CN106786647A - A kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles - Google Patents

Abstract

A kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles, outer voltage uses sliding formwork PI composite non-linear control algolithms, and current inner loop is using repetition PI nonlinear control algorithms.The method uses synchronous rotating angle first, set up the lower order system model of dq coordinate systems, PI feedforward decoupling controllers are designed according to dq DC Models, PI repetitive controllers are designed based on internal model control, set up the controlled output function of current inner loop PI repetitive controllers；Accurately and quickly to obtain the current reference value of current inner loop, the new sliding formwork PI nonlinear control algorithms of invention DC voltage, according to exponential approach rate form design sliding-mode surface switching function, set up out the control function of outer voltage sliding formwork PI controllers.Outer shroud sliding formwork PI complex control algorithms of the present invention can improve the steady-state behaviour and response speed of DC voltage, effectively reduce voltage pulsation；Repeating PI nonlinear control algorithms can realize the DAZ gene of current signal, improve the tracing control precision of harmonic compensation current instruction.

Description

A kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles

Technical field

The invention belongs to active filter control field, more particularly to a kind of three-phase four-wire system parallel connection APF two close cycles non-thread Property composite control method.

Background technology

Shunt (Active Power Filter, APF) is used as a kind of solution harmonic pollution in electric power net Effective means, harmonic wave, negative-sequence current and the reactive power that it can exist to network system realizes accurate, effective in real time benefit Repay.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 that electric current loop is controlled using list PI to apply the control strategy on Active Power Filter-APF earliest, directly The stream additional independent electric supply installation of side voltage.At present to the research of active filter topological structure comparative maturity, now Through going to be powered to DC side without independent DC source substantially, but use outer voltage current inner loop double-loop control strategy. Most of active filters use conventional three-phase PWM converter structure, are that this Shunt compensation performance is improved Depend on used control method.

The primary method of control for being presently used for APF DC voltages has：It is 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, and needs cannot be met 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 is big to be caused to damage Consume the compensation performance for increasing and reducing 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.There is traditional PI control for APF current inner loop control methods The control methods such as algorithm processed, Hysteresis control.Conventional PI control algorithm can realize tracking well when reference signal is direct current Control, but harmonic wave command signal for changing constantly cannot realize DAZ gene.Hysteresis control is a kind of transient feedback Control system, though having the advantages that high precision, fast response time, can obtain preferable tracking performance, its switching frequency ripple Dynamic larger, output filter design is difficult.

The content of the invention

The invention aims to improve the deficiency that above-mentioned control method is present, for three-phase four-wire system parallel connection active electrical Force filter, there is provided a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles, the method can improve direct current Stable state accuracy, response speed of the side voltage in load changing and reference voltage saltus step, effectively reduce voltage pulsation, and without quiet Difference tracking changing currents with time command signal, improves control accuracy.

The technical solution adopted in the present invention is：

A kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles, comprises the following steps：

Step 1：Detection supply voltage U_s(abc), mains side electric current I_s(abc), load-side electric current I_L(abc), APF compensation electric current I_f(abc)Capacitance voltage U upper and lower with DC side_dc1、U_dc2；

Step 2：By the upper and lower capacitance voltage sum U of DC side_dc(U_dc=U_dc1+U_dc2) and DC side reference voltage level U_{dc_ref} Make comparisons, draw error signal, this error signal obtains current inner loop instruction current I by sliding formwork PI controllers_ref(dq0)；

Step 3：The load-side electric current I that will be detected in step 1_L(abc)Through i_p-i_qCurrent Detection Algorithm is obtained under dq coordinate systems Harmonic wave instruction current I_h(dq0), by harmonic wave instruction current I_h(dq0)With current inner loop instruction current I is obtained in step 2_ref(dq0)Coordinate, Obtain final instruction currentBy instruction currentPAF compensation electric currents I under dq coordinate systems in matching step 1_f(dq0) Input repeats PI controllers and obtains output voltage instruction signal U_dq0；

Step 4：The upper and lower capacitance voltage U of DC side that will be detected in step 1_dc1、U_dc2The PI controls of input neutral-point potential balance Device, obtains balance of voltage factor f；

Step 3：The supply voltage detected in step 1 is obtained into system phase information by phase-locked loop systems, then by gained The voltage command signal U exported in phase information, step 3_dq0SVPWM moulds are sent into the balance of voltage factor f obtained in step 4 Block, produces switching pulse signal, controls APF devices, exports compensation harmonic electric current；

Step 6：Whether subsequent work cycle detection mains input side current harmonic content is 0, if now current harmonics contains Amount is not 0 return to step 1, repeat step 1.

