Direct-current fault simulation method for medium-voltage direct-current system

Abstract

The invention relates to the technical field of power system fault simulation, and discloses a DC fault simulation method for a medium-voltage DC system, and the method comprises the steps: constructing an equivalent circuit containing line distribution parameters, and representing the transmission characteristics of resistance, inductance and capacitance per unit length, a linear mathematical model of arc voltage and arc length is established based on arc discharge experiment data, a dynamic resistance curve is generated in combination with an arc length time increase function, an initial value and a change rate of dynamic resistance are extracted as characteristic parameters, and a mapping relation table of the characteristic parameters with metallic short circuit and mild / severe arc faults is established. And according to a target fault type, matching a dynamic resistance parameter, injecting the dynamic resistance parameter into an equivalent circuit, solving a differential equation containing a time-varying resistor, and outputting a high-fidelity DC fault current signal. The method solves the problem that static resistance simulation cannot reproduce arc dynamic characteristics, and significantly improves the accuracy of fault simulation.

Description

Technical Field

[0001] The present invention relates to the technical field of power system fault simulation, and particularly to a DC fault simulation method for a medium-voltage DC system. Background Art

[0002] The current DC fault simulation method for medium-voltage DC systems has the problem of insufficient reduction of dynamic characteristics. Existing technologies such as the patent CN114282334B "A DC transmission line fault simulation method and device based on PSS / E" adopt a T-type equivalent circuit model. Although it can simulate the characteristics of line distributed parameters, it relies on a fixed resistance value to simulate the fault branch and cannot reflect the time-varying process of the resistance in an actual arc fault. This method has a significant error in simulating the current decay characteristics at the initial stage of arc development, especially in terms of insufficient adaptability to the common arc reignition phenomenon in medium-voltage DC systems, resulting in a decrease in the simulation accuracy of the fault current waveform.

[0003] Another patent CN118688593A "A method for constructing the dynamic morphology and conductance parameters of an arc in insulating oil" proposes an arc time-varying resistance model, but focuses on the insulating oil medium environment and does not integrate the coupling relationship between line distributed parameters and arc dynamic characteristics. There is no mapping mechanism established between the generation process of its arc conductance parameters and the fault type, and it needs to rely on experimental data for repeated calibration, making it difficult to be directly applied to the fast simulation of multiple types of faults in medium-voltage DC systems and reducing the engineering practicability. Summary of the Invention

[0004] The present invention provides a DC fault simulation method for a medium-voltage DC system, and its main purpose is to solve the problem of low simulation accuracy caused by insufficient reduction of the time-varying characteristics of arc resistance and the lack of fault type mapping in existing fault simulation methods.

[0005] To achieve the above object, a DC fault simulation method for a medium-voltage DC system provided by the present invention includes: Construct an equivalent circuit including line distributed parameters; Collect arc discharge experimental data of the medium-voltage DC system under fault simulation conditions, and establish a mathematical model between the arc voltage and the arc length; Embed the mathematical model into the equivalent circuit, and generate a dynamic resistance curve in combination with the arc time constant; Establish a mapping relationship table between the fault type parameters and the characteristic parameters in the dynamic resistance curve; Based on the mapping relationship table and the dynamic resistance curve, simulate a DC fault signal with time-varying resistance parameters matching the target fault type.

[0006] Optionally, the constructing an equivalent circuit including line distributed parameters includes: The line characteristics of the medium-voltage DC system are characterized by line distribution parameters, where the line distribution parameters include resistance per unit length, inductance per unit length, and capacitance per unit length; Calculate the total resistance, total inductance, and total capacitance according to the line length and the line distribution parameters; Distribute the total capacitance to the sending end and the receiving end of the equivalent circuit to form parallel capacitors, and connect the total resistance and the total inductance in series to form an impedance branch; Integrate the parallel capacitors and the impedance branch to form a π-type equivalent circuit.

[0007] Optionally, the establishment of the mathematical model of the arc voltage and the arc length includes: Extract the corresponding relationship between the arc length and the arc voltage according to the arc discharge experimental data; Fit an arc voltage-arc length function based on the corresponding relationship and linear regression; Verify the goodness of fit of the arc voltage-arc length function and output the mathematical model of the arc voltage and the arc length.

[0008] Optionally, the embedding of the mathematical model into the equivalent circuit and the generation of a dynamic resistance curve in combination with the arc time constant include: Set the physical model of the growth of the arc length with time; Calculate the time-varying arc voltage of the medium-voltage DC system based on the mathematical model and the physical model; Convert the time-varying arc voltage into a time-varying resistance according to the fault current value, so as to generate a dynamic resistance curve including the arc time constant.

[0009] Optionally, the time-varying resistance is: ; Where, is the time-varying resistance, is the arc voltage-arc length proportionality coefficient, is the initial arc length, is the arc length growth rate, is the time identifier, is at the fault point current at the moment, is the arc time constant, is the current of the previous simulation step, is the time interval.

[0010] Optionally, the establishment of the mapping relationship table between the fault type parameters and the characteristic parameters in the dynamic resistance curve includes: Extract the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters; Define metal short circuit, mild arc fault, and severe arc fault as fault type parameters; Associate the fault type parameters with the characteristic parameters, and construct a mapping relationship table from fault types to characteristic parameters based on the parameter combinations obtained after association.

[0011] Optionally, extracting the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters includes: Select the starting point of the dynamic resistance curve as the initial resistance value; Derive the resistance change rate through the curve slope of the dynamic resistance curve.

[0012] Optionally, the resistance change rate is calculated using the forward difference method.

