CN110535150B - Predictive dead beat repetitive control optimization method combining instant sampling - Google Patents

Predictive dead beat repetitive control optimization method combining instant sampling Download PDF

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CN110535150B
CN110535150B CN201910884966.9A CN201910884966A CN110535150B CN 110535150 B CN110535150 B CN 110535150B CN 201910884966 A CN201910884966 A CN 201910884966A CN 110535150 B CN110535150 B CN 110535150B
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control
beat
sampling
delay
dead beat
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CN110535150A (en
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任国东
李旭
都瑞雪
赵东争
许超
王振浩
成龙
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Heihe Power Supply Co Of State Grid Heilongjiang Electric Power Co ltd
State Grid Heilongjiang Nenjiang Electric Power Bureau Co ltd
Northeast Electric Power University
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Heihe Power Supply Co Of State Grid Heilongjiang Electric Power Co ltd
State Grid Heilongjiang Nenjiang Electric Power Bureau Co ltd
Northeast Dianli University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/26—Arrangements for eliminating or reducing asymmetry in polyphase networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/50—Arrangements for eliminating or reducing asymmetry in polyphase networks

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Abstract

A predictive dead beat repeated control optimization method combining instant sampling belongs to the technical field of power control and application. The invention aims at solving the control delay problem of dead beat control, and provides a predictive dead beat repeated control optimization method combining instant sampling, which is used for optimizing a control algorithm of the dead beat control based on predictive dead beat control compensation and combining the instant sampling method. The PWM is equivalent to ZOH, which is equivalent to 0.5 beat delay, the dead beat control is adopted for compensation, in order to effectively reduce the control delay of 1.5 beat, the sampling point is set at the peak for sampling through instant sampling, and the sampling point is advanced by 0.5 beat; predictive dead beat and repetitive control are combined. The invention effectively improves the stability margin and the control precision of the system, then combines the repeated control algorithm to realize high control precision, and comprehensively optimizes the current inner loop, so that the current inner loop simultaneously takes the response speed, the control precision and the stability margin into consideration.

