Series capacitor compensation damping loop device and method

Abstract

The application relates to the technical field of power system stability control, and discloses a series capacitor compensation damping loop device and method, which comprises the following steps: acquiring line harmonic current effective values of each order in a current period and real-time environmental temperature, and calling physical temperature of a previous period; based on a first mechanism of skin effect, calculating a dynamic AC resistance value modulated by temperature at a target frequency; iteratively calculating a thermal equilibrium real-time physical temperature of the current period in combination with Newton cooling law; based on the temperature and line broadband total current effective value, calculating a thermal magnetic coupling dynamic inductance value by considering a spontaneous magnetization decay mechanism of a ferromagnetic Curie temperature; and then extracting a system accurate characteristic damping ratio; when the system accurate characteristic damping ratio deviates from a target safety damping ratio, generating a transient voltage injection instruction for driving an active current converter, and executing adaptive damping reconstruction. The application realizes deep perception and active feedforward compensation of a multi-physical field nonlinear coupling evolution process, and significantly improves the safe and stable operation level of a power grid device.

Description

Technical Field

[0001] This invention belongs to the field of power system stability control technology, and particularly relates to a series capacitor compensation damping circuit device and method. Background Technology

[0002] With the rapid development of long-distance, high-capacity AC / DC hybrid power grids, series capacitor compensation devices play a crucial role in improving the power transmission capacity and transient stability of transmission lines. To effectively suppress the subsynchronous resonance phenomenon caused by the interaction between series capacitors and line inductance and to limit transient overcurrent impacts, damping circuits composed of reactors and resistors are commonly used as the core protection measure in engineering practice. However, traditional damping circuit designs mainly rely on passive devices with fixed parameters, whose physical characteristics exhibit significant dynamic evolution under complex operating conditions. Specifically, broadband harmonic distortion currents in transmission lines can induce high-frequency skin effects, leading to uneven current distribution within the damping resistor, causing localized severe temperature rises, and resulting in nonlinear drift of resistivity with temperature changes. Simultaneously, the DC bias magnetization effect generated by the fundamental current and continuous heat accumulation superimpose each other, causing the reactor core material to gradually approach deep saturation. When the physical temperature approaches the Curie temperature of ferromagnetic materials, the spontaneous magnetization intensity irreversibly decays, causing a sharp decrease in dynamic inductance. This nonlinear interaction of multiple physics fields, formed by the deep coupling of electric, thermal, and magnetic fields, causes a severe shift in the inherent resonant frequency of the damping circuit, resulting in a significant reduction in the system's characteristic damping ratio below the safety threshold. Existing conventional damping control technologies simply treat resistance and inductance parameters as static constants. They cannot detect in real time the dynamic modulation effects of harmonic current spectrum distribution, ambient temperature changes, and thermal accumulation processes on physical parameters, nor do they possess the ability to implement precise feedforward compensation during detuning transients. This leads to the failure of resonance suppression functions, thereby posing a significant threat to the safe and stable operation of critical power grid equipment. Summary of the Invention

[0003] The purpose of this invention is to provide a series capacitor compensation damping circuit device and method to solve the above-mentioned problems.

[0004] This invention is implemented as follows: a series capacitor compensation damping circuit method includes the following steps: S1, obtaining the effective values ​​of each harmonic current of the line in the current control cycle and the real-time ambient temperature, and calling the physical temperature of the previous control cycle; S2, calculating the dynamic AC resistance value modulated by the physical temperature at the target frequency based on the first mechanism of the skin effect; S3, power coupling the dynamic AC resistance value at each harmonic frequency with the corresponding effective values ​​of each harmonic current of the line, and iteratively calculating the real-time physical temperature of the thermal balance in the current control cycle using Newton's law of cooling; S4, obtaining the effective value of the line broadband total current, and calculating the thermomagnetic coupling dynamic inductance value based on the real-time physical temperature of the thermal balance and the effective value of the line broadband total current, considering the spontaneous magnetization decay mechanism of the Curie temperature of ferromagnetic materials; S5, calculating the precise characteristic damping ratio of the system based on the dynamic AC resistance value and the thermomagnetic coupling dynamic inductance value at the subsynchronous resonance target frequency; S6, when the precise characteristic damping ratio of the system deviates from the preset target safe damping ratio, generating a transient voltage injection command to drive the active converter and performing adaptive damping reconstruction.

[0005] A further technical solution, in step S2, the step of calculating the dynamic AC resistance value modulated by physical temperature at the target frequency includes: constructing a resistivity temperature compensation term based on the ambient baseline temperature to characterize the intrinsic resistance drift of the damping element material as the physical temperature changes; extracting the geometric dimension parameters, target frequency, and permeability of the damping element to construct a high-frequency skin depth coefficient; and performing a nonlinear mapping between the high-frequency skin depth coefficient and the resistivity temperature compensation term, so that the output dynamic AC resistance value is positively correlated with the change in physical temperature and monotonically increases, and positively correlated with the change in target frequency and nonlinearly increases.

[0006] A further technical solution, in step S3, the step of iteratively calculating the real-time physical temperature of the thermal balance in the current control cycle using Newton's law of cooling includes: multiplying and summing the dynamic AC resistance value at each harmonic frequency with the square of the effective value of the corresponding harmonic current in the line to obtain the total harmonic Joule heat generation power of the damping circuit in the current control cycle; obtaining the convective heat dissipation power dissipated by the damping circuit to the environment based on the comprehensive convective heat transfer coefficient of the damping circuit, the effective heat dissipation surface area, and the temperature difference between the physical temperature of the previous control cycle and the real-time ambient temperature; using the net difference between the total harmonic Joule heat generation power and the convective heat dissipation power as the heat change rate, and combining the equivalent comprehensive heat capacity of the damping circuit with the discrete sampling time step to perform time-dimensional heat accumulation update, thereby obtaining the real-time physical temperature of the thermal balance in the current control cycle.

[0007] A further technical solution, in step S4, the step of calculating the thermomagnetic coupling dynamic inductance value considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material includes: setting the absolute saturation critical current value of the core at a reference temperature; constructing a saturation critical point decay function based on the degree to which the real-time physical temperature of thermal equilibrium approaches the Curie temperature of the reactor core material, so that the real-time effective saturation critical current value decreases nonlinearly with the increase of the real-time physical temperature of thermal equilibrium; using the ratio of the effective value of the total broadband current of the line to the real-time effective saturation critical current value as the saturation depth characteristic variable, establishing a magnetic saturation envelope function that smoothly transitions between the unsaturated core inductance value and the hollow inductance value, obtaining the thermomagnetic coupling dynamic inductance value, and the thermomagnetic coupling dynamic inductance value decays towards the hollow inductance value with the increase of the saturation depth characteristic variable.

[0008] A further technical solution, in step S5, the step of calculating the precise characteristic damping ratio of the system includes: based on the typical second-order oscillation response characteristics of the damping circuit, using the dynamic AC resistance value at the subsynchronous resonance target frequency as the positive gain parameter, the rated capacitance value of the series compensation capacitor as the positive frequency deviation parameter, and the thermomagnetic coupling dynamic inductance value as the negative frequency deviation parameter; defining the precise characteristic damping ratio of the system as a characteristic state parameter that is directly proportional to the dynamic AC resistance value and directly proportional to the square root of the ratio of the rated capacitance value and the thermomagnetic coupling dynamic inductance value.

[0009] A further technical solution, in step S6, the step of generating the transient voltage injection command to drive the active converter includes: calculating the target equivalent resistance required to maintain the transient stability of the system based on the preset target safety damping ratio, the rated capacitance value of the series compensation capacitor, and the thermomagnetic coupling dynamic inductance value; extracting the difference between the target equivalent resistance and the dynamic AC resistance value at the subsynchronous resonance target frequency as the feedforward active compensation impedance injection amount; real-time acquisition of the instantaneous AC current in the subsynchronous resonance frequency band, calculating the proportional compensation voltage generated by the instantaneous AC current flowing through the feedforward active compensation impedance injection amount; calculating the differential feedforward decoupling voltage generated by the rate of change of the instantaneous AC current flowing through the filter inductor of the grid-connected interface of the active converter; and superimposing the proportional compensation voltage and the differential feedforward decoupling voltage in phase to generate the transient voltage injection command to drive the active converter.

