Modeling and simulation method of 3,5th harmonic current excited by series arc resistance inter-turn short circuit

Abstract

The application discloses a modeling simulation method for exciting 3, 5 harmonic currents based on series resistance arc inter-turn short circuit, and is characterized by comprising the following steps: according to the current arc process and circuit principle during the series resistance arc inter-turn short circuit, a digital circuit simulation model is established; the digital circuit simulation model is used to output analog electrical quantities, according to the fault development process, in the digital circuit simulation model, circuit equivalent simulation is carried out according to proportional ladder units or non-equal proportional ladder unit combination, dynamic simulation of the series resistance arc inter-turn short circuit and display and restoration of the electrical characteristic change are completed. The dynamic real-time waveform data of the calculation simulation are used to verify the monitoring principle and function of the related fault monitoring and protection device, and test and check the reliability and accuracy of the monitoring technology and the device, so that the principle and performance simulation test of the inter-turn short circuit fault monitoring or protection device can be carried out in a laboratory environment.

Description

Technical Field

[0001] This invention relates to the field of power fault simulation technology, and in particular to a modeling and simulation method based on the generation of 3rd and 5th harmonic currents by inter-turn short circuits with series reactance arcing. Background Technology

[0002] In reactive power compensation systems of power transmission and distribution networks, parallel compensation capacitor banks (hereinafter referred to as parallel capacitors) that can be switched on and off are used. 1000kV UHV substations typically use parallel capacitors of approximately 180Mvar to 240Mvar at a voltage level of 110kV in the third winding of the transformer. 500kV EHV substations typically use parallel capacitors of approximately 45Mvar to 60Mvar at a voltage level of 66kV or 35kV in the third winding of the transformer. 220kV and 110kV substations also configure appropriate capacity parallel capacitors in the low-voltage winding of the transformer according to the principle of local compensation to compensate for reactive power flow, improve the power factor, and control and stabilize voltage levels. Typically, in standardized designs, one group of parallel capacitors is configured with series reactors with a series reactance rate of 12%, while the other group is configured with series current-limiting reactors with a series reactance rate of 5-6%. Current-limiting series reactors are used to limit inrush current during frequent switching. A series reactor with a 12% series reactance ratio is configured in a parallel-connected group. Simultaneously, it also suppresses the amplification of the third harmonic of the power system by parallel-connected groups with 5-6% series reactance ratios. Therefore, in the switching sequence, the 12% series reactance ratio parallel-connected group is always switched on first and switched off last to prevent the amplification of the third harmonic caused by the independent operation of the 5-6% series reactance ratio parallel-connected group. In outdoor substations, dry-type air-core reactors are typically used for parallel-connected series reactors. The main faults of dry-type air-core reactors, whether parallel or series reactors, are inter-strand short circuits, inter-turn short circuits, and surface flashover discharges.

[0003] To prevent transformers or reactors from malfunctioning during use, this paper simulates the causes and processes of reactor and transformer malfunctions. This simulation helps staff to promptly identify the causes of malfunctions, cut off the source of the malfunction, understand the trend of malfunctions, and avoid greater losses. Summary of the Invention

[0004] Therefore, the purpose of this invention is to provide a modeling and simulation method for generating 3rd and 5th harmonic currents based on inter-turn short circuits with series withstand arcing. This method simulates the arcing discharge characteristics at the short-circuit point during an inter-turn fault, which exhibits a recurring process with the power frequency cycle: arcing upon short-circuit occurrence, zero-crossing turn-off, arc extinguishing, delayed turn-on, and arc reignition. A computer digital simulation circuit model is established, and simulation calculations are performed using the model to reconstruct and reproduce the dynamic characteristics of the fault process. In particular, the unique characteristics and mechanism of stable 3rd and 5th harmonic currents appearing after an inter-turn short circuit in a parallel capacitor bank are revealed. The dynamic real-time waveform data from the simulation is used to verify the monitoring principles and functions of relevant fault monitoring and protection devices, and to test and verify the reliability and accuracy of the monitoring technology and devices. Simulation experiments on the principles and performance of inter-turn short-circuit fault monitoring or protection devices can be conducted in a laboratory environment.

[0005] To achieve the above objectives, the present invention provides a modeling and simulation method for 3rd and 5th harmonic currents induced by inter-turn short circuits with series reactance arcing, comprising the following steps:

[0006] S1. Based on the current arcing process and circuit principle during inter-turn short circuit with series arc resistance, establish a digital circuit simulation model.

[0007] S2. Using the digital circuit simulation model, simulate the fault development process. Based on the fault development process, perform equivalent circuit simulation in the digital circuit simulation model by combining proportional or non-proportional stepped units to complete the dynamic process of series arc-induced inter-turn short circuit, display the changes in electrical characteristics, and simulate the restoration of fault cases.

[0008] More preferably, the digital circuit simulation model includes an equivalent simulation part of the power system, an equivalent simulation part of the substation and capacitor bank, and an equivalent simulation part of the filter bank of the AC system of the DC-DC converter station that affects the harmonic characteristics of the system; wherein, the equivalent simulation part of the power system includes a generator and an ideal dual-winding step-up transformer; the equivalent simulation part of the substation includes a step-down transformer and a switchable parallel capacitor bank; the generator is used to provide a stable voltage, and the ideal dual-winding step-up transformer is used to step up the stable voltage to meet the power supply standard;

[0009] The step-down transformer is used to step down the high voltage input from the step-up transformer in the power system. The switchable parallel capacitor bank includes a series reactor and a capacitor. The series reactor coil is set to simulate an inter-turn short-circuit fault with an increasing number of turns. When simulating the short circuit, it is equivalent to a combination of proportional or non-proportional stepped units to realize the simulation of the early, middle and late stages of the short-circuit fault development.

[0010] Furthermore, preferably, in the digital circuit simulation model, based on the relationship between the short-circuit circulating current ampere-turn balance flux caused by the number of short-circuit turns and the total ampere-turns of the overall coil, the following real-time electromagnetic induction ampere-turn balance equation is established:

[0011] N12*I1(t)+N2*I2(t)=0

[0012] Where N12 is a normal number of turns, i.e., primary side turns, I1(t) is the real-time current of the coil, i.e., primary side current; N2 is the number of short-circuit turns, i.e. secondary side turns, I2(t) is the real-time current of the short-circuit loop, i.e., secondary side current.

