An alternating current contactor residual electrical life prediction method based on mixed effect model

Abstract

The application discloses an alternating current contactor residual electric life prediction method based on a mixed effect model. The method introduces the competitive failure and degradation correlation characteristics of three-phase contactors into the residual electric life prediction method, and the obtained performance degradation model conforms to the actual performance evolution law of the product. The mixed effect degradation modeling method and the maximum likelihood estimation method and other technical means are adopted, so that the electric life prediction can be effectively performed by using the electric arc erosion amount data in the product use process. While the prediction precision is ensured, the method is simple to calculate, provides a theoretical basis for the reliability analysis of switching devices, is convenient for engineering and technical personnel to use, and has strong application value.

Description

Technical Field

[0001] This invention relates to the field of reliability prediction technology for switching devices, and specifically to a method for predicting the remaining electrical lifetime of AC contactors based on a hybrid effect model. Background Technology

[0002] AC contactors are key components in low-voltage power distribution and automatic control systems, playing a crucial role in remotely connecting and disconnecting AC main circuits and high-capacity control circuits. With the continuous and vigorous development of the switchgear industry, the technical requirements for AC contactors are constantly increasing, as their performance directly affects the safety and reliability of the power system. During the service life of AC contactors, with the increase in the number of times the moving and stationary contacts engage, arc erosion caused by electrical stress gradually accumulates, leading to a continuous deterioration in the performance of the AC contactor and ultimately causing its failure. To ensure the safe and stable operation of the system, it is necessary to repair or replace AC contactors in a timely manner before failure occurs; therefore, accurately predicting the remaining electrical life of AC contactors is crucial.

[0003] The three-phase contacts of AC contactors exhibit competitive failure and degradation correlation. On the one hand, the condition for normal operation of an AC contactor is that the cumulative arc erosion of all three phase contacts does not exceed the failure threshold; a failure in any phase contact will lead to contactor failure, which is a typical competitive failure process. On the other hand, since the arc initiation phase angles of the three phase contacts differ by 120°, and the arc erosion generated on each phase contact is determined by the corresponding arc initiation phase angle, there is a correlation in the performance degradation among the three phase contacts. However, existing AC contactor reliability studies usually focus on the failed phase contact, without considering the problem of competitive failure and degradation correlation among the three phase contacts, which may lead to inaccurate predictions of remaining electrical lifetime. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this patent proposes a method for predicting the remaining electrical life of AC contactors based on a mixed-effects model. This method incorporates the characteristics of competing failures and degradation correlations of three-phase contacts into the remaining electrical life prediction method. The resulting performance degradation model conforms to the actual performance evolution law of the product. Employing techniques such as mixed-effects degradation modeling and maximum likelihood estimation, it can effectively utilize arc erosion data during product use for electrical life prediction. While ensuring prediction accuracy, the proposed method is computationally simple, providing a theoretical basis for the reliability analysis of switching devices, facilitating use by engineering technicians, and possessing strong application value.

[0005] The technical solution of this invention to solve the aforementioned technical problem is as follows: A method for predicting the remaining electrical lifetime of AC contactors based on a mixed-effect model is proposed. The specific implementation steps of this method are as follows:

[0006] Step 1: Establish a mixed-effect model for the three-phase contacts of an AC contactor.

[0007] Using cumulative arc erosion as a characteristic quantity of AC contactor performance degradation, a mixed-effect model for three-phase contacts is established by comprehensively considering trend and random terms:

[0008] (1)

[0009] In the formula, This indicates a contact of a certain phase; express Phase contact disconnection The cumulative arc erosion at this time; For the trend term, the parameters are... express The degradation rate of the phase contact; The term is a random term, representing the influence of uncertainties in the degradation process, and at any given time... Independent and identically distributed, satisfying a mean of 0 and a variance of . The normal distribution, i.e. ;