[0013] Optionally, based on the mapping relationship table and the dynamic resistance curve, simulating a DC fault signal with time-varying resistance parameters that matches the target fault type includes: Query the mapping relationship table according to the type identifier of the target fault type to match the corresponding dynamic resistance curve; Convert the matched dynamic resistance curve into a set of time-varying resistance parameters, and inject the set of time-varying resistance parameters into the fault point of the equivalent circuit; Establish a circuit differential equation with time-varying resistance; Use the fourth-order Runge-Kutta method to solve the circuit differential equation, and output the waveform of the current changing with time as the DC fault signal.

[0014] Optionally, the circuit differential equation is: ; Wherein, is the total inductance, is the fault point current at time, is the derivative of the fault point current with respect to time, is the total resistance, is the time-varying resistance, is the DC voltage source, is the time identifier.

[0015] Compared with the prior art, the present invention has the following beneficial effects: Based on the arc voltage-arc length mathematical model and the physical model driven by the time constant, a time-varying resistance curve is generated, which truly reflects the non-linear change characteristics of the arc resistance during the fault process. Compared with the traditional fixed resistance model, the simulation accuracy of the fault current waveform is significantly improved, especially the reduction degree of transient processes such as arc re-ignition and current decay is higher; By extracting the initial resistance value and the change rate of the dynamic resistance curve as characteristic parameters, constructing a mapping relation table for metal short - circuit, mild / severe arc faults, supporting parametric identification and one - key call of fault types, avoiding repeated manual calibration, greatly improving the simulation efficiency of multi - type faults, and reserving an interface for the expansion of new faults; Adopt a π - type equivalent circuit to integrate the line distributed parameters to ensure accurate modeling of long - distance power transmission characteristics; combine the fourth - order Runge - Kutta method to solve the differential equation with time - varying resistance. While ensuring numerical stability, output current waveforms that highly match the real fault recording data, and can provide a high - confidence simulation environment. Brief Description of the Drawings

[0016] Figure 1 It is a schematic flow chart of the DC fault simulation method for a medium - voltage DC system provided by an embodiment of the present invention.

[0017] The realization, functional characteristics and advantages of the object of the present invention will be further described in conjunction with the embodiments with reference to the drawings. Detailed Embodiments

[0018] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0019] The embodiments of the present application provide a DC fault simulation method for a medium - voltage DC system. The execution subject of the DC fault simulation method for the medium - voltage DC system includes but is not limited to at least one of electronic devices such as a server, a terminal, etc. that can be configured to execute the method provided by the embodiments of the present application. In other words, the DC fault simulation method for the medium - voltage DC system can be executed by software or hardware installed on a terminal device or a server device. The server includes but is not limited to: a single server, a server cluster, a cloud server or a cloud server cluster, etc. The server can be an independent server or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, Content Delivery Network (CDN), and big data and artificial intelligence platforms.

[0020] Refer to Figure 1 As shown, it is a schematic flow chart of the DC fault simulation method for a medium - voltage DC system provided by an embodiment of the present invention. In this embodiment, the DC fault simulation method for the medium - voltage DC system includes: S1. Construct an equivalent circuit including line distributed parameters.

[0021] In the embodiment of the present invention, the constructing an equivalent circuit including line distributed parameters includes: The line distribution parameters are used to characterize the line characteristics of a medium-voltage DC system, where the line distribution parameters include the resistance per unit length, the inductance per unit length, and the capacitance per unit length; Calculate the total resistance, total inductance, and total capacitance according to the line length and the line distribution parameters; Distribute the total capacitance to the sending end and the receiving end of the equivalent circuit to form parallel capacitors, and connect the total resistance and the total inductance in series to form an impedance branch; Integrate the parallel capacitors and the impedance branch to form a π-type equivalent circuit.

[0022] Specifically, the line distribution parameters are parameters used to characterize the electrical characteristics per unit length of the transmission line in a medium-voltage DC system, which include the resistance per unit length, the inductance per unit length, and the capacitance per unit length. These parameters can describe the distributed electrical characteristics presented by the line during the process of transmitting electrical energy. For example, the resistance per unit length reflects the resistance loss per kilometer of the line, the inductance per unit length reflects the magnetic field energy storage characteristics per kilometer of the line, and the capacitance per unit length represents the electric field coupling ability per kilometer of the line.

[0023] Specifically, the resistance per unit length is a component of the line distribution parameters, referring to the resistance value per unit length (such as per kilometer) of the transmission line, and its unit is usually ohm per kilometer (Ω / km), which is used to measure the conductive loss characteristics of the line itself.

[0024] Specifically, the inductance per unit length is a type of line distribution parameter, referring to the inductance value per unit length of the transmission line, and the unit is generally henry per kilometer (H / km), which is used to characterize the magnetic field effect and energy storage ability generated when the line transmits current.

[0025] Specifically, the capacitance per unit length belongs to the line distribution parameters, referring to the capacitance value per unit length of the transmission line, and the unit is often farad per kilometer (F / km), which is used to describe the degree of electric field coupling and charge storage ability between phases or between phase and ground of the line.

[0026] Specifically, the total resistance is the total resistance value of the transmission line calculated according to the line length and the resistance per unit length, and its calculation method is the product of the resistance per unit length and the line length, and the unit is ohm (Ω), which represents the total resistance loss of the entire line.

[0027] Specifically, the total inductance is the total inductance value of the transmission line calculated from the line length and the inductance per unit length, obtained by multiplying the inductance per unit length by the line length, and the unit is henry (H), which is used to represent the total magnetic field effect of the entire line.

[0028] Specifically, the total capacitance is the total capacitance value of the transmission line calculated based on the line length and capacitance per unit length, that is, the product of the capacitance per unit length and the line length, with the unit of farad (F), reflecting the total electric field coupling ability of the entire line.

