A DC fault simulation method for medium voltage DC systems

Abstract

The present invention relates to the technical field of power system fault simulation and discloses a method for simulating DC faults in a medium-voltage DC system. The method comprises: constructing an equivalent circuit containing line distributed parameters to characterize the transmission characteristics of resistance, inductance, and capacitance per unit length; establishing a linear mathematical model of arc voltage and arc length based on arc discharge experimental data; generating a dynamic resistance curve in combination with an arc time growth function; extracting the initial value and rate of change of the dynamic resistance as characteristic parameters; constructing a mapping relationship table between the dynamic resistance and metallic short circuits and mild / severe arc faults; matching the dynamic resistance parameters according to the target fault type; injecting the equivalent circuit and solving the differential equation containing the time-varying resistance to output a high-fidelity DC fault current signal. This method solves the problem that static resistance simulation cannot reproduce the dynamic characteristics of the arc 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 in particular to a method for simulating direct current (DC) faults in a medium-voltage DC system. Background Art

[0002] Current methods for simulating faults in medium-voltage DC systems suffer from insufficient dynamic characteristics. Existing technologies, such as patent CN114282334B, "A Method and Apparatus for Simulating DC Transmission Line Faults Based on PSS / E," utilize a T-type equivalent circuit model. While this model can simulate the distributed parameter characteristics of the line, it relies on fixed resistance values ​​to simulate the fault branch and cannot reflect the time-varying resistance of actual arc faults. This method exhibits significant errors when simulating the current decay characteristics in the early stages of arc development. It is particularly inadequate for the arc reignition phenomenon common in medium-voltage DC systems, resulting in reduced accuracy in fault current waveform simulation.

[0003] Another patent, CN118688593A, "A Method for Constructing Dynamic Morphology and Conductivity Parameters of Arcs in Insulating Oil," proposes a time-varying arc resistance model, but it focuses on the insulating oil dielectric environment and fails to integrate the coupling relationship between line distribution parameters and arc dynamic characteristics. The arc conductivity parameter generation process lacks a mapping mechanism to fault types and requires repeated calibration based on experimental data. This makes it difficult to directly apply to the rapid simulation of multiple fault types in medium-voltage DC systems, reducing its engineering practicality. Summary of the Invention

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

[0005] To achieve the above objectives, the present invention provides a method for simulating DC faults in a medium voltage DC system, comprising:

[0006] Construct an equivalent circuit including line distributed parameters;

[0007] Collect arc discharge experimental data of the medium voltage DC system under fault simulation conditions and establish a mathematical model of arc voltage and arc length;

[0008] Embedding the mathematical model into the equivalent circuit and generating a dynamic resistance curve in combination with an arc time constant;

[0009] Establishing a mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve;

[0010] Based on the mapping relationship table and the dynamic resistance curve, a DC fault signal containing time-varying resistance parameters that matches a target fault type is simulated.

[0011] Optionally, constructing an equivalent circuit including line distributed parameters includes:

[0012] The line characteristics of the medium voltage DC system are characterized by using line distributed parameters, wherein the line distributed parameters include resistance per unit length, inductance per unit length, and capacitance per unit length;

[0013] Calculating total resistance, total inductance, and total capacitance based on line length and the line distribution parameters;

[0014] Distributing the total capacitance to the sending end and the receiving end of the equivalent circuit to form a parallel capacitance, and connecting the total resistance and the total inductance in series to form an impedance branch;

[0015] The parallel capacitor and the impedance branch are integrated to form a π-type equivalent circuit.

[0016] Optionally, establishing a mathematical model of arc voltage and arc length includes:

[0017] Extracting the corresponding relationship between arc length and arc voltage according to the arc discharge experimental data;

[0018] Based on the corresponding relationship and linear regression, an arc voltage-arc length function is fitted;

[0019] The goodness of fit of the arc voltage-arc length function is verified and a mathematical model of the arc voltage and arc length is output.

[0020] Optionally, embedding the mathematical model into the equivalent circuit and generating a dynamic resistance curve in combination with an arc time constant includes:

[0021] Setting a physical model for the arc length to increase over time;

[0022] Calculating the time-varying arc voltage of the medium voltage DC system based on the mathematical model and the physical model;

[0023] The time-varying arc voltage is converted into a time-varying resistance according to the fault current value, thereby generating a dynamic resistance curve including an arc time constant.

[0024] Optionally, the time-varying resistor is: ;

[0025] in, is a time-varying resistor, is the arc voltage-arc length proportional coefficient, is the initial arc length, is the arc length growth rate, is a time stamp, is The fault point current at the moment, is the arc time constant, is the current of the previous simulation step, is the time interval.

[0026] Optionally, establishing a mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve includes:

[0027] extracting the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters;

[0028] Define metallic short circuit, mild arc fault, and severe arc fault as fault type parameters;

[0029] The fault type parameter is associated with the characteristic parameter, and a mapping relationship table from the fault type to the characteristic parameter is constructed based on the parameter combination obtained after the associated parameters.

[0030] Optionally, extracting the initial resistance value and resistance change rate of the dynamic resistance curve as characteristic parameters includes:

[0031] Selecting the starting point of the dynamic resistance curve as the initial resistance value;

[0032] The resistance change rate is derived from the slope of the dynamic resistance curve.

[0033] Optionally, the resistance change rate is calculated using a forward difference method.

