CN109981103B - Parameter optimization method and system for bi-second order generalized integrator frequency locking loop - Google Patents
Parameter optimization method and system for bi-second order generalized integrator frequency locking loop Download PDFInfo
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Abstract
The invention relates to a parameter optimization method and system for a bi-quad generalized integrator frequency locking loop, and belongs to the technical field of frequency locking loop adjustment. The method selects the parameter of the frequency locking loop of the biquad generalized integrator, namely the frequency locking loop integral gain coefficient, with the aim of minimum ITAE index, carries out iterative optimization through an evolutionary algorithm, does not need to analyze the mutual influence among modules in the DSOGI-FLL, can quickly and accurately determine the parameter of the frequency locking loop of the biquad generalized integrator, effectively avoids the problems of blindness, randomness and low efficiency of determining the DSOGI-FLL parameter by a heuristic method, and solves the problem that the parameter of the frequency locking loop of the biquad generalized integrator is difficult to determine at present.
Description
Technical Field
The invention relates to a parameter optimization method and system for a bi-quad generalized integrator frequency locking loop, and belongs to the technical field of frequency locking loop adjustment.
Background
The structure of a second-order generalized integrator frequency-locked loop (SOGI-FLL) is shown in fig. 1, which includes two parts, SOGI-QSG (SOGI-quadrature signal generator) and FLL (frequency-locked loop), where for a given sinusoidal input signal V = Vsin (ω t), V is the amplitude of the sinusoidal signal, ω is the angular frequency of the sinusoidal signal, V ' is an estimate of the input signal V in fig. 1, qv ' is the quadrature signal of V ', and ∈ is v For estimation error, ω' is the angular frequency of the signal estimated by FLL, γ is a signal amplification factor, and
wherein gamma is the frequency locking loop integral gain coefficient, and k is the damping coefficient. The basic principle of the SOGI-FLL locking signal frequency is: ε in SOGI-QSG v Product ε of qv' and f as inputs to the FLL module, qv 'and e, when the frequency of the sinusoidal input signal v is less than the output frequency ω' of the FLL v In phase, the product of the twoε f Is greater than 0; qv' and ε when the frequency ω of the input signal is greater than the FLL output frequency ω v Opposite in phase, the product of which is f Less than 0; when ω = ω', ε f And =0. Integrator with gain-gamma in FLL according to epsilon f Gradually adjust the FLL output frequency ω ', and finally make ω' = ω, thereby realizing frequency adaptation. According to the working principle of the frequency-locked loop, neglecting epsilon f The SOGI-FLL frequency-locked loop approximates to a first-order system, i.e. the frequency of the alternating current signal is 2 times omega
Where s is a complex variable often used in transfer functions.
A double second-order generalized integrator frequency-locked loop (DSOGI-FLL) has frequency self-adaption capability and is widely applied to the aspects of power grid synchronous control, positive and negative sequence component extraction, harmonic component detection and the like. The structure of the device is shown in FIG. 2, and comprises two SOGI-QSG modules and an FLL module, wherein the input signals
Is a set of quadrature signals, V is the signal amplitude, ω is the signal angular frequency,
is the signal initial phase angle, v' α For an input signal v α Estimate of (a ∈) vα Is estimation error, qv' α Is v' α Of orthogonal signal x 1α ＝v' α ，
Is x 1α First derivative of (a), x 2α Is x 1α Integral of (2); similarly, v' β For an input signal v β Estimate of (a ∈) vβ To estimate error, qv' β Is v' β Of the orthogonal signal x 1β ＝v' β ，
Is x 1β First derivative of (a), x 2β Is x 1β ω' is the signal frequency, ω, estimated by the FLL ff Is the nominal angular frequency of the signal.
In a two-phase static coordinate system, the estimation error expression in DSOGI-FLL is as follows:
whether or not ω' and ω are equal, for the state variable x 1α 、x 2β All have the following relations
The frequency error signal epsilon of DSOG FLL f Expressed as:
near a steady-state working point, omega '≈ omega, omega' 2 -ω 2 2 ω '(ω' - ω), the frequency response characteristic expression of DSOGI-FLL is therefore:
for a given sinusoidal input signal
And its quadrature signal
x 2α And x 2β Can be respectively expressed as:
the frequency response characteristic of DSOGI-FLL can be expressed as:
due to the fact that
And with
When the two signals are added, the alternating current signals with 2 times of omega frequency are mutually offset, so that the frequency locking response of DSOGI is not influenced by 2 times of frequency fluctuation components, and the dynamic process of the DSOGI is closer to a first-order system.