[0013] In any of the above embodiments, preferably, based on the fact that the local coil inductance disappears after real-time ampere-turn balance during arc combustion and recovers when the arc is extinguished; and considering the equivalent circuit parameters from the primary two-port side, the equivalent resistance can be expressed by the following formula:

[0014]

[0015] Where: Rs is the single-turn resistance, R12 is the equivalent resistance of the primary side of the port, I1 is the coil through current, I2 is the short-circuit loop current, and N2 is the number of short-circuit turns.

[0016] In any of the above embodiments, preferably, the proportional stepped unit or non-proportional stepped unit includes multiple sets of fault series reactance equivalent circuits connected in series, wherein the fault series reactance equivalent circuit includes an inter-turn short-circuit loss series reactance equivalent inductor, an adjustable inter-turn short-circuit circulating current loss equivalent resistor, and a bidirectional short-circuit arc control thyristor simulating the arc extinguishing and reigniting process; the bidirectional short-circuit arc control thyristor and the inter-turn short-circuit circulating current loss equivalent resistor are connected in series and then connected in parallel across the inter-turn short-circuit loss series reactance equivalent inductor as a whole.

[0017] In any of the above embodiments, preferably, the bidirectional short-circuit arc control thyristor triggering angle is used to control the turn-on and turn-off times and durations of the positive and negative half-waves respectively, simulating the changes in the reignition characteristics after the arc of the positive and negative half-wave arc short circuit is extinguished; the equivalent resistance of the inter-turn short-circuit circulating current loss is used to simulate the characteristics of the equivalent resistance of the active power loss generated by the circulating current after the inter-turn short circuit, and the equivalent inductance of the inter-turn short-circuit loss series reactance is used to simulate the characteristics of the inductance loss increasing as the inter-turn short circuit continues to expand.

[0018] In any of the above embodiments, preferably, in S2, the dynamic simulation test of the arc-induced inter-turn short circuit of the series reactor is completed according to the equivalent combination of proportional or non-proportional stepped units. This includes simulating the series reactor using a dry-type hollow series reactor, using stepped timing control to control the triggering and conduction angle of the bidirectional thyristor, and simulating the nonlinear expansion process of the short-circuit turn of the dry-type hollow series reactor after a fault; specifically, it includes the following steps:

[0019] S201. Based on the data when a short circuit fault actually occurs, when the inductance loss is 100%, the number of short circuit turns is 40 turns. The equivalent inductance of the inter-turn short circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short circuit circulating current loss are reduced proportionally or non-proportionally according to the preset number of steps.

[0020] S202. When the equivalent inductance of the inter-turn short-circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short-circuit circulating current loss are reduced according to the gradient, the current of each series equivalent resistance is calculated as the short-circuit circulating current increases to about 15 to 30 times the rated current.

[0021] In any of the above embodiments, preferably, in S201, when the equivalent inductance of the inter-turn short-circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short-circuit circulating current loss are reduced proportionally or non-proportionally according to a preset number of steps; it also includes simulating the delayed short-circuit discharge arc reignition time after the series reactance voltage peak in one power frequency cycle according to different triggering angles, with a preset number of steps of 5 times and the inductance loss gradient being a non-proportional gradient.

[0022] In any of the above embodiments, preferably, the content of the 3rd and 5th harmonics in the digital circuit simulation model under different inductance loss levels, and the content of the 3rd and 5th harmonics under different triggering angles are also included.

[0023] In any of the above embodiments, preferably, the content of the 3rd and 5th harmonics obtained in the digital circuit simulation model is compared with the actual parameters of the inter-turn fault case of the dry air-core reactor, and the parameters in the digital circuit simulation model are adjusted according to the comparison results.

[0024] This application discloses a modeling and simulation method for generating 3rd and 5th harmonic currents based on inter-turn short circuits caused by series reactance arcing. This method establishes a digital circuit simulation model, performs simulation calculations using the model, and then reconstructs and reproduces the dynamic characteristics of the fault process. It restores and reveals the unique characteristics and mechanisms of stable 3rd and 5th harmonic currents after an inter-turn short circuit in a parallel capacitor bank. Furthermore, it uses real-time dynamic waveform data from the simulation to verify the monitoring principles and functions of relevant fault monitoring and protection devices, testing and verifying the reliability and accuracy of the monitoring technology and its devices. Simulation tests of the principles and performance of inter-turn short-circuit fault monitoring or protection devices can be conducted in a laboratory environment. The method utilizes fault models and simulation methods for calculation and simulation, and leverages power system digital simulation platforms such as RTDS (Real-Time Digital Simulation System) to generate fault characteristics and features, and outputs fault electrical characteristics converted from digital quantities to physical analog quantities. This facilitates the verification of the technical principles and functional correctness of the fault monitoring or protection technology. Attached Figure Description

[0025] Figure 1 The flowchart shows the modeling and simulation method of the present invention based on the generation of 3rd and 5th harmonic currents by inter-turn short circuit with series reactance arcing.

[0026] Figure 2 This is a short-circuit circulating current waveform diagram generated by computer simulation based on the actual short-circuit fault principle of this invention;

[0027] Figure 3 This is a typical current waveform of the faulted phase in the parallel capacitor bank lc circuit after an inter-turn short circuit according to the present invention.

[0028] Figure 4 This is a schematic diagram of an inter-turn short circuit in a certain layer of the coil in this invention;

[0029] Figure 5 A schematic diagram illustrating the electromagnetic induction principle of a short circuit between turns of an air-core coil.

[0030] Figure 6 The circuit principle model diagram of the fault turn fault characteristics of the present invention is shown in the figure. The equivalent resistance of the bidirectional thyristor valve series is connected in parallel with the inductor.

[0031] Figure 7 This is a waveform diagram of the arc current during the mid-stage of the inter-turn short-circuit fault development of the hollow coil of the present invention (with an inductance loss of approximately 50%).

