CN105656035A - Control circuit and method of unified power quality controller - Google Patents

Abstract

The invention relates to a control circuit and method of a unified power quality controller. The control circuit comprises a control loop and a major loop which are connected. The control loop comprises a bypass filter, inductive current If(s) passes through the bypass filter GB (s) so that filtered inductive current can be obtained, the difference between a voltage loop specified value and a transformer primary voltage V1(s), an inductive current loop output value and the filtered inductive current are superposed, and output voltage Vs (s) of a serial connection part of the unified power quality controller (UPQC) is obtained through a transformer output gain ki. The function of enhancing damping characteristics is achieved, and stable control of the UPQC is achieved.

Description

Control circuit and method of unified power quality controller

Technical Field

The invention relates to the technical field of power electronics, in particular to a control circuit and a control method of a unified power quality controller.

Background

The Unified Power Quality Controller (UPQC) is a back-to-back structure formed by connecting a series active power filter and a parallel active power filter through a common direct current bus capacitor, and has the main functions of compensating voltage and current quality problems, specifically, power grid voltage fluctuation, distortion, load reactive power, harmonic current and the like.

The output voltage of the series part of the UPQC is filtered by an LC filter to remove high-frequency components and then is connected to the system in series. However, due to the introduction of the LC filter, the UPQC has an underdamping characteristic, and the stability of the system is affected. In order to realize damping control of UPQC, the filter capacitor current is sampled frequently by the series part to carry out double closed-loop control of the voltage outer ring current inner ring, and meanwhile, in order to play an overcurrent protection effect on the device, the inductor current sampling is needed, so that the hardware cost of the system is increased, and the controller is more complex.

Disclosure of Invention

The invention aims to provide a control circuit and a control method of a unified power quality controller.

The technical scheme for solving the technical problems is as follows: a control circuit of a unified power quality controller, comprising a control loop and a main loop, wherein the control loop (10) is connected with the main loop (20), wherein the control loop (10) comprises a band-pass filter;

inductive current I_f(s) pass through a bandpass filter G_B(s) obtaining the filtered inductive current, setting the voltage loop to a given valueAnd the primary voltage V of the transformer₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the UPQC series part of the unified power quality controller_s(s)。

The invention has the beneficial effects that: and after passing through the band-pass filter, the sampling current feeds back the resonant current to the system modulation wave for closed-loop control, so that the damping characteristic is enhanced, and the stable control of UPQC is realized.

On the basis of the technical scheme, the invention can be further improved as follows.

Further, still include:

given value of voltage loopAnd feedback sampling value V₂(s) comparing to obtain the inductance current fingerThe instruction value is adjusted through a current loop to obtain the output voltage V of the series connection part of the UPQC_s(s) output voltage V of said series portion of UPQCs_s(s) obtaining a load output voltage V in said main circuit (20) via a filter and a transformer₂(s) the load outputs a voltage V₂(s) is fed back into the control loop (10) as a voltage loop feedback value.

Further, still include:

according to the load output voltage V₂(s) and said voltage loop setpointAnd obtaining a system closed loop transfer function.

Further, the system closed loop transfer function is calculated according to the following formula:

$G_{V_2}\left(s\right)=\frac{V_2\left(s\right)}{{V_2}^{*}\left(s\right)}=\frac{(L_{l}s+r_l)({\mathrm{nk}}_v{k}_c{k}_i+{\mathrm{nk}}_i)}{a_1{s}^3+a_2{s}^2+a_{3}s+a_4}$

$G_B\left(s\right)=({\mathrm{\ω}}_0/Q)/(s^2+{\mathrm{\ω}}_{0}s/Q+{\mathrm{\ω}}_0^2)$