[0010] A series capacitor compensation damping circuit device includes: a basic parameter acquisition module for acquiring the effective values ​​of each harmonic current of the line in the current control cycle and the real-time ambient basic temperature, and calling the physical temperature of the previous control cycle; a resistance dynamic analysis module for calculating the dynamic AC resistance value modulated by the physical temperature at the target frequency based on the first mechanism of the skin effect; a thermal balance calculation module for power coupling the dynamic AC resistance value at each harmonic frequency with the corresponding effective values ​​of each harmonic current of the line, and iteratively calculating the real-time physical temperature of the thermal balance in the current control cycle using Newton's law of cooling; and a thermomagnetic... The coupling calculation module is used to obtain the effective value of the broadband total current of the line, and calculate the thermomagnetic coupling dynamic inductance value based on the real-time physical temperature of thermal balance and the effective value of the broadband total current of the line, considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material; the characteristic damping ratio extraction module is used to calculate the precise characteristic damping ratio of the system based on the dynamic AC resistance value and the thermomagnetic coupling dynamic inductance value at the subsynchronous resonance target frequency; the impedance adaptive reconstruction execution module is used to generate a transient voltage injection command to drive the active converter when the precise characteristic damping ratio of the system deviates from the preset target safe damping ratio, so as to execute adaptive damping reconstruction.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0012] 1. Based on the first-principles mechanism of the skin effect, Newton's law of cooling, and the spontaneous magnetization decay mechanism of the Curie temperature of ferromagnetic materials, this invention realizes real-time and high-precision calculation of the drift of the "electric-thermal-magnetic" multi-field coupling parameters of damping elements under complex working conditions, eliminating the problem of damping characteristic evaluation distortion caused by the traditional control technology that simply regards the resistance and inductance parameters as static constants.

[0013] 2. The solution dynamically compares the real-time calculated system's precise characteristic damping ratio with the target safe damping ratio, which can accurately deduce the amount of feedforward active compensation impedance injection. Combined with proportional compensation and differential decoupling voltage in phase superposition to generate converter control commands, it provides the system with flexible and precise active feedforward damping reconfiguration.

[0014] 3. This invention can quickly respond and actively compensate for the damping ratio dropped due to parameter detuning of the damping circuit under extreme conditions such as deep saturation of the line under high current bias and severe local temperature rise in high frequency skin effect, thus preventing the failure of the resonance suppression function and effectively ensuring the stable operation of long-distance power transmission systems. Attached Figure Description

[0015] Figure 1 A multi-physics deep coupling logic block diagram of a series capacitor compensation damping circuit method provided by the present invention;

[0016] Figure 2This invention provides a structural block diagram of a series capacitor compensation damping circuit device. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0018] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0019] The series capacitor compensation damping circuit method refers to a technical solution in power systems that uses series capacitors to compensate transmission lines and combines this with a damping circuit to suppress instability phenomena such as subsynchronous resonance. This method aims to improve the stability and transmission capacity of power systems.

[0020] like Figure 1 As shown, an embodiment of the present invention provides a series capacitor compensation damping circuit method, which includes the following steps:

[0021] S1. Obtain the effective values ​​of each harmonic current of the line and the real-time ambient base temperature for the current control cycle, and retrieve the physical temperature from the previous control cycle. The effective value of each harmonic current of the line refers to the effective value of harmonic currents of various frequencies generated by factors such as nonlinear loads in the power line, in addition to the fundamental current. These harmonic currents generate additional losses and heat when flowing in the damping elements. The physical temperature refers to the actual operating temperature of key components in the damping circuit (such as damping resistors, reactor cores, etc.). This temperature directly affects the electrical parameters of the components.

[0022] S2. Based on the first-principle mechanism of the skin effect, calculate the dynamic AC resistance value modulated by physical temperature at the target frequency. The first-principle mechanism of the skin effect refers to the phenomenon that when a high-frequency alternating current passes through a conductor, the current tends to concentrate on the surface of the conductor. This effect causes the effective resistance of the conductor to increase with increasing frequency, and its degree is affected by factors such as conductor material, geometry, and temperature. The dynamic AC resistance value refers to the AC resistance value of the damping element in the damping circuit. This value is not fixed but changes in real time with factors such as current frequency and element physical temperature.

[0023] S3. The dynamic AC resistance values ​​at each harmonic frequency are power-coupled with the corresponding effective values ​​of the harmonic currents in the line. Using Newton's law of cooling, the real-time physical temperature of the thermal equilibrium during the current control cycle is iteratively calculated. Newton's law of cooling is a fundamental law governing heat transfer between an object and its surrounding environment, describing the relationship between the object's heat dissipation rate and the temperature difference between the object and the environment. This law is commonly used to calculate the thermal equilibrium state of an object under specific conditions. The real-time physical temperature of the thermal equilibrium refers to the actual physical temperature exhibited by the damping circuit element when continuous heating and dissipation reach a dynamic equilibrium. This temperature is a key indicator for evaluating the component's operating state and parameter changes.

[0024] S4. Obtain the effective value of the broadband total current of the line. Based on the real-time physical temperature of the thermal balance and the effective value of the broadband total current of the line, calculate the thermomagnetic coupling dynamic inductance value considering the Curie temperature spontaneous magnetization decay mechanism of ferromagnetic materials. The Curie temperature spontaneous magnetization decay mechanism of ferromagnetic materials refers to the sharp decrease in the spontaneous magnetization intensity inside the ferromagnetic material when the temperature rises and approaches its Curie temperature, resulting in a significant decrease in the permeability of the material, which in turn affects the inductance value of the inductor element. The thermomagnetic coupling dynamic inductance value refers to the inductance value of the reactor element in the damping circuit. This value changes in real time due to the combined influence of factors such as the physical temperature of the element, the magnitude of the current flowing through it, and the magnetic properties of the core material.

[0025] S5. Based on the dynamic AC resistance value and the thermomagnetic coupling dynamic inductance value at the subsynchronous resonance target frequency, calculate the system's precise characteristic damping ratio. The subsynchronous resonance target frequency refers to the specific frequency point at which the power system may resonate within the subsynchronous frequency range. This frequency is an important reference for evaluating system stability. The system's precise characteristic damping ratio refers to the damping characteristic index of the power system at the subsynchronous resonance target frequency. This ratio reflects the system's ability to suppress oscillations, and its magnitude is directly related to the system's stability.

[0026] S6. When the system's precise characteristic damping ratio deviates from the preset target safe damping ratio, a transient voltage injection command is generated to drive the active converter, and adaptive damping reconfiguration is executed. The target safe damping ratio refers to the minimum damping ratio threshold preset to ensure the stable operation of the power system. When the actual system damping ratio is lower than this threshold, compensation measures need to be taken. An active converter is a power electronic device capable of actively controlling voltage or current output. In this method, the active converter is used to inject transient voltage to achieve active adjustment of damping characteristics. The transient voltage injection command refers to the command to control the active converter to inject voltage at a specific time and in a specific manner. This command is used to achieve rapid adjustment of the system's damping characteristics. Adaptive damping reconfiguration refers to a dynamic control strategy that restores the system's damping characteristics to a safe level by adjusting the damping loop parameters or injecting compensation amount in real time when the system's damping characteristics deviate from the preset safe range.

[0027] This embodiment provides a method for compensating a series capacitor damping circuit, specifically including the following steps:

[0028] In step S1, the effective values ​​of each harmonic current of the line in the current control cycle and the real-time ambient temperature are obtained, and the physical temperature of the previous control cycle is retrieved.

[0029] Specifically, obtaining the effective values ​​of each harmonic current in a power line can be achieved in several ways. For example, one approach involves installing current transformers on the power line to collect the line current signal into a data acquisition unit. Then, Fourier transform or digital filters are used to perform spectral analysis on the collected current signal to extract each harmonic component and calculate its effective value. Another approach is to use a wavelet transform-based method to perform multi-resolution decomposition of the line current signal, identify and separate harmonic components within different frequency ranges, and then calculate the effective value of each harmonic.

[0030] To obtain the real-time ambient baseline temperature, an ambient temperature sensor can be deployed near the damping loop device. This sensor periodically measures the surrounding air temperature and transmits the data to the control system. Alternatively, real-time temperature data for the area can be obtained from a weather station or regional environmental monitoring network and used as the ambient baseline temperature input.

[0031] To retrieve the physical temperature from the previous control cycle, a storage unit can be set up in the control system to store the calculated or measured physical temperature of the damping element at the end of each control cycle, and read this value from the storage unit at the beginning of the next control cycle. Alternatively, a temperature sensor can be installed on the surface of the damping element to monitor the element temperature in real time, and the instantaneous temperature value can be recorded at the end of each control cycle as the retrieval data for the next cycle. In particular, during the first control cycle of system initial operation, cold start, or control system initialization, since there is no historical iterative calculation data, the control system directly assigns the physical temperature from the previous control cycle to the currently acquired real-time ambient baseline temperature to ensure the smooth start of thermal balance iterative calculation and the tight closed loop of control logic.

[0032] In step S2, based on the first mechanism of the skin effect, the dynamic AC resistance value modulated by the physical temperature at the target frequency is calculated.

[0033] One way to calculate the dynamic AC resistance is by consulting a pre-established resistance-frequency-temperature lookup table. This lookup table is pre-calibrated based on experimental data or simplified models, and the corresponding dynamic AC resistance value is directly obtained from the table according to the current target frequency and physical temperature. Another approach is to estimate using an empirical formula. This empirical formula is based on a simplified physical model of the skin effect and temperature effect, and outputs an approximate dynamic AC resistance value by inputting the target frequency and physical temperature.

[0034] In step S3, the dynamic AC resistance value at each harmonic frequency is coupled with the corresponding effective value of the harmonic current of the line, and the real-time physical temperature of the thermal balance in the current control cycle is calculated iteratively using Newton's law of cooling.