[0029] Specifically, the shunt capacitance is a capacitance element formed by distributing the total capacitance to the sending end and receiving end of the equivalent circuit. It is connected in parallel with the impedance branch and is used to simulate the influence of the distributed capacitance of the transmission line on the electrical characteristics of the system.

[0030] Specifically, the impedance branch is a circuit branch formed by the series connection of the total resistance and total inductance. Among them, the total resistance reflects the loss characteristics of the line, and the total inductance reflects the magnetic field characteristics of the line. This branch is used to characterize the impedance characteristics of the transmission line.

[0031] Specifically, the π-type equivalent circuit is a circuit model used to simulate the distributed parameter characteristics of the transmission line. Its structure is in the shape of the Greek letter "π", consisting of capacitors connected in parallel at both ends and resistance and inductance branches connected in series in the middle, and can effectively reflect the distributed parameter effect of the medium-voltage DC system line.

[0032] Furthermore, characterizing the line characteristics of the medium-voltage DC system using the line distributed parameters includes the following steps: First, obtain the resistance per unit length of the line through the line design document or experimental measurement , inductance per unit length and capacitance per unit length . For example, obtain from the medium-voltage DC line design data .

[0033] Next, the line length of the medium-voltage DC system is usually relatively long (such as more than 10 km), and its electrical characteristics need to be described by the distributed parameter model. The distributed parameter model regards the line as composed of countless tiny units, and each unit contains , and can more accurately reflect the voltage, current distribution and traveling wave propagation characteristics along the line. Compared with the lumped parameter model (using only one resistance, inductance, and capacitance to represent the line), its error is smaller when simulating long-distance lines.

[0034] Finally, use circuit simulation software (such as PSCAD / EMTDC) or mathematical calculation tools (such as MATLAB) to model and process the distributed parameters, and generate the distributed parameter model of the line by inputting the measured or designed parameters.

[0035] Furthermore, calculating the total resistance, total inductance and total capacitance according to the line length and line distributed parameters includes the following steps: First, when the line length , calculate the total resistance, total inductance and total capacitance according to the following calculation formulas: Total resistance: , where is the line length (unit: km), then ; Total inductance: , then ; Total capacitance: , then .

[0036] Specifically, based on the principle of calculus, the line is regarded as a series connection of countless unit-length elements, and the total parameters are obtained by accumulating the resistance, inductance, and capacitance of each element. This calculation method conforms to the basic principles of electromagnetism, such as Ohm's law (resistance in series) and the series / parallel characteristics of inductance and capacitance (here it is series accumulation).

[0037] Furthermore, by comparing the short-circuit test data of the actual line (such as short-circuit current, voltage attenuation characteristics) with the theoretical simulation results of the calculated total parameters, the accuracy of the calculation is verified. If the error exceeds 5%, it is necessary to re-check the parameter acquisition or calculation process.

[0038] Specifically, the steps of distributing the total capacitance to the sending end and receiving end of the equivalent circuit to form parallel capacitors and connecting the total resistance and total inductance in series to form an impedance branch are as follows: First, divide the total capacitance into two equal parts, namely the sending-end parallel capacitor and the receiving-end parallel capacitor . For example, when the total capacitance is , ;

[0039] This distribution method stems from the classic structure of the π-type equivalent circuit. By concentrating the distributed capacitance into parallel capacitors at both ends, the electric field effect of the distributed capacitance along the line can be approximately simulated.

[0040] Next, connect the total resistance and the total inductance in series to form the middle impedance branch. For example, is connected in series with , and this branch reflects the resistance loss and inductive energy storage characteristics of the line, and its impedance value [[ID=5,3]] ( is the angular frequency) is used to describe the blocking effect of the line on the current.

[0041] Finally, use circuit drawing software (such as Eagle, OrCAD) to draw the circuit topology to ensure that the sending-end parallel capacitor , the impedance branch , and the receiving-end parallel capacitor are connected in sequence to form a π-type structure.

[0042] Further, integrating the shunt capacitance and the impedance branch to form a π-type equivalent circuit includes the following steps: First, connect the sending-end shunt capacitance to the input end of the equivalent circuit, and connect the receiving-end shunt capacitance to the output end, with an impedance branch connected in series in the middle to form a " "-shaped topology. For example, connect one end of to the input node and one end of the impedance branch, ground the other end of , connect the other end of the impedance branch to one end of , and ground the other end of and use it as the output node.

[0043] Next, apply an input step voltage signal (such as a 10 kV DC voltage), simulate and calculate the output voltage and current responses of the equivalent circuit, and compare them with the transient response data of the actual line. For example, if the voltage decay time constant of the actual line during a fault is , the simulation results of the π-type equivalent circuit should be within to verify the accuracy of the model.

[0044] Finally, if the deviation between the simulation results and the actual data is large, adjust the distribution ratio of the total capacitance (such as non-uniform distribution) or introduce additional distributed parameter correction terms (such as series capacitance) until the electrical characteristics of the equivalent circuit are consistent with those of the actual line.

[0045] Generally speaking, this step constructs a π-type equivalent circuit containing the distributed parameters of the line, solving the problem of simulation errors caused by the lumped parameter model in the prior art. The lumped parameter model ignores the distributed characteristics of the line, which will cause large simulation errors in the fault current and voltage waveforms in the medium-voltage DC system (especially for long-distance lines). The medium-voltage DC system has a high voltage level (1 kV - 35 kV) and a long line, and the distributed parameter effect is significant (such as uneven current distribution caused by capacitive coupling). The π-type equivalent circuit can accurately simulate the traveling wave propagation speed and wave impedance of the line through the combination of shunt capacitance and impedance branch. <\

[0046] S2. Collect the arc discharge experimental data of the medium-voltage DC system under fault simulation conditions, and establish a mathematical model of the arc voltage and the arc length.

