A PTC resistance selection method for overvoltage suppression of an electromagnetic voltage transformer

Abstract

The application provides a PTC resistance selection method for overvoltage suppression of an electromagnetic voltage transformer, and belongs to the technical field of electromagnetic voltage transformers, and comprises the following steps: firstly, recording electrical parameters of the transformer under normal and overvoltage operation states and parameters of overvoltage suppression resistance; based on the data, establishing a transformer operation equation group considering multiple factors, and fitting to obtain operation parameters; then, using an overvoltage suppression effect evaluation model, optimizing the parameters of the overvoltage suppression resistance through a genetic algorithm, and taking the minimum overvoltage and duration as the target; and finally, according to the optimization result, selecting a suitable model from existing PTC resistance products as the final configuration. The method combines electromagnetism theory, thermodynamic principles, optimization algorithms and engineering practice, and solves the technical problem that the overvoltage protection scheme in the prior art mostly adopts an empirical design method and lacks a systematic and quantitative optimization process.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic voltage transformers, and particularly relates to a PTC resistance selection method for overvoltage suppression of an electromagnetic voltage transformer. BACKGROUND

[0002] As a key device in power systems, electromagnetic voltage transformers are widely used in fields such as voltage measurement, relay protection and electric energy metering. With the continuous expansion of the power grid scale and the sustained growth of electricity demand, power systems are facing more complex operating environments and higher reliability requirements. Under this background, the overvoltage suppression performance of electromagnetic voltage transformers becomes particularly important.

[0003] Traditional electromagnetic voltage transformers mainly rely on their own impedance characteristics and magnetic saturation effects to suppress overvoltage. However, this passive approach often reacts too slowly and has limited suppression effect when facing transient overvoltage. In particular, in the event of short-circuit faults, lightning strikes or switch operations in power systems, high-amplitude, rapidly changing overvoltages can cause serious distortion of the secondary side voltage of the transformer, and even damage the measuring instruments and protection devices connected thereto.

[0004] In order to improve the overvoltage suppression effect, some existing technologies use non-linear resistors, metal oxide arresters and other protection elements. These methods have improved the overvoltage resistance of the transformer to some extent, but also have some limitations. For example, the response speed of non-linear resistors is slow, making it difficult to effectively suppress rapidly rising transient overvoltages; although metal oxide arresters respond quickly, their protection characteristics are fixed and difficult to optimize and adjust according to different working conditions.

[0005] On the other hand, with the development of smart grids, higher requirements are placed on the measurement accuracy and dynamic response of voltage transformers. However, existing overvoltage protection schemes often affect the measurement accuracy of the transformer, especially in normal operating conditions, which can introduce additional non-linear errors.

[0006] In addition, the overvoltage protection schemes in existing technologies mostly use empirical design methods, lacking systematic and quantitative optimization processes. This results in the selection and parameter setting of protection elements in actual applications often requiring long-term testing and adjustment, which not only consumes time and effort, but also makes it difficult to adapt to different types of transformers and diverse application scenarios. SUMMARY

[0007] Therefore, the present application provides a PTC resistance selection method for overvoltage suppression of an electromagnetic voltage transformer, which can solve the technical problem that existing overvoltage protection schemes mostly use empirical design methods, lacking systematic and quantitative optimization processes.

[0008] The present application is implemented as follows:

[0009] The present application provides a PTC resistance selection method for overvoltage suppression of an electromagnetic voltage transformer, comprising the following steps:

[0010] S10, selecting a plurality of PTC resistors with different parameters as overvoltage suppression resistors of the electromagnetic voltage transformer, and installing them one by one, and performing subsequent steps S20 and S30 on each PTC resistor;

[0011] S20, recording electrical parameters of the electromagnetic voltage transformer in a normal operating state and PTC resistance parameters of the overvoltage suppression resistor, as normal operation data, wherein the electrical parameters include primary side voltage, secondary side voltage, primary side current, secondary side current, output power, power factor, harmonic content, overvoltage, and overvoltage duration; and the PTC resistance parameters include normal temperature resistance, Curie temperature, temperature coefficient, voltage coefficient, and power density;

[0012] S30, adjusting the operating environment of the electromagnetic voltage transformer, and applying voltage in a stepwise increasing manner, and recording electrical parameters, overvoltage parameters, and PTC resistance parameters of the overvoltage suppression resistor of the electromagnetic voltage transformer under different voltages, as pressurized operation data; wherein the overvoltage parameters include overvoltage and overvoltage duration;

[0013] S40, establishing an operating equation set of the electromagnetic voltage transformer considering electrical parameters, overvoltage parameters, and PTC resistance parameters, including voltage equation, current equation, power equation, temperature equation, PTC resistance characteristic equation, and overvoltage response equation;

[0014] S50, fitting parameters of the operating equation set according to the normal operation data and the pressurized operation data, to obtain a fitted operating equation set;

[0015] S60, based on the fitted operating equation set, establishing an overvoltage suppression effect evaluation model, which takes overvoltage and overvoltage duration as main evaluation indexes;

[0016] S70, optimizing PTC resistance parameters using a genetic algorithm, taking PTC resistance parameters of the initially selected plurality of PTC resistors with different parameters as an initial population, using the overvoltage suppression effect evaluation model to calculate fitness values of each group of parameters, taking minimization of overvoltage and overvoltage duration as an objective function, and setting population size, crossover probability, mutation probability, and iteration number;

[0017] S80, executing the genetic algorithm to obtain optimal PTC resistance parameters;

[0018] S90, according to the optimal PTC resistance parameters obtained, select the model closest in characteristics from the existing PTC resistance products as the final overvoltage suppression resistance selection result.

[0019] Wherein, the formula of the equation set is expressed as follows:

[0020] 1. Voltage equation, specifically expressed as:

[0021]

[0022] In the formula, V1 is the primary side voltage (input); V2 is the secondary side voltage (output); N1, N2 are the number of turns of the primary and secondary windings; I1, I2 are the primary and secondary currents; R2 is the resistance of the secondary winding; L2 is the self-inductance of the secondary winding; M is the mutual inductance coefficient; ω is the angular frequency (2πf, f is the working frequency); C s is the distributed capacitance; t is time;

[0023] This equation takes into account the basic principles of transformers, including the turns ratio, secondary impedance, mutual inductance effect and the influence of distributed capacitance.

[0024] 2. Current equation, specifically expressed as:

[0025]

[0026]

[0027] In the formula, Z1 is the total impedance of the primary side; I m is the magnetizing current; R c is the equivalent resistance of core loss; X m is the magnetizing reactance; Z1 can be calculated as follows:

[0028]

[0029] In the formula, R1 is the resistance of the primary winding; L1 is the self-inductance of the primary winding; R PTC is the current resistance value of the PTC resistance.

[0030] 3. Power equation, specifically expressed as:

[0031]

[0032] P = |V1||I1|cosφ;

[0033] Q = |V1||I1|sinφ;

[0034]

[0035] where S is apparent power; P is active power; Q is reactive power; PF is power factor; φ is phase angle between voltage and current, is the conjugate complex of the primary side current.

[0036] 4. Temperature equation, specifically expressed as:

[0037]

[0038]

[0039]

[0040] where T is PTC resistance temperature; t is time; m is PTC resistance mass; c p is PTC resistance specific heat; P loss is total loss power; h is heat transfer coefficient; A is PTC resistance surface area; T amb is ambient temperature; P core is core loss; k h is hysteresis loss coefficient; k e is eddy current loss coefficient; B m is maximum magnetic flux density.

[0041] 5. PTC resistance characteristic equation, specifically expressed as:

[0042]

[0043] where R PTC is current resistance value of PTC resistance; R0 is normal temperature resistance value; a is temperature coefficient; T0 is reference temperature (usually room temperature); T is current temperature; β is voltage coefficient; V is voltage applied on PTC resistance; γ is dynamic response coefficient.

[0044] 6. Overvoltage response equation, specifically expressed as:

[0045] V ov (t) = V peak e -t / τ sin(ωt) + V nom ;

[0046]

[0047] where V ov (t) is change of overvoltage with time; V peak is overvoltage peak value; τ is decay time constant; ω is overvoltage oscillation angular frequency; V nom is rated voltage; t ovis the overvoltage duration; H(x) is the Heaviside step function (1 when x>0, otherwise 0); V th is the overvoltage threshold voltage; V peak can be estimated by the following way:

[0048]

[0049] where k ov is the overvoltage coefficient; di / dt is the current rate of change; L eq is the equivalent inductance; these equations together constitute a complex equation set, covering various aspects of electromagnetic voltage transformers, including electrical characteristics, thermal characteristics, PTC resistance characteristics and overvoltage response. They comprehensively consider electrical parameters, overvoltage parameters and PTC resistance parameters, providing a comprehensive mathematical model for subsequent optimization process.

