CN108649780B - LCL filter parameter optimization method considering inverter stability under weak grid - Google Patents
LCL filter parameter optimization method considering inverter stability under weak grid Download PDFInfo
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Abstract
The invention discloses a LCL filter parameter optimization method considering inverter stability under a weak power grid, which comprises the following steps: s1, establishing an inverter grid-connected output impedance model; s2, analyzing the influence of the grid impedance on the stability of the inverter grid-connected system; s3, establishing a multi-target LCL filter parameter optimization model considering the power grid impedance influence; s4, solving the optimization model by adopting a particle swarm algorithm improved based on a compression factor method; and S5, optimizing LCL filter parameters. The optimization model is suitable for LCL filter parameter design under the condition of intensive access of a weak power grid or multiple inverters; the standard satisfaction is introduced into an evaluation index, the optimization degree is evaluated quantitatively, various indexes such as filtering performance, economic cost and the like can be better considered through comparison, and the overall optimization of parameters of an LCL filter and a current loop is realized; the method provides a theoretical basis for analyzing the dense access stability of the inverter under the new energy station, and provides guidance for parameter design of the grid-connected inverter under the weak grid.
Description
Technical Field
The invention relates to the technical field of analyzing the grid-connected electric energy quality of a plurality of inverters, in particular to a LCL filter parameter optimization method considering the stability of an inverter under a weak power grid.
Background
In order to solve the problems of climate deterioration, resource exhaustion and the like, the application proportion of a distributed power generation system based on renewable energy sources such as wind energy, solar energy and the like in a power system is gradually increased, and the high-power-to-power ratio operation of new energy sources becomes a normal state. As a connection unit between a new energy power generation system and a power grid, a grid-connected inverter plays an important role in converting direct current electric energy into high-quality alternating current electric energy and feeding the high-quality alternating current electric energy into the power grid, and an LCL type filter is widely applied to grid-connected equipment due to a good high-frequency harmonic suppression effect.
Because the amplitude-frequency characteristic of the LCL filter has a resonance peak at the resonance frequency, and the phase jumps by 180 degrees, if the parameter design is not reasonable, some frequency harmonics can be amplified, and grid-connected current is seriously distorted. In addition, the mutual coupling between the parameters of the LCL filter itself also brings difficulties to the design of the parameters of the filter.
In combination with actual design experience, the prior art introduces a general design method of parameters of an LCL filter, and performs constraint calculation through conditions such as switching current ripple, fundamental reactive power, switching frequency harmonic content and the like.
The prior art also proposes to design the filter parameters with the aim of minimizing the damping loss, and although the method realizes the improvement of a certain performance aspect of the filter, the interaction between the parameters is not considered, and the design result can be obtained only by repeating the trial and error.
In order to intuitively represent the value range of each parameter meeting the requirement of each index, the influence of each parameter on the performance of the filter is represented on the same plane by a curve in a graphic form, each parameter is optimized in a selectable area, and the design process is simplified.
The LCL filter optimization methods are all independent analysis and calculation under an ideal power grid, and the designed inverter cannot stably operate easily under the condition of high-ratio access of a new power electric field.
At present, an LCL filter and controller parameter integrated design method is provided for a control scheme of single-inverter side current feedback by combining the limitation of current control on filter parameters, the design flow is simplified, but the influence of grid-connected stability under a weak power grid is not considered in the design process, so that the LCL filter parameters based on the grid side current feedback scheme widely applied in engineering need to be optimally designed on the premise of considering the impedance of the power grid and the current control.
Disclosure of Invention
The invention aims to provide an LCL filter parameter optimization method considering inverter stability under a weak power grid. Firstly, a mathematical model of the LCL grid-connected inverter is established, and the influence of the grid impedance on the inverter is researched by an impedance analysis method. On the basis, constraint conditions of inverter stability under a weak power grid on LCL parameter design are determined, a multi-objective optimization model with the minimum damping loss, the minimum manufacturing cost and the best current tracking performance as targets is established by combining other external characteristic requirements of a filter, and a particle swarm algorithm with compression factors is adopted for solving. And comparing and analyzing the optimization results of the traditional optimization scheme and the design scheme by taking the standard satisfaction index as a basis. And finally, building an LCL grid-connected inverter simulation model in Matlab/Simulink, and verifying the feasibility of theoretical analysis.
In order to achieve the above object, the present invention provides a method for optimizing LCL filter parameters considering inverter stability under weak grid, comprising the following steps:
s1, establishing an inverter grid-connected output impedance model;
s2, analyzing the influence of the grid impedance on the stability of the inverter grid-connected system;
s3, establishing a multi-target LCL filter parameter optimization model considering the power grid impedance influence;
s4, solving the optimization model by adopting a particle swarm algorithm improved based on a compression factor method;
and S5, optimizing LCL filter parameters.
