Cascaded frequency converters and their carrier phase shift optimization methods

Abstract

This invention provides a cascaded frequency converter and its carrier phase shift optimization method. The cascaded frequency converter includes a transformer and N power units, where N is an integer greater than 1. The transformer includes a primary winding and N secondary windings, which are electrically connected to the N power units respectively. The carrier phase shift optimization method includes: (a) establishing a first objective function for the primary harmonic current of the transformer based on a mathematical model of the transformer; (b) obtaining the carrier phase shift angle function of each power unit; (c) obtaining a second objective function based on the first objective function and the carrier phase shift angle functions of all power units; and (d) determining the optimization objective, reconstructing the second objective function based on the optimization objective to obtain the optimization function, and obtaining the N carrier phase shift angles of the N power units based on the optimization function.

Description

Technical Field

[0001] This case concerns cascaded frequency converters, particularly a cascaded frequency converter and its carrier phase-shifting optimization method. Background Technology

[0002] In a frequency converter topology that includes a multi-winding transformer, the primary winding of the transformer is connected to the grid side, and the multiple secondary windings of the transformer are connected to multiple power units. Each power unit consists of an active front end (AFE), a DC bus, and an inverter unit. When the active front end of the power unit starts up, it generates a large number of switching harmonics, which are directly injected into the transformer and then coupled to the grid side, causing the grid-side harmonics to fail to meet IEEE 519 requirements.

[0003] To eliminate switching subharmonics, existing technologies mostly employ carrier phase-shifting schemes. The first existing scheme involves carrier phase shifting of N power units in any output phase, where the carrier phase shift angles of these N power units are 0, 180 / N, ..., 180*(N-1) / N degrees, respectively. The second existing scheme divides all power units into M groups and performs carrier phase shifting on each group, where the carrier phase shift angles of these M groups of power units are 0, 360 / M, ..., 360*(M-1) / M degrees, respectively.

[0004] However, when the aforementioned existing solutions are applied to the carrier phase shift on the cascade side, they can cancel the harmonics between power units. But when applied to the carrier phase shift on the transformer side such as frequency converters, the influence of the transformer coupling parameters on the carrier phase shift is not considered. Therefore, its phase shift effect is limited and it is difficult to completely cancel the switching subharmonics.

[0005] Therefore, developing a cascaded frequency converter and its carrier phase-shifting optimization method that can improve upon the existing technologies is an urgent need at present. Summary of the Invention

[0006] The purpose of this invention is to provide a cascaded frequency converter and its carrier phase shift optimization method. This method incorporates the transformer's coupling parameters into the process of obtaining the carrier phase shift angle of each power unit in the cascaded frequency converter, and obtains the corresponding carrier phase shift angle based on the desired optimization objective. Therefore, this invention optimizes the primary harmonic current of the transformer without increasing system cost, effectively improving grid-connected current and enhancing system performance.

[0007] To achieve the above objectives, this invention provides a carrier phase shift optimization method applicable to cascaded frequency converters. The cascaded frequency converter includes a transformer and N power units, where N is an integer greater than 1. The transformer includes a primary winding and N secondary windings, which are electrically connected to the N power units respectively. The carrier phase shift optimization method includes: (a) establishing a first objective function for the primary harmonic current of the transformer based on a mathematical model of the transformer; (b) obtaining the carrier phase shift angle function for each power unit; (c) obtaining a second objective function based on the first objective function and the carrier phase shift angle functions of all power units; and (d) determining the optimization objective, reconstructing the second objective function based on the optimization objective to obtain the optimization function, and obtaining the N carrier phase shift angles of the N power units based on the optimization function.

[0008] To achieve the above objectives, this invention also provides a cascaded frequency converter. The cascaded frequency converter includes a transformer, N power units, and a carrier phase-shift controller, where N is an integer greater than 1. The transformer includes a primary winding and N secondary windings, which are electrically connected to the N power units respectively. The carrier phase-shift controller is structured as follows: (a) establishing a first objective function for the primary harmonic current of the transformer based on a mathematical model of the transformer; (b) obtaining the carrier phase-shift angle function for each power unit; (c) obtaining a second objective function based on the first objective function and the carrier phase-shift angle functions of all power units; and (d) determining an optimization objective, reconstructing the second objective function based on the optimization objective to obtain an optimization function, and obtaining the N carrier phase-shift angles of the N power units based on the optimization function. Attached Figure Description

[0009] Figure 1 This is a schematic diagram of the architecture of a cascaded frequency converter, which is a preferred embodiment of this case.