[0010] Regarding the correlation of cumulative arc erosion between three-phase contacts, it is assumed that... It follows a vector with a mean vector of zero and a covariance matrix of... The ternary normal distribution, i.e. ;

[0011] As the number of disconnections increases, the amount of arc erosion on the contacts accumulates. When the accumulated arc erosion reaches the failure threshold, the contactor cannot reliably disconnect, and the contactor is considered to have failed. This is achieved through random variables. To represent the threshold value, let's assume the three-phase contact failure threshold. Independent and identically distributed, all following a mean of 1. variance is The normal distribution, i.e. ;

[0012] Step 2: Estimate the parameters in the mixed-effects model

[0013] Step 2.1 Estimation of Trend Term Parameters

[0014] The mixed-effect model established in step one shows that an AC contactor Cumulative arc erosion of phase contacts Follow the mean variance is The normal distribution, i.e. Therefore, model parameters The log-likelihood function is:

[0015] (2)

[0016] In the formula, for The current number of times the phase contact has been broken;

[0017] For parameters Taking the partial derivative, we get:

[0018] (3)

[0019] Let equation (3) equal to zero, we can obtain The maximum likelihood estimator is:

[0020] (4)

[0021] Step 2.2 Random Term Parameter Estimation

[0022] Random items One implementation can be achieved by The calculations were obtained, and then based on different time points... The specific implementation involves estimating the model parameters involved using the maximum likelihood estimation method;

[0023] The probability density function of the ternary normal distribution is expressed as follows:

[0024] (5)

[0025] In the formula, ;

[0026] According to equation (5), we can obtain The likelihood function is:

[0027] (6)

[0028] In the formula, This represents the current number of segments.

[0029] Therefore, according to equation (6), we can obtain The log-likelihood function is:

[0030] (7)

[0031] In the formula, This represents the current number of segments.

[0032] From equation (7) on the covariance matrix Taking the partial derivative, we get:

[0033] (8)

[0034] Let equation (8) equal to zero, we can obtain The maximum likelihood estimator is:

[0035] (9)

[0036] Step 3: Calculate the reliability function

[0037] Record the current number of segments as ,at this time The degradation of the phase contact is The corresponding phase failure threshold is Starting from the current number of segments, and then... In the secondary disconnection, the failure condition of the AC contactor is the amount of degradation of any phase contact. Exceeding the failure threshold Therefore, the reliability function is:

[0038] (10)

[0039] For the random variable in equation (10) To find the expectation, equation (10) can be written as: (11)

[0040] In the formula, The probability density function representing the contact failure threshold;

[0041] random variables cumulative distribution function substitution By performing an integral transform on the triple integral, the integration interval can be... Change to Then equation (11) can be written as:

[0042] (12)

[0043] In the formula, This is the cumulative distribution function of the contact failure threshold; It is the inverse function of the cumulative distribution function of the contact failure threshold; For random items The cumulative distribution function;

[0044] For the calculation of the triple integral in equation (12), the Riemann method and other techniques are used to solve the integration problem, and the reliability function is finally approximated as:

[0045] (13)

[0046] In the formula, It refers to the number of divisions within the integration interval;

[0047] Step 4: Predict remaining lifespan

[0048] The expected remaining lifetime is used as an estimate of the remaining lifetime point, and is calculated using the following formula:

[0049] (14)

[0050] In the formula, For already separated The remaining lifetime point estimate at the next time; for The cumulative distribution function;

[0051] Based on the mathematical relationship between reliability and cumulative distribution function:

[0052] (15)

[0053] By combining equations (14) and (15), the remaining lifetime point estimate can be obtained. for:

[0054] (16)

[0055] To perform an approximate calculation of the reliability integral, take... The upper limit of integration is given, and its reliability function satisfies Approximately zero, therefore equation (16) can be written as:

[0056] (17)

[0057] Similarly, by applying Riemannian techniques to solve the integration problem of equation (17), we can obtain:

[0058] (18)

[0059] Substituting equation (13) into equation (18), we get:

[0060] (19)

[0061] In the formula, This represents the number of divisions into which the integration interval is divided.