$\left\{\begin{array}{c}{a}_1=(L_l+n^2{L}_t)L_f{C}_f\\ a_2=(L_l+n^2{L}_t)r_f{C}_f+(r_l+n^2{r}_t)L_f{C}_f+k_c{k}_i(L_l+n^2{L}_t)L_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{L}_t{C}_f\\ a_3=(r_l+n^2{r}_t)r_f{C}_f+n^2(L_f+L_t)+(1+{\mathrm{nk}}_v{k}_c{k}_i)L_l+k_c{k}_i(r_l+n^2{r}_t)C_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{r}_t{C}_f\\ a_4=n^2{r}_t+n^2{r}_f+n^2{k}_c{k}_i+(1+{\mathrm{nk}}_v{k}_c{k}_i)r_l+G_B{k}_i{n}^2\end{array}\right.$

wherein,for the closed loop transfer function of the system, V₂(s) is the load output voltage,for setting the voltage loop to a value of L_l、r_lIs the load impedance, k_vAs a voltage loop proportional system, k_cIs the current loop proportionality coefficient, k_iFor the transformer output gain, a₁、a₂、a₃And a₄Is a parameter factor, n is the number of turns of the transformer, G_B(s) is a band-pass filter, ω₀Is the resonant frequency of the band-pass filter, Q is the quality factor, L_f、r_fIs the series filter impedance of the UPQC, C_fIs a series filter capacitor, L, of the UPQC_t、r_tIs the transformer leakage impedance.

Another technical solution of the present invention for solving the above technical problems is as follows: a method of controlling a unified power quality controller comprising control circuitry of a unified power quality controller as described above, the method comprising:

inductive current I_f(s) pass through a bandpass filter G_B(s) obtaining a filtered inductor current;

setting the voltage ring to a given valueAnd the primary voltage V of the transformer₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the UPQC series part of the unified power quality controller_s(s)。

The invention has the beneficial effects that: and after passing through the band-pass filter, the sampling current feeds back the resonant current to the system modulation wave for closed-loop control, so that the damping characteristic is enhanced, and the stable control of UPQC is realized.

On the basis of the technical scheme, the invention can be further improved as follows.

Further, still include:

given value of voltage loopAnd feedback sampling value V₂(s) comparing to obtain an inductive current instruction value;

adjusting the inductive current instruction value through a current loop to obtain the output voltage V of the series part of the UPQC_s(s)；

Output voltage V of the series part of the UPQC_s(s) obtaining a load output voltage V in said main loop via a filter and a transformer₂(s)；

The load output voltage V₂(s) is fed back into the control loop as a voltage loop feedback value.

Further, still include:

according to the load output voltage V₂(s) and said voltage loop setpointAnd obtaining a system closed loop transfer function.

Further, the system closed loop transfer function is calculated according to the following formula:

$G_{V_2}\left(s\right)=\frac{V_2\left(s\right)}{{V_2}^{*}\left(s\right)}=\frac{(L_{l}s+r_l)({\mathrm{nk}}_v{k}_c{k}_i+{\mathrm{nk}}_i)}{a_1{s}^3+a_2{s}^2+a_{3}s+a_4}$

$G_B\left(s\right)=({\mathrm{\ω}}_0/Q)/(s^2+{\mathrm{\ω}}_{0}s/Q+{\mathrm{\ω}}_0^2)$

$\left\{\begin{array}{c}{a}_1=(L_l+n^2{L}_t)L_f{C}_f\\ a_2=(L_l+n^2{L}_t)r_f{C}_f+(r_l+n^2{r}_t)L_f{C}_f+k_c{k}_i(L_l+n^2{L}_t)L_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{L}_t{C}_f\\ a_3=(r_l+n^2{r}_t)r_f{C}_f+n^2(L_f+L_t)+(1+{\mathrm{nk}}_v{k}_c{k}_i)L_l+k_c{k}_i(r_l+n^2{r}_t)C_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{r}_t{C}_f\\ a_4=n^2{r}_t+n^2{r}_f+n^2{k}_c{k}_i+(1+{\mathrm{nk}}_v{k}_c{k}_i)r_l+G_B{k}_i{n}^2\end{array}\right.$

wherein,for the closed loop transfer function of the system, V₂(s) is the load output voltage,for setting the voltage loop to a value of L_l、r_lIs the load impedance, k_vAs a voltage loop proportional system, k_cIs the current loop proportionality coefficient, k_iFor the transformer output gain, a₁、a₂、a₃And a₄Is a parameter factor, n is the number of turns of the transformer, G_B(s) is a band-pass filter, ω₀Is the resonant frequency of the band-pass filter, Q is the quality factor, L_f、r_fIs the series filter impedance of the UPQC, C_fIs a series filter capacitor, L, of the UPQC_t、r_tIs the transformer leakage impedance.

