Control method for adaptive virtual impedance resonance suppression in grid-connected systems with parallel inverters

Abstract

This invention discloses a control method for adaptive virtual impedance resonance suppression in a grid-connected system of parallel inverters. Based on the active and reactive power output commands from the upstream system to the grid-connected inverters, the corresponding current command signal is obtained through power calculation and coordinate transformation. This current command signal is then added to the higher harmonic components of the grid-connected current, which is the equivalent series virtual impedance of each inverter, as the input signal for the current controller. This suppresses resonance caused by the coupling between the inverter output impedance and the grid line impedance. Furthermore, the method adaptively adjusts the virtual impedance value based on the line impedance from each inverter to the common coupling point, ensuring that the equivalent total impedance of each branch is equal, thereby achieving higher accuracy in active power distribution and reactive power equivalence. Additionally, a switching circulating current suppression strategy can be selected based on the inverter's DC bus power supply mode to address the zero-sequence circulating current problem in parallel inverter systems with a common DC bus and those containing DC switchgear. This invention improves the reliability and stability of inverter operation.

Description

Technical Field

[0001] This invention relates to the field of new energy power generation and microgrid technology, specifically to a control method for adaptive virtual impedance resonance suppression in a grid-connected system with a parallel inverter. Background Technology

[0002] With the introduction of the national "30·60 target," the penetration rate of distributed generation in the power system will inevitably continue to increase, which will bring new challenges to the security and stability of my country's power system. Due to the increasing prevalence of grid-connected distributed generation of new energy sources, the power grid can no longer be considered an ideal voltage source model. The increased number of long-distance transmission lines and transformer stages required for power supply in remote areas makes transformer leakage reactance non-negligible, leading to a weak grid characteristic. Under weak grid conditions, due to the coupling between parallel inverters and between the inverter and the grid, the system will experience resonance. In distributed generation systems, when multiple grid-connected inverters are connected to the same point of common coupling, harmonic interactions between inverters and between the inverter and the grid may trigger resonance, causing overvoltage and overcurrent phenomena in the system, threatening the safe and stable operation of the system, and in severe cases, leading to complete system instability. Summary of the Invention

[0003] The purpose of this invention is to provide a control method for adaptive virtual impedance resonance suppression in a grid-connected system of parallel inverters, so as to solve the resonance problem of a multi-inverter parallel system under weak grid conditions.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A control method for adaptive virtual impedance resonance suppression in a grid-connected system with parallel inverters includes:

[0006] The voltage at the common coupling point and the current into the grid of the parallel inverters are sampled respectively.

[0007] Calculate the corresponding current command based on the active power and reactive power command values ​​and the common coupling point voltage given by the superior system;

[0008] A high-pass filter is used to extract the high-frequency harmonic components of the grid-connected current as negative feedback, which is equivalent to connecting a virtual impedance in series on each inverter side.

[0009] The difference between the grid current and the calculated current command is then added to the high-frequency harmonic component of the grid current as the input of the quasi-proportional resonant (QPR) controller.

[0010] The difference between the grid-connected current and the output value of the QPR controller is obtained through the grid-connected current feedback loop and used as the modulation voltage.

[0011] Based on the line impedance from each inverter to the common coupling point, the virtual impedance value of each branch in series is adaptively adjusted to make the total impedance of each branch equal.

[0012] Furthermore, if we represent the inverter as an equivalent Thevenin circuit model, with all inverters having identical parameters, then the voltage source transfer function G(s) and output impedance Z of each inverter will be... o (s) are all the same, namely:

[0013]

[0014]

[0015] In the formula, L1, L2, and C are the inverter-side inductance, grid-connected-side inductance, and filter capacitor of the LCL filter, respectively, and K... PWM G is the transfer function from the modulated wave to the inverter-side voltage. c H(s) is the QPR controller, H(s) is the current feedback loop used to suppress the inherent resonance of LCL, and s is the differential operator.

[0016] Furthermore, the step of calculating the corresponding current command based on the active power, reactive power command values, and common coupling point voltage given by the superior system includes:

[0017] The voltage at the common coupling point u pcc After the abc / dq transformation, the voltage u at the common coupling point is obtained. pcc The component u on the dq axis d u q ;

[0018] Calculate the current command using the following formula:

[0019]

[0020] In the formula, i d i q These are the components of the current command on the dq axis, P ref Q ref These are the given active power and reactive power command values, respectively.