[0034] Optionally, simulating a DC fault signal containing time-varying resistance parameters that matches a target fault type based on the mapping relationship table and the dynamic resistance curve includes:

[0035] Querying the mapping relationship table according to the type identifier of the target fault type and matching the corresponding dynamic resistance curve;

[0036] Converting the matched dynamic resistance curve into a time-varying resistance parameter set, and injecting the time-varying resistance parameter set into the fault point of the equivalent circuit;

[0037] Formulate differential equations for circuits involving time-varying resistance;

[0038] The fourth-order Runge-Kutta method is used to solve the circuit differential equation, and a waveform of the current varying with time is output as a DC fault signal.

[0039] Optionally, the circuit differential equation is: ;

[0040] in, is the total inductance, is The fault point current at the moment, is the time derivative of the fault point current, is the total resistance, is a time-varying resistor, is a DC voltage source, It is a time stamp.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] Based on the arc voltage-arc length mathematical model and the time constant-driven physical model, a time-varying resistance curve is generated to truly reflect the nonlinear variation of 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 for transient processes such as arc reignition and current decay.

[0043] By extracting the initial resistance value and change rate of the dynamic resistance curve as characteristic parameters, a mapping table with metallic short circuits and mild / severe arc faults is constructed. This supports parameterized identification and one-click call of fault types, eliminating manual recalibration and significantly improving the simulation efficiency of multiple fault types. It also reserves interfaces for the expansion of new fault types.

[0044] A π-type equivalent circuit is used to integrate line distribution parameters to ensure accurate modeling of long-distance transmission characteristics. The fourth-order Runge-Kutta method is combined to solve differential equations containing time-varying resistance. While ensuring numerical stability, the output current waveform is highly consistent with the actual fault recording data, providing a high-confidence simulation environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A schematic flow chart of a method for simulating DC faults in a medium voltage DC system according to an embodiment of the present invention.

[0046] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0047] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0048] An embodiment of the present application provides a method for simulating a DC fault in a medium-voltage DC system. The execution subject of the method for simulating a DC fault in a medium-voltage DC system includes but is not limited to at least one of the electronic devices such as a server and a terminal that can be configured to execute the method provided in the embodiment of the present application. In other words, the method for simulating a DC fault in a medium-voltage DC system can be executed by software or hardware installed in 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 it can be 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 networks (CDNs), and big data and artificial intelligence platforms.

[0049] Reference Figure 1 FIG. 1 is a flow chart of a method for simulating a DC fault in a medium voltage DC system according to an embodiment of the present invention. In this embodiment, the method for simulating a DC fault in a medium voltage DC system includes:

[0050] S1. Construct an equivalent circuit including the line distributed parameters.

[0051] In an embodiment of the present invention, the step of constructing an equivalent circuit including line distributed parameters includes:

[0052] The line characteristics of the medium voltage DC system are characterized by using line distributed parameters, wherein the line distributed parameters include resistance per unit length, inductance per unit length, and capacitance per unit length;

[0053] Calculating total resistance, total inductance, and total capacitance based on line length and the line distribution parameters;

[0054] Distributing the total capacitance to the sending end and the receiving end of the equivalent circuit to form a parallel capacitance, and connecting the total resistance and the total inductance in series to form an impedance branch;

[0055] The parallel capacitor and the impedance branch are integrated to form a π-type equivalent circuit.

[0056] Specifically, line distributed parameters characterize the electrical characteristics per unit length of a medium-voltage DC transmission line. These parameters include resistance per unit length, inductance per unit length, and capacitance per unit length. These parameters describe the distributed electrical characteristics of a line during power transmission. For example, resistance per unit length reflects the line's resistive losses per kilometer, inductance per unit length reflects the magnetic field energy storage characteristics per kilometer, and capacitance per unit length indicates the line's electric field coupling capability per kilometer.

[0057] Specifically, resistance per unit length is a component of the line distributed parameters, and refers to the resistance value per unit length (e.g. per kilometer) of the transmission line. Its unit is usually ohm per kilometer (Ω / km), and is used to measure the conductive loss characteristics of the line itself.

[0058] Specifically, inductance per unit length is a type of line distributed parameter, which refers to the inductance value per unit length of the transmission line. The unit is generally Henry per kilometer (H / km), which is used to characterize the magnetic field effect and energy storage capacity generated by the line when transmitting current.

[0059] Specifically, capacitance per unit length is a line distribution parameter, which refers to the capacitance value per unit length of the transmission line. The unit is usually farad per kilometer (F / km), which is used to describe the degree of electric field coupling between line phases or relative to the ground and the charge storage capacity.

[0060] In detail, the total resistance is the total resistance value of the transmission line calculated based on the line length and the resistance per unit length. It is calculated as the product of the resistance per unit length and the line length. The unit is ohm (Ω), which represents the total resistance loss of the entire line.

[0061] In detail, the total inductance is the total inductance of the transmission line calculated from the line length and the inductance per unit length. It is obtained by multiplying the inductance per unit length by the line length. The unit is Henry (H) and is used to represent the sum of the magnetic field effects of the entire line.

[0062] In detail, the total capacitance is the total capacitance value of the transmission line calculated based on the line length and the capacitance per unit length, that is, the product of the capacitance per unit length and the line length. The unit is farad (F), which reflects the total electric field coupling capability of the entire line.

