NSGA-ii algorithm-based parameter optimization method for LCL-type grid-connected inverter filter in weak power grid

Abstract

Disclosed in the present invention is an NSGA-II algorithm-based parameter optimization method for LCL-type grid-connected inverter filters in a weak power grid, comprising: modeling a single-phase inversion system in a weak power grid, and using inverter side inductance L1, grid side inductance L2, filtering capacitance C and passive damping resistance R as parameters to be optimized; setting boundary constraints for a total inductance value L, the inverter side inductance L1, the grid side inductance L2 and the filtering capacitance C; constructing objective functions of a switching frequency harmonic attenuation ratio η, an inverter end inductor current ripple ΔIripple, a damping resistor power consumption PR_loss and a resonant frequency fr; and on the basis of an NSGA-II algorithm model, using said parameters as decision variables, performing iterative optimization on the plurality of objective functions according to the boundary constraints so as to obtain a parameter solution set of optimal solutions, and selecting a group of typical values from the parameter solution set as optimization solutions. The present invention can significantly improve the filtering effect and the weak grid resistance of filters.

Description

Parameter optimization method for LCL type grid-connected inverter filter in weak power grid based on NSGA-II algorithm Technical Field

[0001] The present invention belongs to the field of inverter filters, and in particular relates to a parameter optimization method for a weak grid LCL type grid-connected inverter filter based on an NSGA-II algorithm. Background Art

[0002] Grid-connected inverters are key equipment supporting the integration of renewable energy into the grid. Compared to L and LC filters, LCL filters offer superior suppression of high-frequency harmonics. Their specific performance depends primarily on the LCL parameters, making filter parameter design crucial. However, filter parameter design requires more restrictions, requires more computational effort, and suffers from poor accuracy. Furthermore, due to weak grid conditions, comprehensive consideration is required for system safety and control robustness under multiple operating conditions.

[0003] Early filter design methods relied on extensive engineering experience and adopted a trial-and-error approach to parameter design in conjunction with electromagnetic characteristics. Sufficient experimental results, combined with graphical methods, led to the development of traditional filter parameter design methods, such as those found in the literature "Xinbo Ruan. Control Techniques for LCL-Type Grid-Connected Inverters. Beijing, CN: Science Press, 2015."

[0004] In the paper "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, August 2018," a single parameter in the LCL filter is optimized, but the optimal filtering effect of the entire system cannot be guaranteed.

[0005] Summary of the Invention

[0006] The present invention provides a parameter optimization method for a weak grid LCL type grid-connected inverter filter based on the NSGA-II algorithm, which greatly improves the filtering effect and weak grid resistance capability of the filter.

[0007] A parameter optimization method for a weak grid LCL type grid-connected inverter filter based on the NSGA-II algorithm includes:

[0008] A single-phase inverter system under a weak power grid is modeled, with the inverter-side inductor L1, the grid-side inductor L2, the filter capacitor C, and the passive damping resistor R as parameters to be optimized.

[0009] Set the limit constraints for the total inductance L, inverter-side inductance L1, grid-side inductance L2, and filter capacitor C;

[0010] Construct the switching frequency harmonic attenuation ratio η and the inverter end inductor current ripple ΔI ripple , Damping resistor power consumption P R_loss and the resonant frequency f r The objective function of

[0011] Based on the NSGA-II algorithm model, the parameters to be optimized are used as decision variables. According to the limit constraints, the parameter solution set of the optimal solution is obtained through iterative optimization of multiple objective functions, and a set of typical values ​​is selected from the parameter solution set as the optimized solution.

[0012] The decision variables based on the NSGA-II algorithm model are: X = [L1, L2, C, R]

[0013] In this model, the single variable principle is used to analyze the influence of each parameter on the system; the parameter changes are all linearly increased and are changed based on the parameters of the traditional trial and error method.

[0014] In the limit constraint, the total inductance value L must meet two conditions: first, the maximum current generated by the voltage drop across the inductor must be limited; second, the current ripple must be reduced to within the allowable range. In other words, the following inequality constraints must be met:

[0015] Where V g_max , I g_max is the peak value of the grid side voltage and current, V dc is the DC side voltage, ΔI ripple-ma is the maximum current ripple on the inverter side, f s is the switching frequency, and ω0 is the grid frequency.