[0050] Specifically, the step S10 comprises:

[0051] Step 101, determining the voltage and current range of the positive temperature coefficient resistance according to the rated voltage and rated current of the electromagnetic voltage transformer;

[0052] Step 102, considering the temperature coefficient, Curie temperature and power density of the positive temperature coefficient resistance, determining the preliminary range of these parameters;

[0053] Step 103, selecting positive temperature coefficient resistors with different resistance values, the resistance value range being between one time and ten times of the zero point of the secondary side load impedance of the transformer;

[0054] Step 104, selecting at least five positive temperature coefficient resistance samples with different parameter combinations from different manufacturers;

[0055] Step 105, installing the selected positive temperature coefficient resistance samples in the secondary side of the electromagnetic voltage transformer respectively, in series with the secondary winding;

[0056] The step S20 specifically comprises:

[0057] Step 201, connecting the electromagnetic voltage transformer to a standard voltage source and a standard load, setting the voltage source output to the rated primary voltage of the transformer;

[0058] Step 202, measuring the primary side voltage, secondary side voltage, primary side current, secondary side current, output power and power factor of the transformer using high-precision voltmeter, ammeter and power analyzer;

[0059] Step 203, measuring the harmonic content of voltage and current using a harmonic analyzer;

[0060] Step 204, simulate overvoltage by applying one point two times rated voltage for a moment on primary side and quickly recovering to rated voltage, record secondary side voltage waveform using high-speed oscilloscope;

[0061] Step 205, measure resistance value of positive temperature coefficient resistance at different temperatures using precision resistance tester, obtain its room temperature resistance value, temperature coefficient and Curie temperature;

[0062] Step 206, determine voltage coefficient by measuring resistance value at different voltages, calculate power density according to physical size of positive temperature coefficient resistance and maximum allowed power consumption;

[0063] Step 207, repeat all measurements at least three times, take average value as final recorded data;

[0064] The step S30 specifically comprises:

[0065] Step 301, place electromagnetic voltage transformer in controllable temperature and humidity environment cabin, set initial environment temperature to twenty degrees Celsius and relative humidity to fifty percent;

[0066] Step 302, use programmable power supply, start from rated primary voltage of transformer, gradually increase voltage by fifty percent amplitude at each step until one hundred fifty percent of rated voltage is reached;

[0067] Step 303, at each voltage level, maintain stability for five minutes, then record all electrical parameters;

[0068] Step 304, for overvoltage parameters, at each voltage level, additionally apply a voltage spike with one hundred milliseconds duration and one point two times amplitude of current voltage, record overvoltage peak value and duration;

[0069] Step 305, use infrared thermal imager to monitor temperature change of positive temperature coefficient resistance in real time, record steady-state temperature at each voltage level;

[0070] Step 306, repeat above process but environment temperature is set to zero degrees Celsius, forty degrees Celsius and sixty degrees Celsius respectively to investigate temperature influence on system performance;

[0071] Step 307, organize all measurement data into data table, including all electrical parameters, overvoltage parameters and positive temperature coefficient resistance parameters at different environment temperatures and voltage levels;

[0072] The step S40 specifically comprises:

[0073] Step 401, based on electromagnetism theory and thermodynamics principle, establish mathematical model describing working characteristics of electromagnetic voltage transformer;

[0074] Step 402, the mathematical model includes six main equations: voltage equation, current equation, power equation, temperature equation, positive temperature coefficient resistance characteristic equation and overvoltage response equation;

[0075] Step 403, the voltage equation describes the relationship between the primary side and the secondary side voltage, considering the turns ratio, impedance and mutual inductance effect;

[0076] Step 404, the current equation describes the composition of the primary side current, including load current, excitation current and leakage current;

[0077] Step 405, the power equation expresses the power characteristics of the system, including apparent power, active power, reactive power and power factor;

[0078] Step 406, the temperature equation describes the temperature change of the positive temperature coefficient resistance, considering the heat generation and heat dissipation process;

[0079] Step 407, the positive temperature coefficient resistance characteristic equation expresses the relationship between resistance value and temperature, voltage, including temperature effect and voltage effect;

[0080] Step 408, the overvoltage response equation describes the characteristics of the overvoltage event, including overvoltage amplitude and duration;

[0081] Among them, the step S50 specifically includes:

[0082] Step 501, divide the experimental data obtained in steps S20 and S30 into two groups: normal operation data and pressure increase operation data;

[0083] Step 502, use the least squares method to fit the unknown parameters in the operation equation set;

[0084] Step 503, for the voltage equation, the fitting parameters include mutual inductance coefficient and distributed capacitance;

[0085] Step 504, for the current equation, the fitting parameters include core loss equivalent resistance and magnetizing reactance;

[0086] Step 505, for the power equation, mainly verify the consistency of the calculated value and the measured value;

[0087] Step 506, for the temperature equation, the fitting parameters include thermal conductivity coefficient and core loss coefficient;

[0088] Step 507, for the positive temperature coefficient resistance characteristic equation, the fitting parameters include temperature coefficient, voltage coefficient and dynamic response coefficient;

[0089] Step 508, for the overvoltage response equation, the fitting parameters include decay time constant and overvoltage coefficient;

[0090] Step 509, using Levenberg-Marquardt algorithm for nonlinear least squares fitting;

[0091] Step 510, using cross-validation method, randomly divide the data set into training set and validation set, repeat the fitting process several times, take the average result as the final parameter value;

[0092] Step 511, calculate the confidence interval of each parameter to evaluate the reliability of the fitting;

[0093] Step 512, using the fitted equation set to predict the validation set data, calculate the root mean square error and the determination coefficient to evaluate the overall performance of the model;

[0094] Among them, the step S60 specifically includes:

[0095] Step 601, based on the fitted operating equation set, a comprehensive evaluation model is constructed;

[0096] Step 602, the model takes overvoltage and overvoltage duration as the main evaluation index, while considering the accuracy, loss and temperature rise of the transformer;

[0097] Step 603, define a comprehensive score function, which is the weighted sum of overvoltage, overvoltage duration, transformer accuracy, loss and temperature rise;

[0098] Step 604, the score function uses S-shaped function, for example, the function used for overvoltage score;

[0099] Step 605, the initial value of the weight coefficient is set according to expert experience;

[0100] Step 606, using Monte Carlo simulation method, a large number of samples are randomly generated in the possible value range of the positive temperature coefficient resistor parameter;

[0101] Step 607, calculate the comprehensive score for each sample, analyze the score distribution of these samples, and get the sensitivity of the positive temperature coefficient resistor parameter to the system performance;

[0102] Step 608, using response surface method to construct the approximate relationship between the positive temperature coefficient resistor parameter and the score function;

[0103] Step 609, select central composite design as the test design method, select appropriate sampling points in the positive temperature coefficient resistor parameter space;

[0104] Step 610, simulate and calculate these sampling points to get the corresponding score values;

[0105] Step 611, fitting the response surface using a second order polynomial model;

[0106] Step 612, determining the polynomial coefficients using least squares method;

[0107] Step 613, testing the significance and goodness of fit of the model by analysis of variance;

[0108] The step S70 specifically comprises:

[0109] Step 701, defining the chromosome encoding scheme used in the genetic algorithm, each chromosome representing a set of positive temperature coefficient resistance parameters, including normal temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient and power density;

[0110] Step 702, adopting real number encoding method, each parameter represented by a real number;

[0111] Step 703, setting the value range of the parameters;

[0112] Step 704, defining the fitness function, using the overvoltage suppression effect evaluation model established in step S60 as the basis of the fitness function, but it needs to be normalized;

[0113] Step 705, setting the parameters of the genetic algorithm, including population size, crossover probability, mutation probability and maximum iteration number;

[0114] Step 706, generating the initial population, using the positive temperature coefficient resistors with multiple different parameters selected in step S10 as part of the population, and the remaining individuals are supplemented by random generation within the parameter value range;

[0115] Step 707, executing the main loop of the genetic algorithm, including evaluation, selection, crossover, mutation, elite preservation and population update;

[0116] Step 708, selecting parent individuals using roulette wheel selection method;

[0117] Step 709, performing crossover operation using arithmetic crossover method;

[0118] Step 710, performing mutation operation using Gaussian mutation;

[0119] Step 711, copying the top two individuals in the current population with the highest fitness directly to the next generation;

[0120] Step 712, checking the termination condition, if the maximum iteration number is reached or the optimal solution has not been significantly improved for fifty consecutive generations, the algorithm is terminated;

[0121] The step S80 specifically comprises:

[0122] Step 801, obtaining the optimal positive temperature coefficient resistance parameters output by the genetic algorithm, including the room temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, and power density;