[0021] The current command component i on the dq axis d i q After dq / αβ transformation, the current command value in the αβ coordinate system is obtained as i. а i β .

[0022] Furthermore, the expression for the virtual impedance is:

[0023]

[0024] In the formula, Z vi Let K be the virtual impedance of the i-th inverter connected in series. vi Let K be the virtual impedance coefficient of the i-th inverter. PWM G is the transfer function from the modulated wave to the inverter-side voltage. h (s) is a high-pass filter, G c (s) is the QPR controller, s is the differential operator, and L1 and C are the inverter-side inductor and filter capacitor of the LCL filter, respectively.

[0025] Furthermore, the transfer function H(s) of the grid-connected current feedback loop is:

[0026] H(s)=K0s 2 +K1s+K2+K3s -1

[0027]

[0028] In the formula, s is the differential operator, L1, L2, and C are the inverter-side inductance, grid-connected-side inductance, and filter capacitor of the LCL filter, respectively. line Let ξ be the line impedance from the inverter to the point of common coupling, ξ be the resonant damping ratio of the filter system, ξ0 be the damping coefficient of the fundamental resonance control, ω0 be the fundamental angular frequency, ω1 be the natural resonant angular frequency of the LCL, and K be the line impedance from the inverter to the point of common coupling. PWM This is the transfer function from the modulated wave to the inverter-side voltage.

[0029] Furthermore, the step of adaptively adjusting the virtual impedance value based on the line impedance from each inverter to the common coupling point to make the total impedance of each branch equal includes:

[0030] When the inverter line impedance changes, the difference in line impedance between the two inverter branches is calculated using the following formula:

[0031] Z oi +Z vi +sL linei =Z oj +Z vj +sL linej

[0032] In the formula, Z oi Z oj Let Z be the output impedances of the i-th and j-th inverters, respectively, i ≠ j, and Z oi =Z oj Z vi Z vj L represents the virtual impedance of the i-th inverter and the j-th inverter connected in series, respectively. linei L linejLet be the line impedances from the i-th inverter to the common coupling point and the j-th inverter to the common coupling point, respectively, and s be the differential operator;

[0033] Based on the difference in line impedance between the two inverter branches, the virtual impedance coefficients of the two inverters are adjusted in real time to ensure that the difference in virtual impedance coefficients between the two inverters is proportional to the difference in line impedance, thus guaranteeing that the total impedance of each branch is always equal.

[0034] Furthermore, the difference in virtual impedance coefficients between the two inverters is directly proportional to the difference in line impedance as follows:

[0035]

[0036] In the formula, K vi K vj Let L1 and C be the virtual impedance coefficients of the i-th and j-th inverters, respectively, and let K be the inductance and capacitance of the LCL filter on the inverter side, respectively. PWM G is the transfer function from the modulated wave to the inverter-side voltage. h (s) is a high-pass filter, G c (s) is the QPR controller.

[0037] Furthermore, the control method for adaptive virtual impedance resonance suppression in a grid-connected parallel inverter system further includes: selecting different switching circulating current suppression strategies according to the DC bus power supply mode of the inverter.

[0038] Furthermore, the selection of different switching circulating current suppression strategies based on the inverter's DC bus power supply mode includes:

[0039] When the inverter is in independent power supply mode, there is no zero-sequence circulating current between inverters, and the modulation wave voltage of SVPWM modulation is not changed.

[0040] When the inverter is a common DC bus type or a type with DC switch cabinet, there is a zero-sequence circulating current between the inverters. The zero-sequence current value is obtained by adding the grid-connected three-phase currents and injecting the circulating current component obtained by the zero-sequence current value through the circulating current controller into the modulation wave voltage of SVPWM modulation.

[0041] Furthermore, the circulating current controller employs a PR regulator with a fundamental angular frequency of three harmonics, and its transfer function is:

[0042]

[0043] In the formula, K p K is the proportionality coefficient. r ω is the resonance coefficient, ω0 is the fundamental angular frequency, and s is the differential operator.

