A Phase Compensation Method for Multi-quasi-resonant Controller

Abstract

The present invention provides a phase compensation method for a multi-quasi-resonant controller, which relates to the technical field of new energy power electronic equipment, including: determining the control object of the multi-quasi-resonant controller, establishing a control system, and establishing a mathematical model of the control object; determining the system error transfer function and system characteristic equation of the control system, performing system stability analysis on the control system, and determining the system stability conditions; designing the proportional term and phase compensation part of the multi-quasi-resonant controller so that the proportional term and the phase compensation part meet the system stability conditions; designing the resonance bandwidth and resonance term gain of the multi-quasi-resonant controller according to the system stability conditions; and performing phase compensation on the multi-quasi-resonant controller through the proportional term, phase compensation part, resonance bandwidth and resonance term gain. The present invention simplifies the design process, reduces the amount of calculation, improves the control performance and applicability, and solves the problems of complex design, high amount of calculation and insufficient control performance in the design of traditional control systems.

Description

Technical Field

[0001] The present invention relates to the technical field of new energy power electronic equipment, and in particular to a phase compensation method for a multi-quasi-resonance controller. Background Art

[0002] In the field of renewable energy, especially in wind and solar power generation systems, the inverter is one of the key core components. The inverter converts direct current into alternating current, ensuring that the renewable energy system can be connected to the power grid and operate stably. However, as the complexity and scale of renewable energy power generation systems continue to increase, the inverter control system is also facing more and more challenges.

[0003] Multi-quasi-resonant controller (MQRSC) can be considered as a "generalized integrator" of multiple sinusoidal signals, which can achieve zero-error tracking of sinusoidal periodic signals and suppression of specific sub-sinusoidal harmonic interference, and is widely used in voltage or current output control in renewable energy power generation systems. Proportional multi-quasi-resonant controller (PMQRSC) achieves tracking of reference signals and suppression of periodic interference signals by connecting multiple resonant controllers in parallel, and is widely used in renewable energy power electronic equipment.

[0004] However, when designing control parameters, achieving excellent harmonic suppression performance means that a large number of quasi-resonant terms need to be connected in parallel, and high-order resonant terms will introduce large phase lags, which will lead to system instability. Specifically, the traditional method needs to calculate the phase compensation angle for each resonant controller. As the number of resonant controllers increases, the design process becomes complicated and time-consuming. On the other hand, the traditional PMQRSC needs to consider the coupling of control parameters during design, which involves a large number of repeated calculations, increasing the difficulty of design and development. In addition, the traditional control method has insufficient performance when dealing with complex and frequently changing loads. Summary of the invention

[0005] In view of this, an embodiment of the present application provides a phase compensation method for a multi-quasi-resonant controller, which aims to simplify the design process, reduce the amount of calculation, and at the same time improve the control performance, improve the performance and applicability of the control system, and solve the problems of design complexity, high calculation amount and insufficient control performance encountered in the design process of traditional new energy power generation inverter control systems.

[0006] The embodiment of the present application provides the following technical solution: a phase compensation method of a multi-quasi-resonant controller, comprising:

[0007] Determine a control object of a multi-quasi-resonant controller, and establish a control system between the multi-quasi-resonant controller and the control object;

[0008] Establishing a mathematical model of the control object, determining a system error transfer function and a system characteristic equation of the control system according to the mathematical model, and performing a system stability analysis on the control system in combination with the system error transfer function and the system characteristic equation to determine a system stability condition;

[0009] The proportional term of the proportional controller of the multi-quasi-resonant controller Design the phase compensation part of the multi-quasi-resonant controller Design so that the proportional term and the phase compensation section respectively satisfying the system stability conditions;

[0010] According to the system stability condition, the equivalent resonant bandwidth in the system stable state is taken as the target bandwidth, and the target bandwidth control coefficient is calculated according to the target bandwidth. The resonant bandwidth of the multi-quasi-resonant controller is controlled by the target bandwidth control coefficient. is the target bandwidth;

[0011] The resonant term gain of the multi-quasi-resonant controller Design and determine the resonant gain under the condition that the system stability condition is met ;

[0012] The proportional term obtained by , the phase compensation part , the resonance bandwidth and the resonant gain , phase compensation is performed on the multi-quasi-resonant controller.

[0013] According to an embodiment of the present application, establishing a mathematical model of the control object includes:

[0014] According to the system structure of the controlled object, the transfer function and system parameters of the controlled object are determined, and the system parameters are substituted into the transfer function to obtain the discrete transfer function of the controlled object.