[0123] Step 802, recalculating the overvoltage suppression effect evaluation model using these parameters to obtain the theoretically optimal overvoltage suppression effect and overvoltage duration;

[0124] Step 803, performing sensitivity analysis to evaluate the impact of each parameter on the final result;

[0125] Step 804, based on the optimal parameters, changing the value of only one parameter each time and observing the changes in the output results;

[0126] Step 805, calculating the sensitivity coefficient of each parameter;

[0127] Step 806, performing Monte Carlo simulation to evaluate the stability of the optimal solution;

[0128] Step 807, randomly generating a thousand sets of parameter combinations within a small range around the optimal parameters and calculating the evaluation model outputs of these combinations;

[0129] Step 808, statistically analyzing the results of the thousand simulations to calculate the mean, standard deviation, and 95% confidence interval;

[0130] Step 809, performing cross-validation to evaluate the generalization ability of the optimal solution;

[0131] Step 810, randomly dividing the experimental data into five parts, using four of them to re-execute steps S40 to S70 to obtain a new set of optimal parameters;

[0132] Step 811, using the remaining one part of data to verify the performance of this set of parameters;

[0133] Step 812, repeating this process five times, each time using a different subset of data as the validation set;

[0134] Step 813, comparing the results of the five cross-validations;

[0135] Step 814, performing limit condition testing to evaluate the performance of the optimal solution under extreme conditions;

[0136] Step 815, simulating several extreme working conditions, such as the highest working temperature, maximum allowed voltage, and maximum load current, and calculating the overvoltage suppression effect under these conditions;

[0137] Among them, the step S90 specifically includes:

[0138] Step 901, determine the target value and allowable deviation of the key parameters based on the optimal positive temperature coefficient resistor parameters obtained in step S80;

[0139] Step 902, establish a positive temperature coefficient resistor product database containing product models and detailed parameters of major positive temperature coefficient resistor manufacturers on the market;

[0140] Step 903, collect information through manufacturers' official websites and product manuals, direct contact with manufacturers, and network crawler technology from electronic component distributors' websites;

[0141] Step 904, each record in the database contains fields such as manufacturer, model, room temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, power density, maximum working voltage, maximum working current, volume, price, etc.;

[0142] Step 905, develop a parameter matching algorithm to find the closest actual product to the optimal parameters in the product database;

[0143] Step 906, use weighted Euclidean distance as a similarity measure;

[0144] Step 907, execute the parameter matching process, including distance calculation, sorting, candidate product selection, detailed evaluation, and final selection;

[0145] Step 908, detailed evaluation of the selected candidate products, including calculation of overvoltage suppression effect using the evaluation model established in step S60, checking whether the maximum working voltage and maximum working current meet the application requirements, and considering whether the volume meets the installation space limit of the transformer;

[0146] Step 909, consider the above factors to select the best positive temperature coefficient resistor product;

[0147] Optionally, the step S10 further includes:

[0148] Step 108, determine the maximum size limit of the positive temperature coefficient resistor based on the structural characteristics and installation space of the electromagnetic voltage transformer;

[0149] Step 109, consider the working environment of the electromagnetic voltage transformer to determine the environmental conditions that the positive temperature coefficient resistor needs to meet, including working temperature range, humidity range, altitude, etc.;

[0150] Step 110, select a positive temperature coefficient resistor with corresponding reliability and durability based on the expected service life of the electromagnetic voltage transformer;

[0151] Step 111, consider the cost factor and set an upper limit for the price of the positive temperature coefficient resistor;

[0152] Step 112, according to the application scene of the electromagnetic voltage transformer, the response speed requirement of the positive temperature coefficient resistor is considered;

[0153] Optionally, the step S40 further includes:

[0154] Step 409, a magnetic circuit model of the electromagnetic voltage transformer is established, considering the nonlinear characteristics and hysteresis effect of the core;

[0155] Step 410, a thermal model of the electromagnetic voltage transformer is established, considering the thermal coupling effect of the winding, core and positive temperature coefficient resistor;

[0156] Step 411, a parasitic capacitance model of the electromagnetic voltage transformer is established, considering the distributed capacitance between windings and between windings and core;

[0157] Step 412, a dynamic response model of the positive temperature coefficient resistor is established, considering its transient characteristics under fast voltage change;

[0158] Step 413, the above models and main equation sets are integrated to form a complete electromagnetic voltage transformer system model;

[0159] Optionally, the step S60 further includes:

[0160] Step 614, a nonlinear mapping model is constructed using an artificial neural network to capture the complex relationship between the positive temperature coefficient resistor parameters and system performance;

[0161] Step 615, a multi-layer perceptron structure is adopted, the input layer is the positive temperature coefficient resistor parameter, the hidden layer uses ReLU activation function, and the output layer is the system performance index;

[0162] Step 616, the neural network is trained using the back propagation algorithm, the mean square error is used as the loss function, and the Adam optimizer is used for parameter update;

[0163] Step 617, the generalization ability of the neural network model is evaluated using the K-fold cross-validation method;

[0164] Step 618, the neural network model is compared with the polynomial response surface model, and the model with better performance is selected as the final evaluation model;

[0165] Optionally, the step S70 further includes:

[0166] Step 713, an adaptive genetic algorithm is adopted to dynamically adjust the crossover probability and mutation probability;

[0167] Step 714, the cross probability and the mutation probability are related to the population diversity and the optimal individual fitness, the mutation probability is increased when the population diversity is reduced, and the cross probability is increased when the optimal individual fitness stagnates;

[0168] Step 715, a taboo search strategy is introduced, a taboo table is maintained to record the recently visited solutions to avoid the algorithm falling into local optimum;

[0169] Step 716, the island model is used to parallelize the genetic algorithm, the total population is divided into several sub-populations, each sub-population evolves independently, and individual migration is performed between sub-populations at regular intervals;

[0170] Step 717, after the algorithm converges, a local search method is used to fine-tune the optimal solution to further improve the quality of the solution;

[0171] Optionally, the step S80 further includes:

[0172] Step 816, reliability analysis is performed to evaluate the stability of the optimal positive temperature coefficient resistance parameter in long-term operation;

[0173] Step 817, using the accelerated life test method, aging test is performed under harsh conditions such as high temperature, high pressure and high humidity;

[0174] Step 818, a Weibull distribution model is established to predict the failure rate and average trouble-free operation time of the positive temperature coefficient resistance;

[0175] Step 819, failure mode and effect analysis is performed to identify possible failure modes and their effects on system performance;

[0176] Step 820, based on the reliability analysis results, the optimal parameters are adjusted as necessary to balance performance and reliability requirements.

[0177] Compared with the prior art, the PTC resistance selection method for overvoltage suppression of an electromagnetic voltage transformer provided by the application has the following beneficial effects:

[0178] Firstly, the application selects the positive temperature coefficient resistance through a systematic and quantitative method, achieving rapid and accurate overvoltage suppression. Compared with the traditional passive suppression method, the positive temperature coefficient resistance selected by the method can respond to voltage changes within milliseconds, effectively suppressing transient overvoltage.

[0179] Secondly, the application establishes a detailed mathematical model and an optimization algorithm to accurately select the parameters of the positive temperature coefficient resistance. This method not only considers the electrical characteristics of the transformer, but also considers the thermal characteristics, environmental factors and other factors, making the selection result more comprehensive and reliable.

[0180] Thirdly, the method has good adaptability and scalability. By adjusting the weight coefficients of the evaluation model and optimizing the parameters of the algorithm, it can be flexibly adapted to different types of electromagnetic voltage transformers and various application scenarios. This flexibility enables the method to be widely applied to voltage transformers of different voltage levels and capacities, greatly improving its practicality.

[0181] Fourthly, the method effectively ensures the measurement accuracy of the electromagnetic voltage transformer while improving the overvoltage suppression performance. Through accurate modeling and optimization, the influence of the selected positive temperature coefficient resistor on the transformer under normal operating conditions is minimized.

[0182] Fifthly, the method greatly improves the efficiency and accuracy of parameter selection by introducing advanced optimization methods such as genetic algorithms and artificial neural networks. Compared with traditional exhaustive search or simple gradient descent methods, this method can quickly find the global optimal solution in a larger parameter space, avoiding getting stuck in local optima.