[0032] Figure 8 This is a waveform diagram of the coil current during the later stage of the inter-turn short circuit fault development of the hollow coil of the present invention (with an inductance loss of about 90%).

[0033] Figure 9 Waveform diagram of an inter-turn short-circuit fault case of a 35kV 3×20Mvar group with a 12% series reactance rate reactance;

[0034] Figure 10 This is the electrical wiring diagram of the power system for the digital circuit simulation model of this invention;

[0035] Figure 11 This is a circuit diagram of the equivalent circuit of the fault phase series reactance of the steady-state model of the fixed-proportion unit in this invention;

[0036] Figure 12 This is a computer simulation model of a 35kV 3×20Mvar group 12% series reactance reactance inter-turn short circuit fault case according to the present invention;

[0037] Figure 13(a) is a waveform diagram of the fault phase in the simulation experiment of the inter-turn short circuit fault of the present invention;

[0038] Figure 13(b) is a schematic diagram of the 3rd and 5th harmonic current content values ​​in the fault simulation shown in Figure 13(a).

[0039] Figure 14 The waveform of the fault phase current is recorded for a case of inter-turn short circuit fault in a 35kV 3×20Mvar group with 12% series reactance.

[0040] Figure 15 The neutral point voltage waveform is shown in the computer simulation results of the inter-turn short-circuit fault case of this invention.

[0041] Figure 16 The present invention provides a case study of an inter-turn short-circuit fault, showing the three-phase current waveform and harmonic content within the transformer angle.

[0042] Figure 17 The simulation test of this invention shows the 3rd / 5th harmonic content at 90% inductance loss;

[0043] Figure 18 The simulation test of this invention shows the 3rd / 5th harmonic content at 80% inductance loss;

[0044] Figure 19 The simulation test of this invention shows the 3rd / 5th harmonic content at 50% inductance loss;

[0045] Figure 20 The third / fifth harmonic content is given by 20% inductance loss in the simulation test of this invention. Detailed Implementation

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1 As shown, one embodiment of the present invention provides a modeling and simulation method for 3rd and 5th harmonic currents induced by inter-turn short circuits with series reactance arcing, comprising the following steps:

[0048] S1. Based on the current arcing process and circuit principle during inter-turn short circuit with series arc resistance, establish a digital circuit simulation model.

[0049] S2. Using the digital circuit simulation model, simulate the fault development process. In the digital circuit simulation model, perform circuit equivalent simulation according to the combination of proportional stepped units or non-proportional stepped units to complete the dynamic process of series arc-induced inter-turn short circuit, display the changes in electrical characteristics, and recreate the fault case simulation.

[0050] It should be noted that when establishing the digital circuit simulation model, statistical analysis based on actual fault cases shows that, due to the relatively small circulating current of inter-turn short circuits (the circulating current of a large parallel reactance short circuit is approximately 150-300 times the normal line-turn current), the rate of expansion of the number of faulty turns caused by the high temperature and arcing of the short-circuited lines in a series reactance inter-turn short circuit is also much slower. After several minutes of development and expansion, when the number of short-circuited turns in the inter-turn short circuit fault continues to develop and expand to about 30-40 turns (the inductance loss caused by 1 turn is about 3%), the equivalent inductance of the series reactance will become very small until it disappears completely. Because the equivalent inductance and reactance of the series reactance decrease, the impedance of the entire circuit actually increases, so the current in the circuit will not increase, but will decrease instead.

[0051] In actual fault cases, capacitive series reactor faults are most common in 500kV ultra-high voltage substations equipped with dry-type hollow series reactors with a 12% series reactance rate. Analysis and statistical research of approximately 10 cases where fault waveform recording was initiated after a fault revealed the following fault patterns:

[0052] (1) The development of inter-turn short circuits in series reactors is relatively slow, and it will last for several minutes (1 to 5 minutes) to tens of minutes (1 to 5 minutes or up to 30 minutes).

[0053] (2) The continuous development of inter-turn short circuits has caused a continuous nonlinear decrease in the equivalent reactance.

[0054] (3) Stable 3rd and 5th harmonics will be generated during the inter-turn fault process.

[0055] (4) The faults eventually led to the dry-type air-core reactor catching fire and spontaneously combusting.

[0056] Studies have found that during inter-turn short circuits, on the one hand, as the number of turns increases, the equivalent reactance decreases and the equivalent resistance increases. On the other hand, since inter-turn short circuits exist in the form of electric arcing in each power frequency cycle, in the early stages of the fault, there will still be residual insulation film at the high-temperature damage or injury caused by the short-circuit circulating current arc at the short-circuit point. More importantly, as the short-circuit aluminum conductor heats up and melts under 15-30 times the short-circuit circulating current, the continuous arc burning and ablation at the short-circuit point, along with the pulling action of electrodynamic forces, will form developing arc-erosion gaps and grooves. Simultaneously, because the inter-turn potential is at the level of tens of volts, when the arc burns in the gap, due to the low sustaining voltage (recovery voltage), the air insulation in the gap, which is a few millimeters to tens of millimeters wide, will temporarily recover after the short-circuit current crosses zero. The arc will not immediately reignite, and will reignite after being extinguished for about 2-6 ms. Therefore, the short-circuit circulating current waveform will be as follows: Figure 2 As shown, the short-circuit circulating current is not a continuous sine wave, but an intermittent wave. Figure 2 The continuous sine wave with medium to high amplitude is the normal series reactance terminal voltage waveform, while the intermittent waveform with low amplitude is the simulated inter-turn short-circuit loop and arc current waveform (the current in the short-circuit loop cannot be directly recorded during actual faults). Figure 3 The waveform diagram shows the presence of significant 3rd and 5th harmonic currents in the lc circuit excited by an arc-induced inter-turn short-circuit fault.

