A Phase-Locked Loop Design Method Based on Notch Filter and Compensator

Abstract

The phase-locked loop design method based on the notch filter and the compensator of the present invention, the phase-locked loop controller includes a control constant link, a notch filter link and a compensator link, the notch filter link is used to remove the double frequency harmonic component introduced into the q-axis of the rotating synchronous coordinate system due to the low-order harmonic components of the grid voltage and the imbalance of the three-phase grid voltage, and two poles are added at the double frequency of the fundamental wave to ensure the suppression ability of the phase-locked loop to high-frequency harmonics; the compensator link introduces a pole and a zero point to solve the phase drop problem caused by the introduction of the notch filter, so that the phase-locked loop meets the phase margin requirements at the cut-off frequency. The phase-locked loop design method based on the notch filter and the compensator of the present invention can solve the problems of phase-locked loop accuracy and stability of the three-phase converter under the working conditions of high content of low-order harmonic components of the grid voltage (such as the 5th), unbalanced three-phase grid voltage, sudden changes in grid voltage, sudden changes in frequency, etc.

Description

Technical Field

[0001] The present invention relates to a phase-locked loop, and more specifically, to a phase-locked loop design method based on a notch filter and a compensator. Background Art

[0002] When the three-phase converter adopts the control method based on the rotating synchronous coordinate system, the grid voltage needs to be accurately phase-locked. However, the actual grid voltage is not an ideal sinusoidal waveform, and it contains some low-order harmonic components (such as the 5th harmonic). There will also be power quality problems such as unbalanced three-phase grid voltage, temporary rise and fall of grid voltage, and frequency change. When these power quality problems occur, the phase-locking performance of the traditional controller consisting of only a simple proportional link or proportional integral link will be greatly affected, the frequency of the phase lock will fluctuate greatly, the accuracy of the phase lock will decrease, and even the frequency oscillation of the phase lock will diverge. This will cause the grid-connected current harmonics of the three-phase converter to increase, or even the entire control to fail, resulting in device shutdown or more serious consequences. Summary of the invention

[0003] In order to overcome the disadvantages of the above technical problems, the present invention provides a phase-locked loop design method based on a notch filter and a compensator.

[0004] The present invention discloses a phase-locked loop design method based on a notch filter and a compensator, wherein the input reference signal of the phase-locked loop controller is 0, and the feedback signal is the q-axis component of the three-phase AC power grid voltage in a rotating synchronous coordinate system; the phase-locked loop controller comprises a control constant link, a notch filter link and a compensator link, wherein the control constant link is determined by the response speed or cut-off frequency required by the closed-loop system constituted by the phase-locked loop; the notch filter link is used to remove the double frequency harmonic component introduced into the q-axis of the rotating synchronous coordinate system due to the low-order harmonic components of the power grid voltage and the unbalanced three-phase power grid voltage, and the notch filter link adds two poles at the double frequency of the fundamental wave to ensure the suppression capability of the phase-locked loop to high-frequency harmonics, so that the phase-locked loop has an attenuation rate of -40 dB / dec at high frequencies; the compensator link introduces a pole and a zero point to solve the phase drop problem caused by the introduction of the notch filter, so that the phase-locked loop meets the phase margin requirement at the cut-off frequency, thereby ensuring the phase-locked accuracy and stability of the phase-locked loop in steady and transient states.

[0005] The phase-locked loop design method based on the notch filter and the compensator of the present invention, the transfer functions of the control constant link, the notch filter link, and the compensator link are respectively F(s), H(s), the output of the compensator is transferred through the system function Output to three-phase AC grid, k 0 To control the parameters, is the amplitude of the three-phase AC grid voltage, s is the Laplace operator; the open-loop transfer function l(s) of the phase-locked loop is:

[0006]

[0007] The phase-locked loop design method based on the notch filter and the compensator of the present invention, the notch filter link adopts the transfer function F(s) shown in formula (2):

[0008]

[0009] Where: 0 is the frequency of the three-phase AC power grid.