[0183] In summary, the present application solves the technical problem that most overvoltage protection schemes in the prior art use empirical design methods and lack systematic and quantitative optimization processes. BRIEF DESCRIPTION OF DRAWINGS

[0184] Figure 1 A flowchart of the method provided by the present application. DETAILED DESCRIPTION

[0185] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0186] As shown in Figure 1 Fig. 1 is a flowchart of a PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer provided by the present application. The method includes the following steps:

[0187] S10, select a plurality of PTC resistors with different parameters, respectively, as overvoltage suppression resistors of the electromagnetic voltage transformer, and install them one by one, and perform subsequent steps S20 and S30 for each PTC resistor;

[0188] S20, record the electrical parameters of the electromagnetic voltage transformer under normal operating conditions and the PTC resistor parameters of the overvoltage suppression resistor, denoted as normal operating data. The electrical parameters include primary side voltage, secondary side voltage, primary side current, secondary side current, output power, power factor, harmonic content, overvoltage, and overvoltage duration. The PTC resistor parameters include normal temperature resistance, Curie temperature, temperature coefficient, voltage coefficient, and power density;

[0189] S30, adjust the operating environment of the electromagnetic voltage transformer, stepwise increase the applied voltage, record the electrical parameters of the electromagnetic voltage transformer, overvoltage parameters and PTC resistance parameters of the overvoltage suppression resistance under different voltages, as pressure increase operation data; the overvoltage parameters include overvoltage and overvoltage duration;

[0190] S40, establish an operating equation group of the electromagnetic voltage transformer considering the electrical parameters, overvoltage parameters and PTC resistance parameters, including voltage equation, current equation, power equation, temperature equation, PTC resistance characteristic equation and overvoltage response equation;

[0191] S50, according to the normal operation data and the pressure increase operation data, fit the parameters of the operating equation group to obtain the fitted operating equation group;

[0192] S60, based on the fitted operating equation group, establish an overvoltage suppression effect evaluation model, which takes overvoltage and overvoltage duration as the main evaluation indexes;

[0193] S70, optimize the PTC resistance parameters using genetic algorithm, take the PTC resistance parameters of the PTC resistance with multiple different initial parameters as the initial population, use the overvoltage suppression effect evaluation model to calculate the fitness value of each group of parameters, take minimizing overvoltage and overvoltage duration as the objective function, and set the population size, crossover probability, mutation probability and iteration number;

[0194] S80, execute the genetic algorithm to obtain the optimal PTC resistance parameters;

[0195] S90, according to the obtained optimal PTC resistance parameters, select the model closest in characteristics from the existing PTC resistance products as the final overvoltage suppression resistance selection result.

[0196] The specific embodiments of the above steps are described in detail as follows:

[0197] The specific embodiment of step S10 is: first, according to the rated voltage and rated current of the electromagnetic voltage transformer, the voltage and current range of the PTC resistance is preliminarily determined. Generally, the rated voltage of the PTC resistance should be not less than 1.5 times the rated voltage of the secondary side of the transformer, and the rated current should be not less than 1.2 times the rated current of the secondary side of the transformer. Secondly, the temperature coefficient, Curie temperature and power density of the PTC resistance are considered. The temperature coefficient is usually between 0.01 and 0.1 / ℃, the Curie temperature should be higher than 50-100℃ of the normal working temperature of the transformer, and the power density is generally 0.1-1 W / cm 3The range of PTC resistance values is usually between 0.1 and 10 times the load impedance on the secondary side of the transformer. Finally, at least 5 PTC resistance samples with different parameter combinations are selected from different manufacturers to ensure sufficient samples for subsequent testing and optimization. The purpose of this step is to provide diversified PTC resistance samples for subsequent testing and optimization, so as to find the most suitable parameter combination.

[0198] The specific implementation of step S20 is as follows: First, the selected PTC resistance is respectively installed on the secondary side of the electromagnetic voltage transformer in series with the secondary winding. Then, the transformer is connected to a standard voltage source and a standard load, and the voltage source output is set to the rated primary voltage of the transformer. Next, the primary side voltage, secondary side voltage, primary side current, secondary side current, output power and power factor of the transformer are measured using high-precision voltmeter, ammeter and power analyzer. At the same time, the harmonic content of voltage and current is measured using a harmonic analyzer. For overvoltage voltage and overvoltage duration, a high-speed oscilloscope is used to record the voltage waveform on the secondary side by instantaneously applying 1.2 times the rated voltage on the primary side and quickly returning to the rated voltage. In addition, the resistance value of the PTC resistance at different temperatures is measured using a precision resistance tester, so as to obtain its normal temperature resistance value, temperature coefficient and Curie temperature. The voltage coefficient can be determined by measuring the resistance value at different voltages, and the power density can be calculated according to the physical size of the PTC resistance and the maximum allowed power consumption. All measurements are repeated at least 3 times, and the average value is taken as the final recorded data. The purpose of this step is to establish a comprehensive baseline data set to provide reliable input for subsequent modeling and optimization.

[0199] The specific implementation of step S30 is as follows: First, the electromagnetic voltage transformer is placed in a controllable temperature and humidity environment chamber, and the initial environment temperature is set to 20℃ and the relative humidity is set to 50%. Then, using a programmable power supply, the voltage is gradually increased from the rated primary voltage of the transformer at an amplitude of 5% per step until it reaches 150% of the rated voltage. At each voltage level, keep stable for 5 minutes, then record all electrical parameters. For overvoltage parameters, at each voltage level, an additional voltage spike with a duration of 100ms and an amplitude of 1.2 times the current voltage is applied, and the overvoltage peak value and duration are recorded. At the same time, the temperature change of the PTC resistance is monitored in real time using an infrared thermal imager, and the steady-state temperature at each voltage level is recorded. Repeat the above process, but set the environment temperature to 0℃, 40℃ and 60℃ respectively to investigate the effect of temperature on system performance. Finally, all the measured data are arranged into a data table, including all electrical parameters, overvoltage parameters and PTC resistance parameters under different environment temperatures and voltage levels. The purpose of this step is to obtain comprehensive performance data of the system under different working conditions, providing rich experimental basis for subsequent mathematical modeling.

[0200] The specific implementation of step S40 is: first, based on electromagnetic theory and thermodynamic principles, a mathematical model is established to describe the working characteristics of the electromagnetic voltage transformer. This model includes six main equations: voltage equation, current equation, power equation, temperature equation, PTC resistance characteristic equation, and overvoltage response equation. The voltage equation describes the relationship between the primary side and secondary side voltages, taking into account the turns ratio, impedance, and mutual inductance effects: where V1 and V2 are the primary and secondary side voltages, N1 and N2 are the winding turns, I1 and I2 are the currents, R2 and L2 are the secondary side resistance and inductance, M is the mutual inductance coefficient, ω is the angular frequency, C s is the distributed capacitance. The current equation describes the composition of the primary side current: where Z1 is the total impedance on the primary side, I m is the magnetizing current. The power equation expresses the power characteristics of the system: P = |V1||I1|cosφ, Q = |V1||I1|sinφ, where S is the apparent power, P is the active power, Q is the reactive power, and PF is the power factor. The temperature equation describes the temperature change of the PTC resistance: where T is the PTC resistance temperature, m is the mass, c p is the specific heat capacity, P loss is the loss power, h is the heat conduction coefficient, A is the surface area, and T amb is the ambient temperature. The PTC resistance characteristic equation expresses the relationship between resistance value, temperature, and voltage: where R PTC is the PTC resistance value, R0 is the normal temperature resistance value, α is the temperature coefficient, T0 is the reference temperature, β is the voltage coefficient, and γ is the dynamic response coefficient. The overvoltage response equation describes the characteristics of the overvoltage event: ov (t) = V peak e -t / τ sin(ωt) + V nom , where V ov (t) is the overvoltage voltage, V peak is the overvoltage peak value, τ is the decay time constant, V nom is the rated voltage, t ov is the overvoltage duration, H(x) is the unit step function, and V th is the overvoltage threshold voltage.

[0201] Specifically: 1. Voltage equation, specifically expressed as:

[0202]

[0203] where V1 is the primary voltage (input); V2 is the secondary voltage (output); N1, N2 are the primary and secondary winding turns; I1, I2 are the primary and secondary currents; R2 is the secondary winding resistance; L2 is the secondary winding self-inductance; M is the mutual inductance; ω is the angular frequency (2πf, f is the operating frequency); C s is the distributed capacitance; t is time;

[0204] This equation takes into account the basic principles of a transformer, including the turns ratio, secondary impedance, mutual inductance effects, and the influence of distributed capacitance.

[0205] 2. The current equation, which is specifically expressed as:

[0206]

[0207]

[0208] where Z1 is the total primary impedance; I m is the magnetizing current; R c is the core loss equivalent resistance; X m is the magnetizing reactance; Z1 can be calculated by:

[0209]

[0210] where R1 is the primary winding resistance; L1 is the primary winding self-inductance; R PTC is the current resistance value of the PTC resistor.

[0211] 3. The power equation, which is specifically expressed as:

[0212]

[0213] P = |V1||I1|cosφ;

[0214] Q = |V1||I1|sinφ;

[0215]

[0216] where S is the apparent power; P is the active power; Q is the reactive power; PF is the power factor; φ is the phase angle between voltage and current, is the conjugate complex of the primary current.

