阅读说明：本技术 一种基于陷波滤波器和补偿器的锁相环设计方法 (Phase-locked loop design method based on notch filter and compensator ) 是由 王超 郭志强 任其广 解亚洲 丁宁 陈早军 李强 于 2021-08-12 设计创作，主要内容包括：本发明的基于陷波滤波器和补偿器的锁相环设计方法,锁相环控制器包括控制常量环节、陷波滤波器环节和补偿器环节,陷波滤波器环节用于去除由于电网电压低次谐波成分和三相电网电压不平衡所引入到旋转同步坐标系q轴的二倍频谐波分量,在基波的二倍频处添加两个极点,以保证锁相环对高频谐波的抑制能力；补偿器环节引入一个极点和一个零点,以解决引入陷波滤波器所导致的相位突减问题,使锁相环满足在截止频率处相位裕度的要求。本发明的基于陷波滤波器和补偿器的锁相环设计方法,可解决三相变流器在电网电压低次谐波成分含量高(如5次),电网电压三相不平衡,电网电压突变,频率突变等工况下的锁相环精度和稳定性的问题。(According to the phase-locked loop design method based on the notch filter and the compensator, a phase-locked loop controller comprises a control constant link, a notch filter link and a compensator link, wherein the notch filter link is used for removing a double-frequency harmonic component introduced to a q axis of a rotating synchronous coordinate system due to low-order harmonic component of a power grid voltage and unbalanced three-phase power grid voltage, and two poles are added at the double-frequency part of a fundamental wave so as to ensure the inhibition capability of the phase-locked loop on high-frequency harmonic; a pole and a zero point are introduced into a compensator link to solve the problem of phase sudden reduction caused by introducing a notch filter, so that the phase-locked loop meets the requirement of phase margin at a cut-off frequency. The phase-locked loop design method based on the notch filter and the compensator can solve the problems of the phase-locked loop precision and stability of the three-phase converter under the working conditions of low grid voltage, high harmonic component content (such as 5 times), three-phase unbalance of grid voltage, sudden grid voltage change, sudden frequency change and the like.)

1. A design method of a phase-locked loop based on a notch filter and a compensator is characterized in that an input reference signal of a phase-locked loop controller is 0, and a feedback signal is a q-axis component of a three-phase alternating current power grid voltage under a rotating synchronous coordinate system; the method is characterized in that: 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 a closed-loop system formed by a phase-locked loop; the notch filter link is used for removing a double-frequency harmonic component introduced to a q axis of a rotating synchronous coordinate system due to low-order harmonic component of a power grid voltage and unbalanced three-phase power grid voltage, and two poles are added at the double-frequency position of a fundamental wave in the notch filter link so as to ensure the inhibition capability of the phase-locked loop on high-frequency harmonic waves and enable the phase-locked loop to have an attenuation speed of-40 dB/dec at a high frequency position; a pole and a zero point are introduced into a compensator link to solve the problem of phase sudden reduction caused by introducing a notch filter, so that the phase-locked loop meets the requirement of phase margin at a cut-off frequency, and the phase-locked precision and stability of the phase-locked loop under a steady state and a transient state are further ensured.

2. The method of claim 1, wherein: the transfer functions of the control constant element, the notch filter element and the compensator element are respectivelyF(s), H(s), the output of the compensator is transferred via the system transfer functionOutput to a three-phase AC network, k₀In order to control the parameters of the device,the amplitude of the voltage of the three-phase alternating current power grid is shown, and s is a Laplace operator; the open loop transfer function l(s) of the phase locked loop is:

3. the method of claim 2, wherein: the notch filter element uses a transfer function f(s) as shown in equation (2):

wherein: omega₀The frequency of the three-phase ac power grid.

4. A method as claimed in claim 3, wherein the notch filter and compensator based phase locked loop design method comprises: the compensator stage uses a transfer function h(s) as shown in equation (3):

wherein-z₀、-p₀Zero and pole introduced for the compensator link.

5. A method as claimed in claim 3, wherein the notch filter and compensator based phase locked loop design method comprises: the open loop transfer function l(s) of the phase locked loop is:

wherein: control parameter k₀Is selected to ensure | l (j ω_c)|＝1，ω_cIs the cut-off frequency of the phase-locked loop at the frequency omega of the three-phase AC network₀Is selected.

