CN113705147B - DC micro-grid fault arc modeling and simulation method and system - Google Patents
DC micro-grid fault arc modeling and simulation method and system Download PDFInfo
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Abstract
The invention discloses a direct current micro-grid fault arc modeling and simulation method and system, wherein the method comprises the following steps: simulating arc faults generated by different arc lengths and occurrence positions, and collecting arc current data of a branch where the arc faults are located; respectively analyzing and fitting the corresponding relation between the current drop value, the line current and the arc length when the arc fault occurs, wherein the relation between the volt-ampere characteristic of the arc current in the time domain range, the occurrence position and the arc length, the relation between the pink noise characteristic of the arc current in the frequency domain range, the occurrence position and the arc length, and obtaining a time domain fitting relation and a frequency domain fitting relation; establishing a simulation model of the direct current micro-grid fault arc based on the time domain fitting relation and the frequency domain fitting relation; and running a simulation model, and outputting a simulation result of the direct current micro-grid fault arc. The invention simulates the arc faults in the direct current micro-grid system, combines the time domain and frequency domain characteristics of the arc current, and comprehensively and accurately approaches to the actual arc data.
Description
Technical Field
The invention relates to the technical field of electrical engineering, in particular to a direct current micro-grid fault arc modeling and simulation method and system.
Background
With the high-speed development of new energy technology and direct current systems, various direct current sources, such as photovoltaic, energy storage, solid-state lighting and the like, the direct current micro-grid represented by buildings, ships and automobiles is promoted to rapidly grow due to continuous penetration application of the energy storage and the charges. Since the dc micro-grid can connect a renewable energy system to a power distribution grid, researchers are focusing on technologies capable of supporting the wide application of the dc micro-grid. However, direct current fault arc in the direct current micro-grid system, which is caused by loosening of cable joints, poor contact, insulation breakage of wires and the like, is difficult to detect and is not easy to extinguish, and the generated high temperature can cause fire disaster, so that the safety and reliability of the direct current micro-grid can be influenced, and the popularization and application of the direct current micro-grid are not facilitated. Because the direct current micro-grid system is complex, the types and the occurrence points of arc faults are more, and in order to research the arc characteristics and the protection measures later, the establishment of a corresponding arc mathematical model is necessary. The parameters of the existing arc model are difficult to determine, the simulation result and the actual experimental result have larger differences, and the influence of the experimental parameters on the arc characteristics cannot be reflected in the model.
Therefore, arc characteristics and mathematical models thereof are performed for the voltage and current levels and the structural complexity of the direct current microgrid.
Disclosure of Invention
The invention aims to provide a direct current micro-grid fault arc modeling and simulation method and system, which are used for solving the problems in the prior art, simulating an arc fault in a direct current micro-grid system, combining the time domain and frequency domain characteristics of an arc current, and being more comprehensively and accurately close to actual arc data.
In order to achieve the above object, the present invention provides the following solutions: the invention provides a direct current micro-grid fault arc modeling and simulation method, which comprises the following steps:
simulating arc faults generated by different arc lengths and arc occurrence positions, and collecting fault arc current data of a branch where the arc faults are located;
based on the fault arc current data, respectively analyzing and fitting the corresponding relation between a current drop value, line current and arc length when an arc fault occurs, wherein the relation between the volt-ampere characteristic of the arc current in a time domain range, the occurrence position and the arc length is analyzed, the relation between the pink noise characteristic of the arc current in a frequency domain range, the occurrence position and the arc length is analyzed, and a time domain fitting relation and a frequency domain fitting relation are obtained;
establishing a simulation model of the direct current micro-grid fault arc based on the time domain fitting relation and the frequency domain fitting relation;
and running the simulation model and outputting a simulation result of the direct current micro-grid fault arc.
Optionally, simulating arc faults generated by different arc lengths and occurrence positions comprises:
constructing a direct-current micro-grid fault arc test experiment platform, wherein the direct-current micro-grid fault arc test experiment platform comprises a direct-current micro-grid system and an arc generating device, and the arc generating device is connected in series at different positions of the direct-current micro-grid system;
and adjusting the arc length of the arc generating device and the position where the arc fault occurs, and simulating the arc faults generated by different arc lengths and generating positions.