[0063] In detail, the shunt capacitor is a capacitive element formed by distributing the total capacitance to the sending and receiving ends of the equivalent circuit. It is connected in parallel with the impedance branch and is used to simulate the impact of the distributed capacitance of the transmission line on the electrical characteristics of the system.

[0064] In detail, the impedance branch is a circuit branch formed by the total resistance and total inductance in series, where 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.

[0065] In detail, the π-type equivalent circuit is a circuit model used to simulate the distributed parameter characteristics of transmission lines. Its structure is in the shape of the Greek letter "π", consisting of capacitors connected in parallel at both ends and resistor and inductor branches connected in series in the middle. It can effectively reflect the distributed parameter effects of medium-voltage DC system lines.

[0066] Furthermore, characterizing the line characteristics of the medium voltage DC system using line distributed parameters includes the following steps:

[0067] First, obtain the resistance per unit length of the circuit through circuit design documents or experimental measurements , inductance per unit length and capacitance per unit length For example, from the design data of medium voltage DC line .

[0068] Next, the line length of the medium voltage DC system is usually long (such as more than 10km), and its electrical characteristics need to be described by a distributed parameter model. The distributed parameter model regards the line as consisting of countless tiny units, each of which contains , which can more accurately reflect the voltage and current distribution and traveling wave propagation characteristics along the line. Compared with the lumped parameter model (which uses only one resistor, inductor, and capacitor to represent the line), it has smaller errors when simulating long-distance lines.

[0069] Finally, the distributed parameters are modeled and processed using circuit simulation software (such as PSCAD / EMTDC) or mathematical calculation tools (such as MATLAB), and the distributed parameter model of the circuit is generated by inputting the measured or designed parameters.

[0070] Furthermore, calculating the total resistance, total inductance, and total capacitance based on the line length and line distribution parameters includes the following steps:

[0071] First, when the line length When , calculate the total resistance, total inductance and total capacitance according to the following formula:

[0072] Total resistance: ,in, is the line length (unit: km), then ;

[0073] Total inductance: ,but ;

[0074] Total capacitance: ,but .

[0075] Specifically, based on the principles of calculus, the circuit is considered to be a series connection of countless unit-length units. The resistance, inductance, and capacitance of each unit are accumulated to obtain the total parameters. This calculation method conforms to the basic principles of electromagnetics, such as Ohm's law (resistors in series) and the series / parallel characteristics of inductors and capacitors (here, series accumulation).

[0076] Furthermore, the accuracy of the calculations is verified by comparing actual line short-circuit test data (such as short-circuit current and voltage decay characteristics) with theoretical simulation results of the calculated total parameters. If the error exceeds 5%, the parameter acquisition or calculation process needs to be re-verified.

[0077] Specifically, distributing the total capacitance to the sending end and the receiving end of the equivalent circuit to form parallel capacitance, and connecting the total resistance and the total inductance in series to form an impedance branch includes the following steps:

[0078] First, the total capacitance It is evenly divided into two parts, namely the parallel capacitor at the sending end and the receiving end parallel capacitor For example, the total capacitance hour, ;

[0079] This distribution method is derived from the classic structure of the π-type equivalent circuit. By concentrating the distributed capacitance into parallel capacitance at both ends, it can approximately simulate the electric field effect of the distributed capacitance along the line.

[0080] Next, the total resistance and total inductance connected in series to form an impedance branch in the middle. For example, and In series, this branch reflects the resistance loss and inductance energy storage characteristics of the line, and its impedance value ( is the angular frequency), which is used to describe the resistance of the line to the current.

[0081] Finally, use circuit drawing software (such as Eagle, OrCAD) to draw the circuit topology, ensuring that the sending end is connected in parallel with the capacitor. , impedance branch , receiving end parallel capacitance Connect in sequence to form a π-shaped structure.

[0082] Furthermore, integrating the parallel capacitor and the impedance branch to form a π-type equivalent circuit includes the following steps:

[0083] First, connect the capacitor in parallel to the sending end Connected to the input end of the equivalent circuit, the receiving end is connected in parallel with the capacitor Connected to the output end, with an impedance branch in the middle Connect in series to form " shape topology. For example, the input node connection One end of the impedance branch and one end of the The other end of the impedance branch is connected to the ground. One end, The other end is grounded and serves as the output node.

[0084] Next, by inputting a step voltage signal (such as 10kV DC voltage), the output voltage and current response of the equivalent circuit are simulated and calculated, and compared 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 equivalent circuit should be range to verify the accuracy of the model.

[0085] Finally, if the simulation results deviate significantly from the actual data, the distribution ratio of the total capacitance can be adjusted (e.g., non-even distribution) or additional distributed parameter correction terms (e.g., series capacitance) can be introduced until the electrical characteristics of the equivalent circuit are consistent with the actual circuit.

[0086] In general, this step addresses the simulation errors caused by the use of lumped parameter models in existing technologies by constructing a π-type equivalent circuit that incorporates the distributed parameters of the line. Lumped parameter models ignore the distributed characteristics of the line, leading to significant simulation errors in fault current and voltage waveforms in medium-voltage DC systems, especially long-distance lines. Medium-voltage DC systems have high voltage levels (1kV-35kV) and long lines, resulting in significant distributed parameter effects (such as uneven current distribution due to capacitive coupling). The π-type equivalent circuit, through its combination of parallel capacitors and impedance branches, accurately simulates the traveling wave propagation velocity and wave impedance of the line.