[0044] According to the above technical solution, the embodiments of the present invention have at least the following effects:

[0045] 1. The method provided by this invention can effectively suppress the harmonic resonance problem of multi-inverter parallel systems under weak power grids. At the same time, it can adaptively adjust the virtual impedance value according to the line impedance to achieve impedance matching of each line, so that the system has higher accuracy of active power distribution and reactive power distribution.

[0046] 2. The method provided by this invention further selects a switching circulating current suppression strategy based on the increased DC bus power supply mode of the inverter, which solves the zero-sequence circulating current problem of inverter systems with common DC bus and parallel structure with DC switch cabinet, broadens the applicable scenarios of this invention, and improves the reliability and stability of inverter operation. Attached Figure Description

[0047] Figure 1 This is a system structure block diagram of the parallel inverter grid-connected system control method in a specific embodiment of the present invention;

[0048] Figure 2 This is a current control block diagram in a specific embodiment of the present invention;

[0049] Figure 3 This is a flowchart of the adaptive virtual impedance adjustment process in a specific embodiment of the present invention;

[0050] Figure 4 This is a block diagram of the circulation suppression strategy in a specific embodiment of the present invention. Detailed Implementation

[0051] The present invention will be further described below with reference to specific embodiments. These embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0052] As mentioned earlier, under weak grid conditions, when multiple grid-connected inverters are connected to the same common connection point of the grid, the harmonic interactions between inverters and between inverters and the grid may cause resonance, resulting in overvoltage and overcurrent phenomena in the system, threatening the safe and stable operation of the system.

[0053] Therefore, based on the three-phase LCL type grid-connected inverter, this invention proposes a control method for adaptive virtual impedance resonance suppression in a parallel inverter grid-connected system. In this embodiment, a dual-unit inverter is used as an example for illustration.

[0054] like Figure 1 As shown, the parallel inverter grid-connected system includes two parallel inverters, an LCL filter, and a grid module. The two parallel inverters consist of Inverter 1 and Inverter 2. Each inverter is connected to its DC input at one end and to an LCL filter at the other end. The LCL filter is connected to the line impedance L.line Connected to the common coupling point PCC; virtual impedance Z v It is connected in series between the LCL filter and the line impedance; the power grid module is a weak power grid, i.e., the power grid impedance L g It cannot be ignored.

[0055] In this process, a Thevenin equivalent circuit model of the inverter is established. Assuming the parameters of the two inverters are identical, the voltage source transfer function G(s) and output impedance Z of the two inverters are then determined. o (s) are all the same, namely:

[0056]

[0057]

[0058] In the formula, L1, L2, and C are the inverter-side inductance, grid-connected-side inductance, and filter capacitor of the LCL filter, respectively, and K... PWM G is the transfer function from the modulated wave to the inverter-side voltage. c H(s) is the QPR controller, H(s) is the current feedback loop used to suppress the inherent resonance of LCL, and s is the differential operator.

[0059] Combination Figure 1 , Figure 2 As shown, a control method for adaptive virtual impedance resonance suppression in a grid-connected system with parallel inverters includes:

[0060] Step S1: Sample the voltage at the common coupling point of the parallel inverter connected to the grid and the grid current.

[0061] In each sampling period, the voltage u at the common coupling point is sampled. pcc , grid current i g The grid-connected current i g After abc / aβ transformation, the grid current i is obtained. g Component i on the aβ axis a i β .

[0062] Step S2: Calculate the corresponding current command based on the active power and reactive power command values ​​and the common coupling point voltage given by the upper-level system;

[0063] The voltage at the common coupling point u pcc After the abc / dq transformation, the voltage u at the common coupling point is obtained. pcc The component u on the dq axis d u q .

[0064] Calculate the current command using the following formula:

[0065]

[0066] In the formula, i d i q These are the components of the current command on the dq axis, P ref Q ref These are the given active power and reactive power command values, respectively. From the above equation, it can be seen that by controlling i... d To achieve active power control of the grid-connected inverter output, i is controlled. q To achieve reactive power control of the grid-connected inverter output.

[0067] The current command component i on the dq axis d i q After dq / αβ transformation, the current command component i in the αβ coordinate system is obtained. а i β .

[0068] Step S3: A high-pass filter is used to extract the high-frequency harmonic components of the grid-connected current as negative feedback, which is equivalent to connecting a virtual impedance in series on each inverter side.

