Five-order polynomial Schwarz alternating current arc model parameter extraction method

Abstract

The invention discloses a five-order polynomial Schwarz alternating current arc model parameter extraction method in the technical field of arc fault detection. The five-order polynomial Schwarz alternating current arc model parameter extraction method comprises the following steps that 1) a current signal and a voltage signal of an alternating current arc are obtained through a current sensor and a voltage sensor respectively; 2) constructing a five-order polynomial Schwarz alternating current arc model based on the analysis of the current signal and the voltage signal of the alternating current arc; the method comprises the steps of (1) establishing a first-order polynomial Schwarz alternating current arc model, (2) establishing a second-order polynomial Schwarz alternating current arc model, (3) establishing a discrete form of the fifth-order polynomial Schwarz alternating current arc model, (4) establishing an objective function for model parameter extraction, and (5) calculating parameters of the fifth-order polynomial Schwarz alternating current arc model based on a flower pollination optimization algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of arc fault detection, and in particular to a method for extracting parameters of an AC arc model. Background Art

[0002] Electric energy and electrical equipment play a huge role in production and life in modern society. However, once an AC arc fault occurs in the AC distribution system, it is very easy to quickly ignite the surrounding flammable and explosive materials, thereby causing a fire, posing a major threat to personal safety and property safety. Therefore, timely detection and prevention of arc faults and ensuring the stable operation of the AC distribution system are crucial to maintaining public safety.

[0003] The generation and development of AC arc faults are affected by many factors. Creating an experimental environment or simulating AC fault arcs on an existing power system requires additional costs, and the actual operation is difficult and dangerous. Arc fault detection based on arc models can simulate arc behavior under different current and voltage conditions, which helps researchers analyze the characteristics and laws of arc faults and reduce complex and repetitive experiments. Therefore, further improving the performance of arc models is of great significance to suppressing the hazards of arc faults.

[0004] The black box model is the most commonly used arc mathematical model. It regards the arc as a two-terminal circuit element and focuses on the macroscopic performance of the arc in the circuit without delving into the physical and chemical processes inside it. Since AM Cassie proposed the first arc black box model in 1939, the arc black box model has been widely used in arc simulation and arc fault prediction. In 1943, Mayr derived the local thermal balance equation to describe the arc from the perspective of energy balance. The Mayr model and the Cassie model together constitute the basic framework of the arc black box model.

[0005] In view of the limitations of the traditional arc black box model in some complex situations, researchers have proposed a variety of improvement methods. Some scholars have established a mathematical model of the arc based on the internal mechanism of arc formation and the measured results of temperature data during its evolution. Some researchers have proposed a black box model that can accurately simulate the electrical characteristics of small current vacuum arcs. Some researchers have corrected a variety of traditional arc models taking into account the time-varying characteristics of arc parameters, and used polynomial models to model the arc. Based on the influence of arc length on the arc, some researchers have proposed an improved Schwarz AC arc model that considers dynamic arc length. Some researchers have used the arc gap energy balance theory to adjust the arc length parameters on the basis of the classic "cybernetic" arc model, establish an arc model, and intuitively reflect the characteristics of the arc in the arc changes. However, the current research does not consider the role of current changes in the time constant during the arc evolution process, so the current model lacks the ability to accurately fit the complex nonlinearity of arc current and voltage signals.

[0006] In arc modeling, parameter extraction is the most challenging part and has an important impact on the performance of the arc model. It is related to whether the model can accurately describe the characteristics of the arc. For different working conditions, it is necessary to re-acquire the experimental data under the working conditions and perform a series of data processing to obtain the values ​​of the model parameters. Some researchers use grid search method and least squares method to identify the parameters of the arc model. The heuristic algorithm regards the extraction of arc parameters as an optimization process, adjusts the parameters by random initial values, minimizes the error of the objective function, and thus finds the optimal parameters. Compared with the grid search method, the heuristic algorithm has the advantages of fast convergence speed and high convergence accuracy in extracting arc parameters. Summary of the invention

[0007] In view of the deficiencies in the prior art, the present invention provides a fifth-order polynomial Schwarz AC arc model parameter extraction method, which solves the problems existing in the arc fault modeling and parameter extraction process in the background technology.

