Fourier Warrington direct current arc static model and parameter identification method thereof

Abstract

The invention discloses a Fourier Warrington direct-current arc static model and a parameter identification method thereof in the technical field, and the method comprises the following steps: 1), collecting a current signal of a direct-current arc through a current sensor, and collecting a voltage signal of the direct-current arc through a voltage sensor; 2) on the basis of static volt-ampere characteristic analysis of the direct-current arc, constructing a Fourier Warrington direct-current arc static model, and 3) constructing a target function for model parameter identification; and 4) identifying Fourier Warrington direct current arc static model parameters by using a single sine optimization algorithm. According to the method, the problems existing in the direct current arc fault modeling and parameter identification process are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of arc fault detection, and in particular to a DC arc static model and a parameter identification method thereof. Background Art

[0002] Compared with AC systems, DC systems have advantages such as high power density and low transmission loss. They have been widely used in photovoltaic power generation, electric vehicles, data centers, and all-electric aircraft. However, during the long-term operation of DC systems, the aging and wear of cable insulation can easily lead to arc faults in the system. DC arc faults do not have a zero point. Compared with AC arc faults, DC arc faults are more likely to produce continuous and stable arcing. The high temperature generated by DC arc faults can easily ignite nearby combustible materials, causing fires in DC systems. Therefore, how to effectively detect DC arc faults in the system is of great significance.

[0003] Generally, the research on arc fault detection methods based on experiments is dangerous, and the simulation of arc faults in actual DC systems is costly. DC arc models provide a more flexible and low-cost approach for the research on arc fault detection methods. The research on arc fault detection methods based on models is an important research direction in the current field of arc faults. Static characteristics are the essential characteristics of DC arc faults, which mainly describe the arc voltage under different current conditions. The DC arc static model regards the DC arc as a component in the circuit and discovers the law between arc voltage and arc current through a large amount of data mining. Early static models include the Anton model, the Nottingham model and the Warrington model. Among them, the Nottingham model and the Warrington model are improved versions of the Anton model under low and high current conditions. The model extends the relationship between arc voltage and arc current from the first order to the nth order (n is a parameter in the model), thereby enhancing the model's ability to fit the arc static characteristic curve. The earliest AC arc model was the arc energy balance theory proposed by Cassie in the late 1830s, as well as the Cassie model proposed by Cauchy in the late 1830s and the Mayr model considering conduction and radiation proposed by Mayer in the late 1830s. However, these two classic models have their own scope of application: the Cassie model is suitable for simulating arc phenomena under conditions of large current and small resistance. The Mayr model is based on the principles of thermal ionization, thermal inertia and thermal balance, and is more suitable for simulating arcs under conditions of small current. Stokes and Oppenlander found that there is a turning point in the arc current. Before the turning point, the arc voltage decreases when the current increases, and after the turning point, the arc voltage increases when the current increases. Stokes and Oppenlander modeled the static characteristics of the arc after the turning point. Paukert used the arc model for currents less than 100A and greater than 100A, respectively, to show the unique static characteristics of the arc at different current levels. Andrea proposed a static model based on the inverse tangent function suitable for small currents to avoid polarity differences caused by the current direction. However, none of the above models can fully describe the inconsistency of the static characteristics of the arc before and after the turning point.

[0004] Accurately identifying the parameters of the DC arc static model has an important impact on the performance of the model. Some researchers have identified the parameters of the DC arc static model based on analytical methods, grid search methods, and least squares methods. The heuristic algorithm regards the identification of arc parameters as an optimization process without considering the gradient information of the problem to be optimized. It is an important research direction in the current optimization field. Compared with the grid search method, the heuristic algorithm has the advantages of fast convergence speed and high convergence accuracy in identifying arc parameters. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a Fourier Warrington DC arc static model and a parameter identification method thereof, and implements model parameter identification based on a single sine optimization algorithm, thereby solving the problems existing in the DC arc fault modeling and its parameter identification process.

[0006] The object of the present invention is achieved by: a Fourier Warrington DC arc static model and a parameter identification method thereof, comprising the following steps:

[0007] Step 1) using a current sensor to collect a current signal of a DC arc, and using a voltage sensor to collect a voltage signal of a DC arc;

[0008] Step 2) Based on the analysis of the static volt-ampere characteristics of the DC arc, a Fourier Warrington DC arc static model is constructed. The Fourier Warrington DC arc static model is shown in formula (1);

[0009] (1)

[0010] in, and are the voltage and current of the arc respectively; parameters , , , , , and n are adjustable arc model parameters;

[0011] Step 3) constructing the objective function for model parameter identification;

[0012] Step 4) Use the single sine optimization algorithm to identify the parameters of the Fourier Warrington DC arc static model.