Let in the above formula
Due to the fact that
Then
Then there are
Wherein gamma is a frequency locking loop integral gain coefficient, and it can be seen that DSOGI-FLL and SOGI-FLL have similar frequency locking response characteristics, but the frequency locking response of DSOGI is not affected by 2 frequency multiplication fluctuation components, the dynamic process of the DSOGI is closer to a first-order system, and the transition process is smoother. It adjusts the time t s The estimated values are:
it can be seen that the parameter Γ has an important influence on the response characteristic of the frequency locking loop and is a key parameter of the frequency locking loop, but the prior art is directed at the frequency locking principle and the response characteristic of the DSOGI-FLL, no determination method for the parameter Γ is given, the larger the value Γ is, the better the value Γ is, because the larger Γ is, the longer the adjustment time t of the FLL is s The smaller the response speed of FLL, that is, the faster the response speed of FLL, but because the DSOGI module and the FLL module are interdependent, the above formula holds that the relation of the adjusting time of the FLL and the DSOGI module needs to be considered, if the value of the parameter gamma in the above formula is too large (corresponding to t calculated according to the above formula) s Too small) will result in too strong a dynamic coupling effect of the FLL and DSOGI parts, resulting in a non-decreasing increase in the tuning time of the FLL, whose dynamics can no longer be approximated using a first order system. Because the frequency-locked loop of the biquad generalized integrator is a nonlinear system, and the DSOGI module and the FLL module are interdependent, it is difficult to derive the integral gain coefficient gamma of the frequency-locked loop under a certain target by means of theory.
Disclosure of Invention
The invention aims to provide a parameter optimization method of a frequency locking loop of a biquad generalized integrator, which aims to solve the problem that the integral gain coefficient gamma of the frequency locking loop is difficult to determine by adopting a theoretical means at present; the invention also provides a parameter optimization system of the frequency locking loop of the biquad generalized integrator, which aims to solve the problem that the integral gain coefficient gamma of the frequency locking loop is difficult to determine by adopting a theoretical means at present.
The invention provides a parameter optimization method of a biquad generalized integrator frequency-locked loop for solving the technical problem, which comprises the following steps:
1) Selecting an ITAE index of a biquadratic generalized integrator frequency locking loop to construct a fitness function, wherein the ITAE index is an integral of the absolute value of the difference between the real frequency of a signal in a set time after the signal frequency is mutated and the frequency estimation value of the output signal of the biquadratic generalized integrator frequency locking loop multiplied by time;
2) And performing iterative optimization on the frequency locking loop integral gain coefficient by using an evolutionary algorithm, and selecting the corresponding frequency locking loop integral gain coefficient when the ITAE index is minimum as a parameter of the frequency locking loop of the biquad generalized integrator.
Meanwhile, the invention also provides a parameter optimization system of the bi-quad generalized integrator frequency-locked loop, which comprises a memory, a processor and a computer program stored in the memory and running on the processor, wherein the processor is coupled with the memory, and the processor executes the computer program to realize the following steps:
1) Selecting an ITAE index of a biquadratic generalized integrator frequency locking ring to construct a fitness function, wherein the ITAE index is the integral of the absolute value of the difference between the real frequency of a signal in a set time after the signal frequency mutation and the frequency estimation value of the output signal of the biquadratic generalized integrator frequency locking ring multiplied by time;
2) And performing iterative optimization on the frequency locking loop integral gain coefficient by using an evolutionary algorithm, and selecting the corresponding frequency locking loop integral gain coefficient when the ITAE index is minimum as a parameter of the frequency locking loop of the biquad generalized integrator.
The invention selects the parameter frequency locking loop integral gain coefficient of the biquad generalized integrator frequency locking loop by taking the minimum ITAE index as the target, carries out iterative optimization through an evolutionary algorithm, does not need to analyze the mutual influence among modules in the DSOGI-FLL, can quickly and accurately determine the parameter of the biquad generalized integrator frequency locking loop, effectively avoids the problems of blindness, randomness and low efficiency of determining the DSOGI-FLL parameter by a heuristic method, and solves the problem that the parameter of the biquad generalized integrator frequency locking loop is difficult to determine at present.
