Full-wave and chopping response simulation test method for lightning impulse of transformer

Abstract

The invention relates to a transformer lightning impulse full-wave and chopping response simulation test method, which comprises the following steps of: constructing a transformer model, carrying out frequency response analysis (FRA) on a transformer, and generating a transformer admittance model by adopting vector fitting; a lightning impulse test circuit model is established, the impulse test circuit comprises a multi-stage Marx impulse voltage generator MIG, a voltage divider and a chopper, an equivalent circuit state-space equation of the lightning impulse test circuit is established, and full-wave and chopping time domain response of a transformer is obtained by solving the state-space equation in a time domain; and calculating the output full-wave and chopping impulse response voltage based on the time domain response. Compared with the prior art, the method has the advantages that each element in the transformer impact test circuit is accurately modeled, and the output impact voltage is obtained by solving the equivalent circuit equation in the state space system and calculating the time domain signals of all state variables, so that the accuracy of the whole test system is ensured.

Description

Technical Field

[0001] The present invention relates to the field of lightning protection for transformer insulation testing, and in particular to a method for accurately simulating full wave (Full Wave, FW) and chopped wave (Chopped Wave, CW) pulses in the time domain for offshore booster station transformer insulation testing. Background Art

[0002] The sea is an area with strong lightning activity. Even if the main transformer is arranged indoors, the main transformer oil pillow is still exposed to the outdoors and may be struck by lightning. When the oil pillow is struck by lightning, the overvoltage generated will cause insulation damage to the equipment in the booster station. Therefore, the insulation system of the transformer must be evaluated to determine whether it can withstand the stress caused by lightning. According to the IEC 60076 standard, newly produced high-voltage transformers usually use full impulse voltage and chopping impulse voltage.

[0003] In order to obtain a standard LI waveform with predefined rise and tail times and ensure that overshoot is minimized, it is necessary to accurately modify the parameters of the Marx impulse generator commonly used in high-voltage laboratories, including the forward and tail resistances and the number of series and parallel stages. Errors in these parameters may produce non-standard waveforms, especially in chopping tests, which will subject the transformer insulation to high stress and may cause insulation failure. Therefore, before conducting the test, it is necessary to develop an accurate circuit modeling method to predict the shape and parameters of the generated waveform to ensure that a standard waveform is obtained at the transformer terminals in a shorter test time. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for testing insulation performance by accurately simulating FW and CW pulses in the time domain.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A full-wave and chopping-wave response simulation test method for a transformer lightning impulse, comprising the steps of:

[0007] Construct a transformer model, perform frequency response analysis (FRA) on the transformer, and use vector fitting to generate the transformer admittance model;

[0008] The lightning impulse test circuit model established includes a multi-stage Marx impulse voltage generator MIG, a voltage divider and a chopper;

[0009] The equivalent circuit state space equation of the lightning impulse test circuit is constructed, and the full-wave and chopping time domain responses of the transformer are obtained by solving the state space equation in the time domain; the full-wave and chopping impulse response voltages of the transformer are obtained based on the time domain response.

[0010] As a preferred technical solution, the frequency response analysis FRA uses an FRA test device containing a variable frequency AC voltage source to excite the transformer winding, and the FRA test device is provided with a cable resistor to avoid reflection of the measurement cable;

[0011] In the FRA test, the wiring of the transformer terminals is consistent with the lightning impulse test. All terminals except the tested terminal are grounded, and the transfer function of the transformer admittance from the tested terminal to the ground is obtained:

[0012]

[0013] Extract the transformer high frequency admittance from the transfer function:

[0014]

[0015] Where V1(jω) and V2(jω) are the measured input and output voltages in the frequency domain, ω=2πf is the discrete angular frequency vector, V3(jω) is the voltage drop between the transformer terminal and the oil tank, I2 is the current passing through it, and R is the cable resistance.

[0016] After taking FRA measurements and performing vector fitting, the transformer model is considered as a black box and its admittance is estimated in the Laplace domain as follows:

[0017]

[0018] In the formula, d and e are constants, and c i and p i are the residues and poles, determined by the admittance formula. n+m represents the number of poles, and s represents the Laplace variable;

[0019] The RLC circuit model of the transformer obtained by estimating the admittance in the Laplace domain: R0 and C0 are generated by d and e, the real poles and residues form n branches containing R and L elements, and the conjugate poles and residues generate m branches containing R, L, C and G:

[0020]

[0021] R i =-p i / c i L i =1 / c i

[0022]

[0023]

[0024] After the transformer RLC circuit model is established, its passivity is checked; if the real part of the admittance has a positive eigenvalue, no passivity check is performed.