Drawings

Fig. 1 is a schematic diagram of a control circuit of a unified power quality controller according to an embodiment of the present invention;

fig. 2 is a flowchart of a control method of a unified power quality controller according to an embodiment of the present invention;

FIG. 3 is a waveform diagram of a closed loop transfer function of the system according to an embodiment of the present invention;

fig. 4 is a flowchart of another control method of a unified power quality controller according to an embodiment of the present invention.

In the drawings, the components represented by the respective reference numerals are listed below:

10. control loop, 2, main loop.

Detailed Description

The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.

Aiming at the under-damping characteristic caused by the LC filter in the control of the series part of the UPQC, the application performs closed-loop control by sampling the inductive current and feeding back the resonant current to the system modulation wave after passing through the band-pass filter, thereby playing a role in increasing the damping characteristic of the system and further realizing the stable control of the UPQC. Reference may be made in particular to the schematic diagram of the control circuit of a unified power quality controller as shown in fig. 1.

The control circuit comprises a control loop 10 and a main loop 20, the control loop 10 is connected with the main loop 20, and the control loop 10 comprises a band-pass filter.

Specifically, the inductor current I_f(s) pass through a bandpass filter G_B(s) obtaining the filtered inductive current, setting the voltage loop to a given valueAnd the primary voltage V of the transformer₁Difference in(s), inductance currentThe loop output value and the filtered inductive current are superposed and output by a transformer with a gain k_iObtaining the output voltage V of the UPQC series part of the unified power quality controller_s(s)。

Here, when the system resonates, an inductor current I is caused_f(s) a resonant current appears, the inductive current I_fAnd(s) after passing through a band-pass filter, extracting resonance information, introducing a control link to perform closed-loop control, and reducing the content of resonance voltage in the output voltage of the UPCQ serial part as much as possible so as to improve the quality of the output voltage.

In this embodiment, the voltage ring set pointAnd feedback sampling value V₂(s) comparing to obtain an inductive current instruction value, and adjusting the inductive current instruction value through a current loop to obtain the output voltage V of the UPQC series connection part_s(s) output voltage V of said series portion of UPQCs_s(s) obtaining a load output voltage V in said main circuit 20 via a filter and a transformer₂(s) the load outputs a voltage V₂(s) is fed back into the control loop 10 as a voltage loop feedback value.

In the present embodiment, the voltage V is output according to the load₂(s) and voltage ring set pointAnd obtaining a system closed loop transfer function. The system closed loop transfer function can be known according to the formula (1), and the system closed loop transfer function is finally obtained through the formula (2) and the formula (3):

$G_{V_2}\left(s\right)=\frac{V_2\left(s\right)}{{V_2}^{*}\left(s\right)}=\frac{(L_{l}s+r_l)({\mathrm{nk}}_v{k}_c{k}_i+{\mathrm{nk}}_i)}{a_1{s}^3+a_2{s}^2+a_{3}s+a_4}---\left(1\right)$

$G_B\left(s\right)=({\mathrm{\ω}}_0/Q)/(s^2+{\mathrm{\ω}}_{0}s/Q+{\mathrm{\ω}}_0^2)---\left(2\right)$

$\left\{\begin{array}{c}{a}_1=(L_l+n^2{L}_t)L_f{C}_f\\ a_2=(L_l+n^2{L}_t)r_f{C}_f+(r_l+n^2{r}_t)L_f{C}_f+k_c{k}_i(L_l+n^2{L}_t)L_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{L}_t{C}_f\\ a_3=(r_l+n^2{r}_t)r_f{C}_f+n^2(L_f+L_t)+(1+{\mathrm{nk}}_v{k}_c{k}_i)L_l+k_c{k}_i(r_l+n^2{r}_t)C_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{r}_t{C}_f\\ a_4=n^2{r}_t+n^2{r}_f+n^2{k}_c{k}_i+(1+{\mathrm{nk}}_v{k}_c{k}_i)r_l+G_B{k}_i{n}^2\end{array}\right.---\left(3\right)$