[0087] S2. Collect arc discharge experimental data of the medium voltage DC system under fault simulation conditions and establish a mathematical model of arc voltage and arc length.

[0088] In an embodiment of the present invention, establishing a mathematical model of arc voltage and arc length includes:

[0089] Extracting the corresponding relationship between arc length and arc voltage according to the arc discharge experimental data;

[0090] The arc voltage-arc length function is fitted based on the corresponding relationship and linear regression.

[0091] In detail, the arc voltage-arc length function may be expressed as: ;

[0092] in, is the arc voltage, is the arc voltage-arc length proportional coefficient, is the arc length;

[0093] The goodness of fit of the arc voltage-arc length function is verified and a mathematical model of the arc voltage and arc length is output.

[0094] Specifically, the medium voltage DC system refers to a DC power transmission system with a voltage level between 1kV and 35kV. It 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.

[0095] Specifically, fault simulation conditions refer to medium-voltage DC system fault scenarios artificially set up in a laboratory environment, including metallic short circuits, arc faults, and other types, which are used to reproduce the fault conditions in actual operation to obtain experimental data.

[0096] In detail, 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 fault simulation conditions.

[0097] In detail, arc length refers to the physical distance between the positive and negative electrodes during arc discharge. Its unit is meter (m). It is a key parameter to characterize the arc morphology and directly affects the arc voltage and resistance characteristics.

[0098] Specifically, arc voltage refers to the potential difference between the two ends of the arc during the arc discharge process. Its unit is volt (V). Its value is related to factors such as arc length and arc current, and reflects the energy loss characteristics of the arc.

[0099] In detail, linear regression fitting is a statistical analysis method used to determine the linear functional relationship between two variables. The experimental data are fitted by the least squares method to obtain the best linear fitting equation.

[0100] In detail, the arc voltage-arc length function is a mathematical expression that describes the linear relationship between arc voltage and arc length. This function is used to characterize the basic electrical characteristics of arc discharge.

[0101] In detail, goodness of fit is an indicator used to evaluate how well a regression model fits the experimental data. It is often represented by the coefficient of determination R². The closer the R² value is to 1, the more accurately the model fits the data.

[0102] Furthermore, collecting arc discharge experimental data of the medium voltage DC system under fault simulation conditions includes the following steps:

[0103] First, build an experimental platform consisting of a medium-voltage DC power supply (e.g., a 10kV DC power supply), an arc generator (a discharge device with adjustable electrode spacing), a fault current injection circuit (including a current-limiting resistor and switch), and a data acquisition system (an oscilloscope or DAQ device with a sampling frequency ≥ 100kHz). For example, the power supply can be a programmable DC power supply, and the arc generator's electrodes can be made of copper alloy with an adjustable spacing between 0.001 and 0.1m.

[0104] Next, high-voltage probes (range 0-20kV, accuracy ±1%) are connected in parallel at both ends of the arc to measure the arc voltage, a laser rangefinder (resolution 10μm) is used to monitor the arc length in real time, and a Hall current sensor (range 0-5kA, accuracy ±0.5%) is connected in series with the fault circuit to collect the fault current.

[0105] Secondly, three types of arc faults were set up: metallic short circuit (arc length of 0m), mild arc fault (arc length of 0.01-0.05m), and severe arc fault (arc length of 0.05-0.1m). The experiment was repeated 10 times for each type to eliminate accidental errors.

[0106] Then, maintain the laboratory temperature at 25±2°C and humidity at 50±5% to prevent environmental factors from interfering with the arc characteristics. For example, control the environmental parameters using a constant temperature and humidity chamber and preheat the equipment for 30 minutes before each experiment.

[0107] Finally, a fault current threshold trigger (e.g., 100A) is used. 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 100kHz. The recording time is ≥50ms (covering the entire arc development process). The data segment of the stable arc burning stage (e.g., arc length fluctuation ≤5%) is manually marked, and the mean of the arc length and voltage in this segment is extracted as the valid data point. At least 50 sets of valid data are obtained for each fault type.

[0108] Furthermore, establishing a mathematical model of arc voltage and arc length includes the following steps:

[0109] First, the arc length of the stable burning stage of the arc under the same fault type is screened from the arc discharge experimental data. Corresponding arc voltage For example, a minor arc fault ( ), record the corresponding arc voltages of 20V, 20.5V, 19.8V and other 10 groups of data; organize the data points into a two-dimensional table, listing arc length (unit: m) and voltage (unit: V), use Excel or MATLAB software to draw a visual scatter plot, and preliminarily judge the linear correlation.

[0110] 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 by matrix operation, the formula is: ,in, is the arc length data vector, is the voltage data vector

[0111] In general, existing technologies often use fixed arc resistance models, which fail to account for the dynamic variation of arc voltage with arc length, leading to large fault simulation errors. This step reduces simulation errors by using a linear model driven by experimental data. For example, when the arc length increases from 0.01m to 0.05m, the voltage calculated by the fixed resistance model remains 10V, while the actual voltage increases from 10V to 50V.

[0112] In general, the arc voltage-arc length model accurately reflects the physical characteristics of the arc, making the electrical characteristics of the medium voltage DC system fault simulation (such as fault current waveform and protection device operation time) more consistent with actual operating data.