[0062] Compared with existing technologies, the advantages of this invention are as follows: The method proposed in this invention considers the characteristics of competitive failure and degradation correlation among three-phase contacts, utilizes the arc erosion data of the three-phase contacts to establish a performance degradation model, and ultimately estimates the remaining lifetime point. The analytical process of the method proposed in this invention is scientific, reasonable, and closely related to actual conditions. The calculation process is simple, the remaining lifetime prediction results are reliable, and it is convenient for engineering technicians to use, thus having strong practical application value. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without creative effort.

[0064] Figure 1 This is a flowchart of an embodiment of the AC contactor residual electrical lifetime prediction method based on a hybrid effect model according to the present invention.

[0065] Figure 2 The data represents the performance degradation test data of the AC contactor in Example 1 when it is switched on and off 27,000 times.

[0066] Figure 3 The reliability function curve obtained according to the method of the present invention is shown when the AC contactor in Example 1 is switched on and off 27,000 times. Detailed Implementation

[0067] The technical content of the present invention will be described in detail below with reference to specific embodiments and accompanying drawings. In the following text, "*" is equivalent to "×", that is, the multiplication sign in the arithmetic operator.

[0068] This invention provides a method for predicting the remaining electrical lifetime of AC contactors based on a hybrid effect model (hereinafter referred to as the method). The specific implementation steps of the method are as follows:

[0069] Step 1: Establish a mixed-effect model for the three-phase contacts of an AC contactor.

[0070] Arc erosion-induced electrical wear is the primary failure mode of AC contactors. Each time the moving and stationary contacts break, arc erosion occurs on the contacts. When the cumulative arc erosion reaches the failure threshold, the contactor fails. During the service life of an AC contactor, each phase contact is subjected to electrical stress upon breaking, and each instance of electrical stress generates random arc erosion. Therefore, according to the central limit theorem, the cumulative arc erosion after a certain number of breaks can be considered to approximately follow a normal distribution.

[0071] Based on the above analysis, cumulative arc erosion is used as a characteristic quantity of AC contactor performance degradation. A mixed-effect model for three-phase contacts is established, comprehensively considering both trend and random terms. For the trend term, a linear model is adopted to characterize the overall degradation trend of cumulative arc erosion. For the random term, it is assumed to follow a normal distribution, and further, it is assumed that the random component of the cumulative arc erosion of the three-phase contacts follows a ternary normal distribution to characterize the correlation of degradation among different phase contacts. Furthermore, due to factors such as contact material properties, contactor structure, and manufacturing process, the cumulative arc erosion threshold of the three-phase contacts is random and varies among them. To address the randomness and variability of the failure threshold of each phase contact in reality, a normality assumption is used to characterize it.

[0072] Specifically, the mixed-effect model for cumulative arc erosion is as follows:

[0073] (1)

[0074] In the formula, This indicates a contact of a certain phase; express Phase contact disconnection The cumulative arc erosion at this time; For the trend term, the parameters are... express The degradation rate of the phase contact; The term is a random term, representing the influence of uncertainties such as the stochastic dynamics of the degradation process, and at any given time... Independent and identically distributed, satisfying a mean of 0 and a variance of . The normal distribution, i.e. .

[0075] Regarding the correlation of cumulative arc erosion between three-phase contacts, it is assumed that... It follows a vector with a mean vector of zero and a covariance matrix of... The ternary normal distribution, i.e. This is used to characterize the statistical correlation of the three-phase contact performance degradation process.

[0076] As the number of disconnections increases, the amount of arc erosion on the contacts accumulates. When the accumulated arc erosion reaches the failure threshold, the contactor cannot reliably disconnect, and is therefore considered to have failed. This is achieved through random variables. To represent the threshold value, let's assume the three-phase contact failure threshold. Independent and identically distributed, all following a mean of 1. variance is The normal distribution, i.e. This is used to represent the randomness of the threshold for cumulative arc erosion at different phase contacts.