[0057] Therefore, based on the arcing process of the short-circuit current in ablated slits and trenches caused by arcing short circuits and its circuit principle, the repeated process of short-circuiting, arc burning, zero-crossing turn-off, arc extinguishing, delayed turn-on, and arc reignition of inter-turn short circuits can be simulated by synchronously controlling the connection of the inter-turn short circuit with ideal switches or thyristors. This simulates the characteristics and fault development process of the continuous, stable, and significant number of harmonic currents, mainly the 3rd, 5th, and 7th orders, appearing in the parallel-capacitor LC circuit current during the inter-turn short circuit induced or caused by arcing short circuits. Digital circuit simulation technology is used to establish a digital circuit model with consistent principles and mechanisms, and a reasonable simulation method is set to reveal the fault mechanism and characteristics and reconstruct specific faults. Fault case studies explain the special electrical characteristics and features that appear in the faults, providing a basis for monitoring faults and verifying and testing monitoring technologies and devices to exhibit fault characteristics consistent with real faults. For example, using the RTDS real-time digital simulation system, a modeling and simulation method is established based on the common 12% and 5-6% series reactance rate current-limiting series reactance arc-induced inter-turn short circuit of parallel capacitor banks to induce 3rd and 5th harmonic currents. A digital circuit model is established, and the digital-to-physical conversion capability of the RTDS real-time digital simulation system is used to output simulated electrical quantities to conduct dynamic simulation tests of series reactance arc-induced inter-turn short circuits. This verifies and tests the monitoring technology and monitoring devices for monitoring series reactance inter-turn short circuit faults, ensuring their correctness and functionality.

[0058] like Figure 4-6As shown, in another embodiment of the present invention, when calculating the parameters of the digital circuit simulation model, the inter-turn short-circuit fault of the inductor coil is a breakdown discharge caused by a non-metallic direct short circuit (discharge through the damaged or failed polyester film) due to reduced or damaged insulation at a certain point between adjacent turns. When there is an electric arc at the short-circuit point, the arc circulating current Ic1 = Ic2 + Ic, and a short-circuit circulating current Ic2 flows between the short-circuited turns. The current in the short-circuit loop is tens to hundreds of times the coil current Ic, and the current direction is opposite to the coil current.

[0059] When a short circuit occurs between adjacent turns in a hollow coil, the short-circuited turn is hinged to the normal turn through an alternating electromagnetic field. The electromagnetic induction principle between the short-circuited turn and the normal turn on a certain small scale in the adjacent space is analogous to the induction relationship between two well-coupled primary and secondary independent coils. For example... Figure 6 As shown, the overall coil is divided into three series-connected parts: L11, L12, and L13, with corresponding inductances of k11*L, k12*L, and k13*L, and corresponding turns of N11, N12, and N13, respectively. Several turns in coil L12 experience inter-turn short circuits, with N2 turns being the short-circuited turns, equivalent to the secondary coil L2 of L12. Coils L2 and L12 exhibit complete magnetic flux coupling, similar to an ideal transformer. A magnetic flux ampere-turn balance relationship based on the principle of electromagnetic induction is formed between the short-circuited turns and the normally connected turns within a certain spatial range, where magnetic flux is tightly hinged.

[0060] In the digital circuit simulation model, based on the relationship between the short-circuit circulating current ampere-turn balance flux caused by the number of short-circuit turns and the total ampere-turns of the overall coil, the following real-time electromagnetic induction ampere-turn balance equation is established:

[0061] N12*I1(t)+N2*I2(t)=0 Formula 1

[0062] Where N12 is a certain number of normal turns, i.e., primary side turns, I1(t) is the real-time current of the coil, i.e., primary side current; N2 is the number of short-circuit turns, i.e. secondary side turns, I2(t) is the real-time current of the short-circuit loop, i.e. secondary side current.

[0063] According to the principle that when the arc burns, the inductance of the local coil disappears after the real-time ampere-turn balance is achieved, L12 = 0; when the arc is extinguished, the inductance of the local coil recovers, L12 = k12 * L; and considering the equivalent circuit parameters from the two-port primary side, the equivalent resistance can be expressed by the following formula:

[0064]

[0065] Where: Rs is the single-turn resistance, R12 is the equivalent resistance of the primary side of the port, I1 is the coil through current, I2 is the short-circuit loop current, and N2 is the number of short-circuit turns.

[0066] Based on actual measurements and theoretical calculations, when using a 12% series reactance for short-circuit testing, with 1 to 10 turns in the short-circuit loop, the short-circuit loop current is approximately 30 to 40 times the coil current, i.e., I2 / I1 = (30 to 40) times. For 5 to 6% series reactance, the short-circuit loop current is approximately 15 to 30 times the coil current.

[0067] Because the ampere-turns of commonly used series reactors (6% and 12%) are much smaller than those of shunt reactors, the short-circuit circulating current of their short-circuit turns is approximately 15 to 40 times the normal current (the short-circuit circulating current of large shunt reactors is enormous, ranging from 150 to 300 times). Therefore, in actual conductor short-circuit faults, at the initial stage of the short circuit caused by the high temperature damage or injury from the arc generated by the short-circuit circulating current, there will still be residual insulation film. As the aluminum conductor of the short-circuit turn heats up and melts under a short-circuit circulating current of 15-30 times, the short circuit point will continue to burn and erode due to the arc. The pulling force of electric force and other actions will form a developing arc ablation gap and groove. Therefore, the short-circuit circulating current is extinguished after the arc current crosses zero due to the brief recovery of air insulation of a distance of a few millimeters to close to 10 millimeters. After the extinguishing and opening, it reignites in the next power frequency half-wave cycle after a delay of 1 to 3 ms due to the reapplication of the turn potential. The process is equivalent to the reignition / opening and extinguishing / turn-off process of the inter-turn short-circuit arc after shorting the bypass part of the inductance by an ideal switch or thyristor synchronous control.