Furthermore, the invention also provides a specific evolutionary algorithm to improve the efficiency and accuracy of iterative optimization, wherein the evolutionary algorithm adopts a particle swarm algorithm.
Further, in order to avoid excessive overshoot of the bi-quad generalized integrator frequency locking loop, the fitness function further includes a penalty term determined by an overshoot, and the fitness function is specifically expressed as:
F＝1/J ITAE_M
wherein F is the fitness value, J ITAE_M Is ITAE comprehensive index, t i For the integration duration, time 0 corresponds to the time when the signal frequency changes suddenly, e (t) is the frequency estimation error, sigma is the overshoot of the frequency-locked loop output of the biquad integrator, delta (sigma) is a function of sigma, and w 1 Is the weight of the error, w 2 Is a weight of the overshoot, and w 1 >>w 2 。
Further, in order to accurately describe the influence of the overshoot, the expression of the function of the overshoot is as follows:
σ a the allowed overshoot of the frequency locked loop.
Further, in order to improve the efficiency of iterative optimization, the method further comprises the step of determining an optimization interval of the integral gain coefficient of the frequency locking loop before the optimization iteration, and enabling the optimization iteration to be performed in the optimization interval, wherein the lower limit of the optimization interval is the integral gain coefficient of the frequency locking loop corresponding to the time when the adjustment time of the frequency locking loop FLL is equal to the adjustment time of the biquad generalized integrator DSOGI of the set multiple.
Furthermore, in order to quickly determine the upper limit of the optimizing interval, the invention also provides a determination mode of the upper limit, the upper limit of the optimizing interval is determined by a forward and backward method at the lower limit of the optimizing interval, and the integral gain coefficient of the frequency-locked loop is gradually increased according to a certain step length by taking the lower limit as a reference until the output of the frequency-locked loop of the biquadratic generalized integrator has overshoot and oscillation with a set degree.
Drawings
FIG. 1 is a block diagram of the structure of a prior art SOGI-FLL;
FIG. 2 is a block diagram of a prior art DSOGI-FLL;
FIG. 3 is a comparison graph of DSOGI-FLL output waveforms under different parameters in the embodiment of the present invention;
FIG. 4 is a schematic diagram of a global optimal fitness value convergence curve obtained by an embodiment of the present invention;
fig. 5 is a comparison diagram of response curves of a frequency-locked loop corresponding to a value of a typical parameter f in an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating the principle of obtaining the e (t) signal in the ITAE indicator according to the present invention;
FIG. 7 is a schematic diagram illustrating a step change in signal frequency according to an embodiment of the present invention;
FIG. 8 is a diagram illustrating a convergence curve of the global optimum fitness value of a 400Hz system in an embodiment of the present invention;
fig. 9 is a frequency locked loop response graph for a 400Hz system in an embodiment of the invention.
Detailed Description
Method embodiment
In order to illustrate the influence of a gamma value on the response characteristic of a frequency-locked loop, a simulation model is set up in matlab/simulink with reference to fig. 2, and two-phase signals v in the model α 、v β From three-phase signals u abc The signal u is obtained by abc-alpha-beta coordinate transformation, because the invention needs to consider the condition that the signal frequency fluctuates, at the moment, omega is changed, the integral of omega in a time range can not be expressed by omega any more, and the phase angle theta represents the integral of omega in the time range, the signal u in the invention abc The expression is as follows:
the actual frequency f = ω/2 π, ω is the angular frequency of the signal, θ is the integral of ω from time 0 to the current time t, and the signal is transformed by abc- α β to v αβ Then inputting the mixture into DSOGI-FLL.