[0113] S3. Embed the mathematical model into the equivalent circuit and generate a dynamic resistance curve in combination with the arc time constant.

[0114] In an embodiment of the present invention, embedding the mathematical model into the equivalent circuit and generating a dynamic resistance curve in combination with an arc time constant includes:

[0115] Setting a physical model for the arc length to increase over time;

[0116] Calculating the time-varying arc voltage of the medium voltage DC system based on the mathematical model and the physical model;

[0117] The time-varying arc voltage is converted into a time-varying resistance according to the fault current value, thereby generating a dynamic resistance curve including an arc time constant.

[0118] In detail, the time-varying resistor is:

[0119] ;

[0120] in, is a time-varying resistor, is the arc voltage-arc length proportional coefficient, is the initial arc length, is the arc length growth rate, is a time stamp, is The fault point current at the moment, is the arc time constant, is the current of the previous simulation step, is the time interval.

[0121] In detail, the expression of the physical model can be:

[0122] ;

[0123] in, is The arc length at the time, is the initial arc length, is the arc length growth rate, is a time stamp, is the arc time constant.

[0124] In detail, arc length refers to the physical distance between the positive and negative electrodes during the arc discharge process. Its unit is meter (m). It is a key parameter to characterize the arc morphology and reflects the development process of the arc as it changes over time.

[0125] In detail, the initial arc length is the arc length at the moment of fault occurrence, which is represented by the symbol It is expressed in meters (m). Its value is determined by the fault type and initial conditions and is used to set the initial state of the physical model.

[0126] Specifically, the arc resistance is determined by the current at the previous moment, which is consistent with the inertial characteristics 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 current value at the previous moment is used to calculate the resistance at the current moment.

[0127] In detail, the arc length growth rate refers to the rate of change of the arc length over time, which is represented by the symbol It is expressed in meters per second (m / s) and reflects how fast the arc expands during a fault, which is determined by the physical properties of the arc and environmental conditions.

[0128] In detail, the arc time constant is a parameter that characterizes the time characteristics of the arc length growth process, and is represented by the symbol It is expressed in seconds (s) and is used to describe the speed at which the arc length grows to a stable state, reflecting the dynamic characteristics of the arc.

[0129] In detail, the time-varying arc voltage refers to the potential difference between the two ends of the arc that changes with time during the fault process. The unit is volt (V). Its value is determined by the arc length and the arc voltage-arc length proportional coefficient, reflecting the dynamic changes of arc energy loss.

[0130] Specifically, time-varying resistance refers to the resistance value that changes with time during a fault process. The unit is ohm (Ω), which is calculated from the time-varying arc voltage and fault current and is used to characterize the dynamic characteristics of the arc resistance.

[0131] In detail, the dynamic resistance curve is a curve that describes the change of time-varying resistance over time. It is used to intuitively display the dynamic change law of arc resistance during the fault process and provide key parameters for medium voltage DC system fault simulation.

[0132] Furthermore, during the arc fault process, the arc length increases exponentially with time. This model is based on arc physics theory and experimental data fitting. For example, when an arc occurs, the arc length increases from the initial value to Start, over time It gradually increases and eventually tends to a stable value. Its mathematical expression is as follows:

[0133] ;

[0134] Furthermore, the initial arc length It is set according to the fault type, such as metallic short circuit , mild arc fault , severe arc fault ; Arc length growth rate It is measured by arc discharge experiment. For example, in 10kV medium voltage DC system, the arc fault ; Arc time constant It is determined by the arc time constant experiment and reflects the arc heat diffusion and cooling characteristics. .

[0135] In detail, the model output is compared with the arc development process captured by a high-speed camera, e.g. When , the measured value is ,error , in line with engineering requirements.

[0136] Furthermore, calculating the time-varying arc voltage based on the mathematical model and the physical model includes the following steps:

[0137] First, call the established arc voltage-arc length function ,in is the arc voltage-arc length ratio coefficient (e.g. V / m); Then, the physical model Substituting into the arc voltage function, we get the expression of time-varying arc voltage: .

[0138] For example, when hour, , .

[0139] Furthermore, converting the time-varying arc voltage into the time-varying resistance according to the fault current value includes the following steps:

[0140] First, according to Ohm's law , the time-varying resistance is ,in is the fault point current (unit: A), calculated from the equivalent circuit;

[0141] Then, the fault current waveform is obtained by solving the differential equation containing the equivalent circuit. For example, in a 10kV system, when the metallic short circuit , when arc fault occurs Changes over time;

[0142] Finally, substituting the time-varying arc voltage and fault current, we obtain the expression for the time-varying resistance:

[0143] .

[0144] For example, when hour, .

[0145] Furthermore, generating a dynamic resistance curve includes: As the horizontal axis (step size 0.001s), calculate the ,For example arrive , a total of 51 data points; and use MATLAB or Python to plot Curve, the horizontal axis is time (ms), the vertical axis is resistance ( ), marking key parameters .

[0146] Furthermore, the curve is compared with the actual fault recording data, e.g. When the model curve shows the resistance , measured value ,error , meeting engineering precision requirements.