Preferably, in step S1, the inverter grid-connected output impedance model includes a control system and an LCL type filter; the control system adopts a current regulator controlled by a PI controller, and the LCL type filter is provided with an inductor L1Capacitor C and inductor L2(ii) a Wherein, the inductance L2Is the grid-connected current igDamping resistors R and inductors L, respectively1And an inductance L2Parallel, electric network equivalent inductance LgSeries connection and inductance L2Series, grid voltage UgEquivalent inductance L with power gridgAre connected in series;
output impedance Z in inverter grid-connected output impedance modeloExpressed as:
in the formula of UpccIs the common connection point voltage; s is Laplace operator, Gig(s)＝Kp+KiS is the transfer function of a current regulator controlled by a PI controller, KpIs a proportionality coefficient, KiIs an integral coefficient; ginvThe equivalent gain of the inverter is represented, and the equivalent gain is the ratio of the direct-current voltage to the amplitude of the triangular carrier wave.
Preferably, the step S2 further includes the following steps:
equivalent of grid-connected inverter Noton as controlled current source IsParallel output impedance ZoThe power grid system is equivalent to a Thevenin circuit; grid-connected current IgThe expression is as follows:
in the formula, Zg(s) is the grid impedance; the stability of the output current depends on
The value of (d);
from equation (1), the expression can be derived:
wherein H(s) ═ (1/(1+ Z)g(s)/Zo(s)) is similar to a system closed loop transfer function with negative feedback, with a positive gain of 1 and a feedback gain of Zg(s)/Zo(s)。
Preferably, in step S3, the LCL filter parameter optimization mathematical model is expressed as
In the formula, hj(x, u) ═ 0 denotes the equality constraint in the optimization model, gk(x, u) is less than or equal to 0 to represent inequality constraint of the optimization model, and the inequality constraint form a constraint boundary; objective function f1Representing damping loss PlossMinimum, objective function f2Represents the total inductance LtMinimum, objective function f3The maximum loop gain amplitude at the fundamental frequency is shown, and the minimum steady-state error is ensured; weight coefficient omega of each sub-targetiReflecting the importance degree of the index; u ═ L1,L1,R,C,Kp,Ki]Represents a control variable, wherein L1Is an inverter side inductor of a filter, L2Is a network side inductor, C represents a filter capacitor, R is a damping resistor, KpTo the current regulator proportionality coefficient, KiIs an integral coefficient; x ═ fc,Tf0,Ih]Represents a state variable, wherein fcIs an equivalent open-loop system G(s) ═ Zg(s)/ZoCutoff frequency of(s), Tf0Representing the loop gain at the fundamental frequency, IhIs the effective value of the harmonic current near the switching frequency of the filter capacitor.
Preferably, in step S3, the constraint condition of inverter stability under weak grid to LCL parameter design includes: system equality constraint, grid-connected stability constraint, grid-connected harmonic current constraint, filter total inductance constraint and filter capacitor reactive power constraint.
Preferably, the system equation constraints comprise the following processes:
loop gain amplitude T at fundamental frequencyfoThe approximate expression is:
in the formula, KpwmThe gain is amplified by an inverter bridge, and f is a fundamental frequency;
harmonic current effective value I near the switching frequency of the filter capacitorhComprises the following steps:
in the formula, whRepresenting harmonic angular frequency, UhRepresenting the effective value, L, of the harmonic voltages on both sides of the filter capacitortIs the total inductance of the filter;
for the cut-off frequency fc，Zg/ZoAt this frequency, the amplitude is 1, which yields:
the grid-connected stability constraint comprises the following processes:
the characteristic polynomial of the single-loop feedback system H(s) is:
Δ(s)＝a0s4+a1s3+a2s2+a3s+a4(8)，
in the formula, a0＝L1C(Zg+L2)，a1＝RC(Zg+(L1+L2))，a2＝L1+L2+RCKpGinv+Zg，a3＝Ginv(Kp+RCKi)，a4＝GinvKi；
And stably converting the grid connection into an inequality (9):
the phase margin is set to be 30-60 degrees, and the following can be obtained:
30°≤g3(x,u)＝180°-[90°-argZo(x,u)]≤60° (10)，
for capacity PNThe maximum inductance value of the power grid to be adapted within the allowable range is as follows:
wherein f is the fundamental frequency;
the grid-connected harmonic current constraint comprises the following processes:
limiting the harmonic content near the switching frequency and the frequency multiplication of the switching frequency to be less than the grid-connected rated current IN0.3% of (a), can obtain:
in the formula, VinvOutputting harmonic voltage for a bridge arm of the inverter;
the filtering total inductance constraint includes the following processes:
balance current tracking capability, high-frequency harmonic attenuation capability and total filter inductance LtThe upper and lower limits are selected as follows:
in the formula,. DELTA.Iripple_maxThe maximum allowable ripple value of the phase current can be taken as the peak value of the fundamental frequency current, I, of 15 percentmpPeak value of phase current, EmpRepresenting the peak value of the phase voltage, UdcIs the DC side voltage of the inverter, fswRepresents the switching frequency;
the filter capacitor reactive power constraint comprises the following processes:
limiting reactive power of filter capacitor not to exceed rated power PN5% of (A), can obtain:
in the formula of UNThe rated voltage of the inverter.