[0015] According to an embodiment of the present application, the control object is any one of a single-phase grid-connected inverter, an active filter and a constant voltage and constant frequency inverter.

[0016] According to an embodiment of the present application, the system stability condition includes:

[0017] make The extreme point is zInside the unit circle of the plane, Maintain zero gain within the system bandwidth; where, is the proportional term, is the discrete transfer function of the controlled object;

[0018] make The extreme point is z The control object satisfies the zero gain phase shift characteristic within the unit circle of the plane; wherein, is the discrete expression of phase compensation of multi-quasi-resonant controller, is the phase frequency of the phase compensation part, and , L is the compensation factor.

[0019] According to an embodiment of the present application, the resonance bandwidth of the multi-quasi-resonant controller is for: ; The grid frequency deviation of the control object.

[0020] According to an embodiment of the present application, the resonance term gain of the multi-quasi-resonant controller Design and determine the resonant gain under the condition that the system stability condition is met ,include:

[0021] According to the pole analysis method, The extreme point is z The resonant gain value when the plane is within the unit circle is the resonant gain .

[0022] According to an embodiment of the present application, the resonance term gain of the multi-quasi-resonant controller Design also includes:

[0023] According to the harmonic components of the control object, the resonance term and the resonance order of the resonance term of the multi-quasi-resonance controller are determined to adjust the resonance term gain of the multi-quasi-resonance controller. Make a design.

[0024] According to an embodiment of the present application, the method further includes: establishing a simulation model, measuring the output waveform and current of the control object under different grid frequencies, and performing performance verification on the control system after phase compensation.

[0025] The present invention proposes a novel MQRSC phase compensation method. Based on the mathematical equivalent relationship between repetitive control (RC) and quasi-resonant control, this method introduces the repetitive control phase advance compensation design method into MQRSC. Compared with the traditional phase compensation method, there is no need to calculate the compensation angle of each resonant term, which simplifies the design complexity, avoids the shortcoming of inaccurate actual compensation caused by the discreteness of the quasi-resonant controller after phase compensation, and reduces the amount of calculation in the design process, while having good control performance. This method provides a complete controller parameter design scheme for multi-quasi-proportional resonant control, and verifies the effectiveness of PMQRSC based on the new phase compensation method based on a single-phase grid-connected inverter simulation experimental platform.

[0026] The specific advantages are as follows:

[0027] 1. Simplify the design process: By adopting a new phase compensation technology, the complex phase compensation calculation in traditional design is omitted, which significantly simplifies the design process of PMQRSC and reduces the design complexity.

[0028] 2. Reduce the amount of calculation: This method avoids a large number of repeated calculations in traditional design, reduces the amount of calculation in the design process, and improves design efficiency.

[0029] 3. Improve control performance: The new phase compensation technology can provide excellent control performance while simplifying the design, ensuring stable and efficient operation of the system.

[0030] In summary, the present invention solves the complex problem of phase compensation calculation in traditional PMQRSC design by introducing a new phase compensation technology, making the design of new energy power generation inverter control system simpler and more efficient, which not only reduces the design complexity and calculation amount, but also improves the performance and applicability of the control system. It has important application value and promotion prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0032] Figure 1 A flow chart for designing a proportional multi-quasi-resonant controller based on a phase compensation method according to an embodiment of the present invention;

[0033] Figure 2 A control structure diagram of a single-phase grid-connected inverter in an embodiment of the present invention;

[0034] Figure 3 is a control block diagram of a grid-connected inverter in an embodiment of the present invention;

[0035] Figure 4 It is a PMQRSC system control structure diagram in an embodiment of the present invention;

[0036] Figure 5 In the embodiment of the present invention When taking different values The pole distribution map of

[0037] Figure 6 In the embodiment of the present invention When taking different values Amplitude-frequency response curve;

[0038] Figure 7 is the compensation factor in the embodiment of the present invention L When taking different values Phase-frequency response curve of

[0039] Figure 8 K in the embodiment of the present invention n When the value is 400 The pole distribution map of

[0040] FIG9 (a) and FIG9 (b) are respectively the inverter output waveform and the grid-connected current THD when the grid frequency is 50 Hz in the PMQRSC system according to an embodiment of the present invention;

[0041] FIG. 10 (a) and FIG. 10 (b) are respectively the inverter output waveform and the grid-connected current THD when the grid frequency is 50.4 Hz under the PMQRSC system in an embodiment of the present invention;

[0042] FIG. 11( a ) and FIG. 11( b ) respectively show the inverter output waveform and the grid-connected current THD when the grid frequency is 49.6 Hz in the PMQRSC system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0044] The following describes the implementation methods of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.