[0047] In the embodiment of the present invention, establishing the mathematical model of the arc voltage and the arc length includes: extracting the corresponding relationship between the arc length and the arc voltage according to the arc discharge experimental data; fitting an arc voltage - arc length function based on the corresponding relationship and linear regression.

[0048] Specifically, the expression of the arc voltage-arc length function can be: ; where is the arc voltage, is the arc voltage-arc length proportionality coefficient, is the arc length of the arc;

[0049] Verify the goodness of fit of the arc voltage-arc length function and output the mathematical model of the arc voltage and the arc length.

[0050] Specifically, the medium-voltage DC system refers to a DC power transmission system with a voltage level between 1 kV and 35 kV, which has the characteristics of high transmission efficiency and low line loss, and is widely used in new energy grid connection, urban rail transit and other fields.

[0051] Specifically, the fault simulation conditions refer to the medium-voltage DC system fault scenarios artificially set in the laboratory environment, including types such as metallic short circuit and arc fault, which are used to reproduce the fault states in actual operation to obtain experimental data.

[0052] Specifically, the arc discharge experimental data refers to the real-time measurement data of parameters such as arc voltage, arc length, and fault current during the arc discharge process collected by experimental equipment under the fault simulation conditions.

[0053] Specifically, the arc length is the physical distance between the positive and negative electrodes during arc discharge, with the unit of meter (m). It is a key parameter characterizing the arc shape and directly affects the arc voltage and resistance characteristics.

[0054] Specifically, the arc voltage refers to the potential difference across the arc during the arc discharge process, with the unit of volt (V). Its value is related to factors such as arc length and arc current, and reflects the energy loss characteristics of the arc.

[0055] Specifically, linear regression fitting is a statistical analysis method used to determine the linear functional relationship between two variables. By fitting the experimental data using the least squares method, the best linear fitting equation is obtained.

[0056] Specifically, the arc voltage-arc length function is a mathematical expression describing the linear relationship between the arc voltage and the arc length, and this function is used to characterize the basic electrical characteristics of arc discharge.

[0057] Specifically, the goodness of fit is an index used to evaluate the fitting degree of the regression model to the experimental data, usually represented by the coefficient of determination R². The closer the R² value is to 1, the higher the fitting accuracy of the model to the data.

[0058] Furthermore, collecting the arc discharge experimental data of the medium-voltage DC system under the fault simulation conditions includes the following steps: First, build an experimental platform that includes a medium-voltage DC power supply (such as a 10 kV DC power supply), an arc generator (a discharge device with adjustable electrode spacing), a fault current injection circuit (including a current-limiting resistor and a switch), and a data acquisition system (an oscilloscope or DAQ device with a sampling frequency ≥ 100 kHz). For example, the power supply uses a programmable DC power supply, and the electrode material of the arc generator is copper alloy, with an adjustable spacing range of 0.001 - 0.1 m.

[0059] Next, connect a high-voltage probe (range 0 - 20 kV, accuracy ±1%) in parallel across the arc to measure the arc voltage, use a laser rangefinder (resolution 10 μm) to monitor the arc length in real time, and connect a Hall current sensor (range 0 - 5 kA, accuracy ±0.5%) in series in the fault circuit to collect the fault current.

[0060] Secondly, set three types of faults: metallic short circuit (arc length is 0 m), mild arc fault (arc length is 0.01 - 0.05 m), and severe arc fault (arc length is 0.05 - 0.1 m). Repeat the experiment 10 times for each type to eliminate accidental errors.

[0061] Then, keep the laboratory temperature at 25 ± 2 °C and humidity at 50 ± 5% to avoid interference from environmental factors on the arc characteristics. For example, control the environmental parameters through a thermo-hygrostat, and preheat the equipment for 30 minutes before each experiment.

[0062] Finally, use a fault current threshold trigger (such as 100 A). When the current exceeds the threshold, the data acquisition system synchronously records the time-domain waveforms of the arc voltage, arc length, and current at a sampling rate of 100 kHz, with a recording duration ≥ 50 ms (covering the entire process of arc development), and manually mark the data segment of the stable arc combustion stage (such as arc length fluctuation ≤ 5%). Extract the average values of the arc length and voltage within this segment as valid data points, and obtain at least 50 groups of valid data for each fault type.

[0063] Furthermore, establishing a mathematical model of arc voltage and arc length includes the following steps: First, from the arc discharge experimental data, screen out the arc lengths and the corresponding arc voltages at the stable arc combustion stage under the same fault type. For example, in the case of a mild arc fault ( ), record 10 groups of corresponding arc voltages such as 20 V, 20.5 V, 19.8 V, etc.; and organize the data points into a two-dimensional table with columns of arc length (unit: m) and voltage (unit: V), and use software such as Excel or MATLAB to draw a visual scatter plot to preliminarily judge the linear correlation.

[0064] Next, the least squares method is used for linear regression, and the objective function is to minimize the mean square error between the predicted voltage and the measured voltage; and the proportional coefficient k is solved through matrix operations, and the formula is , where is the arc length data vector, is the voltage data vector

[0065] Generally speaking, in the prior art, a fixed arc resistance model is often used, and the dynamic change of the arc voltage with the arc length is not considered, resulting in a large error in fault simulation. This step will reduce the simulation error through an experiment data-driven linear model. For example, when the arc length increases from 0.01 m to 0.05 m, the voltage calculated by the fixed resistance model is always 10 V, while the actual voltage increases from 10 V to 50 V.