Preferably, the step S4 further includes the following steps:
based on a particle swarm algorithm improved by a compression factor method, searching high-quality solutions in different areas, and after finding an individual extreme value and a global extreme value, updating respective speed and position of each particle according to a formula (15) and a formula (16):
in the formula (I), the compound is shown in the specification,
are the positions of the individual extreme points of the particle i in the d-dimension in the k-th iteration;
is the velocity of the particle i in the d-th dimension in the k-th iteration,
is the velocity of particle i in dimension d in the (k + 1) th iteration;
is the position of the particle i in the d-dimension in the k-th iteration,
is the d-dimension of particle i in the (k + 1) th iterationThe position of (a); c. C1And c2Is an acceleration factor; rand1And rand2Is [0,1 ]]A random number in between, and a random number,
and
is [0,1 ] in the kth iteration]A random number in between; χ is the compression factor.
Preferably, the compression factor χ is chosen according to the following equation (17):
in the formula, parameter
And is
Preferably, in step S5, the process of optimizing the LCL filter parameters includes:
s51, recording original data; the method comprises the steps of (1) inverter grid-connected system parameters, algorithm parameters and the like;
s52, determining weight coefficients of all sub-targets according to an entropy weight method, and converting a multi-target optimization problem into a single-target optimization problem;
s53, initializing a particle population, and position vectors and velocity vectors of particles;
s54, calculating the adaptive value of each particle in the population, and aiming at pbestAnd gbestUpdating, namely updating the speed and the position of the particles according to the formula (15) and the formula (16);
and S55, finishing optimization when the absolute value of the error is less than a given value or the number of cycles reaches the maximum number of cycles, outputting an optimal control variable determination value, and returning to the step S54 to continue iteration if the absolute value of the error is less than the given value or the number of cycles reaches the maximum number of cycles.
Compared with the prior art, the invention has the beneficial effects that:
(1) the coupling effect caused by the power grid impedance can seriously reduce the stability margin of a grid-connected system, and for a parameter design method which does not take the grid-connected stability into account under ideal power grid conditions, the inverter cannot stably operate under a weak power grid due to the large power grid impedance in actual operation.
(2) The optimal numerical solution is obtained by adopting the PSO with the compression factor, and the optimization model is particularly suitable for LCL filter parameter design under the condition of weak power grid or multi-inverter intensive access.
(3) The method introduces the standardized satisfaction degree into the evaluation index, quantitatively evaluates the optimization degree, can better give consideration to various indexes such as filtering performance, economic cost and the like through comparison, and realizes the integral optimization of parameters of the LCL filter and the current loop.
(4) The research result of the invention can provide theoretical basis for analyzing the intensive access stability of the inverter under the new energy station, and also provide important guidance for parameter design of the grid-connected inverter under the weak grid.
Drawings
FIG. 1 is a schematic diagram of the LCL inverter grid-connected topology of the present invention;
FIG. 2 is a block diagram of grid-connected inverter control of the present invention;
FIG. 3 is a schematic diagram of an inverter grid-connected equivalent impedance network of the present invention;
FIG. 4 is a grid-connected system root trace diagram under different grid impedances;
FIG. 5 is a graph showing comparison between the satisfaction degree of each index of the second embodiment of the present invention and the first embodiment based on the minimum damping loss.
Fig. 6a is based on the scheme with minimum damping losses-the grid-tie situation at the ideal grid.
Fig. 6b illustrates a grid connection situation of the ideal grid.
Fig. 7 is based on the inverter-to-grid impedance frequency characteristic when the damping loss is minimum for a short-circuit ratio of 10.
Fig. 8 shows the inverter-grid impedance frequency characteristic in case of embodiment two with a short-circuit ratio of 10 according to the present invention.
Fig. 9a is based on a grid connection situation when the damping loss is minimum for a short-circuit ratio of 10.
