CN103400019A - Matlab/Simulink-based alternating current (AC) fault arc simulation method - Google Patents

Matlab/Simulink-based alternating current (AC) fault arc simulation method Download PDF

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CN103400019A
CN103400019A CN2013103770742A CN201310377074A CN103400019A CN 103400019 A CN103400019 A CN 103400019A CN 2013103770742 A CN2013103770742 A CN 2013103770742A CN 201310377074 A CN201310377074 A CN 201310377074A CN 103400019 A CN103400019 A CN 103400019A
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arc
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electric arc
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fault
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CN103400019B (en
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刘鹏
张峰
张士文
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Shanghai Jiaotong University
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Abstract

The invention relates to a Matlab/Simulink-based alternating current (AC) fault arc simulation method. The method comprises the following steps of 1) based on a mathematical model of a direct current (DC) arc, assuming a mathematical model of dynamic volt-ampere characteristics of the arc according to the relation between the static characteristics and dynamic characteristics of the arc, thus building dynamic mathematical models of a low-voltage series AC fault arc in a resistance system and a resistance and inductance system; 2) determining the combustion process of the AC fault arc by analyzing the dynamic mathematical models of the AC fault arc; 3) building a simulation model of the AC fault arc via Matlab/Simulink software according to the combustion process and dynamic mathematical models of the AC fault arc; and 4) operating the simulation model of the AC fault arc in the resistance system and the resistance and inductance system, and outputting the simulation results of the simulation model. Compared with the prior art, the method has the advantages of high simulation accuracy, accurate analysis of the dynamic characteristics of the arc, strong universality and the like.