[0068] On the other hand, to verify the rationality of using thyristors for circuit control simulation, further research is needed on the relationship between the thyristor triggering angle and the discontinuous waveform of the short-circuit loop current, as well as the third and fifth harmonics. Figure 7 As shown, the short-circuit current and coil current in a simulated three-phase parallel capacitor bank undergo a short-circuit current arc burning process during the intermediate stage of a simulated three-phase parallel capacitor bank's c-phase series reactance fault. The short-circuit current and coil current (with 50% inductance loss, simulated voltage peak followed by arc reignition 2 milliseconds later, and thyristor triggering angle of 36 degrees) are intermittent waveforms. The curve with the higher peak value represents the reference voltage Uc (kV), and the curve with the lower peak value represents the current amplified tenfold, Ic1*10 (kA). Figure 8 As shown, the simulated C-phase series short circuit exhibits significant inductance loss (90%) in the later stages of inter-turn short circuit development, along with a longer arc extinguishing time, corresponding to a larger triggering angle (65 degrees). The waveforms of the coil and LC circuit currents (Ic) after thyristor triggering are displayed. At the cursor position, the 3rd harmonic current content exceeds 22%, and the 5th harmonic current content reaches approximately 13%. Figure 9The actual fault current waveform of the 35kV parallel series reactor in a 500kV substation, occurring approximately 5 minutes after the fault, was recorded. The third harmonic current content exceeded 20%, and the fifth harmonic current content reached approximately 10% or more, demonstrating a high degree of similarity in waveform and harmonic current characteristics between the two scenarios. The actual fault waveform (after approximately 5 minutes of fault development, with inductance loss reaching 80-90%) matches the simulation results. Therefore, the digital circuit simulation model can be constructed using the following structure.

[0069] like Figure 10 As shown, in one embodiment of the present invention, the digital circuit simulation model includes an equivalent simulation part of the power system, an equivalent simulation part of the substation and capacitor bank, and an equivalent simulation part of the filter bank of the AC system of the DC-DC converter station that affects the harmonic characteristics of the system; wherein, the equivalent simulation part of the power system includes a generator and an ideal double-winding step-up transformer; wherein G is an infinite generator constant voltage source, T is an ideal double-winding step-up transformer with no short-circuit impedance and no loss, X S For the equivalent system inductive reactance, R S The equivalent system resistance is defined. The equivalent simulation section of the substation includes a step-down transformer and a switchable parallel capacitor bank; the generator is used to provide a stable voltage, and the ideal dual-winding step-up transformer is used to step up the stable voltage to meet power supply standards.

[0070] The step-down transformer is used to step down the high voltage input from the step-up transformer in the power system. The switchable parallel capacitor bank includes a series reactor and capacitors; wherein STB is the step-down transformer, and SC is the switchable parallel capacitor bank (composed of series reactor X). L and capacitor X C (Composition); Simulating inter-turn short-circuit faults by setting up a developing fault on the coil of a series reactor, with the number of turns increasing. During short-circuit simulation, equivalent values ​​are performed using either proportional or non-proportional stepped unit combinations to simulate the early, middle, and late stages of short-circuit fault development. Other power system components that may affect the absorption and amplification characteristics of the 3rd, 5th, and 7th harmonics, such as the equivalent components of DC converter station lines and their filter banks, include the equivalent line reactance X. L AC field filtering and compensation capacitor banks (possibly including switched capacitors SC, 3rd and 12th / 24th order filter banks), and parallel reactors X for balancing the capacitive compensation capacity at power frequency. g (For computational simulation purposes, there are no parallel reactors in the actual AC field.)

[0071] The electrical wiring of the parallel capacitor bank unit in the figure is a three-phase group using a star connection, consisting of a 12% (or 5-6%) current-limiting series reactance and parallel capacitors.

[0072] like Figure 11 Therefore, in one embodiment of this application, a proportional or non-proportional stepped unit is used as a fault series reactance equivalent circuit to simulate a series reactance short-circuit fault. The proportional or non-proportional stepped unit includes multiple sets of fault series reactance equivalent circuits connected in series. The fault series reactance equivalent circuit includes an inter-turn short-circuit loss series reactance equivalent inductor, an adjustable inter-turn short-circuit circulating current loss equivalent resistor, and a bidirectional short-circuit arc control thyristor that simulates the arc ignition, extinction, and reignition process. The bidirectional short-circuit arc control thyristor and the inter-turn short-circuit circulating current loss equivalent resistor are connected in series and then connected in parallel across the inter-turn short-circuit loss series reactance equivalent inductor. In the diagram, C represents the capacitance of the parallel capacitor bank, R represents the equivalent normal loss resistance of the series reactance, L1 to L5 represent the series reactance inductance of the inter-turn short-circuit loss with equal or non-equal proportions, ΔR represents the equivalent resistance of the inter-turn short-circuit circulating current loss, and V1 to V5 represent the bidirectional thyristor valves simulating the short-circuit arc extinction-reignition characteristics.

[0073] Furthermore, different trigger angles of the bidirectional short-circuit arc-controlled thyristor are used to control the turn-on and turn-off times and durations of the positive and negative half-waves, simulating the changes in the reignition characteristics after the arc of the positive and negative half-wave arc short circuit is extinguished; the equivalent resistance of the inter-turn short-circuit circulating current loss is used to simulate the characteristics of the equivalent resistance of the active power loss generated by the circulating current after the inter-turn short circuit, and the equivalent inductance of the inter-turn short-circuit loss series reactance is used to simulate the characteristics of the inductance loss increasing as the inter-turn short circuit continues to expand.

[0074] Furthermore, in S2, the dynamic simulation test of arc-induced inter-turn short circuit of the series reactor is completed according to the equivalent combination of proportional or non-proportional stepped units. This includes simulating the series reactor using a dry-type hollow series reactor, using stepped timing control to control the triggering and conduction angle of the bidirectional thyristor, and simulating the nonlinear expansion process of the short-circuit turn of the dry-type hollow series reactor after a fault; specifically, it includes the following steps:

[0075] S201. Based on the data when a short circuit fault actually occurs, when the inductance loss is 100%, the number of short circuit turns is 40 turns. The equivalent inductance of the inter-turn short circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short circuit circulating current loss are reduced proportionally or non-proportionally according to the preset number of steps.

[0076] S202. When the equivalent inductance of the inter-turn short-circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short-circuit circulating current loss are reduced according to the gradient, the current of each series equivalent resistance is calculated as the short-circuit circulating current increases to about 15 to 30 times the rated current.