[0025] As a preferred technical solution, the multi-level Marx impulse voltage generator MIG model is as follows:

[0026] Each stage of the MIG model includes a spark gap SG; one side of the spark gap SG is connected to the transformer terminal to be tested, and the other side is connected to the charging resistor R L Connect the DC power supply V G ; The spark gap SG is connected in parallel with an equivalent surge capacitor; a series resistor R is set between the spark gap SG of each level and the terminal to be tested of the transformer and the next level s And the parallel resistor R p ;

[0027] The MIG model consists of two stages;

[0028] In the first stage, a DC power supply V G Through the charging resistor R L Charging the equivalent surge capacitor of the MIG model;

[0029] In the second stage, the spark gap SG is triggered and the equivalent surge capacitor of the MIG model is connected to the series resistor R s The capacitor of the transformer to be tested is discharged to form a wavefront time, and then the parallel resistor R p Discharge wave tail time, charging resistance R L As an open circuit.

[0030] As a preferred technical solution, the MIG model generates the required lightning impulse waveform through a circuit in series or in parallel, wherein the circuit of the MIG model includes a plurality of units in series, each of which includes a plurality of elements in parallel, and the MIG can be bypassed or short-circuited at certain stages;

[0031] The MIG model is provided with a control charging resistor as a switch in each circuit stage, which connects the circuit during charging and isolates the circuit during discharging. The closing and opening of the switch are represented by adjusting the resistance value of the control charging resistor before simulation to control the switch of the circuit to obtain the required lightning impulse waveform.

[0032] As a preferred technical solution, the spark gap of the MIG model adopts a stray inductance L SG Instead of connecting a resistor in series; the series resistor R sAnd the parallel resistance and equivalent surge capacitor C S Set the stray inductance L S ,L P and L CS .

[0033] As a preferred technical solution, the voltage divider adopts a multi-stage damping capacitor voltage divider; each stage is equipped with its own capacitor C div , a damping resistor R div and a stray inductance L div ;

[0034] The chopper includes a spark gap, a grading capacitor C chop And the damping resistor R chop Used to generate chopper LI voltage; the spark gap SGs of the chopper can be replaced by a resistor R SG and inductor L SG Indicates the switch.

[0035] As a preferred technical solution, each element of the voltage divider and chopper model is provided with a stray inductance; the output ends of the MIG, voltage divider and chopper are connected to the transformer terminals through wires, and the wires are respectively provided with stray inductance L A , L B and L C .

[0036] As a preferred technical solution, the method assigns a state variable to each capacitor voltage and inductor current, and constructs the state space equation of the lightning impulse test circuit as follows:

[0037]

[0038] Where:

[0039]

[0040] Among them, L tr and R tr The matrix contains the transformer model inductors L1, L2..., L n+m and resistors R0, R1, R2..., R n+m Elements; R chop The matrix includes the resistance of the chopper circuit, L C,div The matrix contains the inductor L of the voltage divider circuit div , and the inductance L of the wire C ; C tr and G tr is a symmetric matrix involving capacitance and conductance in the transformer circuit; C G is a MIG capacitor C SThe Q and P matrices contain 0, +1, -1.

[0041] After solving the state space equation of the lightning impulse test circuit to obtain the state variables, the expected output lightning impulse response voltage at the transformer end is determined according to the established lightning impulse test circuit:

[0042]

[0043] In the formula, I div is the inductance of the voltage divider circuit, V div,z is the voltage of the voltage divider circuit, R div,z is the resistance of the voltage divider circuit, L div,z is the inductance of the voltage divider circuit and z is the component number.

[0044] As a preferred technical solution, when simulating a full-wave lightning impulse test, the method sets the initial values ​​of all state variables in the state space equation of the lightning impulse test circuit and the calculation formula for the expected output LI voltage at the transformer end to zero, except that the state variables related to the MIG-level capacitor voltage are set to the initial DC charging voltage.