[0147] In general, existing technologies often use fixed resistance models (e.g., 1Ω) without considering the dynamic changes in arc resistance, resulting in large fault simulation errors. This step reduces simulation errors by introducing an arc time constant and a dynamic resistance curve. For example, when simulating a 0.05m arc length arc fault in a 10kV system, the fixed resistance model calculates a fault current of 10kA, while the actual measurement is 8.3kA, an error of 20.5%. The dynamic resistance model, on the other hand, calculates a value of 8.5kA, an error of 2.4%.

[0148] In general, the dynamic resistance curve accurately reflects the time-varying characteristics of arc resistance, making the electrical parameters of medium voltage DC system fault simulation (such as fault current waveform and protection operation time) more consistent with actual operating data.

[0149] S4. Establish a mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve.

[0150] In an embodiment of the present invention, the step of establishing a mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve includes:

[0151] extracting the initial resistance value and the resistance change rate of the dynamic resistance curve as characteristic parameters;

[0152] Define metallic short circuit, mild arc fault, and severe arc fault as fault type parameters;

[0153] The fault type parameter is associated with the characteristic parameter, and a mapping relationship table from the fault type to the characteristic parameter is constructed based on the parameter combination obtained after the associated parameters.

[0154] In detail, extracting the initial resistance value and resistance change rate of the dynamic resistance curve as characteristic parameters includes:

[0155] Selecting the starting point of the dynamic resistance curve as the initial resistance value;

[0156] The resistance change rate is derived from the slope of the dynamic resistance curve.

[0157] In detail, the expression of the characteristic parameter can be as follows:

[0158] ;

[0159] in, is the characteristic parameter, is the initial resistance value, is the resistance change rate, is a time-varying resistor, It is a time stamp.

[0160] In detail, the dynamic resistance curve is a curve that describes the change of arc resistance over time during a medium voltage DC system fault process. Its horizontal axis is time and the vertical axis is resistance value. It reflects the time-varying characteristics of arc resistance and is the key basis for fault type identification.

[0161] Specifically, the initial resistance value is the dynamic resistance curve at the starting point of time The resistance value is represented by the symbol It is expressed in ohms (Ω) and is used to characterize the arc resistance state at the moment a fault occurs. The initial resistance values ​​of different fault types vary significantly.

[0162] In detail, the resistance change rate is the dynamic resistance curve in The slope at It is expressed in ohms per second (Ω / s), which reflects the speed of change of arc resistance at the initial stage of fault and reflects the dynamic characteristics of arc development.

[0163] Specifically, the fault type parameter is a classification identifier used to characterize different fault types in the medium voltage DC system, including metallic short circuit, mild arc fault, and severe arc fault. Each type corresponds to specific physical phenomena and electrical characteristics.

[0164] In detail, the mapping relationship table is to map the fault type parameters with the dynamic resistance curve characteristic parameters (initial resistance value , resistance change rate The associated table is used to establish the corresponding relationship between fault types and characteristic parameters, which facilitates the rapid identification and simulation of fault types.

[0165] Furthermore, extracting the initial resistance value and resistance change rate of the dynamic resistance curve includes the following steps:

[0166] First, directly select the dynamic resistance curve in The resistance value at this moment is taken as the initial resistance value For example, a dynamic resistance curve is When the resistance is 0.01Ω, =0.01Ω; verify the accuracy of the extracted value by comparing it with the actual resistance data at the moment of fault occurrence (such as the initial resistance recorded by an oscilloscope), and the error must be ≤1%. If the dynamic resistance curve is generated by simulation, it is necessary to ensure that the initial conditions of the simulation model are consistent with the actual fault (such as the initial arc length ).

[0167] In detail, by calculating the dynamic resistance curve in The first derivative at is used to obtain the resistance change rate For discrete data points, the forward difference method is used for approximate calculation, and the formula is ,in , For the next time point (such as ); If the dynamic resistance curve is hour, hour, ,but .

[0168] Furthermore, the least squares method can be used to fit Nearby curves (such as arrive ), and then derive the fitting function. For example, the fitting function is ,but .

[0169] Furthermore, a metallic short circuit is defined as a fault in which the electrodes are in direct contact, and the arc length is , initial resistance value , resistance change rate Close to 0. For example, a short circuit fault caused by contact adhesion of a circuit breaker; a mild arc fault is defined as a small arc length. Arc fault, for , for , such as a minor discharge fault on the line; a severe arc fault is defined as a long arc length Arc fault, , such as severe arc faults caused by insulator breakdown.

[0170] Furthermore, associating the fault type parameters with the characteristic parameters and constructing a mapping relationship table includes the following steps:

[0171] First, at least 20 experiments were conducted for each fault type to obtain the dynamic resistance curve and extract and , calculate the statistical mean and standard deviation. For example, in the metallic short circuit experiment, The mean is 0.005Ω and the standard deviation is 0.001Ω.

[0172] Then, according to the statistical results, the threshold range of the characteristic parameters is set, such as the metallic short circuit and , mild arc fault and , severe arc fault and ;

[0173] Finally, a two-dimensional table is used to construct a mapping relationship table, in which the columns are fault type parameters and behavior characteristic parameter ranges.

[0174] In general, existing technologies often use a single parameter (such as steady-state resistance) to identify fault types, leading to misjudgments. This step reduces misjudgment by mapping the dual characteristic parameters of initial resistance value and resistance change rate. For example, a fault with an initial resistance value of 0.05Ω and a resistance change rate of 15Ω / s can be accurately identified as a mild arc fault using the mapping table. However, traditional methods based solely on a steady-state resistance of 0.1Ω might misjudge it as a severe fault.