[0045] In the field of power electronics systems, the internal model principle is to embed the dynamic model of the reference signal or external interference signal into the controller so that the system can track the input or suppress the interference without static error. For example, the proportional-integral controller contains the dynamic model of the step signal 1 / s, so it can achieve zero-error tracking of the step signal. However, the equipment of the new energy power generation system needs to process the periodic signal.

[0046] Proportional resonant control can accurately track periodic signals of specific frequencies by building a model of a single sinusoidal periodic signal. In practical applications, periodic interference signals often appear periodic and produce harmonic interference to the output. Proportional multi-resonant controllers track reference signals and suppress periodic interference signals by connecting multiple resonant controllers in parallel. They are widely used in new energy power electronic devices, such as active filters, grid-connected inverters, and constant voltage and frequency inverters. In order to improve the adaptability to changes in the frequency of periodic signals, PMQRSC with resonant bandwidth has become a general form of proportional multi-resonant control, and its expression is as follows (1):

[0047] (1)

[0048] In the formula, is a proportional term; is the gain of each resonant term; is the resonant angular frequency; is the resonant bandwidth. It can be seen that PMQRSC has many parameters, and its design becomes more complicated as the number of resonances increases. Currently, it mainly relies on graphical methods such as the system open-loop Bode plot and root locus to design according to stability and steady-state error requirements. Due to the coupling of controller parameters, a large number of repeated calculations are required. Although more resonant terms mean better harmonic interference suppression, the parallel resonant terms will introduce phase delay, which may cause system instability. At this time, phase compensation needs to be introduced. The traditional phase compensation method is to introduce a phase compensation angle at the resonant frequency, and its expression is as follows (2):

[0049] (2)

[0050] In the formula, is the phase compensation angle. In traditional phase compensation design, Each resonance can be designed and selected through its Nyquist curve or Bode diagram, which will undoubtedly increase the difficulty of design. In addition, when applied in actual digital control systems, PMQRSC needs to be discretized. However, the discrete method will affect the phase compensation accuracy of PMQRSC, which will cause the actual compensation angle to be inconsistent with the designed compensation angle, and the system control performance will not meet expectations or even be unstable. For formula (2), the pre-corrected bilinear transformation method has higher accuracy when discretizing the resonant controller, so the pre-corrected bilinear transformation method is generally used for discretization, and its discretized expression is as follows (3):

[0051] (3)

[0052] In the formula is the sampling time, and the coefficient expressions are as follows:

[0053] (4)

[0054] It can be seen that the discretized PMQRSC expression is more complicated, and the expression coefficients are related to the phase compensation angle, which means that the phase compensation accuracy will also be affected by the discretization method.

[0055] Repetitive control (RC) includes the mathematical model of periodic signals and can play an integral role on any periodic signal, so it can achieve error-free tracking of the reference fundamental signal and suppression of harmonic interference signals. According to the Laplace transform, the mathematical model of the periodic signal can be expressed as the following formula (5):

[0056] (5)

[0057] In the formula, is the period time of the periodic signal, and Q is the internal model coefficient of RC. Obviously, compared with PMQRSC, the expression of RC is much simpler, and its design and implementation also become simpler accordingly. In fact, studies have shown that the RC in formula (5) can be equivalent to a proportional term, an integral term, and the sum of an infinite number of quasi-resonant terms, but the dynamic response of repetitive control is slow due to the inherent one-beat delay of the internal model. One simple way to improve its dynamic response is to remove the large delay in the numerator and write it as RC1, and its expression becomes the following formula (6):

[0058] (6)

[0059] In fact, both formula (5) and formula (6) can be equivalent to a proportional term, an integral term, and an infinite number of quasi-resonant terms. The equivalent proof is as follows:

[0060] Based on mathematical formula (7):

[0061] (7)

[0062] For RC, we have the following formula (8):

[0063] (8)

[0064] Q is usually a constant less than 1 or a zero-phase low-pass filter to improve the stability margin of the system. , formula (8) can be written as the following formula (9):

[0065] (9)

[0066] Multiply both above and below , we can get the following formula (10):

