PTC (Positive Temperature Coefficient) resistor selecting and matching method for overvoltage suppression of electromagnetic voltage transformer

Abstract

The invention provides a PTC (Positive Temperature Coefficient) resistor selecting and matching method for overvoltage suppression of an electromagnetic voltage transformer, which belongs to the technical field of electromagnetic voltage transformers and comprises the following steps of: firstly, recording electrical parameters of the transformer in normal and pressurization operation states and parameters of an overvoltage suppression resistor; based on the data, a mutual inductor operation equation set considering multiple factors is established, and operation parameters are obtained through fitting. And then, optimizing parameters of an overvoltage suppression resistor through a genetic algorithm by utilizing an overvoltage suppression effect evaluation model, and taking minimization of overvoltage voltage and duration as a target. And finally, according to an optimization result, selecting a proper model from the existing PTC resistor products as final configuration. According to the method disclosed by the invention, the electromagnetic theory, the thermodynamic principle, the optimization algorithm and the engineering practice are combined, so that the technical problems that most overvoltage protection schemes in the prior art adopt empirical design methods and lack systematic and quantitative optimization processes are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic voltage transformers, and in particular relates to a PTC resistor matching method for overvoltage suppression of an electromagnetic voltage transformer. Background Art

[0002] As a key device in the power system, electromagnetic voltage transformers are widely used in voltage measurement, relay protection, and energy metering. With the continuous expansion of the power grid and the continuous growth of electricity demand, the power system faces a more complex operating environment and higher reliability requirements. In this context, 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 method often does not react quickly enough when facing transient overvoltages, and the suppression effect is limited. Especially in the case of short circuit faults, lightning strikes or switching operations in the power system, the high-amplitude, rapidly changing overvoltages generated may cause serious distortion of the transformer secondary voltage, and even damage the connected measuring instruments and protection equipment.

[0004] In order to improve the overvoltage suppression effect, some existing technologies use protection elements such as nonlinear resistors and metal oxide arresters. Although these methods have improved the overvoltage tolerance of the transformer to a certain extent, they also have some limitations. For example, the response speed of nonlinear resistors is slow, and it is difficult to effectively suppress the rapidly rising transient overvoltage; although metal oxide arresters respond quickly, their protection characteristics are fixed and it is difficult to optimize and adjust according to different working conditions.

[0005] On the other hand, with the development of smart grid, higher requirements are put forward for the measurement accuracy and dynamic response of voltage transformers. However, the existing overvoltage protection schemes often affect the measurement accuracy of the transformer, especially in normal working conditions, which may introduce additional nonlinear errors.

[0006] In addition, most of the overvoltage protection solutions in the existing technology adopt empirical design methods and lack a systematic and quantitative optimization process. As a result, in practical applications, the selection and parameter setting of protection components often require long-term testing and adjustment, which is not only time-consuming and labor-intensive, but also difficult to adapt to different types of transformers and diverse application scenarios. Summary of the invention

[0007] In view of this, the present invention provides a PTC resistor matching method for overvoltage suppression of an electromagnetic voltage transformer, which can solve the technical problem that most overvoltage protection schemes in the prior art adopt empirical design methods and lack a systematic and quantitative optimization process.

[0008] The present invention is achieved in that:

[0009] The present invention provides a PTC resistor matching method for overvoltage suppression of an electromagnetic voltage transformer, comprising the following steps:

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

[0011] S20, recording the electrical parameters of the electromagnetic voltage transformer under normal operating conditions and the PTC resistance parameters of the overvoltage suppression resistor, and recording them as normal operating 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; the PTC resistance parameters include normal temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, and power density;

[0012] S30, adjusting the operating environment of the electromagnetic voltage transformer, increasing the applied voltage in steps, recording the electrical parameters, overvoltage parameters and PTC resistance parameters of the electromagnetic voltage transformer under different voltages, and recording them as boost operation data; the overvoltage parameters include: overvoltage voltage and overvoltage duration;

[0013] S40, establishing an operation equation group of the electromagnetic voltage transformer taking into account electrical parameters, overvoltage parameters and PTC resistance parameters, including a voltage equation, a current equation, a power equation, a temperature equation, a PTC resistance characteristic equation and an overvoltage response equation;

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

[0015] S60, based on the fitted operating equation group, establishing an overvoltage suppression effect evaluation model, the model uses overvoltage voltage and overvoltage duration as main evaluation indicators;

[0016] S70, optimizing the PTC resistor parameters by using a genetic algorithm, taking the PTC resistor parameters of the PTC resistors with multiple different parameters initially selected as the initial population, using the overvoltage suppression effect evaluation model to calculate the fitness value of each group of parameters, taking minimizing the overvoltage voltage and the overvoltage duration as the objective function, setting the population size, crossover probability, mutation probability and number of iterations;

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

[0018] S90. According to the obtained optimal PTC resistor parameters, a model with the closest characteristics is selected from existing PTC resistor products as the final overvoltage suppression resistor selection result.

[0019] The formula for running the equation group is as follows:

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

[0021]

[0022] Where, V1 is the primary voltage (input); V2 is the secondary voltage (output); N1, N2 are the turns of the primary and secondary windings; 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 coefficient; ω is the angular frequency (2πf, f is the operating frequency); C s is the distributed capacitance; t is the time;

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

[0024] 2. The current equation is expressed as:

[0025]

[0026]

[0027] Where, 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] Where 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 resistor.

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

[0031]

[0032] P=|V1||I1|cosφ;

[0033] Q=|V1||I1|sinφ;

[0034]

[0035] In the formula, 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 number of the primary current.

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

[0037]

[0038]

[0039]

[0040] Where, T is the temperature of the PTC resistor; t is the time; m is the mass of the PTC resistor; c p P is the specific heat capacity of PTC resistor; loss is the total power loss; h is the thermal conductivity; A is the PTC resistor 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.