[0010] The phase-locked loop design method based on the notch filter and the compensator of the present invention, the compensator link adopts the transfer function H(s) shown in formula (3):

[0011]

[0012] Among them, -z 0 , -p 0 These are the zeros and poles introduced by the compensator link.

[0013] The phase-locked loop design method based on the notch filter and the compensator of the present invention, the open-loop transfer function l(s) of the phase-locked loop is:

[0014]

[0015] Among them: control parameter k 0 The choice should ensure that |l(jω c )|=1,ω c is the cut-off frequency of the phase-locked loop, which is the frequency of the three-phase AC power grid ω 0 Select nearby.

[0016] The beneficial effects of the present invention are as follows: the phase-locked loop based on the notch filter and the compensator of the present invention is designed with a control constant link, a notch filter link, and a compensator link. The notch filter link is used to remove the double frequency harmonic components introduced into the q-axis of the rotating synchronous coordinate system due to the low-order harmonic components of the power grid voltage and the imbalance of the three-phase power grid voltage. By adding two poles at the double frequency of the fundamental wave, the suppression capability of the phase-locked loop to high-frequency harmonics is ensured, so that the phase-locked loop has an attenuation rate of -40dB / dec at high frequencies; by introducing a pole and a zero point in the compensator link, the phase sudden reduction problem caused by the introduction of the notch filter is solved, so that the phase-locked loop meets the phase margin requirement at the cutoff frequency, thereby ensuring the phase-locked accuracy and stability of the phase-locked loop in steady state and transient state.

[0017] It can be seen that the phase-locked loop design method based on the notch filter and the compensator of the present invention can solve the problems of phase-locked loop accuracy and stability of the three-phase converter under conditions such as high content of low-order harmonic components in the grid voltage (such as the 5th), unbalanced three-phase grid voltage, sudden grid voltage changes, and sudden frequency changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The schematic diagram of the phase locking based on the notch filter and the compensator of the present invention;

[0019] Figure 2 This is a comparison diagram of the phase-locked loop phase-locked results of the method proposed by the present invention and the traditional method based on the PI link controller when the three-phase voltage of the power grid is unbalanced;

[0020] Figure 3 This is a comparison diagram of the phase-locked loop phase-locked results of the method proposed by the present invention and the traditional method based on the PI link controller when the grid voltage suddenly changes;

[0021] Figure 4 This is a comparison diagram of the phase-locked loop phase-locked results of the method proposed in the present invention and the traditional method based on the PI link controller when the power grid frequency suddenly changes. DETAILED DESCRIPTION

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0023] like Figure 1 As shown, the principle diagram of the phase lock based on the notch filter and the compensator of the present invention is given. The phase-locked loop controller consists of three links, the control constant link, the notch filter link and the compensator link. First, the input reference signal and feedback signal of the controller are consistent with the traditional control method. The reference signal is 0, and the feedback signal is the q-axis component of the three-phase grid voltage in the rotating synchronous coordinate system. Second, the error obtained by making a difference between the reference signal and the feedback signal first passes through the control constant link, and its value is mainly determined by the response speed or cut-off frequency required by the closed-loop system. Third, the output of the control constant link passes through the notch filter link again, which is mainly used to remove the low-order harmonic components of the grid voltage (such as the 5th) and the unbalanced three-phase grid voltage, and the frequency of the q-axis of the rotating synchronous coordinate system is twice the grid frequency. At the same time, in order not to affect the system's ability to suppress high-frequency harmonics, two poles are added at the double frequency of the fundamental wave, so that the loop still has an attenuation rate of -40dB / dec at high frequencies.

[0024] Fourth, the output of the notch filter link passes through the compensator link, which is mainly used to solve the phase drop problem caused by the introduction of the notch filter, so as to meet the system's phase margin requirements at the cutoff frequency, and then ensure the phase-locked accuracy and stability of the entire system under steady-state and transient conditions. Fifth, the output of the compensator link is the phase-locked frequency deviation signal, whose value is subtracted from the grid fundamental frequency to obtain the final phase-locked frequency. The phase-locked frequency and the phase generated by the voltage-controlled oscillator can be used to control the three-phase converter.