[0067] (10)

[0068] According to the coefficient expressions in formula (4), let , substituting into formula (10), we can get the following formula (11):

[0069] (11)

[0070] Where T0 is the period of the periodic signal, is the fundamental signal angular frequency, is the bandwidth factor of the equivalent resonant controller. It can be seen that RC can be equivalent to a negative proportional term and the sum of infinite quasi-resonant terms, that is, proportional multi-quasi-resonance. Similarly, the equivalent expression of RC1 can be obtained as follows (12):

[0071] (12)

[0072] By comparing formula (11) and formula (12), it can be seen that the difference lies in the proportional term, which means that the resonant control part equivalent to these two repetitive controls is the same, which provides a theoretical basis for the new phase compensation method proposed in the present invention.

[0073] For repetitive control, in order to maintain system stability, a compensator needs to be designed to compensate for the system phase delay. Since the actual phase advance cannot be achieved in the actual control system, phase compensation is usually achieved by combining it with a large delay in the numerator of the repetitive control. For RC, the discrete expression after phase compensation is as follows (13):

[0074] (13)

[0075] Where N is equal to the ratio of the sampling frequency to the fundamental frequency, which can be regarded as the number of samples per cycle of repeated control.

[0076] However, for RC1, since there is no large delay link in the numerator, phase advance compensation cannot be performed directly, but the quasi-resonance term in its equivalent expression is the same as RC. With the help of this idea, the present invention discloses a new phase compensation method for proportional multi-quasi-resonance, that is, using a large delay link combined with a phase advance link to achieve phase compensation for proportional multi-quasi-resonance control.

[0077] The phase compensation discrete expression of the proportional multi-quasi-resonant controller disclosed in the present invention is the following formula (14): (14)

[0078] In the formula, is formula (3), This is the phase compensation part.

[0079] Based on this, the embodiment of the present invention discloses a phase compensation method for a multi-quasi-resonant controller, which applies the repetitive control phase advance compensation method to the multi-quasi-resonant control based on the equivalent relationship between repetitive control and multi-quasi-resonant control. The method solves the problem of cumbersome calculation and complex discreteness of the traditional PMQRSC phase compensation angle.

[0080] The design flow chart of the phase compensation method of the multi-quasi-resonant controller according to the embodiment of the present invention is as follows: Figure 1 The design steps are as follows:

[0081] (1) determining a control object of a multi-quasi-resonant controller, and establishing a control system between the multi-quasi-resonant controller and the control object;

[0082] (2) establishing a mathematical model of the control object, determining a system error transfer function and a system characteristic equation of the control system based on the mathematical model, and performing a system stability analysis on the control system in combination with the system error transfer function and the system characteristic equation to determine a system stability condition;

[0083] (3) The proportional term of the proportional controller of the multi-quasi-resonant controller Design the phase compensation part of the multi-quasi-resonant controller Design so that the proportional term and the phase compensation section respectively satisfying the system stability conditions;

[0084] (4) According to the system stability condition, the equivalent resonant bandwidth of the system in a stable state is taken as the target bandwidth, a target bandwidth control coefficient is obtained according to the target bandwidth calculation, and the resonant bandwidth of the multi-quasi-resonant controller is controlled by the target bandwidth control coefficient. is the target bandwidth;

[0085] (5) Resonance gain of the multi-quasi-resonant controller Design and determine the resonant gain under the condition that the system stability condition is met ;

[0086] (6) The proportion term obtained by , the phase compensation part , the resonance bandwidth and the resonant gain , phase compensation is performed on the multi-quasi-resonant controller.

[0087] In specific implementation, the embodiment of the present invention specifically includes the following steps:

[0088] Step 1: Establish a mathematical model of the control object. According to the system structure of the control object, determine the transfer function and system parameters of the control object, substitute the system parameters into the transfer function, and obtain the discrete transfer function of the control object, that is, the mathematical expression of the control object.

[0089] This embodiment uses a single-phase grid-connected inverter as the control object, and the structure is as follows: Figure 2 As shown in the figure, it mainly consists of an inverter bridge, an L-type filter, a phase-locked loop (PLL), and a current controller. The inverter bridge type is a single-phase three-level diode clamp type, and the PLL is a second-order generalized integral phase-locked loop. The control block diagram of the system is shown in Figure 3 As shown in the figure, is the current controller; is a digitally controlled delay and The transfer function of the controlled object can be obtained as follows (15):

[0090] (15)

[0091] The system parameters are shown in Table 1 below:

[0092] Table 1 Inverter system parameters

[0093]

[0094] Substituting the parameters, we can get the discrete transfer function It is the following formula (16):

[0095] (16)

[0096] Step 2: System stability analysis.

