CN107769775A - A kind of adaptive variable-gain quick response phaselocked loop improved method - Google Patents
A kind of adaptive variable-gain quick response phaselocked loop improved method Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03L—AUTOMATIC CONTROL, STARTING, SYNCHRONISATION OR STABILISATION OF GENERATORS OF ELECTRONIC OSCILLATIONS OR PULSES
- H03L7/00—Automatic control of frequency or phase; Synchronisation
- H03L7/06—Automatic control of frequency or phase; Synchronisation using a reference signal applied to a frequency- or phase-locked loop
- H03L7/08—Details of the phase-locked loop
- H03L7/10—Details of the phase-locked loop for assuring initial synchronisation or for broadening the capture range
- H03L7/107—Details of the phase-locked loop for assuring initial synchronisation or for broadening the capture range using a variable transfer function for the loop, e.g. low pass filter having a variable bandwidth
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Abstract
The invention discloses a kind of phaselocked loop improved method based on adaptive variable-gain, for realizing quick response, including：Power network three-phase voltage signal is sampled, becoming three-phase voltage of changing commanders using Clark conversion and Park is converted to two-phase voltageu d Withu q ；According to the phaselocked loop based on synchronous coordinate system（SRF‑PLL）Nonlinear mathematical model, obtain the phaselocked loop open-loop transfer function containing non-linear phase demodulation link；Open-loop cut-off frequency is obtained by transmission functionω c With input deviationeRelation, structure contain amplitudeA, nonlinear system deviationeAnd linear system deviationu q Variable-gain function, reduce mission nonlinear degree；Conventional PI control device is transformed using the variable-gain function, designs Adaptive Integral gainInstead of originalk i , obtain adaptive variable-gain phase-locked loop systems；By carrying out time-domain analysis to closed loop equivalent linear system, complete systematic parameter and adjust.The present invention is by building Gain-scheduling control, reduce the nonlinearity of open cycle system, the coupled relation between angular speed and angle is reduced, realizes the reduction of phaselocked loop dynamic transition time, and dynamic response comparative analysis is carried out to traditional phase-locked loop systems and improved phase-locked loop systems using emulation platform.
Description
Technical field
The present invention relates to the phaselocked loop improved method of adaptive variable-gain, for realizing system quick response.
Background technology
With the rapid development of Power Electronic Technique, the role that phaselocked loop is served as wherein is more and more important.Phaselocked loop
Feature is using the frequency and phase of the reference signal control loop internal oscillation signal of outside input, reaches the outer of electronic equipment
Portion's input signal purpose synchronous with the oscillator signal of inside.This technology is highly useful in data collecting system, because logical
Phaselocked loop is crossed, different data collecting plate cards can be caused to share same sampling clock, so that sampling clock is also synchronous,
Accuracy increases substantially.On the other hand, the phase demodulation link of phaselocked loop utilizesMode realize, work as outside
When input signal is small-signal, the angle of deviationeIt is intended to zero, sin noweWitheAlmost overlap, can be approximated to be linearly,
Lock is mutually accurate, and dynamic response is rapid.But when external input signal is big signal, the angle of deviationeIt is larger, sineCan not
Ignore, sin noweNonlinear degree it is larger, cut-off frequencyω c Reduce, the actual value of bandwidth is smaller than theoretical value, phaselocked loop
The transit time of system increases, and corresponding dynamic responding speed is slack-off.
Such as a kind of quick three-phase voltage phase-locked loop method of the patent of application number 201510834014.8 and its dynamic response
Energy analysis method, comprises the following steps：The first step, three-phase power grid voltage is sampled, then obtaining two-phase by coordinate transform revolves
Turn component of voltage under coordinate system；Second step, class adjuster is obtained according to open-loop transfer function, sample frequency and fundamental wave angular frequency and joined
The root locus of number change；High order system equivalent-simplification is turned into typical case by the 3rd step, root locus by the method for closed loop dominant apices
Second-order system, obtain damped coefficient corresponding to two kinds of three-phase voltage phaselocked loops；4th step, two kinds are respectively obtained according to damped coefficient
The convergence time of typical second-order system corresponding to voltage phaselocked loop；5th step, pair of two kinds of three-phase voltage phaselocked loops is calculated respectively
Slope of the curve answered at zero crossing, and according to two slope of a curves compare two three-phase voltage phaselocked loops reach stable state when
Between.