[0066] Generally speaking, the arc voltage - arc length model accurately reflects the physical characteristics of the arc, making the electrical characteristics (such as the fault current waveform and the operating time of the protection device) of the medium-voltage DC system fault simulation more consistent with the actual operation data.

[0067] S3. Embed the mathematical model into the equivalent circuit and generate a dynamic resistance curve in combination with the arc time constant.

[0068] In the embodiment of the present invention, the embedding of the mathematical model into the equivalent circuit and generating a dynamic resistance curve in combination with the arc time constant includes: Set the physical model of the arc length increasing with time; Calculate the time-varying arc voltage of the medium-voltage DC system based on the mathematical model and the physical model; Convert the time-varying arc voltage into a time-varying resistance according to the fault current value, so as to generate a dynamic resistance curve including the arc time constant.

[0069] Specifically, the time-varying resistance is: ; where is the time-varying resistance, is the arc voltage - arc length proportional coefficient, is the initial arc length, is the arc length growth rate, is the time identifier, is at the fault point current at the moment, is the arc time constant, is the current of the previous simulation step, is the time interval.

[0070] Specifically, the expression of the physical model can be: ; Among them, is the arc length at moment, is the initial arc length, is the arc length growth rate, is the time identifier, is the arc time constant.

[0071] Specifically, the arc length refers to the physical distance between the positive and negative electrodes during the arc discharge process. Its unit is meter (m), which is a key parameter characterizing the arc shape and reflects the development process of the arc over time.

[0072] Specifically, the initial arc length is the arc length at the moment of fault occurrence, denoted by the symbol , with the unit of meter (m). Its value is determined by the fault type and initial conditions and is used for setting the initial state of the physical model.

[0073] Specifically, the arc resistance is determined by the current at the previous moment, which conforms to the inertial characteristic of the arc response in actual faults (thermal inertia causes the resistance change to lag behind the current). In the Runge - Kutta method iteration, the resistance at the current moment is calculated using the current value at the previous moment.

[0074] Specifically, the arc length growth rate refers to the rate of change of the arc length over time, denoted by the symbol , with the unit of meter per second (m / s). It reflects the speed of the arc expansion during the fault process and is determined by the arc physical characteristics and environmental conditions.

[0075] Specifically, the arc time constant is a parameter characterizing the time characteristic during the arc length growth process, denoted by the symbol , with the unit of second (s). It is used to describe the speed at which the arc length grows to the steady state and reflects the dynamic characteristics of the arc.

[0076] Specifically, the time - varying arc voltage refers to the potential difference across the arc that changes over time during the fault process. Its unit is volt (V), and its value is jointly determined by the arc length and the arc voltage - arc length proportionality coefficient, reflecting the dynamic change of the arc energy loss.

[0077] Specifically, the time - varying resistance refers to the resistance value that changes over time during the fault process. Its unit is ohm (Ω), which is calculated from the time - varying arc voltage and the fault current and is used to characterize the dynamic characteristics of the arc resistance.

[0078] Specifically, the dynamic resistance curve is a curve describing the change of the time - varying resistance over time, which is used to visually display the dynamic change law of the arc resistance during the fault process and provides key parameters for the fault simulation of the medium - voltage DC system.

[0079] Furthermore, during the fault, the arc length increases with time following an exponential law, and this model is obtained by fitting based on arc physics theory and experimental data. For example, when an arc occurs, the arc length starts from the initial value and increases with time gradually, and finally tends to a stable value. Its mathematical expression is as follows: ; Furthermore, the initial arc length is set according to the fault type, such as metal short - circuit , mild arc fault , severe arc fault ; the arc length growth rate is obtained by measuring through arc discharge experiments. For example, in a 10 kV medium - voltage DC system, for mild arc faults ; the arc time constant is determined by arc time constant experiments, reflecting the arc heat diffusion and cooling characteristics, usually .

[0080] Specifically, comparing the model output with the arc development process captured by a high - speed camera. For example, at , the model calculates the arc length , the measured value is , and the error meets the engineering requirements.

[0081] Furthermore, calculating the time - varying arc voltage based on the mathematical model and physical model includes the following steps: First, call the established arc voltage - arc length function , where is the arc voltage - arc length proportionality coefficient (such as V / m); then, substitute the physical model into the arc voltage function to obtain the time - varying arc voltage expression: .

[0082] For example, when , , .

[0083] Furthermore, converting the time - varying arc voltage to a time - varying resistance according to the fault current value includes the following steps: First, according to Ohm's law , the time - varying resistance is , where is the fault point current (unit: A), obtained by calculating from the equivalent circuit; Next, the fault current waveform is obtained by solving the differential equation containing the equivalent circuit. For example, in a 10 kV system, during a solid short circuit , during an arc fault varies with time;

[0084] Finally, substituting the time-varying arc voltage and fault current, the time-varying resistance expression is obtained: .

[0085] For example, when , .

[0086] Furthermore, generating the dynamic resistance curve includes: taking time as the abscissa (step size 0.001 s), calculating the at each moment, for example to , a total of 51 data points; and using MATLAB or Python to plot curve, the horizontal axis is time (ms), the vertical axis is resistance ( ), and key parameters are marked.

[0087] Furthermore, comparing the curve with the actual fault recording data. For example, at , the model curve shows that the resistance , the measured value , the error , meeting the engineering accuracy requirements.

[0088] Generally speaking, in the prior art, a fixed resistance model (such as 1 Ω) is often adopted, without considering the dynamic change of the arc resistance, resulting in a large fault simulation error. In this step, by introducing the arc time constant and the dynamic resistance curve, the simulation error is reduced. For example, when simulating an arc fault with an arc length of 0.05 m in a 10 kV system, the fault current calculated by the fixed resistance model is 10 kA, the actual measurement is 8.3 kA, and the error is 20.5%; while the calculated value of the dynamic resistance model is 8.5 kA, and the error is 2.4%.