Optionally, the direct current microgrid system comprises a direct current source, a storage battery, a resistance load and a plurality of constant power loads, the electric arc generating device comprises a screw rod sliding table, a copper rod, a driver and a controller, and the driver controls the controller to separate the copper rod for arc discharge.
Optionally, the simulating arc faults generated by different arc lengths and occurrence positions, and collecting the fault arc current data of the branch where the arc faults are located includes:
setting the output voltage of the direct current source to be 110V, adjusting the controller to enable the two copper bars to be in full contact, and starting an experiment;
recording the current waveform of the arc generating device under normal conditions;
adjusting the controller to separate the two copper bars for arc discharge, and recording the current waveform of the arc generating device in the whole process;
changing the arc length, the arc fault occurrence position, the branch voltage where the arc is located and the arc current, repeating the previous step, and recording the arc current under different arc lengths and arc fault occurrence positions.
Optionally, based on the arc current, obtaining the relation between the current drop value and the line current when the arc occurs through polynomial fitting is shown as a formula (1),
D(I)＝d 1 +d 2 I+d 3 I 2 (1)
wherein d 1 、d 2 、d 3 For calculation of the coefficient, D is the current dip value and I is the arc current.
Optionally, said analyzing and fitting the relationship of the volt-ampere characteristic of the arc current in the time domain range to said occurrence location, said arc length comprises: obtaining a functional relation between load current and time of each group of experimental data based on quadratic polynomial fitting;
obtaining a function of a quadratic polynomial coefficient relative to experimental parameters based on a polynomial fitting method, and obtaining the relation between the current volt-ampere characteristics of the branch circuit where the arc is and the experimental parameters as shown in formulas (2) - (3):
y＝f 1 x 2 +f 2 x+f 3 (2)
f i (d，I)＝f i1 +f i2 d+f i3 I+f i4 dI+f i5 d 2 +f i6 I 2 (3)
wherein f 1 、f 2 、f 3 For the fitting coefficient, x is the abscissa of the current volt-ampere characteristic curve, y is the ordinate of the current volt-ampere characteristic curve, f i1 、f i2 、f i3 、f i4 、f i5 、f i6 To calculate the coefficients, d is the arc length and I is the arc current.
Optionally, said analyzing and fitting the relationship of pink noise characteristics of said arc current in the frequency domain range to said occurrence location, said arc length comprises:
calculating the pink noise power spectrum density MSA of each group of experimental data;
according to the pink noise power spectral density function, based on a least square method, fitting to obtain the relationship between the pink noise equation parameter and the current and the arc length as shown in the formula (4):
wherein A is 1 、A 2 、A 3 、γ 1 、γ 2 、γ 3 、c 1 、c 2 、c 3 To calculate the coefficients, d is the arc length, I is the arc current, S is the Power Spectral Density (PSD), f is the frequency, and a, γ and c are correlation constants.
Optionally, the simulation model of the direct current micro-grid fault arc is shown as formula (5):
wherein at t 0 Time of day, I 1 And I 0 Relation of (2)As shown in formula (6):
I 1 (I p ，d，t 0 )＝I 0 (t 0 ) (6)
wherein t is 0 For arc fault occurrence time, I 0 For the current of the branch where the arc generating device is before the arc fault occurs, I 1 Is the current of the branch where the arc generating device is located after the arc fault occurs, I P For real-time load current before arc fault occurs, D is arc length, D (I P ) The current drop value when fault arc occurs, P is power spectral density, a is random gain of noise, random jitter in actual fault arc current is simulated, and t is time. Also provided is a direct current micro-grid fault arc modeling and simulation system: comprises a direct current micro-grid fault arc time domain module (1), a direct current micro-grid fault arc frequency domain module (2), a real-time current receiving module (3) and a signal superposition module (4),
the direct current micro-grid fault arc time domain module (1) is used for simulating the time domain characteristics of direct current micro-grid fault arc current signals;
the direct current micro-grid fault arc frequency domain module (2) is used for simulating the frequency domain characteristics of direct current micro-grid fault arc current signals;
the real-time current receiving module (3) is used for receiving the real-time current of the branch circuit;
the signal superposition module (4) is used for superposing the simulation signal of the direct current micro-grid fault arc time domain module (1), the simulation signal of the direct current micro-grid fault arc frequency domain module (2) and the simulation signal of the real-time current receiving module (3) to form a final direct current micro-grid fault arc simulation model.
