A method for predicting the life of filter capacitors of an inverter system based on an LCL filter

Abstract

The application discloses a kind of based on LCL filter's inverter system filter capacitor life prediction method, belong to power electronic converter technical field, specific steps are as follows: using Fourier analysis to calculate the effective value of each order harmonic amplitude of capacitor current, and calculate joule loss and dielectric loss;Actual working condition is loaded to inverter system, and the hot spot temperature of capacitor is calculated;According to capacitor hot spot temperature, joule loss and dielectric loss, the expected life of single capacitor is calculated;Through monte carlo analysis statistical method, the failure life histogram of capacitor is obtained, and the coefficient of weibull distribution is obtained by using weibull distribution fitting;And single capacitor life is converted into capacitor group life.The above-mentioned based on LCL filter's inverter system filter capacitor life prediction method is used, the real working condition is considered to predict, the joule loss, dielectric loss and capacitor hot spot temperature of capacitor are estimated by temperature acquisition, and single capacitor life is extended to capacitor group life.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power electronic converter, and particularly to a filter capacitor life prediction method of an inverter system based on an LCL filter. BACKGROUND

[0002] LCL filter is widely used in renewable energy field, compared with single inductance filter, it can realize higher harmonic attenuation, and also can reduce the weight of components. However, as a three-order system, the resonance peak of LCL filter affects the stability of the system, which depends on time delay and current control scheme. The most commonly used resonance damping method is passive damping and active damping. In renewable energy, such as photovoltaic power generation and wind power generation, their high maintenance cost promotes the reliability of power electronic system to become more and more critical. However, the capacitor is the weakest component in the power electronic system. The existing capacitor life prediction analysis is all for the DC bus aluminum electrolytic capacitor or directly uses the life model provided by the capacitor manufacturer to estimate. However, the LCL filter commonly used in new energy applications is often affected by working conditions, environmental temperature, heat dissipation conditions and other factors to affect its life. Especially when the LCL filter produces resonance current, it will affect the life of the capacitor, resulting in reduced system reliability. SUMMARY

[0003] The purpose of the present application is to solve the technical problems existing in the prior art.

[0004] To achieve the above purpose, the present application provides a filter capacitor life prediction method of an inverter system based on an LCL filter, and the specific steps are as follows:

[0005] Step S1: Collecting the parameters of the inverter system based on the LCL filter, and calculating the effective value of the harmonic amplitude of the capacitor current by using Fourier analysis;

[0006] Step S2: Calculating the Joule loss and dielectric loss according to the effective value of the harmonic amplitude of the capacitor current;

[0007] Step S3: Loading the actual working condition of the inverter system, and calculating the capacitor hotspot temperature caused by the harmonic current;

[0008] Step S4: Calculating the expected life of a single capacitor according to the capacitor hotspot temperature, Joule loss and dielectric loss;

[0009] Step S5: Obtaining the failure life histogram of the capacitor by using the Monte Carlo analysis statistical method, and obtaining the coefficient of Weibull distribution by using Weibull distribution fitting;

[0010] Step S6: Converting the life of a single capacitor into the life of a capacitor group according to the capacitor connection diagram and the shape coefficient of Weibull distribution.

[0011] Preferably, in step S1, the formula for calculating the inverter output voltage data by Fourier transform is as follows:

[0012]

[0013]

[0014] wherein α k represents the intersection point of the modulation wave and the carrier wave in SPWM, k takes a value in the range of 1 to 2N, N is the carrier ratio, M is the inverter modulation ratio, n is the harmonic order, a n and b n are Fourier series coefficients, U dc is the DC side voltage, ω o is the fundamental angular frequency, T c is the carrier period, i and j are the i-th and j-th intersection points of the modulation wave and the carrier wave in a fundamental period, respectively, and m n is the inverter output voltage data.

[0015] The formula for calculating the effective value of the amplitude of each order harmonic of the capacitor current is as follows:

[0016]

[0017]

[0018] wherein Z C (n) is the impedance of the LCL filter, s is a complex variable, L i is the inverter side inductance, L g is the grid side inductance, C f is the filter capacitance, and i C (n) is the effective value of the amplitude of each order harmonic of the capacitor current.