[0010] Figure 2A An example of a cascaded frequency converter circuit structure is shown.

[0011] Figure 2B exemplify Figure 2A The circuit structure of a power unit in a cascaded frequency converter.

[0012] Figure 2C exemplify Figure 2A Another power unit circuit structure in a cascaded frequency converter.

[0013] Figure 3A Another circuit structure for a cascaded frequency converter is shown.

[0014] Figure 3B exemplify Figure 3A The circuit structure of a power unit in a cascaded frequency converter.

[0015] Figure 3C exemplify Figure 3A Another power unit circuit structure in a cascaded frequency converter.

[0016] The reference numerals in the attached figures are explained as follows:

[0017] 1: Cascaded frequency converters

[0018] 11: Transformer

[0019] 111: Primary winding

[0020] 112: Secondary winding

[0021] 12: Power Unit

[0022] 13: Carrier Phase Shift Controller

[0023] 14: Filter

[0024] 2: Power Grid

[0025] 3: Load

[0026] U0: Primary harmonic voltage

[0027] U1, U2, U N Secondary harmonic voltage

[0028] i0: Primary harmonic current

[0029] i1, i2, i N Secondary harmonic current

[0030] L0, L1, L N : Self-awareness

[0031] M 01 M 0N M 10 M 1N M N0 M N1 Mutual induction

[0032] A: Mutual inductance matrix

[0033] A -1 Inverse matrix

[0034] θ1, θ2, θ n Carrier phase shift angle

[0035] h: Switching harmonic multiple

[0036] A h Harmonic amplitude

[0037] ω c Carrier angular frequency

[0038] k, k1, k2: Phase shift coefficients

[0039] angle

[0040] p f Fundamental current amplitude parameters

[0041] λ1, λ2, λ z AC resistance parameters Detailed Implementation

[0042] Some typical embodiments that embody the features and advantages of this invention will be described in detail in the following description. It should be understood that this invention can have various variations in different forms, all of which do not depart from the scope of this invention, and the descriptions and illustrations therein are for illustrative purposes only and not intended to limit this invention.

[0043] Figure 1 This is a schematic diagram of the architecture of a cascaded frequency converter according to a preferred embodiment of this invention. Figure 1 As shown, the cascaded frequency converter 1 of this invention is coupled between the power grid 2 and the load 3, and includes a transformer 11, N power units 12, and a carrier phase shift controller 13, where N is an integer greater than 1. The transformer 11 includes a primary winding 111 and N secondary windings 112. The primary winding 111 is electrically connected to the power grid 2, and the N secondary windings 112 are respectively electrically connected to the N power units 12, that is, the first to Nth secondary windings 112 are respectively electrically connected to the first to Nth power units 12. The active front end in the power unit 12 is controlled by a pulse width modulation signal. The carrier phase shift controller 13 is configured to acquire the carrier phase shift angle of the pulse width modulation signal of the N power units 12. In some embodiments, the secondary windings 112 are directly connected to the corresponding power units 12. In other embodiments, the cascaded inverter 1 further includes N filters 14, each filter 14 being electrically connected between the corresponding secondary winding 112 and the power unit 12, wherein the filter 14 may be, for example, but not limited to, an inductor filter.

[0044] The secondary winding 112 can be a single-phase or multi-phase structure, and correspondingly, the power unit 12 can be a single-phase or multi-phase structure. Furthermore, the power unit 12 can be a two-level (such as a single-phase bridge, three-phase bridge topology, etc.) or multi-level structure, and can be a rectifier topology or a back-to-back topology. Moreover, the output terminals of the N power units 12 can be connected in series, parallel, or cascade.