In step 1, U_sk(k=a, b, c) is three-phase access point voltage；U_kN(k=a, b, c) is each bridge arm midpoint electricity of three-phase Position；I_sk(k=a, b, c), I_lk(k=a, b, c), I_fk(k=a, b, c) is respectively mains input current, load current and compensation electricity Stream；R is the equivalent resistance of circuit and inductance；L is flat ripple inductance；C₁、C₂It is the upper and lower electric capacity of DC side, C₁=C₂=C electric capacity two ends Voltage is U_dc1And U_dc2；R₁、R₂It is equalizing resistance, R₁=R₂=R_c。

To simplify the design of parallel connection APF control systems, if switch is in perfect condition, ignore the influence of switch parameter；Together Shi Caiyong synchronous rotating angles, the close coupling high order system model under abc coordinate systems is transformed to the low order of dq0 coordinate systems System model.If U_si(i=d, q, 0) is access point voltage, S under dq0 coordinate systems_i(i=d, q, 0) is in parallel under dq0 coordinate systems APF bridge arms turn on switch function, I_fi(i=d, q, 0) is parallel connection APF compensation electric current under dq0 coordinate systems, then the mathematics of parallel connection APF Model is：

In step 2, C₁、C₂It is the upper and lower electric capacity of DC side, U_dc1(s) and U_dc2S () is the Lars shape of upper and lower electric capacity both end voltage Formula；I_dS () is Laplce's form of d shaft currents；R₁=R₂=R_cIt is the upper and lower equalizing resistance of DC side.

Harmonic current and reactive current are compensated only in APF normal operating conditions, is to simplify derivation, make the q shaft currents be Zero, then be using the transmission function of d shaft currents derivation active filter DC voltage：

According to the mentality of designing of current transformer traditional double closed loop controller, it is G to make current closed-loop transmission function_ic(s).Due to electricity Pressure outer shroud 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 The design process of controller, then obtaining outer voltage open loop Transmission Function is：

T in formula_v=R_cC, the system is a typical second-order system, and the design for eliminating zero pole point simplify control device is obtained 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 voltage change 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 the compensation effect of active filter can be caused reducing.

In order to overcome disadvantages mentioned above, the present invention to use new sliding formwork PI controllers, its control principle and biography in DC voltage System PI controls are similar, and difference is：The control parameter of sliding formwork PI controllers is joined with system change, the control of PI controllers Number carrys out positive definite by sliding mode controller, and the change that do so can in real time according to DC side adjusts PI control parameters, so as to meet Requirement of the system to DC voltage dynamic and steady-state behaviour.The output of sliding formwork PI controllers as current inner loop current reference Value i_{fd_ref}, next main research sliding formwork PI controllers, mainly include the design of sliding-mode surface and the accessibility of 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 is straight The controller for flowing side is mainly used for the stability contorting of voltage, and its control freedom degree variable uses Direct Variable DC side total 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 processed is：

K is normal number in formula.

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 biography System PI controllers can immediately arrive at the PI controllers based on sliding formwork control：

K in formula_sp, k_siIt is the parameter of PI controllers, they are determined according to designed sliding-mode surface by sliding mode controller The size of its value, it is mainly characterized by obtaining appropriate PI control parameters according to the change of system.Using formula DC side electricity The transmission function and sliding formwork PI controllers expression formula of pressure can obtain the Dynamic Closed Loop function of DC voltage：

Wherein a=1/R_dcC, b=1/C.

To ensure the stability contorting of DC voltage, the Dynamic Closed Loop function according to DC voltage can obtain a ShiShimonoseki It is formula：

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_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 controllers, for example with root-locus technique etc.；It is simultaneously The DC voltage fluctuation that elimination system is produced near sliding formwork control face, respectively the differential and integral parameter in PI controllers add 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 saturation letter Number：

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 is in the presence of the premise for being Sliding Mode Controller application, Lee for generally choosing Ya Punuofu functions are：

And time derivation is obtained：

K is normal number in formula, andMore than zero, set up permanent less than zero of above formula then demonstrates the steady of designed sliding mode controller It is qualitative.

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, 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}。

In step 3, the inner ring complex controll based on digital PI controls and Repetitive controller is mainly composed in parallel by two parts：1) PI controllers.Difference between harmonic wave command value and actual value is modulated, improves the dynamic property of APF systems.2) repeat to control Device processed.Elimination system periodicity tracking error, improves the control accuracy of harmonic compensation current instruction.Because PI regulations are to be based on opening The pass cycle, and Repetitive controller is to be based on the primitive period, therefore both are in time decouplings.

The PI controllers that electric current loop is used control expression formula for：

In formula, K_pIt is proportional control factor, T_iIt is integration time constant, e is error signal.In PI control systems, ratio Partial effect is the error of the system that timely responds to, and the effect of integral part is the static error of elimination system, improves system Static characteristic.But PI controls are difficult to accomplish DAZ gene to the current command signal in APF, do not reach control and require.

By deriving, we can show that dq0 shaft voltages are to the transmission function of electric current；

Below by taking d shaft currents as an example, the design of the current loop controller using PI controls is introduced.Expressed according to PI controllers Formula and voltage can obtain open loop and the closed loop transfer function, of continuous domain PI control electric current rings to the transmission function of electric current：

From closed loop transfer function, closed-loop current control is a typical second-order system, eliminates zero pole point and simplifies control The design of device processed can simplify after electric current loop open loop and closed loop transfer function,：

τ=L/K in formula_p。

Repetitive controller is the high stable state accuracy control method based on internal model principle, be widely used in it is various need to realize it is high-precision Spend the occasion of control.The design difficulty of repetitive controller is the design of compensator, and the effect of compensator is to carry out school to system Just, system is made to decay to 0 in low-frequency range, in high band energy rapid decay.If compensator is：

S (z)=k_rz^kF₁(z)F₂(z) (19)

Wherein k_rIt is Repetitive controller gain, is set to 1.F₁Z () is averaging filter, its expression formula is：

F₂Z () is second-order low-pass filter；z^kIt is differentiation element, takes k=3.