The direct current micro-grid fault arc time domain module (1), the direct current micro-grid fault arc frequency domain module (2) and the real-time current receiving module (3) are connected with the signal superposition module (4).
The invention discloses the following technical effects:
compared with classical models such as a Cassie model and a Mayr model, the direct current micro-grid fault arc modeling and simulation method and system provided by the invention combine the time domain and frequency domain characteristics of arc current, and are more comprehensively and accurately close to actual arc data. The invention comprehensively considers the influences of the branch voltage level of the arc, the arc length and the fault arc occurrence position on the arc, and the simulation result and the model library are influenced by the factors, thereby being more practical. The direct current micro-grid fault arc model established by the invention has the advantages that the relevant data of the model are all derived from actual experimental data to be fitted, and the reliability is high. Meanwhile, the direct-current micro-grid experimental platform, the system simulation and the fault arc model simulation provide convenience for researching the fault arc of the direct-current micro-grid.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a circuit diagram of a DC micro-grid fault arc system for testing in accordance with an embodiment of the present invention;
fig. 2 is a schematic diagram of a direct current micro-grid fault arc simulation model construction flow in an embodiment of the invention;
FIG. 3 is a schematic diagram of a DC micro-grid fault arc simulation model in an embodiment of the invention;
FIG. 4 is a simulated current time domain waveform of a classical Cassie model;
FIG. 5 is a schematic diagram of a time domain waveform of a model simulation current according to an embodiment of the present invention;
FIG. 6 is a graph showing the time domain waveform of the experimental result current in the embodiment of the invention;
FIG. 7 is a waveform diagram of a current frequency domain of a simulation result of a classical Cassie model;
FIG. 8 is a waveform diagram of a current frequency domain of a simulation result of a proposed model in an embodiment of the present invention;
FIG. 9 is a waveform diagram of the experimental result current frequency domain in the embodiment of the invention;
fig. 10 is a schematic flow chart of a direct current micro-grid fault arc modeling and simulation method in an embodiment of the invention.
Wherein 1 is a direct current micro-grid fault arc time domain module, 2 is a direct current micro-grid fault arc frequency domain module, 3 is a real-time current receiving module, and 4 is a signal superposition module.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The invention provides a direct current micro-grid fault arc modeling and simulation method, which is shown in fig. 10. The method comprises the following steps:
s100, constructing a direct current micro-grid fault arc test experimental platform for simulating arc faults generated by different arc lengths and occurrence positions.
In this embodiment, the dc micro-grid fault arc test experiment platform includes a dc micro-grid system and an arc generating device, where the arc generating device is connected in series to different positions of the dc micro-grid system. In this embodiment, the dc micro-grid system includes a dc source, a storage battery, two constant power loads and a resistive load, where the dc source and the storage battery supply power, and the constant power loads and the resistive loads simulate different load types of the dc micro-grid. The electric arc generating device comprises a screw rod sliding table, copper bars, a driver, a controller and a stepping motor, wherein the controller controls the driver to further drive the stepping motor to enable the screw rod sliding table to move, and the two copper bars arranged on the screw rod sliding table are separated for arc discharge. The arc generating device is connected in series into each branch of the direct current micro-grid, so that the actually generated arc faults can be simulated.