Description

Predictive dead beat repetitive control optimization method combining instant sampling
Technical Field
The invention belongs to the technical field of power control and application.
Background
The low-voltage distribution network mainly supplies power for residents and rural networks, has various loads and large fluctuation, and has the power quality problems of serious harmonic pollution, three-phase unbalance, large reactive load and the like. The harmonic current can generate local resonance in the power distribution network, so that equipment such as a transformer and the like generate larger additional loss, and the operation of the equipment is influenced or even threatened; the unbalance of the three phases can cause the voltage of a certain phase to be too high or too low, thereby seriously affecting the normal operation of equipment, and causing additional loss of equipment such as a neutral line, a generator and the like; reactive power can lead to reduced line load capacity, additional line losses, etc. Thus, the low voltage distribution network requires an appropriate compensation treatment scheme to handle it. At present, the PWM converter can compensate harmonic waves, unbalance and reactive power at the same time, has high response speed and stepless regulation, and is an effective means for treating the electric energy quality problem of the low-voltage distribution network.
The key link of the PWM converter is a current inner loop control algorithm, and the traditional control mode of the current inner loop algorithm comprises model prediction control, hysteresis control, PI control, proportional resonance control, repeated control, no-difference terrible control and the like. The model predictive control has the characteristics of high response speed, higher control precision and the like by searching the optimal point control through model prediction, but the theory has difficulty in analyzing the stability and the control precision; the hysteresis control is a variable structure control mode, is real-time control, has high response speed and simple algorithm, but the output frequency change is unfavorable for the design of a filter and is difficult to theoretically analyze; the PI control algorithm is mature and stable, but the response speed is slower; the proportional resonance control achieves high-precision control by making a certain frequency have high gain, however, harmonic compensation requires a proportional resonance controller for each frequency, and the algorithm is complex. The repeated control can realize high gain of multiple frequencies to realize high-precision control but has slow response speed; the dead beat control has the characteristics of quick response, no overshoot, simple algorithm, easy analysis and the like, is widely researched and applied, but has the problems of control precision and stability margin due to the problem of control delay.
Disclosure of Invention
The invention aims at solving the control delay problem of dead beat control, and provides a predictive dead beat repeated control optimization method combining instant sampling, which is used for optimizing a control algorithm of the dead beat control based on predictive dead beat control compensation and combining the instant sampling method.
The method comprises the following steps:
(1) Equivalent PWM to ZOH, equivalent to 0.5 beat delay, adopting predictive dead beat control to compensate; the k control period is a predictive dead beat control model:
Figure BDA0002207035310000011
wherein L is the actual inductance value, i ref (k+2) is a k-time command current, i (k) is a k-time sampling current flowing into the inverter, u inv (k) Inverter output voltage calculated for the kth time, u s (k) Is u inv (k) The corresponding actual grid voltage during output; establishing its closed loop transfer function
Figure BDA0002207035310000012
wherein ,
Figure BDA0002207035310000013
setting inductance value for system, G LCL (z) is:
Figure BDA0002207035310000021
wherein ,TS Is a control period; ZOH equivalent is 0.5 beat delay, ZOH approximate equivalent is:
Figure BDA0002207035310000022
(2) In order to effectively reduce the control delay of 1.5 beats, a sampling point is set at a peak for sampling through instant sampling, the sampling point is advanced by 0.5 beats, the average value of the ripple voltage of the switching of the sampling point is 0, the total control delay is shortened to 1 beat, and the feedback voltage is sampled at the moment through LCL high-frequency filtering
Figure BDA0002207035310000023
Delay is shortened to 0.5 beat;
consider the sampled voltage
Figure BDA0002207035310000024
Equal to the actual voltage u s (k) Approximating the ZOH and delay half-beat links as delay one-beat links, and establishing closed loop transfer functions before and after optimization:
Figure BDA0002207035310000025
(3) Combining predictive dead beat and repetitive control to establish an error transfer function of the whole system:
Figure BDA0002207035310000026
through the small gain theorem, the stability of the repeated control system is ensured
||Q(z)[1-k rc B(z)G(z)]||＜1 (7)
wherein ,krc For repeatedly controlling the proportionality coefficient, Q (z) is an internal model transfer function, Q (z) adopts a zero-phase shift low-pass filter, and the z-domain transfer function is as follows:
Q(z)＝0.2z+0.6+0.2z -1 (8)
b (z) is a compensation transfer function
Figure BDA0002207035310000027
The invention effectively improves the stability margin and the control precision of the system, then combines the repeated control algorithm to realize high control precision, and comprehensively optimizes the current inner loop, so that the current inner loop simultaneously takes the response speed, the control precision and the stability margin into consideration. The system gives consideration to control precision, response speed and stability margin, and effectively compensates the dead beat control delay problem.
Drawings
FIG. 1 is a diagram of an on-the-fly sampling optimization execution process for predictive dead beat control;
FIG. 2 is a block diagram of an optimized instant sampling combined dead beat architecture;
FIG. 3 is a schematic diagram of a test field sensor arrangement;
FIG. 4 is a graph of an on-the-fly sampling optimization execution process for predictive dead beat control;
FIG. 5 is a block diagram of an optimized instant sampling combined dead beat architecture;
FIG. 6 is a block diagram of an optimized instantaneous sampling combined deadbeat repetitive control;
FIG. 7 is when k rc K when=0.15 L An amplitude-frequency characteristic curve of the formula (7) as a variable;
FIG. 8 is a graph of the amplitude versus frequency characteristic of equation (6);
FIG. 9 is a three-phase load current waveform;
FIG. 10 is a graph of the net side current waveform after compensation using dead beat control;
FIG. 11 is a graph of the net side current waveform after dead beat control compensation using instantaneous sampling optimization;
FIG. 12 is a graph of the net side current waveform after dead beat repetitive control compensation using instantaneous sampling optimization;
FIG. 13 is a set k L At=1.8, the current waveform diagram is repeatedly controlled without optimized prediction dead beat;
FIG. 14 is a set k L At=1.8, the optimized predictive dead beat repetitive control current waveform map;
FIG. 15 is a set k L At=0.6, the current waveform diagram is repeatedly controlled without optimized prediction dead beat;
FIG. 16 is a set k L At=0.6, optimized predictive dead beat repetitive controlAnd (5) generating a current waveform diagram.
Detailed Description
The method comprises the following steps:
(1) For the actual dead beat control system, after sampling is completed, one control period is needed to calculate, so that 1 beat delay is generated, PWM is equivalent to ZOH for accurately describing PWM modulation characteristics, the ZOH is equivalent to 0.5 beat delay, the 1.5 beat delay leads to instability of dead beat control, and predictive dead beat control is adopted to compensate first. The k control period is a predictive dead beat control mathematical model:
Figure BDA0002207035310000031
wherein L is the actual inductance value, i ref (k+2) is a command current at time k. i (k) is the sampling current flowing into the inverter at the moment k, u inv (k) Inverter output voltage calculated for the kth time, u s (k) Is u inv (k) And outputting corresponding actual grid voltage.
Output u is completed in calculation due to the actual grid voltage inv (k) Afterwards, consider the pre-sampling of the feed-forward voltage
Figure BDA0002207035310000034
Approximate actual voltage u s (k) Establishing a closed loop transfer function as formula (2)
Figure BDA0002207035310000032
wherein ,
Figure BDA0002207035310000033
the inductance value is set for the system, the inductance value is equal to the actual inductance value as much as possible to obtain high control precision,
G LCL (z) is:
Figure BDA0002207035310000041
wherein ,TS For the control period. ZOH is equivalent to a 0.5 beat delay,
the approximate equivalent of ZOH is:
Figure BDA0002207035310000042
(2) The instantaneous sampling is a sampling method for shifting the sampling time to the loading time of the modulation signal, and in order to effectively reduce the 1.5 beat control delay, the method is adopted for further optimizing the predictive dead beat control. The sampling point is set at the peak for sampling through instant sampling, the sampling point is advanced by 0.5 beat, the average value of the switching ripple voltage of the sampling point is 0, the problem of aliasing with switching noise is effectively avoided, and the total control delay is shortened to 1 beat. For the feedforward voltage sampling, the switching ripple is subjected to LCL high-frequency filtering, so that the switching ripple voltage component is greatly attenuated, and the feedforward voltage can be sampled directly before the PWM loading time, and the feedforward voltage is sampled at the moment
Figure BDA0002207035310000043
The delay is reduced to 0.5 beats.
Consider the sampled voltage
Figure BDA0002207035310000044
Equal to the actual voltage u s (k) The ZOH and the delay half-beat link are approximated as delay one-beat links, and closed loop transfer functions before and after optimization can be established as shown in a formula (5):
Figure BDA0002207035310000045
(3) The repeated control can well eliminate steady-state periodic errors, improves the control precision of the system, combines predictive dead beat and repeated control, and establishes an error transfer function of the whole system as shown in a formula (6):
Figure BDA0002207035310000046
through the small gain theorem, the stability of the repeated control system is ensured
||Q(z)[1-k rc B(z)G(z)]||＜1 (7)
wherein ,krc For repeatedly controlling the proportionality coefficient, Q (z) is an internal model transfer function, Q (z) adopts a zero phase shift low pass filter,
the z-domain transfer function is:
Q(z)＝0.2z+0.6+0.2z -1 (8)
b (z) is a compensation transfer function. In order to ensure the stability of the system,
the B (z) is as follows:
Figure BDA0002207035310000051
the predictive dead beat repeated control optimization method is used for combining instant sampling, the predictive dead beat control is used for enabling a control system to be stable, the instant sampling algorithm is combined for optimizing the sampling time, the whole control delay is effectively reduced from 1.5 beats to 1 beat, and the dead beat sampling feedforward voltage at the kth time is used
Figure BDA0002207035310000052
And the actual voltage u s (k) The delay is reduced from 1.5 beats to 0.5 beats, and then the control accuracy of the system is further improved by combining a repeated control algorithm.
PWM (Pulse Width Modulation) pulse width modulation technique;
ZOH (Zero Order Hold) is a zero order keeper;
the LCL filter is a structural form of the filter, the head part is a group of inductors connected in series, the middle part is a parallel safety capacitor, and the tail part is connected in series with a group of inductors.
(1) As shown in figure 1, the dead beat sampling feedforward voltage is sampled at the wave crest by reasonably optimizing the sampling position
Figure BDA0002207035310000053
Advance during loading PWMAnd line sampling effectively reduces the system control delay. />
(2) Modeling dead-beat control systems before and after adding immediate sampling optimization, respectively as shown in fig. 2 and 3, establishing transfer functions as shown in formula (5), and analyzing stability margin and control accuracy before and after optimizing the system as shown in fig. 4 and 5, wherein k L Is that
Figure BDA0002207035310000054
Stability margin of the optimized system is 0 < k L ＜2。
(3) As shown in FIG. 6, a control model is built to incorporate a repetitive control system, and to ensure the stability of the control system, the appropriate k is obtained by determining the inductance variation range requirement rc Values to ensure the establishment of equation (7) (small gain theorem), e.g. when k rc K when=0.15 L As shown in FIG. 7, the amplitude-frequency characteristic of equation (7) for the variable, it can be seen that 0.2 < k L The addition of the repetitive control system is stable at < 1.8, and the amplitude-frequency characteristic curve of the analytical formula (6) is shown in FIG. 8, and the degree of attenuation is at 50Hz and the frequency of the multiple after the addition of the repetitive control system.
The experimental analysis experiment shows that the three-level PWM converter compensates three-phase unbalance, harmonic wave and reactive current, fig. 9 shows three-phase load current waveforms, and THD of load current of each phase is 19.6% of phase A, 10.3% of phase B and 20.1% of phase C. Fig. 10 shows that the net side current after compensation is controlled by dead beat only, and the net side current is balanced, and the three-phase THD is reduced to about 5.5%. Fig. 11 shows the net side current waveform after the model machine is compensated by the optimized predictive dead beat control, and the three-phase THD is directly reduced to about 3%. FIG. 12 is a sample machine employing k rc When the three-phase THD is=0.04, the optimized prediction dead beat repeatedly controls the compensated current waveform at the net side, the three-phase THD is reduced to about 2.7%, the waveform is smoother, the three-phase balance degree is further improved, and the neutral line current is further reduced, so that the control accuracy is effectively improved by the control algorithm.
By modifying k in the control program L To verify the robustness of the system when k is set L When=1.8, the current waveform is repeatedly controlled by non-optimized and optimized predictive dead beatAs shown in fig. 13 and 14, respectively, the waveform of the non-optimized predictive dead beat repetitive control current is oscillated, and the optimized predictive dead beat repetitive control compensation is stable, and THD is about 3%. When setting k L When=0.6, the non-optimized and optimized predicted dead beat repetitive control current waveforms are shown in fig. 15 and 16, respectively, the non-optimized predicted dead beat repetitive control waveform THD is about 5.5%, and the optimized predicted dead beat repetitive control waveform THD is about 4.8%, so that the optimized dead beat repetitive control system has better stability against inductance variation.