[0077] Step 2: Estimate the parameters in the mixed-effects model

[0078] Step 2.1 Estimation of Trend Term Parameters

[0079] The mixed-effect model established in step one shows that an AC contactor Cumulative arc erosion of phase contacts Follow the mean variance is The normal distribution, i.e. Therefore, model parameters The log-likelihood function is:

[0080] (2)

[0081] In the formula, for The current number of times the phase contact has been broken.

[0082] For parameters Taking the partial derivative, we get:

[0083] (3)

[0084] Let equation (3) equal to zero, we can obtain The maximum likelihood estimator is:

[0085] (4)

[0086] Step 2.2 Random Term Parameter Estimation

[0087] Random items One implementation can be achieved by The calculations were obtained, and then based on different time points... Specific implementation The maximum likelihood estimation method is used to estimate the parameters of the model involved.

[0088] The probability density function of the ternary normal distribution is expressed as follows:

[0089] (5)

[0090] In the formula, .

[0091] According to equation (5), we can obtain The likelihood function is:

[0092] (6)

[0093] In the formula, This represents the current number of segments.

[0094] Therefore, according to equation (6), we can obtain The log-likelihood function is:

[0095] (7)

[0096] In the formula, This represents the current number of segments.

[0097] From equation (7) on the covariance matrix Taking the partial derivative, we get:

[0098] (8)

[0099] Let equation (8) equal to zero, we can obtain The maximum likelihood estimator is:

[0100] (9)

[0101] Step 3: Calculate the reliability function

[0102] Record the current number of segments as ,at this time The degradation of the phase contact is The corresponding phase failure threshold is Starting from the current number of segments, the count continues... In the secondary disconnection, the failure condition of the AC contactor is the amount of degradation of any phase contact. Exceeding the failure threshold Therefore, the reliability function is:

[0103] (10)

[0104] For the random variable in equation (10) To find the expectation, equation (10) can be written as: (11)

[0105] In the formula, The probability density function represents the contact failure threshold.

[0106] random variables cumulative distribution function substitution By performing an integral transform on the triple integral, the integration interval can be... Change to Then equation (11) can be written as:

[0107] (12)

[0108] In the formula, This is the cumulative distribution function of the contact failure threshold; It is the inverse function of the cumulative distribution function of the contact failure threshold; For random items The cumulative distribution function.

[0109] For the calculation of the triple integral in equation (12), the Riemann method and other techniques are used to solve the integration problem, and the reliability function is finally approximated as:

[0110] (13)

[0111] In the formula, It refers to the number of divisions within the integration interval.

[0112] Step 4: Predict remaining lifespan

[0113] The expected remaining lifetime is used as an estimate of the remaining lifetime point (i.e., the remaining number of breaks), calculated using the following formula:

[0114] (14)

[0115] In the formula, For already separated The remaining lifetime point estimate at the next time; for The cumulative distribution function.

[0116] Based on the mathematical relationship between reliability and cumulative distribution function:

[0117] (15)

[0118] By combining equations (14) and (15), the remaining lifetime point estimate can be obtained. for:

[0119] (16)

[0120] To perform an approximate calculation of the reliability integral, take... The upper limit of integration is given, and its reliability function satisfies Approximately zero, therefore equation (16) can be written as:

[0121] (17)

[0122] Similarly, by applying Riemannian techniques to solve the integration problem of equation (17), we can obtain:

[0123] (18)

[0124] Substituting equation (13) into equation (18), we get:

[0125] (19)

[0126] In the formula, This represents the number of divisions into which the integration interval is divided.