[0019] Preferably, in step S2, the formula for calculating the Joule loss and dielectric loss is as follows:

[0020]

[0021] wherein ESR is the equivalent series resistance of the capacitor, i C (n) is the effective value of the amplitude of each order harmonic of the capacitor current, n is the harmonic order, δ is the dissipation factor of the capacitor, ω n is the angular frequency of the n-th harmonic, and C f is the filter capacitance.

[0022] Preferably, in step S3, the formula for calculating the capacitor hot spot temperature is as follows:

[0023] T h = ΔT + T a= P loss R th + T a

[0024] Wherein, R th is the equivalent thermal resistance of the capacitor, T a is the ambient temperature, and ΔT is the temperature rise amplitude caused by the total power loss.

[0025] Preferably, in step S4, the expected life of a single capacitor is calculated according to the following formula:

[0026]

[0027] Wherein, L0 is the rated life of the capacitor, T0 is the rated temperature of the capacitor, V x is the actual operating voltage of the capacitor, V0 is the rated voltage of the capacitor, and n2 is the voltage stress coefficient of the capacitor.

[0028] Preferably, in step S5, the rated voltage, the rated life, and the equivalent hot spot temperature are respectively subjected to a normal probability density function distribution with a 5% change through a Monte Carlo analysis statistical method, a failure year histogram of the capacitor is obtained, and the parameters of the Weibull distribution are obtained by fitting the Weibull distribution.

[0029] Preferably, in step S6, the capacitor group life calculation formula is as follows:

[0030] F bank (t) = 1 - Π(1 - F i (t))

[0031] Wherein, F i (t) represents the failure function of a single capacitor.

[0032] Therefore, the present application has the following beneficial effects by adopting the above-mentioned inverter system filter capacitor life prediction method based on an LCL filter:

[0033] (1) The capacitor life is predicted by loading real working conditions, avoiding the direct use of the capacitor life formula without considering the influence of real environment and resonance current on the life.

[0034] (2) The Fourier analysis is used to calculate the effective value of the capacitor current resonance amplitude in the application scenario, without the need for simulation or current collection and temperature collection to estimate the joule loss and dielectric loss of the capacitor and the capacitor hot spot temperature.

[0035] (3) The capacitor connection diagram and the shape coefficient of the Weibull distribution convert the life of a single capacitor into the life of a capacitor group, realizing the prediction of the overall capacitor group life.

[0036] The technical solutions of the present application will be further described in detail through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 A flow chart of a life prediction method of filter capacitors of an inverter system based on an LCL filter according to the present application;

[0038] Figure 2 A normal probability density function distribution graph of a rated voltage according to the present application;

[0039] Figure 3 A normal probability density function distribution graph of a rated life according to the present application;

[0040] Figure 4 A normal probability density function distribution graph of an equivalent hot spot temperature according to the present application;

[0041] Figure 5 A histogram of capacitor failure years obtained by Monte Carlo simulation according to the present application;

[0042] Figure 6 A Weibull distribution graph of a single capacitor according to the present application;

[0043] Figure 7 A schematic diagram of a home photovoltaic inverter system according to the present application;

[0044] Figure 8 A graph of a capacitor hot spot temperature and an ambient temperature according to the present application;

[0045] Figure 9 A connection diagram of an LCL filter capacitor according to the present application;

[0046] Figure 10 A Weibull distribution graph of a capacitor group according to the present application. DETAILED DESCRIPTION

[0047] EMBODIMENT

[0048] In order to make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the following will be combined with the accompanying drawings for the embodiments of the present application to make a clear and complete description of the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations.

[0049] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present application.

[0050] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0051] refer to Figure 1 A method for predicting the lifetime of filter capacitors in an inverter system based on an LCL filter, the specific steps of which are as follows:

[0052] Step S1: Collect inverter system parameters based on LCL filter. This embodiment takes a 2.6kW residential photovoltaic inverter system as an example. The residential photovoltaic inverter system is as follows: Figure 7 As shown in the table below:

[0053]

[0054] The formula for calculating the inverter output voltage data using Fourier transform is as follows:

[0055]

[0056]

[0057] Where, α k This represents the intersection of the modulating wave and the carrier wave in SPWM. The value of k ranges from 1 to 2N, where N is the carrier ratio, M is the inverter modulation ratio, n is the harmonic order, and a... n and b n These are the Fourier series coefficients. U dc This is the DC side voltage. ω o T is the fundamental angular frequency. c Let m be the carrier period, i and j be the intersection points of the i-th and j-th modulated waves and the carrier wave within one fundamental period, respectively. n This is the inverter output voltage data.