[0045] Figure 2A An example of a cascaded frequency converter circuit structure is shown, wherein the secondary winding 112 is a three-phase structure. Figure 2B exemplify Figure 2A The circuit structure of a power unit in a cascaded frequency converter, wherein power unit 12 is a three-phase two-level structure. Figure 2C exemplify Figure 2AAnother circuit structure of the power unit of the cascaded frequency converter, wherein the power unit 12 is a three-phase three-level structure including clamping diodes. Figure 3A Another circuit structure of a cascaded frequency converter is shown, in which the secondary winding 112 is a single-phase structure. Figure 3B exemplify Figure 3A The circuit structure of a power unit in a cascaded frequency converter, wherein the power unit 12 is a single-phase three-level structure including clamping diodes. Figure 3C exemplify Figure 3A Another circuit structure for the power unit of the cascaded frequency converter, where power unit 12 is a single-phase two-level structure. Of course, Figures 2A to 3C The circuit topology shown is for illustrative purposes only and is not intended to be limited to this case.

[0046] The carrier phase shift optimization method applicable to cascaded frequency converters will be described in detail below, and the carrier phase shift optimization method is executed by the carrier phase shift controller 13 of the cascaded frequency converter 1.

[0047] Please see Figure 1 . Figure 1 The mathematical model of the transformer 11 shown is as follows:

[0048]

[0049]

[0050]

[0051]

[0052] Where U0 is the primary harmonic voltage of transformer 11, and U1, U2, ..., U... N Let i1, i2, ..., i3 be the secondary harmonic voltages of the transformer 11 corresponding to the 1st to Nth power units 12, i0 be the primary harmonic currents of the transformer 11, and i1, i2, ..., i3 be the secondary harmonic voltages of the transformer 11. N These represent the secondary harmonic currents of the transformer 11 corresponding to the 1st to Nth power units 12, respectively; L0 is the self-inductance of the primary winding 111; and L1, ..., L2 are the secondary harmonic currents of the transformer 11. N These represent the self-inductance of the first to Nth secondary windings 112, respectively. 0x M x0 M represents the mutual inductance between the primary winding 111 and the x-th secondary winding 112, where x is an integer between 1 and N. ab Let be the mutual inductance between the a-th secondary winding 112 and the b-th secondary winding 112, where a and b are integers between 1 and N, and a and b are not equal.

[0053] From equation (1), the matrix form of the mathematical model of transformer 11 can be obtained:

[0054]

[0055] Among them, U=[U0 U1 U2...U N ] T A is the mutual inductance matrix of transformer 11.

[0056]

[0057] The state equations of the mathematical model can then be obtained:

[0058]

[0059] Among them, A -1 Let be the inverse of matrix A.

[0060] The secondary harmonic voltage generated by power unit 12 can be expressed as:

[0061]

[0062] Where n is a positive integer less than or equal to N, θ n Let A be the carrier phase shift angle of the nth power unit 12, h be the switching subharmonic multiple, and A be the carrier phase shift angle of the nth power unit 12. h Let ω be the harmonic amplitude when the switching harmonic multiple is h. c This is the carrier angular frequency.

[0063] Based on the mathematical model of transformer 11 described above, a first objective function for the primary harmonic current i0 of transformer 11 can be established. The following examples illustrate two methods for determining the first objective function.

[0064] In the first method, since U0 is the primary harmonic voltage of transformer 11, the switching subharmonic voltage in U0 can be ignored, and the target equation for optimizing the primary harmonic current i0 can be derived from equation (3):

[0065]

[0066] in, For A -1 The parameters in the equation. By transforming equation (5), the first objective function can be determined as:

[0067]

[0068] The first objective function only considers the influence of a certain harmonic h for now. The influence of other harmonics will be considered later. Substituting equation (4) into equation (6) yields the change shape of the first objective function:

[0069]

[0070] In the second approach, since the primary side of transformer 11 is connected to power grid 2, the switching subharmonics in the primary harmonic voltage U0 can be considered as being caused by the secondary harmonic voltage coupled to the primary side. Therefore, the optimization of the primary harmonic current i0 can be converted into the optimization of the primary harmonic voltage U0. The target equation for optimizing the primary harmonic voltage U0 can be derived from equation (3):

[0071]

[0072] Neglecting the influence of the primary harmonic current i0, equation (8) can be further transformed into:

[0073]

[0074] Substituting equation (3) into equation (9), the first objective function can be determined as:

[0075] F(U)=m sum1 ·U1+m sum2 ·U2+...+m sumN ·U N (10)

[0076] Where, m sum1 m sum2 ... m sumN The constants related to the mutual inductance parameters of transformer 11 are U1, U2, ..., U... N The coefficients, whose actual values ​​can be calculated from equations (3) and (9), will not be shown here. The first objective function only considers the influence of a certain harmonic h for now. The influence of other harmonics will be considered later. Substituting equation (4) into equation (10) yields the change shape of the first objective function:

[0077]

[0078] The first objective function can be determined through the two methods described above, and the corresponding carrier phase shift angles θ1, θ2, ..., θ3 can be obtained by optimizing equations (7) or (11). N However, since the first objective function is an N-dimensional function, the optimization equation becomes more complex when considering multiple switching subharmonics (i.e., considering multiple different values ​​of h) and the number of power units 12 is large (i.e., N is relatively large). Therefore, it is possible to establish carrier phase shift angles θ1, θ2, ..., θ... N The relationships between these relationships are used to reduce the dimensionality of the first objective function, thereby reducing optimization complexity and facilitating the optimization of the carrier phase shift angle. The following explains how to establish the carrier phase shift angles θ1, θ2, ..., θ... N The relationship between them reduces the dimensionality of the first objective function.

[0079] In this design, the N carrier phase shift angles of the N power units can be divided into M phase shift groups, each containing at least one carrier phase shift angle, where M is a positive integer less than or equal to N. The number of carrier phase shift angles contained in different phase shift groups can be equal or unequal, and this design does not impose any restrictions. There is a specific relationship function between the carrier phase shift angles within the same phase shift group, and a specific relationship function exists between the M phase shift groups. For example, the N carrier phase shift angles can be divided into three phase shift groups, i.e., M = 3. The relationship function between the carrier phase shift angles in the first phase shift group is g1(k1,j), the relationship function between the carrier phase shift angles in the second phase shift group is g2(k1,j), and the relationship function between the carrier phase shift angles in the third phase shift group is g3(k1,j), where k1 is the first phase shift coefficient. The relationship function between the carrier phase shift angles of the three phase shift groups is f(k2,i), where k2 is the second phase shift coefficient, and the first phase shift coefficient k1 and the second phase shift coefficient k2 can be equal or unequal. j represents the j-th power unit within each phase shift group, where j is a positive integer less than or equal to N / M; i represents the i-th phase shift group among the M phase shift groups, where i is a positive integer less than or equal to M. In some embodiments, the N carrier phase shift angles can be divided into three phase shift groups, i.e., M = 3. The phase shift angles of the carriers in the first phase shift group are a1, those in the second phase shift group are a2, and those in the third phase shift group are a3. The relationship function between the carrier phase shift angles of the three phase shift groups can be f(k2,i). Furthermore, a1, a2, and a3 can be equal or unequal.

[0080] For ease of understanding, we will take k1=k2=k as an example below, and here we assume M=N and the carrier phase shift function (i.e., the relationship function between phase shift groups) is... Let's take θ as an example. i Let be the carrier phase shift angle in the i-th phase shift group, k be the phase shift coefficient, i be a positive integer less than or equal to M, and α be a constant. Substituting the carrier phase shift function into the first objective function (equation (7) or (11)) yields the second objective function, which is:

[0081]

[0082] in, To incorporate the angles generated by trigonometric functions when substituting the carrier phase shift function into the first objective function, p(h,k) is the amplitude function. The second objective function is a one-dimensional function of k. It should be noted that substituting the carrier phase shift function into different first objective functions will result in different expressions for the second objective function. Formula (12) is a simplified illustration of the second objective function.

[0083] Therefore, the optimization problem for the first objective function, which is an N-dimensional function, can be transformed into the optimization problem for the second objective function, which is a one-dimensional function. Furthermore, according to equation (12), the optimization problem for the second objective function can be transformed into the optimization problem for the magnitude function p(h,k).

[0084] Correspondingly, after determining the required optimization objective, the second objective function can be reconstructed based on the optimization objective to obtain the optimization function, and the optimal value of the phase shift coefficient k in the optimization function can be calculated. The optimal value of the phase shift coefficient k is then substituted into the carrier phase shift function to obtain the carrier phase shift angle of all power units 12. The optimization objective may be, for example, to make the switching subharmonics of a certain multiple meet the preset requirements, to minimize the harmonic loss of the primary winding 111 of the transformer 11, or to minimize the total harmonic distortion of the primary harmonics of the transformer 11, but it is not limited to these.