[0016] The inverter-side inductor L1 and the grid-side inductor L2 must meet the following constraints: L1≥L2

[0017] Where, T s is the switching period, is the current ripple coefficient, is the inductor voltage drop coefficient, ω0 is the grid frequency, V in Indicates the filter input voltage (i.e., inverter output voltage), I L1 Indicates the inverter side inductor current, V C Represents the filter capacitor node voltage, V gIndicates the grid side voltage.

[0018] The filter capacitor C must meet the following constraints:

[0019] Where: P O is the grid-side output rated power; ω0 is the grid frequency; λ C V is the ratio of capacitor reactive power to rated output active power; g is the grid side voltage.

[0020] In the objective function, the switching frequency harmonic attenuation ratio η is the highest priority optimization target, as shown in the following formula:

[0021] Where, I g (s) is the expression of the grid current in the complex frequency domain, I L1 (s) is the expression of the inverter side inductor current in the complex frequency domain, ω s is the switching angular frequency, s=jω s The condition is when the frequency is the switching angular frequency.

[0022] In the objective function, the inverter-side inductor current ripple needs to be minimized:

[0023] In the formula, the inverter output voltage V in ≈V dc , V dc is the DC voltage, L1 is the inverter side inductor, f s is the switching frequency.

[0024] In the objective function, it is necessary to minimize the power consumption of the damping resistor P R_loss :

[0025] Where V g represents the grid side voltage, and ω0 is the grid frequency.

[0026] In the objective function, in order to meet the low-pass characteristics of the LCL filter, the resonant frequency is selected as:

[0027] Where, f s 、f r are the switching frequency and the resonant frequency, respectively, and f0 represents the grid frequency. Since the conditions related to the three variables are not linear, two objective functions that need to be minimized are used to ensure that the resonant frequency is within the allowable range: F1 = 10f0 - f r F2=f r -0.5f s

[0028] Finally, the overall objective function is min[η,ΔIripple ,P R_loss ,F1,F2]

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] The present invention adopts a multi-objective optimization genetic algorithm (NSGA-II) for parameter selection of LCL filter grid-connected inverter system under weak grid conditions. First, the single-phase inverter system under weak grid is modeled, the influence of different filter parameters on system stability is analyzed, and the selection criteria of parameter solutions for enhancing system stability are proposed. Based on the traditional trial-and-error method, the limit constraints of the parameters are given, and multiple optimization targets for the system are given. A typical solution is selected from the obtained optimization solution set. A large number of trial-and-error processes are eliminated, the system's resistance to weak grid conditions is enhanced, and the harmonic distortion rate is further reduced while meeting the grid connection requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] FIG1 is a topological structure of a grid-connected inverter with an LCL filter according to an embodiment of the present invention;

[0032] FIG2 is a closed-loop control block diagram of an LCL type grid-connected inverter system according to an embodiment of the present invention;

[0033] FIG3 is a flow chart of the NSGA-II algorithm according to an embodiment of the present invention;

[0034] FIG4 is a diagram showing a trend of closed-loop pole movement of a system when filter parameters increase according to an embodiment of the present invention;

[0035] FIG5 is an optimization parameter solution set according to an embodiment of the present invention;

[0036] FIG6 is a diagram showing the system response under conventional parameters according to an embodiment of the present invention;

[0037] FIG7 shows the system response under optimized parameters in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be noted that the following examples are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0039] The grid-connected inverter topology used in the embodiment of the present invention is an LCL type circuit with a capacitor in series with a resistor, as shown in FIG1 . dc 、C dc is the DC voltage and filter capacitor; L1, L2, L g are the equivalent inductances of the inverter side, grid side and grid respectively; R1, R2, R g are the corresponding line resistances; v in 、v g is the inverter bridge output voltage and grid voltage; iL1 、i g 、i c 、i g_ref They are the inverter side current, grid current, capacitor current and grid reference current respectively. i (s) is the grid-connected current controller and H is the capacitor current feedback controller.