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

[0042]

[0043] In the formula, R PTC is the current resistance value of the PTC resistor; R0 is the resistance value at room temperature; α is the temperature coefficient; T0 is the reference temperature (usually room temperature); T is the current temperature; β is the voltage coefficient; V is the voltage applied to the PTC resistor; and γ is the 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 the change of overvoltage over time; V peak is the overvoltage peak value; τ is the decay time constant; ω is the overvoltage oscillation angular frequency; V nom is the rated voltage; t ovis the duration of overvoltage; H(x) is the Heaviside step function (1 when x>0, otherwise 0); V th is the overvoltage threshold voltage; V peak It can be estimated by:

[0048]

[0049] In the formula, k ov is the overvoltage coefficient; di / dt is the current change rate; L eq is the equivalent inductance; these equations together form a complex set of equations that cover all aspects of the electromagnetic voltage transformer, 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 the subsequent optimization process.

[0050] Specifically, the step S10 includes:

[0051] Step 101, determining the voltage and current range of the positive temperature coefficient resistor 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 resistor, determining the preliminary range of these parameters;

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

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

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

[0056] Wherein, the step S20 specifically includes:

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

[0058] Step 202: Use a high-precision voltmeter, ammeter and power analyzer to measure the primary voltage, secondary voltage, primary current, secondary current, output power and power factor of the transformer;

[0059] Step 203: Use a harmonic analyzer to measure the harmonic content of voltage and current;

[0060] Step 204, simulating overvoltage by instantaneously applying 1.2 times the rated voltage on the primary side and quickly restoring to the rated voltage, and recording the secondary side voltage waveform using a high-speed oscilloscope;

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

[0062] Step 206, determining the voltage coefficient by measuring the resistance value at different voltages, and calculating the power density according to the physical size and the maximum allowable power consumption of the positive temperature coefficient resistor;

[0063] Step 207, all measurements are repeated at least three times, and the average value is taken as the final recorded data;

[0064] Wherein, the step S30 specifically includes:

[0065] Step 301, placing the electromagnetic voltage transformer in a controllable temperature and humidity environment chamber, setting the initial environment temperature to 20 degrees Celsius and the relative humidity to 50%;

[0066] Step 302, using a programmable power supply, starting from the rated primary voltage of the transformer, gradually increasing the voltage by 5% per step until it reaches 150% of the rated voltage;

[0067] Step 303: Keep stable for five minutes at each voltage level, and then record all electrical parameters;

[0068] Step 304: For the overvoltage parameter, at each voltage level, apply an additional voltage spike with a duration of 100 milliseconds and an amplitude of 1.2 times the current voltage, and record the overvoltage peak value and duration;

[0069] Step 305: Use an infrared thermal imager to monitor the temperature change of the positive temperature coefficient resistor in real time, and record the steady-state temperature at each voltage level;

[0070] Step 306, repeat the above process, but set the ambient temperature to 0 degrees Celsius, 40 degrees Celsius and 60 degrees Celsius respectively to examine the impact of temperature on system performance;

[0071] Step 307, collating all the measured data into a data table, including all electrical parameters, overvoltage parameters and positive temperature coefficient resistance parameters under different ambient temperatures and voltage levels;

[0072] Wherein, the step S40 specifically includes:

[0073] Step 401: Based on electromagnetic theory and thermodynamic principles, a mathematical model describing the working characteristics of an electromagnetic voltage transformer is established;

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

[0075] Step 403, the voltage equation describes the relationship between the primary and secondary voltages, taking into account the turns ratio, impedance and mutual inductance effects;

[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 resistor, taking into account the heat generation and heat dissipation process;

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

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

[0081] Wherein, the step S50 specifically includes:

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

[0083] Step 502: fitting the unknown parameters in the running equation group using the least square method;

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

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

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

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

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

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

[0090] Step 509: Use the Levenberg-Marquardt algorithm to perform nonlinear least squares fitting;

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

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

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

[0094] Wherein, the step S60 specifically includes:

[0095] Step 601: construct a comprehensive evaluation model based on the fitted operating equation group;

[0096] Step 602: The model uses overvoltage and overvoltage duration as main evaluation indicators, while considering the accuracy, loss and temperature rise of the transformer;

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

[0098] Step 604: The scoring function adopts an S-type function, such as a function used for overvoltage scoring;

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

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

[0101] Step 607: Calculate a comprehensive score for each sample, analyze the score distribution of these samples, and obtain the sensitivity of the positive temperature coefficient resistor parameters to the system performance;

[0102] Step 608: Use response surface methodology to construct an approximate relationship between the positive temperature coefficient resistor parameter and the scoring function;

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

[0104] Step 610: Perform simulation calculation on these sampling points to obtain corresponding scoring values;

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

[0106] Step 612: Determine the polynomial coefficients using the least squares method;

[0107] Step 613: test the significance and goodness of fit of the model through variance analysis;

[0108] Wherein, the step S70 specifically includes:

[0109] Step 701, define a chromosome encoding scheme used in the genetic algorithm, where each chromosome represents a set of positive temperature coefficient resistor parameters, including room temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient and power density;

[0110] Step 702: adopt real number encoding mode, and each parameter is represented by a real number;

[0111] Step 703: setting the value range of the parameter;

[0112] Step 704, defining a fitness function, using the overvoltage suppression effect evaluation model established in step S60 as the basis of the fitness function, but requiring normalization processing;

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

[0114] Step 706, generating an initial population, using the multiple positive temperature coefficient resistors with different parameters selected in step S10 as a part of the population, and supplementing the remaining individuals by randomly generating them within the parameter value range;

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

[0116] Step 708: Select the parent individual by using the roulette wheel selection method;

[0117] Step 709: Perform crossover operation using arithmetic crossover method;

[0118] Step 710: Perform mutation operation using Gaussian mutation;

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

[0120] Step 712: Check the termination condition. If the maximum number of iterations is reached or there is no significant improvement in the optimal solution for fifty consecutive generations, terminate the algorithm.