Suppose the signal frequency ω is 98 π rad/s (49 Hz) at 0-0.2s, and abruptly changes to 100 π rad/s (50 Hz) at 0.2s. Next, the simulation is performed on the situation when the f value changes gradually from 20 to 300, several FLL simulation waveforms corresponding to typical f values are extracted from the FLL simulation waveforms, the result is shown in fig. 3, as can be seen from the simulation result in fig. 3, f is in the range of 20 to 70, and as f increases, the FLL adjustment time t is increased s Gradually decrease and adjustThe process is very close to a first-order inertia link, and basically has no overshoot; but in the range of 100 to 300, t is increased with Γ s Not only is the reduction not continued, but also the increase is carried out, and obvious overshoot and oscillation occur in the adjusting process, and the obvious difference occurs in the transition process of the first-order inertia link. That is, when the value of the parameter Γ is too large, the dynamic coupling effect of the FLL and the SOGI is too strong, so that the adjustment time of the FLL is not decreased or increased, and the dynamic characteristic of the FLL cannot be approximated by using a first-order inertia element. The optimization method is a parameter determination method aiming at minimizing an ITAE index, a fitness function is established through the ITAE index, iterative search is carried out by utilizing a particle swarm algorithm, and a frequency locking ring integral gain coefficient gamma which enables the ITAE index to be the minimum is determined, so that the determination of the frequency locking ring parameters of the biquadratic generalized integrator is realized. The following describes a parameter optimization process of a bi-quad generalized integrator frequency locking loop in a power grid in detail.
1. And establishing a fitness function by using an ITAE index of a biquadratic generalized integrator frequency locking loop.
In the parameter optimization of the PID control, an ITAE index is widely applied with good practicability and selectivity, and the ITAE index refers to the integral of an absolute value of an error multiplied by time. For DSOGI-FLL, ITAE index refers to the integral of the absolute value of the difference between the real frequency of a signal and the frequency estimation value of the frequency locking loop output signal of the biquad generalized integrator within a set time after the frequency mutation of the signal multiplied by the time; thus, the ITAE indices are:
wherein J is ITAE index, t i For integration time, e (t) is the error, e (t) is the difference between the actual frequency f of the input signal and the estimated frequency f' of the frequency locked loop output, as shown in fig. 6, for example, the three-phase input signal is:
the actual frequency f = ω/2 π, ω is the angular frequency of the signal, θ is the integral of ω from time 0 to the current time t, and the signal is transformed by abc- α β to v αβ And then inputting the signal to the DSOGI-FLL, wherein the output frequency f '= omega'/(2 pi) of the FLL, omega 'is an estimated value of the angular frequency of the signal output by the frequency locking loop, and e (t) = f (t) -f' (t).
As shown in fig. 7, when the frequency of the signal changes in steps, the curve shape of f' (t) is different under different f values, and as shown in fig. 3, there is no oscillation in some curves, but the response is slow (e.g. f = 20), there is a fast response in some curves, but there is a significant oscillation (e.g. f = 250), so that e (t) is different under different f values, and thus ITAE is different, and thus the ITAE index is used to optimize the f value here.
Because the frequency locking ring of the biquad generalized integrator is possible to generate overshoot in the adjusting process, in order to avoid the overshoot, the invention adds a punishment item to form a comprehensive ITAE index on the basis of the ITAE index:
and the particle fitness F is:
F＝1/J ITAE_M
wherein J ITAE_M For the comprehensive ITAE index, F is the fitness value, t i For integration duration, time 0 corresponds to time when signal frequency changes suddenly, e (t) is frequency estimation error, sigma is overshoot output by the frequency-locked loop of the biquad integrator, delta (sigma) is a function of sigma, and w is 1 Is the weight of the error, w 2 Is a weight of overshoot, and w 1 >>w 2 。
Wherein F is the fitness value of the particle, w 1 、w 2 As a weight value, w 2 >>w 1 In this example, w is taken 1 ＝1，w 2 =1000, σ is the overshoot of the frequency locked loop output, δ (σ) is a function of σ:
wherein σ a For the amount of overshoot allowed by the frequency locked loop, this embodiment is set to 1% of the frequency overshoot.
2. Iterative optimization is carried out on the frequency locking loop integral gain coefficient by utilizing an evolutionary algorithm, and the corresponding frequency locking loop integral gain coefficient when the fitness is maximum (namely the comprehensive ITAE index is minimum) is selected as a parameter gamma of the frequency locking loop of the biquad generalized integrator.
The PSO algorithm is an evolutionary computing technology based on group intelligence, which is inspired from the predation behavior of a bird group, has the characteristics of parallel processing, good robustness and the like, and can find a global optimal solution of the problem in a relatively large generalization. In the PSO algorithm, the solution of each optimization problem is a particle in a d-dimensional target search space, m particles form a group, the performance of each particle depends on a Fitness Value (Fitness Value) determined by an objective function of the problem to be optimized, the flying direction and the flying speed of each particle are determined by a speed, and the particles follow the current optimal particle to search in the solution space. The PSO is initialized to a population of random particles (random solution) and then an optimal solution is found by iteration.