[0127] Example 1

[0128] The remaining electrical life of the low-voltage electrical products described in this invention can be implemented on an electrical life testing device. This testing device can be used for electrical life testing of low-voltage electrical appliances, and can complete the setting of test parameters, debugging of the testing device, and automatic execution of the life test. It can also monitor the test current and voltage in real time during the AC contactor electrical life test. Preferably, this testing device can calculate the performance characterization parameters of the low-voltage electrical products and determine the fault type.

[0129] Specifically, in this embodiment, the low-voltage electrical appliances may further include products such as AC contactors, miniature circuit breakers, molded case circuit breakers, and frame circuit breakers. In this embodiment, taking an AC contactor as an example, its electrical life is predicted under AC-4 conditions (i.e., the test current is 6 times the rated current and the test voltage is 1 times the rated voltage).

[0130] In this embodiment, an AC-4 test is performed on an AC contactor. The test contact operates in a random disconnection mode (i.e., the release commands of the moving and stationary contacts are uniformly distributed within one current cycle), and the load neutral point is not connected to the power supply neutral point. Based on historical data and expert experience, the given three-phase contact failure threshold distribution parameters are as follows: , .

[0131] This embodiment provides a method for predicting the remaining electrical lifetime of AC contactors based on a mixed-effects model. The specific implementation steps of this method are as follows:

[0132] Step 1: Establish a mixed-effect model for the three-phase contacts of an AC contactor.

[0133] During the operation of an AC contactor, arc erosion accumulates continuously on the contacts. When the accumulated arc erosion of a certain phase contact exceeds the failure threshold, the AC contactor fails. Based on the central limit theorem and considering the degradation correlation among the three-phase contacts, a mixed-effect model for accumulated arc erosion is established as follows:

[0134]

[0135] Step 2: Estimate the parameters in the mixed-effects model

[0136] Based on the model parameters of the trend term, the estimated values ​​of the degradation rate of each phase contact are obtained according to Equation (4), as shown in Table 1.

[0137] Table 1 Degradation ratea i Parameter estimation

[0138]

[0139] For the model parameters of the random term, the parameters characterizing the degradation correlation can be obtained from equation (9). The estimated value:

[0140]

[0141] Step 3: Calculate the reliability function

[0142] According to the mixed-effects model, record the current number of segments. The cumulative amount of arc erosion is as follows Figure 1 As shown. Failure threshold for each phase contact. ,Pick The specific expression of the reliability function is obtained as follows:

[0143]

[0144] From this, the reliability function can be obtained, such as Figure 2 As shown.

[0145] Step 4: Predict remaining lifespan

[0146] After the first three steps, integrate the obtained reliability function and let... , , This leads to a point estimate of the remaining lifetime:

[0147]

[0148] Finally, the point prediction results for the remaining lifetime are as follows:

[0149]

[0150] This means that the AC contactor will fail after 12,649 switching cycles.

[0151] This invention proposes a method for predicting the remaining electrical life of AC contactors based on a mixed-effects model. Addressing practical engineering needs, it comprehensively analyzes the characteristics of competing failures and degradation correlations among three-phase contacts. First, a mixed-effects model is established. Second, methods for estimating model parameters and calculating reliability under the current state are provided. Finally, the remaining life prediction is achieved. The proposed method's analytical process is scientific, reasonable, and closely reflects actual conditions. The remaining life prediction results are reliable. Furthermore, the proposed method is computationally simple, convenient for engineering technicians, and has strong application value.