[0217] 4. The temperature equation, which is specifically expressed as:

[0218]

[0219]

[0220]

[0221] where T is the PTC resistance temperature; t is time; m is the PTC resistance mass; c p is the PTC resistance specific heat capacity; P loss is the total loss power; h is the heat transfer coefficient; A is the PTC resistance surface area; T amb is the ambient temperature; P core is the core loss; k h is the hysteresis loss coefficient; k e is the eddy current loss coefficient; B m is the maximum magnetic flux density.

[0222] 5. The PTC resistance characteristic equation is specifically expressed as:

[0223]

[0224] where R PTC is the current resistance value of the PTC resistance; R0 is the normal temperature resistance value; a is the temperature coefficient; T0 is the reference temperature (usually room temperature); T is the current temperature; b is the voltage coefficient; V is the voltage applied on the PTC resistance; g is the dynamic response coefficient.

[0225] 6. The overvoltage response equation is specifically expressed as:

[0226] V ov (t) = V peak e -t / τ sin (ot) + V nom

[0227]

[0228] where V ov (t) is the change of the overvoltage with time; V peak is the overvoltage peak value; t is the decay time constant; w is the overvoltage oscillation angular frequency; V nom is the rated voltage; t ov is the overvoltage duration; H(x) is the Heaviside step function (1 when x>0, otherwise 0); V th is the overvoltage threshold voltage; V peak can be estimated by the following way:

[0229]

[0230] where k ov is the overvoltage coefficient; di / dt is the current change rate; L eqThe equations represent the equivalent inductance; together they form a complex set of equations covering various aspects of electromagnetic voltage transformers, including electrical characteristics, thermal characteristics, PTC resistance characteristics, and overvoltage response. They comprehensively consider electrical parameters, overvoltage parameters, and PTC resistance parameters, providing a comprehensive mathematical model for subsequent optimization processes.

[0231] The following is a description of how the parameters used are obtained:

[0232] 1. Voltage and current parameters (V1, V2, I1, I2): Acquisition method: direct measurement; Measurement equipment: high-precision digital multimeter or oscilloscope; Measurement method: connect the multimeter or oscilloscope probe in parallel (to measure voltage) or in series (to measure current) to the corresponding circuit position.

[0233] 2. Number of winding turns (N1, N2): Source: Current transformer design specifications or data sheets provided by the manufacturer.

[0234] 3. Winding resistance (R1, R2): Acquisition method: direct measurement; Measurement equipment: precision resistance tester; Measurement method: with the transformer de-energized, connect the tester to both ends of the winding for measurement.

[0235] 4. Winding self-inductance (L1, L2) and mutual inductance coefficient (M): Acquisition method: measurement and calculation; Measurement equipment: LCR tester; Measurement method:

[0236] Step 1: Measure the primary side self-inductance L1 (secondary side open circuit);

[0237] Step 2: Measure the secondary side self-inductance L2 (primary side open circuit);

[0238] Step 3: Measure the total inductance L T (Secondary side short circuit, measured from primary side); Calculate mutual inductance coefficient:

[0239] 5. Distributed capacitance (C) s Acquisition method: Measurement; Measurement equipment: Precision capacitance tester; Measurement method: With the transformer de-energized, connect the tester between the primary and secondary windings for measurement.

[0240] 6. Operating frequency (f): Source: Standard frequency of power system (usually 50Hz or 60Hz).

[0241] 7. Core loss equivalent resistance (R) c ) and magnetizing reactance (X m Acquisition method: Calculated after measurement through no-load test; Measurement equipment: Power analyzer;

[0242] Experimental steps:

[0243] Step 1, apply rated voltage to primary side, open circuit on secondary side;

[0244] Step 2, measure primary side voltage V1, current I0 and power P0; calculation method:

[0245]

[0246]

[0247] 8. PTC resistance parameters (R0, a, b, g): acquisition method: experimental measurement and data fitting; measurement equipment: programmable power supply, precision resistance tester, temperature sensor, data acquisition system;

[0248] Experimental steps:

[0249] Step 1, measure the resistance value of PTC resistance at different temperatures;

[0250] Step 2, measure the resistance value of PTC resistance at different voltages;

[0251] Step 3, apply rapidly changing voltage and measure the dynamic response of PTC resistance; data fitting: use least squares method to fit experimental data to obtain parameter values.

[0252] 9. PTC resistance quality (m) and specific heat capacity (c p ): mass: measured using a precision balance; specific heat capacity: consult material data manual or determine by calorimeter experiment.

[0253] 10. Thermal conductivity (h) and surface area (A): thermal conductivity: consult material data manual or determine by thermal conductivity experiment. Surface area: calculated according to the geometric size of PTC resistance.

[0254] 11. Ambient temperature (T amb ): acquisition method: direct measurement. Measurement equipment: thermometer or temperature sensor.

[0255] 12. Core loss coefficient (kh, k e ):

[0256] Acquisition method: through no-load loss test and data fitting.

[0257] Measurement equipment: power analyzer, variable frequency power supply.

[0258] Experimental steps:

[0259] Step 1, perform no-load test at different frequencies and voltages (corresponding to different magnetic flux densities);

[0260] Step 2, measure core loss under each condition;

[0261] Step 3, Data Fitting: Use least squares method to fit the experimental data to obtain coefficient values.

[0262] 13. Maximum magnetic flux density (B m ):

[0263] Calculation method: In the formula, A core is the cross-sectional area of the core, which can be obtained from the design specifications of the transformer.

[0264] 14. Overvoltage coefficient (k ov ) and equivalent inductance (L eq ):

[0265] Obtaining method: Through overvoltage test and data analysis.

[0266] Measuring equipment: high-speed oscilloscope, current probe.

[0267] Step 1, simulate overvoltage conditions (such as switch operation or lightning strike);

[0268] Step 2, record voltage and current waveform:

[0269] Step 3, analyze the waveform to obtain the overvoltage coefficient and equivalent inductance.

[0270] 15. Overvoltage threshold voltage (V th ): Source: determined according to the design specifications of the transformer and the requirements of the power system.

[0271] The purpose of this step is to establish a comprehensive mathematical model to provide a theoretical basis for subsequent parameter fitting and optimization.

[0272] The specific implementation of step S50 is: first, divide the experimental data obtained in steps S20 and S30 into two groups: normal operation data and pressure increase operation data. Then, use the least squares method to fit the unknown parameters in the operation equation group. Specifically, for the voltage equation, the fitting parameters include mutual inductance M and distributed capacitance C s ; for the current equation, the fitting parameters include core loss equivalent resistance R c and magnetizing reactance X m ; for the power equation, mainly verify the consistency of the calculated value and the measured value; for the temperature equation, the fitting parameters include thermal conductivity coefficient h and core loss coefficient k h , k e ; for the PTC resistance characteristic equation, the fitting parameters include temperature coefficient α, voltage coefficient β and dynamic response coefficient γ; for the overvoltage response equation, the fitting parameters include decay time constant τ and overvoltage coefficient k ovThe Levenberg-Marquardt algorithm, which combines the advantages of gradient descent and Gauss-Newton methods, is used for nonlinear least squares fitting, which can effectively handle nonlinear problems. To improve the accuracy of the fitting, the cross-validation method is used to randomly divide the data set into a training set (80%) and a validation set (20%), repeat the fitting process several times, and take the average result as the final parameter value. At the same time, the confidence interval of each parameter is calculated to evaluate the reliability of the fitting. Finally, the fitted equation set is used to predict the validation set data, and the root mean square error (RMSE) and the determination coefficient (R2) are calculated to evaluate the overall performance of the model. If the RMSE is large or the R2 is small, the model structure needs to be reconsidered or more experimental data needs to be added. The purpose of this step is to obtain a mathematical model that can accurately describe the system behavior through data fitting, providing a reliable foundation for the subsequent optimization process.