In step 4, the upper and lower electric capacity voltage difference of DC side is only related to zero-axis current, by the way of zero-axis current is controlled Reach the control requirement for controlling upper and lower capacitor voltage balance.The upper and lower electric capacity voltage difference of DC side is to the transmission function of zero axle：

Because there is divider resistance and upper and lower electric capacity is equal in magnitude, upper and lower electric capacity voltage difference very little is controlled using simple PI System can just reach the requirement of neutral-point potential balance.It is G to make current inner loop closed loop transfer function,_ic(s), then using pole zero cancellation method The upper and lower electric capacity voltage balancing control open-loop transfer function of DC side after simplification is：

In step 5, space vector modulation (SVPWM) is based on average equivalent principle, to electricity substantially in a switch periods Pressure vector is combined, and makes its average value equal with given voltage vector.By command voltage signal U_dq0Through coordinate transform, obtain To the command signal U containing phase information_αβ, according to command signal U_αβSector where decision instruction space vector, it is determined that switch week The fundamental space vector that phase is used, and then determine fundamental space vector action time and switching point time, to modulate SVPWM Switching pulse signal, controls APF devices, exports compensation harmonic electric current.

A kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles of the present invention, technique effect is as follows：

1：For three-wire system split capacitor formula Active Power Filter-APF, determine that PI controllers are joined by sliding mode controller Number, stable state accuracy and response speed during raising load changing and reference voltage saltus step, reduces DC side power attenuation to ensure The compensation ability of parallel active filter；Low stable state accuracy caused by system low bandwidth is made up by repetitive controller, it is right to realize The DAZ gene of time-varying command signal, improves the tracing control precision of harmonic compensation current instruction.

2：Outer shroud sliding formwork PI complex control algorithms in the new non-linear composite control method of two close cycles can improve direct current The steady-state behaviour and response speed of side voltage, effectively reduce voltage pulsation.

3：Repeating PI nonlinear control algorithms can realize the DAZ gene of current signal, improve harmonic compensation current and refer to The tracing control precision of order.

Brief description of the drawings

Fig. 1 is the three-phase four-wire system parallel connection non-linear composite control method flow chart of the new two close cycles of APF.

Fig. 2 is three-phase and four-line split capacitor formula parallel connection type APF main circuit topology figures.

Fig. 3 is the three-phase and four-line parallel connection non-linear composite control method overall control figure of the new two close cycles of APF.

Fig. 4 is outer voltage sliding formwork PI complex controll block diagrams.

Fig. 5 is that current inner loop repeats PI complex controll block diagrams.

Fig. 6 is neutral-point potential balance PI control block diagrams.

Fig. 7 is space vector sector distribution map.

Fig. 8 (a) is the dynamic process experimental waveform figure of PI controllers.

Fig. 8 (b) is the dynamic process experimental waveform figure of sliding formwork PI controllers.

Fig. 9 (a) is the steady-state current waveform figure of PI controllers.

Fig. 9 (b) is the steady-state current waveform figure for repeating PI controllers.

Figure 10 (a) is the frequency analysis figure of PI controllers.

Figure 10 (b) is the frequency analysis figure for repeating PI controllers.

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 three-phase four-wire systems parallel connection non-linear composite control method flow chart of the new two close cycles of APF.

A kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles, concretely comprises the following steps：

Step (1)：Detection supply voltage U_s(abc), mains side electric current I_s(abc), load-side electric current I_L(abc), APF compensation electric current I_f(abc)Capacitance voltage U upper and lower with DC side_dc1、U_dc2。

Step (2)：By the upper and lower capacitance voltage sum U of DC side_dc(U_dc=U_dc1+U_dc2) and DC side reference voltage level U_{dc_ref}Make comparisons, draw error signal, this error signal obtains current inner loop instruction current by sliding formwork PI controllers I_ref(dq0)。

Step (3)：By the load-side electric current I of detection in step (1)_L(abc)Through i_p-i_qCurrent Detection Algorithm obtains dq coordinates The lower harmonic wave instruction current I of system_h(dq0), by harmonic wave instruction current I_h(dq0)Current inner loop instruction current is obtained with step (2) I_ref(dq0)Coordinate, obtain final instruction currentBy instruction currentPAF under dq coordinate systems in matching step (1) Compensation electric current I_f(dq0)Input repeats PI controllers and obtains output voltage instruction signal U_dq0。

Step (4)：By the upper and lower capacitance voltage U of DC side of detection in step (1)_dc1、U_dc2Input neutral-point potential balance PI Controller, obtains balance of voltage factor f.

Step (5)：The supply voltage of detection in step (1) is obtained into system phase information by phase-locked loop systems, then will The voltage command signal U of output in gained phase information, step (3)_dq0Sent into the balance of voltage factor f obtained in step (4) SVPWM modules, produce switching pulse signal, control APF devices, export compensation harmonic electric current.

Step (6)：Whether subsequent work cycle detection mains input side current harmonic content is 0, if now current harmonics Content is not for 0 returns to step (1), repeat step (1).

Fig. 2 is three-phase and four-line split capacitor formula parallel connection type APF main circuit topology figures.

