CN116845893A - Parameter optimization method for weak current network LCL type grid-connected inversion filter based on NSGA-II algorithm - Google Patents
Parameter optimization method for weak current network LCL type grid-connected inversion filter based on NSGA-II algorithm Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention discloses a weak current network LCL type grid-connected inversion filter parameter optimization method based on NSGA-II algorithm, which comprises the following steps: modeling a single-phase inversion system under a weak current network, and enabling an inversion side inductance L to be 1 Network side inductance L 2 The filter capacitor C and the passive damping resistor R are used as parameters to be optimized; setting an inductance total value L and an inversion side inductance L 1 Network side inductance L 2 Limit constraint of the filter capacitor C; constructing a switching frequency harmonic attenuation ratio eta and an inversion end inductance current ripple delta I ripple Damping resistor power consumption P R_loss And resonant frequency f r Is a target function of (2); based on NSGA-II algorithm model, taking parameters to be optimized as parametersAnd (3) a decision variable, namely obtaining a parameter solution set of an optimal solution for a plurality of objective functions through iterative optimization according to the limit constraint, and picking a group of typical values from the parameter solution set to serve as the optimal solution. The invention can greatly improve the filtering effect and the weak network resistance of the filter.
Description
Technical Field
The invention belongs to the field of inversion filters, and particularly relates to a parameter optimization method of a weak current network LCL type grid-connected inversion filter based on an NSGA-II algorithm.
Background
The grid-connected inverter is key equipment for supporting new energy grid connection, compared with an L and LC type filter, the LCL type filter has a better inhibition effect on high-frequency harmonic waves, the specific performance of the LCL type filter is mainly dependent on LCL parameters, and therefore the design of the filter parameters is very important. However, the parameter design requirement of the filter is more limited, the calculated amount is larger, and the accuracy is poor; in addition, due to the condition of a weak power grid, the safety and the control robustness of the system under multiple operation conditions are more required to be comprehensively considered.
The early filter design method adopts a trial-and-error method to carry out parameter design according to a large amount of engineering experience and electromagnetic characteristics, and a traditional filter parameter design method is formed through full experimental results and a graphical method, such as the document "Xinbo Ruan. Control Techniques for LCL-Type Grid-Connected Inverters.Beijing, CN: science Press,2015.
In the literature "s.jayalath and m.hanif," An LCL-Filter Design With Optimum Total Inductance and Capacitance, "in IEEE Transactions on Power Electronics, vol.33, no.8, pp.6687-6698, aug.2018," individual parameters in the LCL filter are optimized, but the optimal filtering effect of the whole system is not guaranteed.
Disclosure of Invention
The invention provides a weak current network LCL type grid-connected inversion filter parameter optimization method based on NSGA-II algorithm, which greatly improves the filtering effect and weak network resistance of the filter.
A weak current network LCL type grid-connected inversion filter parameter optimization method based on NSGA-II algorithm comprises the following steps:
modeling a single-phase inversion system under a weak current network, and enabling an inversion side inductance L to be 1 Network side inductance L 2 The filter capacitor C and the passive damping resistor R are used as parameters to be optimized;
setting an inductance total value L and an inversion side inductance L 1 Network side inductance L 2 Limit constraint of the filter capacitor C;
constructing a switching frequency harmonic attenuation ratio eta and an inversion end inductance current ripple delta I ripple Damping resistor power consumption P R_loss And resonant frequency f r Is a target function of (2);
based on an NSGA-II algorithm model, taking parameters to be optimized as decision variables, obtaining a parameter solution set of an optimal solution for a plurality of objective functions through iterative optimization according to limit constraint, and picking a group of typical values from the parameter solution set to serve as the optimal solution.
The decision variables based on NSGA-II algorithm model are:
X＝[L 1 ,L 2 ,C,R]
in the model, the influence of each parameter on a system is analyzed by adopting a single variable principle on the parameters; the parameter changes are all linear increases and are changed based on the parameters of the traditional trial-and-error method.
In the limit constraint, the total inductance value L needs to satisfy two conditions: first, it is necessary to limit the maximum current generated by the voltage drop across the inductor; secondly, the ripple of the current needs to be reduced to be within an allowable range; i.e. the following inequality constraint needs to be satisfied:
wherein V is g_max 、I g_max For peak grid side voltage and current, V dc Is the DC side voltage, deltaI ripple-ma For maximum current ripple on the inverting side, f s For switching frequency omega 0 Is the grid frequency.