Such as phaselocked loop dynamic property improved method of the patent based on sliding filter of application number 201510227128.6, step
Suddenly include：By three-phase voltageu a 、u b 、u c Two-phase voltage is converted to by Clark conversion and Park conversionu d 、u q .By acquisitionu d
After differentiating divided by angular frequency parameter, then again withu q Addition obtains, willu q Differentiate after divided by angular frequency parameter, then
Again withu d Addition obtains；WillBy obtaining fundamental positive sequence voltage magnitude after sliding filter；WillPass through sliding filter
Entered again by adjuster, the output of adjuster plus the line voltage angular frequency that phaselocked loop measures is obtained after default angular frequency afterwards
Row integration obtains the electric network voltage phase that phaselocked loop measures, and is fed back to input and completes closed-loop control.
The content of the invention
For above-mentioned existing technical problem, the present invention utilizes a kind of improvement of adaptive variable-gain quick response phaselocked loop
Method.The realization of this method is according to phase-locked loop systems open-loop bandwidth, builds Adaptive Integral gain, reduces the non-linear of system
Change degree, improves the response speed of system, and the application proposes the validity and correctness of method by simulating, verifying.
To achieve the above object, concrete scheme of the invention is as follows：
Adaptive variable-gain quick response phaselocked loop improved method, comprises the following steps
Step 1：By the voltage in three-phase static coordinate systemu a 、u b 、u c Be converted to voltage in two-phase rotating coordinate systemu d 、u q ；
Step 2：Phaselocked loop based on synchronous coordinate system（SRF-PLL）Nonlinear mathematical model, obtain containing non-linear phase demodulation link
Phaselocked loop open-loop transfer function；
Step 3：The open-loop cut-off frequency of the transmission function obtained according to step 2ω c With input deviationeRelation, structure become
Gain functionF(e)；
Step 4：Utilize the variable-gain function in step 3F(e)Conventional PI control device is transformed, designs Adaptive Integral gain
Instead of originalk i , obtain adaptive variable-gain phase-locked loop systems；
Step 5：System closed loop equivalent linear model is established, and carries out time-domain analysis.
Wherein, the voltage become in step 1 using Clark in three-phase static coordinate system of changing commandersu a 、u b 、u c It is straight to be converted to two-phase
Voltage in angular coordinate systemu α 、u β , specific formula is as follows：
Then become using Park and changed commandersu α 、u β Be converted under two-phase rotating coordinate systemu d 、u q 。
WhereinFed back for the output angle of phaselocked loop.
In step 2, the phaselocked loop based on synchronous coordinate system of foundation（SRF-PLL）Nonlinear mathematical model.Because
Voltage conversion in three-phase static coordinate system is in two-phase rotating coordinate system in voltage course, and the phase demodulation link of phaselocked loop utilizesMode realize that therefore system model has non-linear partial：,For angle
Spend deviation,θFor A phase line voltage angles,For the voltage vector magnitude under synchronous coordinate system..
According to the nonlinear model of phaselocked loop, obtaining non-linear open-loop transmission function is
In formula；
K(e)For non-linear gain, change with input deviation and change.
Transmission function in step 2 obtains open-loop cut-off frequencyω c ：
Influence of the phase demodulation link to input deviation is considered to turn into variable-gain item, utilizes frequency-domain analysis cut-off frequencyω c ；Pass through profit
Use amplitudeA, nonlinear system deviationeAnd linear system deviationu q Build variable-gain functionF(e), the function containing input angle and
Relevant nonlinear information, for bucking-out system nonlinearity.
In formula,k c For adjustment factor.
The present invention is transformed using the integral constant in variable-gain function pair conventional PI control device.
In formula,k i For the storage gain of former phase-locked loop systems.
Closed loop transfer function, during the system closed loop equivalent linear model established in step 5 is as follows：
Natural frequencyω n With damped coefficientRelational expression it is as follows：
Adaptive Integral gainIt is significantly less than the storage gain of conventional phase locked loopsk i , therefore work asInstead ofk i When, damped coefficient
Increase, natural frequencyIt is corresponding to reduce, stillω n Reduce speed not catching up withThe speed of increase, therefore attenuation coefficientIncrease, the rate of decay accelerate, and the response process that system reaches end-state from original state accelerates.Using deviation with
The relation of system damping coefficient.The overshoot of second-order system only it is relevant with damped coefficient, in the case of underdamping, damped coefficient with
Overshoot is in inverse relation, and damping is bigger, and overshoot is smaller, and vice versa.Therefore in the case of deviation is larger, adjusted by adjusting
Save coefficientk c , increase underdamping coefficient as far as possible, increase the rate of decay, reduce the overshoot of system, system oscillation reduces, and is
System stationarity takes a turn for the better.
