KR100973658B1 - Feedback Linearization Control of PWM Converters with LCL Input Filters - Google Patents

Abstract

A system for realizing a PWM converter control method using an LCL filter according to the present invention includes an LCL filter 10 connected to a rear end of an input power source e and a DC power supply connected to a rear end of the LCL filter 10. A PWM converter 20 for converting to a power source, a capacitor C _dc connected to a rear end of the PWM converter 20 to drive a load LOAD, and a reference voltage V _dc of the capacitor C _dc and The controller 30 performs feedback linear control to the PWM converter 20 using the input voltage command V _dc ^* and the converter input current i _g and the input current command i _g ^* .

Accordingly, the present invention implements the feedback linearization control, so that the nonlinear system is linearly controlled by inversely compensating the same dynamic characteristics as the nonlinear dynamic characteristics of the system, thereby providing better responsiveness and transient characteristics than the conventional control method using damping resistance. There is an effect that can be obtained.

LCL Filters, PWM Converters, Controllers, Meters, Estimators

Description

Feedline Linearization Control of PWM Converters with LCL Input Filters}

The present invention relates to a method and system for controlling a PWM converter using an LCL filter. More particularly, the present invention relates to a multi-structure control using a feedback linearization theory to control an AC / DC PWM converter using an LCL filter without using a damping resistor. The present invention relates to a control method and system of a PWM converter using an LCL filter that can obtain excellent response characteristics and transient ecological characteristics.

A typical three-phase AC / DC PWM converter using a boost inductor (L) filter is capable of controlling output DC voltage and controlling sinusoidal input current, but generates switching frequency ripple, causing electromagnetic interference to other equipment connected to the system. Electronic interference) may cause problems.

This problem can be solved by increasing the value of L, but this increases the size and cost of the inductor and degrades the performance due to the reduction of system dynamics.

LC filter or LCL filter is used to prevent this problem, and the LCL filter has the advantage of reducing the switching frequency ripple while using the existing L value that can maintain the dynamic characteristics of the system.

The structure of a PWM converter having such an LCL filter will be described with reference to FIG. 1 below.

1 is a block diagram illustrating a three-phase AC / DC PWM converter with an LCL input filter.

Here, the resistance components and the input line resistances of the inductors L _g and L _c and the capacitor C _f constituting the filter are ignored.

L _g is the supply side filter inductor, L _c is the converter side filter inductor, and C _f is the filter capacitor. I _g is the supply-side current, i is the converter input current, and v _c is the voltage across the filter capacitor. C _dc is the output capacitor, v _dc is the output voltage, and i _L is the output current.

Since the power change rate of the output capacitor C _dc is obtained by the difference between the input power and the output power, the PWM converter using the LCL filter is represented by the nonlinear state equation of Equation 1 including disturbance components.

In Equation 1, subscripts d and q denote synchronizing coordinate systems d and q axes, respectively, and ω denotes synchronizing angular frequency.

Equation 1 originally has a converter reference voltage as an input, but if converted, it can be expressed as a state equation having the converter side current of Equation 2 as an input and a state equation having the converter reference voltage of Equation 3 as an input.

2 is The high frequency ripple rejection characteristics of the LCL filter and the L filter having the same inductance are shown, and Equations 4 and 5 represent the equivalent impedance and the transfer function of the LCL filter, respectively. It can be seen that.

As described above, in the case of the LCL filter, a resonance problem occurs due to the characteristics of the structure, and this should be taken into consideration. Generally, a damping resistor connected in series with C is used, but the resistance causes a loss. It also solves the resonance problem. To design proper active damping, accurate parameter information about filter and power impedance is required, and additional sensor is needed because the capacitor voltage needs to be measured to use virtual resistance.

In addition, a method using active damping without additional sensors and accurate parameter information has been introduced using genetic algorithms.

In the multi-loop structure using the capacitor current, the internal control system controls the capacitor current to solve the resonance problem. In this case, the capacitor current needs to be measured.