[0008] The object of the present invention is achieved by: a fifth-order polynomial Schwarz AC arc model parameter extraction method, comprising the following steps:

[0009] Step 1) using a current sensor and a voltage sensor to obtain a current signal and a voltage signal of an AC arc respectively;

[0010] Step 2) constructing a fifth-order polynomial Schwarz AC arc model based on the analysis of the current signal and voltage signal of the AC arc;

[0011] Step 3) constructing a discrete form of the fifth-order polynomial Schwarz AC arc model;

[0012] Step 4) constructing the objective function for model parameter extraction;

[0013] Step 5) Calculate the parameters of the fifth-order polynomial Schwarz AC arc model based on the flower pollination optimization algorithm.

[0014] Furthermore, the fifth-order polynomial Schwarz AC arc model in step 2) is shown in formula (1):

[0015] (1)

[0016] (2)

[0017] in, is the arc conductance, and are the voltage and current of the arc, respectively, and the parameters , , , , , , , and is an adjustable arc model parameter, , and b are the coefficient of the time constant part, the coefficient of the cooling power, and the power term of the conductance in the cooling power, respectively. , , , , and is the conductivity power term in the time constant The constant parameter in .

[0018] Furthermore, in step 3), the fifth-order polynomial Schwarz AC arc model is constructed into a discrete form as shown in formula (3):

[0019] (3)

[0020] (4)

[0021] in, is the arc voltage at time t, is the arc current at time t, for The first derivative of for The first derivative of .

[0022] Furthermore, in step 4), the objective function is constructed based on formula (5):

[0023] (5)

[0024] (6)

[0025] (7)

[0026] in, is the total number of discrete data points, is the sampling time, is the error equation at time t.

[0027] Furthermore, step 5) specifically includes:

[0028] Step 5-1) Set the number of iterations, set the population size in the optimization algorithm, and randomly generate the positions of individuals in the population;

[0029] Step 5-2) Calculate the fitness value of each individual in the population in the optimization algorithm according to the objective function;

[0030] Step 5-3) Use the flower pollination optimization algorithm to update the position of each individual in the population. The method for updating the position of each individual in the population is shown in formula (8):

[0031] (8)

[0032] (9)

[0033] in, is the position of the jth individual in the population at the k+1th iteration, is the position of the jth individual in the population at the kth iteration, is the scale factor, The first is the moving step length generated by the Lévy flight, is the position of the best individual in the population at the kth iteration, if The fitness value is better than , then use replace ,otherwise remain unchanged; represents the step weight, and Follows uniform distribution, is the Gamma equation;

[0034] Step 5-4) Calculate the current number of iterations. If the current number of iterations is greater than the maximum number of iterations, go to step 5-6), otherwise go to step 5-5);

[0035] Step 5-5) Increase the number of iterations by 1 and go to step 5-2);

[0036] Step 5-6) The result of the fifth-order polynomial Schwarz AC arc model parameter extraction is the position vector of the optimal individual in the population of the optimization algorithm.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention proposes a fifth-order polynomial Schwarz AC arc model, which uses a fifth-order polynomial function to improve the fixed conductance power term of the time constant part in the traditional Schwarz AC arc model. During the operation of the model, the fifth-order polynomial function makes the conductance power term of the time constant part change according to the fifth-order polynomial law of the absolute value of the current, overcoming the insufficient dynamic performance of the model caused by the fixed conductance power term of the time constant part, and enabling the model to effectively adapt to the complex nonlinearity of arc voltage and arc current in different discharge stages.

[0039] The present invention constructs an error equation for model parameter extraction based on the discrete form of the fifth-order polynomial Schwarz AC arc model. The parameters of the fifth-order polynomial Schwarz AC arc model are extracted using a flower pollination optimization algorithm. The flower pollination optimization algorithm can realize adaptive search in the parameter extraction process. Compared with traditional parameter extraction methods such as the least squares method and the grid search method, the flower pollination optimization algorithm can effectively improve the accuracy of parameter extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0041] Figure 1 The figure is a schematic diagram of a process of extracting parameters of a fifth-order polynomial Schwarz AC arc model according to an embodiment of the present invention.

[0042] Figure 2 It is a current curve output by a fifth-order polynomial Schwarz AC arc model, a Schwarz AC arc model, a Mayr AC arc model and a Cassie AC arc model according to an embodiment of the present invention and an actual arc current curve. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] like Figure 1 As shown, this embodiment provides a fifth-order polynomial Schwarz AC arc model parameter extraction method based on a flower pollination optimization algorithm, comprising the following steps:

[0045] Step 1) Use a current sensor and a voltage sensor to obtain the current signal and voltage signal of the AC arc respectively. The sampling rate is 200 kHz. The current signal and the voltage signal each contain 2000 data points.