U in figure_sk(k=a, b, c) is three-phase access point voltage；U_kN(k=a, b, c) is each bridge arm midpoint potential of three-phase；I_sk (k=a, b, c), I_lk(k=a, b, c), I_fk(k=a, b, c) is respectively mains input current, load current and compensation electric current；R It is circuit and the equivalent resistance of inductance；L is flat ripple inductance；C₁、C₂It is the upper and lower electric capacity of DC side, C₁=C₂=C, electric capacity two ends electricity It is U to press_dc1And U_dc2；R₁、R₂It is equalizing resistance, R₁=R₂=R_c。

To simplify the design of parallel connection APF control systems, if switch is in perfect condition, ignore the influence of switch parameter；Together Shi Caiyong synchronous rotating angles, the close coupling high order system model under abc coordinate systems is transformed to the low order of dq0 coordinate systems System model.If U_si(i=d, q, 0) is access point voltage, S under dq0 coordinate systems_i(i=d, q, 0) is in parallel under dq0 coordinate systems APF bridge arms turn on switch function, I_fi(i=d, q, 0) is parallel connection APF compensation electric current under dq0 coordinate systems, then the mathematics of parallel connection APF Model is：

In formula, I_fd、I_fq、I_f0To compensate electric current under dq0 coordinate systems；U_sd、U_sq、U_s0It is supply voltage under dq0 coordinate systems； U_dc1、U_dc2It is the upper and lower capacitance voltage of DC side, C₁=C₂=C；S_d、S_q、S₀It is parallel connection APF bridge arms conducting switch under dq0 coordinate systems Function；R₁、R₂It is DC side equalizing resistance；R is the equivalent resistance of circuit and inductance；L is flat ripple inductance.

Fig. 3 is the three-phase and four-line parallel connection non-linear composite control method overall control figure of the new two close cycles of APF.

As shown in figure 3, a kind of new two close cycles non-thread of three-phase four-wire system split capacitor formula parallel connection APF proposed by the present invention Property composite control method be respectively applied to outer voltage control and current inner loop control.Outer voltage is controlled using new sliding formwork PI Device, its control principle is similar to conventional PI control, and difference is：The control parameter of sliding formwork PI controllers is with system change , the control parameter of PI controllers carrys out positive definite by sliding mode controller, and the change that do so can in real time according to DC side is adjusted PI control parameters, so as to meet requirement of the system to DC voltage dynamic and steady-state behaviour.The output of sliding formwork PI controllers is made It is the current reference value I of current inner loop_ref(dq0), current inner loop is using new repetition PI controllers, its control principle and inner ring biography System PI controls are similar, and difference is：Repeating the compensator in PI controllers can correct to system through row, make system low Frequency range decays to 0, in high band rapid decay, so as to realize the DAZ gene to time-varying command signal, improves harmonic compensation The tracing control precision of current-order.By detecting the appearance that line voltage, mains side electric current, load-side electric current and APF are exported The signal such as electric current and the upper and lower capacitance voltage of DC side, using the new non-linear complex controll side of two close cycles proposed by the present invention Method, obtains the trigger signal of each control device in APF devices, drives each control device, and then control the APF devices output phase The harmonic compensation current of prestige, while maintaining DC capacitor voltage balance, and stabilization in setting value.In figure, U_s(abc)It is three-phase Supply voltage；R is the equivalent resistance of circuit and inductance；L is flat ripple inductance；C₁、C₂It is the upper and lower electric capacity of DC side, electric capacity two ends electricity It is U to press_dc1And U_dc2；U_{dc_ref}It is DC voltage reference value；R₁、R₂It is equalizing resistance；I_f(dq0)It is APF outputs under dq coordinate systems Compensation electric current；I_ref(dq0)It is the current inner loop current reference value of outer voltage output；U_dq0It is the voltage instruction of current inner loop output Signal.

Fig. 4 is the sliding formwork PI complex controll block diagrams of DC voltage.

Harmonic current and reactive current are compensated only in APF normal operating conditions, is to simplify derivation, make the q shaft currents be Zero, then be using the transmission function of d shaft currents derivation active filter DC voltage：

In formula, G_dcS () is the transmission function of DC side d shaft voltages；U_dc1(s) and U_dc2S () is upper and lower electric capacity both end voltage Lars form；I_dS () is Laplce's form of d shaft currents；R₁=R₂=R_cIt is the upper and lower equalizing resistance of DC side.

DC bus capacitor C₁=C₂=C=4000 μ F, resistance R_c=10 Ω, then：

According to the mentality of designing of current transformer traditional double closed loop controller, it is G to make current closed-loop transmission function_ic(s), DC side The sliding formwork PI complex controll block diagrams of voltage are as shown in Figure 4.Because outer voltage response speed is much smaller than current inner loop response speed, Current inner loop is replaced with constant so as to simplify the design process of DC voltage PI controllers, then to obtain outer voltage open loop biography Delivery function is：

T in formula_v=R_cC；G_v1oIt is outer voltage open-loop transfer function；PI (s) is the control function of outer voltage；

G_icS () is current closed-loop transmission function；G_v1S () is the transmission function of active filter DC voltage；R_cFor straight Stream equalizing resistance；C is DC bus capacitor；S is the Laplace variable factor；K_pIt is 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_v1cIt is outer voltage closed-loop drive function；G_v1oIt is outer voltage open loop Transmission Function；K_pFor Outer voltage control parameter；C is DC bus capacitor；S is the Laplace variable factor.