[0273] The specific implementation of step S60 is as follows: First, based on the fitted operating equation set, a comprehensive evaluation model is constructed. This model takes the overvoltage V ov and the overvoltage duration t ov as the main evaluation indicators, while considering other important factors such as the accuracy, loss, and temperature rise of the transformer. Define a comprehensive score function F: F = w1f(V ov ) + w2g(t ov ) + w3h(ε) + w4i(P loss ) + w5j(ΔT), where f, g, h, i, j are the scoring functions for overvoltage, overvoltage duration, transformer accuracy, loss, and temperature rise, and w1 to w5 are the corresponding weight coefficients. The scoring function uses a sigmoid-type function, for example where k is the steepness coefficient, V th is the desired overvoltage threshold. Similarly, define the corresponding scoring functions for other indicators. The initial values of the weight coefficients can be set according to expert experience, for example, w1 = 0.3, w2 = 0.3, w3 = 0.2, w4 = 0.1, w5 = 0.1. Then, use the Monte Carlo simulation method to randomly generate a large number of samples (such as 10000) within the possible value range of the PTC resistance parameters, and calculate the comprehensive score F for each sample. By analyzing the scoring distribution of these samples, the sensitivity of the PTC resistance parameters to the system performance can be obtained. Next, use the Response Surface Methodology (RSM) to construct the approximate relationship between the PTC resistance parameters and the scoring function. Select the Central Composite Design (CCD) as the experimental design method, and select appropriate sampling points in the PTC resistance parameter space. Perform simulation calculations on these sampling points to obtain the corresponding scoring values. Then use a second-order polynomial model to fit the response surface: Where x i The parameters representing the PTC resistor, b0, b i b ii and b ij These are the undetermined coefficients. These coefficients are determined using the least squares method. Finally, the significance and goodness of fit of the model are tested using analysis of variance (ANOVA). If the model is not accurate enough, a higher-order polynomial or other nonlinear model can be considered. This evaluation model will serve as the objective function for subsequent optimization processes. The purpose of this step is to establish a mathematical model that can comprehensively evaluate the performance of the PTC resistor, providing a reliable evaluation criterion for subsequent parameter optimization.

[0274] The specific implementation of step S70 is as follows: First, define the chromosome encoding scheme used in the genetic algorithm. Each chromosome represents a set of PTC resistance parameters, including the room temperature resistance value R0 and the Curie temperature T. c Temperature coefficient α, voltage coefficient β, and power density P d The system uses real-number encoding, where each parameter is represented by a real number. For example, the chromosome structure is [R0, T]. s , α, β, P a The parameter range is set as follows: R0 is between 1Ω and 1000Ω, T... s Between 80℃ and 200℃, α is between 0.01 / ℃ and 0.1 / ℃, and β is between 10... -6 V -2 Up to 10 -4 V -2 Between, P a At 0.1W / cm 3 Up to 1W / em 3 between.

[0275] Secondly, define the fitness function. The overvoltage suppression effect evaluation model established in step S60 is used as the basis for the fitness function, but normalization is required to ensure comparability between different indicators. The fitness function can be expressed as: Where F is the output value of the evaluation model. This processing converts the evaluation score into a fitness value between 0 and 1, with a lower evaluation score indicating a higher fitness.

[0276] Next, set the parameters of the genetic algorithm. Set the population size to 100; this value is large enough to provide sufficient genetic diversity without causing excessive computation. Set the crossover probability to 0.8; this relatively high probability is beneficial for generating new superior individuals. Set the mutation probability to 0.1; this moderate probability introduces a certain degree of randomness while maintaining population stability. Set the maximum number of iterations to 1000; this value is usually sufficient for the algorithm to converge to a good solution.

[0277] Next, an initial population is generated. The PTC resistances of the multiple different parameters selected in step S10 are used as part of the population, and the remaining individuals are supplemented by randomly generating within the parameter value range to ensure the diversity of the initial population.

[0278] After that, the main loop of the genetic algorithm is executed:

[0279] 1. Evaluation: Calculate the fitness value for each individual in the population.

[0280] 2. Selection: Select parent individuals using roulette wheel selection. This method gives higher probability of selection to individuals with higher fitness, but does not completely exclude individuals with lower fitness, helping to maintain population diversity.

[0281] 3. Crossover: Perform crossover operation on selected parent individuals. Arithmetic crossover method is used, that is, weighted average of parameters of parent individuals: Child = aParent1 + (1-a)Parent2, where a is a random number between 0 and 1. This method can produce new individuals between parents, which is beneficial for local search.

[0282] 4. Mutation: Perform mutation operation on the offspring individuals after crossover. Gaussian mutation is used, that is, a random number following normal distribution is added to the original parameter value: Param new = Param old +N(0,σ), where σ is the standard deviation, which can be set to 5% of the parameter value range. This mutation method can explore a small range in parameter space.

[0283] 5. Elite preservation: Copy the top 2% of individuals in the current population directly to the next generation to ensure that the optimal solution is not lost during evolution.

[0284] 6. Update population: Replace the old population with newly generated offspring.

[0285] 7. Check termination condition: If the maximum number of iterations is reached or the optimal solution has not improved significantly (improvement less than 1%) for 50 consecutive generations, terminate the algorithm; otherwise, return to step 1 to continue iteration.

[0286] Finally, record the convergence process of the algorithm and the optimal PTC resistance parameters obtained. The purpose of this step is to efficiently search for the optimal combination of PTC resistance parameters in a vast parameter space through simulated evolution, in order to achieve the best overvoltage suppression effect.

[0287] The specific implementation of step S80 is: first, obtain the optimal PTC resistance parameters output by the genetic algorithm, including room temperature resistance value R0, Curie temperature T stemperature coefficient a, voltage coefficient b, and power density P a Then, using these parameters, the overvoltage suppression effect evaluation model is recalculated to obtain the theoretically optimal overvoltage suppression effect and overvoltage duration.

[0288] Next, a sensitivity analysis is performed to evaluate the degree of influence of each parameter on the final result. The specific method is to change the value of only one parameter (within its allowed range ±10%) based on the optimal parameters, and observe the change in the output result. The sensitivity coefficient of each parameter is calculated: where F is the output of the evaluation model, x i is the i-th parameter. The greater the absolute value of the sensitivity coefficient, the more significant the influence of the parameter on the result.

[0289] Then, a Monte Carlo simulation is performed to evaluate the stability of the optimal solution. A small range (such as ±5%) around the optimal parameters is randomly generated 1000 sets of parameter combinations, and the evaluation model output of these combinations is calculated. The results of the 1000 simulations are statistically analyzed to calculate the mean, standard deviation, and 95% confidence interval. If the standard deviation is small (such as less than 5% of the mean), it indicates that the optimal solution has good stability.

[0290] Next, cross-validation is performed to evaluate the generalization ability of the optimal solution. The experimental data obtained in steps S20 and S30 are randomly divided into 5 parts, and 4 parts of the data are used to re-execute steps S40 to S70 to obtain a new set of optimal parameters. The remaining 1 part of the data is used to verify the performance of this set of parameters. Repeat this process 5 times, each time using a different subset of data as the validation set. Compare the results of the 5 cross-validations, and if the coefficient of variation (standard deviation divided by mean) of the results is less than 10%, it is considered that the optimal solution has good generalization ability.

[0291] Finally, limit condition testing is performed to evaluate the performance of the optimal solution in extreme situations. Several extreme working conditions are simulated, such as the highest working temperature, the maximum allowed voltage, the maximum load current, etc., and the overvoltage suppression effect under these conditions is calculated. If the overvoltage suppression effect still meets the design requirements (such as the overvoltage voltage not exceeding 1.2 times the rated voltage, and the overvoltage duration not exceeding 100ms) under all extreme conditions, it is considered that the optimal solution has good robustness.

[0292] The purpose of this step is to comprehensively evaluate the performance and reliability of the optimal PTC resistance parameters obtained by the genetic algorithm, ensuring that it is not only theoretically optimal, but also maintains stable and reliable performance in actual application.

[0293] The specific implementation of step S90 is as follows: first, according to the optimal PTC resistance parameters obtained in step S80, the target value and the allowable deviation of the key parameters are determined. For example, the target value of the normal temperature resistance value R0 is 52.7Ω, and the allowable deviation is ±5%; the target value of the Curie temperature T s is 125℃, and the allowable deviation is ±10℃; the target value of the temperature coefficient a is 0.065 / ℃, and the allowable deviation is ±10%; the target value of the voltage coefficient b is 5×10 -5 V -2 , and the allowable deviation is ±20%; the target value of the power density P a is 0.5W / cm 3 , and the allowable deviation is ±15%.

[0294] Then, a PTC resistance product database is established. This database contains product models and detailed parameters of major PTC resistance manufacturers on the market. Data can be collected in the following ways: 1) from the official website and product manual of the manufacturer; 2) contact the manufacturer directly to ask for the latest product data; 3) use web crawler technology to collect information from electronic component distributors' websites. Each record in the database should contain the following fields: manufacturer, model, normal temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, power density, maximum working voltage, maximum working current, volume, price, etc.

[0295] Next, a parameter matching algorithm is developed. The goal of this algorithm is to find the actual product closest to the optimal parameters in the product database. The weighted Euclidean distance can be used as a similarity measure:

[0296]

[0297] where x i is the i-th parameter of the actual product, is the i-th parameter of the optimal parameter, w i is the weight of the i-th parameter. The weight can be set according to the importance and sensitivity of the parameter, for example, the weight of the normal temperature resistance value and the Curie temperature can be set to 0.3, the weight of the temperature coefficient can be set to 0.2, and the weight of the voltage coefficient and the power density can be set to 0.1 each.