Inverter side inductance L 1 And net side inductance L 2 The following constraints need to be satisfied:
L 1 ≥L 2
wherein T is s For the switching period of the switch-on and switch-off period,is the current ripple coefficient +.>Is the inductance voltage drop coefficient omega 0 For the grid frequency, V in Representing the filter input voltage (i.e., the inverter side output voltage), I L1 Representing the inductance current at the inversion side, V C Representing the voltage of the capacitor node of the filter, V g Representing the grid side voltage.
The filter capacitor C needs to satisfy the following constraints:
wherein: p (P) O Rated power is output for the network side; omega 0 Is the grid frequency; lambda (lambda) C The power ratio of the reactive power of the capacitor to rated output is calculated; v (V) g Is the grid side voltage.
In the objective function, the switching frequency harmonic attenuation ratio eta is the optimization target with the highest priority, and the optimization target is shown as the following formula:
wherein I is g (s) is a current measurement expression of the power grid in a complex frequency domain, I L1 (s) is the inversion side inductance current expression in the complex frequency domain, ω s For switching angular frequency, s=jω s The expression condition is when the frequency is a switching angular frequency.
In the objective function, it is necessary to minimize the inverter-side inductor current ripple:
in which the inverter outputs a voltage V in ≈V dc ，V dc Is a direct current voltage, L 1 For the inversion side inductance, f s Is the switching frequency.
In the objective function, it is necessary to minimize the damping resistance power consumption P R_loss ：
Wherein V is g Representing the grid side voltage, omega 0 Is the grid frequency.
In order to satisfy the low-pass characteristic of the LCL filter, the resonant frequency is selected in the objective function:
wherein f s 、f r The switching frequency and the resonant frequency, f 0 Representing the grid frequency; since the conditions relating to the three variables are not linear, two objective functions that need to be minimized are used to ensure that the resonant frequency is at the allowable range:
F 1 ＝10f 0 -f r
F 2 ＝f r -0.5f s
finally, the total objective function is min [ eta, delta I ripple ,P R_loss ,F 1 ,F 2 ]
Compared with the prior art, the invention has the following beneficial effects:
the invention adopts a genetic algorithm (NSGA-II) of multi-objective optimization aiming at the parameter selection of the LCL type filter grid-connected inversion system under the weak power grid condition. Firstly, modeling a single-phase inversion system under a weak current network, analyzing the influence of different filter parameters on the stability of the system, and providing a selection standard of a parameter solution for enhancing the stability of the system. The constraint of the parameter limit is given based on the traditional trial-and-error method, a plurality of optimization targets aiming at the system are given, and a typical solution is selected from the obtained optimization solution set. A large number of trial and error processes are omitted, the resistance of the system to weak network conditions is enhanced, and the harmonic distortion rate is further reduced under the condition of meeting grid-connected requirements.
Drawings
FIG. 1 is a grid-connected inverter topology of an LCL filter in an embodiment of the invention;
FIG. 2 is a closed-loop control block diagram of an LCL grid-connected inverter system in an embodiment of the invention;
FIG. 3 is a flowchart of NSGA-II algorithm in an embodiment of the present invention;
FIG. 4 is a graph showing the trend of pole movement of the closed loop of the system when the filter parameters are increased in the embodiment of the invention;
FIG. 5 is a solution set of optimization parameters in an embodiment of the invention;
FIG. 6 is a system response under conventional parameters in an embodiment of the present invention;
FIG. 7 is a system response under optimized parameters in an embodiment of the invention.
Detailed Description
The invention will be described in further detail with reference to the drawings and examples, it being noted that the examples described below are intended to facilitate the understanding of the invention and are not intended to limit the invention in any way.
The grid-connected inversion topology adopted by the embodiment of the invention is an LCL type circuit with a capacitor connected in series with a resistor, as shown in figure 1. V (V) dc 、C dc The capacitor is a direct-current voltage and a filter capacitor; l (L) 1 、L 2 、L g Respectively an inversion side, a network side and electricityNet equivalent inductance; r is R 1 、R 2 、R g The corresponding line resistances are respectively; v in 、v g The voltage of the output end of the inverter bridge and the voltage of the power grid are obtained; i.e L1 、i g 、i c 、i g_ref The current is respectively an inversion side current, a power grid current, a capacitance current and a power grid reference current. G i (s) is a grid-connected current controller, and H is a capacitance current feedback controller.