Fig. 9b shows the grid-connection situation of embodiment two with a short-circuit ratio of 10 according to the present invention.
FIG. 10 is a system bode plot of the change in capacitance C of the present invention.
Fig. 11 shows a system bode diagram of the present invention with a variation in inductance L2.
Detailed Description
The invention discloses a LCL filter parameter optimization method considering inverter stability under a weak power grid, and in order to make the invention more obvious and understandable, the invention is further explained by combining drawings and a specific implementation mode.
The LCL filter parameter optimization method considering the stability of the inverter under the weak grid comprises the following steps:
step S1, an inverter grid-connected output impedance model is established. Specifically, the method comprises the following steps:
the inverter grid-connected output impedance model comprises a control system and an LCL type filter. Fig. 1 is a schematic diagram of a grid-connected structure of a single-phase LCL inverter. Wherein the control system adopts a current regulator, an inductor L, controlled by a PI controller1Capacitor C and inductor L2An LCL type filter forming a grid-connected inverter; r is a damping resistor; u shapegIs the grid voltage; u shapepccIs the common connection point voltage; l isgFor equivalent inductance of the network, igFor current combined with the grid, i.e. inductance L2Is the grid-connected current igDamping resistors R and inductors L, respectively1And an inductance L2Parallel, electric network equivalent inductance LgSeries connection and inductance L2Series, grid voltage UgEquivalent inductance L with power gridgAre connected in series.
Fig. 2 is a block diagram showing the grid-connected inverter control. Wherein G isig(s)＝Kp+KiS is the transfer function of the current regulator controlled by the PI controller, s is the Laplace operator, KpIs a proportionality coefficient, KiIs an integral coefficient; ginvRepresenting the equivalent gain of the inverter, which is DC voltageAnd the amplitude of the triangular carrier wave.
From the grid-connected inverter control block shown in fig. 2, an inverter output impedance model including a control system and a filter, output impedance Z, can be obtainedoCan be expressed as:
and step S2, analyzing the influence of the grid impedance on the stability of the inverter grid-connected system. Specifically, the method comprises the following steps:
the method is characterized in that a grid-connected inverter is equivalent to a controlled current source IsParallel output impedance ZoThe model, the grid system, is generally equivalent to a thevenin circuit, and the schematic diagram of the equivalent impedance network is shown in fig. 3.
Wherein, the grid-connected current IgThe expression is as follows:
in the formula, Zg(s) is the grid impedance.
The stability of the output current depends on the 2 nd term on the right side of the equation of formula (2). Wherein H(s) ═ (1/(1+ Z)g(s)/Zo(s)) is similar to a system closed loop transfer function with negative feedback, with a positive gain of 1 and a feedback gain of Zg(s)/Zo(s). The root trace diagram of the closed-loop system when the impedance of the power grid changes is shown in fig. 4.
The increase of the grid impedance can cause the closed loop pole of the grid-connected control system to gradually move rightwards, and the grid-connected stability is gradually reduced. When there is a pole on the right half-plane, the system loses stability.
From equation (1):
and (III) step S3, establishing a multi-target LCL filter parameter optimization model considering the power grid impedance influence. Specifically, the method comprises the following steps:
the LCL filter parameter optimization mathematical model can be expressed as:
in the formula, hj(x, u) ═ 0 denotes the equality constraint in the optimization model, gk(x, u) ≦ 0 represents an inequality constraint for the optimization model, which together form a constraint boundary. Objective function f1Representing damping loss PlossMinimum, objective function f2Represents the total inductance LtMinimum, objective function f3It shows that the loop gain amplitude at the fundamental frequency is maximum, ensuring that the steady-state error is minimum. Weight coefficient omega of each sub-targetiReflecting the importance of the index, the present embodiment determines each weight coefficient according to the entropy weight method. u ═ L1,L1,R,C,Kp,Ki]Represents a control variable, wherein L1Is an inverter side inductor of a filter, L2Is a network side inductor, C represents a filter capacitor, R is a damping resistor, KpTo the current regulator proportionality coefficient, KiIs an integral coefficient. x ═ fc,Tf0,Ih]Represents a state variable, wherein fcIs an equivalent open-loop system G(s) ═ Zg(s)/ZoCutoff frequency of(s), Tf0Representing the loop gain at the fundamental frequency, IhIs the effective value of the harmonic current near the switching frequency of the filter capacitor.
Constraint conditions of inverter stability under a weak power grid on LCL parameter design comprise system equality constraint, grid-connected stability constraint, grid-connected harmonic current constraint, filter total inductance constraint, filter capacitor reactive power constraint and the like.