[0152] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for predicting the remaining electrical lifetime of an AC contactor based on a mixed-effects model, characterized in that, The specific implementation steps of this method are as follows: Step 1: Establish a mixed-effect model for the three-phase contacts of an AC contactor. Using cumulative arc erosion as a characteristic quantity of AC contactor performance degradation, a mixed-effect model for three-phase contacts is established by comprehensively considering trend and random terms: (1) In the formula, This indicates a contact of a certain phase; express Phase contact disconnection The cumulative arc erosion at this time; For the trend term, the parameters are... express The degradation rate of the phase contact; The term is a random term, representing the influence of uncertainties in the degradation process, and at any given time... Independent and identically distributed, satisfying a mean of 0 and a variance of . The normal distribution, i.e. ; Regarding the correlation of cumulative arc erosion between three-phase contacts, it is assumed that... It follows a vector with a mean vector of zero and a covariance matrix of... The ternary normal distribution, i.e. ; As the number of disconnections increases, the amount of arc erosion on the contacts accumulates. When the accumulated arc erosion reaches the failure threshold, the contactor cannot reliably disconnect, and the contactor is considered to have failed. This is achieved through random variables. To represent the threshold value, let's assume the three-phase contact failure threshold. Independent and identically distributed, all following a mean of 1. variance is The normal distribution, i.e. ; Step 2: Estimate the parameters in the mixed-effects model Step 2.1 Estimation of Trend Term Parameters The mixed-effect model established in step one shows that an AC contactor Cumulative arc erosion of phase contacts Follow the mean variance is The normal distribution, i.e. Therefore, model parameters The log-likelihood function is: (2) In the formula, for The current number of times the phase contact has been broken; For parameters Taking the partial derivative, we get: (3) Let equation (3) equal to zero, we can obtain The maximum likelihood estimator is: (4) Step 2.2 Random Term Parameter Estimation Random items One implementation can be achieved by The calculations were obtained, and then based on different time points... The specific implementation involves estimating the model parameters involved using the maximum likelihood estimation method; The probability density function of the ternary normal distribution is expressed as follows: (5) In the formula, ; According to equation (5), we can obtain The likelihood function is: (6) In the formula, This represents the current number of segments. Therefore, according to equation (6), we can obtain The log-likelihood function is: (7) In the formula, This represents the current number of segments. From equation (7) on the covariance matrix Taking the partial derivative, we get: (8) Let equation (8) equal to zero, we can obtain The maximum likelihood estimator is: (9) Step 3: Calculate the reliability function Record the current number of segments as ,at this time The degradation of the phase contact is The corresponding phase failure threshold is Starting from the current number of segments, and then... In the secondary disconnection, the failure condition of the AC contactor is the degree of degradation of any phase contact. Exceeding the failure threshold Therefore, the reliability function is: （10） For the random variable in equation (10) To find the expectation, equation (10) can be written as: (11) In the formula, The probability density function representing the contact failure threshold; random variables cumulative distribution function substitution By performing an integral transform on the triple integral, the integration interval can be... Change to Then equation (11) can be written as: (12) In the formula, This is the cumulative distribution function of the contact failure threshold; It is the inverse function of the cumulative distribution function of the contact failure threshold; For random items The cumulative distribution function; For the calculation of the triple integral in equation (12), the Riemann method and other techniques are used to solve the integration problem, and the reliability function is finally approximated as: (13) In the formula, It refers to the number of divisions within the integration interval; Step 4: Predict remaining lifespan The expected remaining lifetime is used as an estimate of the remaining lifetime point, and is calculated using the following formula: (14) In the formula, For already separated The remaining lifetime point estimate at the next time; for The cumulative distribution function; Based on the mathematical relationship between reliability and cumulative distribution function: (15) By combining equations (14) and (15), the remaining lifetime point estimate can be obtained. for: (16) To perform an approximate calculation of the reliability integral, we take... The upper limit of integration is given, and its reliability function satisfies Approximately zero, therefore equation (16) can be written as: (17) Similarly, by applying Riemannian techniques to solve the integration problem of equation (17), we can obtain: (18) Substituting equation (13) into equation (18), we get: (19) In the formula, This represents the number of divisions into which the integration interval is divided.

2. The method for predicting the remaining electrical lifetime of an AC contactor based on a mixed-effects model according to claim 1, characterized in that, The contacts of the AC contactor operate in a random disconnection mode, and the load neutral point is not connected to the power supply neutral point. The three-phase contact failure threshold distribution parameters are as follows: , .

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