[0089] Generally speaking, the dynamic resistance curve accurately reflects the time-varying characteristics of the arc resistance, making the electrical parameters (such as the fault current waveform and the protection action time) in the medium-voltage DC system fault simulation more consistent with the actual operation data.

[0090] S4. Establish a mapping relationship table between the fault type parameters and the characteristic parameters in the dynamic resistance curve.

[0091] In the embodiment of the present invention, establishing the mapping relationship table between the fault type parameters and the characteristic parameters in the dynamic resistance curve includes: Extract the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters; Define metal short circuit, mild arc fault, and severe arc fault as fault type parameters; Associate the fault type parameters with the characteristic parameters, and construct a mapping relationship table from fault types to characteristic parameters based on the parameter combinations obtained after association.

[0092] Specifically, the extracting the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters includes: Select the starting point of the dynamic resistance curve as the initial resistance value; Derive the resistance change rate through the curve slope of the dynamic resistance curve.

[0093] Specifically, the expression of the characteristic parameters can be as follows: ; Wherein, is the characteristic parameter, is the initial resistance value, is the resistance change rate, is the time-varying resistance, is the time identifier.

[0094] Specifically, the dynamic resistance curve is a curve that describes the variation of the arc resistance with time during the fault process of the medium-voltage DC system. Its horizontal axis is time and the vertical axis is the resistance value, which reflects the time-varying characteristics of the arc resistance and is the key basis for fault type identification.

[0095] Specifically, the initial resistance value is the resistance value of the dynamic resistance curve at the time starting point , represented by the symbol , with the unit of ohm (Ω), and is used to characterize the arc resistance state at the moment of fault occurrence. The initial resistance values of different fault types are significantly different.

[0096] Specifically, the resistance change rate is the slope of the dynamic resistance curve at , represented by the symbol , with the unit of ohm per second (Ω / s), and reflects the degree of change of the arc resistance in the initial stage of the fault, embodying the dynamic characteristics of the arc development.

[0097] Specifically, the fault type parameter is a classification identifier used to characterize different fault types of the medium-voltage DC system, including metal short circuit, mild arc fault, and severe arc fault. Each type corresponds to specific physical phenomena and electrical characteristics.

[0098] Specifically, the mapping relationship table associates the fault type parameters with the characteristic parameters of the dynamic resistance curve (the initial resistance value , Rate of change of resistance A table for correlation is used to establish the correspondence between fault types and characteristic parameters, facilitating the rapid identification and simulation of fault types.

[0099] Furthermore, extracting the initial resistance value and the rate of change of resistance of the dynamic resistance curve includes the following steps: First, directly select the resistance value of the dynamic resistance curve at as the initial resistance value . For example, if the resistance of a certain dynamic resistance curve at is 0.01 Ω, then = 0.01 Ω; verify the accuracy of the extracted value by comparing the measured resistance data at the moment of fault occurrence (such as the initial resistance recorded by an oscilloscope), and the error should be ≤ 1%. If the dynamic resistance curve is generated by simulation, ensure that the initial conditions of the simulation model are consistent with the actual fault (such as the initial arc length ).

[0100] Specifically, obtain the rate of change of resistance by calculating the first derivative of the dynamic resistance curve at . For discrete data points, approximate the calculation using the forward difference method, and the formula is , where , is the next adjacent time point (such as ); if the dynamic resistance curve is at , , , then .

[0101] Furthermore, the least squares method can be used to fit the curve near (such as to ), and then take the derivative of the fitting function. For example, if the fitting function is , then .

[0102] Furthermore, a metallic short circuit is defined as a fault where the electrodes are in direct contact. At this time, the arc length , the initial resistance value , and the rate of change of resistance is close to 0. For example, a short circuit fault caused by the adhesion of circuit breaker contacts; a mild arc fault is defined as an arc fault with a relatively small arc length , is , is , such as a slight discharge fault in the line; a severe arc fault is defined as an arc fault with a relatively large arc length , , such as a severe arc fault caused by insulator breakdown.

[0103] Further, associating the fault type parameters with the characteristic parameters and constructing a mapping relationship table includes the following steps: First, conduct at least 20 experiments for each fault type, obtain the dynamic resistance curve and extract and , and calculate the statistical mean and standard deviation. For example, in the case of a metallic short circuit experiment, the mean is 0.005 Ω and the standard deviation is 0.001 Ω.

[0104] Next, set the threshold range of the characteristic parameters according to the statistical results. For example, for a metallic short circuit, and , for a mild arc fault, and , for a severe arc fault, and ; Finally, construct a mapping relationship table using a two-dimensional table, where the columns are the fault type parameters and the rows are the ranges of the characteristic parameters.

[0105] Generally speaking, in the prior art, fault types are often identified through a single parameter (such as the steady-state resistance), resulting in misjudgments. In this step, through the mapping of two characteristic parameters, the initial resistance value and the resistance change rate, the misjudgment rate is reduced. For example, for a certain fault with an initial resistance value of 0.05 Ω and a resistance change rate of 15 Ω / s, it is accurately identified as a mild arc fault through the mapping table, while the traditional method may misjudge it as a severe fault based only on the steady-state resistance of 0.1 Ω.

[0106] Furthermore, the mapping relationship table provides a quantitative basis for the rapid identification of fault types. Compared with the traditional waveform analysis method (which takes ≥ 100 ms), the identification time based on the mapping table can be shortened, meeting the requirements of fast protection for medium-voltage DC systems.