[0121] Wherein, the step S80 specifically includes:

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

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

[0124] Step 803: Perform sensitivity analysis to evaluate the influence of each parameter on the final result;

[0125] Step 804: Based on the optimal parameters, only one parameter value is changed each time to observe the change of the output result;

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

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

[0128] Step 807: randomly generate one thousand parameter combinations in a small range around the optimal parameters, and calculate the evaluation model outputs of these combinations;

[0129] Step 808, counting the results of the one thousand simulations, and calculating the mean value, standard deviation, and 95 percent confidence interval;

[0130] Step 809: perform cross validation to evaluate the generalization ability of the optimal solution;

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

[0132] Step 811: Use the remaining data to verify the performance of this set of parameters;

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

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

[0135] Step 814: Perform an extreme condition test to evaluate the performance of the optimal solution under extreme conditions;

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

[0137] Wherein, the step S90 specifically includes:

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

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

[0140] Step 903, collecting information from the official website and product manuals of the manufacturer, directly contacting the manufacturer, and using web crawler technology from the website of the electronic component distributor;

[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 operating voltage, maximum operating current, volume, price, etc.;

[0142] Step 905: Develop a parameter matching algorithm, the goal of which is to find the actual product closest to the optimal parameters in the product database;

[0143] Step 906: Use weighted Euclidean distance as a similarity measure;

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

[0145] Step 908: Conduct a detailed evaluation of the selected candidate product, including calculating its overvoltage suppression effect using the evaluation model established in step S60, checking whether its maximum operating voltage and maximum operating current meet the application requirements, and considering whether its volume meets the installation space limit of the transformer;

[0146] Step 909, comprehensively considering the above factors, selecting 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 according to the structural characteristics and installation space of the electromagnetic voltage transformer;

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

[0150] Step 110: Select a positive temperature coefficient resistor with corresponding reliability and durability according to the expected life of the electromagnetic voltage transformer;

[0151] Step 111, considering the cost factor, setting the upper limit of the price of the positive temperature coefficient resistor;

[0152] Step 112: Consider the response speed requirement of the positive temperature coefficient resistor according to the application scenario of the electromagnetic voltage transformer;

[0153] Optionally, the step S40 further includes:

[0154] Step 409, establishing a magnetic circuit model of the electromagnetic voltage transformer, taking into account the nonlinear characteristics and hysteresis effect of the core;

[0155] Step 410, establishing a thermal model of the electromagnetic voltage transformer, taking into account the thermal coupling effects of the winding, the core and the positive temperature coefficient resistor;

[0156] Step 411, establishing a parasitic capacitance model of an electromagnetic voltage transformer, taking into account the distributed capacitance between windings and between windings and the core;

[0157] Step 412, establishing a dynamic response model of a positive temperature coefficient resistor, taking into account its transient characteristics under rapid voltage changes;

[0158] Step 413, integrating the above model with the main equation group to form a complete electromagnetic voltage transformer system model;

[0159] Optionally, the step S60 further includes:

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

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

[0162] Step 616: Use the back propagation algorithm to train the neural network, use the mean square error as the loss function, and use the Adam optimizer to update the parameters;

[0163] Step 617: Use K-fold cross validation method to evaluate the generalization ability of the neural network model;

[0164] Step 618: compare the neural network model with the polynomial response surface model, and select the model with better performance as the final evaluation model;

[0165] Optionally, the step S70 further includes:

[0166] Step 713: Adopt an adaptive genetic algorithm to dynamically adjust the crossover probability and mutation probability;

[0167] Step 714: The crossover probability and the mutation probability are related to the population diversity and the optimal individual fitness. When the population diversity decreases, the mutation probability increases, and when the optimal individual fitness stagnates, the crossover probability increases.

[0168] Step 715: Introduce a taboo search strategy, maintain a taboo table, record the most recently visited solutions, and prevent the algorithm from falling into a local optimum;

[0169] Step 716: Use the island model parallel genetic algorithm to divide the total population into several sub-populations, each sub-population evolves independently, and individuals migrate between sub-populations regularly;

[0170] Step 717: After the algorithm converges, use the local search method to fine-tune the optimal solution to further improve the quality of the solution;

[0171] Optionally, the step S80 further includes:

[0172] Step 816: Perform reliability analysis to evaluate the stability of the optimal positive temperature coefficient resistor parameters in long-term operation;

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

[0174] Step 818: Establish a Weibull distribution model to predict the failure rate and mean time between failures of the positive temperature coefficient resistor;

[0175] Step 819: Perform failure mode and effect analysis to identify possible failure modes and their impact on system performance;

[0176] Step 820: Based on the reliability analysis results, make necessary adjustments to the optimal parameters to balance performance and reliability requirements.

[0177] Compared with the prior art, the PTC resistor matching method for overvoltage suppression of an electromagnetic voltage transformer provided by the present invention has the following beneficial effects:

[0178] First, the present invention achieves fast and accurate overvoltage suppression by selecting positive temperature coefficient resistors in a systematic and quantitative way. Compared with the traditional passive suppression method, the positive temperature coefficient resistors selected by this method can respond to voltage changes within milliseconds and effectively suppress transient overvoltage.

[0179] Secondly, the present invention realizes the accurate matching of positive temperature coefficient resistor parameters by establishing a detailed mathematical model and optimization algorithm. This method not only takes into account the electrical characteristics of the mutual inductor, but also comprehensively considers the influence of thermal characteristics, environmental factors and other aspects, making the matching result more comprehensive and reliable.

[0180] Third, the method of the present invention has good adaptability and scalability. By adjusting the weight coefficient of the evaluation model and the parameters of the optimization algorithm, it can flexibly adapt to different types of electromagnetic voltage transformers and diversified application scenarios. This flexibility enables the method to be widely used on transformers of different voltage levels and capacities, greatly improving the practicality of the method.