[0040] In order to more intuitively reflect the structure of the system, the closed-loop control block diagram of the inverter system is shown in Figure 2. Current controller G i (s) is the PI controller, H is the proportional feedback, K PWM is the equivalent transfer function of the inverter, is the ratio of the DC voltage to the carrier voltage amplitude. The capacitor in series with the resistor used in the embodiment of the present invention is a simple and effective method to reduce the resonance peak damping, and the capacitor current feedback speeds up the system response.

[0041] To simplify the transfer function, the smaller line impedance values ​​R1 and R2 are ignored. Thus, the transfer function from the inverter output voltage to the grid current and the transfer function of the overall closed-loop system can be obtained:

[0042] Next, the parameters are analyzed and optimized according to the above model.

[0043] Typically, a multi-objective optimization algorithm generates a set of independent solutions to a specific problem, known as a Pareto optimal solution set. This paper uses the NSGA-II algorithm framework, which uses a genetic algorithm to perform hierarchical and rapid non-dominated sorting of individuals in a population, while employing an elitist strategy to prevent the loss of high-performing individuals.

[0044] The main process of the NSGA-II algorithm is shown in Figure 3. First, an initial population P of size N is randomly generated. t , after non-dominated sorting, selection, crossover and mutation, the offspring population Q is generated t , and combine the two populations to form a population R of size 2N t Secondly, a fast non-dominated sort is performed, and the crowding degree of the individuals in each non-dominated layer is calculated. According to the non-dominated relationship and the crowding degree of the individuals, suitable individuals are selected to form a new parent population P. t+1 Finally, a new offspring population Q is generated through the basic operation of the genetic algorithm. t+1 , P t+1 With Q t+1 Merge to form a new population R t+1 , repeat the above steps until the program ends.

[0045] In this parameter design optimization, the main design parameters are the filter inductor and capacitor L1, L2, C and the passive damping resistor R. Therefore, the decision variables based on the NSGA-II algorithm model are: X = [L1, L2, C, R] (3)

[0046] Because the algorithm's optimal solution set is generally quite large, additional criteria are required. In this model, the single-variable principle can be applied to the aforementioned parameters to analyze their impact on the system. Parameter changes are all linear, based on the parameters used in the traditional trial-and-error method. The parameters are varied as follows: L1 (850μH → 1200μH), L2 (500μH → 1200μH), C (4μF → 18μF), and R (2Ω → 9Ω).

[0047] Figure 4 shows that as the filter inductors L1 and L2 increase, the dominant pole approaches the imaginary axis, deteriorating system stability. As the capacitance C increases, the absolute value of the real part of the pole first increases and then decreases. Increasing the resistance R improves system stability. This leads to the optimal solution: ensuring that L1 and L2 are small, R is large, and C is moderate.

[0048] While the filter meets the requirements of harmonic attenuation, the limit constraints of the total inductance L, inverter side inductance L1, grid side inductance L2, and filter capacitor C are set as the constraints of the objective function.

[0049] 1)Total inductance

[0050] The larger the total inductance of the LCL filter, the better the filtering effect; the smaller the inductance, the stronger the response ability. Therefore, 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 current ripple to keep it within the allowable range. In other words, it needs to meet the following inequality constraints:

[0051] Where: V g_max , I g_max is the peak value of grid side voltage and current; the inverter side output voltage V inv ≈V dc .

[0052] 2) Inverter side and grid side inductance

[0053] In terms of engineering manufacturing, to reduce cost and size, the grid-side inductance is often smaller than the inverter-side inductance. The inverter-side inductance must meet the current ripple and voltage drop limits, resulting in the following constraints: L1≥L2 (6)

[0054] Where: switching period T s; Current ripple factor Inductor voltage drop coefficient

[0055] 3) Filter capacitor

[0056] The larger the capacitance value, the smaller the voltage ripple, but the power consumption is also greater; therefore, the upper limit of the capacitance value needs to be considered:

[0057] Where: P O is the grid-side output rated power; ω0 is the grid frequency; the ratio of capacitor reactive power to rated output active power is λ C ≈5%.

[0058] Construct the switching frequency harmonic attenuation ratio η and the inverter end inductor current ripple ΔI ripple , Damping resistor power consumption P R_loss and the resonant frequency f r The objective function.