[0069] A first-order high-pass filter is used to extract the high-frequency harmonic components of the current at the common coupling point PCC. аh i βh This causes significant attenuation of the low-frequency fundamental component signal. The high-frequency harmonic component i... аh i βh Adding it to the QPR current controller can effectively connect virtual impedances in series on each inverter side to discharge high-frequency harmonic currents and improve the inverter output impedance. This allows the grid impedance and the inverter's equivalent output impedance to satisfy the Nyquist stability criterion, suppressing resonance caused by weak grids.

[0070] In this embodiment, the virtual impedance expression for inverter 1 and inverter 2 connected in series is:

[0071]

[0072] In the formula, Z v1 Z is the virtual impedance connected in series with inverter 1. v2 K is the virtual impedance of inverter 2 in series. v1 K represents the virtual impedance coefficient of inverter 1. v2 K represents the virtual impedance coefficient of inverter 2. PWM G is the transfer function from the modulated wave to the inverter-side voltage. h (s) is a high-pass filter, G c (s) is the QPR controller, s is the differential operator, and L1 and C are the inverter-side inductor and filter capacitor of the LCL filter, respectively.

[0073] Step S4: Subtract the grid current from the current command calculated in step S2, and add the difference to the high-frequency harmonic components extracted in step S3 as the input of the QPR controller.

[0074] The grid-connected current i g Component i on the aβ axis a i β The components i of the current command in the αβ coordinate system are respectively а i β The difference is then divided by the high-frequency harmonic component i. аh i βh The sum is used as the input to the QPR controller.

[0075] Step S5: The difference between the grid-connected current and the output value of the QPR controller is obtained through the grid-connected current feedback loop and used as the modulation voltage;

[0076] A grid-connected current feedback control strategy is employed to suppress the resonant spikes of the LCL filter. Specifically, the grid-connected current i... g Component i on the aβ axis a i β The modulated voltage is obtained by subtracting the output value of the QPR controller from the grid-connected current feedback loop.

[0077] The transfer function H(s) of the grid-connected current feedback loop is as follows:

[0078] H(s)=K0s 2 +K1s+K2+K3s -1

[0079]

[0080] In the formula, s is the differential operator, L1, L2, and C are the inverter-side inductance, grid-connected-side inductance, and filter capacitor of the LCL filter, respectively. line Let ξ be the line impedance from the inverter to the point of common coupling, ξ be the resonant damping ratio of the filter system, ξ0 be the damping coefficient of the fundamental resonance control, ω0 be the fundamental angular frequency, ω1 be the natural resonant angular frequency of the LCL, and K be the line impedance from the inverter to the point of common coupling. PWM This is the transfer function from the modulated wave to the inverter-side voltage.

[0081] Step S6: Based on the line impedance from each inverter to the common coupling point, adaptively adjust the virtual impedance value of each branch in series so that the total impedance of each branch is equal.

[0082] Figure 3This is a flowchart of the adaptive virtual impedance adjustment in a specific embodiment of the present invention. When the inverter line impedance changes, the difference in line impedance is calculated through parameter identification, and the virtual impedance coefficient is corrected in real time to ensure that the difference in virtual admittance coefficient is proportional to the difference in line impedance, thereby ensuring that the total impedance of each branch is always equal and achieving current sharing control.

[0083] Specifically, the line impedance value L is calculated through system parameter identification. line1 L line2 If the line impedances are equal, the accuracy requirements for active power distribution and reactive power equalization are met; if the line impedances are unequal, they are not met. The line impedance is calculated using the following formula:

[0084]

[0085] In the formula, u o and u PCC These are the inverter's output voltage and the common coupling point (PCC) voltage, respectively. line Here, t represents the line impedance, and t represents time in seconds.

[0086] After connecting the virtual impedances in series, the total impedance of each branch should be equal, that is, satisfy the following relationship:

[0087] Z o1 +Z v1 +sL line1 =Z o2 +Z v2 +sL line2 (6)

[0088] In the formula, Z o1 Z o2 The output impedances of inverter 1 and inverter 2 are Z, respectively. v1 Z v2 The virtual impedances L and L in series for inverter 1 and inverter 2 are respectively. line1 L line2 Let be the line impedances from inverter 1 to the common coupling point PCC and inverter 2 to the common coupling point PCC, respectively, and s be the differential operator.