[0298] Then, the parameter matching process is executed:

[0299] 1. Calculate the weighted Euclidean distance between each product in the database and the optimal parameters.

[0300] 2. Sort the products by distance from small to large.

[0301] 3. Select the top 10 products with the smallest distance as candidates.

[0302] 4. Detailed evaluation of the 10 candidate products, including:

[0303] a) Calculate their overvoltage suppression effect using the evaluation model established in step S60.

[0304] b) Check if their maximum operating voltage and maximum operating current meet the application requirements.

[0305] c) Consider whether their volume meets the installation space limitations of the transformer.

[0306] 5. Select the best PTC resistor product by considering the above factors.

[0307] The purpose of this step is to convert the theoretically optimal PTC resistor parameters into actual product selection, ensuring that the finally selected PTC resistor can both maximize the theoretical optimal performance and meet the various requirements of practical applications. Through this method, the best balance between theoretical optimization and practical application can be found, providing the most suitable overvoltage suppression solution for electromagnetic voltage transformers.

[0308] This method covers the whole process from initial selection, experimental testing, mathematical modeling, parameter optimization to final product selection. It comprehensively uses electromagnetic theory, thermodynamic principles, mathematical modeling, optimization algorithms and engineering practice, aiming to find the best overvoltage suppression solution for electromagnetic voltage transformers. The advantage of this method is that it not only considers theoretical optimality, but also takes into account various constraints of practical applications, achieving a good balance between performance and reliability. Through this systematic, data-driven method, the overvoltage suppression capability of electromagnetic voltage transformers can be significantly improved, enhancing their reliability and stability under various working conditions.

[0309] Specifically, the principle of the present application is: through a systematic modeling, optimization and verification process, the most suitable positive temperature coefficient resistor parameters for a specific electromagnetic voltage transformer are found. The key to this method to effectively solve the overvoltage suppression problem lies in the following aspects:

[0310] Firstly, the characteristics of positive temperature coefficient resistor are highly matched with the overvoltage suppression requirements. The characteristic of positive temperature coefficient resistor that its resistance value increases sharply when the temperature rises enables it to quickly respond when overvoltage occurs, limiting the current rise and thus suppressing overvoltage. At the same time, when the voltage returns to normal, the positive temperature coefficient resistor can quickly cool down and restore to low resistance state, without affecting the normal operation of the transformer. This adaptive characteristic is the basis for this method to effectively solve the overvoltage problem.

[0311] Secondly, the method establishes a comprehensive and accurate mathematical model, including voltage equations, current equations, power equations, temperature equations, positive temperature coefficient resistance characteristic equations, and overvoltage response equations. These equations comprehensively describe the working characteristics of electromagnetic voltage transformers and positive temperature coefficient resistors and their interactions. Through such detailed modeling, the method can accurately predict the system's response under different parameters, providing a reliable theoretical basis for subsequent optimization processes.

[0312] Thirdly, the method adopts a multi-step and multi-level optimization strategy. From the initial parameter range determination to the response surface method for constructing the evaluation model, and then to the genetic algorithm for global optimization, each step is carefully designed to ensure that the global optimal solution can be found in the complex parameter space. In particular, the genetic algorithm simulates the mechanism of biological evolution, enabling the method to effectively avoid local optima while having strong robustness and adaptability.

[0313] Fourthly, the method focuses on the combination of theory and practice. Through extensive experimental data collection and analysis, the accuracy and reliability of the model are ensured. At the same time, various constraints in actual engineering are considered in the optimization process, such as the market availability of positive temperature coefficient resistors, cost factors, etc., making the final selection result both theoretically optimal and practically feasible.

[0314] Fifthly, the method uses a variety of advanced mathematical tools and algorithms. For example, least squares method for parameter fitting, response surface method for constructing evaluation model, Monte Carlo method for sensitivity analysis, etc. The comprehensive use of these methods ensures the scientificity and reliability of the selection process.

[0315] In addition, the logicality of the method is reflected in its rigorous step design. From initial parameter selection, data collection, model establishment, parameter optimization, to result verification, each step is closely connected, forming a complete closed loop. This systematic approach not only improves the efficiency and accuracy of the selection, but also makes the entire process traceable and reproducible, which is conducive to the continuous improvement and application of the method.

[0316] It is worth noting that the method also considers various influencing factors of positive temperature coefficient resistors in actual applications, such as environmental temperature, load changes, etc. By simulating various working conditions in experimental design and considering these factors in the optimization process, the method ensures the reliability and stability of the selection results in actual applications.

[0317] Finally, the method not only focuses on static performance, but also ensures the effectiveness of the selection results under various working conditions through dynamic response analysis and limit condition testing. This comprehensive consideration enables the positive temperature coefficient resistors selected by the method to perform optimally in actual operation, truly solving the overvoltage problem of electromagnetic voltage transformers.

[0318] In summary, the method of the present application combines electromagnetism theory, thermodynamic principles, optimization algorithms and engineering practices to build a scientific, systematic and reliable PTC resistor selection method.

[0319] To better understand and implement the present application, an example of a specific application scenario of the present application is provided below: A certain power enterprise is upgrading the voltage transformer system of its 110kV substation, and the enterprise hopes to select appropriate PTC resistors to improve the overvoltage suppression capability of the electromagnetic voltage transformer, thereby enhancing the stability and reliability of the system. The enterprise decides to use the method of the present application to select the optimal PTC resistor.

[0320] Step 1: Select multiple PTC resistors with different parameters

[0321] The engineers of the power enterprise selected five PTC resistors with different parameters from the market, labeled as A, B, C, D and E. The initial parameters of these PTC resistors are shown in Table 1:

[0322] Table 1 Initial parameters of PTC resistors

[0323]

[0324] Step 2: Record normal operation data

[0325] The engineers installed these five PTC resistors on five 110kV / 100V electromagnetic voltage transformers of the same model, and recorded the electrical parameters and PTC resistor parameters under normal operating conditions. Here is a set of normal operation data (using PTC resistor A):

[0326] Electrical parameters: primary side voltage: 110kV; secondary side voltage: 100V; primary side current: 0.05A; secondary side current: 55A; output power: 5.5kVA; power factor: 0.98; harmonic content: 1.2%; overvoltage: 0kV (no overvoltage during normal operation); overvoltage duration: 0s (no overvoltage during normal operation).

[0327] PTC resistor A parameters: room temperature resistance: 10Ω; Curie temperature: 120℃; temperature coefficient: 16% / K; voltage coefficient: 0.015V^-2; power density: 1.2W / cm^3.

[0328] Step 3: Record overvoltage operation data

[0329] Next, the engineers simulated different levels of overvoltage by adjusting the operating environment of the voltage transformer. Starting from 110kV and increasing in steps of 5kV up to 130kV, they recorded electrical parameters, overvoltage parameters, and PTC resistance parameters at each voltage level. Here are some data from using PTC resistance A at 125kV:

[0330] Electrical parameters: Primary voltage: 125kV; Secondary voltage: 113.6V; Primary current: 0.057A; Secondary current: 62.5A; Output power: 7.1kVA; Power factor: 0.96; Harmonic content: 1.8%; Overvoltage: 15kV; Overvoltage duration: 0.5s.

[0331] PTC resistance A parameters: Current resistance value: 25Ω; Current temperature: 135°C; Actual temperature coefficient: 18% / K; Actual voltage coefficient: 0.018V^-2; Actual power density: 1.8W / cm^3.

[0332] Step 4: Establishing the operating equation set

[0333] Based on the collected data, the engineers established an electromagnetic voltage transformer operating equation set that takes into account electrical parameters, overvoltage parameters, and PTC resistance parameters. This equation set includes voltage equations, current equations, power equations, temperature equations, PTC resistance characteristic equations, and overvoltage response equations.

[0334] Step 5: Fitting the operating equation set parameters

[0335] Using the collected normal operation data and increased voltage operation data, the engineers fitted the parameters of the operating equation set using the least squares method. During the fitting process, professional mathematical software was used to handle complex nonlinear equation sets. After fitting, a set of equations was obtained that accurately describes the behavior of the voltage transformer and PTC resistance.

[0336] Step 6: Establishing an overvoltage suppression effect evaluation model

[0337] Based on the fitted operating equation set, the engineers established an overvoltage suppression effect evaluation model. This model takes overvoltage and overvoltage duration as the main evaluation indicators. Define a comprehensive score function:

[0338] Score = 100 - (0.5 * overvoltage / rated voltage * 100 + 0.5 * overvoltage duration / maximum allowed duration * 100)

[0339] Where the rated voltage is 110kV and the maximum allowed duration is 1s. The higher the score, the better the overvoltage suppression effect.

