{vlc}=\frac{G_{vlo}}{1+G_{vlo}}=\frac{1}{1+(C/K_p)s}=\frac{1}{1+\mathrm{\&tau;}s}---\left(4\right)$

τ=C/K in formula_p；

The controller of APF DC sides is mainly used for the stability contorting of voltage, and its control freedom degree variable is straight using Direct Variable Stream voltage u_dc, so directly controlled quentity controlled variable can be controlled；According to the principle for choosing sliding-mode surface, definable DC voltage Sliding formwork control face is：

$S=k(u_{dc\_ref}-u_{dc})+\frac{d(u_{dc\_ref}-u_{dc})}{dt}---\left(5\right)$

In formula (5), k is normal number；

The output of sliding mode controller be used for determine PI controller parameters, the PI controllers based on sliding formwork control：

$C_{SMC\_PI}\left(s\right)=\frac{k_{sp}s+k_{si}}{s}---\left(6\right)$

K in formula (6)_sp, k_siFor the parameter of PI controllers, they are according to designed sliding formwork control face (5) by sliding mode controller To determine the size of its value, which is mainly characterized by obtaining appropriate PI control parameters according to the change of system, using formula (2) (6) the Dynamic Closed Loop function of DC voltage can be obtained：

$\frac{u_{dc}\left(s\right)}{u_{dc\_ref}\left(s\right)}=\frac{{\mathrm{bk}}_{sp}(s+k_{si}/k_{sp})}{s^2+(a+{\mathrm{bk}}_{sp})s+{\mathrm{bk}}_{si}}---\left(7\right)$

To ensure the stability contorting of DC voltage, relational expression once can be obtained according to formula (7)：

$\left\{\begin{array}{c}a+{\mathrm{bk}}_{sp}>0\\ {\mathrm{bk}}_{si}>0\end{array}\right.---\left(8\right)$

To set up formula (8), the control parameter output function of PI controllers is designed according to sliding-mode surface (5)：

$\left\{\begin{array}{c}{k}_{sp}=\&lsqb;(1+\mathrm{sgn}(s\left)\right)k_{p+}-(1-\mathrm{sgn}(s\left)\right)k_{p-}\&rsqb;+k_{av\_p}\\ k_{si}=\&lsqb;(1+\mathrm{sgn}(s\left)\right)k_{i+}-\left(1-\mathrm{sgn}\left(s\right)\right)k_{i-}\&rsqb;+k_{av\_i}\end{array}\right.---\left(9\right)$

Control parameter k in formula (9)_p+、k_p-、k_i+、k_i-All it is positive number, these control parameters are in the case where PI controlled output characteristics are met Result of adjusting, they can be adjusted according to the method for standard PI controller；It is simultaneously elimination system in sliding formwork control The DC voltage fluctuation produced near face, respectively PI controllers differential and integral parameter add positive parameter k_{av_p}、k_{av_i}, from Eliminate and the fluctuation problem for causing DC voltage is buffeted by sliding-mode surface, wherein sgn (s) is saturation function：

$\mathrm{sgn}\left(s\right)=\left\{\begin{array}{c}1,s>0\\ -1,s<0\end{array}\right.---\left(10\right)$

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 is present, sliding mode presence is the premise of Sliding Mode Controller application, the generally Li Yapu of selection Promise husband's function is：

$V\left(e_{dc}\right)=\frac{e_{dc}^2}{2}---\left(11\right)$

And time derivation is obtained：

$V\left(e_{dc}\right)=e_{dc}{\stackrel{\&CenterDot;}{e}}_{dc}=e_{dc}(-{\mathrm{ke}}_{dc})=-{\mathrm{ke}}_{dc}^2<0---\left(12\right)$

In formula (12), k is normal number, andMore than zero, formula (12) is permanent less than zero to be set up, then demonstrate designed sliding mode controller Stability；

To eliminate the DC voltage fluctuation that system is produced in sliding formwork control face field, respectively in the differential and integration ginseng of PI controllers Number is plus positive parameter k_{av_p}、k_{av_i}, the fluctuation problem for causing DC voltage is buffeted by sliding-mode surface from eliminating, works as S>When 0, k_sp= 2k_p++k_{av_p}, k_si=2k_i++k_{av_i}；Work as S<When 0, k_sp=2k_p-+k_{av_p}, k_si=2k_i-+k_{av_i}。

6. sliding formwork PI complex control algorithms, the application in APF control systems.