[0035] One approach to calculating power coupling and thermal equilibrium temperature is to first calculate the heat loss generated by each harmonic current across the corresponding dynamic AC resistance, and then sum these losses to obtain the total heat generation power. Next, using a simplified thermal model that considers the component's heat capacity and the temperature difference with the environment, the thermal equilibrium temperature the component will eventually reach under the current heat generation power and ambient temperature is calculated through a stepwise approximation method. Another approach is to use a thermal network model based on the lumped parameter method. This model abstracts the damping component and its heat dissipation path into a series of thermal resistances and heat capacities. By solving the transient response of this thermal network under a given heat generation power and ambient temperature, the real-time physical temperature of the component is obtained iteratively.

[0036] In step S4, the effective value of the broadband total current of the line is obtained. Based on the real-time physical temperature of the thermal balance and the effective value of the broadband total current of the line, the dynamic inductance value of thermomagnetic coupling is calculated considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material.

[0037] One way to obtain the RMS value of the broadband total current of a line is to perform broadband sampling of the line current signal and then directly calculate its RMS value over the entire bandwidth. Another way is to take the square root of the sum of the squares of the RMS values ​​of each harmonic current to obtain the RMS value of the broadband total current of the line.

[0038] One approach to calculating the dynamic inductance of thermomagnetic coupling is to consult a pre-established inductance-current-temperature lookup table. This table is pre-calibrated based on experimental data or a simplified magnetic circuit model, and the corresponding dynamic inductance value is directly obtained from the table according to the current real-time physical temperature of thermal equilibrium and the effective value of the broadband total current of the line. Another approach is to use a simplified model based on hysteresis loop fitting. This model estimates the change in the permeability of the iron core by inputting current and temperature parameters, and then calculates the dynamic inductance value of the reactor.

[0039] In step S5, the precise characteristic damping ratio of the system is calculated based on the dynamic AC resistance value and the thermomagnetic coupling dynamic inductance value at the subsynchronous resonance target frequency.

[0040] One approach to calculating the precise characteristic damping ratio of a system is to utilize a simplified RLC series resonant circuit model. In this model, the damping circuit is equivalent to a combination of resistors, inductors, and capacitors. The system's damping ratio is then calculated using standard circuit theory formulas based on the parameters of this equivalent circuit. Another approach is to perform small-signal perturbation analysis on the system, measuring the system's response characteristics near the subsynchronous resonant target frequency, and estimating the system's damping ratio based on the decay rate of the response curve.

[0041] In step S6, when the precise characteristic damping ratio of the system deviates from the preset target safe damping ratio, a transient voltage injection command is generated to drive the active converter, and adaptive damping reconstruction is performed.

[0042] One way to determine if the damping ratio deviates is to directly compare the calculated precise characteristic damping ratio of the system with a preset target safe damping ratio. If the absolute value of the difference between the two exceeds a preset threshold, a deviation is considered to have occurred. Another way is to set a safe damping ratio range, and trigger a deviation judgment when the calculated damping ratio falls outside this range.

[0043] One way to generate transient voltage injection commands is to calculate the required compensation voltage amplitude and phase using a preset proportional-integral-derivative (PID) controller based on the degree of deviation of the damping ratio, thereby generating the transient voltage injection command. Another approach is to use a fuzzy logic control-based method, generating the corresponding voltage injection command through a fuzzy inference mechanism based on the deviation and rate of change of the damping ratio.

[0044] One way to implement adaptive damping reconfiguration is to send the generated transient voltage injection command to the control unit of the active converter. The active converter then generates a corresponding voltage output based on the command and injects it into the damping loop to change the equivalent damping characteristics of the system. Another way is to adjust the control parameters of the active converter so that its output voltage or current can compensate for insufficient system damping, thereby achieving damping reconfiguration.

[0045] The following example will provide a more detailed explanation of the above technical solution:

[0046] Suppose a long-distance transmission line is equipped with a series capacitor compensation device and a damping circuit to suppress subsynchronous resonance. During a certain control cycle, due to the presence of a nonlinear load in the line, the line current contains abundant broadband harmonic components. Simultaneously, the ambient temperature may also change.

[0047] First, in step S1, the control system acquires the effective values ​​of each harmonic current of the line in real time for the current control cycle. For example, it accurately measures and calculates the effective values ​​of the fundamental, third, and fifth harmonic currents using current sensors and data processing units installed on the line. Simultaneously, an ambient temperature sensor deployed near the damping loop device provides the real-time ambient temperature. Furthermore, the system retrieves the physical temperature of the damping element calculated or measured in the previous control cycle from its internal memory as the initial condition for the current cycle's calculation.

[0048] Next, in step S2, based on the acquired physical temperature of the previous control cycle and the set subsynchronous resonance target frequency, the system calculates the dynamic AC resistance value of the damping element modulated by the physical temperature at the target frequency using the first-principles mechanism of the skin effect. For example, when the physical temperature increases, the resistivity of the damping element increases, and at the same time, the skin effect of the high-frequency current reduces the effective conductive cross-section, thereby causing a significant increase in the dynamic AC resistance value.

[0049] Subsequently, in step S3, the system performs power coupling between the dynamic AC resistance values ​​at each harmonic frequency calculated in step S2 and the effective values ​​of the corresponding harmonic currents obtained in step S1, to calculate the heat loss of the damping element at each harmonic frequency. After accumulating these losses, and combining them with Newton's law of cooling, the system iteratively calculates the real-time physical temperature of the thermal equilibrium for the current control cycle. This iterative process considers the dynamic balance between the element's own heat generation and heat dissipation to the environment, thus obtaining a component temperature closer to the actual temperature. For example, if the heat generation power exceeds the heat dissipation capacity, the component temperature will continue to rise until a new thermal equilibrium point is reached.

[0050] Further, in step S4, the system obtains the effective value of the broadband total current of the line, which reflects the overall current level flowing through the reactor. Based on the real-time physical temperature of thermal equilibrium calculated in step S3 and the effective value of the broadband total current of the line, the system considers the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material and calculates the thermomagnetic coupling dynamic inductance value of the reactor. For example, when the broadband total current of the line is large, the reactor core may tend to saturate, leading to a decrease in inductance value; at the same time, if the component temperature is close to the Curie temperature of the core material, the spontaneous magnetization of the core will decay sharply, further aggravating the decrease in inductance value.

[0051] Then, in step S5, the system calculates the precise characteristic damping ratio of the current system based on the dynamic AC resistance value at the subsynchronous resonance target frequency calculated in step S2 and the thermomagnetic coupling dynamic inductance value calculated in step S4, combined with the rated capacitance value of the series compensation capacitor. This damping ratio is a key indicator for evaluating the subsynchronous resonance stability of the system.

[0052] Finally, in step S6, the system compares the calculated precise characteristic damping ratio of the system with the preset target safe damping ratio. If the precise characteristic damping ratio deviates from the target safe damping ratio, for example, below a safe threshold, the system immediately generates a transient voltage injection command to drive the active converter. This command instructs the active converter to inject a voltage of specific amplitude and phase to compensate for insufficient system damping, thereby performing adaptive damping reconstruction, raising the actual damping ratio of the system to a safe range, and effectively suppressing the occurrence of subsynchronous resonance.

[0053] Through the above steps, this method can sense the dynamic changes in resistance and inductance parameters in the damping circuit caused by the coupling of multiple physical fields such as "electricity-thermal-magnetism" in real time, and accurately evaluate the damping characteristics of the system based on these dynamic parameters. Then, active and adaptive compensation is performed through the active converter to ensure the stable operation of the system under complex operating conditions.

[0054] This application further proposes a step in step S2, namely, calculating the dynamic AC resistance value modulated by physical temperature at the target frequency, which includes: constructing a resistivity temperature compensation term based on the ambient baseline temperature to characterize the intrinsic resistance drift of the damping element material as the physical temperature changes; extracting the geometric dimension parameters, target frequency, and permeability of the damping element to construct a high-frequency skin depth coefficient; performing a nonlinear mapping between the high-frequency skin depth coefficient and the resistivity temperature compensation term, so that the output dynamic AC resistance value is positively correlated with the change in physical temperature and monotonically increases, and positively correlated with the change in target frequency and nonlinearly increases; the specific calculation formula for calculating the dynamic AC resistance value is as follows:

[0055]

[0056] in: This represents the dynamic AC resistance value modulated by physical temperature at the target frequency. This represents the equivalent conductive spread length of the damping element; This represents the diameter of the equivalent conductor cross-section of the damping element; Indicates the set target frequency; Indicates the permeability of free space; This represents the relative permeability of the damping element material; Represents the resistivity at the initial reference temperature; This represents the temperature coefficient of resistance of the damping element material; Indicates the physical temperature of the previous control cycle; This indicates the initial reference temperature.