[0181] Fourthly, the present invention 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 is minimized under normal working conditions.

[0182] Fifth, the present invention 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 and avoid falling into the local optimum.

[0183] In summary, the present invention solves the technical problem that most overvoltage protection solutions in the prior art adopt empirical design methods and lack a systematic and quantitative optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0184] Figure 1 A flow chart of the method provided by the present invention. DETAILED DESCRIPTION

[0185] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0186] like Figure 1 FIG. 1 is a flow chart of a PTC resistor matching method for overvoltage suppression of an electromagnetic voltage transformer provided by the present invention. The method comprises the following steps:

[0187] S10, selecting a plurality of PTC resistors with different parameters, installing them one by one as overvoltage suppression resistors of the electromagnetic voltage transformer, and performing subsequent steps S20 and S30 on each PTC resistor;

[0188] 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;

[0189] S30, adjusting the operating environment of the electromagnetic voltage transformer, increasing the applied voltage in steps, recording the electrical parameters, overvoltage parameters and PTC resistance parameters of the electromagnetic voltage transformer under different voltages, and recording them as boost operation data; the overvoltage parameters include: overvoltage voltage and overvoltage duration;

[0190] S40, establishing an operation equation group of the electromagnetic voltage transformer taking into account electrical parameters, overvoltage parameters and PTC resistance parameters, including a voltage equation, a current equation, a power equation, a temperature equation, a PTC resistance characteristic equation and an overvoltage response equation;

[0191] S50, fitting parameters of the operating equation group according to the normal operating data and the supercharging operating data to obtain a fitted operating equation group;

[0192] S60, based on the fitted operating equation group, establishing an overvoltage suppression effect evaluation model, the model uses overvoltage voltage and overvoltage duration as main evaluation indicators;

[0193] S70, optimizing the PTC resistor parameters by using a genetic algorithm, taking the PTC resistor parameters of the PTC resistors with multiple different parameters initially selected as the initial population, using the overvoltage suppression effect evaluation model to calculate the fitness value of each group of parameters, taking minimizing the overvoltage voltage and the overvoltage duration as the objective function, and setting the population size, crossover probability, mutation probability and number of iterations;

[0194] S80, executing a genetic algorithm to obtain optimal PTC resistance parameters;

[0195] S90. According to the obtained optimal PTC resistor parameters, a model with the closest characteristics is selected from existing PTC resistor products as the final overvoltage suppression resistor selection result.

[0196] The specific implementation methods of the above steps are described in detail below:

[0197] The specific implementation method of step S10 is: first, based on the rated voltage and rated current of the electromagnetic voltage transformer, preliminarily determine the voltage and current range of the PTC resistor. Usually, the rated voltage of the PTC resistor should not be less than 1.5 times the rated voltage of the secondary side of the transformer, and the rated current should not be less than 1.2 times the rated current of the secondary side of the transformer. Secondly, consider the temperature coefficient, Curie temperature and power density of the PTC resistor. The temperature coefficient is usually between 0.01 and 0.1 / ℃, the Curie temperature should be higher than the normal operating temperature of the transformer by 50 to 100℃, and the power density is generally between 0.1 and 1W / cm 3range. Again, select PTC resistors with different resistance values, which are usually between 0.1 and 10 times the load impedance of the secondary side of the transformer. Finally, purchase at least 5 PTC resistor samples with different parameter combinations from different manufacturers to ensure that there are enough samples for subsequent testing and optimization. The purpose of this step is to provide a variety of PTC resistor samples for subsequent testing and optimization in order to find the most suitable parameter combination.

[0198] The specific implementation of step S20 is: first, the selected PTC resistors are respectively installed on the secondary side of the electromagnetic voltage transformer and connected 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, a high-precision voltmeter, an ammeter and a power analyzer are used to measure the primary voltage, secondary voltage, primary current, secondary current, output power and power factor of the transformer. At the same time, a harmonic analyzer is used to measure the harmonic content of the voltage and current. For the overvoltage and overvoltage duration, it can be simulated by applying 1.2 times the rated voltage on the primary side and quickly recovering to the rated voltage, and a high-speed oscilloscope is used to record the secondary voltage waveform. In addition, a precision resistance tester is used to measure the resistance value of the PTC resistor at different temperatures, thereby obtaining 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 is calculated based on the physical size and maximum allowable power consumption of the PTC resistor. 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 benchmark dataset to provide reliable input for subsequent modeling and optimization.

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

[0200] The specific implementation of step S40 is as follows: First, based on electromagnetic theory and thermodynamic principles, a mathematical model describing the working characteristics of the electromagnetic voltage transformer is established. 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 and secondary voltages, taking into account the turns ratio, impedance and mutual inductance effects: Where V1 and V2 are the primary and secondary voltages, N1 and N2 are the number of winding turns, I1 and I2 are the currents, R2 and L2 are the secondary resistance and inductance, M is the mutual inductance, ω is the angular frequency, C s is the distributed capacitance. The current equation describes the composition of the primary current: Where Z1 is the total impedance of 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 resistor: Where T is the PTC resistor temperature, m is the mass, c p is the specific heat capacity, P loss is the power loss, h is the thermal conductivity, A is the surface area, 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 resistance value at room temperature, 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: V ov (t) = V peak e -t / τ sin(ωt)+V nom , Where V ov (t) is the overvoltage, V peak is the overvoltage peak value, τ is the decay time constant, V nom is the rated voltage, t ov is the duration of overvoltage, H(x) is the unit step function, 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 turns of the primary and secondary windings; 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 coefficient; ω is the angular frequency (2πf, f is the operating frequency); C s is the distributed capacitance; t is the time;

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

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

[0206]

[0207]

[0208] Where, 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:

[0209]

[0210] Where 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 resistor.

[0211] 3. Power equation, specifically expressed as:

[0212]

[0213] P=|V1||I1|cosφ;

[0214] Q=|V1||I1|sinφ;

[0215]

[0216] In the formula, 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 number of the primary current.