[0059] 1) Switching frequency harmonic attenuation ratio

[0060] This is the highest priority optimization goal in this optimization design. The smaller the harmonic attenuation, the better the switching frequency harmonic filtering effect, as shown in the following formula:

[0061] 2) Inverter end inductor current ripple

[0062] The switching action of the inverter will cause the inverter-side current to have a dv / dt variation close to the switching frequency, that is, the current ripple. In order to ensure system stability, strengthen control effects, and reduce switching and inductor losses, it is necessary to minimize the inverter current ripple:

[0063] Where: Inverter output voltage V in ≈V dc ; Inverter side inductor L1.

[0064] 3) Damping resistor power consumption

[0065] LCL filters introduce passive damping to enhance system harmonic suppression performance, but also introduce power dissipation, which needs to be minimized:

[0066] 4) Resonant frequency

[0067] In order to meet the low-pass characteristics of the LCL filter, the resonant frequency is generally selected as follows:

[0068] Where: f s 、f rThey are the switching frequency and the resonant frequency. Since the conditions related to the three variables are not linear, bilateral constraints are used as the optimization target, and two objective functions that need to be minimized are used to ensure that the value of the resonant frequency is within the allowable range: F1=10f0-f r (12) F2=f r -0.5f s (13)

[0069] The objective function of the algorithm is min[η,ΔI ripple ,P R_loss ,F1,F2] (14)

[0070] Based on the above, we used Equation (3) as the optimization variable, Equations (4) to (7) as the linear constraints, and Equation (14) as the multi-objective function. We used the NSGA-II algorithm. The basic parameters were set as follows: optimal individual system ParetoFraction 0.4; population size populationsize 300; maximum evolution generations generations 400; stallGenLimit 300; and fitness function deviation TolFun 1e-10. Through iterative optimization, we obtained a set of solutions that achieve multi-objective Pareto optimal solutions, as shown in Figure 5.

[0071] These solutions are not mutually coupled and are all optimal. However, it is still possible to see a clear range of parameter concentration. In the range where all four parameters fall within the majority, a set of typical values ​​is selected as the optimized solution based on the parameter selection criteria. The algorithm's superiority is demonstrated by comparison with traditional solutions. The specific parameters are shown in Table 1.

[0072] Table 1 Comparison between traditional methods and optimization algorithms

[0073] In order to verify the optimization effect of the multi-objective optimization algorithm on the system under weak grid conditions, an embodiment of the present invention builds a simulation model of the grid-connected inverter based on Matlab / Simulink. The specific parameter environment is shown in Table 2.

[0074] Table 2 Simulation system parameters and environment

[0075] Based on the above parameters, simulations were performed on the constructed model, and the system responses under traditional parameters and optimized parameters were obtained as shown in Figures 6 and 7, respectively. They specifically include the coupling voltage, inverter and grid-side currents, capacitor current, and harmonic analysis diagrams.

[0076] As can be seen from the two figures, the parameters designed using the optimization algorithm significantly enhance the inverter system's adaptability to weak grid conditions. When the weak grid inductance reaches 2mH, the traditional solution destabilizes the system, but the optimized solution maintains system stability. A zoomed-in view of the waveform reveals that the current and voltage ripples increase somewhat (5.513 → 6.182A) due to the reduction in the filter parameter values, but remain within the allowable range required for grid-connected design. The resistor power consumption increases significantly (0.245 → 4.838W), but the reduction in the inductance and capacitance values ​​nearly offsets the change in resonant frequency loss. The waveform distortion rate under weak grid conditions decreases significantly, significantly improving the filter's filtering effectiveness and weak grid resistance. The specific distortion rate parameters are shown in Table 3.

[0077] Table 3 Comparison between traditional methods and optimization algorithms

[0078] The embodiments described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing parameters of a weak grid LCL type grid-connected inverter filter based on NSGA-II algorithm, characterized in that: include: The single-phase inverter system under the weak power grid is modeled, and the inverter side inductor L1, the grid side inductor L2, the filter capacitor C and the passive damping resistor R are taken as the parameters to be optimized; Set the limit constraints of the total inductance L, the inverter side inductance L1, the grid side inductance L2, and the filter capacitor C; Construct the switching frequency harmonic attenuation ratio η and the inverter end inductor current ripple ΔI ripple , Damping resistor power consumption P R_loss and the resonant frequency f r The objective function of Based on the NSGA-II algorithm model, the parameters to be optimized are used as decision variables. According to the limit constraints, the parameter solution set of the optimal solution is obtained through iterative optimization of multiple objective functions, and a set of typical values ​​is selected from the parameter solution set as the optimization solution.