[0175] Furthermore, the mapping relationship table provides a quantitative basis for the rapid identification of fault types. Compared with the traditional waveform analysis method (taking ≥100ms), the identification time based on the mapping table can be shortened, meeting the needs of rapid protection of the medium-voltage DC system.

[0176] S5. Based on the mapping relationship table and the dynamic resistance curve, simulate a DC fault signal containing time-varying resistance parameters that matches the target fault type.

[0177] In an embodiment of the present invention, simulating a DC fault signal containing time-varying resistance parameters that matches a target fault type based on the mapping relationship table and the dynamic resistance curve includes:

[0178] Querying the mapping relationship table according to the type identifier of the target fault type and matching the corresponding dynamic resistance curve;

[0179] Converting the matched dynamic resistance curve into a time-varying resistance parameter set, and injecting the time-varying resistance parameter set into the fault point of the equivalent circuit;

[0180] Formulate differential equations for circuits involving time-varying resistance;

[0181] The fourth-order Runge-Kutta method is used to solve the circuit differential equation, and a waveform of the current varying with time is output as a DC fault signal.

[0182] In detail, the circuit differential equation is:

[0183] ;

[0184] in, is the total inductance, is The fault point current at the moment, is the time derivative of the fault point current, is the total resistance, is a time-varying resistor, is a DC voltage source, It is a time stamp.

[0185] Specifically, the target fault type refers to the specific fault type that needs 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.

[0186] In detail, the type identifier is a symbol or code used to uniquely identify the target fault type, for example, the type identifier of "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.

[0187] In detail, 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 fault type and dynamic resistance characteristics can be established to achieve quantitative mapping of fault type.

[0188] In detail, the dynamic resistance curve is a curve that describes the change of arc resistance with time during the fault process of the medium voltage DC system. The horizontal axis is time and the vertical axis is resistance value. It reflects the time-varying characteristics of arc resistance and is a key parameter for fault simulation.

[0189] In detail, the time-varying resistance parameter set is a set of resistance values ​​obtained by discretizing the dynamic resistance curve, which contains resistance parameters at different times and is used to inject into the equivalent circuit to simulate the dynamic change of resistance in actual faults.

[0190] In detail, the equivalent circuit is a circuit model that abstracts and simplifies 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.

[0191] In detail, the circuit differential equation is a mathematical equation that describes the relationship between the current, voltage and other variables of the medium voltage DC system under fault conditions and time. The equation can be used to solve the dynamic response of electrical parameters during the fault process.

[0192] In detail, the fourth-order Runge-Kutta method is a high-precision method for numerically solving differential equations. It approximates the true solution of the equation through iterative calculation. It is suitable for solving circuit differential equations with time-varying parameters, ensuring solution accuracy and stability.

[0193] Furthermore, querying the mapping relationship table according to the type identifier of the target fault type and matching the corresponding dynamic resistance curve includes the following steps:

[0194] First, a type identifier (such as 1, 2, or 3) of a target fault type is received. For example, inputting type identifier 2 indicates simulating a mild arc fault.

[0195] Secondly, the mapping table is stored in a two-dimensional array, with the row index being the type identifier and the column storing the parameter pointers corresponding to the dynamic resistance curve (such as the curve number and storage path). For example, type identifier 2 corresponds to the curve file "mild_arc_resistance.csv".

[0196] Next, a hash table is used for fast lookup with a time complexity of O(1). For example, the mapping table storage location is determined by the hash function h(key)=keymod10, and the corresponding curve parameters are directly read.

[0197] Finally, after the query, it is necessary to verify whether the characteristic parameters of the dynamic resistance curve meet the threshold range of the type identification (for example, the initial resistance value of a mild arc fault should be between 0.01-0.1Ω). If the error exceeds 5%, a re-query is triggered.

[0198] 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:

[0199] First, the dynamic resistance curve is sampled with a time step of 10 μs, for example, 5000 data points are obtained within 0-50 ms to ensure that the Nyquist sampling theorem is met (sampling frequency 100 kHz ≥ 2 times the highest frequency component).

[0200] Next, the continuous curve is converted into a two-dimensional "time-resistance" array, such as , with units of s and Ω respectively.

[0201] The fault point of the equivalent circuit is then set as a replaceable resistor element interface, which supports real-time updating of time-varying resistor parameters. For example, the "Time-Varying Resistor Module" in PSCAD / EMTDC simulation software can be used to import parameter sets via a CSV file.

[0202] Furthermore, based on Kirchhoff's voltage law, the circuit differential equation containing time-varying resistance is established:

[0203] ;

[0204] in, is the total inductance, which is calculated from the line distributed parameters (such as ), is The fault point current at the moment, is the time derivative of the fault point current, is the total resistance (e.g. ), is a time-varying resistor, is a DC voltage source, It is a time stamp.

[0205] Furthermore, the fourth-order Runge-Kutta method is used to solve the circuit differential equation and output the current waveform.

[0206] In detail, take the simulation step size , ensuring that the numerical stability conditions are met ( ).

[0207] Furthermore, the intermediate values ​​are calculated:

[0208] ;

[0209] Furthermore, the current value is updated according to the intermediate value:

[0210] ;

[0211] In detail, the initial conditions , when the fault occurs The time-varying resistance parameter set is injected at the same time.