[0085] For example, in some embodiments, the optimization objective is to make the switching subharmonics of a specific multiple meet a preset requirement, and the corresponding optimization function may be, for example:

[0086]

[0087] Where, p f denoted as the fundamental current amplitude parameter, z is the preset maximum multiple of the switching subharmonic, and C is a constant.

[0088] In other embodiments, the optimization objective is to minimize the harmonic losses of the primary winding 111 of transformer 11, and the corresponding optimization function may be, for example:

[0089] p(k)=λ1·p(1,k) 2 +λ2·p(2,k) 2 +…+λ z ·p(z,k) 2 (14)

[0090] Where λ1, λ2, ..., λ z These are the AC resistance parameters at the corresponding switching frequency.

[0091] In some other embodiments, the optimization objective is to minimize the total harmonic distortion of the primary harmonics of transformer 11, and the corresponding optimization function may be, for example:

[0092]

[0093] Furthermore, different optimization k values ​​will be calculated based on the optimization function formulas (13), (14), or (15), and these k values ​​will be substituted into θ. i The phase shift angle of each carrier can be calculated from the formula.

[0094] In summary, this invention provides a cascaded frequency converter and its carrier phase shift optimization method. In obtaining the carrier phase shift angle of each power unit in the cascaded frequency converter, the coupling parameters of the transformer are taken into consideration, and the corresponding carrier phase shift angle is obtained according to the desired optimization objective. Therefore, this invention optimizes the primary harmonic current of the transformer without increasing system cost, effectively improving grid-connected current and enhancing system performance.

[0095] It should be noted that the above are merely preferred embodiments for illustrating this case, and this case is not limited to the described embodiments. The scope of this case is determined by the appended claims. Furthermore, this case may be modified in various ways by those skilled in the art, but all such modifications shall not depart from the protection sought by the appended claims.

Claims

1. A carrier phase-shift optimization method applicable to cascaded frequency converters, wherein the cascaded frequency converter includes a transformer and N power units, where N is an integer greater than 1, the transformer includes a primary winding and N secondary windings, the N secondary windings being electrically connected to the N power units respectively, and the carrier phase-shift optimization method includes: (a) Based on the mathematical model of the transformer, establish a first objective function for the primary harmonic current of the transformer, wherein the mathematical model is: ， in U0 is the primary harmonic voltage of the transformer, and U1, U2, ..., U... N These represent the secondary harmonic voltages of the transformer corresponding to the 1st to Nth power units, respectively, and A is the mutual inductance matrix of the transformer. i0 is the primary harmonic current, i1, i2, ..., i N These are the secondary harmonic currents of the transformer corresponding to the 1st to Nth power units, respectively; (b) Obtain the carrier phase shift function for each power unit; (c) Obtain a second objective function based on the first objective function and the carrier phase shift function of all the power units; and (d) Determine the optimization objective, reconstruct the second objective function based on the optimization objective to obtain the optimization function, and obtain the N carrier phase shift angles of the N power units according to the optimization function. The N power units are divided into M phase shift angles of the carriers, each phase shift group contains at least one carrier phase shift angle, and there is a specific relationship function between the carrier phase shift angles in the same phase shift group, and there is a specific relationship function between the M phase shift groups. Where M=N, the carrier phase shift function is: θ i Let k be the phase shift angle of the carrier in the i-th phase shift group, k be the phase shift coefficient, and i be a positive integer less than or equal to M. α It is a constant.

2. The carrier phase shift optimization method as described in claim 1, wherein the first objective function determined according to the mathematical model is: ， in , … For A -1 The parameter A -1 Let A be the inverse matrix. n is a positive integer less than or equal to N, h is the switching harmonic multiple, and A h Let ω be the harmonic amplitude when the harmonic multiple of the switch is h. c Let θ be the carrier angular frequency. n This is the carrier phase shift angle of the nth power unit.

3. The carrier phase shift optimization method as described in claim 1, wherein the first objective function determined according to the mathematical model is: ， Where m sum1 m sum2 ... m sumN These are constants related to the mutual inductance parameters of the transformer. n is a positive integer less than or equal to N, h is the switching harmonic multiple, and A h Let ω be the harmonic amplitude when the harmonic multiple of the switch is h. c Let θ be the carrier angular frequency. n This is the carrier phase shift angle of the nth power unit.

4. The carrier phase shift optimization method as described in claim 2 or 3, wherein the first objective function is an N-dimensional function and the second objective function is a one-dimensional function with respect to k.