Description

AC fault electric arc emulation mode based on Matlab/Simulink
Technical field
The present invention relates to a kind of AC fault electric arc emulation mode, especially relate to a kind of electric arc of AC fault based on Matlab/Simulink emulation mode.
Background technology
Along with socioeconomic development, the quantity of fire failure is also followed urban construction and social development and is risen on year-on-year basis, and house inside or household electrical appliance internal wiring are due to long-play and affected by external force, can cause that line insulation is aging, even fracture comes off.Can cause the generation of series and parallel electric arc like this, during arc burning, can produce the combustible of localized hyperthermia around very easily igniting and cause fire.Therefore, the dynamic model that improves low-tension arc helps us to be familiar with better the combustion process of electric arc, and also the detection for low-tension arc provides more approach.
The electric arc dynamic model is that a lot of scientific workers concentrate the object of research for a long time, comprising two kinds of research methods.A kind of method is its Physical-Mathematical Model of research, physical process while being namely the research arc burning, according to law of conservation of energy and arc column plasma characteristics, write out differential equation group, solve the mathematic(al) representation of electric arc, Yi Kexi (Cassie) model and Mai Yeer (Mayr) model are representative.Another kind method is the pure mathematical model of research electric arc, is black-box model.It is by electric arc when as the element at two ends, and the external characteristic while only describing arc burning, take Beland model and Matthews model as representative.The physical process when yet existing Mayr model can accurately not described arc burning, therefore and actual electric arc experimental data difference to some extent; The voltage at Matthews model electric arc two ends during using arc burning is as constant, and electric arc reality is when burning, the voltage at electric arc two ends is not unalterable, by the function of the current value of circuit, therefore the Matthews model is accurately during analog AC electric arc arcing, the variation of electric arc both end voltage and electric current.
Summary of the invention
Purpose of the present invention be exactly provide in order to overcome the defect that above-mentioned prior art exists that a kind of simulation accuracy is high, the electric arc of the AC fault based on the Matlab/Simulink emulation mode of Accurate Analysis electric arc dynamic perfromance, highly versatile.
Purpose of the present invention can be achieved through the following technical solutions:
A kind of electric arc of AC fault based on Matlab/Simulink emulation mode, is characterized in that, comprises the following steps:
1) based on the mathematical model of direct-current arc, relation according to static characteristic of arc and dynamic characteristic, mathematical model to the dynamic volt-ampere characteristic of electric arc proposes hypothesis, thereby sets up the low-voltage series connection AC fault Arc dynamic mathematical model in resistive system and resistance sense system;
2), by the analysis to the AC fault Arc dynamic mathematical model, determine the combustion process of AC fault electric arc;
3), according to combustion process and the dynamic mathematical models of AC fault electric arc, by Matlab/Simulink software, set up the realistic model of AC fault electric arc;
4) realistic model of operation AC fault electric arc in resistive system and resistance sense system, and the simulation result of Output simulation model.
Described step 1) be specially:
11) mathematical model of direct-current arc can be expressed as follows by the experimental formula of Ayrton:
U a = A + B I a
U in formula aFor direct-current arc both end voltage, I aFor the direct-current arc electric current, A, B are constant;
12), according to the relation of static characteristic of arc and dynamic characteristic and the Ayrton experimental formula of static characteristic, the mathematical model of the dynamic volt-ampere characteristic of electric arc proposed to the hypothesis formula be:
u a = a + b i a + c
U in formula aFor alternating current arc both end voltage, i aFor the alternating current arc electric current, a, b, c are constant;
13) when system is resistive system, establishing pull-up resistor is R;
If the alternating-current voltage source of input is u s(t), and
u s(t)=U mSin ω t, wherein U mFor alternating current maximal value, ω are ac frequency
Low-voltage series connection AC fault Arc dynamic mathematical model in resistive system is as follows:
U m sin ωt = i a R + a + b i a + c
The flame current i that obtains aWith electric arc both end voltage u aAs follows respectively:
i a ( t ) = U m sin ωt - cR - a + ( cR + a - U m sin ωt ) 2 - 4 R ( ac + b - cU m sin ωt ) 2 R
u a ( t ) = a + 2 bR U m sin ωt + cR - a + ( cR + a - U m sin ωt ) 2 - 4 R ( ac + b - c U m sin ωt )
When system was the resistance sense system, establishing loaded impedance was z=R+j ω L;
In the resistance sense system, low-voltage series connection AC fault Arc dynamic mathematical model is as follows:
U m sin ωt = i a R + L di a dt + a + b i a + c
With the numerical solution that Euler method solves the above-mentioned differential equation, obtain the recursion formula of flame current:
i a n + 1 = i a n + h L ( U max sin ωt - i a n R - a - b i a n + c )
Wherein h is time step.
Described step 2) be specially:
21) combustion process of AC series electric arc in resistive system: in the positive half period of supply voltage, voltage when the contact two ends increases along with the rising of supply voltage, when reaching voltage breakdown, after the breakdown electric arc in electric arc two ends, take fire, this moment, arc voltage changed along with the variation of flame current, when flame current is reduced to zero, the voltage at electric arc two ends rises to blowout voltage, this moment, flame current entered " zero stops " state, flame current is zero, and the voltage at contact two ends equals the supply voltage in circuit; In the supply voltage negative half-cycle, the generation of electric arc and the process of extinguishing before repetition, the direction of flame current and voltage is with opposite before;
22) combustion process of AC series electric arc in the resistance sense system: due to the existence of inductance, the blowout voltage of electric arc is less than supply voltage, so in flame current zero passage moment, the voltage at electric arc two ends can suddenly change to supply voltage, if electric arc is not restriked, can change along with supply voltage, the after-current of restriking can not undergone mutation yet.