[0013] Furthermore, the formula for constructing the objective function in step 3) is:

[0014] (2)

[0015] in, is the error equation, is the number of data points, t is an integer, and the error equation It is defined as shown in formula (3):

[0016] (3)

[0017] in, The tth arc current data point, is the tth arc voltage data point.

[0018] Furthermore, step 4) specifically includes:

[0019] Step 4-1) Set the number of iterations T, set the population size in the optimization algorithm, and randomly generate the positions of individuals in the population;

[0020] Step 4-2) Calculate the fitness value of each individual in the population in the optimization algorithm according to the objective function;

[0021] Step 4-3) Use the single sine 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 (4):

[0022] (4)

[0023] 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 best individual position of the current population, is the sine operator, , and is a random number in the interval [0,1]. If The fitness value is better than , then use replace ,otherwise remain unchanged;

[0024] Step 4-4) Calculate the current number of iterations. If the current number of iterations is greater than the maximum number of iterations, go to step 4-6), otherwise go to step 4-5);

[0025] Step 4-5) Add 1 to the number of iterations and go to step 4-2);

[0026] Step 4-6) The result of the Fourier Warrington DC arc static model parameter identification is the position vector of the optimal individual in the population of the optimization algorithm.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. The present invention proposes a Fourier Warrington DC arc static model, which uses the Fourier function to improve the constant term in the traditional Warrington DC arc static model. As the arc current value increases, the Fourier function causes the arc voltage value to change according to the Fourier law, overcoming the problem that the traditional Warrington DC arc static model cannot reflect the inconsistent trend of arc static voltage change in the large current interval and the small current interval. The Fourier mechanism enables the Fourier Warrington DC arc static model to effectively adapt to the complex nonlinearity of arc voltage and arc current in different discharge stages.

[0029] 2. The present invention constructs an error equation for parameter identification of the Fourier Warrington DC arc static model. And uses a single sine optimization algorithm to identify the parameters of the Fourier Warrington DC arc static model. In the parameter identification process, the single sine optimization algorithm enables the population to realize adaptive search according to the single sine law and accurately converge to the global optimal value. Compared with traditional parameter identification methods such as the least squares method and the grid search method, the single sine optimization algorithm can effectively improve the accuracy of parameter identification of the Fourier Warrington DC arc static model. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] 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.

[0031] Figure 1 It is a flow chart of the present invention.

[0032] Figure 2 It is the volt-ampere characteristic curve output by the Fourier Warrington DC arc static model, the Warrington DC arc static model and the Andrea arc model in the present invention and the volt-ampere characteristic curve of the actual arc. DETAILED DESCRIPTION

[0033] 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.

[0034] like Figure 1As shown, this embodiment provides a Fourier Warrington DC arc static model and a parameter identification method thereof, comprising the following steps:

[0035] Step 1) using a current sensor and a voltage sensor to obtain a current signal and a voltage signal of a DC arc, respectively, including 16 static characteristic data points;

[0036] Step 2) Based on the analysis of the static volt-ampere characteristics of the DC arc, a Fourier Warrington DC arc static model is constructed. The Fourier Warrington DC arc static model is shown in formula (1);

[0037] (1)

[0038] in, and are the voltage and current of the arc respectively; parameters , , , , and These are adjustable arc model parameters, which are related to external factors such as electrode material, gas pressure, gas medium, and ambient temperature.

[0039] Step 3) Construct the objective function for model parameter identification based on formula (2):

[0040] (2)

[0041] Among them, among them, is the error equation, is the number of data points, t is an integer; the error equation It is defined as shown in formula (3);

[0042] (3)

[0043] in, The tth arc current data point, is the tth arc voltage data point.

[0044] Step 4) Identify the parameters of the Fourier Warrington DC arc static model 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.

[0045] The optimization algorithm is a single sine optimization algorithm. Based on the single sine evolution mechanism, it maintains adaptability during the iteration process, which helps to avoid the algorithm from falling into the local optimum and improve the convergence speed.