[0025] According to the change law based on the dq decomposition of the rotating synchronous coordinate system, the three-phase voltage on the AC side of the three-phase converter can be converted into the following form:

[0026]

[0027]

[0028]

[0029] Where ρ is the phase of the AC side electricity calculated by the phase-locked loop PLL, ω 0 and θ 0 is the frequency and initial phase angle of the AC system. Usually, control ρ(t)=ω 0 t+θ 0 So that V sq = 0. This internal connection can be used to design the controller. If the PLL performance is good, then sin(ω 0 t+θ 0 -ρ)≈ω 0 t+θ 0 -ρ, so the nonlinear relationship in the formula is transformed into a linear relationship as follows:

[0030]

[0031] By taking the derivative of both sides of the above equation and taking the Laplace transform, we can get the transfer function of the system itself:

[0032]

[0033] Assuming that the three-phase voltage on the AC side has a negative sequence component due to imbalance, and interference causes the fifth harmonic, the three-phase voltage expression is as follows:

[0034]

[0035]

[0036]

[0037] where k 1and k 5 They represent the ratio of the negative sequence component and the fifth harmonic to the fundamental amplitude, which can reflect the degree of AC voltage distortion. Assume that the PLL can accurately track the phase of the fundamental signal, that is, ρ(t) = ω 0 t+θ 0 According to the law of dq decoupling transformation, we get the components of the d-axis and q-axis of the AC voltage as:

[0038]

[0039]

[0040] With k 1 The frequency of the relevant AC quantity is twice the frequency, which is close to the fundamental frequency. When a single-phase grounding fault occurs (a more serious three-phase imbalance), k 1 will reach a value of 0.5, making V sd and V sq It will show large fluctuations, which will affect the accuracy of control and even lead to the failure of the phase-locked loop and the collapse of the entire control system.

[0041] Therefore, the controller designed in the present invention includes a notch filter, which is mainly used to eliminate the influence of the double frequency component on the phase-locked result. At the same time, in order not to affect the system's ability to suppress high-frequency harmonics, two poles are added at the double frequency of the fundamental wave, so that the loop still has an attenuation rate of -40dB / dec at high frequencies. According to the above analysis, F(s) can be expressed as follows:

[0042]

[0043] Adding a notch filter will cause the system phase to drop 180 degrees at twice the fundamental frequency, thereby deteriorating the phase margin and causing system instability. Therefore, an additional compensation link H(s) needs to be added, which is expressed as follows:

[0044]

[0045] Consider adding Figure 1 The control constant link is shown, so the open-loop transfer function of the system can be expressed as:

[0046]

[0047] Control parameter k 0 The choice should ensure that |l(jω c )|=1,ω c is the cut-off frequency of the phase-locked loop, which is the frequency of the three-phase AC power grid ω 0 Select something near , such as 45Hz~60Hz.

[0048] Using the actual three-phase converter, the three working conditions of grid voltage unbalance, grid voltage mutation and grid voltage mutation were simulated. Figure 1 The method proposed in the present invention is phase-locked, and compared with the results of the traditional PI-based controller phase-lock, it is obtained Figure 2 , Figure 3 , Figure 4 As shown in Table 1, the simulation parameters are given.

[0049] Table 1

[0050]

[0051] Figure 2 To simulate the three-phase imbalance problem caused by increasing the A-phase voltage of the power grid by 30V and keeping the other two phase voltages unchanged, Figure 2 As shown, a comparison diagram of the phase-locked loop phase-locked results of the method proposed by the present invention and the traditional method based on the PI link controller is given when the three-phase voltage of the power grid is unbalanced. Figure 2 a is the phase-locking result of the traditional method, Figure 2 b is the phase-locked result of the method proposed in the present invention; at this time, the frequency obtained by the traditional PI controller-based phase-locked link obviously fluctuates at twice the fundamental frequency, while the frequency obtained by phase-locking using the method described in the present invention is stable and has no fluctuations, which verifies the effectiveness of this method when the power grid is unbalanced or there are low-order harmonics (such as the 5th harmonic) and is superior to the traditional method.