[0089] Due to the output impedance Z of inverter 1 o1 and the output impedance Z of inverter 2 o2 If they are equal, then equation (6) is transformed into:

[0090] Z v1 +sL line1 =Z v2 +sL line2 (7)

[0091] According to equation (7), when the line impedance L from inverter 1 to the common coupling point is...line1 and the line impedance L from inverter 2 to the common coupling point line2 If they are not the same, the value of the virtual impedance needs to be adjusted to ensure that the equation holds true. Substituting equation (4) into equation (7), we can obtain the formula for calculating the difference between the virtual impedance coefficients of the two branches:

[0092]

[0093] The virtual impedance coefficient is corrected in real time so that the difference between the virtual impedance coefficients of the two inverters is proportional to the difference in line impedance, ensuring that the total impedance of each branch is always equal.

[0094] In a further embodiment, the DC input terminal includes three power supply modes: independent, common DC bus, and with DC switch cabinet. Depending on the inverter's DC bus operating mode, a circulating current control strategy can be switched, increasing the system's applicability across various scenarios.

[0095] Figure 4 This is a block diagram of the circulating current suppression strategy. The three inverter power supply modes are mode1, mode2, and mode3, namely, independent type, common DC bus type, and type with DC switch cabinet.

[0096] If mode=1, the inverter is in independent power supply mode, there is no zero-sequence circulating current between inverters, and the modulation wave voltage of SPWM modulation is not changed.

[0097] If mode≠1, the inverter is either a common DC bus type or a type with a DC switch cabinet. There is a zero-sequence circulating current between the inverters. The zero-sequence current value is calculated by adding the three-phase currents. A circulating current controller is used to inject the circulating current component into SPWM modulation to adjust the duty cycle of the inverter, thereby suppressing the generation of zero-sequence circulating current.

[0098] Since the main component of the low-frequency zero-sequence circulating current is the third harmonic component, a PR regulator with ω0 as the third harmonic of the fundamental frequency can be used to suppress the zero-sequence circulating current. Its transfer function is:

[0099]

[0100] In the formula, K p K is the proportionality coefficient. r ω is the resonance coefficient, ω0 is the fundamental angular frequency, and s is the differential operator.

[0101] This invention, based on the commands from the upper-level system to the grid-connected inverters regarding active and reactive power output, calculates and transforms the power to obtain the corresponding current command signal, which is then added to the higher harmonic components of the grid-connected current (the equivalent virtual impedance of each inverter) as the input signal for the current controller. This suppresses resonance caused by the coupling between the inverter output impedance and the grid line impedance. Furthermore, it adaptively adjusts the virtual impedance value based on the line impedance from each inverter to the common coupling point, ensuring equal equivalent total impedance across all branches, thus achieving higher accuracy in active power distribution and reactive power equivalence. In addition, it can further select a switching circulating current suppression strategy based on the inverter's DC bus power supply mode to address the zero-sequence circulating current problem in parallel inverter systems with a common DC bus and those containing DC switchgear.

[0102] Therefore, this invention can effectively suppress resonance in parallel inverter grid-connected systems, improve the power distribution accuracy of the system, broaden the applicable scenarios of parallel inverters, and improve the reliability and stability of parallel inverter operation.

[0103] The present invention has been disclosed above with reference to preferred embodiments, but it is not intended to limit the present invention. All technical solutions obtained by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the present invention.

Claims

1. A control method of adaptive virtual impedance resonance suppression for a parallel inverter grid-connected system, characterized in that, The method comprises the following steps: sampling the grid-connected point voltage and the grid-connected current of the parallel inverters; calculating the corresponding current command according to the active power and reactive power command values and the grid-connected point voltage given by the upper system; extracting the high-frequency harmonic component of the grid-connected current as negative feedback by using a high-pass filter, and equivalently connecting a virtual impedance in series with each inverter; subtracting the calculated current command from the grid-connected current, and adding the difference to the high-frequency harmonic component of the grid-connected current as the input of the QPR controller; subtracting the grid-connected current through the grid-connected current feedback link from the output value of the QPR controller as the modulation voltage; adapting the virtual impedance value in series with each branch according to the line impedance from each inverter to the grid-connected point, so that the total impedance of each branch is equal; The transfer function of the grid-connected current feedback link is: ； ； where s is a differential operator, L1, L2, C are the inductance of the LCL filter on the inverter side, the inductance on the grid side, and the filter capacitance, respectively, L line is the line impedance from the inverter to the point of common coupling, ξ is the filter system resonance damping ratio, ξ0 is the damping coefficient for the fundamental resonance control, ω0 is the fundamental angular frequency, ω1 is the inherent resonance angular frequency of the LCL, K PWM is the transfer function of the modulation wave to the inverter-side voltage.