The described realistic model of setting up AC fault electric arc by Matlab/Simulink software is specially:
Voltage table in model and reometer are used for gathering arc voltage and current signal, switch is with deciding the generation of electric arc and extinguishing, controllable voltage source is exported the voltage drop of electric arc, controller is according to the voltage and current signal that gathers electric arc, carry out the closed and disconnected of gauge tap, and by the dynamic volt-ampere characteristic of electric arc, calculate and control the output voltage of controllable voltage source, by the spacing that arc electrodes is set, regulate the voltage breakdown of electric arc and the size of blowout voltage simultaneously.
Described step 4) simulation process in needs input voltage, load and arc length parameter.
The simulation result of the realistic model described step 4) comprises the voltage at resistive system and resistance sense system AC fault electric arc two ends and by the electric current of circuit.
Compared with prior art, the present invention has the following advantages:
1) simulation accuracy is high, and than existing Mayr model and Matthews model, the present invention is more approaching with the actual arc data on arc voltage and flame current.
2) Accurate Analysis electric arc dynamic perfromance, the Simulink electric arc mathematic simulated mode that the present invention sets up, be the mathematical model of setting up according to the combustion process of actual arc, the behavioral characteristics of the electric arc of computational analysis accurately.
3) highly versatile, the present invention for resistive system and resistance sense system substantially covered common civilian and industrial load, have certain versatility.
4) the present invention provides an experiment simulation platform for the research of AC fault electric arc, this experiment simulation platform adopts general Matlab/Simulink software, utilize simulation result can further study the specific features of the voltage and current of AC fault electric arc, for theory and experiment basis have been set up in the detection of AC fault electric arc.
The accompanying drawing explanation
Fig. 1 is series connection AC fault Arc System circuit diagram;
Fig. 2 is Arc Modelling that the present invention sets up arc voltage and current waveform in resistive system;
Fig. 3 is Arc Modelling that the present invention sets up arc voltage and current waveform in the resistance sense system;
Fig. 4 is series connection AC fault electric arc realistic model figure;
Fig. 5 is the comparison diagram of electric arc modular simulation current waveform and real data in resistive system;
Fig. 6 is the comparison diagram of electric arc modular simulation voltage waveform and real data in resistive system;
Fig. 7 is the comparison diagram of electric arc modular simulation current waveform and real data in the resistance sense system;
Fig. 8 is the comparison diagram of electric arc modular simulation voltage waveform and real data in the resistance sense system.
Embodiment
The present invention is described in detail below in conjunction with the drawings and specific embodiments.
Embodiment
Simulation calculation of the present invention more all adopts Chinese industrial to exchange electricity consumption with experimental verification, and namely alternating current is handed over frequencies omega=50Hz.In the resistive system of AC single phase shown in Figure 1, make supply voltage
Figure BDA0000372206170000041
R=56.5 Ω, the voltage waveform that COUNTABLY VALUED calculates in resistive system the electric current of series connection AC fault electric arc and two ends as shown in Figure 2.
In AC single phase resistance sense system shown in Figure 1, make supply voltage
Figure BDA0000372206170000042
Z=56.5+j22 Ω, the voltage waveform that COUNTABLY VALUED calculates in the resistance sense system electric current of series connection AC fault electric arc and two ends as shown in Figure 3.
Fig. 4 is the mathematical model of the AC fault electric arc set up according to the present invention, the AC fault electric arc realistic model of building in Matlab/Simulink software.Voltage table 5 and reometer 6 in model are used for gathering arc voltage and current signal, switch 4 use decide the generation of electric arc and extinguish, controllable voltage source 7 is exported the voltage drop of electric arc, controller 3 is according to the voltage and current signal that gathers electric arc, carry out the closed and disconnected of gauge tap 4, and by the dynamic volt-ampere characteristic of electric arc, calculate and control the output voltage of controllable voltage source, by the spacing that arc electrodes is set, regulate the voltage breakdown of electric arc and the size of blowout voltage simultaneously, wherein 1 is input end, and 2 is output terminal.
The resistive System Implementation mode of AC single phase:
Set up the resistive system of series connection AC fault arc test as shown in Figure 1, make supply voltage
Figure BDA0000372206170000051
Load R=56.5 Ω, arc generator comprises a fixed electorde and a traveling electrode according to the standard of UL1699, wherein fixed electorde is a copper rod, traveling electrode is a graphite rod that diameter is 6.4mm, and by the starting the arc end sharpening of carbon-point, the distance of testing seasonal electric arc two ends is 0.2mm, records thus the voltage and current data of electric arc.Use simultaneously Matlab/Simulink software emulation under the same conditions electric arc module shown in Figure 4, voltage current waveform and the actual waveform that can obtain series connection AC fault electric arc in resistive system contrast respectively as shown in Figure 5 and Figure 6.
AC single phase resistance sense System Implementation mode:
If supply voltage in series connection AC fault arc test resistance sense system shown in Figure 1
Figure BDA0000372206170000052
Load z=56.5+j22 Ω, record the voltage and current data of electric arc in experiment porch.Use simultaneously Matlab/Simulink software emulation under the same conditions electric arc module shown in Figure 4, voltage current waveform and the actual waveform that can obtain series connection AC fault electric arc in the resistance sense system contrast respectively as shown in Figure 7 and Figure 8.
The emulated data of the model that the electric current by the serial arc of the 0.15mm of actual measurement in pure resistive system and the data of voltage and Matlab/Simulink software are set up Matthews Arc Modelling, Mayr Arc Modelling and this paper is carried out the FFT frequency analysis in importing to Matlab, its harmonic wave is mainly odd harmonic, will analyze data list to such as table 1.Can see that model that this paper sets up and actual arc data are the most approaching in humorous wave component.
Table 1
Figure BDA0000372206170000053
。