[0057] Dynamic AC resistance value Indicates at a specific target frequency Below, the equivalent AC resistance of a damping element is determined by the skin effect and the change in material resistivity with temperature. This value is a key parameter for evaluating the losses and damping characteristics of a damping element under actual operating conditions. The equivalent conductive spread length of the damping element is also considered. This refers to the effective length through which current actually flows in the damping element. For example, for a coil-shaped damping element, it can refer to the total length of the coil conductor; for a sheet-like or rod-shaped element, it can refer to the geometric length of the current path. This length can be obtained directly from design drawings or through actual measurement. The equivalent conductor cross-sectional diameter of the damping element. This refers to the effective cross-sectional diameter of the conductor in the damping element. For a circular conductor, it is the actual diameter; for a non-circular conductor, an equivalent diameter can be used as an approximation. This diameter is an important parameter affecting the skin effect depth and can be determined through design specifications or geometric measurements. The target frequency is also considered. This refers to the specific frequency point where the dynamic AC resistance value needs to be calculated. In power systems, this could be the fundamental frequency, a specific harmonic frequency, or a subsynchronous resonant frequency, etc. This frequency value is set by system analysis or control requirements. Vacuum permeability It is a physical constant representing the magnetic permeability in a vacuum, and its value is approximately Relative permeability of damping element materials This represents the magnetic permeability of the conductor material of the damping element relative to vacuum. For non-magnetic materials (such as copper and aluminum), its value is close to 1; for ferromagnetic materials, its value is significantly greater than 1. This parameter can usually be obtained from the datasheet provided by the material supplier or determined through experimental testing. Resistivity at the initial reference temperature. The conductor material of the damping element at a certain standard reference temperature The resistivity at a given temperature. This is an inherent property of the material and can usually be found in the material specification sheet. Temperature coefficient of resistance of damping element materials. This indicates the sensitivity of the resistivity of the conductor material in the damping element to temperature changes. This coefficient is typically positive, indicating that resistivity increases with increasing temperature. This parameter can also be obtained from material data sheets or calibrated experimentally. The physical temperature of the previous control cycle. This refers to the actual physical temperature of the damping element inherited from or measured in the previous control cycle at the start of the current control cycle. This temperature reflects the thermal state of the damping element and is a key input for considering the temperature effect in the calculation of dynamic AC resistance. Initial reference temperature Refers to the definition of material resistivity The standard reference temperature. Usually room temperature, for example... or .

[0058] This application refines the calculation of dynamic AC resistance by introducing a specific formula based on the first mechanism of the skin effect and considering physical temperature modulation. This formula incorporates the geometric dimensions of the damping element (equivalent conductive unfolded length). Equivalent conductor cross-sectional diameter Material properties (relative magnetic permeability) resistivity at the initial reference temperature Temperature coefficient of resistance ) and operating conditions (set target frequency) Physical temperature of the previous control cycle They are organically combined. Specifically, the formula contains... This part accurately reflects the relationship between the skin effect depth and frequency, permeability, and temperature-modulated resistivity, while This effect is then mapped onto the overall geometry of the damping element. In this way, the calculation formula can accurately reflect the actual AC resistance characteristics of the damping element at different frequencies and temperatures in real time, thus providing more reliable basic data for subsequent thermal balance calculations, thermomagnetic coupling inductance calculations, and the extraction of the system's precise characteristic damping ratio. This accurate resistance calculation avoids the errors caused by simplified models in traditional methods, enabling the entire series capacitor compensation damping circuit method to more accurately sense the system state and perform adaptive damping reconstruction.

[0059] As a specific implementation method, the above-mentioned technical means can be implemented with reference to the following example. Assume the damping element is a copper wire inductor wound on a non-magnetic frame. When calculating its dynamic AC resistance value, the total length of the copper wire is first obtained from the inductor's design parameters as the equivalent conductive unfolded length. The diameter of the copper wire is obtained as the equivalent conductor cross-sectional diameter. The relative magnetic permeability of copper materials The value can be set to 1, the initial reference temperature. resistivity at the following and temperature coefficient of resistance This information can be found in standard datasheets for copper materials. Vacuum permeability. This is a known constant. In each control cycle, the control system acquires the physical temperature from the previous control cycle. and the target frequency that needs to be analyzed Subsequently, an embedded processor or digital signal processor (DSP) substitutes these parameters into the above formula. In real time, the system calculates the dynamic AC resistance value modulated by physical temperature at the current target frequency. For example, when the target frequency is the subsynchronous resonant frequency, the system can obtain the accurate dynamic AC resistance value at that frequency.

[0060] Through the above technical solution, this application can accurately quantify the influence of the skin effect and physical temperature on the AC resistance value of the damping element. The specific calculation formula comprehensively considers the geometric dimensions, material properties, and actual operating frequency and temperature conditions of the damping element, thus overcoming the problem of inaccurate estimation of dynamic AC resistance values ​​in traditional methods. This high-precision calculation of dynamic AC resistance values ​​provides a more solid and reliable data foundation for subsequent iterative calculations of real-time physical temperature for thermal equilibrium, calculations of thermomagnetic coupling dynamic inductance values, and extraction of the system's precise characteristic damping ratio. Therefore, the entire series capacitor compensation damping circuit method can more accurately reflect the actual operating state of the system, thereby making the generation of adaptive damping reconstruction commands more precise and effectively improving the damping circuit's ability to suppress subsynchronous resonance and the system's operational stability.

[0061] This application further proposes a step in S3, which involves iteratively calculating the real-time physical temperature of the current control cycle using Newton's law of cooling. This step includes: multiplying the dynamic AC resistance value at each harmonic frequency with the square of the effective value of the corresponding harmonic current in the line, and summing the products to obtain the total harmonic Joule heat generation power of the damping circuit in the current control cycle; obtaining the convective heat dissipation power dissipated by the damping circuit to the environment based on the comprehensive convective heat transfer coefficient of the damping circuit, the effective heat dissipation surface area, and the temperature difference between the physical temperature of the previous control cycle and the real-time ambient temperature; using the net difference between the total harmonic Joule heat generation power and the convective heat dissipation power as the heat change rate, and combining the equivalent comprehensive heat capacity of the damping circuit with the discrete sampling time step to perform time-dimensional heat accumulation updates, thereby obtaining the real-time physical temperature of the current control cycle; the specific calculation formula for the real-time physical temperature of the current control cycle is as follows:

[0062]

[0063] in: This indicates the real-time physical temperature of the thermal balance during the current control cycle. Indicates the physical temperature of the previous control cycle; Indicates the discrete sampling time step of the control system; This represents the equivalent total heat capacity of the damping circuit; Indicates the harmonic order; Indicates the highest harmonic order in the analysis; This represents the effective value of the h-th harmonic current in the line. This represents the dynamic AC resistance value at the h-th harmonic frequency; Indicates the fundamental frequency of the power system; Indicates the overall convective heat transfer coefficient; Indicates the effective heat dissipation surface area; This indicates the real-time ambient temperature.

[0064] Real-time physical temperature of thermal equilibrium during the current control cycle This indicates the steady-state or transient physical temperature reached by the damping loop at the end of the current control cycle. This temperature is a key parameter for evaluating the thermal state of the damping loop and directly affects its electrical characteristics, such as resistivity and permeability. The physical temperature of the previous control cycle... This represents the physical temperature of the damping loop at the end of the immediately preceding control cycle. This parameter serves as the starting point for iterative calculations, reflecting the thermal state of the damping loop before the start of the current cycle. The discrete sampling time step of the control system. This refers to the time interval required for a control system to complete one full data acquisition, calculation, and control output. This time step can be a fixed value, such as determined by the system clock or sampling frequency; or it can be a variable value, dynamically adjusted according to the system's operating status or calculated load. The equivalent combined heat capacity of the damping circuit. This indicates the overall heat capacity of the damping circuit. This heat capacity value can be obtained by weighted summing of the specific heat capacity and mass of each component material in the damping circuit (such as conductors, insulating materials, magnetic cores, etc.); or by experimental testing, such as conducting heating and cooling experiments on the damping circuit and measuring its temperature response curve. This represents the total heat power generated within the damping circuit due to current flowing through the resistor. This heat power is the effective value of each harmonic current. Dynamic AC resistance value at the corresponding harmonic frequency The sum of the Joule heat generated. This term reflects the intensity of the heat generated by the damping circuit during operation. This represents the heat power dissipated by the damping circuit to the surrounding environment through convection heat transfer. Among them, To obtain the comprehensive convective heat transfer coefficient, its value can be obtained through empirical formulas or numerical simulations based on factors such as the surface shape of the damping loop, the flow state of the surrounding fluid (e.g., air) (natural or forced convection), and surface roughness. For example, in a specific natural convection cooling scenario, the comprehensive convective heat transfer coefficient can be directly estimated using classical empirical formulas for convective heat transfer. The specific calculation model is as follows: , These are calibration constants related to air properties and component surface shape. The temperature difference between the surface of the damping element and the environment, This is the effective heat dissipation characteristic length of the component. Using this fallback empirical formula, those skilled in the art can directly obtain this parameter without performing complex flow field numerical simulations. Effective heat dissipation surface area refers to the actual surface area of ​​the damping circuit that exchanges heat with the environment; The temperature difference between the damping circuit and the environment drives heat transfer. This reflects the damping circuit's ability to dissipate heat to the environment. Newton's law of cooling is a physical law describing the rate of heat transfer between an object and its surroundings; its core idea is that the rate of heat transfer between an object and its environment is proportional to the temperature difference between them. In this application, this law is used to quantify the damping circuit's ability to dissipate heat to the real-time ambient base temperature. The rate of heat dissipation.