wherein,for the closed loop transfer function of the system, V₂(s) is the load output voltage,for setting the voltage loop to a value of L_l、r_lIs the load impedance, k_vAs a voltage loop proportional system, k_cIs the current loop proportionality coefficient, k_iFor the transformer output gain, a₁、a₂、a₃And a₄Is a parameter factor, n is the number of turns of the transformer, G_B(s) is a band-pass filter, ω₀Is the resonant frequency of the band-pass filter, Q is the quality factor, L_f、r_fIs the series filter impedance of the UPQC, C_fIs a series filter capacitor, L, of the UPQC_t、r_tIs the transformer leakage impedance.

Here, a bode diagram of the closed-loop transfer function can be obtained according to the formula (1), as shown in fig. 3, a high-frequency resonance component is effectively suppressed, a fundamental wave component is not affected, the system damping characteristic is effectively improved on the basis of not increasing the number of sensors, the stability of the series voltage compensation of the UPQC is increased, and the quality of the compensation voltage is improved.

The control circuit of the unified power quality controller provided by the embodiment of the invention converts the inductive current I into the power output voltage_f(s) pass band pass filter G_B(s) obtaining the filtered inductive current, setting the voltage loop to a given valueAnd the primary voltage V of the transformer₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the series part of the UPQC_s(s) thereby playing a role in increasing the damping characteristic of the system and further realizing the stable control of the UPQC.

Fig. 2 is a flowchart of a control method of a unified power quality controller according to an embodiment of the present invention.

Referring to fig. 2, the control circuit comprising the unified power quality controller as described above, i.e. comprising a control loop and a main loop, the method comprises:

step S201, inductive current I_f(s) pass through a bandpass filter G_B(s) obtaining a filtered inductor current.

Step S202, setting the voltage ring to a given valueAnd the primary voltage V of the transformer₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the UPQC series part of the unified power quality controller_s(s)。

As a refinement to the implementation of the present application, the present application also provides another control method for a unified power quality controller, in which a main loop reflects a relationship between voltage and current of a series portion of the UPQC, a power grid, and a load, and a control loop adopts a dual-loop control manner of an outer loop and an inner loop of an inductive current of an outer loop of a load voltage, and specifically, as shown in fig. 4, the method includes:

step S401, setting voltage ring valueAnd feedback sampling value V₂And(s) comparing to obtain an inductive current instruction value.

Step S402, the inductive current instruction value is adjusted through a current loop to obtain the output voltage V of the UPQC serial part_s(s)。

Step S403, outputting voltage V of the series part of the UPQC_s(s) obtaining a load output voltage V in said main loop via a filter and a transformer₂(s)。

Step S404, the load outputs a voltage V₂(s) is fed back into the control loop as a voltage loop feedback value.

In the present embodiment, the voltage V is output according to the load₂(s) and said voltage loop set point V₂ ^*(s) obtaining a system closed loop transfer function. The system closed loop transfer function can be known according to the formula (4), and the system closed loop transfer function is finally obtained through the formula (5) and the formula (6):

$G_{V_2}\left(s\right)=\frac{V_2\left(s\right)}{{V_2}^{*}\left(s\right)}=\frac{(L_{l}s+r_l)({\mathrm{nk}}_v{k}_c{k}_i+{\mathrm{nk}}_i)}{a_1{s}^3+a_2{s}^2+a_{3}s+a_4}---\left(4\right)$

$G_B\left(s\right)=({\mathrm{\ω}}_0/Q)/(s^2+{\mathrm{\ω}}_{0}s/Q+{\mathrm{\ω}}_0^2)---\left(5\right)$