Claims (6)

1. the electric arc of the AC fault based on a Matlab/Simulink emulation mode, is characterized in that, comprises the following steps:
1) based on the mathematical model of direct-current arc, relation according to static characteristic of arc and dynamic characteristic, mathematical model to the dynamic volt-ampere characteristic of electric arc proposes hypothesis, thereby sets up the low-voltage series connection AC fault Arc dynamic mathematical model in resistive system and resistance sense system;
2), by the analysis to the AC fault Arc dynamic mathematical model, determine the combustion process of AC fault electric arc;
3), according to combustion process and the dynamic mathematical models of AC fault electric arc, by Matlab/Simulink software, set up the realistic model of AC fault electric arc;
4) realistic model of operation AC fault electric arc in resistive system and resistance sense system, and the simulation result of Output simulation model.
2. a kind of electric arc of AC fault based on Matlab/Simulink emulation mode according to claim 1, is characterized in that described step 1) be specially:
11) mathematical model of direct-current arc can be expressed as follows by the experimental formula of Ayrton:
U a = A + B I a
U in formula aFor direct-current arc both end voltage, I aFor the direct-current arc electric current, A, B are constant;
12), according to the relation of static characteristic of arc and dynamic characteristic and the Ayrton experimental formula of static characteristic, the mathematical model of the dynamic volt-ampere characteristic of electric arc proposed to the hypothesis formula be:
u a = a + b i a + c
U in formula aFor alternating current arc both end voltage, i aFor the alternating current arc electric current, a, b, c are constant;
13) when system is resistive system, establishing pull-up resistor is R;
If the alternating-current voltage source of input is u s(t), and
u s(t)=U mSin ω t, wherein U mFor alternating current maximal value, ω are ac frequency
Low-voltage series connection AC fault Arc dynamic mathematical model in resistive system is as follows:
U m sin ωt = i a R + a + b i a + c
The flame current i that obtains aWith electric arc both end voltage u aAs follows respectively:
i a ( t ) = U m sin ωt - cR - a + ( cR + a - U m sin ωt ) 2 - 4 R ( ac + b - cU m sin ωt ) 2 R
u a ( t ) = a + 2 bR U m sin ωt + cR - a + ( cR + a - U m sin ωt ) 2 - 4 R ( ac + b - c U m sin ωt )
When system was the resistance sense system, establishing loaded impedance was z=R+j ω L;
In the resistance sense system, low-voltage series connection AC fault Arc dynamic mathematical model is as follows:
U m sin ωt = i a R + L di a dt + a + b i a + c
With the numerical solution that Euler method solves the above-mentioned differential equation, obtain the recursion formula of flame current:
i a n + 1 = i a n + h L ( U max sin ωt - i a n R - a - b i a n + c )
Wherein h is time step.
3. a kind of electric arc of AC fault based on Matlab/Simulink emulation mode according to claim 2, is characterized in that described step 2) be specially:
21) combustion process of AC series electric arc in resistive system: in the positive half period of supply voltage, voltage when the contact two ends increases along with the rising of supply voltage, when reaching voltage breakdown, after the breakdown electric arc in electric arc two ends, take fire, this moment, arc voltage changed along with the variation of flame current, when flame current is reduced to zero, the voltage at electric arc two ends rises to blowout voltage, this moment, flame current entered " zero stops " state, flame current is zero, and the voltage at contact two ends equals the supply voltage in circuit; In the supply voltage negative half-cycle, the generation of electric arc and the process of extinguishing before repetition, the direction of flame current and voltage is with opposite before;
22) combustion process of AC series electric arc in the resistance sense system: due to the existence of inductance, the blowout voltage of electric arc is less than supply voltage, so in flame current zero passage moment, the voltage at electric arc two ends can suddenly change to supply voltage, if electric arc is not restriked, can change along with supply voltage, the after-current of restriking can not undergone mutation yet.
4. a kind of electric arc of AC fault based on Matlab/Simulink emulation mode according to claim 3, is characterized in that, the described realistic model of setting up AC fault electric arc by Matlab/Simulink software is specially:
Voltage table in model and reometer are used for gathering arc voltage and current signal, switch is with deciding the generation of electric arc and extinguishing, controllable voltage source is exported the voltage drop of electric arc, controller is according to the voltage and current signal that gathers electric arc, carry out the closed and disconnected of gauge tap, and by the dynamic volt-ampere characteristic of electric arc, calculate and control the output voltage of controllable voltage source, by the spacing that arc electrodes is set, regulate the voltage breakdown of electric arc and the size of blowout voltage simultaneously.
5. a kind of electric arc of AC fault based on Matlab/Simulink emulation mode according to claim 4, is characterized in that described step 4) in simulation process need input voltage, load and arc length parameter.
6. a kind of electric arc of AC fault based on Matlab/Simulink emulation mode according to claim 4, it is characterized in that described step 4) in the simulation result of realistic model comprise the voltage at resistive system and resistance sense system AC fault electric arc two ends and by the electric current of circuit.
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CN106777632A (en) * 2016-12-07 2017-05-31 国家电网公司 Switching operation in substation causes the acquisition methods of arc process middle impedance Changing Pattern
CN107194043A (en) * 2017-05-04 2017-09-22 国网山东省电力公司济宁供电公司 A kind of breaker hf electric arc modeling method
CN108061832A (en) * 2017-12-04 2018-05-22 辽宁工程技术大学 Tandem type fault electric arc emulation mode based on neutral net black-box model
CN109255170A (en) * 2018-08-28 2019-01-22 电子科技大学 A kind of voltage gradient modeling method based on magnetohydrodynamics emulation
CN109344434A (en) * 2018-08-27 2019-02-15 南方电网科学研究院有限责任公司 Arc simulation method, device, equipment and medium based on harmonic conditions
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CN113484658A (en) * 2021-05-26 2021-10-08 上海红檀智能科技有限公司 Method, system, medium, and electronic device for diagnosing arc fault