Outer shroud control parameter is K_p=1.5, K_I=3, DC bus capacitor C₁=C₂=C=4000 μ F, resistance R_c=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 biography System PI controllers can immediately arrive at the PI controllers based on sliding formwork control：

C in formula_{SMC_PI}S () is the transmission function of the PI controllers based on sliding formwork control；S is the Laplace variable factor； k_sp, k_siIt is the parameter of PI controllers, they are the sizes for determining its value according to designed sliding-mode surface by sliding mode controller, It is mainly characterized by obtaining appropriate PI control parameters according to the change of system.Using DC voltage transmission function and PI controllers based on sliding formwork control can obtain the Dynamic Closed Loop function of DC voltage：

In formula, U_dcS () is Laplce's form of DC voltage；U_{dc_ref}S () is the La Pula of DC side reference voltage This form；S is the Laplace variable factor；k_sp, k_siIt is the parameter of PI controllers；A=1/R_cC, b=1/C, a are resistance R_cWith The inverse of electric capacity C products, b is the inverse of electric capacity C, and C is DC bus capacitor.

To ensure the stability contorting of DC voltage, the Dynamic Closed Loop function according to DC voltage can obtain a ShiShimonoseki It is formula：

In formula, k_sp, k_siIt is the parameter of PI controllers；A=1/R_cC, b=1/C, a are resistance R_cWith falling for electric capacity C products Number, b is the inverse of electric capacity C, and C is DC bus capacitor.

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

K in formula_sp, k_siIt is the parameter of PI controllers；k_p+、k_p-、k_i+、k_i-It is control parameter, and is all positive number；k_{av_p}、k_{av_i} It is the positive parameter that adds of differential and integral parameter in PI controllers.

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：

Conventional PI control device is realized fairly simple, but control parameter fixes；In load changing and with reference to given voltage change 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 the compensation effect of active filter can be caused reducing.

Fig. 5 is that current inner loop repeats PI control block diagrams.

Inner ring complex controll based on digital PI controls and Repetitive controller is mainly composed in parallel by two parts：1) PI controls Device.Difference between harmonic wave command value and actual value is modulated, improves the dynamic property of APF systems.2) repetitive controller.Disappear Except system periodicity tracking error, the control accuracy of harmonic compensation current instruction is improved.Because PI regulations are based on switch periods , and Repetitive controller is to be based on the primitive period, therefore both are in time decouplings.

The PI controllers that electric current loop is used control expression formula for：

In formula, K_pIt is proportional control factor, T_iIt is integration time constant, e is error signal.In PI control systems, ratio Partial effect is the error of the system that timely responds to, and the effect of integral part is the static error of elimination system, improves system Static characteristic.But PI controls are difficult to accomplish DAZ gene to the current command signal in APF, do not reach control and require.

Below by taking d shaft currents as an example, the design of the current loop controller using PI controls is introduced.Expressed according to PI controllers Formula and voltage can obtain open loop and the closed loop transfer function, of continuous domain PI control electric current rings to the transmission function of electric current：

In formula, G_ioS () is open current loop function, G_icS () current closed-loop function, L is input side equivalent inductance, R is circuit Equivalent resistance, s is the Laplace variable factor, T_IIt is integration time constant, K_PIt is differential parameter.

From closed loop transfer function, closed-loop current control is a typical second-order system, using PI controller zero points With the pole zero cancellation method of control object limit, K is made_P/(K_P+K_I)=0.9902, can be two levels by high order system depression of order System.ξ=0.707, ratio and the integral coefficient difference of digital pi regulator are taken according to optimal second-order model and inner ring bandwidth requirement It is set to K_P=1.55, K_I=0.025 is converted into electric current loop open loop and closed loop transfer function, behind z domains：

Repetitive controller is the high stable state accuracy control method based on internal model principle, be widely used in it is various need to realize it is high-precision Spend the occasion of control.In Fig. 5, Q (z)=0.98 is taken.The design difficulty of repetitive controller is the design of compensator, compensator Effect is that system is corrected, and system is decayed to 0 in low-frequency range, in high band energy rapid decay.If compensator S (z) is：

S (z)=k_rz^kF₁(z)F₂(z)

Wherein k_rIt is Repetitive controller gain, is set to 1；z^kIt is differentiation element, takes k=3；F₁Z () is averaging filter, Its expression formula is：

F₂Z () is second-order low-pass filter, system cut-off frequency is 2KHz, damping ratio ξ=0.707, system in the design Sample frequency is 9.6KHz, keeps discretization to obtain using zeroth order：

Fig. 6 is neutral-point potential balance PI control block diagrams.

The upper and lower electric capacity voltage difference of DC side is only related to zero-axis current, and control is reached by the way of zero-axis current is controlled The control requirement of upper and lower capacitor voltage balance.The upper and lower electric capacity voltage difference of DC side is to the transmission function of zero axle：

Because there is divider resistance and upper and lower electric capacity is equal in magnitude, upper and lower electric capacity voltage difference very little is controlled using simple PI System can just reach the requirement of neutral-point potential balance.It is G to make current inner loop closed loop transfer function,_ic(s), then using pole zero cancellation method The upper and lower electric capacity voltage balancing control open-loop transfer function of DC side after simplification is：

In formula, G_v20S () is the upper and lower electric capacity voltage balancing control open-loop transfer function of DC side；G₀S () is that DC side is upper and lower Capacitance voltage difference to zero axle transmission function, G_ic(s) current closed-loop function, PI (s) controller functions；K_pIt is control parameter；s It is the Laplace variable factor；C is DC bus capacitor.