2. The method for optimizing parameters of a weak grid LCL type grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, characterized in that: The decision variables based on the NSGA-II algorithm model are: X = [L1, L2, C, R] In this model, the single variable principle is used to analyze the influence of each parameter on the system; the parameter changes are all linearly increased, and the changes are made on the basis of the parameters of the traditional trial and error method.

3. The method for optimizing parameters of a weak grid LCL type grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, characterized in that: In the limit constraint, the total inductance value L needs to meet two conditions: first, the maximum current generated by the voltage drop on the inductor needs to be limited; second, the current ripple needs to be reduced to within the allowable range; that is, the following inequality constraints need to be satisfied: Where V g_max ,I g_max is the peak value of the voltage and current on the grid side, V dc is the DC side voltage, ΔI ripple-ma is the maximum current ripple on the inverter side, f s is the switching frequency, ω0 is the grid frequency.

4. The method for optimizing parameters of a weak grid LCL type grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, characterized in that: In the boundary constraints, the inverter-side inductor L1 and the grid-side inductor L2 must meet the following constraints: L1 ≥ L2 Where, T s is the switching cycle, is the current ripple factor, is the inductor voltage drop coefficient, ω0 is the grid frequency, V in Indicates the filter input voltage, I L1 Indicates the inverter side inductor current, V C Represents the filter capacitor node voltage, V g Indicates the grid side voltage.

5. The method for optimizing parameters of weak grid LCL type grid-connected inverter filter based on NSGA-II algorithm according to claim 1, characterized in that: In the boundary constraints, the filter capacitor C needs to meet the following constraints: Where: P O is the grid-side output rated power; ω0 is the grid frequency; λ C V is the ratio of capacitor reactive power to rated output active power; g is the grid side voltage.

6. The method for optimizing parameters of weak grid LCL type grid-connected inverter filter based on NSGA-II algorithm according to claim 1, characterized in that: In the objective function, the switching frequency harmonic attenuation ratio η is the highest priority optimization target, as shown in the following formula: In the formula, I g (s) is the expression of the grid current in the complex frequency domain, I L1 (s) is the inductor current expression of the inverter side in the complex frequency domain, ω s is the switching angular frequency, s = jω s The condition is when the frequency is the switching angle frequency.

7. The method for optimizing parameters of weak grid LCL type grid-connected inverter filter based on NSGA-II algorithm according to claim 1 is characterized in that: In the objective function, the inverter inductor current ripple needs to be minimized: In the formula, the inverter output voltage V in ≈V dc , V dc is the DC voltage, L1 is the inverter side inductor, f s is the switching frequency.

8. The method for optimizing parameters of a weak grid LCL type grid-connected inverter filter based on the NSGA-II algorithm according to claim 1, characterized in that: In the objective function, it is necessary to minimize the power consumption of the damping resistor P R_loss : Where V g represents the grid side voltage, and ω0 is the grid frequency.

9. The method for optimizing parameters of weak grid LCL type grid-connected inverter filter based on NSGA-II algorithm according to claim 1, characterized in that: In the objective function, in order to meet the low-pass characteristics of the LCL filter, the resonant frequency is selected as: In the formula, f s 、f r are the switching frequency and the resonant frequency, respectively, and f0 represents the grid frequency. Since the conditions related to the three variables are not linear, two objective functions that need to be minimized are used to ensure that the value of the resonant frequency is within the allowable range: F1=10f0-f r <h2 style=";text-align:left;direction:ltr">F2=f<h2 style=";text-align:left;direction:ltr"> r <h2 style=";text-align:left;direction:ltr"> -0.5f<h2 style=";text-align:left;direction:ltr"> s Finally, the overall objective function is min[η,ΔI ripple ,P R_loss ,F1,F2].

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