Claims (1)

1. A predictive dead beat repetitive control optimization method combining instant sampling is characterized in that: the method comprises the following steps:
(1) Equivalent PWM to ZOH, equivalent to 0.5 beat delay, adopting predictive dead beat control to compensate; the k control period is a predictive dead beat control model:
Figure FDA0002207035300000011
wherein L is the actual inductance value, i ref (k+2) is a k-time command current, i (k) is a k-time sampling current flowing into the inverter, u inv (k) Inverter output voltage calculated for the kth time, u s (k) Is u inv (k) The corresponding actual grid voltage during output; establishing its closed loop transfer function
Figure FDA0002207035300000012
wherein ,
Figure FDA0002207035300000013
setting inductance value for system, G LCL (z) is:
Figure FDA0002207035300000014
wherein ,TS Is a control period; ZOH equivalent is 0.5 beat delay, ZOH approximate equivalent is:
Figure FDA0002207035300000015
(2) In order to effectively reduce the control delay of 1.5 beats, a sampling point is set at a peak for sampling through instant sampling, the sampling point is advanced by 0.5 beats, the average value of the ripple voltage of the switching of the sampling point is 0, the total control delay is shortened to 1 beat, and the feedback voltage is sampled at the moment through LCL high-frequency filtering
Figure FDA0002207035300000016
Delay is shortened to 0.5 beat;
consider the sampled voltage
Figure FDA0002207035300000017
Equal to the actual voltage u s (k) Approximating the ZOH and delay half-beat links as delay one-beat links, and establishing closed loop transfer functions before and after optimization:
Figure FDA0002207035300000018
(3) Combining predictive dead beat and repetitive control to establish an error transfer function of the whole system:
Figure FDA0002207035300000019
through the small gain theorem, the stability of the repeated control system is ensured
||Q(z)[1-k rc B(z)G(z)]||＜1 (7)
wherein ,krc For repeatedly controlling the proportionality coefficient, Q (z) is an internal model transfer function, Q (z) adopts a zero-phase shift low-pass filter, and the z-domain transfer function is as follows:
Q(z)＝0.2z+0.6+0.2z -1 (8)
b (z) is a compensation transfer function
Figure FDA0002207035300000021
/>
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