[0217] 4. Temperature equation, specifically expressed as:

[0218]

[0219]

[0220]

[0221] Where, T is the temperature of the PTC resistor; t is the time; m is the mass of the PTC resistor; c p P is the specific heat capacity of PTC resistor; loss is the total power loss; h is the thermal conductivity; A is the PTC resistor 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.PTC resistance characteristic equation, specifically expressed as:

[0223]

[0224] In the formula, R PTC is the current resistance value of the PTC resistor; R0 is the resistance value at room temperature; α is the temperature coefficient; T0 is the reference temperature (usually room temperature); T is the current temperature; β is the voltage coefficient; V is the voltage applied to the PTC resistor; and γ is the dynamic response coefficient.

[0225] 6. Overvoltage response equation, specifically expressed as:

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

[0227]

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

[0229]

[0230] In the formula, k ov is the overvoltage coefficient; di / dt is the current change rate; L eqis the equivalent inductance; these equations together form a complex set of equations that cover all aspects of the electromagnetic voltage transformer, 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 the subsequent optimization process.

[0231] The following is a description of how to obtain the parameters used:

[0232] 1. Voltage and current parameters (V1, V2, I1, I2): Acquisition method: direct measurement; Measuring equipment: high-precision digital multimeter or oscilloscope; Measuring method: connect the probe of the multimeter or oscilloscope 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: Transformer design specifications or data sheets provided by the manufacturer.

[0234] 3. Winding resistance (R1, R2): Acquisition method: direct measurement; Measuring equipment: precision resistance tester; Measurement method: When the transformer is powered off, 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:

[0239] 5. Distributed capacitance (C s ): Acquisition method: measurement; Measuring equipment: precision capacitance tester; Measuring method: When the transformer is powered off, connect the tester between the primary and secondary windings for measurement.

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

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

[0242] Experimental steps:

[0243] Step 1: Apply rated voltage to the primary side and open the secondary side;

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

[0245]

[0246]

[0247] 8.PTC resistance parameters (R0, α, β, γ): Acquisition method: experimental measurement plus data fitting; Measurement equipment: programmable power supply, precision resistance tester, temperature sensor, data acquisition system;

[0248] Experimental steps:

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

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

[0251] Step 3: Apply a rapidly changing voltage and measure the dynamic response of the PTC resistor; Data fitting: Use the least squares method to fit the experimental data to obtain the parameter value.

[0252] 9.PTC resistor mass (m) and specific heat capacity (c p ): Mass: measured using a precision balance; Specific heat: consult the material data sheet or determine by calorimeter experiment.

[0253] 10. Thermal conductivity (h) and surface area (A): Thermal conductivity: Refer to the material data sheet or determine through thermal conductivity experiments. Surface area: Calculate based on the geometric dimensions of the PTC resistor.

[0254] 11. Ambient temperature (T amb ): Acquisition method: direct measurement. Measuring 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] Measuring 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, measuring the core loss under each condition;

[0261] Step 3: Data fitting: Use the least squares method to fit the experimental data to obtain the coefficient value.

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

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

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

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

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

[0267] Step 1: Simulate overvoltage conditions (such as switching operation or lightning strike);

[0268] Step 2: Record voltage and current waveforms:

[0269] Step 3: Analyze the waveform to obtain the overvoltage factor and equivalent inductance.

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

[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, the experimental data obtained in steps S20 and S30 are divided into two groups: normal operation data and boost operation data. Then, the least squares method is used to fit the unknown parameters in the operation equation group. Specifically, for the voltage equation, the fitting parameters include the mutual inductance coefficient M and the distributed capacitance C s ; For the current equation, the fitting parameters include the core loss equivalent resistance R c and magnetizing reactance X m ; For the power equation, the main purpose is to verify the consistency between the calculated value and the measured value; for the temperature equation, the fitting parameters include the thermal conductivity coefficient h and the 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 ov. The Levenberg-Marquardt algorithm is used for nonlinear least squares fitting, which combines the advantages of the gradient descent method and the Gauss-Newton method and can effectively deal with nonlinear problems. In order 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%). The fitting process is repeated many times, and the average result is taken as the final parameter value. At the same time, the confidence interval of each parameter is calculated to evaluate the reliability of the fit. Finally, the validation set data is predicted using the fitted set of equations, and the root mean square error (RMSE) and the coefficient of determination (R2) are calculated to evaluate the overall performance of the model. If the RMSE is large or the R2 is small, it is necessary to reconsider the model structure or increase the experimental data. The purpose of this step is to obtain a mathematical model that can accurately describe the behavior of the system through data fitting, providing a reliable basis for the subsequent optimization process.