[0045] As a preferred technical solution, the method performs two separate simulations when simulating the chopping lightning impulse experiment:

[0046] First simulation: At a time step smaller than the chopping time t chop In the case of a chopper, the chopper spark gap resistance R SG The resistors are assigned high values ​​to perform full-wave lightning impulse test simulations;

[0047] Second simulation: Chopper spark gap resistance R SG Set to a low value by extracting the chop The state variable value at time is taken as the initial value, and the time step is greater than the chopping time t chop The second simulation is performed under the same conditions, and the state space equation of the test circuit and the expected output lightning impulse response voltage at the transformer end are solved again; the chopped lightning impulse test results are obtained by combining the two test results.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1) The present invention measures the frequency response of the transformer and generates its admittance model using vector fitting (VF) technology. Vector fitting technology can accurately fit the frequency response characteristics of the transformer, thereby generating a high-precision admittance model for subsequent impulse test simulation. In addition, the present invention accurately models each component in the transformer impulse test circuit, including key components such as resistance, inductance and capacitance, to ensure the accuracy of the entire test system.

[0050] 2) After completing the accurate modeling, the present invention calculates the time domain signals of all state variables by solving the equivalent circuit equations in the state space system. The state space system can effectively represent the dynamic behavior of the entire test circuit, and accurately solve the relevant circuit equations through numerical methods to obtain the time domain response of each state variable. Based on these time domain responses, the output impulse voltage can be finally calculated.

[0051] 3) The present invention also accurately models the lightning test system, which can be simulated by a precise computer. The model engineers can quickly and accurately adjust the settings of the impulse generator and the circuit to ensure that the applied impulse waveform meets the standard requirements. At the same time, the present invention reduces the reliance on manual operation, reduces the complexity of operation and the impact of human error on the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of the full-wave and chopping-wave response simulation test method of the transformer lightning impulse of the present invention;

[0053] Figure 2 This is the 12-level MIG circuit diagram, R s ,R P : Series and parallel resistance, C S1 ,C s2 : two equal capacitors, SG: spark gap, V G : Charging DC voltage, R L : Charging resistance;

[0054] Figure 3 This is the MIG connection diagram, N S =12,N P =1;

[0055] Figure 4 (a) is the control resistor R used to simulate the NS and NP arrangement required for MIG A ,R B ,R C ,R D and R E ; (b) is the 12-level MIG equivalent circuit with NS=6, NP=2; L S ,LP ,L CS and L SG Represents the series and parallel resistance, capacitance and stray inductance of the spark gap after triggering. A ,R B ,R C ,R D and R E Responsible for changing the circuit structure. GS is the spark gap resistance after triggering;

[0056] Figure 5 The schematic diagram of the FRA test circuit and the transformer terminal connection method are used to measure and calculate the TF of the transformer admittance;

[0057] Figure 6 The equivalent circuit of a transformer with n real poles and m complex poles;

[0058] Figure 7 Transformer LI test circuit diagram, including chopper and voltage divider circuit, C div : The voltage divider stage capacitance, C chop The chopper's segment capacitance, R m :Used to accelerate the triggering of SG S The resistor, R SG ,L SG : Indicates the spark gap, R div ,L div ,R chop ,L chop : represent the stray resistance and inductance of the voltage divider, the capacitance of the chopper, L A ,L B and L C : stray inductance of copper wire;

[0059] Figure 8 Flowchart for CW simulation in time domain. DETAILED DESCRIPTION

[0060] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0061] Example 1

[0062] The present invention proposes a method that can accurately simulate full wave (Full Wave, FW) and chopped wave (Chopped Wave, CW) pulses in the time domain for the insulation test of offshore substation transformers. According to the international standard IEC 60076, the transformer must be applied with FW and chopped wave CW lightning impulse voltages to verify its insulation performance and impact resistance, which belongs to the field of lightning protection of transformer insulation test. The invention first measures the frequency response of the transformer and generates its admittance model using vector fitting (Vector Fitting, VF) technology. Vector fitting technology can accurately fit the frequency response characteristics of the transformer, thereby generating a high-precision admittance model for subsequent impulse test simulation. In addition, the present invention accurately models each component in the transformer impulse test circuit, including key components such as resistance, inductance and capacitance, to ensure the accuracy of the entire test system. After the modeling is completed, the present invention calculates the time domain signals of all state variables by solving the equivalent circuit equations in the state space system. The state space system can effectively represent the dynamic behavior of the entire test circuit, and accurately solve the relevant circuit equations through numerical methods to obtain the time domain response of each state variable. Based on these time domain responses, the output surge voltage can be calculated. Figure 1 As shown, the precise modeling and full-wave and chopping response simulation test method of the transformer lightning impulse chopping test provided by the present invention comprises the following specific steps:

[0063] Step 1, constructing a Marx Impulse Voltage Generator (MIG) model;

[0064] Step 2: construct a transformer model, measure the frequency response of the transformer, and then use vector fitting technology to obtain its admittance model;

[0065] Step 3: Accurately model the pulse test circuit components of the transformer and construct the voltage divider and chopper models;

[0066] Step 4: Construct a state space equation for a lightning impulse (LI) test circuit. By solving the state space equation in the time domain, the full wave waveform and the chopped wave waveform of the voltage are calculated.

[0067] In step 1, the MIG model is constructed. In each level of the MIG, there is a series resistor R s And the parallel resistor R p ; SG stands for spark gap; C s1 and C s2 Represents two equivalent surge capacitors. Figure 2 As shown, one side of the spark gap SG is connected to the transformer terminal to be tested, and the other side is connected through the charging resistor RL Connect the DC power supply V G ; The spark gap SG is connected in parallel with an equivalent surge capacitor; a series resistor R is set between the spark gap SG of each level and the terminal to be tested of the transformer and the next level s And the parallel resistor R p .

[0068] MIG consists of two stages; in the first stage, a DC power supply V G Through the charging resistor (R L ) charges the MIG capacitor. Similarly, the second stage begins when the spark gap SG is triggered, and the MIG capacitor C s1 and C s2 By R s The capacitor discharge of the test object forms a wavefront time, and then passes through R p The discharge forms the wave tail time. At this stage, the high impedance charging resistor R L can be treated as an open circuit instead. Moreover, C s1 and C s2 An equal value capacitor C s To express:

[0069]

[0070] According to the high-frequency impedance characteristics of the test object, the circuit can be connected in series or in parallel to make the MIG produce the required LI waveform. The circuit contains multiple series units (NS), and each series unit contains multiple parallel components (NP), such as Figure 3 In addition, the MIG may be bypassed or short-circuited at certain stages. Figure 4 As shown in (a), in order to set the settings required by the impulse generator in the simulation, some hypothetical control charging resistors are added to the circuit, including R A ,R B ,R C ,R D and R E These resistors can be used as switches and their values ​​can be adjusted before simulation. When the resistance value is very low, such as a few ohms, it means the switch is closed, and when the resistance is large, such as a few megohms, it means the switch is open. The charging resistor acts as a connection circuit during charging and acts as an isolation circuit during discharge. By adjusting the size of these resistors, the desired waveform can be obtained by controlling the switching of the circuit. The bold R A ,R B ,R C ,R D Indicates parallel connection, bold R E Indicates series connection.

[0071] Components in the circuit such as resistors contain stray capacitance, inductance and resistance which will affect the voltage waveform of the output LI. These factors must be taken into account in order to obtain an accurate model. Figure 4 (b) Taking these factors into account, the model is more accurate than 4(a). In this model, the spark gap is represented by the stray inductance (L SG ) in place of a small resistor (R SG ), R S ,R P and C S The stray inductance is represented by L S ,L P and L CS .

[0072] In step 2, the transfer function (TF) of the transformer impedance or admittance is obtained by using the measurement results of the frequency response analysis (FRA). Then, the circuit model of the transformer is obtained by using the reasonable approximation method of the vector fitting (VF) technology and the measured transfer function TF of the transformer. This is achieved by iteratively improving parameter estimation, adjusting pole positions and optimizing coefficients until a satisfactory fit is obtained. The obtained rational function model can accurately approximate the frequency response of the system within the desired frequency range.

[0073] In order to obtain the measurement data, a FRA test device containing a variable frequency AC voltage source is used to excite the transformer winding. A broadband frequency sweep signal is applied to the input of the transformer and the response at the output is recorded. During the test, input and output data at different frequencies are collected, which reflect the gain and phase characteristics of the transformer at different frequencies. Using the collected data, the transfer function value at each frequency point is obtained by calculating the ratio of the output to the input at that frequency point. In order to obtain the analytical form of the transfer function, a rational function needs to be fitted based on the actual data. The accuracy of the model can be verified by comparing the response predicted by the model with the actual measured response.