(a) System equality constraints
Considering that the capacitive reactance of the filter capacitor is much larger than the inductive reactance of the network side inductor at frequencies lower than the resonance frequency, the loop gain amplitude T at the fundamental frequencyfoCan be expressed approximately as:
in the formula, KpwmFor the inverting bridge amplification gain, f is the fundamental frequency.
Harmonic current effective value I near the switching frequency of the filter capacitorhComprises the following steps:
in the formula, whRepresenting harmonic angular frequency, UhRepresenting the effective value, L, of the harmonic voltages on both sides of the filter capacitortIs the total inductance of the filter.
For the cut-off frequency fc，Zg/ZoThe amplitude is 1 at this frequency.
(b) Grid tied stability constraints
The stability of the grid-connected system mainly depends on a single-loop feedback system H(s), and the characteristic polynomial of the system is as follows:
Δ(s)＝a0s4+a1s3+a2s2+a3s+a4(8)
in the formula, a0＝L1C(Zg+L2)，a1＝RC(Zg+(L1+L2))，a2＝L1+L2+RCKpGinv+Zg，a3＝Ginv(Kp+RCKi)，a4＝GinvKi。
Grid connection stability can be converted into the following inequality:
for the inverter grid-connected system, even if the stability criterion is met, harmonic amplification at the intersection frequency of the grid impedance and the inverter output impedance can still be caused if the stability margin is insufficient. In order to give consideration to grid-connection stability and dynamic response performance, according to actual engineering experience, the phase margin is 30-60 degrees, namely:
30°≤g3(x,u)＝180°-[90°-argZo(x,u)]≤60° (10)
according to the specification of the distributed power grid-connected standard Q/GDW480-2010, the capacity is PNThe maximum inductance value of the power grid to be adapted within the allowable range is as follows:
wherein f is the fundamental frequency.
(c) Grid connected harmonic current constraint
According to the regulations of IEEE Std 929-2000 and IEEE Std1547-2003, the harmonic content near the switching frequency (the switching frequency is the operating frequency of the internal switching tube of the inverter, the frequency influencing the harmonic generation of the inverter and the self-characteristic of the inverter) and the frequency multiplication of the switching frequency (the integral frequency multiplication of the switching frequency) is limited to be less than the grid-connected rated current IN0.3% of the total weight of the components, namely:
in the formula, VinvAnd outputting harmonic voltage for the bridge arm of the inverter.
(d) Total inductance limit of filter
Balance current tracking capability, high-frequency harmonic attenuation capability and total filter inductance LtThe upper and lower limits are selected as follows:
in the formula,. DELTA.Iripple_maxThe maximum allowable ripple value of the phase current is generally 15 percent of the peak value of the fundamental frequency current, ImpPeak value of phase current, EmpRepresenting the peak value of the phase voltage, UdcIs the DC side voltage of the inverter, fswRepresenting the switching frequency.
(e) Filter capacitor reactive power limitation
In order to reduce reactive loss, the reactive power of the filter capacitor is limited not to exceed the rated power PN5% of the total.
In the formula of UNThe rated voltage of the inverter.
And step S4, solving the optimization model by adopting a particle swarm optimization improved based on a compression factor method. Specifically, the method comprises the following steps:
the Particle Swarm Optimization (PSO) improved based on the compression factor method is helpful for enhancing the convergence of the PSO algorithm, and high-quality solutions can be searched in different areas. After finding the individual extrema as well as the global extrema, each particle updates its own velocity and position empirically according to equations (15) and (16).
In the formula (I), the compound is shown in the specification,
are the positions of the individual extreme points of the particle i in the d-dimension in the k-th iteration;
is the velocity of the particle i in the d-th dimension in the k-th iteration,
is the velocity of particle i in dimension d in the (k + 1) th iteration;
is the position of the particle i in the d-dimension in the k-th iteration,
is the position of particle i in dimension d in the (k + 1) th iteration; c. C1And c2Is an acceleration factor; rand1And rand2Is [0,1 ]]A random number in between, and a random number,
and
is [0,1 ] in the kth iteration]A random number in between; χ is a compression factor, and can be selected according to the following equation (17):
in the formula, parameter
And is
And (V) step S5, optimizing the LCL filter parameters. Specifically, the optimization process is as follows:
and S51, recording original data including inverter grid-connected system parameters, algorithm parameters and the like.
And S52, determining the weight coefficient of each sub-target according to an entropy weight method, and converting the multi-target optimization problem into a single-target optimization problem.
S53, initializing the particle population, the position vector and the velocity vector of the particles.
S54, calculating the adaptive value of each particle in the population, and aiming at pbestAnd gbestThe update is performed to update the velocity and position of the particles according to equation (15) and equation (16).