Neutral-point potential balance PI controls are similar to outer voltage PI controls, compare the transmission of both closed loops and understand, will need to only control The K of neutral-point potential balance processed_P、K_ITake outer voltage control parameterCan reach control to require, that is, take：K_P=0.866, K_I=1.732, then have：

Fig. 7 is space vector sector distribution map.

Space vector modulation (SVPWM) is sweared in a switch periods according to nearest Vector modulation principle to fundamental voltage Amount is combined, and makes its composite value equal with reference to the voltage vector for giving.By command voltage signal U_dq0Through coordinate transform, obtain To the command signal U containing phase information_αβ, according to command signal U_αβSector where decision instruction space vector, it is determined that switch week The fundamental space vector that phase is used, and then determine fundamental space vector action time and switching point time, to modulate SVPWM Switching pulse signal, controls APF devices, exports compensation harmonic electric current.

According to experimental result comparative analysis, can be drawn from Fig. 8 (a) and Fig. 8 (b), Fig. 8 (b) is using based on sliding formwork PI The APF in parallel of controller not only makes the DC voltage control have good dynamic property, and in system stable operation still Good stable state compensation performance is can guarantee that, overcoming traditional preset parameter PI DC voltage controls device can not be while takes into account dynamic With the deficiency of steady-state behaviour, sliding formwork PI device simple structures, realization is easily and amount of calculation is small, and rapidity is good, strong robustness, realizes simultaneously Join the optimal control of APF systems.

Electric current after the compensation under two kinds of control methods is measured using oscillograph is compared such as Fig. 9 (a) and Fig. 9 (b) institutes Show, Fig. 9 (b) is the compensation current waveform of compound PI controllers, the compensation electric current based on compound PI controllers with preferable Stable state compensates performance, and compared to the compensation electric current of PI controllers, current sinusoidal degree is high after compensation, and waveform is more smooth；From benefit The experimental result for repaying rear electric current can be analyzed, and the tracking accuracy of harmonic wave instruction current can be significantly improved using compound PI controllers, Can effective compensation harmonic electric current, the THD of reduction source current.

For further analysis compensates current harmonic content using two kinds of three-phases of controller, given using power quality analyzer The compensation current harmonic content gone out under two kinds of controllers, Figure 10 (a) is the three-phase compensation current harmonics analysis of PI controllers, is mended eventually Source current THD values minimum 14.80% after repaying；Figure 10 (b) is the three-phase compensation current harmonics analysis of compound PI controllers, The source current THD values after compensation are 5.21% to the maximum eventually；By can relatively draw：Can significantly be carried using compound PI controllers The tracking accuracy of higher harmonics instruction current, can effective compensation harmonic electric current, the THD of reduction source current.

Claims (6)

1. a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles, it is characterised in that comprise the following steps：

Step 1：Detection supply voltage U_s(abc), mains side electric current I_s(abc), load-side electric current I_L(abc), APF compensation electric current I_f(abc) Capacitance voltage U upper and lower with DC side_dc1、U_dc2；

Step 2：By the upper and lower capacitance voltage sum U of DC side_dc, U_dc=U_dc1+U_dc2, with DC side reference voltage level U_{dc_ref}Work compares Compared with, error signal is drawn, this error signal obtains current inner loop instruction current I by sliding formwork PI controllers_ref(dq0)；

Step 3：The load-side electric current I that will be detected in step 1_L(abc)Through i_p-i_qCurrent Detection Algorithm obtains harmonic wave under dq coordinate systems Instruction current I_h(dq0), by harmonic wave instruction current I_h(dq0)With current inner loop instruction current I is obtained in step 2_ref(dq0)Coordinate, obtain Final instruction currentBy instruction currentPAF compensation electric currents I under dq coordinate systems in matching step 1_f(dq0)Input Repeat PI controllers and obtain output voltage instruction signal U_dq0；

Step 4：The upper and lower capacitance voltage U of DC side that will be detected in step 1_dc1、U_dc2Input neutral-point potential balance PI controllers, obtain To balance of voltage factor f；

Step 5：The supply voltage detected in step 1 is obtained into system phase information by phase-locked loop systems, then by gained phase The voltage command signal U exported in information, step 3_dq0SVPWM modules are sent into the balance of voltage factor f obtained in step 4, is produced Raw switching pulse signal, controls APF devices, exports compensation harmonic electric current；

Step 6：Whether subsequent work cycle detection mains input side current harmonic content is 0, if now current harmonic content is not It is 0 return to step 1, repeat step 1.