X i (t)＝(X i1 (t),X i2 (t),…X id (t))
V i (t)＝(V i1 (t),V i2 (t),…V id (t))
Wherein, X i (t) denotes the position of the particle i at the t-th iteration, V i (t) represents the velocity of particle i at the tth iteration. During each iteration, the particle updates its velocity and position by tracking two "extrema". The first is the optimal solution found by the particle itself, called the individual extremum P i (t)＝(P i1 (t),P i2 (t),…P id (t)), the corresponding fitness value is F Pi (t); the other extreme is the best solution currently found for the whole population, this extreme is the global extreme P g (t)＝(P g1 (t),P g2 (t),…P gd (t))，Corresponding to a fitness value of F Pg (t)。
At the time of the (t + 1) th iteration, the particle i updates its speed and position according to the following rules:
V ik (t+1)＝wV ik (t)+c 1 r(P ik (t)-X ik (t))+c 2 r(P gk (t)-X ik (t))
X ik (t+1)＝X ik (t)+V ik (t+1)
where w is the inertial weight, c 1 、c 2 For the acceleration constant, r is a random number between (0,1), k =1,2, …, d.
Particularly for a biquadratic generalized integrator-frequency locked loop, the parameter to be optimized is f, so that the optimization is carried out in a one-dimensional space, and V in an iterative formula ik (t+1)、V ik (t)、P ik (t)、P gk (t)、X ik (t+1)、X ik (t) all have only one dimension (i.e. one real number), i.e. k can be omitted, X ik (t)、X ik (t + 1) is the gamma value of the ith particle in the t and t +1 iterations, P ik (t) is the individually optimal value of Γ, P, for the ith particle in the tth iteration gk (t) is the population optimal Γ value in the tth iteration of all particles, and by combining the above analysis, the iterative formula of the PSO algorithm can be set as:
V i (t+1)＝wV i (t)+c 1 r(P i (t)-Γ i (t))+c 2 r(P g (t)-Γ i (t)) (1)
Γ i (t+1)＝Γ i (t)+V i (t+1) (2)
in the formula of gamma i (t)、Γ i (t + 1) is the gamma value of the ith particle in the t and t +1 iterations, P i (t) is the individually optimal value of f, P, for the ith particle in the tth iteration g (t) is the population-optimal Γ value in the tth iteration of the total particle. The algorithm flow is as follows:
(1) Initializing various parameters of the particle swarm algorithm, including the size of the swarm, the number of iterations, and the acceleration constant c 1 、c 2 Inertia weight w and particle swarm search range;
(2) Initializing the position of each particle Γ i (0) And an initial velocity V i (0) Calculating a fitness value F for each particle i (0) And take P i (0)＝Γ i (0)，F pi (0)＝F i (0)；
(3) According to the fitness value F of each particle i (t) finding a globally optimal particle P g (t) and its corresponding fitness value F pg (t)；
(4) For each particle, its fitness value F is used i (t) and individual extremum P i (t) corresponding fitness value F pi (t) comparison if F i (t)>F pi (t), then using r i (t) replacement of P i (t) simultaneously with F i (t) replacement of F pi (t); for each particle, its fitness value F is used i (t) and a global extremum P g (t) corresponding fitness value F pg (t) comparison if F i (t)>F pg (t), then using r i (t) replacement of P g (t) simultaneously with F i (t) replacement of F pg (t)。
(4) Updating the velocity V of the particles according to equations (1) and (2) i And a position r i 。
(5) And (4) exiting if the ending condition is met (the error is small or the set maximum iteration number is reached), and returning to (3) if the error is not small.
P obtained after operation of optimization algorithm is finished g And (t) is the final optimal value of the gamma.
Besides the particle swarm algorithm, other evolutionary algorithms such as a genetic algorithm, a fish swarm algorithm and the like can be adopted.
In addition, in order to reduce the number of optimization iterations and improve efficiency and accuracy, the optimization interval of the parameter Γ needs to be determined before iteration optimization is performed.