[0273] The specific implementation of step S60 is as follows: First, a comprehensive evaluation model is constructed based on the fitted operating equations. ov and overvoltage duration t ov As the main evaluation index, other important factors such as the accuracy, loss and temperature rise of the transformer are also considered. A comprehensive scoring function F is defined: F = w1f(V ov )+w2g(t ov )+w3h(ε)+w4i(P loss )+W5j(ΔT), where f, g, h, i, j are scoring functions for overvoltage, overvoltage duration, transformer accuracy, loss, and temperature rise, respectively, and w1 to w5 are corresponding weight coefficients. The scoring function uses a sigmoid function, for example Where k is the steepness coefficient, V th is the desired overvoltage threshold. Similarly, corresponding scoring functions are defined for other indicators. The initial values ​​of the weight coefficients can be set according to expert experience, such as w1=0.3, w2=0.3, w3=0.2, W4=0.1, and w5=0.1. Then, a large number of samples (such as 10,000) are randomly generated within the possible value range of the PTC resistance parameters using the Monte Carlo simulation method, and a comprehensive score F is calculated for each sample. By analyzing the score distribution of these samples, the sensitivity of the PTC resistance parameters to the system performance can be obtained. Next, the response surface methodology (RSM) is used to construct an approximate relationship between the PTC resistance parameters and the scoring function. The central composite design (CCD) is selected as the experimental design method, and appropriate sampling points are selected in the PTC resistance parameter space. These sampling points are simulated and calculated to obtain the corresponding scoring values. The response surface is then fitted using a second-order polynomial model: where x i Represents the various parameters of the PTC resistor, b0, b i , b ii and b ij are the unknown coefficients. These coefficients are determined using the least squares method. Finally, the significance and goodness of fit of the model are tested by 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 of the subsequent optimization process. The purpose of this step is to establish a mathematical model that can comprehensively evaluate the performance of PTC resistors and provide 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 resistor parameters, including the normal temperature resistance value R0, the Curie temperature T c , temperature coefficient α, voltage coefficient β and power density P d . Using real number encoding, each parameter is represented by a real number, for example, the chromosome structure is [R0, T s ,α,β,P a ]. Set the parameter value range: 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 to 10 -4 V -2 Between a At 0.1W / cm 3 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 of the fitness function, but normalization is required to ensure the comparability between different indicators. The fitness function can be expressed as: Where F is the output value of the evaluation model. This process can convert the evaluation score into a fitness value between 0 and 1. The lower the evaluation score, the higher the fitness.

[0276] Then, set the parameters of the genetic algorithm. The population size is set to 100, which is large enough to provide sufficient genetic diversity without causing excessive computational effort. The crossover probability is set to 0.8, a higher probability that is conducive to the generation of new excellent individuals. The mutation probability is set to 0.1, a moderate probability that can introduce a certain amount of randomness while maintaining population stability. The maximum number of iterations is set to 1000, which is usually enough for the algorithm to converge to a good solution.

[0277] Next, an initial population is generated. The PTC resistors with multiple different parameters selected in step S10 are used as a 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: The roulette wheel selection method is used to select parent individuals. This method gives individuals with high fitness a greater probability of being selected, but does not completely exclude individuals with low fitness, which helps maintain population diversity.

[0281] 3. Crossover: Perform a crossover operation on the selected parent individuals. Use the arithmetic crossover method, that is, weighted average the parameters of the parent individuals: Child = αParent1 + (1-α) Parent2, where α is a random number between 0 and 1. This method can generate new individuals between the parents, which is conducive to local search.

[0282] 4. Mutation: Perform mutation operation on the offspring individuals after crossover. Use Gaussian mutation, that is, add a random number that obeys normal distribution 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 range. This variation allows for small-scale exploration in the parameter space.

[0283] 5. Elite retention: The 2% individuals with the highest fitness in the current population are directly copied to the next generation to ensure that the optimal solution will not be lost during the evolution process.

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

[0285] 7. Check the termination condition: If the maximum number of iterations is reached or there is no significant improvement (improvement less than 1%) in the optimal solution for 50 consecutive generations, terminate the algorithm; otherwise, return to step 1 to continue iterating.

[0286] Finally, the convergence process of the algorithm and the optimal PTC resistor parameters are recorded. The purpose of this step is to efficiently search for the optimal PTC resistor parameter combination in a large parameter space by simulating the evolutionary process 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 the room temperature resistance value R0, the Curie temperature T s, temperature coefficient α, voltage coefficient β and power density P a Then, these parameters are used to recalculate the overvoltage suppression effect evaluation model to obtain the theoretically optimal overvoltage suppression effect and overvoltage duration.

[0288] Next, a sensitivity analysis is performed to evaluate the influence of each parameter on the final result. The specific method is to change the value of only one parameter at a time (within its allowable range of ±10%) based on the optimal parameters and observe the changes in the output results. Calculate the sensitivity coefficient of each parameter: Where F is the output of the evaluation model, x i is the i-th parameter. The larger the absolute value of the sensitivity coefficient, the more significant the impact of the parameter on the result.

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

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

[0291] Finally, extreme condition tests are performed to evaluate the performance of the optimal solution under extreme conditions. Several extreme working conditions are simulated, such as the maximum operating temperature, the maximum allowable voltage, the maximum load current, etc., and the overvoltage suppression effect under these conditions is calculated. If the overvoltage suppression effect can still meet the design requirements under all extreme conditions (such as the overvoltage voltage does not exceed 1.2 times the rated voltage, and the overvoltage duration does not exceed 100ms), the optimal solution is considered to have good robustness.

[0292] The purpose of this step is to comprehensively evaluate the performance and reliability of the optimal PTC resistor parameters obtained by the genetic algorithm to ensure that it is not only optimal in theory but also maintains stable and reliable performance in practical applications.

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

[0294] Then, establish a PTC resistor product database. This database contains the product models and detailed parameters of the main PTC resistor manufacturers on the market. Data can be collected in the following ways: 1) Obtain from the manufacturer's official website and product manual; 2) Contact the manufacturer directly to obtain the latest product data; 3) Use web crawler technology to collect information from the website of electronic component distributors. Each record in the database should contain the following fields: manufacturer, model, room temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, power density, maximum operating voltage, maximum operating current, volume, price, etc.

[0295] Next, develop a parameter matching algorithm. The goal of this algorithm is to find the actual product in the product database that is closest to the optimal parameters. You can use the weighted Euclidean distance as the 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 room temperature resistance value and 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 power density can be set to 0.1 each.

[0298] Then, perform the parameter matching process:

[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 smallest to largest.

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

[0302] 4. Conduct a detailed evaluation of the 10 candidate products, including:

[0303] a) Using the evaluation model established in step S60, calculate its overvoltage suppression effect.

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

[0305] c) Consider whether its volume meets the installation space limitation of the transformer.

[0306] 5. Consider the above factors comprehensively and select the best PTC resistor product.

[0307] The purpose of this step is to convert the theoretically optimal PTC resistor parameters into practically available product options, ensuring that the final selected PTC resistor can be as close to the theoretical optimal performance as possible and meet the requirements of practical applications. In this way, the best balance can be found between theoretical optimization and practical application, providing the most suitable overvoltage suppression solution for electromagnetic voltage transformers.