Specifically, as shown in fig. 1, the circuit diagram of the direct current micro-grid system in the embodiment is that the whole system is powered by a 110V direct current source and a 48V storage battery, and the storage battery is connected into a direct current bus by a 110V-to-48V bidirectional DCDC converter; the load adopts a constant power load and a 30 omega resistance load, wherein the constant power load consists of a 110V-to-48V unidirectional DCDC converter and a resistor, and simulates different types of loads in a direct current micro-grid.
S200, adjusting test parameters by a control variable method through a direct current micro-grid actual working condition, repeatedly testing and recording branch fault voltage data and arc current data of an arc, respectively analyzing and fitting the corresponding relation between a current drop value, line current and arc length when an arc fault occurs according to the collected fault voltage data and arc current data, the relation between volt-ampere characteristics of the arc current in a time domain range, the occurrence position and the arc length, the relation between pink noise characteristics of the arc current in a frequency domain range, the occurrence position and the arc length, and obtaining a time domain fitting relation and a frequency domain fitting relation;
setting the output voltage of a direct current source to be 110V, adjusting a controller of an electric arc generating device to enable two copper bars to be in full contact, opening each branch circuit breaker, closing the whole experimental loop, and starting an experiment;
recording current waveforms at two ends of an arc generating device under normal conditions through an oscilloscope;
the controller is regulated to separate the two copper bars for arc discharge, and current waveforms at two ends of the arc generating device in the whole process are recorded through the oscilloscope;
the arc length, the arc fault occurrence position, the branch voltage where the arc is located and the arc current are changed, and the arc currents under different arc lengths and arc fault occurrence positions are recorded.
Arc model building is shown in fig. 2, and comprises preparation work before model building and modeling from the time domain and the frequency domain. The model construction earlier stage work is as described in S100, and comprises the steps of connecting arc generating devices in series at different positions, changing experimental parameters, repeating experiments, recording data, performing time domain characteristic fitting, including current drop value fitting and arc current volt-ampere characteristic fitting, performing frequency domain characteristic fitting, including noise parameter fitting, and finally obtaining a direct current micro-grid fault arc simulation model based on arc time domain and frequency domain characteristics by combining the time domain and frequency domain characteristics.
The specific process comprises the following steps:
1. and analyzing and fitting the relation between the arc current drop value, the line current and the arc length.
(1) Setting different electric arc generating positions, current sizes and electric arc lengths, wherein the electric arc generating positions are shown in figures 1(1 to 7), selecting voltage sizes of 48V and 110V respectively and electric arc lengths of 4A, 6A, 8A, 10A and 12A respectively according to UL1699B experiment standards and common voltage grades of a direct current micro-grid, and the electric arc lengths are 0.5mm, 0.7mm, 0.9mm, 1.1mm and 1.3mm respectively, wherein other experiment conditions are not changed; (2) adjusting an arc generating device to control the copper bars to be separated at a constant speed so as to generate an arc; (3) recording experimental data and current waveforms through an oscilloscope, changing experimental parameters, and repeatedly carrying out experiments, wherein each experimental condition is repeated for 50 groups; (4) the relation between the current drop value and the line current when the arc occurs is obtained through polynomial fitting and is shown as the formula (1):
D(I)＝d 1 +d 2 I+d 3 I 2 (1)
wherein d 1 、d 2 、d 3 For calculation of the coefficient, D is the current dip value and I is the arc current.
2. And analyzing and fitting the relation between the volt-ampere characteristic of the arc current in the time domain range, the occurrence position and the arc length.
(1) Setting different electric arc generating positions, current sizes and electric arc lengths, wherein the electric arc generating positions are shown in figures 1(1 to 7), selecting voltage sizes of 48V and 110V respectively and electric arc lengths of 4A, 6A, 8A, 10A and 12A respectively according to UL1699B experiment standards and common voltage grades of a direct current micro-grid, and the electric arc lengths are 0.5mm, 0.7mm, 0.9mm, 1.1mm and 1.3mm respectively, wherein other experiment conditions are not changed; (2) adjusting an arc generating device to control the copper bars to be separated at a constant speed so as to generate an arc; (3) recording experimental data and current waveforms through an oscilloscope, changing experimental parameters, and repeatedly carrying out experiments, wherein each experimental condition is repeated for 50 groups; (4) and obtaining the functional relation between the load current and time of each group of experimental data based on quadratic polynomial fitting, wherein the functional relation is shown in the formula (2):
y＝f 1 x 2 +f 2 x+f 3 (2)
wherein f 1 、f 2 、f 3 For the fitting coefficient, x is the abscissa of the current volt-ampere characteristic curve and y is the ordinate of the current volt-ampere characteristic curve.