In addition, the problem can be solved by selecting the position of the sensor. If the converter input current is measured and controlled, the converter can be controlled with a smaller damping resistance, but the unit power factor control is difficult, and a damping resistor is required to control the power current.

Feedback linearization theory is a control method that compensates for nonlinear dynamics by inversely compensating nonlinearity of system dynamics, and has been applied to control of parallel active filter and three-phase three-level NPC boost converter, and provides robust and fast response to disturbance. .

In the present invention, in order to solve the problem of the conventional PWM converter having the LCL filter, by applying the feedback linearization theory without using the damping resistor, it is represented by two state equations having the converter input current and the reference voltage as inputs The feedback linearization theory is applied to each, and the control method of the PWM converter using the LCL filter has the effect of reducing the number of sensors by controlling the converter input current to prevent overcurrent and estimating the power supply voltage and the power supply current. To provide a system.

A feature of the present invention for solving the above problems is that the LCL filter 10 is connected between the input power supply and the PWM converter 20, by the capacitor (C) connected to the rear end of the PWM converter 20 described above. The load LOAD is driven and uses the voltage V _dc of the capacitor C, the input voltage command V _dc ^* , the converter input current i _g , and the input current command i _g ^* . In the PWM converter control method using the LCL filter comprising a controller 30 for outputting a control signal to the PWM converter 20, the controller 30 is the converter input current (i _g ) and the reference voltage of the capacitor ( V _dc ) is used as an input, and the feedback linear control is performed for each.

In this case, the capacitor voltage and the converter current are measured by measuring means, and the power supply voltage and the power supply side current are estimated and used by an estimator having a differential, an adder, and a low pass filter therein.

In addition, the controller 30 is characterized in that the anti-wind up circuit is further added to properly limit the value in the integrator in accordance with the limit value of the controller output.

의 오차 동적방정식을 '0'으로 수렴하게 하는 이득을 정함으로써 추종제어를 실시한 후, 그 출력신호를 선형화기로 선형화하는 것을 특징으로 한다.In addition, the feedback linear control may be performed using a reference voltage command and a reference voltage inputted using a follower controller.

After the following control is performed by determining a gain that converges the error dynamic equation of to 0, the output signal is linearized with a linearizer.

의 오차 동적방정식을 0으로 수렴하게 하는 이득을 정함으로써 추종제어를 실시하는 추종제어기와, 상기한 추종제어기의 출력 신호를 선형화하는 선형화기로 구성되며 컨버터 입력전류(i_g)와 커패시터의 기준전압(V_dc)을 입력으로 가지고 각각에 대해 궤환선형 제어를 실시하는 것을 특징으로 한다.In addition, the LCL filter 10 is connected between the input power supply and the PWM converter 20, and the load LOAD is driven by the capacitor C connected to the rear end of the PWM converter 20. Outputs a control signal to the PWM converter 20 by using the voltage V _dc of (C), the input voltage command (V _dc ^* ), the converter input current (i _g ), and the input current command (i _g ^* ). In the PWM converter control system using the LCL filter comprising a controller 30, the controller 30 is expressed by the equation using the input reference voltage command and the reference voltage

The tracking controller performs tracking control by determining the gain that converges the error dynamic equation of 0 to 0, and the linearizer linearizing the output signal of the tracking controller. The converter input current (i _g ) and the reference voltage of the capacitor ( V _dc ) is used as an input, and the feedback linear control is performed for each.

At this time, the controller 30 is characterized in that the anti-wind up circuit is further added to properly limit the value inside the integrator in accordance with the limit value of the controller output.

According to the present invention, the feedback linearization control is performed so that the nonlinear system is linearly compensated by inversely compensating the same dynamic characteristics as the nonlinear dynamic characteristics of the system, so that response and transient characteristics superior to those of the conventional damping resistance control method can be obtained. It works.

In addition, by applying a multiple structure, it is possible to limit the converter input current and thereby prevent the converter overcurrent.