[0052] Figure 3 To simulate the three-phase voltage of the power grid suddenly increasing from 600V to 650V (peak value increasing from 490V to 530V), as Figure 3 As shown, a comparison diagram of the phase-locked loop phase-locked results of the method proposed by the present invention and the traditional method based on the PI link controller is given when the grid voltage suddenly changes. Figure 3 a is the phase-locking result of the traditional method, Figure 3 b is the phase-locked result of the method proposed in the present invention; at this time, the frequency obtained by the traditional PI controller-based phase-locked link has a transient mutation, which returns to normal within two to three grid cycles, while the frequency obtained by phase-locking using the method described in the present invention has almost no fluctuation at the moment of mutation, which verifies the effectiveness of this method when the grid voltage changes suddenly and is superior to the traditional method.

[0053] Figure 4 To simulate the grid frequency suddenly changing from 50Hz to 50.2Hz, Figure 4 As shown, a comparison diagram of the phase-locked loop phase-locked results of the method proposed by the present invention and the traditional method based on the PI link controller is given when the power grid frequency suddenly changes. Figure 4 a is the phase-locking result of the traditional method, Figure 4b is the phase-locked result of the method proposed in the present invention; at this time, the frequency obtained by the traditional PI controller-based phase-locked link has a transient mutation and returns to normal within two power grid cycles, while the frequency obtained by phase-locking using the method described in the present invention can return to normal within one cycle, which verifies the effectiveness of this method when the power grid frequency changes suddenly and is superior to the traditional method.

Claims

1. A phase-locked loop design method based on a notch filter and a compensator, wherein the input reference signal of the phase-locked loop controller is 0 and the feedback signal is the q-axis component of the three-phase AC grid voltage in a rotating synchronous coordinate system; characterized in that: The phase-locked loop controller includes a control constant link, a notch filter link and a compensator link. The control constant link is determined by the response speed or cutoff frequency required by the closed-loop system formed by the phase-locked loop; the notch filter link is used to remove the double frequency harmonic components introduced into the q-axis of the rotating synchronous coordinate system due to the low-order harmonic components of the grid voltage and the unbalanced voltage of the three-phase grid. The notch filter link adds two poles at the double frequency of the fundamental wave to ensure the phase-locked loop's ability to suppress high-frequency harmonics, so that the phase-locked loop has an attenuation rate of -40dB / dec at high frequencies; A pole and a zero are introduced into the compensator link to solve the phase drop problem caused by the introduction of the notch filter, so that the phase-locked loop meets the phase margin requirement at the cutoff frequency, thereby ensuring the phase-locked accuracy and stability of the phase-locked loop in steady and transient states.

2. The phase-locked loop design method based on notch filter and compensator according to claim 1, characterized in that: The transfer functions of the control constant link, notch filter link, and compensator link are respectively F(s), H(s), the output of the compensator is transferred through the system function Output to the three-phase AC power grid, k0 is the control parameter, is the amplitude of the three-phase AC grid voltage, s is the Laplace operator; the open-loop transfer function l(s) of the phase-locked loop is:

3. The phase-locked loop design method based on notch filter and compensator according to claim 2, characterized in that: The notch filter adopts the transfer function F(s) shown in formula (2): Where: ω0 is the frequency of the three-phase AC power grid.

4. The phase-locked loop design method based on notch filter and compensator according to claim 3, characterized in that: The compensator link adopts the transfer function H(s) shown in formula (3): Among them, -z0 and -p0 are the zero and pole introduced by the compensator link.

5. The phase-locked loop design method based on notch filter and compensator according to claim 4, characterized in that: The open-loop transfer function l(s) of the phase-locked loop is: Among them: The selection of control parameter k0 should ensure |l(jω c )|=1,ω c is the cut-off frequency of the phase-locked loop, which is selected near the frequency ω0 of the three-phase AC power grid.

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