$\left\{\begin{array}{c}{a}_1=(L_l+n^2{L}_t)L_f{C}_f\\ a_2=(L_l+n^2{L}_t)r_f{C}_f+(r_l+n^2{r}_t)L_f{C}_f+k_c{k}_i(L_l+n^2{L}_t)L_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{L}_t{C}_f\\ a_3=(r_l+n^2{r}_t)r_f{C}_f+n^2(L_f+L_t)+(1+{\mathrm{nk}}_v{k}_c{k}_i)L_l+k_c{k}_i(r_l+n^2{r}_t)C_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{r}_t{C}_f\\ a_4=n^2{r}_t+n^2{r}_f+n^2{k}_c{k}_i+(1+{\mathrm{nk}}_v{k}_c{k}_i)r_l+G_B{k}_i{n}^2\end{array}\right.---\left(6\right)$

wherein,for the closed loop transfer function of the system, V₂(s) is the load output voltage,for setting the voltage loop to a value of L_l、r_lIs the load impedance, k_vAs a voltage loop proportional system, k_cIs the current loop proportionality coefficient, k_iFor the transformer output gain, a₁、a₂、a₃And a₄Is a parameter factor, n is the number of turns of the transformer, G_B(s) is a band-pass filter, ω₀Is the resonant frequency of the band-pass filter, Q is the quality factor, L_f、r_fIs the series filter impedance of the UPQC, C_fIs a series filter capacitor, L, of the UPQC_t、r_tIs the transformer leakage impedance.

The control method of the unified power quality controller provided by the embodiment of the invention is to convert the inductive current I into the current I_f(s) pass band pass filter G_B(s) obtaining the filtered inductive current, setting the voltage loop to a given valueAnd the primary voltage V of the transformer₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the series part of the UPQC_s(s) thereby playing a role in increasing the damping characteristic of the system and further realizing the stable control of the UPQC.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (8)

1. A control circuit of a unified power quality controller, characterized by comprising a control loop and a main loop, wherein the control loop (10) is connected with the main loop (20), wherein the control loop (10) comprises a band-pass filter;

inductive current I_f(s) pass through a bandpass filter G_B(s) obtaining the filtered inductive current, setting the voltage loop to a given valueAnd the primary side of the transformerPressure V₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the UPQC series part of the unified power quality controller_s(s)。

2. The control circuit of a unified power quality controller as claimed in claim 1, further comprising:

given value of voltage loopAnd feedback sampling value V₂(s) comparing to obtain an inductive current instruction value, and adjusting the inductive current instruction value through a current loop to obtain the output voltage V of the UPQC series connection part_s(s) output voltage V of said series portion of UPQCs_s(s) obtaining a load output voltage V in said main circuit (20) via a filter and a transformer₂(s) the load outputs a voltage V₂(s) is fed back into the control loop (10) as a voltage loop feedback value.

3. The control circuit of a unified power quality controller as claimed in claim 2, further comprising:

according to the load output voltage V₂(s) and said voltage loop setpointAnd obtaining a system closed loop transfer function.

4. The control circuit of claim 3 wherein said system closed loop transfer function is calculated according to the following equation:

$G_{V_2}\left(s\right)=\frac{V_2\left(s\right)}{{V_2}^{*}\left(s\right)}=\frac{(L_{l}s+r_l)({\mathrm{nk}}_v{k}_c{k}_i+{\mathrm{nk}}_i)}{a_1{s}^3+a_2{s}^2+a_{3}s+a_4}$

$G_B\left(s\right)=({\mathrm{\ω}}_0/Q)/(s^2+{\mathrm{\ω}}_{0}s/Q+{\mathrm{\ω}}_0^2)$

$\left\{\begin{array}{c}{a}_1=(L_l+n^2{L}_t)L_f{C}_f\\ a_2=(L_l+n^2{L}_t)r_f{C}_f+(r_l+n^2{r}_t)L_f{C}_f+k_c{k}_i(L_l+n^2{L}_t)L_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{L}_t{C}_f\\ a_3=(r_l+n^2{r}_t)r_f{C}_f+n^2(L_f+L_t)+(1+{\mathrm{nk}}_v{k}_c{k}_i)L_l+k_c{k}_i(r_l+n^2{r}_t)C_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{r}_t{C}_f\\ a_4=n^2{r}_t+n^2{r}_f+n^2{k}_c{k}_i+(1+{\mathrm{nk}}_v{k}_c{k}_i)r_l+G_B{k}_i{n}^2\end{array}\right.$