[0074] Some 50 ohm resistors are used in the FRA test equipment to avoid reflections from the measurement cable. In the FRA test, the wiring of the transformer terminals must be consistent with the LI test, and all terminals except the terminal under test must be grounded. In this way, the transfer function of the transformer's admittance from the terminal under test to ground can be obtained. Figure 5 shown.

[0075] The transfer function is calculated as follows:

[0076]

[0077] Where V1(jω) and V2(jω) are the measured input and output voltages in the frequency domain, respectively, and ω=2πf is the discrete angular frequency vector.

[0078] The admittance of the measured terminal relative to the ground can be obtained by the following formula:

[0079]

[0080] In the formula, V3(jω) is the voltage drop between the transformer terminal and the oil tank, and I2 is the current passing through it. Then, using formula (2) and formula (3), the transformer high-frequency admittance can be extracted from the transfer function:

[0081]

[0082] Wherein, R is the resistance of the cable, which is 50Ω in this embodiment.

[0083] After performing FRA measurements and applying the VF technique, the transformer model can be considered as a black box and its admittance can be estimated in the Laplace domain:

[0084]

[0085] In the formula, d and e are constants, and c i and p i are the residues and poles, determined by the admittance formula. n+m represents the number of poles, and s represents the Laplace variable.

[0086] The transformer circuit model obtained by equation (5) is Figure 6 It means that R0 and C0 are generated by d and e, the real poles and residues form n branches containing R and L elements, and the conjugate poles and residues will produce m branches containing R, L, C and G. These parameters are expressed by equations (6)-(9).

[0087]

[0088]

[0089] After the transformer RLC model is established, its passivity must be checked. If the real part of the admittance has a positive eigenvalue, no passivity check is required.

[0090] Step 3 uses a three-stage damped capacitor divider in the measurement; each stage is equipped with its own capacitor C div , a damping resistor R div and a stray inductance L divWhen capacitors are connected in series, the voltage across each capacitor is inversely proportional to its capacitance. Damping resistors are placed in series with capacitors to absorb excess electrical energy and reduce oscillations and spikes in the circuit, thereby protecting the capacitors from damage. Damping resistors are primarily used to reduce oscillations in circuits that can be caused by rapidly changing voltages. By limiting the amount of current that flows through a circuit, damping resistors help prevent voltage reflections and excessive voltage spikes.

[0091] The chopper includes 12 spark gaps (Spark Gap, SG S ) and 12 grading capacitors C chop And the damping resistor R chop Used to generate the chopper LI voltage. Similar to the spark gap SGs of the MIG, the spark gap SGs of the chopper can be regarded as composed of R SG Resistance and L SG The inductor represents the switch. When the spark gap is turned on, the power supply charges the load and the capacitor. Due to the existence of the spark gap, the current can be accurately cut off when a certain voltage is reached, thus forming a pulse signal. When the spark gap is closed, the current is cut off, but due to the existence of the grading capacitor, the energy stored in the capacitor will continue to supply power to the load, ensuring the voltage stability at the load end. At this time, the damping resistor consumes excess energy and reduces circuit oscillation.

[0092] like Figure 7 As shown, for each component of the voltage divider and chopper models, the stray inductance L is taken into account. div and L chop , because stray inductance is caused by the physical layout of the circuit and the nature of its components. When operating at high frequencies, stray inductance can significantly affect the behavior of the circuit, possibly resulting in undesirable inductive reactance, which affects the overall performance of the circuit. The output of the MIG, voltage divider, and chopper are connected directly to the transformer terminals using some copper wires that are Figure 7 By L A , L B and L C The stray inductance is represented by .

[0093] According to the state space theory of the circuit, step 4 can assign a state variable to each capacitor voltage and inductor current. By applying Kirchhoff's first and second laws and differential equations, the state space equation of the LI test circuit can be obtained as follows:

[0094]

[0095]

[0096] Where:

[0097]

[0098] Among them, L tr and R tr The matrix contains the transformer model inductors L1, L2..., L n+m and resistors R0, R1, R2..., R n+m Elements of R chop The matrix includes the resistance of the chopper circuit, L C,div The matrix contains the inductor L of the voltage divider circuit div , and the inductance L of the copper wire C In addition, C tr and G tr is a symmetric matrix involving the capacitance and conductance in the transformer circuit. Similarly, C G is a MIG capacitor C S The Q and P matrices contain 0, +1, and -1.