[0058] Based on the inverter output voltage data and the impedance of the LCL filter, the effective values ​​of the amplitudes of each order harmonic of the capacitor current are calculated using the following formulas:

[0059]

[0060]

[0061] Among them, Z C (n) represents the impedance of the LCL filter, s is a complex variable, and L i L is the inverter-side inductor. g For the grid-side inductor, C f For the filter capacitor, i C (n) represents the effective values ​​of the harmonic amplitudes of the capacitor current at each order. The resonant amplitude of the capacitor current under the same parameters is obtained through PLECS simulation, and then compared with the Fourier calculation results to ensure the accuracy of the calculation results.

[0062] Step S2: Calculate the Joule loss and dielectric loss according to the effective value of each order harmonic amplitude of the capacitor current.

[0063] The formula for calculating the Joule loss and dielectric loss is as follows:

[0064]

[0065] Where ESR is the equivalent series resistance of the capacitor, i C (n) is the effective value of the amplitude of each order harmonic of the capacitor current, n is the harmonic order, δ is the dissipation factor of the capacitor, ω n is the angular frequency of the nth harmonic, C f is the filter capacitance.

[0066] Step S3: Load the actual working condition of the inverter system, and calculate the capacitor hotspot temperature caused by the harmonic current. The formula for calculating the capacitor hotspot temperature is as follows:

[0067] T h = ΔT + T a = P loss R th + T a

[0068] Where R th is the equivalent thermal resistance of the capacitor, T a is the ambient temperature, and ΔT is the temperature rise amplitude caused by the total power loss.

[0069] Step S4: Calculate the expected life of a single capacitor according to the capacitor hotspot temperature, Joule loss and dielectric loss. The formula for calculating the expected life of a single capacitor is as follows:

[0070]

[0071] Where L0 is the rated life of the capacitor, T0 is the rated temperature of the capacitor, V x is the actual operating voltage of the capacitor, V0 is the rated voltage of the capacitor, and n2 is the voltage stress coefficient of the capacitor, i.e. the power coefficient of the last term. As Figure 8 shown, where the gray curve is the capacitor hotspot temperature and the black curve is the ambient temperature, it can be seen that when the LCL filter resonates, the capacitor hotspot temperature is higher than the ambient temperature.

[0072] Step S5: Make the rated voltage, rated life and equivalent hotspot temperature each subject to a 5% change in the normal probability density function distribution by Monte Carlo analysis statistical method. In order to solve the uncertainty of the capacitor life model and the capacitor parameters, the Monte Carlo simulation statistical method is adopted, and the rated voltage, rated life and equivalent hotspot temperature each subject to a 5% change in the normal probability density function distribution as Figures 2-4The failure time histogram of the capacitor is obtained and fitted with Weibull distribution to obtain the parameters of the Weibull distribution. The histogram of the failure time of the capacitor is fitted with Weibull distribution as shown in the figure, and according to the fitted shape coefficient β = 5.1275, the final single capacitor life prediction value is obtained as shown in the figure Figure 5 The failure time histogram of the capacitor is fitted with Weibull distribution as shown in the figure, and according to the fitted shape coefficient β = 5.1275, the final single capacitor life prediction value is obtained as shown in the figure Figure 6 As shown in the figure, the final single capacitor B10 life of this example is 13.03 years, representing the operating life of 10% of the samples when they fail, which is much smaller than the design life standard of the household photovoltaic inverter.

[0073] Step S6: Convert the single capacitor life to the capacitor bank life according to the capacitor connection diagram and the shape coefficient of the Weibull distribution. In order to improve the life of the capacitor, multiple capacitors can be connected in series or parallel to form a capacitor bank to reduce the electro-thermal stress caused by the resonant current. In this embodiment, the technical solution of all capacitors being connected in series is adopted, as shown in the figure, that is, the failure of any one capacitor will cause the failure of the capacitor bank. Figure 9

[0074] The formula for calculating the life of the capacitor bank is as follows:

[0075] F bank (t)=1-∏(1-F i (t))

[0076] Where F i (t) represents the failure function of the single capacitor.