In addition, according to the present invention, the switching ripple cancellation effect is superior to the L filter of the same capacity, and the resonance problem, which is a disadvantage of the LCL filter, can be solved without using a damping resistor. Also, if the same harmonic characteristics are used as the reference, the size of the inductor can be reduced by using an LCL filter instead of L.

Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

3 is a system block diagram for implementing a control method of a PWM converter using an LCL filter according to the present invention.

A system for realizing a PWM converter control method using an LCL filter according to the present invention includes an LCL filter 10 connected to a rear end of an input power source e and a DC power supply connected to a rear end of the LCL filter 10. A PWM converter 20 for converting to a power source, a capacitor C _dc connected to a rear end of the PWM converter 20 to drive a load LOAD, and a reference voltage V _dc of the capacitor C _dc and The controller 30 performs feedback linear control to the PWM converter 20 using the input voltage command V _dc ^* and the converter input current i _g and the input current command i _g ^* .

In the above configuration, feedback linearization control converts the original nonlinear system model into a simple equivalent equivalent linear model and applies a well-known linear control theory to design a controller to control the system. 2 is represented by a multi-input multi-output system such as Equations 6 and 7. Here, the output and input orders are the same as '2'.

In equation (2), i _gd and v _dc are selected as outputs, and the derivative of the selected output equation (7) until the input appears to obtain a new output equation as shown in (8).

Where y ^ri = [i " _gd , v '" _dc ], u = [i _d , i _q ]

이다.

to be.

The derivative of the output is called the relative degree, and if the sum of the relative indices is equal to the order of the system, there is no internal dynamics, so there is no need to consider the stability of the internal dynamics. In this case, a complete input / output linearization of the nonlinear system is achieved.

In Equation 8, E (x) is a decoupling matrix, and in order to enable input / output decoupling, this matrix must be a regular matrix for all operating points. A nonlinear control input that enables linearization and non-intrusive operation is given by Equation 9.

이다.here,

to be.

Substituting Equation (9) into Equation (8) yields a linearized and uncoupled model such as Equation 10, and since v _i only affects the output y ^ri , it is called a non-interfering control input.

As a control law for the new control input, following control as in Equation 11 is applied.

Here, e ₁ = y _1- y _1ref , e ₂ = y _2- y _2ref , where y _ref is the follow command, which means the power supply reference current (y _1ref ) and output capacitor reference voltage (y _2ref ), and k _ij is the gain. It means. Following control is possible by determining a gain that converges the error dynamic equation of equation (11) to zero.

Since Equation 3 is a linear state equation, the feedback linearization process gives the same result as the non-interference control method through general forward compensation.

As shown in FIG. 4, since the steady state error of the inner loop does not affect the performance of the outer loop, only a proportional gain is used. In FIG. 4, A _i (x) and E _i (x) are represented by Equations 12 and 13.

Fig. 5 shows a control block diagram in which anti-windup is added to properly limit the value inside the integrator in accordance with the limit value of the controller output.

The following control method of Equation 11 is the same as the control method shown in FIG. 6, and it can be seen from Equation 2 that the derivative component of the capacitor, that is, the capacitor current is indirectly controlled through the proportional controller.

Therefore, when feedback linearization is used, the system can be stably controlled without damping resistance.

In the feedback linearization method of the present invention, the capacitor voltage and the converter current are measured by the measuring devices 40 and 50 of FIG. 3, and the power supply voltage and the power current are estimated by the estimator 60 of FIG. 3 to reduce the number of sensors. do.

7 is a block diagram of a power supply current estimator.

As shown in FIG. 7, the dq-axis differential equation for power current estimation is shown in Equation 14, and the estimated current passes through a first-order low pass filter to remove noise caused by the differential process.

The power supply voltage estimation process is the same as the current estimation process, where the estimated power supply voltage is used to extract the control angle through each controller. The dq-axis differential equation for power supply voltage estimation is shown in Equation 15.