(5) Obtaining a function of a quadratic polynomial coefficient relative to experimental parameters according to a polynomial fitting-based method, and finally obtaining the relation between the current volt-ampere characteristic of a branch circuit where the arc is located, the occurrence position and the arc length as shown in a formula (3):
f i (d，I)＝f i1 +f i2 d+f i3 I+f i4 dI+f i5 d 2 +f i6 I 2 (3)
wherein f i1 、f i2 、f i3 、f i4 、f i5 、f i6 To calculate the coefficients, d is the arc length and I is the arc current.
3. And analyzing and fitting the relationship between pink noise characteristics of the arc current in the frequency domain range, the occurrence position and the arc length.
(1) Setting different electric arc generating positions, current sizes and electric arc lengths, wherein the electric arc generating positions are shown in figures 1(1 to 7), selecting voltage sizes of 48V and 110V respectively and electric arc lengths of 4A, 6A, 8A, 10A and 12A respectively according to UL1699B experiment standards and common voltage grades of a direct current micro-grid, and the electric arc lengths are 0.5mm, 0.7mm, 0.9mm, 1.1mm and 1.3mm respectively, wherein other experiment conditions are not changed; (2) adjusting an arc generating device to control the copper bars to be separated at a constant speed so as to generate an arc; (3) recording experimental data and current waveforms through an oscilloscope, changing experimental parameters, and repeatedly carrying out experiments, wherein each experimental condition is repeated for 50 groups; (4) determining the power spectral density (MSA) of each set of experimental data; (5) according to the pink noise power spectral density function, based on a least square method, fitting to obtain a relation between a pink noise equation parameter and current and arc length, wherein the relation is shown in a formula (4):
wherein A is 1 、A 2 、A 3 、γ 1 、γ 2 、γ 3 、c 1 、c 2 、c 3 To calculate the coefficients, d is the arc length, I is the arc current, S is the Power Spectral Density (PSD), f is the frequency, and a, γ and c are correlation constants.
S300, establishing a simulation model of the direct current micro-grid fault arc based on the time domain fitting relation and the frequency domain fitting relation.
The mathematical expression of the DC micro-grid fault arc simulation model is shown as the formula (5):
wherein at t 0 Time of day, I 1 And I 0 The relationship of the two functions is shown in formula (6):
I 1 (I p ，d，t 0 )＝I 0 (t 0 ) (6)
wherein t is 0 For arc fault occurrence time, I 0 For the current of the branch where the arc generating device is before the arc fault occurs, I 1 Is the current of the branch where the arc generating device is located after the arc fault occurs, I P For real-time load current before arc fault occurs, D (I P ) The method is characterized in that the method is used for simulating random jitter in actual fault arc current, d is arc length, P is power spectral density, a is random gain of noise, and t is time. Before an arc fault occurs, the current of a branch where the arc generating device is located is kept constant, when a fault arc occurs, the arc current value can obviously drop suddenly, then gradually and slowly drops according to the rule of the formula, and meanwhile, random jitter characteristics exist.
S400, running a simulation model, and outputting a simulation result of the direct current micro-grid fault arc.
Fig. 3 is a mathematical model of a dc micro-grid fault arc established in accordance with the present invention, the dc micro-grid fault arc model being built in MATLAB/Simulink software. The input end of the model is respectively input with arc current and arc length, 1 is a time domain module of the DC micro-grid fault arc mathematical model established by the invention, 2 is a frequency domain module of the DC micro-grid fault arc mathematical model established by the invention, 3 is a real-time current receiving module, and 4 is a signal superposition module. The specific working process is as follows: the current receiving module receives the real-time current value of the branch, the time domain and frequency domain characteristics in the current state are obtained through the time domain module and the frequency domain module, and finally the characteristics are combined with the real-time current through the signal superposition module to generate fault arc current output.