[0046] Step 2) Based on the analysis of the current signal and voltage signal of the AC arc, a fifth-order polynomial Schwarz AC arc model is constructed. The fifth-order polynomial Schwarz AC arc model is shown in formula (1);

[0047] (1)

[0048] (2)

[0049] in, is the arc conductivity. and are the voltage and current of the arc respectively. , , , , , , , and is an adjustable arc model parameter. , and b are the coefficient of the time constant part, the coefficient of the cooling power, and the power term of the conductance in the cooling power, respectively. , , , , and is the conductivity power term in the time constant The constant parameter in .

[0050] Step 3) Construct the discrete form of the fifth-order polynomial Schwarz AC arc model, as shown in formula (3):

[0051] (3)

[0052] (4)

[0053] in, is the arc voltage at time t, is the arc current at time t. for The first derivative of for The first derivative of .

[0054] Step 4) construct the objective function as shown in formula (5);

[0055] (5)

[0056] (6)

[0057] (7)

[0058] in, is the total number of discrete data points, is the sampling time. is the error equation at time t, as shown in formula (6).

[0059] Step 5) Extract the fifth-order polynomial Schwarz AC arc model parameters based on the optimization algorithm. The present invention adopts a swarm intelligence optimization algorithm. By distributing a group containing a certain number of individuals in the search space and making the individuals evolve according to a certain mechanism, the optimal value in the search space is gradually approached to achieve the purpose of optimization.

[0060] The optimization algorithm is a flower pollination optimization algorithm. It maintains the diversity of the population during the iteration process based on the random walk mechanism, which helps to avoid the algorithm from falling into the local optimum and improve the convergence speed.

[0061] Step 5-1) Set the maximum number of iterations to 500, the population size in the optimization algorithm to 20, and randomly generate the positions of individuals in the population;

[0062] Step 5-2) Calculate the fitness value of each individual in the population in the optimization algorithm according to the objective function;

[0063] Step 5-3) Use the flower pollination optimization algorithm to update the position of each individual in the population. The method for updating the position of each individual in the population is shown in formula (8):

[0064] (8)

[0065] (9)

[0066] in, is the position of the jth individual in the population at the k+1th iteration, is the position of the jth individual in the population at the kth iteration, is the scale factor, The first is the moving step length generated by the Lévy flight, is the position of the best individual in the population at the kth iteration, if The fitness value is better than , then use replace ,otherwise remain unchanged; represents the step weight, and Follows uniform distribution, is the Gamma equation;

[0067] Step 5-4) Calculate the current number of iterations. If the current number of iterations is greater than the maximum number of iterations, go to step 5-6), otherwise go to step 5-5);

[0068] Step 5-5) Increase the number of iterations by 1 and go to step 5-2);

[0069] Step 5-6) The result of the fifth-order polynomial Schwarz AC arc model parameter extraction is the position vector of the optimal individual in the population of the optimization algorithm.

[0070] The above embodiment can realize the accurate extraction of the parameters of the fifth-order polynomial Schwarz AC arc model. The arc energy curve output by the fifth-order polynomial Schwarz AC arc model and the actual arc energy curve are compared. Figure 2 As shown. The arc energy curve output by the model can accurately fit the complex nonlinearity of the actual arc energy curve. The objective function value calculated by formula (2) is 6.7275 (as shown in Table 1). The root mean square errors of the fifth-order polynomial Schwarz AC arc model parameter extraction based on the flower pollination optimization algorithm, genetic algorithm and grid search method are 6.7275, 6.9185 and 9.0944 respectively. The parameter identification accuracy of the flower pollination optimization algorithm has better convergence accuracy than the other two comparison algorithms.

[0071] Table 1 Results of fifth-order polynomial Schwarz AC arc model parameters extracted based on different optimization algorithms

[0072]

[0073] Figure 2The current curves output by the fifth-order polynomial Schwarz AC arc model, Schwarz AC arc model, Mayr AC arc model and Cassie AC arc model and the actual arc current curve are compared, indicating that the fifth-order polynomial Schwarz AC arc model can effectively characterize the zero-break phenomenon of the arc.