[0097] Will Figure 3 The current controller in is replaced by PMQRSC and can be expressed as Figure 4 .in is a proportional controller, is a multi-resonant controller, is the phase compensation part, and .

[0098] Depend on Figure 4 The system error transfer function can be obtained as follows (17):

[0099] (17)

[0100] At this time, the system characteristic equation is as follows (18):

[0101] (18)

[0102] in , which can be regarded as the new control object of the controller. Two stability conditions can be obtained through the characteristic equation:

[0103] (1) The roots (poles) of are inside the unit circle; Maintain zero gain within the system bandwidth; where, is the proportional term, is the discrete transfer function of the controlled object.

[0104] (2) The root (pole) of is within the unit circle. The control object satisfies the zero gain phase shift characteristic; wherein, is the discrete expression of phase compensation of multi-quasi-resonant controller, is the phase frequency of the phase compensation part, and , L is the compensation factor.

[0105] Obviously, condition (1) is easier to satisfy. We only need to find a suitable That's it, need to meet Maintain zero gain within the system bandwidth; for phase compensation For , it is necessary to compensate the phase delay of the controlled object itself so that the controlled object satisfies the characteristic of zero gain phase shift; For example, its gain at the resonant frequency is very large, so there is ,so .

[0106] Step 3: Design the proportional term (The proportional term is a parameter used in a proportional controller to adjust the proportional relationship between the output response and the error signal.)

[0107] first, The value of will affect the stability condition (1). In order to make the stability condition (1) hold, it is necessary to select an appropriate value, so that The root of is inside the unit circle, that is, the new control object The extreme point is z In addition, to ensure that the control object Maintaining a flat amplitude-frequency characteristic within the bandwidth will allow the system's harmonic suppression performance to be fully utilized. Figure 5 As shown, when The value is set in the range of 10 to 40. It can be found that Values ​​range from 10 to 30. The extreme point is always located at z The plane unit circle ensures the stability of the system. Figure 6 Shows the difference Down The amplitude-frequency response curve of Figure 6 It is known that when Take 10 o'clock, The amplitude-frequency characteristic of is relatively flat, so we choose =10.

[0108] Step 3: Design Phase Compensation .

[0109] For phase compensation, it is necessary to compensate the phase delay of the controlled object itself so that the controlled object meets the characteristics of zero gain phase shift. Figure 7 is the compensation factor L Take 1 to 5 hours Phase frequency response curve of Figure 7 It can be seen that when L Take 3 o'clock, The phase compensation link is selected because it is closest to zero phase shift characteristics within 1000 Hz. .

[0110] Step 4: Design Bandwidth .

[0111] Specifically, the wider the resonant bandwidth, the stronger the system's ability to resist frequency fluctuations. According to the system stability conditions, the equivalent resonant bandwidth that can keep the system stable is determined as the target bandwidth. The target bandwidth is calculated to obtain the target control coefficient. Specifically, according to the actual inverter system operating conditions, the grid frequency deviation generally does not exceed ±0.5 Hz, so it can be selected. .

[0112] Step 5: Design the resonant term gain According to the harmonic components of the control object, the resonant term and the resonant order of the resonant term of the multi-quasi-resonant controller are determined; according to the pole analysis method, the The extreme point is z The resonant gain value when the plane is within the unit circle is the resonant gain .

[0113] Since the harmonic components in the single-phase inverter current control system are mainly odd-order low-frequency harmonics below 1000 Hz, a total of 10 resonance items are selected in this embodiment, and the resonance orders are 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19 respectively. For the stable condition (2), K n The value of can be analyzed according to the extreme point analysis method. Figure 8 K n When the value is 400 The pole diagram of . Figure 8 It can be seen that the pole does not exceed the unit circle, and the system is stable. Therefore, K is selected n =400.

[0114] Step 6: Establish a simulation model to verify the performance of the controlled object.

[0115] Establish as Figure 2 The single-phase grid-connected inverter simulation model shown in Figure 1 uses phase-compensated PMQRSC to achieve grid-connected inverter harmonic current suppression. Odd harmonics are added to the grid, and the odd harmonic content is shown in Table 2. The total harmonic distortion (THD) of the grid voltage is 7.3%.