5. The carrier phase shift optimization method as described in claim 4, wherein, Substituting the carrier phase shift function into the first objective function yields the second objective function, which is: ， in To combine the angles generated by the trigonometric functions when substituting the carrier phase shift function into the first objective function, p(h, k) is the amplitude function.

6. The carrier phase shift optimization method as described in claim 5, wherein the optimization objective is to make the switching subharmonics of a certain multiple meet the preset requirements, to minimize the harmonic loss of the primary winding of the transformer, or to minimize the total harmonic distortion of the primary harmonics of the transformer.

7. The carrier phase shift optimization method as described in claim 6, wherein, The optimization function is determined based on the optimization objective and the amplitude function, and the optimal value of the phase shift coefficient in the optimization function is calculated. The optimal value of the phase shift coefficient is then substituted into the carrier phase shift function to obtain the N carrier phase shift angles of the N power units.

8. A cascaded frequency converter, comprising a transformer, N power units, and a carrier phase-shift controller, wherein N is an integer greater than 1, the transformer comprising a primary winding and N secondary windings, the N secondary windings being electrically connected to the N power units respectively, and the carrier phase-shift controller being configured as follows: (a) Based on the mathematical model of the transformer, establish a first objective function for the primary harmonic current of the transformer, wherein the mathematical model is: ， in U0 is the primary harmonic voltage of the transformer, and U1, U2, ..., U... N These represent the secondary harmonic voltages of the transformer corresponding to the 1st to Nth power units, respectively, and A is the mutual inductance matrix of the transformer. i0 is the primary harmonic current, i1, i2, ..., i N These are the secondary harmonic currents of the transformer corresponding to the 1st to Nth power units, respectively; (b) Obtain the carrier phase shift function for each power unit; (c) Obtain a second objective function based on the first objective function and the carrier phase shift function of all the power units; and (d) Determine the optimization objective, reconstruct the second objective function based on the optimization objective to obtain the optimization function, and obtain the N carrier phase shift angles of the N power units according to the optimization function. The N power units are divided into M phase shift angles of the carriers, each phase shift group contains at least one carrier phase shift angle, and there is a specific relationship function between the carrier phase shift angles in the same phase shift group, and there is a specific relationship function between the M phase shift groups. Where M=N, the carrier phase shift function is: θ i Let k be the phase shift angle of the carrier in the i-th phase shift group, k be the phase shift coefficient, and i be a positive integer less than or equal to M. α It is a constant.

9. The cascaded frequency converter as described in claim 8, wherein the first objective function determined according to the mathematical model is: ， in , … For A -1 The parameter A -1 Let A be the inverse matrix. n is a positive integer less than or equal to N, h is the switching harmonic multiple, and A h Let ω be the harmonic amplitude when the harmonic multiple of the switch is h. c Let θ be the carrier angular frequency. n This is the carrier phase shift angle of the nth power unit.

10. The cascaded frequency converter as described in claim 8, wherein the first objective function determined according to the mathematical model is: ， Where m sum1 m sum2 ... m sumN These are constants related to the mutual inductance parameters of the transformer. n is a positive integer less than or equal to N, h is the switching harmonic multiple, and A h Let ω be the harmonic amplitude when the harmonic multiple of the switch is h. c Let θ be the carrier angular frequency. n This is the carrier phase shift angle of the nth power unit.

11. The cascaded frequency converter as described in claim 9 or 10, wherein the first objective function is an N-dimensional function and the second objective function is a one-dimensional function about k.

12. The cascaded frequency converter as described in claim 11, wherein, Substituting the carrier phase shift function into the first objective function yields the second objective function, which is: ， in To combine the angles generated by the trigonometric functions when substituting the carrier phase shift function into the first objective function, p(h, k) is the amplitude function.

13. The cascaded frequency converter as described in claim 12, wherein the optimization objective is to make the switching subharmonics meet the preset requirements, to minimize the harmonic loss of the primary winding of the transformer, or to minimize the total harmonic distortion of the primary harmonics of the transformer.

14. The cascaded frequency converter as described in claim 13, wherein, The optimization function is determined based on the optimization objective and the amplitude function, and the optimal value of the phase shift coefficient in the optimization function is calculated. The optimal value of the phase shift coefficient is then substituted into the carrier phase shift function to obtain the N carrier phase shift angles of the N power units.

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