[0074] Only the Cassie AC arc model has no zero-crossing phenomenon. The performance of the Cassie AC arc model is significantly lower than that of the other three models, but the differences between the Schwarz AC arc model, the Mayr AC model and the fifth-order polynomial Schwarz AC arc model are difficult to display intuitively. The embodiment calculates the fitness values ​​(modeling errors) obtained by different models. The smaller the fitness value, the higher the accuracy of the model. The fitness values ​​corresponding to the fifth-order polynomial Schwarz AC arc model, the Schwarz AC arc model, the Mayr AC model and the Cassie AC model are 6.7275, 7.1351, 11.5543 and 7.8264, respectively. The fitness value corresponding to the fifth-order polynomial Schwarz AC arc model is smaller than that of the other four models, indicating that the fifth-order polynomial Schwarz AC arc model proposed in the present invention improves the traditional fixed value of the conductivity power term based on the fifth-order polynomial law, thereby enhancing the flexibility of the model.

[0075] The above experimental results show that compared with the Schwarz AC arc model, the Mayr AC arc model and the Cassie AC arc model, the fifth-order polynomial Schwarz AC arc model proposed in the present invention can more accurately characterize the complex nonlinearity of arc energy in different discharge stages.

[0076] The above embodiments are only used to help understand the method and core idea of ​​the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A fifth-order polynomial Schwarz AC arc model parameter extraction method, characterized in that: The following steps are involved: Step 1) using a current sensor and a voltage sensor to obtain a current signal and a voltage signal of an AC arc respectively; Step 2) constructing a fifth-order polynomial Schwarz AC arc model based on the analysis of the current signal and voltage signal of the AC arc; Step 3) constructing a discrete form of the fifth-order polynomial Schwarz AC arc model; Step 4) constructing the objective function for model parameter extraction; Step 5) Calculate the parameters of the fifth-order polynomial Schwarz AC arc model based on the flower pollination optimization algorithm.

2. The fifth-order polynomial Schwarz AC arc model parameter extraction method according to claim 1, characterized in that: The fifth-order polynomial Schwarz AC arc model described in step 2) is shown in formula (1): （1） （2） in, is the arc conductance, and are the voltage and current of the arc, respectively, and the parameters , , , , , , , and is an adjustable arc model parameter, , and b are the coefficient of the time constant part, the coefficient of the cooling power, and the power term of the conductance in the cooling power, respectively. , , , , and is the conductivity power term in the time constant The constant parameter in .

3. The fifth-order polynomial Schwarz AC arc model parameter extraction method according to claim 2, characterized in that: In step 3), the fifth-order polynomial Schwarz AC arc model is constructed into a discrete form as shown in formula (3): （3） （4） in, is the arc voltage at time t, is the arc current at time t, for The first derivative of for The first derivative of .

4. The fifth-order polynomial Schwarz AC arc model parameter extraction method according to claim 3, characterized in that: In step 4), the objective function is constructed based on formula (5): （5） （6） （7） in, is the total number of discrete data points, is the sampling time, is the error equation at time t.

5. A fifth-order polynomial Schwarz AC arc model parameter extraction method according to any one of claims 1-4, characterized in that: Step 5) specifically includes: Step 5-1) Set the number of iterations, set the population size in the optimization algorithm, and randomly generate the positions of individuals in the population; Step 5-2) Calculate the fitness value of each individual in the population in the optimization algorithm according to the objective function; Step 5-3) Use the flower pollination optimization algorithm to update the position of each individual in the population. The position update method of each individual in the population is shown in formula (8): （8） （9） in, is the position of the jth individual in the population at the k+1th iteration, is the position of the jth individual in the population at the kth iteration, is the scale factor, The first is the moving step length generated by the Lévy flight, is the position of the best individual in the population at the kth iteration, if The fitness value is better than , then use replace ,otherwise remain unchanged; represents the step weight, and Follows uniform distribution, is the Gamma equation; Step 5-4) Calculate the current number of iterations. If the current number of iterations is greater than the maximum number of iterations, go to step 5-6), otherwise go to step 5-5); Step 5-5) Increase the number of iterations by 1 and go to step 5-2); Step 5-6) The result of the fifth-order polynomial Schwarz AC arc model parameter extraction is the position vector of the optimal individual in the population of the optimization algorithm.

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