[0308] This method covers the entire process from initial selection, experimental testing, mathematical modeling, parameter optimization to final product selection. It combines electromagnetic theory, thermodynamic principles, mathematical modeling, optimization algorithms and engineering practice to find the best overvoltage suppression solution for electromagnetic voltage transformers. The advantage of this method is that it takes into account both theoretical optimality and various constraints of practical applications, and can achieve a good balance between performance and reliability. Through this systematic, data-driven approach, the overvoltage suppression capability of electromagnetic voltage transformers can be significantly improved, and their reliability and stability under various working conditions can be enhanced.

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

[0310] First, the characteristics of the positive temperature coefficient resistor are highly matched with the overvoltage suppression requirements. The characteristic of the positive temperature coefficient resistor that the resistance value increases sharply when the temperature rises enables it to respond quickly when an overvoltage occurs, limit the current rise, and thus suppress the overvoltage. At the same time, when the voltage returns to normal, the positive temperature coefficient resistor can quickly cool down and return to a 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, this method establishes a comprehensive and accurate mathematical model, including voltage equation, current equation, power equation, temperature equation, positive temperature coefficient resistor characteristic equation and overvoltage response equation. These equations fully describe the working characteristics of electromagnetic voltage transformer and positive temperature coefficient resistor and their interaction. Through such detailed modeling, this method can accurately predict the response of the system under different parameters, providing a reliable theoretical basis for the subsequent optimization process.

[0312] Third, this method adopts a multi-step, multi-level optimization strategy. From the initial parameter range determination, to the response surface method to build the evaluation model, to the genetic algorithm for global optimization, each step has been carefully designed to ensure that the global optimal solution can be found in the complex parameter space. In particular, the introduction of the genetic algorithm, whose mechanism of simulating biological evolution enables the method to effectively avoid falling into the local optimum, while having strong robustness and adaptability.

[0313] Fourth, this method focuses on the combination of theory and practice. Through the collection and analysis of a large amount of experimental data, 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 and cost factors of positive temperature coefficient resistors, so that the final selection result is both theoretically optimal and practically feasible.

[0314] Fifth, this method uses a variety of advanced mathematical tools and algorithms. For example, the least squares method is used for parameter fitting, the response surface method is used to build the evaluation model, and the Monte Carlo method is used for sensitivity analysis. The comprehensive application of these methods ensures the scientificity and reliability of the selection process.

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

[0316] It is worth noting that this method also takes into account various influencing factors of positive temperature coefficient resistors in practical applications, such as ambient temperature, load changes, etc. By simulating various working conditions in the experimental design and considering these factors in the optimization process, this method ensures the reliability and stability of the matching results in practical applications.

[0317] Finally, this 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 extreme condition testing. This comprehensive consideration enables the positive temperature coefficient resistor selected by this method to play the best effect in actual operation and truly solve the overvoltage problem of electromagnetic voltage transformers.

[0318] In summary, the method of the present invention constructs a scientific, systematic and reliable positive temperature coefficient resistor matching method by combining electromagnetic theory, thermodynamic principles, optimization algorithm and engineering practice.

[0319] In order to better understand and implement the present invention, an embodiment of a specific application scenario of the present invention is provided below: a power company is upgrading the voltage transformer system for its 110kV substation. The company hopes to select a suitable PTC resistor to improve the overvoltage suppression capability of the electromagnetic voltage transformer to enhance the stability and reliability of the system. The company decides to use the method of the present invention to select the optimal PTC resistor.

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

[0321] The engineers of the power company selected five PTC resistors with different parameters from the market, which were marked 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] Engineers installed these five types of PTC resistors on five 110kV / 100V electromagnetic voltage transformers of the same model, and recorded various electrical parameters and PTC resistor parameters under normal operating conditions. The following is the normal operating data of one group (using PTC resistor A):

[0326] Electrical parameters: primary voltage: 110kV; secondary voltage: 100V; primary current: 0.05A; secondary 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 boost operation data

[0329] Next, the engineers simulated different levels of overvoltage by adjusting the operating environment of the voltage transformer. The voltage was gradually increased from 110kV to 130kV in 5kV steps, and the electrical parameters, overvoltage parameters and PTC resistor parameters at each voltage level were recorded. The following are some data at 125kV when using PTC resistor A:

[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 resistor A parameters: current resistance value: 25Ω; current temperature: 135℃; actual temperature coefficient: 18% / K; actual voltage coefficient: 0.018V^-2; actual power density: 1.8W / cm^3.

[0332] Step 4: Create a running set of equations

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

[0334] Step 5: Fitting the parameters of the running equations

[0335] Using the collected normal operation data and boost operation data, engineers fitted the parameters of the operating equations using the least squares method. During the fitting process, professional mathematical software was used to process complex nonlinear equations. After the fitting was completed, a set of equations that can accurately describe the behavior of the voltage transformer and PTC resistor was obtained.

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

[0337] Based on the fitted operating equations, engineers established an overvoltage suppression effect evaluation model. The model uses overvoltage voltage and overvoltage duration as the main evaluation indicators. A comprehensive scoring function is defined:

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

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

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

[0341] Engineers used genetic algorithms to optimize the parameters of PTC resistors. The parameters of the 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] Use the evaluation model built in step 6 to calculate the fitness value of each set of parameters, with maximizing the score as the objective function.

[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 value: 18Ω; Curie temperature: 128℃; temperature coefficient: 19% / K; voltage coefficient: 0.019V^-2; power density: 1.7W / cm^3.

[0345] This set of parameters showed the best overvoltage suppression effect in the simulation test, with a score of 92 points.