Compared with conventional phase locked loops performance, the present invention, which realizes, to be markedly improved.Between 0 degree ~ 180 degree, adaptive product
Divide gainHave been able to reduce the phase stabilization time, slightly improve the stabilization time of large amplitude saltus step, limit big frequency
Rate deviation.In general, increasing the bandwidth of phaselocked loop, the nonlinearity of system is reduced, it is equivalent to improve damped coefficient, drop
Low system overshoot, improve the dynamic responding speed of system.
Brief description of the drawings
The mathematical modeling block diagram of Fig. 1 phaselocked loops；
Cut-off frequency in Fig. 2 phaselocked loopsω c And deviationeRelationship experiments figure；
In Fig. 3 phaselocked loopsAnd deviationeRelationship experiments figure；
The new phase-locked loop structures block diagrams of Fig. 4
Fig. 5 conventional phase locked loops and the cut-off frequency experimental comparison figure of new phaselocked loop；
The experimental comparison figure of the new phaselocked loops of Fig. 6 and conventional phase locked loops dynamic response time.
Embodiment
In order that the experiment purpose of the present invention becomes apparent from understanding with advantage, below Structure Figure explanation, it is further detailed
Illustrate：
Fig. 1 is the structure chart of phaselocked loop, is by three-phase voltage firstu a 、u b 、u c Be converted to by Clarke conversionu α 、u β , then profit
Become with Park and changed commandersu α 、u β Be converted tou d 、u q 。
Fed back for the output angle of phaselocked loop,θFor A phase line voltage angles,For angular deviation；, whereinFor the voltage vector magnitude under synchronous coordinate system.
In nonlinear mathematical model, phase demodulation link utilizesMode realize, therefore system model
Non-linear partial be present：, this be present in system forward passage.Obtained according to the nonlinear model of phaselocked loop
It is as follows to the open-loop transfer function of the system, formula：
Fig. 2 is cut-off frequency in phaselocked loopω c And deviationeRelationship experiments figure, the non-linear open-loop transmission function in Fig. 1
Cut-off frequency can be obtainedω c Expression, formula is as follows：
According to cut-off frequencyω c Formula, influence of the phase demodulation link to input deviation is considered to turn into variable-gain item, is utilized respectively
Cut-off frequencyω c And deviationeRelation curve and become integral constantAnd deviation e relation curve obtains cut-off frequencyω c
With change integral constantRelation.
Fig. 3 is in phaselocked loopAnd deviation e relationship experiments figure, according to Fig. 2 and cut-off frequencyω c Formula substantially send out
It is existingWith cut-off frequencyω c It is in close relations.
In deviationeWhen being intended to 0,The limit tends to 1, nowu q Tend to 0,Tend to, but deviatione
When larger,u q Increase, the nonlinearity increase of phase-locked loop systems, therefore utilizeAs integral constant is become, by phaselocked loop system
The deviation control of system tends to 0 state in infinitesimal.
Fig. 4 is new phase-locked loop structures block diagram, should more non-linear integral increasings with conventional phase locked loops structure chart compared with
Benefit.According to Fig. 2 cut-off frequenciesω c And deviationeRelation and Fig. 3 become integral constantAnd deviationeRelation obtain cutoff frequency
Rateω c WithRelation, on this basis structure contain amplitudeA, nonlinear system deviationeAnd linear system deviationu q Change
Gain functionF(e)。
The function contains input angle and relevant nonlinear information, for bucking-out system nonlinearity.
Fig. 5 is the cut-off frequency experimental comparison figure of conventional phase locked loops and new phaselocked loop.
Utilize variable-gain functionF(e)Build new Adaptive Integral gainInstead of original storage gaink i :
To the cut-off frequency of traditional phaselocked loopω c Be improved for, formula is as follows
Fig. 6 is the experimental comparison figure of new phaselocked loop and conventional phase locked loops dynamic response time, utilizes variable-gain functionF(e)Change
Make conventional PI control device, the Adaptive Integral gain of designInstead of originalk i , obtain adaptive variable-gain phase-locked loop systems.