[0077] In this example, five 3μF capacitors are connected in parallel to form a capacitor bank, Figure 10 The Weibull distribution of the capacitor bank and the single capacitor is obtained as shown in the figure, and the solid line of the capacitor bank life is 27.56 years, which is less than the 35.57 years of the single capacitor life of the dashed line. Compared with the 13.03 years of life when a single 15μF capacitor is used, the parallel capacitor bank reduces the impact of the resonant current of the LCL filter on the life.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.​

Claims

1. A method for predicting the life of a filter capacitor of an LCL filter-based inverter system, characterized by, The specific steps are as follows: Step S1: Collect the parameters of the inverter system based on the LCL filter, and calculate the effective value of the harmonic amplitude of the capacitor current of each order by Fourier analysis; Step S2: Calculate the Joule loss and dielectric loss according to the effective value of the harmonic amplitude of the capacitor current of each order; Step S3: Load the actual working condition of the inverter system, and calculate the capacitor hotspot temperature caused by the harmonic current; Step S4: Calculate the expected life of a single capacitor according to the capacitor hotspot temperature, Joule loss and dielectric loss; Step S5: Obtain the capacitor failure year histogram by the Monte Carlo analysis statistical method, and obtain the Weibull distribution coefficient by Weibull distribution fitting; Step S6: Convert the life of a single capacitor into the life of a capacitor group according to the capacitor connection diagram and the shape coefficient of the Weibull distribution.

2. The LCL filter-based inverter system filter capacitor lifetime prediction method of claim 1, wherein: In step S1, the formula for calculating the inverter output voltage data by Fourier transform is as follows: wherein α k represents the intersection point of the modulation wave and the carrier wave in SPWM, k ranges from 1 to 2N, N is the carrier ratio, M is the inverter modulation ratio, n is the harmonic order, a n and b n are Fourier series coefficients, U dc is the DC side voltage, ω o is the fundamental angular frequency, T c is the carrier cycle, i and j are the i-th and j-th intersection points of the modulation wave and the carrier wave in a fundamental cycle, respectively, and m n is the inverter output voltage data; The formula for calculating the effective value of the harmonic amplitude of the capacitor current of each order is as follows: wherein Z C (n) is the impedance of the LCL filter, s is a complex variable, L i is the inductance on the inverter side, L g is the inductance on the grid side, C f is the filter capacitance, i C (n) is the effective value of the amplitude of the harmonic of order n of the capacitor current.

3. The LCL filter-based inverter system filter capacitor lifetime prediction method of claim 2, wherein: In step S2, the formula for calculating the Joule loss and dielectric loss is as follows: where ESR is the equivalent series resistance of the capacitor, i C (n) is the effective value of the amplitude of each order harmonic of the capacitor current, n is the harmonic order, δ is the dissipation factor of the capacitor, ω n is the angular frequency of the nth harmonic, C f is the filter capacitor.

4. The method of claim 3, wherein the method further comprises: In step S3, the formula for calculating the capacitor hotspot temperature is as follows: T h = ΔT + T a = P loss R th + T a where R th is the equivalent thermal resistance of the capacitor, T a is the ambient temperature, and ΔT is the temperature rise due to the total power loss.

5. The method of claim 4, wherein: In step S4, the formula for calculating the expected life of a single capacitor is as follows: wherein L0 is a capacitor rated life, T0 is a capacitor rated temperature, V x is a capacitor actual operating voltage, V0 is a capacitor rated voltage, and n2 is a capacitor voltage stress coefficient.

6. The LCL filter-based inverter system filter capacitor lifetime prediction method of claim 4, wherein: In step S5, by the Monte Carlo analysis statistical method, the rated voltage, rated life and equivalent hotspot temperature are respectively subjected to the normal probability density function distribution with 5% variation, the capacitor failure year histogram is obtained, and the Weibull distribution parameters are obtained by Weibull distribution fitting.

7. The method of claim 4, wherein: In step S6, the formula for calculating the life of a capacitor group is as follows: F bank (t) = 1 - Π(1 - F i (t)) where F i (t) represents a failure function of the individual capacitor.

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