2. The control method of claim 1, wherein, The inverters are equivalent to Thevenin equivalent circuit model, and the voltage source transfer function G(s) and the output impedance Z o (s) of each inverter are the same, respectively: ； ； Wherein, L1, L2, C are respectively the inductance of the inverter side, the inductance of the grid side and the filter capacitor of the LCL filter, K PWM G(s) is the transfer function of the modulation wave to the inverter side voltage c (s) is the QPR controller, H(s) is the current feedback link for suppressing the LCL inherent resonance, and s is the differential operator.

3. The control method of claim 1, wherein, the method of calculating the corresponding current command according to the active power and reactive power command values and the grid-connected point voltage given by the upper system comprises: The common coupling point voltage u pcc After the abc / dq transformation, the common coupling point voltage u pcc The component u d , u q ; calculating the current command according to the following formula: ； where i d , i q are the components of the current command on the dq axes, respectively, P ref , Q ref are the given active power, reactive power command values, respectively. The components of the current command in the dq axis i d , The components of the current command in the dq axis i q After dq / αβ transformation, the components of the current command in the αβ coordinate system i а , The components of the current command in the dq axis i β .

4. The control method of claim 1, wherein, the expression of the virtual impedance is: ； wherein, is the virtual impedance of the i-th inverter in series, K vi is the virtual impedance coefficient of the i-th inverter, K PWM is the transfer function of the modulation wave to the inverter-side voltage, G h (s) is a high-pass filter, G c (s) is a QPR controller, s is a differential operator, L1, C are the inverter-side inductance and filter capacitance of the LCL filter, respectively.

5. The control method of claim 1, wherein, the method of adapting the virtual impedance value according to the line impedance from each inverter to the grid-connected point, so that the total impedance of each branch is equal, comprises: when the inverter line impedance changes, calculating the difference between the line impedances of the two inverter branches according to the following formula: ； wherein Z oi , Z oj are the output impedances of the i-th and j-th inverters, respectively, i≠j, and Z oi = Z oj , Z vi , Z vj are virtual impedances in series with the i-th and j-th inverters, respectively, L linei , L linej are the line impedances from the i-th and j-th inverters to the common coupling point, and s is the differential operator; according to the difference between the line impedances of the two inverter branches, real-time correcting the virtual impedance coefficients of the two inverters, so that the difference between the virtual impedance coefficients of the two inverters is proportional to the difference between the line impedances, and the total impedance of each branch is always equal.

6. The control method of claim 5, wherein, the proportional relationship between the difference between the virtual impedance coefficients of the two inverters and the difference between the line impedances is: ； wherein K vi , K vj are the virtual impedance coefficients of the i-th and j-th inverters, respectively, L1, C are the inductance and the capacitance of the LCL filter on the inverter side, K PWM is the transfer function of the modulation wave to the voltage on the inverter side, G h (s) is a high-pass filter, and G c (s) is a QPR controller.

7. The control method of claim 1, wherein, the method further comprises: selecting different circulating current suppression strategies according to the DC bus power supply mode of the inverter.

8. The control method of claim 7, wherein, the method of selecting different circulating current suppression strategies according to the DC bus power supply mode of the inverter comprises: when the inverter is in independent power supply mode, there is no zero sequence circulating current between the inverters, and the modulation voltage of the SVPWM modulation is not changed; when the inverter is in common DC bus mode and DC switch cabinet mode, there is a zero sequence circulating current between the inverters, the three-phase grid-connected currents are added to obtain a zero sequence current value, and the circulating current component obtained by the circulating current controller is injected into the modulation voltage of the SVPWM modulation.

9. The control method of claim 8, wherein, the circulating current controller uses a PR regulator with a fundamental angular frequency of three times the frequency, and its transfer function is: ； where K p is a proportionality factor, K r is a resonance factor, ω0is the fundamental angular frequency, and s is the differential operator.

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