[0107] S5. Based on the mapping relationship table and the dynamic resistance curve, simulate a DC fault signal with time-varying resistance parameters that matches the target fault type.

[0108] In the embodiment of the present invention, the step of simulating a DC fault signal with time-varying resistance parameters that matches the target fault type based on the mapping relationship table and the dynamic resistance curve includes: Query the mapping relationship table according to the type identifier of the target fault type to match the corresponding dynamic resistance curve; Convert the matched dynamic resistance curve into a set of time-varying resistance parameters and inject the set of time-varying resistance parameters into the fault point of the equivalent circuit; Establish a circuit differential equation with time-varying resistance; The fourth-order Runge-Kutta method is used to solve the circuit differential equation, and the waveform of the current changing with time is output as the DC fault signal.

[0109] Specifically, the circuit differential equation is as follows: ; where, is the total inductance, is the fault point current at time, is the derivative of the fault point current with respect to time, is the total resistance, is the time-varying resistance, is the DC voltage source, is the time identifier.

[0110] Specifically, the target fault type refers to the specific fault types that need to be simulated in the medium-voltage DC system fault simulation, including metallic short circuit, mild arc fault, and severe arc fault. Each type corresponds to specific electrical characteristics and physical phenomena.

[0111] Specifically, the type identifier is a symbol or code used to uniquely identify the target fault type. For example, the type identifier for "metallic short circuit" is 1, "mild arc fault" is 2, and "severe arc fault" is 3, which facilitates quick retrieval in the mapping relationship table.

[0112] Specifically, the mapping relationship table is a table that associates fault type parameters with dynamic resistance curve characteristic parameters (initial resistance value, resistance change rate). Through this table, the corresponding relationship between the fault type and the dynamic resistance characteristics can be established to achieve the quantitative mapping of the fault type.

[0113] Specifically, the dynamic resistance curve is a curve that describes the change of the arc resistance with time during the fault process of the medium-voltage DC system. The horizontal axis is time, and the vertical axis is the resistance value, which reflects the time-varying characteristics of the arc resistance and is a key parameter for fault simulation.

[0114] Specifically, the time-varying resistance parameter set is a set of a series of resistance values obtained by discretizing the dynamic resistance curve, including resistance parameters at different times, which are used to inject into the equivalent circuit to simulate the dynamic change of the resistance in the actual fault.

[0115] Specifically, the equivalent circuit is a circuit model obtained by abstracting and simplifying the electrical characteristics of the medium-voltage DC system lines and equipment, including components such as total resistance, total inductance, and parallel capacitance, which is used to simulate the electrical response of the system.

[0116] Specifically, the circuit differential equation is a mathematical equation that describes the relationship between variables such as current and voltage changing with time in the medium-voltage DC system under fault conditions. Through this equation, the dynamic response of electrical parameters during the fault process can be solved.

[0117] Specifically, the fourth-order Runge-Kutta method is a high-precision numerical method for solving differential equations. It approximates the true solution of the equation through iterative calculations and is applicable to solving circuit differential equations with time-varying parameters, ensuring the accuracy and stability of the solution.

[0118] Furthermore, querying the mapping relation table according to the type identifier of the target fault type and matching the corresponding dynamic resistance curve includes the following steps: First, receive the type identifier of the target fault type (such as 1, 2, 3). For example, inputting type identifier 2 represents an analog mild arc fault.

[0119] Second, the mapping relation table is stored using a two-dimensional array. The row index is the type identifier, and the column stores the parameter pointers of the corresponding dynamic resistance curve (such as curve number, storage path). For example, type identifier 2 corresponds to the curve file "mild_arc_resistance.csv".

[0120] Next, use a hash table for fast lookup with a time complexity of O(1). For example, determine the storage location of the mapping table through the hash function h(key) = key mod 10 and directly read the corresponding curve parameters.

[0121] Finally, after the query, it is necessary to verify whether the characteristic parameters of the dynamic resistance curve meet the threshold range of this type identifier (for example, the initial resistance value of a mild arc fault should be between 0.01 - 0.1 Ω). When the error exceeds 5%, trigger a re-query.

[0122] Furthermore, converting the matched dynamic resistance curve into a time-varying resistance parameter set and injecting it into the fault point of the equivalent circuit includes the following steps: First, sample the dynamic resistance curve with a time step of 10 μs. For example, obtain 5000 data points within 0 - 50 ms to ensure compliance with the Nyquist sampling theorem (sampling frequency 100 kHz ≥ 2 times the highest frequency component).

[0123] Next, convert the continuous curve into a "time-resistance" two-dimensional array, such as , with units of s and Ω respectively.

[0124] Then, set the fault point of the equivalent circuit as a replaceable resistor element interface to support real-time update of time-varying resistance parameters. For example, use the "time-varying resistance module" in PSCAD / EMTDC simulation software to import the parameter set through a CSV file.

[0125] Furthermore, establish a circuit differential equation with time-varying resistance based on Kirchhoff's voltage law: ; where is the total inductance, calculated from the line distribution parameters (such as ), is the fault point current at the moment of , is the derivative of the fault point current with respect to time, is the total resistance (such as ), is the time-varying resistance, is the DC voltage source, is the time identifier.

[0126] Furthermore, the fourth-order Runge-Kutta method is used to solve the circuit differential equation and output the current waveform.

[0127] Specifically, take the simulation step size , ensuring that the numerical stability condition ( ) is satisfied.

[0128] Furthermore, calculate the intermediate value: ; Furthermore, update the current value according to the intermediate value: ; Specifically, the initial condition , inject the time-varying resistance parameter set at the fault occurrence time .