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CN103728509B (en) * 2013-12-13 2016-05-25 温州大学 A kind of fault electric arc signal imitation generating means
CN105158540A (en) * 2015-08-11 2015-12-16 南京师范大学 Arc current estimation method adopting arc inductance correction factor
CN105158540B (en) * 2015-08-11 2018-04-24 南京师范大学 A kind of arc current evaluation method using electric arc inductance correction factor
CN106777632A (en) * 2016-12-07 2017-05-31 国家电网公司 Switching operation in substation causes the acquisition methods of arc process middle impedance Changing Pattern
CN107194043A (en) * 2017-05-04 2017-09-22 国网山东省电力公司济宁供电公司 A kind of breaker hf electric arc modeling method
CN108061832A (en) * 2017-12-04 2018-05-22 辽宁工程技术大学 Tandem type fault electric arc emulation mode based on neutral net black-box model
CN108061832B (en) * 2017-12-04 2019-11-12 辽宁工程技术大学 Tandem type fault electric arc emulation mode based on neural network black-box model
CN109344434A (en) * 2018-08-27 2019-02-15 南方电网科学研究院有限责任公司 Arc simulation method, device, equipment and medium based on harmonic conditions
CN109255170A (en) * 2018-08-28 2019-01-22 电子科技大学 A kind of voltage gradient modeling method based on magnetohydrodynamics emulation
CN109255170B (en) * 2018-08-28 2022-03-25 电子科技大学 Arc voltage gradient modeling method based on magnetohydrodynamics simulation
CN109376490A (en) * 2018-12-12 2019-02-22 云南电网有限责任公司电力科学研究院 A kind of cassie-mayr Simulation of Arc Models method
CN112131735A (en) * 2020-09-21 2020-12-25 福州大学 Impedance arc model and simulation method thereof
CN112131735B (en) * 2020-09-21 2022-07-12 福州大学 Impedance arc model and simulation method thereof
CN113094983A (en) * 2021-03-29 2021-07-09 西安交通大学 Online simulation method for multi-dimensional time-varying characteristics of direct-current fault electric arc of photovoltaic system
CN113094983B (en) * 2021-03-29 2022-12-09 西安交通大学 Online simulation method for multi-dimensional time-varying characteristics of direct-current fault electric arc of photovoltaic system
CN113484658A (en) * 2021-05-26 2021-10-08 上海红檀智能科技有限公司 Method, system, medium, and electronic device for diagnosing arc fault

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