wherein,for the closed loop transfer function of the system, V₂(s) is the load output voltage,for setting the voltage loop to a value of L_l、r_lIs the load impedance, k_vAs a voltage loop proportional system, k_cIs the current loop proportionality coefficient, k_iFor the transformer output gain, a₁、a₂、a₃And a₄Is a parameter factor, n is the number of turns of the transformer, G_B(s) is a band-pass filter, ω₀Is the resonant frequency of the band-pass filter, Q is the quality factor, L_f、r_fIs the series filter impedance of the UPQC, C_fIs a series filter capacitor, L, of the UPQC_t、r_tIs the transformer leakage impedance.

5. A control method of a unified power quality controller comprising the control circuit of the unified power quality controller of claim 1, the method comprising:

inductive current I_f(s) pass through a bandpass filter G_B(s) obtaining a filtered inductor current;

setting the voltage ring to a given valueAnd the primary voltage V of the transformer₁(s) the difference, the inductor current loop output value and the filtered inductor current are superposed, and a gain k is output through a transformer_iObtaining the output voltage V of the UPQC series part of the unified power quality controller_s(s)。

6. The method of claim 5, further comprising:

given value of voltage loopAnd feedback sampling value V₂(s) comparing to obtain an inductive current instruction value;

adjusting the inductive current instruction value through a current loop to obtain the output voltage V of the series part of the UPQC_s(s)；

Output voltage V of the series part of the UPQC_s(s) obtaining a load output voltage V in said main loop via a filter and a transformer₂(s)；

The load output voltage V₂(s) is fed back into the control loop as a voltage loop feedback value.

7. The method of claim 6, further comprising:

according to the load output voltage V₂(s) and theVoltage loop set valueAnd obtaining a system closed loop transfer function.

8. The method of claim 7, wherein the system closed loop transfer function is calculated according to the following equation:

$G_{V_2}\left(s\right)=\frac{V_2\left(s\right)}{{V_2}^{*}\left(s\right)}=\frac{(L_{l}s+r_l)({\mathrm{nk}}_v{k}_c{k}_i+{\mathrm{nk}}_i)}{a_1{s}^3+a_2{s}^2+a_{3}s+a_4}$

$G_B\left(s\right)=({\mathrm{\ω}}_0/Q)/(s^2+{\mathrm{\ω}}_{0}s/Q+{\mathrm{\ω}}_0^2)$

$\left\{\begin{array}{c}{a}_1=(L_l+n^2{L}_t)L_f{C}_f\\ a_2=(L_l+n^2{L}_t)r_f{C}_f+(r_l+n^2{r}_t)L_f{C}_f+k_c{k}_i(L_l+n^2{L}_t)L_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{L}_t{C}_f\\ a_3=(r_l+n^2{r}_t)r_f{C}_f+n^2(L_f+L_t)+(1+{\mathrm{nk}}_v{k}_c{k}_i)L_l+k_c{k}_i(r_l+n^2{r}_t)C_f+G_B{k}_i{C}_f{r}_l+k_i{n}^2{r}_t{C}_f\\ a_4=n^2{r}_t+n^2{r}_f+n^2{k}_c{k}_i+(1+{\mathrm{nk}}_v{k}_c{k}_i)r_l+G_B{k}_i{n}^2\end{array}\right.$

wherein,for the closed loop transfer function of the system, V₂(s) is the load output voltage,for setting the voltage loop to a value of L_l、r_lIs the load impedance, k_vAs a voltage loop proportional system, k_cIs the current loop proportionality coefficient, k_iFor the transformer output gain, a₁、a₂、a₃And a₄Is a parameter factor, n is the number of turns of the transformer, G_B(s) is a band-pass filter, ω₀Is the resonant frequency of the band-pass filter, Q is the quality factor, L_f、r_fIs the series filter impedance of the UPQC, C_fIs a series filter capacitor, L, of the UPQC_t、r_tIs the transformer leakage impedance.