And S55, finishing optimization when the absolute value of the error is less than a given value or the number of cycles reaches the maximum number of cycles, outputting an optimal control variable determination value, and returning to the step S54 to continue iteration if the absolute value of the error is less than the given value or the number of cycles reaches the maximum number of cycles.
In a preferred embodiment of the present invention, the parameters of the input and output parameters of the grid-connected inverter are optimally designed, and table 1 shows the system parameters of the grid-connected inverter.
TABLE 1 grid-connected inverter grid-connected system parameters
For the parameter design method provided by the invention, according to the entropy weight method, the linear weighted target function is as follows:
minf＝0.6258f1+0.3097f2-0.0645f3(18)
wherein the objective function f1Representing damping loss PlossMinimum, objective function f2Represents the total inductance LtMinimum, objective function f3It shows that the loop gain amplitude at the fundamental frequency is maximum, ensuring that the steady-state error is minimum.
For comparing and explaining the superiority of the LCL filter parameter optimization method of the present embodiment, a design result based on the minimum damping loss under the same parameter condition is given, and the design result is shown in table 2.
TABLE 2 comparison of optimization results based on damping loss minimization method and LCL filter parameter optimization method of the present invention
In this embodiment, a PSO with a compression factor is used for optimal solution, the number N of the seed groups is 36, the maximum iteration number is 200, and the acceleration coefficient c is taken1＝c22.05, compression factor χ 0.729. After running the program, the resulting filter parameter optimization results are shown in table 2. The invention carries out integral optimization on the parameters of the filter and the current loop, and the current loop proportion parameter K in the current loop control parametersp0.23, integral parameter K of the current loopi＝3220。
In order to comprehensively and quantitatively compare the above effects, a fuzzy membership function can be adopted to evaluate the optimization degree of the two design schemes on each performance of the grid-connected inverter.
For four indexes of manufacturing cost, damping loss, steady-state error and filtering effect, the objective function is minimized, so that a smaller fuzzy membership function is defined as follows:
in the formula (f)iIs the ith objective function value, fiminIs the lower bound of the objective function, fimaxIs the upper limit of the objective function.
When considering the stability margin, the stability margin is best in the range of 30 ° to 60 °, so an intermediate type membership function is defined as:
in the formula, a and b are upper and lower limits of an optimal selection space of the objective function, respectively, and for the stability margin, a is 30 ° and b is 60 °.
The satisfaction index of the design result based on the damping loss minimization method and the LCL filter parameter optimization method of the invention is shown in FIG. 5.
When mu isiThe closer to 1 represents the more satisfied the index i, and the degree of the optimization result is finally judged by standardizing the satisfaction value mu.
Where n represents the number of evaluation indexes, and n is 5 in the present invention. As can be seen from equation (21), in the method based on damping loss minimization, μ is 0.63; in the LCL filter parameter optimization method of the present embodiment, μ is 0.82.
Through the data analysis, the LCL filter parameter optimization method can better give consideration to performance indexes such as filtering effect and stability, and the overall optimization of the LCL filter parameters and the current loop parameters is realized.
In order to verify the accuracy of theoretical analysis, a 10kW LCL grid-connected inverter simulation model is built in a Matlab/Simulink simulation platform, relevant parameters are shown in tables 1 and 2, and simulation analysis is performed on the inverter grid-connected condition under the condition that an ideal power grid and the short-circuit ratio are 10 respectively.
In the ideal grid situation, the inverter grid connection situation based on the damping loss minimization method (scheme one) and the LCL filter parameter optimization method (scheme two) of the present invention is shown in fig. 6a and 6 b. In order to minimize the damping loss, in the first scheme, the minimum value of the damping resistor is selected as much as possible, the attenuation capacity of the high-frequency harmonic current is improved, and the content of the main high-frequency subharmonic current is 0.1%. In the second scheme, the stability of the inverter under the weak grid is taken into consideration, and the damping resistor is required to provide enough damping to suppress resonance under the weak grid condition, so that the damping resistor is large, the content of harmonic current of more than 33 times is increased from 0.1% of the first scheme to 0.16%, but the content does not exceed the limit of 0.3%, and the grid-connected standard is still met.
And reducing the short-circuit ratio to 10, wherein the short-circuit ratio is the minimum grid short-circuit ratio which needs to be adapted by the LCL grid-connected inverter with 10 kW. The system bode diagrams corresponding to the first scheme and the second scheme are shown in fig. 7 and 8. As can be seen from the Berde diagram, the phase margin of the inverter system designed in the first scheme is reduced to-3.7 degrees, the cross-connection frequency of the grid impedance and the inverter output impedance is 640Hz, and the system is in an unstable state. For the second scheme, when the short circuit ratio is 10, the stability margin of the grid-connected system is 33.3 degrees, and the equivalent closed-loop control system is stable at the moment. The grid-connected conditions under the first scheme and the second scheme are simulated, and the simulated grid-connected current waveform and FFT analysis are shown in fig. 9a and 9 b.