[0077] In any of the above embodiments, preferably, in S201, when the equivalent inductance of the inter-turn short-circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short-circuit circulating current loss are reduced proportionally or non-proportionally according to a preset number of steps; it also includes simulating the delayed short-circuit discharge arc reignition time after the series reactance voltage peak in one power frequency cycle according to different triggering angles, with a preset number of steps of 5 times and the inductance loss gradient being a non-proportional gradient.

[0078] For simplicity in simulation, the equivalent inductance and equivalent resistance can be reduced proportionally in 20% increments according to the scale of the inter-turn short circuit development, with the reduction of equivalent inductance being cumulative. The control timing is set according to a 5-level step sequence of 20%, 40%, 60%, 80%, and 100%. The equivalent resistance in series for each level is calculated based on the short-circuit circulating current increasing to approximately 15-30 times (the average value can be set to 25 times) of the rated current. With 100% inductance loss, the number of short-circuit turns is approximately 40. Therefore, the total equivalent short-circuit circulating current thermal effect resistance is 40 turns x 25 x 25 / 1000 turns = 25 times.

[0079] For each 20% inductance loss ratio unit, the equivalent resistance in series after the thyristor valve group is assigned according to the relationship of 25 / 5 equals 5, using 4 to 6 times the equivalent resistance of the normal total loss of series reactance. When the total inductance loss is less than 50% in a fault, a value of 6 times can be assigned; when the total inductance loss is greater than 80% in a fault, a value of 4 times can be assigned.

[0080] Based on the analysis and fitting of several fault cases, it was found that most fault series reactances begin from the initial fault point through the cutting action caused by high-temperature arc erosion, aluminum wire melting, and electrodynamic pulling. This creates an air gap and groove that continues to grow and lengthen as the inter-turn short-circuit fault develops and the number of faulty turns increases. Figure 11 As shown in the dissection photographs after the actual fault, this resulted in a brief extinction of the arc discharge after the arc current crossed to zero. Subsequently, an inter-turn potential was induced in the short-circuit turns. Under the influence of a high-frequency power voltage of tens of volts, the arc discharge resumed between the short-circuit turns and between the burned-out turns, causing the arc to reignite. Therefore, the short-circuit arc exhibits a periodic discharge-arc ignition-arc current zero-crossing extinction-delayed reignition characteristic (equivalent to...). Figure 6 and Figure 10 Controlled triggering and zero-current natural turn-off characteristics of bidirectional thyristor valves

[0081] In any of the above embodiments, preferably, the content of the 3rd and 5th harmonics in the digital circuit simulation model under different inductance loss levels, and the content of the 3rd and 5th harmonics under different triggering angles are also included.

[0082] In any of the above embodiments, preferably, the content of the 3rd and 5th harmonics obtained in the digital circuit simulation model is compared with the actual parameters of the inter-turn fault case of the dry air-core reactor, and the parameters in the digital circuit simulation model are adjusted according to the comparison results.

[0083] The following explanation uses a commonly used and frequently faulty 35kV 3×20Mvar three-phase group with a 12% series reactance rate as an example:

[0084] (1) Collect parameters on the operation of substations and their power systems

[0085] I. Collect information on step-down transformer models, connection groups, turns ratios, capacity, and short-circuit impedance percentages.

[0086] II. The equivalent power supply system on the high-voltage and medium-voltage sides of the step-down transformer is collected according to the power system status and operating conditions, including impedance characteristics (i.e., reactance and resistance ratio). The generator of the power supply system is modeled as an infinite system.

[0087] III. Collect the AC system filter parameters and their connecting line impedance parameters of DC converter stations within a 50km radius of the faulted station. (The harmonic impedance characteristics of the AC filter bank (usually equipped with 3rd, 11th / 13th order filter banks, etc.) of the DC converter station will affect the inter-turn short circuit fault and the generated 3rd, 5th, 7th and 11th harmonics).

[0088] (2) Calculate the equivalent inductance and equivalent resistance of the scaled-up (20%, 5% scale) steps.

[0089] As shown in Tables 1 and 2.

[0090] Table 1 - Parameters of a three-phase group with 35kV 3×20Mvar and 12% series reactance.

[0091] Capacitive reactance (Ω) 28.801 Inductive impedance (Ω) 3.46 Capacitance (μF) 110.52 Inductance (H) 0.011 Equivalent resistance (Ω) 0.035 (approximately 1% of the resistance value) / /

[0092] Table 2 - 35kV 3×20Mvar, 12% series reactance rate, inter-turn fault, 5 series-stage proportional inductors and equivalent resistances.

[0093]

[0094] Note: All calculations above are based on a 50Hz power system.

[0095] Select system parameters, use PSCAD to build a simulation model, and form a model as follows: Figure 12The computer simulation model shown is for a 12% series reactance reactor inter-turn short-circuit fault case. It utilizes parameters from a real fault case to simulate the nonlinear amplification of the short-circuit turns, leading to nonlinear changes in the equivalent inductance and resistance. It also simulates the arc discharge characteristics at the short-circuit point of the series reactor during an inter-turn fault, which exhibit both extinction and reignition characteristics. The simulation depicts the arc-induced short-circuit process where the arc is interrupted by extinction and then reignites after a certain delay (angle). The simulation can reproduce the stable 3rd and 5th harmonic currents that appear after an inter-turn short circuit in the parallel-connector series reactor, as well as the unique characteristics and features of the neutral point voltage under conditions of inductance loss and significant 3rd, 5th, and 7th harmonic currents accompanying the inter-turn short circuit.

[0096] Figure 13(a) shows the computer simulation results—the fault phase current waveform; Figure 13(b) shows the schematic diagram of the 3rd and 5th harmonic current content values; (the current unit in the figure is kA); Table 3 shows the statistics of current at each frequency and neutral point offset voltage data of the thyristor valve group at different trigger angles (simulating a phase c fault, with the phase a voltage as the 0-degree reference angle).

[0097] Table 3 shows the coil current and neutral point voltage offset data after arc reignition under different arc extinguishing times / triggering angles with 90% inductance loss.