2. a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles according to claim 1, its feature exists In：In step 1, U_sk(k=a, b, c) is three-phase access point voltage；U_kN(k=a, b, c) is each bridge arm midpoint potential of three-phase；I_sk (k=a, b, c), I_lk(k=a, b, c), I_fk(k=a, b, c) is respectively mains input current, load current and compensation electric current；R It is circuit and the equivalent resistance of inductance；L is flat ripple inductance；C₁、C₂It is the upper and lower electric capacity of DC side, C₁=C₂=C electric capacity both end voltages It is U_dc1And U_dc2；R₁、R₂It is equalizing resistance, R₁=R₂=R_c；

To simplify the design of parallel connection APF control systems, if switch is in perfect condition, ignore the influence of switch parameter；Adopt simultaneously With synchronous rotating angle, the close coupling high order system model under abc coordinate systems is transformed to the lower order system of dq0 coordinate systems Model, if U_si(i=d, q, 0) is access point voltage, S under dq0 coordinate systems_i(i=d, q, 0) is parallel connection APF bridges under dq0 coordinate systems Arm turns on switch function, I_fi(i=d, q, 0) is parallel connection APF compensation electric current under dq0 coordinate systems, then the Mathematical Modeling of parallel connection APF For：

$\left\{\begin{array}{c}L\frac{{\mathrm{dI}}_{fd}}{dt}=U_{sd}-{\mathrm{RI}}_{fd}-S_d(U_{dc1}+U_{dc2})+{\mathrm{L\&omega;I}}_{fq}\\ L\frac{{\mathrm{dI}}_{fq}}{dt}=U_{sq}-{\mathrm{RI}}_{fq}-S_q(U_{dc1}+U_{dc2})-{\mathrm{L\&omega;I}}_{fd}\\ L\frac{{\mathrm{dI}}_{f0}}{dt}=U_{s0}-{\mathrm{RI}}_{f0}-S_0(U_{dc1}+U_{dc2})\\ C\frac{{\mathrm{dU}}_{dc1}}{dt}=S_d{I}_{fd}+S_q{I}_{fq}+S_0{I}_{f0}-\frac{U_{dc1}}{R_1}\\ C\frac{{\mathrm{dU}}_{dc2}}{dt}=S_d{I}_{fd}+S_q{I}_{fq}+S_0{I}_{f0}-\frac{U_{dc2}}{R_2}-\sqrt{3}{I}_{f0}\end{array}\right.---\left(1\right).$

3. a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles according to claim 1, its feature exists In：In step 2,

C₁、C₂It is the upper and lower electric capacity of DC side, U_dc1(s) and U_dc2S () is the Lars form of upper and lower electric capacity both end voltage；I_dS () is d Laplce's form of shaft current；R₁=R₂=R_cIt is the upper and lower equalizing resistance of DC side；

In APF normal operating conditions, harmonic current and reactive current are compensated only for, to simplify derivation, it is zero to make q shaft currents, It is using the transmission function of d shaft currents derivation active filter DC voltage then：

$G_{dc}\left(s\right)=\frac{U_{dc1}\left(s\right)}{I_d\left(s\right)}=\frac{U_{dc2}\left(s\right)}{I_d\left(s\right)}=\frac{R_c}{R_{c}Cs+1}---\left(2\right)$

According to the mentality of designing of current transformer traditional double closed loop controller, it is G to make current closed-loop transmission function_ic(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 to be controlled so as to simplify DC voltage PI The design process of device, then obtaining outer voltage open loop Transmission Function is：

$G_{v1o}=PI\left(s\right)G_{ic}\left(s\right)G_{v1}\left(s\right)=\frac{K_p(T_{v}s+1)R_c}{T_{v}s(R_{c}Cs+1)}---\left(3\right)$

T in formula_v=R_cC, the system is a typical second-order system, and the design for eliminating zero pole point simplify control device obtains closed loop Transmission function：

$G_{v1c}=\frac{G_{v1o}}{1+G_{v1o}}=\frac{1}{1+(C/K_p)s}=\frac{1}{1+\mathrm{\&tau;}s}---\left(4\right)$

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 side total voltage U_dc, so directly controlled quentity controlled variable can be controlled；According to the principle for choosing sliding-mode surface, definable DC side electricity The sliding formwork control face of pressure is：

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

K is normal number in formula；

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 traditional PI Controller can immediately arrive at 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_sp, k_siIt is the parameter of PI controllers, they are that its value is determined according to designed sliding-mode surface by sliding mode controller Size, it is mainly characterized by obtaining appropriate PI control parameters according to the change of system；Using formula DC voltage Transmission function and sliding formwork PI controllers expression formula can obtain the Dynamic Closed Loop function of DC voltage：

$\frac{u_{dc}\left(s\right)}{u_{dc\_ref}\left(s\right)}=\frac{R_c{k}_{si}s+R_c{k}_{sk}}{R_c{\mathrm{Cs}}^2+(1+R_c)s+R_c{k}_{si}}=\frac{{\mathrm{bk}}_{sp}(s+k_{si}/k_{sp})}{s^2+(a+{\mathrm{bk}}_{sp})s+{\mathrm{bk}}_{si}}---\left(7\right)$

Wherein a=1/R_dcC, b=1/C；

To ensure the stability contorting of DC voltage, the Dynamic Closed Loop function according to DC voltage can obtain relation Formula：

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

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

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

Control parameter k in formula_p+、k_p-、k_i+、k_i-All it is positive number, these control parameters are whole in the case where PI controlled output characteristics are met Result is determined, they can be adjusted according to the method for standard PI controllers, while for elimination system is attached in sliding formwork control face The nearly DC voltage fluctuation for producing, respectively the differential and integral parameter in PI controllers add positive parameter k_{av_p}、k_{av_i}, from elimination 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 is in the presence of the premise for being Sliding Mode Controller application, the Li Yapu for generally choosing Promise husband's function is：