When the value of the gamma is small, the response characteristic of the frequency-locked loop can be approximately analyzed according to a first-order inertia element, and the response time of the first-order inertia element is reduced along with the increase of the value of the gamma. Therefore, only a small value of Gamma is needed to be determined as a lower limit, and the response characteristic of the frequency-locked loop below the value of Gamma can be according to a first-order inertia loopThe response time is not as good as the gamma value, and the optimization is not necessarily involved. The embodiment selects the frequency locking loop to adjust the time t s Is 10t SOGI The corresponding parameter gamma is taken as the lower limit of the optimization interval of the parameter gamma, namely
t s ＝10t SOGI
In the formula, t SOGI Is the adjustment time of the SOGI-QSG. When the input signal is v = Vsin (ω t), the response of the SOGI-QSG is:
wherein
The adjustment time of the SOGI-QSG is:
in DSOGI-FLL, ω' is the output frequency of the frequency locked loop, tracking the frequency ω of the input signal, which is typically near the nominal frequency for the grid (i.e., ω ≈ ω) e ，ω e For the grid nominal frequency), ω ' tracks the frequency ω of the input signal, and therefore ω ' is also near the grid nominal frequency (i.e., ω ' ≈ ω) e ) Therefore, the adjustment time t of the SOGI SOGI ≈10/kω e 。
Thus:
wherein gamma is down For the lower limit of the optimization interval of the parameter Γ, Γ down Corresponding frequency-locked loop adjustment time t s ＝10t SOGI Can be considered ast s Is far greater than t SOGI (namely the response speed of the frequency-locked loop is far slower than that of a biquadratic generalized integrator), so that the dynamic coupling effect between the FLL and the SOGI module is small, and the response characteristic of the frequency-locked loop can be approximated according to a first-order system, and the ratio of the frequency-locked loop to the response characteristic of the SOGI module is more than gamma down The smaller parameter Γ corresponds to t s Larger (greater than 10 t) SOGI ) The dynamic coupling effect between the FLL and the SOGI module is smaller, and the corresponding frequency-locked loop response characteristic can also be approximated to a first-order system, and the adjustment time of the first-order system is increased along with the reduction of the parameter gamma, so that the ratio gamma is larger than that of the first-order system down The small parameter gamma corresponds to a regulation time ratio gamma down The corresponding adjusting time is long, and the optimization is not needed to be participated.
The upper limit of the optimizing interval is determined by a forward and backward method at the lower limit of the optimizing interval, and the integral gain coefficient of the frequency-locked loop is gradually increased according to a certain step length by taking the lower limit as a reference until overshoot and oscillation of a set degree appear at the output of the frequency-locked loop of the biquad generalized integrator (generally, the overshoot exceeds 10% of the frequency overshoot as a judgment standard). The process is as follows: firstly, using lower limit gamma of parameter gamma down Based on the length of advance and retreat, the length is increased by a step length h, i.e. let Γ = Γ down + h, where the initial step length h takes a value and Γ down Similarly, judging whether the overshoot amount of the output of the DSOGI-FLL exceeds 10% of the frequency overshoot amount, if not, enabling the advancing and retreating step length h =2h, continuously increasing the gamma value to enable gamma = gamma + h, judging the output of the DSOGI-FLL again until the output of the DSOGI-FLL has obvious overshoot and oscillation, and taking the corresponding parameter gamma at the moment as the upper limit gamma of the optimization interval up . Therefore, when the Quantum Particle Swarm Optimization (QPSO) is adopted, the determined optimization interval [ gamma ] can be set down ，Г up ]The method is carried out in the inner process.
System embodiment
The parameter optimization system of the bi-quad generalized integrator frequency locking loop comprises a memory, a processor and a computer program stored on the memory and running on the processor, wherein the processor is coupled with the memory, and the processor realizes the following steps when executing the computer program:
1) Selecting an ITAE index of a biquad generalized integrator frequency locking loop to construct a fitness function, wherein the ITAE index is an integral of an absolute value multiplied by time of a difference between a real signal frequency and a frequency estimation value of a biquad generalized integrator frequency locking loop output signal within a set time after a signal frequency mutation;
2) And performing iterative optimization on the frequency locking loop integral gain coefficient by using an evolutionary algorithm, and selecting the corresponding frequency locking loop integral gain coefficient when the ITAE index is minimum as a parameter of the frequency locking loop of the biquad generalized integrator.
The specific implementation means of the above steps have been described in the embodiments of the method, and are not described herein again.