As can be seen from fig. 9a and 9b, the grid-connected current in the first scheme has severe distortion, the harmonic near the impedance cross-over frequency of 640Hz is greatly amplified, and the harmonic oscillation phenomenon causes that the system cannot normally operate under the weak grid condition. For the second scheme, the grid-connected system of the inverter is stable, grid-connected current has better sine degree, the harmonic current content meets the grid-connected standard, and the inverter can stably work under the condition of the power grid.
In the actual production or use process, the parameters of the components such as the inductance and the capacitance may fluctuate in a large range, and the grid impedance and the inverter impedance are plotted in bode diagrams as shown in fig. 10 and fig. 11 by considering the variation of the values of the components of ± 20%, so that the robustness of the analysis system to the filter parameters is realized.
As can be seen from fig. 10 and 11, since the passive damping method is robust, the control system is less sensitive to parameter variations, and a large margin is left in filter parameter design, the minimum stability margin of the control system is still around 30 ° even if the inductance capacitance has a deviation of ± 20%. Therefore, the LCL filter parameter design scheme provided by the invention can be well suitable for the actual situation of wide-range change of the main circuit parameters.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (8)
1. An LCL filter parameter optimization method considering inverter stability under a weak grid is characterized by comprising the following steps:
s1, establishing an inverter grid-connected output impedance model;
s2, analyzing the influence of the grid impedance on the stability of the inverter grid-connected system;
s3, establishing a multi-target LCL filter parameter optimization model considering the power grid impedance influence;
s4, solving the optimization model by adopting a particle swarm algorithm improved based on a compression factor method;
s5, optimizing LCL filter parameters;
in step S1, the inverter grid-connected output impedance model includes a control system and an LCL filter; the control system adopts a current regulator controlled by a PI controller, and the LCL type filter is provided with an inductorL1Capacitor C and inductor L2(ii) a Wherein, the inductance L2Is the grid-connected current igDamping resistors R and inductors L, respectively1And an inductance L2Parallel, electric network equivalent inductance LgSeries connection and inductance L2Series, grid voltage UgEquivalent inductance L with power gridgAre connected in series;
output impedance Z in inverter grid-connected output impedance modeloExpressed as:
in the formula of UpccIs the common connection point voltage; s is Laplace operator, Gig(s)＝Kp+KiS is the transfer function of a current regulator controlled by a PI controller, KpIs a proportionality coefficient, KiIs an integral coefficient; ginvThe equivalent gain of the inverter is represented, and the equivalent gain is the ratio of the direct-current voltage to the amplitude of the triangular carrier wave.
2. The LCL filter parameter optimization method of claim 1, wherein said step S2 further comprises the following steps:
equivalent of grid-connected inverter Noton as controlled current source IsParallel output impedance ZoThe power grid system is equivalent to a Thevenin circuit; grid-connected current IgThe expression is as follows:
in the formula, Zg(s) is the grid impedance; the stability of the output current depends on
The value of (d);
from equation (1), the expression can be derived:
wherein H(s) ═ 1/(1+ Z)g(s)/Zo(s)) is similar to a system closed loop transfer function with negative feedback, with a positive gain of 1 and a feedback gain of Zg(s)/Zo(s)。
3. The LCL filter parameter optimization method of claim 2, wherein in step S3, the LCL filter parameter optimization mathematical model is expressed as
In the formula, hj(x, u) ═ 0 denotes the equality constraint in the optimization model, gk(x, u) is less than or equal to 0 to represent inequality constraint of the optimization model, and the inequality constraint form a constraint boundary; objective function f1Representing damping loss PlossMinimum, objective function f2Represents the total inductance LtMinimum, objective function f3The maximum loop gain amplitude at the fundamental frequency is shown, and the minimum steady-state error is ensured; weight coefficient omega of each sub-targetiReflecting the importance of the target; u ═ L1,L1,R,C,Kp,Ki]Represents a control variable, wherein L1Is an inverter side inductor of a filter, L2Is a network side inductor, C represents a filter capacitor, R is a damping resistor, KpTo the current regulator proportionality coefficient, KiIs an integral coefficient; x ═ fc,Tf0,Ih]Represents a state variable, wherein fcIs an equivalent open-loop system G(s) ═ Zg(s)/ZoCutoff frequency of(s), Tf0Representing the loop gain at the fundamental frequency, IhIs the effective value of the harmonic current near the switching frequency of the filter capacitor.