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

And time derivation is obtained：

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

K is normal number in formula, andMore than zero, above formula is permanent less than zero to set up the stabilization for then demonstrating designed sliding mode controller Property；

Buffeting of the sliding mode controller in sliding-mode surface field is difficult to avoid that, is produced in sliding formwork control face field to eliminate system DC voltage fluctuation, respectively PI controllers differential and integral parameter add positive parameter k_{av_p}、k_{av_i}, from elimination by sliding formwork Buffet the fluctuation problem for causing DC voltage in face；Work 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}。

4. a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles according to claim 1, its feature exists In：In step 3,

Inner ring complex controll based on digital PI controls and Repetitive controller is mainly composed in parallel by two parts：1) PI controllers, it is right Difference between harmonic wave command value and actual value is modulated, and improves the dynamic property of APF systems；2) repetitive controller, eliminates system System periodicity tracking error, improves the control accuracy of harmonic compensation current instruction, because PI regulations are to be based on switch periods, and Repetitive controller is to be based on the primitive period, therefore both are in time decouplings；

The PI controllers that electric current loop is used control expression formula for：

$u\left(t\right)=K_{p}e+\frac{K_p}{T_i}{\&Integral;}_0^{t}edt---\left(12\right)$

In formula, K_pIt is proportional control factor, T_iIt is integration time constant, e is error signal；In PI control systems, proportional parts Effect be the system that timely responds to error, the effect of integral part is the static error of elimination system, improve system static state Characteristic；But PI controls are difficult to accomplish DAZ gene to the current command signal in APF, do not reach control and require；

By deriving, show that dq0 shaft voltages are to the transmission function of electric current；

$G_i\left(s\right)=\frac{I_d\left(s\right)}{U_d\left(s\right)}=\frac{I_q\left(s\right)}{U_q\left(s\right)}=\frac{I_0\left(s\right)}{U_0\left(s\right)}=\frac{1}{Ls+R}---\left(13\right)$

Below by taking d shaft currents as an example, the design of the current loop controller using PI controls is introduced；According to PI controllers expression formula with And voltage can obtain open loop and the closed loop transfer function, of continuous domain PI control electric current rings to the transmission function of electric current：

$G_{io}\left(s\right)=PI\left(s\right)G_i\left(s\right)=\frac{K_P(T_{I}s+1)}{T_{I}s(Ls+R)}---\left(14\right)$

$G_{ic}\left(s\right)=\frac{G_{io}\left(s\right)}{1+G_{io}\left(s\right)}=\frac{K_P}{L}\frac{s+1/T_I}{s^2+(K_p/L+R/L)s+K_P/\left({\mathrm{LT}}_I\right)}---\left(15\right)$

From closed loop transfer function, closed-loop current control is a typical second-order system, eliminates zero pole point simplify control device Design can simplify after electric current loop open loop and closed loop transfer function,：

$G_{io}\left(s\right)=\frac{K_P}{Ls}---\left(17\right)$

$G_{ic}\left(s\right)=\frac{1}{1+(L/K_P)s}=\frac{1}{1+\mathrm{\&tau;}s}---\left(18\right)$

τ=L/K in formula_p；

The effect of compensator is that system is corrected, and system is decayed to 0 in low-frequency range, in high band energy rapid decay；If Compensator is：

S (z)=k_rz^kF₁(z)F₂(z) (19)

Wherein k_rIt is Repetitive controller gain, is set to 1, F₁Z () is averaging filter, its expression formula is：

$F_1\left(z\right)=\frac{z+1}{2z}---\left(20\right)$

F₂Z () is second-order low-pass filter；z^kIt is differentiation element, takes k=3.

5. a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles according to claim 1, its feature exists In：In step 4,

The upper and lower electric capacity voltage difference of DC side is only related to zero-axis current, control is reached by the way of zero-axis current is controlled upper and lower The control of capacitor voltage balance requires that the upper and lower electric capacity voltage difference of DC side is to the transmission function of zero axle：

$G_0\left(s\right)=\frac{U_{dc1}\left(s\right)-U_{dc2}\left(s\right)}{I_0\left(s\right)}=\frac{\sqrt{3}}{Cs}---\left(21\right)$

Because there is divider resistance and upper and lower electric capacity be equal in magnitude, upper and lower electric capacity voltage difference very little, using simple PI controls just The requirement of neutral-point potential balance can be reached, it is G to make current inner loop closed loop transfer function,_icS (), then simplified using pole zero cancellation method The upper and lower electric capacity voltage balancing control open-loop transfer function of DC side afterwards is：

$G_{v20}\left(s\right)=PI\left(s\right)G_{ic}\left(s\right)G_0\left(s\right)=\frac{\sqrt{3}{K}_p}{Cs}---\left(22\right).$

6. a kind of three-phase four-wire system parallel connection non-linear composite control method of APF two close cycles according to claim 1, its feature exists In：In step 5, space vector modulation SVPWM is based on average equivalent principle, and basic voltage vectors are added in a switch periods To combine, make its average value equal with given voltage vector；By command voltage signal U_dq0Through coordinate transform, obtain containing phase The command signal U of position information_αβ, according to command signal U_αβSector where decision instruction space vector, determines that switch periods are used Fundamental space vector, and then determine fundamental space vector action time and switching point time, modulate SVPWM switching pulses Signal, controls APF devices, exports compensation harmonic electric current.