In order to verify the feasibility and the effect of the invention, the process of determining the parameter f by adopting the PSO algorithm is simulated, and the PSO algorithm parameters are set as follows: the total population is 10, the maximum iteration number is 100,w =1,c 1 ＝c 2 =1.5, the simulation duration is 0.5s, and the integration start time should be 0.2s when calculating the ITAE index because the signal frequency abruptly changes at 0.2s. In order to avoid excessive overshoot and oscillation during the regulation, the overshoot σ is allowed a Take 1% of the frequency mutation. Thus, the fitness function F in this example is:
F＝1/J ITAE_M
optimizing the Γ according to the flow of the PSO algorithm to obtain a global optimal fitness value convergence curve as shown in FIG. 4, wherein the optimal parameter value obtained through optimization is as follows: r =77.54.
In order to illustrate the effect of the invention, a simulation model of corresponding DSOGI-FLL is built and simulated for Γ =50 and Γ =100 in simulink, and the simulation result is shown in fig. 5, where t1=31ms is the adjustment time of the frequency-locked loop at Γ =77.54, and t2=43ms is the adjustment time of the frequency-locked loop at Γ = 100. When the frequency locked loop output is not overshot when the Gamma =50, but the response speed is slow, the time for stabilizing within the error band of +/-1% of the frequency break variable is taken as the adjusting time, namely, the frequency locked loop output is stabilized at (f) after the frequency break is performed d ±ΔH×0.01)Hz(f d For the theoretical value after frequency mutation,. DELTA.H is the frequency mutation amount, in this example f d =50Hz, Δ H =1 Hz), the adjustment time is 70ms, which is greater than the frequency-locked loop adjustment time t1 (31 ms) of the present invention. When the f =100, the initial response speed of the frequency locking loop is high, but 5% of overshoot exists, and the adjustment time of the frequency locking loop which is finally stabilized in a 1% error band of the frequency abrupt change is 43ms and is also larger than 31ms.
Although the DSOGI-FLL frequency-locked loop response is slightly overshot by adopting the optimization method, the overshoot amount does not exceed 1% of the frequency mutation amount, and the adjustment time for stabilizing in the error band of 1% of the frequency mutation amount is 31ms and is less than the adjustment time when the Gamma =50 and the Gamma = 100. Therefore, comprehensively, the DSOGI-FLL frequency locking loop obtained by the invention has small overshoot, shorter adjustment time and more ideal response characteristic.
The embodiment of the invention aims at DSOGI-FLL in a power grid system, and the rated frequency of the DSOGI-FLL is generally 50Hz. Besides being applied to a power grid system, the DSOGI-FLL can also be used in other systems with rated frequency, for example, a 400Hz power supply system (aerospace) to realize the functions of frequency tracking, synchronous control and the like, and in order to obtain good frequency locking loop response characteristics, the parameter optimization method can also be adopted.
It should be noted that, because the frequency of the 400Hz signal is high, the maximum solving step length is not easy to exceed 5e-5s when calculating the signal fitness value, so as to avoid an excessive simulation error. The fitness convergence curve of the DSOGI-FLL in the Gamma value optimizing process of a 400Hz power supply system is shown in fig. 8, the obtained parameter optimization value Gamma =609.4905, the response curve of the DSOGI-FLL adopting the parameter is shown in fig. 9, and it can be seen that the adjusting time of the DSOGI-FLL stabilized in a 1% error band of the frequency mutation quantity is 4ms, and the overshoot is less than 1% of the frequency mutation quantity.
The parameter optimization method of the bi-quad generalized integrator frequency locking loop can be well applied to a 400Hz system. Meanwhile, the optimal gamma values corresponding to 50Hz and 400Hz systems are different, so when DSOGI-FLL is applied to a system with large signal rated frequency difference, the gamma value is optimized and selected according to the difference of the system rated frequency so that the gamma value is matched with the signal frequency, and further good dynamic response characteristics are obtained. Therefore, the method can be applied to the parameter determination of the DSOGI-FLL under various frequencies.