And selecting an occurrence position as a constant power load side according to a built mathematical model of the direct current micro-grid fault arc, inputting an arc current of 10A and an arc length of 1.1mm, and obtaining an arc current waveform chart. Fig. 4-6 are time domain comparison graphs of simulation results, classical Cassie model simulation results and experimental results of fault arc current waveforms with current of 10A and arc length of 1.1mm at a constant power load side, and fig. 7-9 are time domain comparison graphs of simulation results, classical Cassie model simulation results and experimental results of fault arc current waveforms with current of 10A and arc length of 1.1mm at a constant power load side. It can be obviously seen that the simulation result of the arc current is very similar to the actual arc current data in time domain and frequency domain, and the original classical Cassie arc model has larger difference with the actual arc current when being applied to a direct current micro-grid system.
The above embodiments are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solutions of the present invention should fall within the protection scope defined by the claims of the present invention without departing from the design spirit of the present invention.
Claims (9)
1. A DC micro-grid fault arc modeling and simulation method is characterized in that: the method comprises the following steps:
simulating arc faults generated by different arc lengths and arc occurrence positions, and collecting fault arc current data of a branch where the arc faults are located;
based on the fault arc current data, respectively analyzing and fitting the corresponding relation between a current drop value, line current and arc length when an arc fault occurs, wherein the relation between the volt-ampere characteristic of the arc current in a time domain range, the occurrence position and the arc length is analyzed, the relation between the pink noise characteristic of the arc current in a frequency domain range, the occurrence position and the arc length is analyzed, and a time domain fitting relation and a frequency domain fitting relation are obtained;
establishing a simulation model of the direct current micro-grid fault arc based on the time domain fitting relation and the frequency domain fitting relation;
and running the simulation model and outputting a simulation result of the direct current micro-grid fault arc.
2. The direct current micro-grid fault arc modeling and simulation method according to claim 1, wherein the method comprises the following steps: the simulating arc faults generated by different arc lengths and occurrence positions comprises the following steps:
constructing a direct-current micro-grid fault arc test experiment platform, wherein the direct-current micro-grid fault arc test experiment platform comprises a direct-current micro-grid system and an arc generating device, and the arc generating device is connected in series at different positions of the direct-current micro-grid system;
and adjusting the arc length of the arc generating device and the position where the arc fault occurs, and simulating the arc faults generated by different arc lengths and generating positions.
3. The direct current micro-grid fault arc modeling and simulation method according to claim 2, wherein the method comprises the following steps: the direct-current micro-grid system comprises a direct-current source, a storage battery, a resistance load and a plurality of constant-power loads, wherein the electric arc generating device comprises a screw rod sliding table, copper bars, a driver and a controller, and the driver controls the controller to separate the copper bars for arc discharge.
4. The direct current micro-grid fault arc modeling and simulation method according to claim 3, wherein the method comprises the following steps: simulating arc faults generated by different arc lengths and occurrence positions, and collecting fault arc current data of a branch where the arc faults are located comprises:
setting the output voltage of the direct current source to be 110V, adjusting the controller to enable the two copper bars to be in full contact, and starting an experiment;
recording the current waveform of the arc generating device under normal conditions;
adjusting the controller to separate the two copper bars for arc discharge, and recording the current waveform of the arc generating device in the whole process;
changing the arc length, the arc fault occurrence position, the branch voltage where the arc is located and the arc current, repeating the previous step, and recording the arc current under different arc lengths and arc fault occurrence positions.
