CN113890398A - PR control and PI control equivalent method considering frequency dynamic characteristics - Google Patents

PR control and PI control equivalent method considering frequency dynamic characteristics Download PDF

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CN113890398A
CN113890398A CN202111180500.4A CN202111180500A CN113890398A CN 113890398 A CN113890398 A CN 113890398A CN 202111180500 A CN202111180500 A CN 202111180500A CN 113890398 A CN113890398 A CN 113890398A
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CN113890398B (en
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马俊鹏
王鹏
程松
吴子豪
王若谷
王辰曦
王顺亮
刘天琪
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Sichuan University
Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd
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Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
    • H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters

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Abstract

本发明公开了一种考虑频率动态特性的PR控制与PI控制等效方法，具体为：建立PR控制器以及PI控制器模型，分别以这两种控制器为基准，在不考虑频率动态特性的情况下推导对应的等效模型；计及频率的动态特性，对等效模型中的参考电流、反馈电流、调制信号以及锁相环进行修正，使等效后的控制器的动态性能与原始控制器完全一致。本发明在系统遭受扰动导致参考频率与实际频率不一致的情况下，通过对等效模型中的信号进行修正从而实现了PR控制器与PI控制器的精确化等效。

Figure 202111180500

The invention discloses an equivalent method for PR control and PI control considering frequency dynamic characteristics. The corresponding equivalent model is deduced under different conditions; considering the dynamic characteristics of the frequency, the reference current, feedback current, modulation signal and phase-locked loop in the equivalent model are corrected, so that the dynamic performance of the equivalent controller is the same as the original control. device is completely consistent. The present invention realizes the precise equivalence of the PR controller and the PI controller by correcting the signals in the equivalent model when the system is disturbed and the reference frequency is inconsistent with the actual frequency.