Claims (4)
1. A parameter optimization method of a bi-quad generalized integrator frequency-locked loop is characterized by comprising the following steps:
1) Selecting an ITAE index of a biquadratic generalized integrator frequency locking loop to construct a fitness function, wherein the ITAE index is an integral of the absolute value of the difference between the real frequency of a signal in a set time after the signal frequency is mutated and the frequency estimation value of the output signal of the biquadratic generalized integrator frequency locking loop multiplied by time; the fitness function further comprises a penalty term determined by the overshoot, and the fitness function is specifically expressed as:
F＝1/J ITAE_M
wherein F is the fitness value, J ITAE_M Is ITAE comprehensive index, t i For integration duration, time 0 corresponds to time when signal frequency changes suddenly, e (t) is frequency estimation error, sigma is overshoot output by the frequency-locked loop of the biquad integrator, delta (sigma) is a function of sigma, and w is 1 Is the weight of the error, w 2 Is a weight of the overshoot, and w 1 >>w 2 ；
The expression of the function of the overshoot is:
σ a the allowed overshoot of the frequency-locked loop;
2) Iterative optimization is carried out on the frequency locking loop integral gain coefficient by using an evolutionary algorithm, and the corresponding frequency locking loop integral gain coefficient when the ITAE index is minimum is selected as a parameter of a bi-quad generalized integrator frequency locking loop; determining an optimization interval of the integral gain coefficient of the frequency locking loop before optimization iteration, and enabling the optimization iteration to be carried out in the optimization interval, wherein the lower limit of the optimization interval is the integral gain coefficient of the frequency locking loop corresponding to the condition that the adjustment time of the frequency locking loop FLL is equal to the adjustment time of the DSOGI of the biquadratic generalized integrator with set multiple; the upper limit of the optimizing interval is determined by a forward and backward method at the lower limit of the optimizing interval, and the integral gain coefficient of the frequency-locked loop is gradually increased according to a certain step length by taking the lower limit as a reference until the output of the frequency-locked loop of the biquadratic generalized integrator has overshoot and oscillation with a set degree.
2. The method for optimizing parameters of a biquad generalized integrator frequency-locked loop according to claim 1, wherein the evolutionary algorithm in step 2) is a particle swarm algorithm.
3. A system for optimizing parameters of a biquad generalized integrator frequency locked loop, the system comprising a memory and a processor, and a computer program stored in the memory and executed on the processor, the processor being coupled to the memory, the processor implementing the following steps when executing the computer program:
1) Selecting an ITAE index of a biquadratic generalized integrator frequency locking loop to construct a fitness function, wherein the ITAE index is an integral of the absolute value of the difference between the real frequency of a signal in a set time after the signal frequency is mutated and the frequency estimation value of the output signal of the biquadratic generalized integrator frequency locking loop multiplied by time; the fitness function further comprises a penalty term determined by the overshoot, and the fitness function is specifically expressed as follows:
F＝1/J ITAE_M
wherein F is the fitness value, J ITAE_M Is ITAE comprehensive index, t i For the integration duration, time 0 corresponds to the time when the signal frequency changes abruptly, and e (t) is the frequency estimation errorThe difference, σ is the overshoot of the frequency locked loop output of the biquad integrator, δ (σ) is a function of σ, w 1 Is the weight of the error, w 2 Is a weight of overshoot, and w 1 >>w 2 ；
The expression of the function of the overshoot is:
σ a the allowed overshoot of the frequency-locked loop;
2) Iterative optimization is carried out on the frequency locking loop integral gain coefficient by using an evolutionary algorithm, and the corresponding frequency locking loop integral gain coefficient when the ITAE index is minimum is selected as a parameter of a bi-quad generalized integrator frequency locking loop; determining an optimization interval of the integral gain coefficient of the frequency locking loop before optimization iteration, and enabling the optimization iteration to be carried out in the optimization interval, wherein the lower limit of the optimization interval is the integral gain coefficient of the frequency locking loop corresponding to the time when the adjusting time of the frequency locking loop FLL is equal to the adjusting time of the DSOGI of the biquad generalized integrator with set multiple; the upper limit of the optimizing interval is determined by a forward and backward method at the lower limit of the optimizing interval, and the integral gain coefficient of the frequency-locked loop is gradually increased according to a certain step length by taking the lower limit as a reference until the output of the frequency-locked loop of the biquadratic generalized integrator has overshoot and oscillation with a set degree.
4. The parameter optimization system of the biquad generalized integrator frequency-locked loop according to claim 3, wherein the evolutionary algorithm in step 2) is a particle swarm algorithm.
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