Technical Field

The present invention relates to a phase-locked loop, and more particularly, to a method for designing a phase-locked loop based on a notch filter and a compensator.

Background

When the three-phase converter adopts a control method based on a rotating synchronous coordinate system, accurate phase locking needs to be carried out on the voltage of a power grid. However, the actual grid voltage is not an ideal sinusoidal waveform, and contains some low-order harmonic components (such as 5-order harmonic), and power quality problems such as three-phase grid voltage imbalance, grid voltage sag, frequency variation, and the like also occur. When the power quality problems occur, the phase locking performance of the traditional controller which is only composed of a simple proportional link or a proportional-integral link is greatly influenced, the frequency of the phase locking has larger fluctuation, the precision of the phase locking is reduced, and even the frequency oscillation of the phase locking is dispersed. This can lead to increased grid-connected current harmonics of the three-phase converter and even to a total control failure, resulting in a plant shutdown or more serious consequences.

Disclosure of Invention

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

The invention relates to a phase-locked loop design method based on a notch filter and a compensator.A reference signal input to a phase-locked loop controller is 0, and a feedback signal is a q-axis component of a three-phase alternating current network voltage under a rotating synchronous coordinate system; the method is characterized in that: 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 a closed-loop system formed by a phase-locked loop; the notch filter link is used for removing a double-frequency harmonic component introduced to a q axis of a rotating synchronous coordinate system due to low-order harmonic component of a power grid voltage and unbalanced three-phase power grid voltage, and two poles are added at the double-frequency position of a fundamental wave in the notch filter link so as to ensure the inhibition capability of the phase-locked loop on high-frequency harmonic waves and enable the phase-locked loop to have an attenuation speed of-40 dB/dec at a high frequency position; a pole and a zero point are introduced into a compensator link to solve the problem of phase sudden reduction caused by introducing a notch filter, so that the phase-locked loop meets the requirement of phase margin at a cut-off frequency, and the phase-locked precision and stability of the phase-locked loop under a steady state and a transient state are further ensured.

According to the phase-locked loop design method based on the notch filter and the compensator, the transfer functions of the control constant link, the notch filter link and the compensator link are respectivelyF(s), H(s), the output of the compensator is transferred via the system transfer functionOutput to a three-phase AC network, k₀In order to control the parameters of the device,the amplitude of the voltage of the three-phase alternating current power grid is shown, and s is a Laplace operator; the open loop transfer function l(s) of the phase locked loop is:

according to the phase-locked loop design method based on the notch filter and the compensator, the notch filter adopts a transfer function F(s) as shown in a formula (2):

wherein: omega₀The frequency of the three-phase ac power grid.

In the phase-locked loop design method based on the notch filter and the compensator, the compensator adopts a transfer function H(s) as shown in a formula (3):

wherein-z₀、-p₀Zero and pole introduced for the compensator link.

The invention relates to a phase-locked loop design method based on a notch filter and a compensator, wherein the open-loop transfer function l(s) of the phase-locked loop is as follows:

wherein: control parameter k₀Is selected to ensure | l (j ω_c)|＝1，ω_cIs the cut-off frequency of the phase-locked loop at the frequency omega of the three-phase AC network₀Is selected.

The invention has the beneficial effects that: the phase-locked loop based on the notch filter and the compensator is provided with a control constant link, a notch filter link and a compensator link, wherein the notch filter link is used for removing a double-frequency harmonic component introduced to a q axis of a rotating synchronous coordinate system due to low-order harmonic component of grid voltage and unbalanced three-phase grid voltage, and two poles are added at the double-frequency position of fundamental waves to ensure the inhibition capability of the phase-locked loop on high-frequency harmonic waves, so that the phase-locked loop has an attenuation speed of-40 dB/dec at a high frequency position; the phase sudden reduction problem caused by the introduction of the notch filter is solved by introducing a pole and a zero point in the compensator link, so that the phase-locked loop meets the requirement of phase margin at the cut-off frequency, and the phase-locked precision and stability of the phase-locked loop under the steady state and the transient state are further ensured.