Reduce the nonlinearity of open cycle system, reduce the coupled relation between angular speed and angle, realize phaselocked loop dynamic transition time
Reduce.
Claims (7)
1. a kind of adaptive variable-gain quick response phaselocked loop improved method, it is characterised in that this method comprises the following steps
Step 1：Voltage ua, ub, uc in three-phase static coordinate system is converted into voltage ud, uq in two-phase rotating coordinate system；
Step 2：Phaselocked loop nonlinear mathematical model based on synchronous coordinate system, obtain the phaselocked loop containing non-linear phase demodulation link
Open-loop transfer function；
Step 3：The open-loop cut-off frequency ω c and input deviation e of the transmission function obtained according to step 2 relation, structure become
Gain function F (e)；
Step 4：Conventional PI control device is transformed using the variable-gain function F (e) in step 3, designs Adaptive Integral gainGeneration
For original storage gainki, obtain adaptive variable-gain phase-locked loop systems；
Step 5：System closed loop equivalent linear model is established, and carries out time-domain analysis.
2. adaptive variable-gain quick response phaselocked loop improved method according to claim 1, it is characterised in that the step
Rapid one specifically includes：
By line voltage ua, ub, uc in three-phase static coordinate system, be converted to by Clark conversion in two-phase rest frame
Voltage u α, u β；
Then become change commanders u α, u β using Park and be converted to ud, uq under two-phase rotating coordinate system
WhereinFed back for the output angle of phaselocked loop.
3. adaptive variable-gain quick response phaselocked loop improved method according to claim 1 or 2, it is characterised in that institute
Step 2 is stated to specifically include：
Phase demodulation link utilizesMode realize that therefore phaselocked loop model has non-linear partial Asine, its
In, θ is A phase line voltage angles,For angular deviation；, whereinFor synchronous seat
Voltage vector magnitude under mark system.
4. it is so as to obtain non-linear open-loop transmission function
Wherein, θ is A phase line voltage angles,For angular deviation；WhereinFor under synchronous coordinate system
Voltage vector magnitude, kp are the proportional gain of phase-locked loop systems, and ki is the storage gain of phase-locked loop systems,
For non-linear gain, change with input deviation and change.
5. adaptive variable-gain quick response phaselocked loop improved method according to claim 3, it is characterised in that the step
Rapid three specifically include：
Influence of the phase demodulation link to input deviation is considered to turn into variable-gain item, utilizes frequency-domain analysis cut-off frequency ω c；
Make deviation e be changed by 0 ~ π, obtain cut-off frequency ω c and deviation e relation curve and become integral constantAnd deviation e
Relation curve, both of which reduce with deviation e increase, and mission nonlinear degree is larger；In the section of-π ~ 0, relation curve with
0 ~ π curve is mirrored into symmetric relation；
Build variable-gain function F (e)
In formula,k c For adjustment factor.
6. adaptive variable-gain quick response phaselocked loop improved method according to claim 4, it is characterised in that the step
Rapid four specifically include：
Transformed using the integral constant of variable-gain function pair pll controller
In formula,k i For the storage gain of former phase-locked loop systems,k c For the adjustment parameter of adaptive variable-gain phase-locked loop systems.
7. adaptive variable-gain quick response phaselocked loop improved method according to claim 5, it is characterised in that the step
Rapid five specifically include：
Establish system closed loop equivalent linear model
Natural frequencyω n With damped coefficientRelational expression it is as follows：
；
Adaptive Integral gainIt is significantly less than the storage gain of conventional phase locked loopsk i , therefore work asInstead ofk i When, damped coefficient
Increase, natural frequencyIt is corresponding to reduce, stillω n Reduce speed not catching up withThe speed of increase；In underdamping situation
Under, the growth that the input of system responds over time finally decays to steady-state value, and its rate of decay depends primarily on attenuation coefficient；By adjusting adjustment factork c , increase underdamping coefficient as far as possible, increase the rate of decay, accelerate response speed.
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| CN114123289A (en) * | 2021-11-29 | 2022-03-01 | 国网浙江省电力有限公司 | Flexible direct current transmission system and oscillation suppression method thereof |
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| CN114123289A (en) * | 2021-11-29 | 2022-03-01 | 国网浙江省电力有限公司 | Flexible direct current transmission system and oscillation suppression method thereof |
| CN114123289B (en) * | 2021-11-29 | 2023-08-25 | 国网浙江省电力有限公司 | Flexible direct current transmission system and oscillation suppression method thereof |
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