[0340] Step 7: Optimize PTC resistor parameters using a genetic algorithm

[0341] Engineers used a genetic algorithm to optimize the parameters of PTC resistors. The parameters of five initially selected PTC resistors were used as the initial population, and the following genetic algorithm parameters were set: population size: 50; crossover probability: 0.8; mutation probability: 0.1; number of iterations: 100.

[0342] The fitness value of each parameter group is calculated using the evaluation model established in step 6, with the goal of maximizing the score.

[0343] Step 8: Execute the genetic algorithm

[0344] The engineers executed a genetic algorithm and, after 100 iterations, obtained the optimal PTC resistor parameters: room temperature resistance: 18Ω; Curie temperature: 128℃; temperature coefficient: 19% / K; voltage coefficient: 0.019V^-2; power density: 1.7W / cm^3.

[0345] These parameters demonstrated the best overvoltage suppression effect in the simulation test, achieving a score of 92.

[0346] Step 9: Select the final PTC resistor

[0347] Based on the obtained optimal PTC resistor parameters, the engineers selected the model with the closest characteristics from existing PTC resistor products. They found a PTC resistor with the model number XYZ-18, whose parameters are as follows: room temperature resistance: 18Ω; Curie temperature: 130℃; temperature coefficient: 19% / K; voltage coefficient: 0.02V^-2; power density: 1.7W / cm^3.

[0348] The parameters of this PTC resistor are very close to the optimization results, and it was selected as the final overvoltage suppression resistor.

[0349] Validation and application:

[0350] To verify the actual effect of the selected PTC resistor, the engineers conducted a series of laboratory tests and field trials.

[0351] 1. Laboratory testing:

[0352] Engineers simulated various overvoltage scenarios in a laboratory environment, including lightning strikes, switching operations, and system failures. The effectiveness of using the optimized PTC resistor was compared with the original protection scheme. Table 2 below shows some of the test results:

[0353] Table 2 Test Results

[0354] Overvoltage type Overvoltage amplitude Original overvoltage duration New overvoltage duration Improvement effect Lightning strike 200 kV 0.8 ms 0.3 ms 62.5％ Switching operation 150 kV 5 ms 2 ms 60％ System fault 130 kV 50 ms 15 ms 70％

[0355] 2. Field test:

[0356] After the good results in the laboratory tests, the engineers conducted a 3-month field test in a 110 kV substation. Ten voltage transformers were selected, of which five were installed with the optimized PTC resistors, and the other five remained with the original protection scheme as the control group. During the test period, all overvoltage events and their impacts were recorded. Table 3 below is a summary of the test results:

[0357] Table 3 Experimental results table

[0358] Indicator Original scheme New scheme Improvement effect Total number of overvoltage events 15 15 - Average overvoltage duration 12 ms 4 ms 66.7％ Number of equipment trips 3 0 100％ Equipment damage events 1 0 100％ System stability improvement - - 35％

[0359] Conclusion: By applying the PTC resistor selection method of the present application, the power company successfully selected the optimal overvoltage suppression PTC resistor for the electromagnetic voltage transformer of its 110 kV substation. This method not only considers the complex relationship between electrical parameters, overvoltage parameters and PTC resistor parameters, but also realizes the global optimization of parameters through genetic algorithm. The laboratory tests and field tests show that the optimized PTC resistor significantly improves the overvoltage suppression capability of the voltage transformer, which can reduce the overvoltage duration by 60-70% on average. This not only improves the reliability and life of the equipment, but also greatly enhances the stability of the entire power system.

[0360] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer, characterized in that, Includes the following steps: S10. Select multiple PTC resistors with different parameters and install them one by one as overvoltage suppression resistors for electromagnetic voltage transformers. Then, perform subsequent steps S20 and S30 for each PTC resistor. S20. Record the electrical parameters of the electromagnetic voltage transformer under normal operating conditions and the PTC resistance parameters of the overvoltage suppression resistor, and record them as normal operating data. The electrical parameters include primary side voltage, secondary side voltage, primary side current, secondary side current, output power, power factor, harmonic content, overvoltage, and overvoltage duration. The PTC resistance parameters include room temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, and power density. S30. Adjust the operating environment of the electromagnetic voltage transformer by gradually increasing the applied voltage in steps. Record the electrical parameters, overvoltage parameters, and PTC resistance parameters of the corresponding overvoltage suppression resistor of the electromagnetic voltage transformer under different voltages, and record them as boosted operation data. The overvoltage parameters include: overvoltage voltage and overvoltage duration. S40. Establish a set of operating equations for the electromagnetic voltage transformer that takes into account electrical parameters, overvoltage parameters, and the PTC resistance parameters mentioned in steps S20 and S30, including voltage equations, current equations, power equations, temperature equations, PTC resistance characteristic equations, and overvoltage response equations. S50. Based on the normal operation data and boost operation data, fit the parameters of the operating equation set to obtain the fitted operating equation set. S60. Based on the fitted set of operating equations, an overvoltage suppression effect evaluation model is established, which uses overvoltage voltage and overvoltage duration as the main evaluation indicators. S70. Optimize the PTC resistor parameters using a genetic algorithm. Use the PTC resistor parameters of several initially selected PTC resistors with different parameters as the initial population. Use the overvoltage suppression effect evaluation model to calculate the fitness value of each parameter group. Take minimizing the overvoltage voltage and overvoltage duration as the objective function. Set the population size, crossover probability, mutation probability and number of iterations. S80. Execute the genetic algorithm to obtain the optimal PTC resistor parameters; S90. Based on the obtained optimal PTC resistor parameters, select the model with the closest characteristics from the existing PTC resistor products as the final overvoltage suppression resistor selection result.

2. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 1, characterized in that, The voltage equation is specifically expressed as follows: In the formula, V1 is the primary voltage; V2 is the secondary voltage; N1 and N2 are the number of turns in the primary and secondary windings, respectively; I1 and I2 are the primary and secondary currents, respectively; R2 is the secondary winding resistance; L2 is the secondary winding self-inductance; M is the mutual inductance coefficient; ω is the angular frequency; C s t represents the distributed capacitance; t represents time.

3. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 2, characterized in that, The current equation is specifically expressed as follows: In the formula, Z1 is the total impedance of the primary side; I m For magnetizing current; R c X is the equivalent resistance of the core loss; m It is a magnetized reactance.

4. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 3, characterized in that, The power equation is specifically expressed as follows: P = |V1||I1|cosφ; Q = |V1||I1|sinφ; In the formula, S is apparent power; P is active power; Q is reactive power; PF is power factor; φ is the phase angle between voltage and current. It is the conjugate complex number of the primary current.

5. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 4, characterized in that, The temperature equation is specifically expressed as follows: In the formula, T is the temperature of the PTC resistor; t is time; m is the mass of the PTC resistor; c p P represents the specific heat capacity of the PTC resistor; loss Total power loss; h is the thermal conductivity coefficient; A is the surface area of ​​the PTC resistor; T amb For ambient temperature; P core For core loss; k h k is the hysteresis loss coefficient. e B is the eddy current loss coefficient; m This represents the maximum magnetic flux density.

6. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 5, characterized in that, The PTC resistance characteristic equation is specifically expressed as follows: In the formula, R PTC R0 is the current resistance value of the PTC resistor; α is the resistance value at room temperature; T0 is the reference temperature; T is the current temperature; β is the voltage coefficient; V is the voltage applied to the PTC resistor; γ is the dynamic response coefficient.

7. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 6, characterized in that, The overpressure response equation is specifically expressed as follows: V ov (t)=V peak yes -t / τ sin(ωt)+V nom ; In the formula, V ov (t) represents the change of overvoltage over time; V peak τ is the overvoltage peak value; ω is the decay time constant; V is the overvoltage oscillation angular frequency; nom Rated voltage; t ov V represents the duration of overvoltage; H(x) is the Heaviside step function; V th This is the overvoltage threshold voltage.

8. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 7, characterized in that, The method for calculating the total primary impedance is as follows: In the formula, R1 is the resistance of the primary winding; L1 is the self-inductance of the primary winding; R PTC This is the current resistance value of the PTC resistor.

9. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 8, characterized in that, The method for estimating the overpressure peak value is as follows: In the formula, k ov The overvoltage coefficient is denoted by di / dt; the current change rate is denoted by L. eq It is the equivalent inductance.

10. The method for selecting a PTC resistor for overvoltage suppression in an electromagnetic voltage transformer according to claim 9, characterized in that, The method for calculating the maximum magnetic flux density is as follows: In the formula, A core Let be the cross-sectional area of ​​the iron core.

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