[0098]

[0099] Among them, the 3rd harmonic current content exceeds 22% at a trigger angle of 215 degrees (equivalent to a 65-degree delay after the peak voltage of phase C inductor), and the 5th harmonic current content reaches approximately 10-13%. 150 degrees corresponds to a 0-degree delay (corresponding to the highest peak point of the phase C series reactance voltage waveform). The reference voltage waveform time for the trigger angle is the 0-degree point of the sine wave of phase A bus voltage. Due to the capacitive current applied to the reactance, the actual series reactance voltage is out of phase with the bus voltage. Therefore, when simulating a phase B series reactance fault, 30 degrees corresponds to a 0-degree delay after the peak voltage of phase A, and when simulating a phase A series reactance fault, 270 degrees corresponds to a 0-degree delay after the peak voltage.

[0100] Table 4-35kV 3×20Mvar group 12% series reactance rate reactance inter-turn short circuit fault case recording harmonic current variation table.

[0101]

[0102]

[0103] The waveform data from the actual fault case (after about 5 minutes of fault development, the inductance loss reached 80-90%) is in very good agreement with the simulation results. Figure 14The analysis of current waveforms and harmonic content in actual fault cases shows that the 3rd harmonic current content ranges from 11.3% to 33%, and the 5th harmonic current content ranges from 4.4% to 14%. After about 5 minutes of fault development, due to the increase in the number of short-circuit turns and the formation of arc erosion cutting gaps and grooves, the arc combustion becomes more unstable, and the reignition time after the arc is extinguished increases (the trigger angle increases), leading to a sharp increase in the 3rd and 5th harmonics. This characteristic is consistent with the simulation characteristics.

[0104] Figure 15 The neutral point voltage waveform (unit: kV) in the figure is shown in the computer simulation results of a case of inter-turn short-circuit fault in a 35kV 3×20Mvar group with a 12% series reactance rate reactor. The harmonics are mainly the 5th, 11th, 13th, and 3rd orders.

[0105] Figure 16 For another 35kV 3x20Mvar group 12% series reactance reactance inter-turn short circuit fault case, the three-phase current waveform and harmonic content of the transformer in the corner are analyzed (the current waveform in the middle column of the figure is the fault phase waveform, where the harmonic content at the cursor moment is converted to the 3rd order of the fault capacitor bank branch outside the corner as 8.2% and the 5th order as 13%). The harmonic current shows that the 5th order is greater than the 3rd order.

[0106] As can be seen from the harmonic content calculated in Table 3, with the instability of the short-circuit circulating current arc and the increase in the duration and angle of the circulating current interruption caused by the arc harmonics, the content of the 3rd harmonic increases nonlinearly and gradually. The 5th harmonic current first increases nonlinearly and gradually, and then gradually decreases after a certain angle (205 degrees in Table 1). Moreover, before that, the content of the 5th harmonic current is greater than that of the 3rd harmonic.

[0107] In actual fault case waveforms ( Figure 16 The simulation also found that the 5th harmonic current exceeded the 3rd harmonic current, proving the correctness of the simulation characteristics.

[0108] As the short-circuit turns expand, the short-circuit circulating current, based on the principle of electromagnetic induction ampere-turn balance, will inevitably decrease gradually. Therefore, as the inter-turn short circuit develops further, the number of short-circuit turns increases, the short-circuit circulating current decreases, and the inductance loss increases. At this point, the overall series reactance characteristic tends to be non-inductive, the coil magnetic flux also tends to zero, and the induced electromotive force of the coil turns becomes very small. Consequently, the time for the arc current to extinguish and reignite after crossing zero will become longer. Therefore, consistent with the trend shown in the simulation results of Figure 13 and Table 3 in the simulation case, the content of the third harmonic current in the harmonic current will reach 20-30%, and the content of the fifth harmonic current will be around 6-10%.

[0109] Down Figures 17-20This is a graph showing the harmonic content rate curves under different inductance losses and firing angles. The horizontal axis represents the firing delay angle, and the vertical axis represents the content rate of the 3rd and 5th harmonic currents in the coil current (branch current). Table 5 shows the simulation results based on the actual parameters of the inter-turn fault case of the dry air-core reactor with a series reactance rate of 12% in phase C of the 335kV 3×20Mvar group in Figure 13 and the simulation results based on the computer simulation model. Table 5 simulates the delayed short-circuit discharge arc reignition time after the series reactance voltage peak in one power frequency cycle under five cases with inductance losses of 90%, 80%, 50%, 40%, and 20%, according to the delayed reignition characteristics after the discharge arc is extinguished, according to different firing angles. For phase C, 150 degrees is the 0 delay time; for phase A, 270 degrees is the 0 delay time; and for phase B, 30 degrees is the 0 delay time.

[0110] Table 5 presents the actual parameters and simulation results based on a computer simulation model for the inter-turn fault case of a 35kV 3×20Mvar group C-phase dry air-core reactor with a 12% series reactance rate, according to Figure 13.

[0111]

[0112]

[0113]

[0114] The comparison between the above simulation experiments and actual fault cases shows that this simulation model realizes the characteristics and variation law of arc ignition-arc extinction-delayed reignition with arc short circuit characteristics; it realizes the restoration of the fault process of specific cases, conducts fault characteristic analysis of specific cases, and demonstrates the restoration of fault electrical characteristics and features.

[0115] Fault models and simulation methods are used for calculation and simulation. Power system digital simulation platforms such as RTDS (Real-Time Digital Simulation System) are employed to generate fault characteristics and features, and output fault electrical characteristics by converting digital quantities into physical analog quantities. This is used to verify the technical principles and functional correctness of fault monitoring or protection technologies.