5. The direct current micro-grid fault arc modeling and simulation method according to claim 1, wherein the method comprises the following steps: based on the arc current, obtaining the relation between the current drop value and the line current when the arc occurs through polynomial fitting as shown in a formula (1),
D(I)＝d 1 +d 2 I+d 3 I 2 (1)
wherein d 1 、d 2 、d 3 For calculation of the coefficient, D is the current dip value and I is the arc current.
6. The direct current micro-grid fault arc modeling and simulation method according to claim 1, wherein the method comprises the following steps: the analyzing and fitting the relationship of the volt-ampere characteristic of the arc current in the time domain range to the occurrence location, the arc length comprises: obtaining a functional relation between load current and time of each group of experimental data based on quadratic polynomial fitting;
obtaining a function of a quadratic polynomial coefficient relative to experimental parameters based on a polynomial fitting method, and obtaining the relation between the current volt-ampere characteristics of the branch circuit where the arc is and the experimental parameters as shown in formulas (2) - (3):
y＝f 1 x 2 +f 2 x+f 3 (2)
f i (d，I)＝f i1 +f i2 d+f i3 I+f i4 dI+f i5 d 2 +f i6 I 2 (3)
wherein f 1 、f 2 、f 3 For the fitting coefficient, x is the abscissa of the current volt-ampere characteristic curve, y is the ordinate of the current volt-ampere characteristic curve, f i1 、f i2 、f i3 、f i4 、f i5 、f i6 To calculate the coefficients, d is the arc length and I is the arc current.
7. The direct current micro-grid fault arc modeling and simulation method according to claim 1, wherein the method comprises the following steps: the analyzing and fitting the relationship between pink noise characteristics of the arc current in the frequency domain range and the occurrence position and the arc length comprises:
calculating the pink noise power spectrum density MSA of each group of experimental data;
according to the pink noise power spectral density function, based on a least square method, fitting to obtain the relationship between the pink noise equation parameter and the current and the arc length as shown in the formula (4):
wherein A is 1 、A 2 、A 3 、γ 1 、γ 2 、γ 3 、c 1 、c 2 、c 3 To calculate the coefficients, d is the arc length, I is the arc current, S is the Power Spectral Density (PSD), f is the frequency, and a, γ and c are correlation constants.
8. The direct current micro-grid fault arc modeling and simulation method according to claim 1, wherein the method comprises the following steps: the simulation model of the direct current micro-grid fault arc is shown in the formula (5):
wherein at t 0 Time of day, I 1 And I 0 The relation of (2) is shown in the formula (6):
I 1 (I p ，d，t 0 )＝I 0 (t 0 ) (6)
wherein t is 0 For arc fault occurrence time, I 0 For the current of the branch where the arc generating device is before the arc fault occurs, I 1 Is the current of the branch where the arc generating device is located after the arc fault occurs, I P For real-time load current before arc fault occurs, D is arc length, D (I P ) The current drop value when fault arc occurs, P is power spectral density, a is random gain of noise, random jitter in actual fault arc current is simulated, and t is time.
9. A direct current micro-grid fault arc modeling and simulation system for implementing the direct current micro-grid fault arc modeling and simulation method according to claims 1-8, characterized in that: comprises a direct current micro-grid fault arc time domain module (1), a direct current micro-grid fault arc frequency domain module (2), a real-time current receiving module (3) and a signal superposition module (4),
the direct current micro-grid fault arc time domain module (1) is used for simulating the time domain characteristics of direct current micro-grid fault arc current signals;
the direct current micro-grid fault arc frequency domain module (2) is used for simulating the frequency domain characteristics of direct current micro-grid fault arc current signals;
the real-time current receiving module (3) is used for receiving the real-time current of the branch circuit;
the signal superposition module (4) is used for superposing the simulation signal of the direct current micro-grid fault arc time domain module (1), the simulation signal of the direct current micro-grid fault arc frequency domain module (2) and the simulation signal of the real-time current receiving module (3) to form a final direct current micro-grid fault arc simulation model;
the direct current micro-grid fault arc time domain module (1), the direct current micro-grid fault arc frequency domain module (2) and the real-time current receiving module (3) are connected with the signal superposition module (4).
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