[0065] The proposed solution introduces an accurate thermal balance model based on Newton's law of cooling to iteratively calculate the real-time physical temperature of the damping circuit. Specifically, within each control cycle, the physical temperature of the previous control cycle is first obtained. and the real-time ambient base temperature of the current control cycle And combined with the effective values ​​of each harmonic current of the line and the dynamic AC resistance values ​​at each harmonic frequency calculated in step S2. Subsequently, by power coupling the dynamic AC resistance values ​​at each harmonic frequency with the corresponding effective values ​​of the line harmonic currents, the total heat power generated inside the damping circuit due to the Joule heating effect was accurately calculated, i.e. Meanwhile, according to Newton's law of cooling, combined with the comprehensive convective heat transfer coefficient... Effective heat dissipation surface area And the temperature difference between the damping circuit and the environment. The heat power dissipated by the damping loop to the environment is calculated. The difference between these two heat power terms, i.e., the net rate of change of heat, is multiplied by the discrete sampling time step of the control system. Divide by the equivalent combined heat capacity of the damping circuit. This gives the temperature change within the current control cycle. This temperature change is then added to the physical temperature of the previous control cycle. The above allows for iterative calculation of the real-time physical temperature of the thermal equilibrium during the current control cycle. This method accurately models the internal heating and external heat dissipation processes of the damping circuit, making temperature prediction no longer a simple empirical estimate, but a dynamic calculation based on physical mechanisms. This provides a more accurate temperature input for subsequent calculation of the dynamic inductance value of thermomagnetic coupling and extraction of the system's precise characteristic damping ratio, significantly improving the accuracy and reliability of the entire adaptive damping reconstruction method.

[0066] As a specific implementation method, the above-mentioned technical means can be implemented with reference to the following example. In the power system control center, a high-performance digital signal processor (DSP) or embedded controller can be configured to perform this iterative calculation. At the beginning of each control cycle, the processor receives the effective values ​​of the line harmonic currents for each harmonic of the current control cycle from the sensor interface. and real-time ambient base temperature It also reads the physical temperature from the internal memory of the previous control cycle. Meanwhile, the dynamic AC resistance values ​​at each harmonic frequency calculated in step S2 are... It will also be provided to the processor. The processor then calculates the equivalent combined heat capacity of the damping circuit based on the pre-stored data. Comprehensive convective heat transfer coefficient and effective heat dissipation surface area These parameters are used for real-time calculations using the formulas described above. For example, the processor iterates through all harmonic orders h (from 1 to N), calculates the heat power generated by each harmonic component, and sums them to obtain the total internal heat source. Next, the heat dissipation term is calculated. Finally, these values ​​are substituted into the formulas to calculate the real-time physical temperature of the thermal equilibrium for the current control cycle. Calculation results It will be stored for the next control cycle. This information is simultaneously transmitted to the thermomagnetic coupling calculation module for subsequent dynamic inductance value calculation.

[0067] Through the above technical solution, this application can accurately iteratively calculate the real-time physical temperature of the damping circuit. By power coupling the effective values ​​of each harmonic current of the line with the corresponding dynamic AC resistance values, and combining Newton's law of cooling, this method can comprehensively consider the Joule heat loss inside the damping circuit and the convective heat dissipation effect of the external environment. This dynamic thermal balance model based on physical mechanisms overcomes the problems of inaccurate or lagging temperature estimation in traditional methods, making the perception of the thermal state of the damping circuit more real-time and accurate. Therefore, in the subsequent calculation of the thermomagnetic coupling dynamic inductance value, an inductance value closer to the actual operating condition can be obtained, thereby making the calculation of the system's precise characteristic damping ratio more accurate. This high-precision temperature information is the basis for realizing effective adaptive damping reconstruction, thus ensuring that the series capacitor compensation damping circuit can maintain stable damping characteristics under various operating conditions and effectively suppress subsynchronous resonance.

[0068] This application further proposes a step in step S4, which involves calculating the thermomagnetic coupling dynamic inductance value considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material. This step includes: setting the absolute saturation critical current value of the core at a reference temperature; constructing a saturation critical point decay function based on the degree to which the real-time physical temperature of thermal equilibrium approaches the Curie temperature of the reactor core material, such that the real-time effective saturation critical current value decreases non-linearly with the increase of the real-time physical temperature of thermal equilibrium; using the ratio of the effective value of the total broadband current of the line to the real-time effective saturation critical current value as a saturation depth characteristic variable, establishing a magnetic saturation envelope function that smoothly transitions between the unsaturated core inductance value and the hollow inductance value, and obtaining the thermomagnetic coupling dynamic inductance value, wherein the thermomagnetic coupling dynamic inductance value decays towards the hollow inductance value with the increase of the saturation depth characteristic variable; the specific calculation formula for the thermomagnetic coupling dynamic inductance value is as follows:

[0069]

[0070] in: This represents the dynamic inductance value of the thermomagnetic coupling; This represents the hollow inductance value of the reactor after it has reached full deep saturation; This represents the core inductance value at the reference temperature when it is unsaturated. This indicates the effective value of the total broadband current of the line; This represents the absolute saturation critical current value of the iron core at the reference temperature; This indicates the real-time physical temperature of the thermal balance during the current control cycle. This indicates the Curie temperature of the reactor core material.

[0071] Thermomagnetic coupling dynamic inductance value This refers to the equivalent inductance value of a reactor under actual operating conditions, after considering current saturation and temperature effects (especially the Curie temperature spontaneous magnetization decay mechanism). This value is dynamically changing and more accurately reflects the magnetic characteristics of the reactor under different operating conditions. The hollow inductance value of the reactor after full deep saturation is also included. Inductance refers to the inductance value exhibited by the reactor when the core material is fully saturated and its permeability approximates that of free space. This value is primarily determined by the coil geometry and can usually be obtained through reactor design parameters or by measurement under extreme saturation conditions. The reference temperature represents the unsaturated core inductance value. This refers to the inductance value of the reactor core at a predetermined reference temperature, before magnetic saturation occurs. This value reflects the initial magnetic characteristics of the core material at its normal operating point and can be obtained through experimental testing or by consulting a material handbook. (The last sentence appears to be unrelated and refers to the effective value of the total broadband current in the circuit.) This refers to the effective value of the total current flowing through the circuit, including fundamental and harmonic components. This value is an important indicator of the magnitude of the circuit current and can be obtained by real-time acquisition and effective value calculation using a current sensor, or by processing it using a digital signal processor. The absolute saturation critical current value of the iron core at the reference temperature. This refers to the effective current value at which the reactor core begins to enter deep saturation at a predetermined reference temperature. This value is a key parameter characterizing the magnetic saturation properties of the core material and is typically provided by the reactor manufacturer or determined experimentally. The real-time physical temperature of the thermal equilibrium during the current control cycle is also relevant. This refers to the actual physical temperature of the damping circuit obtained through thermal balance calculations within the current control cycle. This temperature reflects the temperature state of the damping circuit when it reaches a dynamic equilibrium between heat generation due to losses and heat dissipation from the environment during operation. Its accuracy is crucial for evaluating the thermal properties of materials. Curie temperature of reactor core material. The Curie temperature is the critical temperature at which a ferromagnetic material loses its ferromagnetism and transforms into paramagnetism. When the core temperature approaches or exceeds the Curie temperature, its permeability drops sharply, leading to a significant decrease in inductance. This temperature is an inherent property of the material and can be obtained by consulting a material handbook.

[0072] This application's solution introduces a nonlinear model that comprehensively considers current saturation and thermal effects to accurately calculate the dynamic inductance value of thermomagnetic coupling. This model uses the hollow inductance value after the reactor has reached full deep saturation. and the core inductance value at the reference temperature when unsaturated Based on this, the transition relationship of inductance value between unsaturated and saturated states was constructed. Specifically, the effective value of the broadband total line current in the denominator term... The absolute saturation critical current value of the iron core at the reference temperature The ratio quantifies the influence of current on the magnetic saturation of the iron core. Furthermore, this model innovatively incorporates the real-time physical temperature of the thermal equilibrium during the current control cycle. Curie temperature of reactor core material ,pass This section takes into account the spontaneous magnetization decay mechanism at the Curie temperature of ferromagnetic materials. near When this term approaches zero, it effectively increases the saturation current term in the denominator, thus leading to an increase in the inductance value. Towards The (hollow inductance value) is close to and accurately reflects the decrease in the permeability of the iron core at high temperatures. In this way, the calculation formula can dynamically and non-linearly adjust the inductance value, reflecting not only current saturation but also the attenuation effect of temperature on magnetic properties, thus providing a more accurate dynamic inductance value for thermomagnetic coupling under various operating conditions. This precise inductance value is the basis for subsequent calculations of the system's accurate characteristic damping ratio, thereby providing a reliable input for adaptive damping reconstruction and ensuring the effectiveness and stability of the compensation strategy.