[0212] In detail, the current value obtained by solving Stored in chronological order as waveform files in CSV or binary format, containing timestamps (accuracy 1μs) and current values ​​(accuracy 0.1A), for example Time output .

[0213] In general, existing technologies use fixed resistance or simple time-varying models, which leads to large errors in fault signal simulation. This step matches the dynamic resistance curve through a mapping table and combines it with the fourth-order Runge-Kutta method for precise solution, reducing simulation errors.

[0214] In general, through parameterized mapping and numerical solution, the fault signal can be quickly generated (50ms simulation time ≤100ms), and the correlation coefficient between the current waveform and the actual fault recording data is ≥0.98, which can truly reflect the dynamic characteristics of the arc resistance during the fault development process and provide a reliable basis for protection device testing.

[0215] In general, the type identification of the target fault type drives the mapping table query. The output dynamic resistance curve is discretized to form a time-varying resistance parameter set, which serves as the time-varying input of the circuit differential equation. The total inductance and total resistance required to solve the differential equation are determined by the previous equivalent circuit construction step, and the DC voltage source parameters are set by the system rated values. The final output current waveform depends on the parameter consistency of all previous steps.

[0216] In the several embodiments provided by the present invention, it should be understood that the disclosed methods can be implemented in other ways.

[0217] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0218] The embodiments of the present application can acquire and process relevant data based on artificial intelligence technology. Artificial intelligence is the theory, method and technology of using digital computers or machines controlled by digital computers to simulate, extend and expand human intelligence, perceive the environment, acquire knowledge and use knowledge to achieve optimal results.

[0219] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents 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 comprises: Constructing a π-type equivalent circuit including line distributed parameters, including: using line distributed parameters to characterize the line characteristics of the medium voltage DC system, wherein the line distributed parameters include unit length resistance, unit length inductance and unit length capacitance; calculating the total resistance, total inductance and total capacitance according to the line length and the line distributed parameters; and converting the total capacitance into Divided into two parts, the sending end parallel capacitor and the receiving end parallel capacitor , connecting the total resistance and the total inductance in series to form an impedance branch, and integrating the parallel capacitance and the impedance branch to form a π-type equivalent circuit; Collect arc discharge experimental data from a medium voltage DC system under fault simulation conditions. From this data, screen out discrete data points of the arc length and corresponding arc voltage during the stable burning phase under the same fault type, and establish a mathematical model of arc voltage and arc length. The mathematical model is embedded in the equivalent circuit and combined with the arc time constant to generate a dynamic resistance curve. The calculation formula for the time-varying resistance is: ； in, is a time-varying resistor, is the arc voltage-arc length proportional coefficient, is the initial arc length, is the arc length growth rate, is a time stamp, is The fault point current at the moment, is the arc time constant, is the current of the previous simulation step, is a time interval, wherein the initial arc length is set according to the fault type, and the fault type includes: metallic short circuit, mild arc fault, and severe arc fault; Establishing a mapping relationship table between fault type parameters and characteristic parameters in the dynamic resistance curve, including: extracting the initial resistance value and resistance change rate of the dynamic resistance curve as characteristic parameters, and calculating the resistance change rate by forward difference method; Based on the mapping relationship table and the dynamic resistance curve, simulating a DC fault signal containing time-varying resistance parameters that matches a target fault type includes: Querying the mapping relationship table according to the type identifier of the target fault type and matching the corresponding dynamic resistance curve; Converting the matched dynamic resistance curve into a time-varying resistance parameter set, and injecting the time-varying resistance parameter set into the fault point of the equivalent circuit; Formulate differential equations for circuits involving time-varying resistance; The fourth-order Runge-Kutta method is used to solve the circuit differential equation. The simulation step size is set to meet the numerical stability condition, and the waveform of the current changing with time is output as the DC fault signal. The numerical stability condition of the simulation step size is ,in, is the simulation step size, is the total inductance, is the total resistance, It is a time-varying resistor.

2. The DC fault simulation method for a medium voltage DC system according to claim 1, characterized in that: The method of establishing a 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, an arc voltage-arc length function is fitted; The goodness of fit of the arc voltage-arc length function is verified and a mathematical model of the arc voltage and arc length is output.

3. 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 an arc time constant includes: Setting a physical model for the arc length to increase over time; Calculating the time-varying arc voltage of the medium voltage DC system based on the mathematical model and the physical model; The time-varying arc voltage is converted into a time-varying resistance according to the fault current value, thereby generating a dynamic resistance curve including an arc time constant.

4. The DC fault simulation method for a medium voltage DC system according to claim 1, characterized in that: The establishing of a 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; Define metallic short circuit, mild arc fault, and severe arc fault as fault type parameters; The fault type parameter is associated with the characteristic parameter, and a mapping relationship table from the fault type to the characteristic parameter is constructed based on the parameter combination obtained after the associated parameters.

5. The DC fault simulation method for a medium voltage DC system according to claim 4, characterized in that: The extracting 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; The resistance change rate is derived from the slope of the dynamic resistance curve.

6. The method for simulating DC faults in a medium voltage DC system according to claim 1, wherein: The circuit differential equation is: ； in, is the total inductance, is The fault point current at the moment, is the time derivative of the fault point current, is the total resistance, is a time-varying resistor, is a DC voltage source, It is a time stamp.

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