[0046] Step 4-1) Set the number of iterations T to 500, the number of populations in the optimization algorithm to 20, and randomly generate the positions of individuals in the population;

[0047] Step 4-2) Calculate the fitness value of each individual in the population in the optimization algorithm according to the objective function;

[0048] Step 4-3) Use the single sine 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 (4):

[0049] (4)

[0050] middle, 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 best individual position of the current population, is the sine operator, , and is a random number in the interval [0,1]. If The fitness value is better than , then use replace ,otherwise remain unchanged;

[0051] Step 4-4) Calculate the current number of iterations. If the current number of iterations is greater than the maximum number of iterations, go to step 4-6), otherwise go to step 4-5);

[0052] Step 4-5) Add 1 to the number of iterations and go to step 4-2);

[0053] Step 4-6) The result of the Fourier Warrington DC arc static model parameter identification is the position vector of the optimal individual in the population of the optimization algorithm.

[0054] The above embodiment can realize accurate identification of the parameters of the Fourier Warrington DC arc static model. The arc volt-ampere characteristic output by the Fourier Warrington DC arc static model and the actual arc volt-ampere characteristic curve are as follows: Figure 2As shown in the figure, 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 0.3051. The root mean square errors of the Fourier Warrington DC arc static model parameter identification based on the single sine optimization algorithm, genetic algorithm and grid search method are 0.3051, 0.4816 and 0.5703 respectively. The single sine optimization algorithm has better convergence accuracy than the other two comparison algorithms.

[0055] Figure 2 The volt-ampere characteristic curves output by the Fourier Warrington DC arc static model, the Warrington DC arc static model and the Andrea arc model are compared with the volt-ampere characteristic curve of the actual arc, indicating that the Fourier Warrington DC arc static model can effectively describe the phenomenon that the arc voltage in the arc volt-ampere static curve has inconsistent changing trends in the large current range and the small current range.

[0056] The embodiment calculates the fitness values ​​(RMSE) obtained by different models. The smaller the fitness value, the higher the accuracy of the model. Table 1 shows the fitness values ​​corresponding to the Fourier Warrington DC arc static model, the Warrington DC arc static model and the Andrea arc model, which are 0.5329, 0.8144 and 0.9987 respectively. It can be seen from the figure that the Hook static model can more accurately track the nonlinear changes of the actual static curve near the turning point. However, the output voltage of the Warrington DC arc static model and the Andrea arc model decreases with the increase of current, and it is impossible to show the phenomenon that the change rules of the large current area and the small current area in the arc static curve are inconsistent.

[0057] Table 1 Comparison of fitness values ​​of different arc models

[0058]

[0059] From the above analysis, it can be seen that the Fourier Warrington DC arc static model can more effectively fit the nonlinear characteristics of the arc static curve compared with the Warrington static model and the Andrea static model.

[0060] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

[0061] 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 Fourier Warrington DC arc static model and parameter identification method thereof, characterized in that: The following steps are involved: Step 1) using a current sensor to collect a current signal of a DC arc, and using a voltage sensor to collect a voltage signal of a DC arc; Step 2) Based on the analysis of the static volt-ampere characteristics of the DC arc, a Fourier Warrington DC arc static model is constructed. The Fourier Warrington DC arc static model is shown in formula (1); （1） in, and are the voltage and current of the arc respectively; parameters , , , , , and n are adjustable arc model parameters; Step 3) constructing the objective function for model parameter identification; Step 4) Use the single sine optimization algorithm to identify the parameters of the Fourier Warrington DC arc static model.

2. The Fourier Warrington DC arc static model and parameter identification method according to claim 1, characterized in that: The formula for constructing the objective function in step 3) is: （2） in, is the error equation, is the number of data points, t is an integer, and the error equation It is defined as shown in formula (3): （3） in, The tth arc current data point, is the tth arc voltage data point.

3. The Fourier Warrington DC arc static model and parameter identification method according to claim 2, characterized in that: Step 4) specifically includes: Step 4-1) Set the number of iterations T, set the population size in the optimization algorithm, and randomly generate the positions of individuals in the population; Step 4-2) Calculate the fitness value of each individual in the population in the optimization algorithm according to the objective function; Step 4-3) Use the single sine 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 (4): （4） 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 best individual position of the current population, is the sine operator, , and is a random number in the interval [0,1]. If The fitness value is better than , then use replace ,otherwise remain unchanged; Step 4-4) Calculate the current number of iterations. If the current number of iterations is greater than the maximum number of iterations, go to step 4-6), otherwise go to step 4-5); Step 4-5) Add 1 to the number of iterations and go to step 4-2); Step 4-6) The result of the Fourier Warrington DC arc static model parameter identification is the position vector of the optimal individual in the population of the optimization algorithm.

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