[0073] As a specific implementation method, the above-mentioned technical means can be implemented with reference to the following example. In practical applications, a reactor with a ferrite or amorphous alloy core can be selected as the damping element. First, the hollow inductance value is determined through the technical parameters provided by the reactor manufacturer or laboratory tests. (For example, measured at extremely high currents), and the core inductance value when unsaturated at a reference temperature of 25°C. and absolute saturation critical current value At the same time, the datasheet for the core material was consulted to obtain its Curie temperature. During system operation, the effective value of the broadband total current of the line is obtained in real time through current transformers and data acquisition units. Real-time physical temperature of thermal equilibrium during the current control cycle. The output is then from the thermal balance calculation module of the previous step (S3). All these parameters are input into a digital signal processor (DSP) or microcontroller, which has the above calculation formula built in. The DSP calculates the parameters based on the real-time acquired data. and and preset , , , The dynamic inductance value of thermomagnetic coupling under the current operating conditions is calculated in real time. For example, when the line current increases, causing the core to approach saturation, or when the damping circuit temperature rises to near the Curie temperature, the calculated... This will be reduced accordingly, thus providing accurate dynamic inductance parameters for subsequent damping ratio calculations.

[0074] Through the above technical solution, this application provides a method for accurately quantifying the dynamic inductance value of a reactor's thermomagnetic coupling. This method not only considers the influence of current saturation on the inductance value but also innovatively incorporates the Curie temperature spontaneous magnetization decay mechanism of the core material, enabling the inductance value calculation to dynamically adapt to changes in the core's magnetic properties under different current and temperature conditions. This significantly improves the accuracy of the inductance value calculation and avoids the large errors that may occur in traditional models under extreme operating conditions. Therefore, the precise characteristic damping ratio of the system calculated based on this accurate inductance value will more realistically reflect the system's damping state, thus providing a more reliable and accurate input for subsequent adaptive damping reconstruction. This effectively improves the control accuracy and system stability of the series capacitor compensation damping circuit, especially under complex operating environments such as high current and high temperature, and can more effectively suppress subsynchronous resonance.

[0075] This application further proposes a step in step S5, which involves calculating the precise characteristic damping ratio of the system, including: based on the typical second-order oscillation response characteristics of the damping circuit, using the dynamic AC resistance at the subsynchronous resonance target frequency as a positive gain parameter, the rated capacitance of the series compensation capacitor as a positive frequency deviation parameter, and the thermomagnetically coupled dynamic inductance as a negative frequency deviation parameter; defining the precise characteristic damping ratio of the system as a characteristic state parameter that is directly proportional to the dynamic AC resistance value and directly proportional to the square root of the ratio of the rated capacitance value to the thermomagnetically coupled dynamic inductance value; the specific calculation formula for the precise characteristic damping ratio of the system is as follows:

[0076]

[0077] The specific formula for calculating the precise characteristic damping ratio of this computational system is used to quantify the damping characteristics of the series capacitor compensation damping circuit at the subsynchronous resonant target frequency. Its function is to provide a precise mathematical model reflecting the relationship between the system's energy dissipation and energy storage capabilities at a specific frequency, thus providing an accurate basis for subsequent damping reconstruction. This formula can be calculated in real-time by a digital signal processor (DSP) or microcontroller (MCU) in the control system, or it can be hardware-accelerated using a field-programmable gate array (FPGA). The damping ratio represents the precise characteristic damping ratio of the system at the subsynchronous resonance target frequency. This parameter indicates the degree of damping of the system at this frequency. It is conceptually defined as the ratio of energy dissipation to energy storage during oscillation and is a key indicator of system stability. This damping ratio can be a dimensionless value and is typically used to assess the system's ability to suppress subsynchronous resonance. This parameter represents the dynamic AC resistance value at the subsynchronous resonance target frequency. It indicates the equivalent dynamic AC resistance of the damping circuit at this frequency. Its function is to reflect the system's ability to dissipate resonant current at a specific frequency. This value can be obtained using the method described in step S2 above, which calculates the dynamic AC resistance value based on the skin effect first-order mechanism and considers the physical temperature modulation effect. This parameter indicates the rated capacitance of the series compensation capacitor. It represents the nominal capacitance value of the series compensation capacitor. Its function is to provide capacitive energy storage characteristics in the system and is one of the important parameters determining the system's resonant frequency and damping characteristics. This value is usually a fixed parameter determined during system design and can be obtained from the capacitor's nameplate or technical specifications. This parameter represents the dynamic inductance value of thermomagnetic coupling, which takes into account thermal and magnetic saturation effects. Its function is to reflect the inductive energy storage characteristics of the system and to account for the influence of temperature and current on the inductance value during actual operation. This value can be obtained using the method described in step S4 above for calculating the dynamic inductance value of thermomagnetic coupling, based on the real-time physical temperature of thermal equilibrium and the effective value of the broadband total current of the line, while considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material.

[0078] This application's solution quantifies the precise characteristic damping ratio of a series capacitor-compensated damping circuit at the subsynchronous resonant target frequency by introducing a specific mathematical formula. This calculation process closely relies on the dynamic parameters obtained and calculated in previous steps S1 to S4. Specifically, in step S5, the precise characteristic damping ratio of the system... The calculation first requires obtaining the dynamic AC resistance value at the subsynchronous resonant target frequency. This resistance value is not fixed, but is precisely calculated in step S2 based on the skin effect and physical temperature modulation effect, reflecting the actual loss characteristics of the damping element at the actual operating temperature and frequency. Simultaneously, the calculation also requires obtaining the thermomagnetic coupling dynamic inductance value. The inductance value, determined through step S4, comprehensively considers the real-time physical temperature of thermal equilibrium and the effective value of the total broadband current of the line, and incorporates the spontaneous magnetization decay mechanism of the Curie temperature of ferromagnetic materials, thus accurately reflecting the magnetic saturation characteristics and temperature effects of the reactor under different operating conditions. Furthermore, the rated capacitance value of the series compensation capacitor... As inherent energy storage parameters of the system, they also directly participate in the calculation of the damping ratio. This is achieved by substituting these dynamically changing resistance and inductance values, which are affected by actual operating conditions, along with the fixed capacitance value, into a specific formula. In this system, the damping level at the subsynchronous resonant target frequency can be evaluated in real time and with high accuracy. This precise calculation based on dynamic parameters overcomes the errors caused by using fixed parameters or simplified models in traditional methods, making the evaluation of the system's damping characteristics closer to actual operating conditions. This provides a solid data foundation for subsequent adaptive damping reconstruction, thereby effectively improving the accuracy and effectiveness of the entire compensation method.

[0079] As a specific implementation, the step of calculating the precise characteristic damping ratio of the above-described system can be implemented in an embedded controller. This controller can employ a high-performance digital signal processor (DSP), such as the TMS320 series DSP chip from TI, or a microcontroller (MCU) with floating-point arithmetic capabilities, such as the STM32H7 series from STMicroelectronics. The calculation formula can be predefined in the controller's firmware. This is achieved when the dynamic AC resistance value at the subsynchronous resonant target frequency is obtained from the preceding step S2. The dynamic inductance value of the thermomagnetic coupling is obtained from the preceding step S4. And the rated capacitance value of the series compensation capacitor is known. Then, the DSP or MCU will call the corresponding mathematical library functions to perform floating-point multiplication, division, and square root operations, substituting these parameters into the formula. This allows for the real-time calculation of the system's precise characteristic damping ratio at the subsynchronous resonant target frequency. The calculation results can be stored in the controller's memory and passed as input parameters to the subsequent impedance adaptive reconfiguration execution module.

[0080] Through the above technical solution, this application can accurately calculate the characteristic damping ratio of the system at the subsynchronous resonance target frequency based on dynamically changing resistance and inductance parameters. This precise quantification avoids the errors caused by parameter simplification or fixation in traditional methods, making the evaluation of the system's damping characteristics more realistic and reliable. Since the calculation of the damping ratio considers multiple complex physical mechanisms such as the skin effect, physical temperature modulation, thermal balance, thermomagnetic coupling, and Curie temperature spontaneous magnetization decay, it can more accurately reflect the actual damping level of the power system under different operating conditions. This precise damping ratio information provides high-quality input for subsequent adaptive damping reconstruction, thereby generating more accurate transient voltage injection commands, effectively suppressing subsynchronous resonance, and significantly improving the control accuracy of the series capacitor compensation damping circuit and the stability of system operation.