4. The LCL filter parameter optimization method of claim 3,
in step S3, the constraint conditions of inverter stability under the weak grid on the LCL parameter design include: system equality constraint, grid-connected stability constraint, grid-connected harmonic current constraint, filter total inductance constraint and filter capacitor reactive power constraint.
5. The LCL filter parameter optimization method of claim 4,
the system equation constraints include the following processes:
loop gain amplitude T at fundamental frequencyfoThe approximate expression is:
in the formula, KpwmThe gain is amplified by an inverter bridge, and f is a fundamental frequency;
harmonic current effective value I near the switching frequency of the filter capacitorhComprises the following steps:
in the formula, whRepresenting harmonic angular frequency, UhRepresenting the effective value, L, of the harmonic voltages on both sides of the filter capacitortIs the total inductance of the filter;
for the cut-off frequency fc，Zg/ZoAt this frequency, the amplitude is 1, which yields:
the grid-connected stability constraint comprises the following processes:
the characteristic polynomial of the single-loop feedback system H(s) is:
Δ(s)＝a0s4+a1s3+a2s2+a3s+a4(8)，
in the formula, a0＝L1C(Zg+L2)，a1＝RC(Zg+(L1+L2))，a2＝L1+L2+RCKpGinv+Zg，a3＝Ginv(Kp+RCKi)，a4＝GinvKi；
And stably converting the grid connection into an inequality (9):
the phase margin is set to be 30-60 degrees, and the following can be obtained:
30°≤g3(x,u)＝180°-[90°-argZo(x,u)]≤60° (10)，
for capacity PNThe maximum inductance value of the power grid to be adapted within the allowable range is as follows:
wherein f is the fundamental frequency;
the grid-connected harmonic current constraint comprises the following processes:
limiting the switching frequency and limiting the harmonic content near the frequency multiplication of the switching frequency to be smaller than the grid-connected rated current IN0.3% of (a), can obtain:
in the formula, VinvOutputting harmonic voltage for a bridge arm of the inverter;
the filtering total inductance constraint includes the following processes:
balance current tracking capability, high-frequency harmonic attenuation capability and total filter inductance LtThe upper and lower limits are selected as follows:
in the formula,. DELTA.Iripple_maxTaking the maximum allowable ripple value of phase current as a basisPeak frequency current 15%, ImpPeak value of phase current, EmpRepresenting the peak value of the phase voltage, UdcIs the DC side voltage of the inverter, fswRepresents the switching frequency;
the filter capacitor reactive power constraint comprises the following processes:
limiting reactive power of filter capacitor not to exceed rated power PN5% of (A), can obtain:
in the formula of UNThe rated voltage of the inverter.
6. The LCL filter parameter optimization method of claim 5, wherein the step S4 further comprises the following steps:
based on a particle swarm algorithm improved by a compression factor method, searching high-quality solutions in different areas, and after finding an individual extreme value and a global extreme value, updating respective speed and position of each particle according to a formula (15) and a formula (16):
in the formula (I), the compound is shown in the specification,
are the positions of the individual extreme points of the particle i in the d-dimension in the k-th iteration;
is the velocity of the particle i in the d-th dimension in the k-th iteration,
is that the particle i is inThe speed of the d-th dimension in k +1 iterations;
is the position of the particle i in the d-dimension in the k-th iteration,
is the position of particle i in dimension d in the (k + 1) th iteration; c. C1And c2Is an acceleration factor; rand1And rand2Is [0,1 ]]A random number in between, and a random number,
and
is [0,1 ] in the kth iteration]A random number in between; χ is the compression factor.
7. The LCL filter parameter optimization method of claim 6, wherein the compression factor χ is chosen according to equation (17):
in the formula, parameter
And is
8. The LCL filter parameter optimization method of claim 7, wherein the step S5, the process of optimizing the LCL filter parameters comprises:
s51, recording original data; the method comprises the steps of (1) inverter grid-connected system parameters and algorithm parameters;
s52, determining weight coefficients of all sub-targets according to an entropy weight method, and converting a multi-target optimization problem into a single-target optimization problem;
s53, initializing a particle population, and position vectors and velocity vectors of particles;
s54, calculating the adaptive value of each particle in the population, and aiming at pbestAnd gbestUpdating, namely updating the speed and the position of the particles according to the formula (15) and the formula (16);
and S55, finishing optimization when the absolute value of the error is less than a given value or the number of cycles reaches the maximum number of cycles, outputting an optimal control variable determination value, and returning to the step S54 to continue iteration if the absolute value of the error is less than the given value or the number of cycles reaches the maximum number of cycles.
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