[0129] Specifically, store the obtained current value in chronological order as a waveform file in the CSV or binary format, including the time stamp (precision 1 μs) and the current value (precision 0.1 A). For example, output at .

[0130] Generally speaking, in the prior art, a fixed resistance or a simple time-varying model is adopted, resulting in a large simulation error of the fault signal. In this step, the dynamic resistance curve is matched through a mapping relation table, and the fourth-order Runge-Kutta method is combined for accurate solution to reduce the simulation error.

[0131] Generally speaking, through parameterized mapping and numerical solution, the rapid generation of fault signals is achieved (simulation time ≤ 100 ms for 50 ms), and the correlation coefficient between the current waveform and the actual fault recording data ≥ 0.98, which can truly reflect the dynamic characteristics of the arc resistance during the fault development process and provide a reliable basis for the protection device test.

[0132] Generally speaking, the type identifier of the target fault type drives the mapping table query. The output dynamic resistance curve forms a time-varying resistance parameter set after discretization and is input as the time-varying term of the circuit differential equation. The total inductance and total resistance required for solving the differential equation are determined by the previous equivalent circuit construction step, and the DC voltage source parameters are set by the system rated value. The finally output current waveform depends on the parameter consistency of all previous steps.

[0133] In several embodiments provided by the present invention, it should be understood that the disclosed method can be implemented in other ways.

[0134] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms.

[0135] The embodiments of the present application can acquire and process relevant data based on artificial intelligence technology. Among them, artificial intelligence is the theory, method and technology that uses a digital computer or a machine controlled by a digital computer to simulate, extend and expand human intelligence, perceive the environment, acquire knowledge and use knowledge to obtain the best results.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for simulating DC faults in a medium-voltage DC system, characterized in that, The method includes: Constructing an equivalent circuit including line distribution parameters; Collecting arc discharge experimental data of the medium voltage DC system under fault simulation conditions, and establishing a mathematical model of arc voltage and arc length; Embedding the mathematical model into the equivalent circuit, and generating a dynamic resistance curve in combination with the arc time constant; Establishing a mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve; Based on the mapping relationship table and the dynamic resistance curve, simulating a DC fault signal with time-varying resistance parameters matching the target fault type, including: Querying the mapping relationship table according to the type identifier of the target fault type to match the corresponding dynamic resistance curve; Converting the matched dynamic resistance curve into a set of time-varying resistance parameters, and injecting the set of time-varying resistance parameters into the fault point of the equivalent circuit; Establishing a circuit differential equation with time-varying resistance; Using the fourth-order Runge-Kutta method to solve the circuit differential equation, and outputting the waveform of current changing with time as the DC fault signal.

2. The DC fault simulation method for the medium-voltage DC system according to claim 1, characterized in that The constructing of the equivalent circuit including line distribution parameters includes: Using line distribution parameters to characterize the line characteristics of the medium voltage DC system, where the line distribution parameters include resistance per unit length, inductance per unit length, and capacitance per unit length; Calculating the total resistance, total inductance, and total capacitance according to the line length and the line distribution parameters; Allocating the total capacitance to the sending end and the receiving end of the equivalent circuit to form parallel capacitors, and connecting the total resistance and the total inductance in series to form an impedance branch; Integrating the parallel capacitors and the impedance branch to form a π-type equivalent circuit.

3. The DC fault simulation method for the medium-voltage DC system according to claim 1, characterized in that, The establishing of the mathematical model of arc voltage and arc length includes: Extracting the corresponding relationship between arc length and arc voltage according to the arc discharge experimental data; Based on the corresponding relationship and linear regression, fitting an arc voltage-arc length function; Verifying the goodness of fit of the arc voltage-arc length function and outputting the mathematical model of arc voltage and arc length.

4. The DC fault simulation method for a medium-voltage DC system according to claim 1, characterized in that, The embedding of the mathematical model into the equivalent circuit and generating a dynamic resistance curve in combination with the arc time constant includes: Setting a physical model for the growth of the arc length with time; Calculating the time-varying arc voltage of the medium voltage DC system based on the mathematical model and the physical model; Converting the time-varying arc voltage into a time-varying resistance according to the fault current value, so as to generate a dynamic resistance curve including the arc time constant.

5. The DC fault simulation method for a medium-voltage DC system according to claim 4, characterized in that The time-varying resistance is: ； Among them, is a time-varying resistance, is the arc voltage-arc length proportionality coefficient, is the initial arc length, is the arc length growth rate of the arc, is the time identifier, is at the fault point current at the moment of, is the arc time constant, is the current of the previous simulation step, is the time interval.

6. The DC fault simulation method for a medium-voltage DC system according to claim 1, characterized in that The establishing of the mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve includes: Extracting the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters; Defining metallic short circuit, mild arc fault, and severe arc fault as fault type parameters; Associating the fault type parameters with the characteristic parameters, and constructing a mapping relationship table from fault type to characteristic parameters based on the parameter combinations obtained after association.

7. The DC fault simulation method for the medium-voltage DC system according to claim 6, wherein The extracting of the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters includes: Selecting the starting point of the dynamic resistance curve as the initial resistance value; Deriving the resistance change rate through the curve slope of the dynamic resistance curve.

8. The DC fault simulation method for a medium-voltage DC system according to claim 7, characterized in that, The resistance change rate is calculated by the forward difference method.

9. The DC fault simulation method for a medium-voltage DC system according to claim 1, wherein The circuit differential equation is: ； Among them, is the total inductance, is the fault point current at the moment, is the derivative of the fault point current with respect to time, is the total resistance, is the time-varying resistance, is the DC voltage source, is the time identifier.

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