Therefore, the method for designing the phase-locked loop based on the notch filter and the compensator can solve the problems of the accuracy and the stability of the phase-locked loop of the three-phase converter under the working conditions of low grid voltage, high harmonic component content (such as 5 times), three-phase unbalance of grid voltage, sudden grid voltage change, sudden frequency change and the like.

Drawings

FIG. 1 is a schematic diagram of a notch filter and compensator based phase lock of the present invention;

FIG. 2 is a comparison graph of the phase-locked result of the phase-locked loop using the method of the present invention and the conventional PI-based method when the three phases of the grid voltage are unbalanced;

FIG. 3 is a comparison graph of the phase-locked result of the phase-locked loop using the method of the present invention and the conventional PI-based method when the grid voltage is suddenly changed;

fig. 4 is a comparison graph of phase-locked results of the phase-locked loop using the method of the present invention and the conventional PI-based loop controller when the frequency of the power grid changes abruptly.

Detailed Description

The invention is further described with reference to the following figures and examples.

As shown in fig. 1, which shows a schematic diagram of the phase lock based on the notch filter and the compensator of the present invention, the phase lock loop controller is composed of three links, a control constant link, a notch filter link and a compensator link. Firstly, an input reference signal and a feedback signal of the controller are consistent with those of a traditional control method, the reference signal is 0, and the feedback signal is a q-axis component of the three-phase grid voltage under a rotating synchronous coordinate system. Secondly, the error obtained by subtracting the reference signal and the feedback signal passes through a control constant element, and the value of the error is mainly determined by the response speed or cut-off frequency required by a closed-loop system. Thirdly, the output of the constant control link passes through a notch filter link and is mainly used for removing low-order harmonic components (such as 5 times) caused by low-order harmonic components of the power grid voltage and three-phase power grid voltage unbalance, the frequency of a q axis of a rotating synchronous coordinate system is introduced to be low-order harmonic components of double frequency of the power grid frequency, and meanwhile, in order not to influence the suppression capability of the system on high-frequency harmonic, two poles are added at the position of double frequency of fundamental wave, so that the loop still has the attenuation speed of minus 40dB/dec at a high frequency position.

And fourthly, the output of the notch filter link passes through the compensator link, and the method is mainly used for solving the problem of phase abrupt reduction caused by introducing the notch filter, thereby meeting the requirement of a phase margin of the system at a cut-off frequency, and further ensuring the phase locking precision and stability of the whole system under the conditions of steady state and transient state. Fifthly, the output of the compensator link is a phase-locked frequency deviation signal, the value of the phase-locked frequency deviation signal is subtracted from the fundamental frequency of the power grid to obtain the final phase-locked frequency, and the phase-locked frequency and the phase generated by the voltage-controlled oscillator can be used for controlling the three-phase converter.

According to the variation rule based on the decomposition of the rotating synchronous coordinate system dq, the three-phase voltage on the alternating current side of the three-phase converter can be converted into the following form:

wherein rho is the phase position, omega, of the alternating-current side electric quantity calculated by the phase-locked loop PLL₀And theta₀The frequency and the initial phase angle of the ac system. In general, control ρ (t) ═ ω₀t+θ₀Thereby making V_sq0. This allows for the design of the controller through this inherent linkage. Sin (ω) if the PLL performs well₀t+θ₀-ρ)≈ω₀t+θ₀- ρ, the nonlinear relationship in this model translates into a linear relationship as follows:

the derivation is carried out on the two sides of the above formula, and laplace transform is taken, so that the transfer function of the system can be obtained as follows:

assuming that the three-phase voltage on the alternating current side has five harmonics due to the occurrence of negative sequence components caused by unbalance and the problem of interference, the expression of the three-phase voltage is as follows:

wherein k is₁And k₅The negative sequence component and the ratio of the fifth harmonic to the fundamental amplitude are respectively expressed, and the distortion degree of the alternating voltage can be reflected. It is assumed that the PLL can accurately track the phase of the fundamental wave signal at this time, i.e., ρ (t) ═ ω₀t+θ₀. According to the rule of dq decoupling transformation, we obtain that the components of the d-axis and q-axis of the alternating voltage are respectively:

and k is₁The related alternating current frequency is double frequency and is close to the fundamental frequency, and when a single-phase earth fault occurs (a more serious three-phase imbalance condition), k₁Will reach a value of 0.5, thereby causing V_sdAnd V_sqExhibiting large fluctuations that affect the accuracy of the control and even lead to failure of the phase locked loop or even breakdown of the entire control system.