8 (a) shows the current feedback root locus when the system is linearized by the feedback linearization method of the present invention, and FIG. 8 (b) shows the gain margin and phase margin. Here, the transfer function of the plant is as shown in Equation 5, and the controller obtained by Equation 11 is used. All the muscles are located in the left half and the gain does not go to the right half even if the gain is high. 8 (b) shows a bode diagram of the open loop transfer function, and it can be seen that the gain margin and the phase margin are sufficiently large.

In order to compare the performance of the controller of the present invention and the PI controller with forward compensation of the load current, a simulation was performed using PSim.

In addition to the method of the present invention, a PI controller using power current control was compared.

The sensor measures the supply voltage and supply current and the d-axis current is controlled to zero. L _g is 1.5 mH, L _c is 2 mH, and C _f is 10 uF. The resonant frequency of the LCL filter is 1.72 [kHz] and the switching frequency is 5 [kHz].

Another 50Ω resistive load was applied at 0.3 seconds while the 330Ω resistive load was connected and removed at 0.5 seconds.

9 and 10 show the respective simulation results.

In Example 1 shown in FIG. 9, a damping resistor 5Ω is used to prevent resonance, but some resonance can be observed when a load is applied, and it can be seen that the performance of the filter is reduced by the damping resistor.

Example 2 shown in FIG. 10 shows the performance of the proposed controller. Although the damping resistor is not used, resonance is hardly seen and the transient response of the DC link voltage is superior to that of the PI controller.

In the case of using a general L filter, the power supply current switching ripple component is 3.94% and almost 4%, while the power supply switching ripple component of Example 1 is reduced to 1.26%, and the power supply switching ripple component of Example 2 is Decreased to 0.71%.

The gains used in the simulation are k ₁₁ = 7.05 × 10 ³ , k ₁₂ = 2.0 × 10 ⁷ , k ₁₃ = 2.5 × 10 ⁸ , k ₂₁ = 1.05 × 10 ⁴ , k ₂₂ = 3.68 × 10 ⁷ , k ₂₃ = 4.32 X 10 ¹⁰ , k ₂₄ = 4.28 x 10 ¹¹ , and k _p = 8000.

The switching frequency of the IGBT PWM converter is 5 [kHz], the LCL filter and damping resistance values are the same as in the simulation, the three-phase input line voltage is 220Vrms, the converter capacitor is 1950 [uF] and the output voltage command is 340. [V], the converter load was carried out according to the present invention using 330 // 50 [Ω].

Fig. 11 shows the power supply voltage used in the embodiment of the present invention, which includes some fifth and seventh harmonics and unbalances.

12 shows a control angle generated using the estimated power supply current and the estimated power supply voltage used in the method according to the present invention, and shows no difference from the actual value.

Figure 13 shows the performance of the PI controller using the measured power supply current, Figure 14 shows the performance of the control method according to the invention.

이다.The gains of the PI current controller used in the experiment are k _p = ω _c L _T and k _i = ω _c R (ω _c = 4000, L _T = 0.0035, R = 0.1), and the gain of the PI voltage controller is

to be.

The load of 50 [Ω] was applied in parallel while the resistor of 330 [Ω] was connected and operated, and the power current and converter voltage response characteristics were observed.

When the load was applied, the q-axis supply current increased to about 15 [A] in the PI controller, and the converter voltage showed about 5 [V]. On the other hand, in the controller of the present invention, the q-axis supply current increased to about 12 [A], and the converter voltage showed a change smaller than 2.5 [V].

Therefore, it can be seen that the overshoot and steady state ripple of the proposed controller are smaller than those of the PI controller, and the transient performance of the converter voltage is also excellent in the controller according to the present invention.

Figure 15 shows the power supply phase voltage of the controller according to the present invention and the actually measured power supply current, and it can be seen that the switching ripple component is hardly seen in the current.

1 is a block diagram illustrating a three-phase AC / DC PWM converter with an LCL input filter.