[0116] Table 2. Power grid background harmonic content

[0117]

[0118] The simulation results show that:

[0119] (1) When the grid frequency becomes 50 Hz, the inverter output waveform and grid-connected current THD analysis of the control system based on PMQRC are shown in Figures 9(a) and 9(b). The results show that when the background harmonic of the grid is 7.3%, the PMQRSC based on the new phase compensation proposed in this embodiment can still output a relatively high-quality grid-connected current.

[0120] (2) When the grid frequency fluctuates at 49.6 Hz and 50.4 Hz, the output waveform and current THD analysis of the PMQRSC system are shown in Figures 10(a), 10(b), 11(a), and 11(b). Obviously, the PMQRSC based on the new design method proposed in this embodiment can still have good performance when the frequency fluctuates.

[0121] The PMQRC phase compensation method proposed in the present invention is applicable to all industrial facilities that need to have periodic signal processing capabilities, including but not limited to inverters, servo motors, steering gears and other devices. Any equivalent replacement or modification based on the method scheme and inventive concept of the present invention shall be covered within the protection scope of the present invention.

[0122] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A phase compensation method for a multi-quasi-resonant controller, characterized in that: include: Determine a control object of a multi-quasi-resonant controller, and establish a control system between the multi-quasi-resonant controller and the control object; Establishing a mathematical model of the control object, determining a system error transfer function and a system characteristic equation of the control system according to the mathematical model, and performing a system stability analysis on the control system in combination with the system error transfer function and the system characteristic equation to determine a system stability condition; The proportional term of the proportional controller of the multi-quasi-resonant controller Design the phase compensation part of the multi-quasi-resonant controller Design so that the proportional term and the phase compensation section respectively satisfying the system stability conditions; According to the system stability condition, the equivalent resonant bandwidth in the system stable state is taken as the target bandwidth, and the target bandwidth control coefficient is calculated according to the target bandwidth. The resonant bandwidth of the multi-quasi-resonant controller is controlled by the target bandwidth control coefficient. is the target bandwidth; The resonant term gain of the multi-quasi-resonant controller Design and determine the resonant gain under the condition that the system stability condition is met ; The proportional term obtained by , the phase compensation part , the resonance bandwidth and the resonant gain , phase compensation is performed on the multi-quasi-resonant controller.

2. The multi-quasi-resonant controller phase compensation method according to claim 1, characterized in that: Establishing a mathematical model of the control object includes: According to the system structure of the controlled object, the transfer function and system parameters of the controlled object are determined, and the system parameters are substituted into the transfer function to obtain the discrete transfer function of the controlled object.

3. The multi-quasi-resonant controller phase compensation method according to claim 1, characterized in that: The control object is any one of a single-phase grid-connected inverter, an active filter and a constant voltage and constant frequency inverter.

4. The multi-quasi-resonant controller phase compensation method according to claim 2, characterized in that: The system stability conditions include: make The extreme point is z In the unit circle of the plane, Maintain zero gain within the system bandwidth; where, is the proportional term, is the discrete transfer function of the controlled object; make The extreme point is z The control object satisfies the zero gain phase shift characteristic within the unit circle of the plane; wherein, is the discrete expression of phase compensation of multi-quasi-resonant controller, is the phase frequency of the phase compensation part, and , L is the compensation factor.

5. The multi-quasi-resonant controller phase compensation method according to claim 1, characterized in that: The resonant bandwidth of the multi-quasi-resonant controller for: ; The grid frequency deviation of the control object.

6. The multi-quasi-resonant controller phase compensation method according to claim 4, characterized in that: The resonant term gain of the multi-quasi-resonant controller Design and determine the resonant gain under the condition that the system stability condition is met ,include: According to the pole analysis method, The extreme point is z The resonant gain value when the plane is within the unit circle is the resonant gain .

7. The multi-quasi-resonant controller phase compensation method according to claim 6, characterized in that: The resonant term gain of the multi-quasi-resonant controller Design also includes: According to the harmonic components of the control object, the resonance term and the resonance order of the resonance term of the multi-quasi-resonance controller are determined to adjust the resonance term gain of the multi-quasi-resonance controller. Make a design.

8. The multi-quasi-resonant controller phase compensation method according to claim 1, characterized in that: The method further includes: establishing a simulation model, measuring the output waveform and current of the control object under different grid frequencies, and verifying the performance of the control system after phase compensation.

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