[0099] Formula (10) and (11) can be rewritten as:

[0100]

[0101] After solving equation (12) to obtain the state variables, according to Figure 7 The LI test circuit shown can determine the expected output LI response voltage at the transformer end as:

[0102]

[0103] In the formula, I div is the inductance of the voltage divider circuit, V div,z is the voltage of the voltage divider circuit, R div,z is the resistance of the voltage divider circuit, L div,z is the inductance of the voltage divider circuit; z is the component number.

[0104] MATLAB programming code and its ordinary differential equation (ODE) function are used to solve equations (12) and (13). By solving these equations, the desired output LI voltage can be obtained.

[0105] When simulating the full-wave FW LI test, the initial values ​​of all state variables in Equations (12) and (13) are set to zero, except for the state variable related to the MIG stage capacitor voltage, which is set to the initial DC charging voltage.

[0106] The process of simulating chopping CF LI is similar, but there are some differences. Because the spark gap of the chopper is at the chopping time t chopare triggered, and their role after triggering changes from open circuit to short circuit, so two separate simulations are required in the case of chopped LI experimental simulation. First, at a time step smaller than the chopping time t chop In this case, the R SG The full-wave LI test simulation is performed by assigning high values ​​to the resistors. chop The state variable value at the moment, solve (12) and (13) again, for the time step greater than the chopping time t chop In the second simulation, the chopper R SG Set to a low value to chop The state variable values ​​obtained at the moment are taken as their initial values. The state variables of the final chopping LI test are obtained by combining the results of the two tests. SG It has a significant effect on the rate of voltage collapse and overshoot after cutting. Figure 8 The flowchart in provides a detailed schematic diagram of the method used to perform CW simulations in the time domain.

[0107] Example 2

[0108] As a second aspect of the present invention, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above method. In addition to the above-mentioned processor, memory and interface, any device with data processing capability in which the device in the embodiment is located may also include other hardware according to the actual function of the device with data processing capability, which will not be described in detail.

[0109] Example 3

[0110] As a third aspect of the present invention, the present application also provides a computer-readable storage medium on which computer instructions are stored, and when the instructions are executed by a processor, the above method is implemented. The computer-readable storage medium can be an internal storage unit of any device with data processing capabilities described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. Further, the computer-readable storage medium can also include both an internal storage unit of any device with data processing capabilities and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and can also be used to temporarily store data that has been output or is to be output.

[0111] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A transformer lightning impulse full-wave and chopping response simulation test method, characterized in that the steps include: Construct a transformer model, perform frequency response analysis (FRA) on the transformer, and use vector fitting to generate the transformer admittance model; The lightning impulse test circuit model established includes a multi-stage Marx impulse voltage generator MIG, a voltage divider and a chopper; The equivalent circuit state space equation of the lightning impulse test circuit is constructed, and the full-wave and chopping time domain responses of the transformer are obtained by solving the state space equation in the time domain; the full-wave and chopping impulse response voltages of the transformer are obtained based on the time domain response.

2. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 1, characterized in that: The frequency response analysis FRA uses an FRA test device containing a variable frequency AC voltage source to excite the transformer winding, and the FRA test device is provided with a cable resistor to avoid reflection of the measurement cable; In the FRA test, the wiring of the transformer terminals is consistent with the lightning impulse test. All terminals except the tested terminal are grounded, and the transfer function of the transformer admittance from the tested terminal to the ground is obtained: Extract the transformer high frequency admittance from the transfer function: Where V1(jω) and V2(jω) are the measured input and output voltages in the frequency domain, ω=2πf is the discrete angular frequency vector, V3(jω) is the voltage drop between the transformer terminal and the oil tank, I2 is the current passing through it, and R is the cable resistance. After taking FRA measurements and performing vector fitting, the transformer model is considered as a black box and its admittance is estimated in the Laplace domain as follows: In the formula, d and e are constants, and c i and p i are the residues and poles, determined by the admittance formula, n+m represents the number of poles, and s represents the Laplace variable; The RLC circuit model of the transformer obtained by estimating the admittance in the Laplace domain: R0 and C0 are generated by d and e, the real poles and residues form n branches containing R and L elements, and the conjugate poles and residues generate m branches containing R, L, C and G: R i =-p i / c i L i =1 / c i After the transformer RLC circuit model is established, its passivity is checked; if the real part of the admittance has a positive eigenvalue, no passivity check is performed.

3. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 1, characterized in that: The multi-level Mar x The impulse voltage generator MIG model is as follows: Each stage of the MIG model includes a spark gap SG; one side of the spark gap SG is connected to the transformer terminal to be tested, and the other side is connected to the charging resistor R L Connect DC power supply V G ; The spark gap SG is connected in parallel with an equivalent surge capacitor; a series resistor R is set between the spark gap SG of each level and the terminal to be tested of the transformer and the next level s And the parallel resistor R p ; The MIG model consists of two stages; In the first stage, a DC power supply V G Through the charging resistor R L Charging the equivalent surge capacitor of the MIG model; In the second stage, the spark gap SG is triggered and the equivalent surge capacitor of the MIG model is connected to the series resistor R s The capacitor of the transformer to be tested is discharged to form a wavefront time, and then the parallel resistor R p Discharge wave tail time, charging resistance R L As an open circuit.

4. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 3, characterized in that: The MIG model generates the required lightning impulse waveform through a circuit in series or in parallel, wherein the circuit of the MIG model comprises a plurality of units in series, each of which comprises a plurality of elements in parallel, and the MIG can be bypassed or short-circuited at certain stages; The MIG model is provided with a control charging resistor as a switch in each circuit stage, which connects the circuit during charging and isolates the circuit during discharging. The closing and opening of the switch are represented by adjusting the resistance value of the control charging resistor before simulation to control the switch of the circuit to obtain the required lightning impulse waveform.

5. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 3, characterized in that: The spark gap of the MIG model described adopts the stray inductance L SG Instead of connecting a resistor in series; the series resistor R s And the parallel resistance and equivalent surge capacitor C S Set the stray inductance L S ,L P and L CS .

6. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 1, characterized in that: The voltage divider described uses a multi-stage damping capacitor voltage divider; each stage is equipped with its own capacitor C div , a damping resistor R div and a stray inductance L div ; The chopper includes a spark gap, a grading capacitor C chop And the damping resistor R chop Used to generate chopper LI voltage; the spark gap SGs of the chopper can be replaced by a resistor R SG and inductor L SG Indicates the switch.

7. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 6, characterized in that: Each element of the voltage divider and chopper model is provided with a stray inductance; the output ends of the MIG, voltage divider and chopper are connected to the transformer terminals through wires, and the wires are respectively provided with stray inductances L A , L B and L C .

8. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 1, characterized in that: The method assigns a state variable to each capacitor voltage and inductor current, and constructs the state space equation of the lightning impulse test circuit as follows: Where: Among them, L tr and R tr The matrix contains the transformer model inductance L1, L 2... ,L n+m and resistors R0, R1, R2..., R n+m Elements; R chop The matrix includes the resistance of the chopper circuit, L C,div The matrix contains the inductor L of the voltage divider circuit div , and the inductance L of the wire C ; C tr and G tr is a symmetric matrix involving capacitance and conductance in the transformer circuit; C G is a MIG capacitor C S The Q and P matrices contain 0, +1, -1. After solving the state space equation of the lightning impulse test circuit to obtain the state variables, the expected output lightning impulse response voltage at the transformer end is determined according to the established lightning impulse test circuit: In the formula, I div is the inductance of the voltage divider circuit, V div,z is the voltage of the voltage divider circuit, R div,z is the resistance of the voltage divider circuit, L div,z is the inductance of the voltage divider circuit and z is the component number.

9. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 8, characterized in that: When simulating a full-wave lightning impulse test, the method sets the initial values ​​of all state variables in the state space equation of the lightning impulse test circuit and the transformer end expected output LI voltage calculation formula to zero, except that the state variable related to the MIG-level capacitor voltage is set to the initial DC charging voltage.

10. A transformer lightning impulse full-wave and chopping response simulation test method according to claim 9, characterized in that: The method performs two separate simulations when simulating the chopping lightning impulse experiment: First simulation: At a time step smaller than the chopping time t chop In the case of a chopper, the chopper spark gap resistance R SG The resistors are assigned high values ​​to perform full-wave lightning impulse test simulations; Second simulation: Chopper spark gap resistance R SG Set to a low value by extracting the chop The state variable value at time is taken as the initial value, and the time step is greater than the chopping time t chop The second simulation is performed under the same conditions, and the state space equation of the test circuit and the expected output lightning impulse response voltage at the transformer end are solved again; the chopped lightning impulse test results are obtained by combining the two test results.

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