Therefore, the controller designed by the invention comprises a notch filter which is mainly used for eliminating the influence of the second harmonic component on the phase locking result, and simultaneously, in order not to influence the suppression capability of the system on high-frequency harmonics, two poles are added at the second harmonic frequency of the fundamental wave, so that the loop still has the attenuation speed of-40 dB/dec at high frequency. From the above analysis, f(s) can be expressed as follows:

the addition of the notch filter causes the system phase to dip 180 degrees at twice the fundamental frequency, thus worsening the phase margin and causing system instability. Therefore, an additional compensation element h(s) needs to be added, which is expressed as follows:

consider adding a control constant as shown in fig. 1, so that the open-loop transfer function of the system can be expressed as:

control parameter k₀Is selected to ensure | l (j ω_c)|＝1，ω_cIs the cut-off frequency of the phase-locked loop at the frequency omega of the three-phase AC network₀Is selected, for example, from 45Hz to 60 Hz.

The method disclosed by the invention is used for simulating three working conditions of three-phase unbalance of the grid voltage, sudden change of the grid voltage and sudden change of the grid voltage respectively by using a three-phase converter which is actually applied, phase locking is carried out by adopting the method disclosed by the invention and is compared with the phase locking result of a traditional controller based on a PI link, and the results shown in the figures 2, 3 and 4 are obtained. As shown in table 1, simulation parameters are given.

TABLE 1

Fig. 2 is a graph for simulating a three-phase imbalance problem caused by a 30V increase of a phase voltage of a power grid and an unchanged voltage of other two phases, as shown in fig. 2, which shows a comparison between a phase-locked loop result obtained by using the method of the present invention and a phase-locked loop result obtained by using a conventional PI-based loop controller when the three phases of the power grid are unbalanced, where fig. 2a is a phase-locked result obtained by using a conventional method, and fig. 2b is a phase-locked result obtained by using the method of the present invention; at the moment, the frequency obtained by adopting the traditional phase-locking link based on the PI controller obviously has the fluctuation of the second harmonic of the fundamental wave, while the frequency obtained by adopting the phase-locking link of the method of the invention is stable and has no fluctuation, thereby verifying the effectiveness of the method when the power grid is unbalanced or has low-order harmonic (such as 5-order harmonic) and being superior to the traditional method.

Fig. 3 is a graph simulating that the three-phase voltage of the power grid suddenly increases from 600V to 650V (the peak value increases from 490V to 530V), as shown in fig. 3, comparing the phase-locked result of the phase-locked loop using the method of the present invention with the phase-locked result of the conventional PI-based loop controller when the voltage of the power grid suddenly changes, fig. 3a is the phase-locked result of the conventional method, and fig. 3b is the phase-locked result of the method of the present invention; at the moment, the frequency obtained by adopting the traditional phase locking link based on the PI controller has transient sudden change and is approximately recovered to be normal in two to three power grid cycles, and the frequency obtained by adopting the phase locking method of the invention has almost no fluctuation at the sudden change moment, so that the effectiveness of the method is verified when the power grid voltage changes suddenly and is superior to that of the traditional method.

Fig. 4 is a graph for simulating that the frequency of the power grid suddenly changes from 50Hz to 50.2Hz, as shown in fig. 4, comparing the phase-locked result of the phase-locked loop of the method of the present invention with the phase-locked loop of the conventional PI-based loop controller when the frequency of the power grid suddenly changes, where fig. 4a is the phase-locked result of the conventional method, and fig. 4b is the phase-locked result of the method of the present invention; at the moment, the frequency obtained by adopting the traditional phase locking link based on the PI controller has transient sudden change and is approximately recovered to be normal in two power grid cycles, and the frequency obtained by adopting the phase locking method of the invention can be recovered to be normal in one cycle, so that the effectiveness of the method in the sudden change of the power grid frequency is verified and is superior to that of the traditional method.