[0081] This application further proposes a step S6, namely, generating a transient voltage injection command to drive the active converter, comprising: calculating the target equivalent resistance required to maintain the transient stability of the system based on a preset target safety damping ratio, the rated capacitance value of the series compensation capacitor, and the thermomagnetic coupling dynamic inductance value; extracting the difference between the target equivalent resistance and the dynamic AC resistance value at the subsynchronous resonance target frequency as the feedforward active compensation impedance injection amount; real-time acquisition of the instantaneous AC current in the subsynchronous resonance frequency band, calculating the proportional compensation voltage generated by the instantaneous AC current flowing through the feedforward active compensation impedance injection amount; calculating the differential feedforward decoupling voltage generated by the rate of change of the instantaneous AC current flowing through the filter inductor of the grid-connected interface of the active converter; superimposing the proportional compensation voltage and the differential feedforward decoupling voltage in phase to generate a transient voltage injection command to drive the active converter; the specific calculation formula for generating the transient voltage injection command to drive the active converter includes:

[0082] First, calculate the feedforward active compensation impedance injection amount:

[0083] Then, generate the transient voltage injection command:

[0084] in: Indicates the amount of impedance injection for feedforward active compensation; This indicates the preset target safety damping ratio; This represents the dynamic inductance value of the thermomagnetic coupling; This indicates the rated capacitance value of the series compensation capacitor; This represents the dynamic AC resistance value at the subsynchronous resonance target frequency; This indicates a transient voltage injection command to drive the active converter; This represents the instantaneous alternating current in the subsynchronous resonant frequency band. This represents the solid-state inductance value of the filter inductor at the grid-connected interface of the active converter; It represents the calculus-integral rate of change of the instantaneous alternating current at subsynchronous resonance.

[0085] Calculate the amount of feedforward active compensation impedance injection The purpose is to determine the equivalent resistance value that needs to be injected into the system to adjust the system's damping ratio to a preset safety level. Its function is to quantify the difference between the current system damping and the target damping and convert it into an operable impedance. This calculation can be performed by a high-performance computing unit such as a digital signal processor (DSP) or a field-programmable gate array (FPGA), using real-time acquired system parameters. The preset target safety damping ratio is... This represents the minimum damping level that the system should maintain at the subsynchronous resonant frequency to ensure stable system operation. This value is typically preset based on power system operating experience, simulation analysis, or safety standards. It can be stored in the controller's non-volatile memory and loaded during system startup, or dynamically adjusted under specific operating modes. (Thermomagnetic coupling dynamic inductance value) This reflects the dynamic inductance characteristics of the inductor in the damping circuit under actual operating conditions (including temperature and current saturation effects). Its function is to provide real-time, accurate values ​​of the system inductance parameters, serving as a key input for calculating the system damping ratio and compensation impedance. This value can be calculated in step S4 above and transmitted to subsequent calculation modules in real time. The rated capacitance value of the series compensation capacitor... The fixed capacitance value of the series compensation capacitor is a fundamental parameter in a series compensation system. Its role, along with the inductance value, is to determine the system's resonant frequency and impedance characteristics. This value is typically determined during system design and stored as a constant in the control system. The dynamic AC resistance value at the subsynchronous resonant target frequency... This represents the actual AC resistance value of the damping circuit at the subsynchronous resonant target frequency, a value modulated by physical temperature. Its function is to provide real-time, accurate values ​​of the system resistance parameters, serving as a crucial input for calculating the system damping ratio and compensation impedance. This value can be calculated using the aforementioned step S2 and transmitted in real-time to subsequent calculation modules.

[0086] Generate transient voltage injection command The aim is to generate a specific voltage waveform command based on the calculated compensation impedance injection amount, used to drive the active converter to inject compensation voltage into the grid. Its function is to transform the theoretically calculated impedance compensation into an actual physical control quantity. This command can be generated by the pulse width modulation (PWM) module in the controller, converting the calculation results into a specific switching signal, or generated through a lookup table and interpolation algorithm. The instantaneous AC current in the subsynchronous resonant frequency band... This represents the real-time current signal within the subsynchronous resonant frequency range. Its function is to serve as a reference for transient voltage injection commands, ensuring that the injected voltage is synchronized with the resonant current in the system, thereby achieving effective damping enhancement. This current can be measured in real-time by a line current sensor, and the subsynchronous resonant frequency component can be extracted using a bandpass filter. The solid-state inductance value of the filter inductor at the grid-connected interface of the active converter. This represents the fixed inductance value of the filter inductor at the connection point between the active converter and the power grid. Its function is to ensure the accuracy and stability of the injected voltage by considering the output characteristics and filtering requirements of the active converter when generating transient voltage injection commands. This value is usually determined during the design of the active converter and stored as a constant in the control system. The integral rate of change of the instantaneous AC current at subsynchronous resonance. This represents the rate of change of the instantaneous AC current in the subsynchronous resonant frequency band over time. Its function is to introduce a current rate of change term when generating transient voltage injection commands, thereby achieving more precise voltage control, especially providing faster response and more stable damping effects when the current changes rapidly. This rate of change can be obtained by digitally differentiating the real-time measured instantaneous AC current in the subsynchronous resonant band.

[0087] In this application, when the system's precise characteristic damping ratio deviates from the preset target safe damping ratio, in order to achieve adaptive damping reconfiguration, it is first necessary to accurately quantify the required compensation amount. This is achieved by calculating the feedforward active compensation impedance injection amount. This application can determine the target safety damping ratio based on a preset target. Real-time thermomagnetic coupling dynamic inductance value The rated capacitance value of the series compensation capacitor and the dynamic AC resistance value at the subsynchronous resonant target frequency. The equivalent impedance to be injected is determined. This calculation step transforms the difference between the current system state and the target state into a specific impedance value, providing a clear basis for subsequent voltage injection. Subsequently, based on the calculated feedforward active compensation impedance injection amount... Combined with the instantaneous AC current of the subsynchronous resonant frequency band acquired in real time Solid-state inductance value of the filter inductor at the grid-connected interface of the active converter and the differential integral rate of change of the instantaneous alternating current at subsynchronous resonance Generate transient voltage injection commands to drive the active converter. The generation of this instruction not only considers the required impedance compensation but also achieves precise control of the system's dynamic response by introducing a current rate-of-change term. In this way, the active converter can inject precise compensation voltage into the grid according to the instruction, thereby effectively changing the system's equivalent damping characteristics. This scheme achieves precise suppression of subsynchronous resonance by decomposing the complex damping reconstruction problem into the calculation of impedance injection and the generation of transient voltage instructions. The aforementioned steps S1 to S5 provide precise perception of the system's operating state and accurate evaluation of dynamic parameters, providing reliable input for the calculation of compensation impedance in this step. For example, precise thermomagnetic coupling dynamic inductance values. and dynamic AC resistance value Ensured the amount of compensation impedance injection This ensures high accuracy and avoids the undercompensation or overcompensation problems caused by parameter uncertainties in traditional methods. This close logical connection enables the entire method to respond adaptively to changes in system damping in real time. Therefore, when the system damping deviates from the safe range, it can quickly and effectively perform adaptive damping reconstruction, significantly improving the stability and reliability of the series capacitor compensation damping circuit.

[0088] As a specific implementation, the steps for generating the transient voltage injection command to drive the active converter can be implemented as follows: First, in the control system, a high-performance digital signal processor (DSP) can be responsible for executing the feedforward active compensation impedance injection. The DSP receives a preset target safety damping ratio from the front-end module in real time. Thermomagnetic coupling dynamic inductance value The rated capacitance value of the series compensation capacitor and the dynamic AC resistance value at the subsynchronous resonant target frequency. .For example, It can be a preset constant, such as 0.2; and This is then calculated and updated in real time by the aforementioned physical model. The DSP uses these parameters, according to the formula... The required impedance injection amount is calculated. Then, the DSP or another dedicated control unit, such as a high-speed microcontroller, is responsible for generating transient voltage injection commands. The control unit will collect the instantaneous AC current of the subsynchronous resonant frequency band in the line in real time. This can be achieved by connecting a bandpass filter to the output of the current transformer, which only allows current signals within the subsynchronous resonant frequency range to pass through. Simultaneously, the control unit will also... Perform digital differentiation to obtain its integral rate of change. Solid-state inductance value of the filter inductor at the grid-connected interface of an active converter. As a known constant, such as 1mH, it is stored in the controller's memory. Ultimately, the control unit will calculate... Real-time measurement Calculated And fixed Substitute into the formula This generates a specific voltage command. This voltage command is then sent to the pulse width modulation (PWM) module of the active converter, which drives its power semiconductor devices to perform switching operations, thereby injecting the required compensation voltage into the grid.

[0089] Through the above technical solution, this application can transform the theoretical damping compensation requirement into a voltage injection command executable by the active converter, achieving rapid, accurate, and adaptive suppression of subsynchronous resonance. This precise calculation based on real-time dynamic parameters avoids the compensation errors caused by traditional fixed or empirical parameters, ensuring that the system damping can be effectively adjusted to a safe level under various operating conditions. This significantly improves the stability and operational reliability of the series capacitor compensation damping circuit, effectively preventing system oscillations and equipment damage caused by subsynchronous resonance.

[0090] In other implementations, such as Figure 2 As shown, this application proposes a series capacitor compensation damping circuit device, comprising: a basic parameter acquisition module, used to acquire the effective values ​​of each harmonic current of the line in the current control cycle and the real-time ambient basic temperature, and to call the physical temperature of the previous control cycle; a resistance dynamic analysis module, used to calculate the dynamic AC resistance value modulated by the physical temperature at the target frequency based on the first mechanism of the skin effect; and a heat balance calculation module, used to power couple the dynamic AC resistance value at each harmonic frequency with the corresponding effective values ​​of each harmonic current of the line, and iteratively calculate the real-time physical temperature of the heat balance in the current control cycle using Newton's law of cooling. The system comprises: a thermomagnetic coupling calculation module, used to obtain the effective value of the broadband total current of the line, and calculate the dynamic inductance value of thermomagnetic coupling based on the real-time physical temperature of thermal balance and the effective value of the broadband total current of the line, considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material; a characteristic damping ratio extraction module, used to calculate the precise characteristic damping ratio of the system based on the dynamic AC resistance value and the dynamic inductance value of thermomagnetic coupling at the subsynchronous resonance target frequency; and an impedance adaptive reconstruction execution module, used to generate a transient voltage injection command to drive the active converter when the precise characteristic damping ratio of the system deviates from the preset target safe damping ratio, so as to execute adaptive damping reconstruction.