In order to more intuitively embody the structure of the system, a closed-loop control block diagram of the inverted system is shown in fig. 2. Current controller G i (s) is a PI controller, H is proportional feedback, K PWM The equivalent transfer function of the inverter is the ratio of the direct current voltage to the carrier voltage amplitude. The capacitor series resistance adopted by the embodiment of the invention is a simple and effective method for reducing resonance peak damping, and the capacitor current feedback accelerates the system reaction.
To simplify the transfer function, the smaller line impedance value R is omitted 1 、R 2 . Therefore, the transfer function of the output voltage of the inversion end to the power grid current and the transfer function of the whole closed loop system can be obtained:
next, the parameters are analytically optimized according to the above model.
In general, the multi-objective optimization algorithm model can obtain a set of solutions according to a specific problem, and the solutions have no coupling relation with each other, which is called Pareto optimal solution set. The invention selects NSGA-II algorithm framework, classifies individuals of the population based on genetic algorithm and sorts the individuals rapidly and nondominately, and prevents excellent individuals from losing through elite strategy.
The main flow of NSGA-II algorithm is shown in FIG. 3. First, an initial population P of size N is randomly generated t Through non-passingDominant ordering, selection, crossover and variation, yielding a offspring population Q t And combining the two populations together to form a population R of size 2N t . Secondly, carrying out rapid non-dominant ranking, simultaneously carrying out crowding calculation on individuals in each non-dominant layer, and selecting proper individuals to form a new parent population P according to non-dominant relationship and crowding of the individuals t+1 . Finally, a new offspring population Q is generated by basic operations of the genetic algorithm t+1 Will P t+1 And Q is equal to t+1 Combining to form a new population R t+1 The above operation is repeated until the condition for ending the program is satisfied.
In the parameter design optimization of this time, the main parameter of the design is the filter inductance capacitance L 1 、L 2 The resistance R of C and passive damping, therefore the decision variables based on NSGA-II algorithm model are:
X＝[L 1 ,L 2 ,C,R] (3)
since the optimal solution set of an algorithm is typically relatively large in number, some additional criteria are needed. In the model, the influence of each parameter on the system can be analyzed by adopting a single variable principle on the parameters. The parameter changes are all linear increases and are changed based on the parameters of the traditional trial-and-error method. On the basis, the respective parameter changes are respectively as follows: l (L) 1 (850μH→1200μH),L 2 (500μH→1200μH),C(4μF→18μF),R(2Ω→9Ω)。
As can be seen from fig. 4, in the filter inductance L 1 、L 2 In the increasing process, the dominant pole is always close to the virtual axis, and the stability of the system is poor; in the process of increasing the capacitance C, the absolute value of the real part of the pole is increased and then decreased; as the resistance R increases, the system stability is enhanced. This results in the selection condition for the optimal solution: guarantee L 1 、L 2 Smaller, larger R and moderate C.
Setting an inductance total value L and an inversion side inductance L when the filter meets the requirements of harmonic attenuation and the like 1 Network side inductance L 2 The limit constraint of the filter capacitor C is used as the constraint condition of the objective function.
1) Total value of inductance
The total inductance of the LCL filter is larger, and the filtering effect is better; the inductance is smaller and the response capability becomes stronger. The total inductance needs to meet two conditions: on the one hand, it is necessary to limit the maximum current generated by the voltage drop across the inductor; on the other hand, it is necessary to reduce the ripple of the current to be within the allowable range; that is, the following inequality constraint needs to be satisfied:
wherein: v (V) g_max 、I g_max The voltage and current peak value is the power grid side voltage and current peak value; inverter side output voltage V inv ≈V dc 。
2) Inverter side and network side inductor
In terms of engineering manufacture, in order to reduce cost and volume, the inductance value of the network side is often smaller than the inductance of the inversion side, and the inductance of the inversion side needs to meet the limitations of current ripple and voltage drop on the inductance, so that the following constraints are obtained:
L 1 ≥L 2 (6)
wherein: switching period T s The method comprises the steps of carrying out a first treatment on the surface of the Current ripple coefficientInductance drop coefficient->
3) Filter capacitor
The larger the capacitance value is, the smaller the voltage ripple is, but the larger the power consumption is; therefore, the upper limit of the capacitance value needs to be considered:
wherein: p (P) O Rated power is output for the network side; omega 0 Is the grid frequency; the power ratio lambda of the reactive power of the capacitor to the rated output C ≈5％。
Constructing a switching frequency harmonic attenuation ratio eta and an inversion end inductance current ripple delta I ripple Damping resistor power consumption P R_loss And resonant frequency f r Is a target function of (a).