[0116] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A modeling and simulation method based on the generation of 3rd and 5th harmonic currents by inter-turn short circuit with series reactance arcing, characterized in that, Includes the following steps: S1. Based on the current arcing process and circuit principle during inter-turn short circuit with series arc resistance, establish a digital circuit simulation model. S2. Using the aforementioned digital circuit simulation model, the fault development process is simulated. In the digital circuit simulation model, equivalent circuit simulation is performed according to a combination of proportional or non-proportional stepped units to complete the dynamic process of series reactance arc-induced inter-turn short circuit, the display of electrical characteristic changes, and the simulation of fault case reconstruction. The proportional or non-proportional stepped unit includes multiple sets of fault series reactance equivalent circuits connected in series. The fault series reactance equivalent circuit includes an equivalent inductor for inter-turn short-circuit loss series reactance, an adjustable equivalent resistor for inter-turn short-circuit circulating current loss, and a bidirectional short-circuit arc control thyristor simulating the arc ignition and reignition process. The bidirectional short-circuit arc control thyristor simulating the arc ignition and reignition process is connected in series with the equivalent resistor for inter-turn short-circuit circulating current loss, and then connected in parallel across the equivalent inductor for inter-turn short-circuit loss series reactance as a whole.

2. The modeling and simulation method for 3rd and 5th harmonic currents excited by inter-turn short circuit based on series reactance arcing as described in claim 1, characterized in that, The digital circuit simulation model includes an equivalent simulation part of the power system, an equivalent simulation part of the substation and capacitor bank, and an equivalent simulation part of the filter bank of the AC system of the DC-DC converter station that affects the harmonic characteristics of the system. The equivalent simulation of the power system includes a generator, an ideal double-winding step-up transformer, and... The equivalent simulation section of the substation includes a step-down transformer and a switchable parallel capacitor bank; the generator is used to provide a stable voltage, and the ideal dual-winding step-up transformer is used to step up the stable voltage to meet the power supply standard; The step-down transformer is used to step down the high voltage input from the step-up transformer in the power system. The switchable parallel capacitor bank includes a series reactor and a capacitor. The series reactor coil is set to simulate an inter-turn short-circuit fault with an increasing number of turns. When simulating the short circuit, it is equivalent to a combination of proportional or non-proportional stepped units to realize the simulation of the early, middle and late stages of the short-circuit fault development.

3. The modeling and simulation method for 3rd and 5th harmonic currents excited by inter-turn short circuit based on series reactance arcing as described in claim 2, characterized in that, In the digital circuit simulation model, based on the relationship between the short-circuit circulating current ampere-turn balance flux caused by the number of short-circuit turns and the total ampere-turns of the overall coil, the following real-time electromagnetic induction ampere-turn balance equation is established: Where N12 represents a certain number of normal turns, i.e., primary side turns. N1 is the real-time current flowing through the coil, i.e., the primary current; N2 is the number of short-circuit turns, i.e., the secondary turns. This is the real-time current of the short-circuit loop, i.e., the secondary current.

4. The modeling and simulation method for 3rd and 5th harmonic currents induced by inter-turn short circuit based on series reactance arcing as described in claim 3, characterized in that, Based on the fact that the local coil inductance disappears after the real-time ampere-turn balance is achieved during arc combustion, and recovers when the arc is extinguished; and considering the equivalent circuit parameters from the primary two-port side, the equivalent resistance can be expressed by the following formula: Where: Rs is the single-turn resistance, and R12 is the equivalent resistance of the primary side of the port. For the current flowing through the coil, N is the short-circuit loop current, and N2 is the number of short-circuit turns.

5. The modeling and simulation method for 3rd and 5th harmonic currents excited by inter-turn short circuit based on series reactance arcing as described in claim 1, characterized in that, By using different trigger angles of the bidirectional short-circuit arc-controlled thyristor to control the turn-on and turn-off times and durations of the positive and negative half-waves, the reignition characteristics of the arc after the arc of the positive and negative half-wave arc short circuit are simulated. The equivalent resistance of the inter-turn short-circuit circulating current loss is used to simulate the characteristics of the equivalent resistance of the active power loss generated by the circulating current after the inter-turn short circuit, and the equivalent inductance of the inter-turn short-circuit loss series reactance is used to simulate the characteristics of the inductance loss increasing as the inter-turn short circuit continues to expand.

6. The modeling and simulation method for 3rd and 5th harmonic currents excited by inter-turn short circuit based on series reactance arcing as described in claim 1, characterized in that, In S2, the dynamic simulation test of arc-induced inter-turn short circuit of series reactor is completed by combining proportional or non-proportional stepped units. This includes simulating the series reactor using dry-type hollow series reactor, using stepped timing control to control the triggering and conduction angle of bidirectional thyristors, and simulating the nonlinear expansion process of the short-circuit turn of the dry-type hollow series reactor after the fault. Specifically, the following steps are included: S201. Based on the data when a short circuit fault actually occurs, when the inductance loss is 100%, the number of short circuit turns is 40 turns. The equivalent inductance of the inter-turn short circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short circuit circulating current loss are reduced proportionally or non-proportionally according to the preset number of steps. S202. When the equivalent inductance of the inter-turn short-circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short-circuit circulating current loss are reduced according to the gradient, the current of each series equivalent resistance is calculated as the short-circuit circulating current increases to 15 to 30 times the rated current.

7. The modeling and simulation method for 3rd and 5th harmonic currents induced by inter-turn short circuit based on series reactance arcing as described in claim 6, characterized in that, In S201, when the equivalent inductance of the inter-turn short-circuit loss series reactance and the equivalent resistance of the adjustable inter-turn short-circuit circulating current loss are reduced proportionally or non-proportionally according to a preset number of steps, it also includes simulating the delayed short-circuit discharge arc reignition time after the series reactance voltage peak in one power frequency cycle according to different triggering angles with a preset number of steps of 5 and the inductance loss gradient being a non-proportional gradient.

8. The modeling and simulation method for 3rd and 5th harmonic currents excited by inter-turn short circuit based on series reactance arcing as described in claim 6, characterized in that, It also includes the content of the 3rd and 5th harmonics in digital circuit simulation models under different inductance loss levels; and the content of the 3rd and 5th harmonics under different triggering angles.

9. The modeling and simulation method for 3rd and 5th harmonic currents induced by inter-turn short circuit based on series reactance arcing as described in claim 5, characterized in that, The content of the third and fifth harmonics obtained from the digital circuit simulation model is compared with the actual parameters of the inter-turn fault case of the dry air-core reactor. The parameters in the digital circuit simulation model are adjusted according to the comparison results.

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