[0091] This application, through the aforementioned technical solution, achieves a deep sensing capability for the nonlinear coupling evolution process of multiple physical fields (electro-thermal-magnetic) in a damping circuit. Traditional damping control techniques treat physical parameters as static constants, failing to adapt to the dynamic parameter drift caused by the superposition of high-frequency skin effect and fundamental large-current bias magnetization effect resulting from broadband harmonic distortion currents in actual operating conditions. This leads to a severe shift in the inherent resonant frequency of the damping circuit, causing the system's characteristic damping ratio to fall below the safety boundary. This application addresses this by using a basic parameter acquisition module to collect multi-dimensional operating data in real time, a resistance dynamic analysis module to accurately calculate the dynamic AC resistance value based on the first-order mechanism of the skin effect, a thermal balance calculation module to iteratively solve for the real-time physical temperature of the thermal balance through power coupling and Newton's law of cooling, a thermomagnetic coupling calculation module to calculate the dynamic inductance value of the thermomagnetic coupling by comprehensively considering the Curie temperature spontaneous magnetization decay mechanism, and a characteristic damping ratio extraction module to obtain the accurate characteristic damping ratio of the system. When the damping ratio deviates from the safety threshold, the impedance adaptive reconstruction execution module immediately generates a transient voltage injection command, driving the active converter to perform adaptive damping reconstruction. This closed-loop control mechanism effectively overcomes the shortcomings of traditional technologies in lacking dynamic perception and active compensation capabilities. It can provide flexible and precise active feedforward compensation in system detuning transients, thereby avoiding resonance suppression failure and significantly improving the safe and stable operation level of power grid equipment.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for compensating damping circuits with series capacitors, characterized in that, Includes the following steps: S1. Obtain the effective value of each harmonic current of the line in the current control cycle and the real-time ambient temperature, and call the physical temperature of the previous control cycle. S2. Based on the first mechanism of the skin effect, calculate the dynamic AC resistance value modulated by physical temperature at the target frequency; S3. Power couple the dynamic AC resistance value at each harmonic frequency with the corresponding effective value of the line harmonic current, and iteratively calculate the real-time physical temperature of the thermal balance in the current control cycle using Newton's cooling law. S4. Obtain the effective value of the broadband total current of the line. Based on the real-time physical temperature of the thermal balance and the effective value of the broadband total current of the line, calculate the dynamic inductance value of thermomagnetic coupling considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material. S5. Calculate the precise characteristic damping ratio of the system based on the dynamic AC resistance value and the thermomagnetic coupling dynamic inductance value at the subsynchronous resonance target frequency. S6. When the precise characteristic damping ratio of the system deviates from the preset target safe damping ratio, a transient voltage injection command is generated to drive the active converter, and adaptive damping reconstruction is performed.

2. The series capacitor compensation damping circuit method according to claim 1, characterized in that, Step S2, the step of calculating the dynamic AC resistance value modulated by physical temperature at the target frequency, includes: A resistivity temperature compensation term based on the ambient baseline temperature is constructed to characterize the intrinsic resistance drift of the damping element material as the physical temperature changes. Extract the geometric parameters, target frequency, and permeability of the damping element to construct a high-frequency skin depth coefficient; The high-frequency skin depth coefficient is nonlinearly mapped to the resistivity temperature compensation term, so that the output dynamic AC resistance value is positively correlated with the change of physical temperature and monotonically increases, and positively correlated with the change of target frequency and nonlinearly increases.

3. The series capacitor compensation damping circuit method according to claim 1 or 2, characterized in that, Step S3, the step of iteratively calculating the real-time physical temperature of the thermal equilibrium for the current control cycle using Newton's law of cooling, includes: The total harmonic Joule heat generation power of the damping circuit in the current control cycle is obtained by multiplying the dynamic AC resistance value at each harmonic frequency with the square of the effective value of the corresponding harmonic current of each line and summing the product. Based on the comprehensive convective heat transfer coefficient of the damping loop, the effective heat dissipation surface area, and the temperature difference between the physical temperature of the previous control cycle and the real-time ambient base temperature, the convective heat dissipation power dissipated by the damping loop to the environment is obtained. The net difference between the total harmonic Joule heat generation power and the convective heat dissipation power is used as the heat change rate. The heat accumulation update in the time dimension is performed by combining the equivalent comprehensive heat capacity of the damping circuit and the discrete sampling time step to obtain the real-time physical temperature of the heat balance in the current control cycle.

4. The series capacitor compensation damping circuit method according to claim 1, characterized in that, Step S4, the step of calculating the dynamic inductance value of thermomagnetic coupling considering the spontaneous magnetization decay mechanism at the Curie temperature of ferromagnetic materials, includes: Set the absolute saturation critical current value of the iron core at the reference temperature; Based on the degree to which the real-time physical temperature of thermal equilibrium approaches the Curie temperature of the reactor core material, a saturation critical point decay function is constructed, so that the real-time effective saturation critical current value decreases nonlinearly with the increase of the real-time physical temperature of thermal equilibrium. Using the ratio of the effective value of the broadband total current of the line to the real-time effective saturation critical current value as the saturation depth characteristic variable, a magnetic saturation envelope function that smoothly transitions between the unsaturated iron core inductance value and the hollow inductance value is established to obtain the thermomagnetic coupling dynamic inductance value. Moreover, the thermomagnetic coupling dynamic inductance value decreases towards the hollow inductance value as the saturation depth characteristic variable increases.

5. The series capacitor compensation damping circuit method according to claim 1, characterized in that, Step S5, the step of calculating the precise characteristic damping ratio of the system, includes: Based on the typical second-order oscillation response characteristics of the damping circuit, the dynamic AC resistance at the subsynchronous resonance target frequency is used as the positive gain parameter, the rated capacitance of the series compensation capacitor is used as the positive frequency deviation parameter, and the thermomagnetic coupling dynamic inductance is used as the reverse frequency deviation parameter. The precise characteristic damping ratio of the system is defined as a characteristic state parameter that is directly proportional to the dynamic AC resistance value and directly proportional to the square root of the ratio of the rated capacitance value and the thermomagnetic coupling dynamic inductance value.

6. The series capacitor compensation damping circuit method according to claim 1, characterized in that, Step S6, the step of generating the transient voltage injection command to drive the active converter, includes: Based on the preset target safety damping ratio, the rated capacitance of the series compensation capacitor, and the dynamic inductance of the thermomagnetic coupling, the target equivalent resistance required to maintain the transient stability of the system is calculated in reverse. The difference between the target equivalent resistance and the dynamic AC resistance value at the subsynchronous resonant target frequency is extracted as the feedforward active compensation impedance injection amount. Real-time acquisition of instantaneous AC current in the subsynchronous resonant frequency band, and calculation of the proportional compensation voltage generated by the injection amount of the instantaneous AC current through the feedforward active compensation impedance. Calculate the differential feedforward decoupling voltage generated by the rate of change of the instantaneous alternating current flowing through the filter inductor of the grid-connected interface of the active converter; The proportional compensation voltage and the differential feedforward decoupling voltage are superimposed in phase to generate a transient voltage injection command to drive the active converter.

7. A series capacitor compensation damping circuit device, characterized in that, include: The basic parameter acquisition module is used to obtain the effective values ​​of each harmonic current of the line in the current control cycle and the real-time ambient basic temperature, and to call the physical temperature of the previous control cycle. The resistance dynamic analysis module is used to calculate the dynamic AC resistance value modulated by the physical temperature at the target frequency based on the first mechanism of the skin effect. The thermal balance calculation module is used to power couple the dynamic AC resistance value at each harmonic frequency with the corresponding effective value of the line harmonic current, and iteratively calculate the real-time physical temperature of the thermal balance in the current control cycle in combination with Newton's law of cooling. The thermomagnetic coupling calculation module is used to obtain the effective value of the broadband total current of the line. Based on the real-time physical temperature of the thermal balance and the effective value of the broadband total current of the line, the thermomagnetic coupling dynamic inductance value is calculated considering the spontaneous magnetization decay mechanism of the Curie temperature of the ferromagnetic material. The characteristic damping ratio extraction module is used to calculate the accurate characteristic damping ratio of the system based on the dynamic AC resistance value and the thermomagnetic coupling dynamic inductance value at the subsynchronous resonance target frequency. The impedance adaptive reconfiguration execution module is used to generate a transient voltage injection command to drive the active converter when the precise characteristic damping ratio of the system deviates from the preset target safe damping ratio, so as to perform adaptive damping reconfiguration.

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