1) Switching frequency harmonic attenuation ratio
The method is an optimization target with highest priority of the optimization design, and the smaller the harmonic attenuation degree is, the better the switching frequency harmonic filtering effect is, as shown in the following formula:
2) Inverter-side inductor current ripple
The inverter switching action can cause dv/dt change of the inverter side current approaching to the switching frequency, namely current ripple, in order to ensure stable and enhanced control effect of the system, reduce loss of the switch and the inductor, and minimize reverse current ripple:
wherein: inverter output voltage V in ≈V dc The method comprises the steps of carrying out a first treatment on the surface of the Inverter side inductance L 1 。
3) Damping resistor power consumption
LCL filters introduce passive damping to enhance system harmonic rejection performance, but also introduce power consumption, which needs to be minimized:
4) Resonant frequency
In order to meet the low pass characteristics of LCL filters, the resonant frequency is generally selected as follows:
wherein: f (f) s 、f r The switching frequency and the resonant frequency are respectively. Because the conditions related to the three variables are nonlinear, bilateral constraint is carried out as an optimization target, and the two objective functions needing to be minimized are used for ensuring that the value of the resonant frequency is within the allowable range:
F 1 ＝10f 0 -f r (12)
F 2 ＝f r -0.5f s (13)
the objective function of such an algorithm is
min[η,ΔI ripple ,P R_loss ,F 1 ,F 2 ] (14)
In summary of the above, the NSGA-II algorithm is used with equation (3) as the optimization variable, equations (4) - (7) as the linear constraint, and equation (14) as the multi-objective function. The basic parameters are set as follows: the optimal individual is paretoFraction 0.4; population size powersize 300; maximum evolutionary algebraic generations 400; stop algebraic stallGenLimit 300; the fitness function deviates from TolFun 1e-10. Thus, a solution set of the multi-objective Pareto optimal solution is obtained through iterative optimization, as shown in fig. 5.
The resulting solutions are not coupled to each other and are also optimal solutions. However, it can still be seen that the parameters have obvious concentrated intervals, and in the mode intervals of all the four parameters, a group of typical values are selected as an optimization solution according to the parameter selection standard, and the superiority of the algorithm is reflected by comparison with the conventional solution, and the specific parameters are shown in table 1.
Table 1 comparison of conventional methods with optimization algorithms
In order to verify the optimizing effect of a multi-objective optimizing algorithm on a system under the condition of weak current network, the embodiment of the invention builds a simulation model of the grid-connected inverter based on Matlab/Simulink, and the specific parameter environment is shown in Table 2.
TABLE 2 simulation System parameters and Environment
According to the parameters, simulation is carried out on the built model, and the system response under the traditional parameters and the system response under the optimized parameters are respectively shown in fig. 6 and 7, and specifically comprise the voltage at the coupling position, the inversion and network side current, the capacitance current and the harmonic analysis chart.
From the two graphs, the parameters designed by using the optimization algorithm obviously enable the inversion system to have stronger adaptability to the weak network conditions, when the inductance value of the weak current network reaches 2mH, the system of the traditional solution is unstable, but the optimization solution can still keep the stability of the system. The waveform local amplification can show that the ripple wave of the current and the voltage is increased to a certain extent (5.513-6.182A) due to the reduction of the parameter value of the filter, but still is within the allowable range of the grid-connected design requirement; the power consumption of the resistor is obviously increased (0.245 to 4.838W), but the resonance frequency loss change can be almost offset by the reduction of the inductance and capacitance values. The waveform distortion rate under the weak current network condition is obviously reduced, the filtering effect and the weak network resistance of the filter are greatly improved, and the specific parameters of the distortion rate are shown in table 3.
TABLE 3 comparison of conventional methods with optimization algorithms
The foregoing embodiments have described in detail the technical solution and the advantages of the present invention, it should be understood that the foregoing embodiments are merely illustrative of the present invention and are not intended to limit the invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the invention.