[0346] Step 9: Select the Final PTC Resistor

[0347] Based on the optimal PTC resistor parameters obtained, engineers selected the model with the closest characteristics from the existing PTC resistor products. They found a PTC resistor model XYZ-18, whose parameters are as follows: room temperature resistance value: 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 were very close to the optimization results and was selected as the final overvoltage suppression resistor.

[0349] Verification and Application:

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

[0351] 1. Laboratory testing:

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

[0353] Table 2 Test results

[0354] Overvoltage type Overvoltage amplitude Original scheme overvoltage duration New solution overvoltage duration Improvement effect Lightning strike 200kV 0.8ms 0.3ms 62.5％ Switch Operation 150kV 5ms 2ms 60％ System failure 130kV 50ms 15ms 70％

[0355] 2. Field test:

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

[0357] Table 3 Experimental results

[0358] index Original plan New Solution Improvement effect Total number of overvoltage events 15 15 - Average overvoltage duration 12ms 4ms 66.7％ Equipment trip times 3 0 100％ Equipment damage incident 1 0 100％ Improved system stability - - 35％

[0359] Conclusion: By applying the PTC resistor selection method of the present invention, the power company successfully selected the optimal overvoltage suppression PTC resistor for the electromagnetic voltage transformer of its 110kV substation. This method not only takes into account the complex relationship between electrical parameters, overvoltage parameters and PTC resistor parameters, but also realizes the global optimization of parameters through genetic algorithms. The results of laboratory tests and field tests show that the optimized PTC resistor significantly improves the overvoltage suppression capability of the voltage transformer and 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 description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer, characterized in that: The following steps are involved: S10, selecting a plurality of PTC resistors with different parameters, installing them one by one as overvoltage suppression resistors of the electromagnetic voltage transformer, and performing subsequent steps S20 and S30 on each PTC resistor; S20, recording the electrical parameters of the electromagnetic voltage transformer under normal operating conditions and the PTC resistance parameters of the overvoltage suppression resistor, and recording them as normal operating 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; the PTC resistance parameters include normal temperature resistance value, Curie temperature, temperature coefficient, voltage coefficient, and power density; S30, adjusting the operating environment of the electromagnetic voltage transformer, increasing the applied voltage in steps, recording the electrical parameters, overvoltage parameters and PTC resistance parameters of the electromagnetic voltage transformer under different voltages and the corresponding overvoltage suppression resistor as boost operation data; the overvoltage parameters include: overvoltage voltage and overvoltage duration; S40, establishing an operation equation group of the electromagnetic voltage transformer taking into account electrical parameters, overvoltage parameters and the PTC resistance parameters in step S20 and step S30, including a voltage equation, a current equation, a power equation, a temperature equation, a PTC resistance characteristic equation and an overvoltage response equation; S50, fitting the parameters of the operating equation group according to the normal operating data and the supercharging operating data to obtain a fitted operating equation group; S60, based on the fitted operating equation group, establishing an overvoltage suppression effect evaluation model, the model uses overvoltage voltage and overvoltage duration as main evaluation indicators; S70, optimizing the PTC resistor parameters by using a genetic algorithm, taking the PTC resistor parameters of the PTC resistors with multiple different parameters initially selected as the initial population, using the overvoltage suppression effect evaluation model to calculate the fitness value of each group of parameters, taking minimizing the overvoltage voltage and the overvoltage duration as the objective function, setting the population size, crossover probability, mutation probability and number of iterations; S80, executing a genetic algorithm to obtain optimal PTC resistance parameters; S90. According to the obtained optimal PTC resistor parameters, a model with the closest characteristics is selected from existing PTC resistor products as the final overvoltage suppression resistor selection result.

2. The method for selecting PTC resistors for overvoltage suppression of electromagnetic voltage transformer according to claim 1, characterized in that: The voltage equation is specifically expressed as: Where V1 is the primary voltage; V2 is the secondary voltage; N1, N2 are the turns of the primary and secondary windings; 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 coefficient; ω is the angular frequency; C s is the distributed capacitance; t is the time.

3. The method for selecting PTC resistors for overvoltage suppression of electromagnetic voltage transformer according to claim 2, characterized in that: The current equation is specifically expressed as: Where, 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.

4. The method for selecting PTC resistors for overvoltage suppression of electromagnetic voltage transformer according to claim 3, characterized in that: The power equation is specifically expressed as: P=|V1||I1|cosφ; Q=|V1||I1|sinφ; In the formula, 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 number of the primary current.

5. The method for selecting PTC resistors for overvoltage suppression of electromagnetic voltage transformer according to claim 4, characterized in that: The temperature equation is specifically expressed as: Where, T is the PTC resistor temperature; t is the time; m is the mass of PTC resistor; c is p P is the specific heat capacity of PTC resistor; loss is the total power loss; h is the thermal conductivity; A is the PTC resistor 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.

6. A PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer according to claim 5, characterized in that: The PTC resistance characteristic equation is specifically expressed as: In the formula, R PTC is the current resistance value of the PTC resistor; R0 is the resistance value at room temperature; α is the temperature coefficient; 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. A PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer according to claim 6, characterized in that: The overvoltage response equation is specifically expressed as: V ov (t)=V peak yes -t / τ sin(ωt)+V nom ; Where V ov (t) is the change of overvoltage over time; V peak is the overvoltage peak value; τ is the decay time constant; ω is the overvoltage oscillation angular frequency; V nom is the rated voltage; t ov is the duration of overvoltage; H(x) is the Heaviside step function; V th is the overvoltage threshold voltage.

8. A PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer according to claim 7, characterized in that: The calculation method of the total impedance of the primary side is: Where 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 resistor.

9. A PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer according to claim 8, characterized in that: The estimation method of the overvoltage peak value is: In the formula, k ov is the overvoltage coefficient; di / dt is the current change rate; L eq is the equivalent inductance.

10. A PTC resistor selection method for overvoltage suppression of an electromagnetic voltage transformer according to claim 9, characterized in that: The calculation method of the maximum magnetic flux density is: In the formula, A core is the core cross-sectional area.

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