Figure 202111180500

Description

PR control and PI control equivalent method considering frequency dynamic characteristics
Technical Field
The invention belongs to the field of inverter control, and particularly relates to a PR control and PI control equivalent method considering frequency dynamic characteristics.
Background
PI controllers can maintain infinite gain at the dc component, and therefore PI controllers are widely used to track dc reference signals without steady state errors. However, for current control in a stationary coordinate system, tracking without steady-state error of the current reference signal cannot be achieved due to the limited gain of the PI controller at the corresponding frequency. Unlike the PI controller, the PR controller can achieve infinite gain at the corresponding frequency, and thus can track the ac signal without steady-state error. Based on the characteristics of the PI controller, the AC signal in the alpha beta static coordinate system can be converted into the DC signal in the dq rotary coordinate system through coordinate transformation, so that zero steady-state error control is realized.
Since the fundamental principle of a PR controller is to achieve infinite gain at a selected resonant frequency, which is similar in principle to an integrator in a PI controller, the resonant part of a PR controller can be considered as a generalized integrator. At present, many scholars derive the equivalence of the PR controller in the α β stationary coordinate system and the PI controller in the dq rotating coordinate system, and when the reference frequency is consistent with the frequency output by the phase-locked loop PLL, that is, when the frequency dynamic characteristic is ignored, the PR controller in the α β stationary coordinate system and the PI controller in the dq rotating coordinate system are completely equivalent, and the dynamic performance of the systems in the two control modes is basically consistent.
However, the grid frequency cannot be kept at a constant value all the time, the frequency fluctuates within a certain range when the system is disturbed, and the reference frequency is inconsistent with the actual frequency, so that the performance of the PR controller and the equivalent PI controller is greatly different, that is, the equivalent PI controller cannot completely reflect the dynamic performance of the PR controller in the α β stationary coordinate system.
Disclosure of Invention
The invention aims to provide a PR control and PI control equivalent method considering frequency dynamic characteristics, which enables the dynamic performances of two controllers to be basically consistent by modifying signals in an equivalent controller under the condition that a reference frequency is inconsistent with an actual frequency due to disturbance of a power grid.
The invention discloses a PR control and PI control equivalent method considering frequency dynamic characteristics, which comprises the following steps of:
step 1: and establishing a PR controller model, and deducing a PI controller model corresponding to the PR controller model in the synchronous rotating coordinate system under the condition of not considering the dynamic characteristic of frequency by taking the PR controller in the static coordinate system as a reference.
Step 2: and correcting the reference current, the feedback current, the modulation signal and the phase-locked loop of the PI controller under the synchronous rotating coordinate system by considering the dynamic characteristic of the frequency.
And step 3: the PI controller in the rotating coordinate system is used as a reference, and the PR controller in the static coordinate system is derived under the condition that the frequency dynamic characteristic is not considered.
And 4, step 4: the reference current, feedback current, and modulation signal of the PR controller in the stationary coordinate are modified in consideration of frequency dynamics.
Further, step 1 specifically comprises:
the transfer function of the PR controller in the stationary frame is:
Figure RE-GDA0003339305720000021
wherein, ω is0At a nominal angular frequency, kpIs proportional gain, k, of the PR controllerrFor PR controller resonant gain, s is Laplace operator, and j represents complex number.
When the frequency dynamic characteristic is not considered, the transfer function of the PI controller under the equivalent rotating coordinate system is expressed as follows:
Figure RE-GDA0003339305720000022
the expression of the output voltage after passing through the PI controller is obtained according to the formula (2) and is as follows:
Figure RE-GDA0003339305720000023
wherein u isdAnd uqRespectively representing d-axis and q-axis voltages, Δ i, output by the PI controllerdAnd Δ iqRepresenting d-axis and q-axis current errors, respectively.
Further, in step 2, the relevant signal of the PI controller needs to be corrected, and the specific correction principle is as follows:
the corrected current reference value under the dq coordinate system is as follows:
Figure RE-GDA0003339305720000024
wherein, IdqrefmFor corrected reference current input of PI controller under rotating coordinate system, IdqrefαβThe reference current input of the PR controller under a static coordinate system is shown, omega' is the output angular frequency of the phase-locked loop PLL, and t is a time variable.
Feedback current i after correction under dq coordinate systemdmAnd iqmComprises the following steps:
Figure RE-GDA0003339305720000031
wherein ia、ibAnd icRepresenting the three-phase current actually output by the inverter.
Modified modulation signal v in dq coordinate systemαβmExpressed as:
Figure RE-GDA0003339305720000032
wherein u isdqRepresenting the dq-axis voltage vector output by the PI controller.
Modified phase-locked loop input e in dq coordinate systemqmExpressed as:
Figure RE-GDA0003339305720000033
wherein e isdqDenotes the equivalent of the output of the resonant controller in the α β coordinate system in the dq coordinate system, and Im denotes taking the imaginary part of the output.
Further, step 3 specifically comprises:
the transfer function of a PR controller in a stationary coordinate system, without considering the frequency dynamics, is equivalent to:
Figure RE-GDA0003339305720000034
the expression of the output voltage after passing through the PR current controller is obtained according to formula (8) as follows:
Figure RE-GDA0003339305720000041
wherein u isαAnd uβRespectively representing the alpha and beta axis voltages, Δ i, of the PR controller outputαAnd Δ iβRepresenting the alpha and beta axis current errors, respectively.
Further, in step 4, the relevant signal of the equivalent PR controller needs to be corrected, and the specific correction principle is as follows:
corrected current reference value i under alpha beta coordinate systemαβrefmComprises the following steps:
Figure RE-GDA0003339305720000042
wherein，idqrefRepresenting the dq-axis reference current.
Feedback current i after correction under alpha beta coordinate systemam、ibm、icmComprises the following steps:
Figure RE-GDA0003339305720000043
Figure RE-GDA0003339305720000044
wherein idqmIs a modified dq-axis current i in an alpha beta coordinate systemαβIs the actual output current of the inverter under the alpha beta coordinate system.
Corrected three-phase modulation signal v under alpha and beta coordinate systemam、vbm、vcmCan be expressed as:
Figure RE-GDA0003339305720000045
wherein u isαβRepresenting the α β axis voltage vector output by the PR controller.
Figure RE-GDA0003339305720000051
Wherein v isdmAnd vqmRespectively represent the d-axis and q-axis modulation signals after being corrected under the dq coordinate system.
The beneficial technical effects of the invention are as follows:
the invention provides an equivalent method of PR control and PI control under the condition of considering frequency dynamic characteristics, which corrects the reference current, the feedback current, the modulation signal and the phase-locked loop of an equivalent controller, thereby realizing the accurate equivalence of the PR controller and the PI controller under the condition that the reference frequency is inconsistent with the actual frequency due to the disturbance of a system, and ensuring that the dynamic performances of the two controllers are basically consistent.
Drawings
FIG. 1 is a block diagram of an inverter system;
FIG. 2 is a block diagram of an ideal PR controller in a stationary coordinate system;
FIG. 3 is a block diagram of an equivalent PI controller for a PR controller under a rotating coordinate system;
FIG. 4 illustrates the correction of the reference current input to the PI controller in dq rotation coordinate system;
FIG. 5 illustrates the correction of the feedback current of the PI controller;
FIG. 6 illustrates the modification of the modulation signal of the PI controller;
FIG. 7 shows the construction of a phase locked loop with feedback in the PI controller, thus equivalent to the phase locked loop of the PR controller in the stationary frame;
FIG. 8 is a block diagram of a PI controller under a rotating coordinate system;
FIG. 9 is a block diagram of an equivalent PR controller for a PI controller in a stationary coordinate system;
FIG. 10 illustrates correction of reference current input in a stationary frame;
FIG. 11 illustrates the correction of the feedback current of the PR controller;
FIG. 12 illustrates modifying the modulation signal of the PR controller;
FIG. 13 is a comparison graph of frequency response waveforms before and after correction of an equivalent PI controller based on a PR controller;
fig. 14 is a comparison graph of frequency response waveforms before and after correction by an equivalent PR controller with reference to a PI controller.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The inverter operating structure using the PR controller is shown in FIG. 1, UdcIs the DC side voltage of the inverter iLabcFor the inverter output current, LfAnd L1Respectively a filter inductor and a line inductor. By making a pair iLabcSampling, and PR controlling to obtain modulated wave
Figure RE-GDA0003339305720000064
And obtaining a switching signal after PWM modulation to complete the control of the grid-connected inverter.
FIG. 2 is a block diagram of an ideal PR controller in a stationary coordinate system, the transfer function of the PR controller obtained according to the structure of FIG. 2 is:
Figure RE-GDA0003339305720000061
wherein, ω is0At a nominal angular frequency, kpIs proportional gain, k, of the PR controllerrFor the PR controller resonant gain, s is the Laplace operator.
Based on fig. 2, an equivalent PI controller transfer function can be obtained as:
Figure RE-GDA0003339305720000062
fig. 3 is a block diagram of an equivalent PI controller of the PR controller in a rotating coordinate system, and an expression of an output voltage of the PI current controller obtained according to fig. 3 is:
Figure RE-GDA0003339305720000063
wherein u isdAnd uqRespectively representing d-axis and q-axis voltages, Δ i, output by the PI controllerdAnd Δ iqRepresenting d-axis and q-axis current errors, respectively.
Fig. 4-7 are modified schematic diagrams of equivalent PI controllers based on a PR controller, and fig. 4 shows the modification of the reference current input of the PI controller in a dq rotation coordinate system, where the corresponding expressions are:
Figure RE-GDA0003339305720000071
wherein, IdqrefmFor corrected reference current input of PI controller under rotating coordinate system, IdqrefαβIs PR under a static coordinate systemThe reference current input of the controller, ω', is the output angular frequency of the phase locked loop PLL.
Fig. 5 shows the principle of correcting the feedback current of the PI controller as shown in equation (19).
Figure RE-GDA0003339305720000072
Wherein ia、ibAnd icRepresenting the three-phase current actually output by the inverter.
FIG. 6 shows a modified PI controller modulation signal vαβmCan be expressed as:
Figure RE-GDA0003339305720000073
fig. 7 shows that a phase-locked loop with feedback is constructed in the PI controller, so that the phase-locked loop is equivalent to the phase-locked loop of the PR controller in the stationary coordinate system, and the equivalent principle is as follows:
Figure RE-GDA0003339305720000074
wherein e isdqDenotes the equivalent of the output of the resonant controller in the α β coordinate system in the dq coordinate system, and Im denotes taking the imaginary part of the output.
Fig. 8 is a block diagram of a typical PI controller in a rotating coordinate system, and the principle of the phase-locked loop PLL is consistent with that of the block diagram (r) in fig. 4, all for realizing the construction of a phase-locked loop with feedback in the PI controller. The corresponding PR controller transfer function expression from FIG. 5 can be found as:
Figure RE-GDA0003339305720000075
fig. 9 is a block diagram of an equivalent PR controller under a static coordinate system for a PI controller, and an expression of an output voltage of the PR current controller obtained according to fig. 6 is as follows:
Figure RE-GDA0003339305720000081
wherein u isαAnd uβRespectively representing the alpha and beta axis voltages, Δ i, of the PR controller outputαAnd Δ iβRepresenting the alpha and beta axis current errors, respectively.
Fig. 10-12 are schematic diagrams of the modified equivalent PR controller based on the PI controller, and fig. 10 shows the modification of the reference current input in the stationary coordinate system, and the corresponding expression is:
Figure RE-GDA0003339305720000082
wherein iαβrefmAnd the corrected current reference value under the alpha beta coordinate system is shown.
Fig. 11 illustrates the correction of the feedback current of the PR controller, based on the following principle:
Figure RE-GDA0003339305720000083
Figure RE-GDA0003339305720000084
wherein iam、ibm、icmRepresents the corrected feedback current i in the alpha beta coordinate systemdqmIs a modified dq-axis current i in an alpha beta coordinate systemαβIs the actual output current of the inverter under the alpha beta coordinate system.
Fig. 12 shows the correction of the modulation signal of the PR controller, which is based on the following principle:
Figure RE-GDA0003339305720000091
Figure RE-GDA0003339305720000092
wherein v isam、vbm、vcmAnd the three-phase modulation signal after correction in the alpha and beta coordinate system is shown.
The following compares the results of the conventional control with the method proposed by the present invention by way of specific examples.
The main circuit parameters shown in fig. 1 are as follows: u shapedc＝750V，Lf＝5mH，L1The PR controller parameters shown in fig. 2 are as follows, 30 mH: k is a radical ofp＝30，kr＝100，ωnThe parameters of the controller in fig. 3-8 are the same as in fig. 2 at 314 rad/s. The rated frequency of the system in initial operation is 50Hz, the rated frequency is suddenly changed to 49Hz at 1.2s when the PI controller equivalent method taking the PR controller as the reference is verified, and the rated frequency is suddenly changed to 49.5Hz at 1.2s when the PR controller equivalent method taking the PI controller as the reference is verified.
Fig. 13 is a comparison graph of frequency response waveforms before and after correction of the equivalent PI controller based on the PR controller, and as can be obtained from the partially enlarged view in fig. 9, when the system is started, the difference of frequency dynamic characteristics corresponding to the equivalent PI controller before and after correction is large, and the frequency dynamic response of the PI controller after correction completely coincides with that of the original PR controller. Meanwhile, it can also be obtained from fig. 9 that steady-state frequency differences still exist in the PI controllers before and after the correction after the frequency disturbance, and the transient state and steady-state frequency responses of the corrected PI controller are completely consistent with those of the original PR controller.
Fig. 14 is a comparison diagram of frequency response waveforms before and after modification of an equivalent PR controller based on a PI controller, when a system is started, a frequency response corresponding to the modified PR controller is completely consistent with an original PI controller, and after a system frequency is disturbed, frequency dynamic characteristics corresponding to the original PI controller and the modified PR controller are completely consistent, while an unmodified PR controller has not only a steady-state frequency error but also a transient frequency response characteristic that is significantly different from that of the original PI controller. By the two examples, the effectiveness of the proposed equivalent method of the PR controller and the PI controller considering the frequency dynamic characteristic is verified.