2 is Graph showing high frequency ripple rejection characteristics of LCL and L filters with the same inductance.

3 is a system block diagram for implementing a control method of a PWM converter using an LCL filter according to the present invention.

4 is a block diagram of a nonlinear controller.

FIG. 5 is a controller block diagram with anti-windup added. FIG.

6 is a block diagram of a feedback linearized controller in accordance with the present invention.

7 is a block diagram of a power supply current estimator.

8 is a graph showing the current feedback root locus, gain margin and phase margin when the system is linearized by the feedback linearization method of the present invention.

9 is a graph showing a power supply side current and an output voltage when a damping resistor is used.

10 is a graph showing the power supply side current and the output voltage according to the present invention.

11 is a graph showing the power supply voltage used in the embodiment of the present invention.

12 is a graph showing a control angle generated using the estimated power supply current and the estimated power supply voltage used in the method according to the present invention.

13 is a graph showing the performance of the PI controller using the measured power supply current.

14 is a graph showing the performance of the control method according to the present invention.

15 is a graph showing the power supply phase voltage and the actually measured power supply current of the controller according to the present invention.

* Description of the symbols for the main parts of the drawings *

10: LCL filter 20: PWM converter

30: controller 40, 50: measuring instrument

60: estimator

Claims (6)

The LCL filter 10 is connected between the input power supply and the PWM converter 20, and the load LOAD is driven by the capacitor C connected to the rear end of the PWM converter 20. The capacitor C Controller to output the control signal to the PWM converter 20 using the voltage (V _dc ), the input voltage command (V _dc ^* ) and the converter input current (i _g ) and the input current command (i _g ^* ). In the PWM converter control method using an LCL filter comprising (30), The controller 30 performs a feedback linear control for each of the converter input current (i _g ) and the reference voltage (V _dc ) of the capacitor as inputs, and the feedback linear control is input using a follower controller. Equation using reference voltage command and reference voltage

Following control is performed by determining a gain that converges the error dynamic equation of to 0, and then the output signal is linearized by a linearizer. In the above equation, v _i (i = 1, 2) is a ratio. It is an interference control input, and e ₁ = y _1- y _1ref , e ₂ = y _2- y _2ref , and y _ref is a following command, which means the power supply reference current (y _1ref ) and the output capacitor reference voltage (y _2ref ). k _ij is a method of controlling a FDM converter using an ELCEL filter meaning gain. The EL filter according to claim 1, wherein the capacitor voltage and the converter current are measured through measuring means, and the power supply voltage and the power supply current are estimated and used through an estimator having a differential, an adder, and a low pass filter therein. Method of control of the feedable UMM converter. The method of claim 1, wherein the controller (30) further comprises an anti-wind-up circuit. delete The LCL filter 10 is connected between the input power supply and the PWM converter 20, and the load LOAD is driven by the capacitor C connected to the rear end of the PWM converter 20. The capacitor C Controller to output the control signal to the PWM converter 20 using the voltage (V _dc ), the input voltage command (V _dc ^* ) and the converter input current (i _g ) and the input current command (i _g ^* ). A PWM converter control system using an LCL filter comprising 30, The controller 30 uses the input reference voltage command and the reference voltage.

The tracking controller performs tracking control by determining the gain that converges the error dynamic equation of 0 to 0, and the linearizer linearizing the output signal of the tracking controller. The converter input current (i _g ) and the reference voltage of the capacitor ( V _dc ) as an input, characterized in that to perform a feedback linear control for each, v _i (i = 1, 2) in the above equation is a non-interference control input, e ₁ = y ₁ -y _1ref , e ₂ = y _2- y _2ref , y _ref is the following command, which means the reference current (y _1ref ) and the output capacitor reference voltage (y _2ref ) at the power supply side, and k _ij is the _{FDM using the Elsiel} filter for gain. Converter control system. 6. The control system of a FDM converter according to claim 5, wherein the controller (30) further comprises an anti-wind-up circuit.

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