Claims (9)
1. A weak current network LCL type grid-connected inversion filter parameter optimization method based on NSGA-II algorithm is characterized by comprising the following steps:
modeling a single-phase inversion system under a weak current network, and enabling an inversion side inductance L to be 1 Network side inductance L 2 The filter capacitor C and the passive damping resistor R are used as parameters to be optimized;
setting an inductance total value L and an inversion side inductance L 1 Network side inductance L 2 Limit constraint of the filter capacitor C;
constructing a switching frequency harmonic attenuation ratio eta and an inversion end inductance current ripple delta I ripple Damping resistor power consumption P R_loss And resonant frequency f r Is a target function of (2);
based on an NSGA-II algorithm model, taking parameters to be optimized as decision variables, obtaining a parameter solution set of an optimal solution for a plurality of objective functions through iterative optimization according to limit constraint, and picking a group of typical values from the parameter solution set to serve as the optimal solution.
2. The method for optimizing parameters of the weak grid LCL grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, wherein decision variables based on a NSGA-II algorithm model are as follows:
X＝[L 1 ,L 2 ,C,R]
in the model, the influence of each parameter on a system is analyzed by adopting a single variable principle on the parameters; the parameter changes are all linear increases and are changed based on the parameters of the traditional trial-and-error method.
3. The method for optimizing parameters of the weak grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, wherein in the limit constraint, the total inductance value L needs to satisfy two conditions: first, it is necessary to limit the maximum current generated by the voltage drop across the inductor; secondly, the ripple of the current needs to be reduced to be within an allowable range; i.e. the following inequality constraint needs to be satisfied:
wherein V is g_max 、I g_max For peak grid side voltage and current, V dc Is the DC side voltage, deltaI ripple-ma For maximum current ripple on the inverting side, f s For switching frequency omega 0 Is the grid frequency.
4. The method for optimizing parameters of weak current network LCL grid-connected inverter filter based on NSGA-II algorithm as set forth in claim 1, wherein in the limit constraint, the inverter side inductance L 1 And net side inductance L 2 The following constraints need to be satisfied:
L 1 ≥L 2
wherein T is s For the switching period of the switch-on and switch-off period,is the current ripple coefficient +.>Is the inductance voltage drop coefficient omega 0 For the grid frequency, V in Representing the filter input voltage, I L1 Representing the inductance current at the inversion side, V C Representing the voltage of the capacitor node of the filter, V g Representing the grid side voltage.
5. The method for optimizing parameters of the weak grid LCL grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, wherein in the limit constraint, the filter capacitor C is required to meet the following constraint:
wherein: p (P) O Rated power is output for the network side; omega 0 Is the grid frequency; lambda (lambda) C The power ratio of the reactive power of the capacitor to rated output is calculated; v (V) g Is the grid side voltage.
6. The optimization method for parameters of the weak grid LCL grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, wherein in an objective function, a switching frequency harmonic attenuation ratio eta is an optimization target with highest priority, and the optimization target is represented by the following formula:
wherein I is g (s) is a current measurement expression of the power grid in a complex frequency domain, I L1 (s) is the inversion side inductance current expression in the complex frequency domain, ω s For switching angular frequency, s=jω s The expression condition is when the frequency is a switching angular frequency.
7. The method for optimizing parameters of the weak current network LCL grid-connected inversion filter based on NSGA-II algorithm according to claim 1, wherein in the objective function, it is necessary to minimize the inductance current ripple of the inversion end:
in which the inverter outputs a voltage V in ≈V dc ，V dc Is a direct current voltage, L 1 For the inversion side inductance, f s Is the switching frequency.
8. The method for optimizing parameters of a weak current network LCL grid-connected inverter filter based on NSGA-II algorithm as set forth in claim 1, wherein the objective function requires minimizing the damping resistor power consumption P R_loss ：
Wherein V is g Representing the grid side voltage, omega 0 Is the grid frequency.
9. The method for optimizing parameters of a weak grid LCL grid-connected inverter filter based on NSGA-II algorithm according to claim 1, wherein in the objective function, in order to satisfy the low-pass characteristic of the LCL filter, the resonant frequency is selected by:
wherein f s 、f r The switching frequency and the resonant frequency, f 0 Representing the grid frequency; since the conditions relating to the three variables are not linear, two objective functions that need to be minimized are used to ensure that the resonant frequency is at the allowable range:
P 1 ＝10f 0 -f r
F 2 ＝f r -0.5f s
finally, the total objective function is min [ eta, delta I ripple ，P R_loss ，F 1 ，F 2 ]。
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