Claims (5)

1. A PR control and PI control equivalent method considering frequency dynamic characteristics is characterized by comprising the following steps:
step 1: establishing a PR controller model, and deducing a PI controller model corresponding to a synchronous rotation coordinate system under the condition of not considering the dynamic characteristics of frequency by taking a PR controller under a static coordinate system as a reference;
step 2: correcting the reference current, the feedback current, the modulation signal and the phase-locked loop of the PI controller under the synchronous rotating coordinate system by considering the dynamic characteristic of the frequency;
and step 3: taking a PI controller under a synchronous rotating coordinate system as a reference, and deducing a PR controller corresponding to the PI controller under a static coordinate system under the condition of not considering the dynamic characteristic of frequency;
and 4, step 4: the reference current, feedback current, and modulation signal of the PR controller in the stationary coordinate are modified in consideration of frequency dynamics.
2. The equivalent method of PR control and PI control considering frequency dynamics as claimed in claim 1, wherein the step 1 specifically comprises:
the transfer function of the PR controller in the stationary frame is:
Figure FDA0003297057040000011
wherein, ω is0At a nominal angular frequency, kpIs proportional gain, k, of the PR controllerrFor PR controller resonance gain, s is Laplace operator, j represents complex number;
when the frequency dynamic characteristic is not considered, the transfer function of the PI controller under the synchronous rotating coordinate system is expressed as follows:
Figure FDA0003297057040000012
the expression of the output voltage after passing through the PI controller is obtained according to the formula (2) and is as follows:
Figure FDA0003297057040000021
wherein u isdAnd uqRespectively representing d-axis and q-axis voltages, Δ i, output by the PI controllerdAnd Δ iqRepresenting d-axis and q-axis current errors, respectively.
3. The equivalent method of PR control and PI control considering frequency dynamics as claimed in claim 2, wherein the step 2 requires modification of the signal of the PI controller, and the specific modification principle is:
the corrected current reference value under the dq coordinate system is as follows:
Figure FDA0003297057040000022
wherein, IdqrefmFor corrected reference current input of PI controller under rotating coordinate system, IdqrefαβThe reference current input of the PR controller under a static coordinate system is shown, omega' is the output angular frequency of the phase-locked loop PLL, and t is a time variable;
feedback current i after correction under dq coordinate systemdmAnd iqmComprises the following steps:
Figure FDA0003297057040000023
wherein ia、ibAnd icThree-phase current representing actual output of the inverter;
modified modulation signal v in dq coordinate systemαβmExpressed as:
Figure FDA0003297057040000024
wherein u isdqA dq axis voltage vector representing the output of the PI controller;
modified phase-locked loop input e in dq coordinate systemqmExpressed as:
Figure FDA0003297057040000025
wherein e isdqRepresents the equivalence of the output of the PR controller in the dq coordinate system under the alpha beta coordinate system; im denotes taking the imaginary part of the output.
4. The equivalent method of PR control and PI control considering frequency dynamics as claimed in claim 3, wherein said step 3 is specifically:
the transfer function of a PR controller in a stationary coordinate system, without considering the frequency dynamics, is equivalent to:
Figure FDA0003297057040000031
the expression of the output voltage after passing through the PR controller is obtained according to formula (8) as follows:
Figure FDA0003297057040000032
wherein u isαAnd uβRespectively representing the alpha and beta axis voltages, Δ i, of the PR controller outputαAnd Δ iβRepresenting the alpha and beta axis current errors, respectively.
5. The equivalent method of PR control and PI control considering frequency dynamics as claimed in claim 4, wherein the PR controller signal is modified in step 4 according to the following specific modification principle:
corrected current reference value i under alpha beta coordinate systemαβrefmComprises the following steps:
Figure FDA0003297057040000033
wherein idqrefRepresents a dq-axis reference current;
the feedback current of the PR controller is corrected according to the following principle:
idqm＝iαβe-jω′t (11)
feedback current i after correction under alpha beta coordinate systemam、ibm、icmComprises the following steps:
Figure FDA0003297057040000041
wherein idqmIs a modified dq-axis current i in an alpha beta coordinate systemαβThe actual output current of the inverter under an alpha beta coordinate system;
the modulation signal of the PR controller is corrected by the following principle:
Figure FDA0003297057040000042
wherein u isαβAn α β axis voltage vector representing the output of the PR controller;
corrected three-phase modulation signal v under alpha and beta coordinate systemam、vbm、vcmCan be expressed as:
Figure FDA0003297057040000043
wherein v isdmAnd vqmRespectively represent the d-axis and q-axis modulation signals after being corrected under the dq coordinate system.
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CN110138253A (en) * 2019-06-28 2019-08-16 盐城正邦环保科技有限公司 A kind of photovoltaic combining inverter control method that multi-resonant PR and PI jointly controls
CN112039359A (en) * 2020-07-29 2020-12-04 盐城工学院 Current control method of quasi-PCI (peripheral component interconnect) and PI (proportional integral) combined control single-phase photovoltaic grid-connected inverter
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CN112968468A (en) * 2021-02-05 2021-06-15 山东大学 Grid-connected converter negative sequence current control method and system under single dq-PI current control structure

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CN115714547A (en) * 2023-01-09 2023-02-24 四川大学 Method for balancing voltage of cascade PWM rectifier based on consistency control
CN115714547B (en) * 2023-01-09 2023-04-14 四川大学 Method for balancing voltage of cascaded PWM rectifier based on consistency control

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