Method for traction network voltage recovery and oscillation suppression with overshoot compensation and active damping

Abstract

The application discloses a traction network voltage recovery and oscillation suppression method with overshoot compensation and active damping, comprising: performing Hilbert-Huang transformation on the catenary voltage signal, and extracting the instantaneous frequency, amplitude and phase of the dominant oscillation mode; constructing a mode priority queue according to the oscillation energy proportion, and calculating the damping current amplitude weight coefficient in combination with the residual capacity of the energy storage unit; generating the pre-compensation damping current component corresponding to each mode and linearly superimposing to form a composite damping current instruction; online optimizing the weight coefficient and phase pre-compensation amount in the control process; and when the oscillation energy meets the exit condition, the damping current is smoothly reduced according to an S-shaped curve until the active damping mode is exited. The application can realize the collaborative suppression of multi-mode oscillation, and improve the oscillation attenuation efficiency and system operation stability in the traction network voltage recovery process.

Description

Technical Field

[0001] This invention relates to the field of railway power supply technology, and in particular to a method for traction network voltage recovery and oscillation suppression using overshoot compensation and active damping. Background Technology

[0002] The traction power supply system of rail transit plays a crucial role in providing continuous and stable power to electric locomotives. Traction loads are characterized by severe fluctuations, high randomness, and high power density. During operation, such as starting, accelerating, regenerative braking, crossing phase-splitting zones, and multi-car cooperative operation, electric locomotives can cause rapid and significant disturbances to the overhead contact line voltage. When the disturbance energy exceeds the system's absorption capacity, the overhead contact line voltage will drop or oscillate. If not suppressed in time, this may affect the stable operation of the locomotive and even trigger protection mechanisms, causing train service interruptions.

[0003] To suppress traction grid voltage fluctuations and accelerate voltage recovery, existing technologies typically introduce energy storage units into the traction power supply system for power compensation, and combine overshoot compensation and active damping strategies. The overshoot compensation strategy sets an initial compensation power greater than the current predicted energy deficit, using excess driving force to overcome system inertia and achieve rapid voltage recovery. The active damping strategy, on the other hand, monitors the oscillation signal parameters of the system voltage in real time and injects a damping current component opposite to the oscillation phase into the grid to attenuate the oscillation amplitude and suppress voltage fluctuations. The two strategies work together to maintain system operational stability while ensuring rapid voltage recovery.

[0004] However, existing active damping strategies have inherent limitations in addressing actual traction network oscillations. Current methods assume that traction network oscillations exhibit a single dominant frequency mode and accordingly generate a single-frequency anti-phase damping current component to suppress them by applying it to the energy storage unit. However, in actual traction networks, operating conditions such as high-frequency switching of the locomotive traction converter, rapid increases and decreases in regenerative braking power, and coordinated switching of multiple distributed energy storage units may simultaneously excite multiple oscillation modes. For example, the interaction between the locomotive rectifier / inverter unit and the grid-side inductors and capacitors may excite low-frequency power oscillations of 5 to 20 Hz; the interaction between converter switching harmonics and traction network distributed parameters may excite mid-frequency harmonic oscillations of 100 to 300 Hz. Under conditions of coexisting multi-mode oscillations, the traditional single-frequency anti-phase current strategy faces fundamental difficulties: the damping current designed for a single frequency mode not only fails to simultaneously suppress oscillations of other frequency modes but may also inject additional energy into non-target modes due to phase mismatch, exacerbating the oscillation amplitude of non-dominant modes and potentially even causing system instability. Summary of the Invention

[0005] To address the technical problem that existing active damping strategies cannot achieve coordinated suppression of multimodal oscillations due to the single frequency assumption under conditions of coexistence of multimodal oscillations, this invention provides a method for traction network voltage recovery and oscillation suppression using overshoot compensation and active damping.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] This invention discloses a method for traction network voltage recovery and oscillation suppression using overshoot compensation and active damping, comprising the following steps:

[0008] The first step is to perform Hilbert-Huang transform on the contact network voltage timing signal to extract the instantaneous frequency, instantaneous amplitude and instantaneous phase of each of the N dominant oscillation modes;

[0009] The second step is to calculate the oscillation energy ratio of each dominant oscillation mode based on its instantaneous amplitude, and then sort the N dominant oscillation modes from high to low according to their oscillation energy ratios to generate a mode priority queue.

[0010] The third step is to obtain the real-time remaining capacity of each energy storage unit along the line, and based on the real-time remaining capacity of each energy storage unit and the oscillation energy ratio of each dominant oscillation mode in the mode priority queue, calculate the damping current amplitude weighting coefficient corresponding to each energy storage unit for each dominant oscillation mode.

[0011] The fourth step is to generate an anti-phase damping current reference waveform at the detection point that is out of phase with the dominant oscillation mode based on the instantaneous frequency and instantaneous phase of the dominant oscillation mode. Then, based on the electrical distance between the access point of each energy storage unit and the oscillation source, perform independent phase pre-compensation on the anti-phase damping current reference waveform to obtain the pre-compensated damping current component of the energy storage unit for the dominant oscillation mode.

[0012] The fifth step is to linearly superimpose all the pre-compensated damping current components corresponding to each energy storage unit according to their respective damping current amplitude weighting coefficients to generate a unique composite damping current command for each energy storage unit, and then send the unique composite damping current command and overshoot compensation power to the corresponding energy storage unit simultaneously.

[0013] The sixth step involves real-time monitoring of the residual oscillation energy of each dominant oscillation mode during the injection of composite damping current into the energy storage unit. A recursive least squares method with a forgetting factor is used to simultaneously update the damping current amplitude weighting coefficient and phase pre-compensation amount corresponding to each energy storage unit online.

[0014] Step 7: When the residual oscillation energy of all dominant oscillation modes is lower than the preset energy threshold and continues for a preset time window, control each energy storage unit to gradually reduce the amplitude of its unique composite damping current according to the S-curve until it reaches zero, and exit the active damping mode.

[0015] Further: The first step includes:

[0016] Empirical mode decomposition is performed on the contact network voltage timing signal to obtain a set of intrinsic mode function components;

[0017] Perform a Hilbert transform on each intrinsic mode function component and calculate the instantaneous amplitude function and instantaneous frequency function of that intrinsic mode function component;

[0018] The intrinsic mode function components whose time average of instantaneous amplitude function is greater than a preset amplitude threshold are identified as dominant oscillation modes. The intrinsic mode function component with the largest time average of instantaneous amplitude function is marked as the first dominant oscillation mode, and the rest are marked as the second dominant oscillation mode to the Nth dominant oscillation mode in descending order of the time average of instantaneous amplitude function.

[0019] Extract the instantaneous frequency function of each dominant oscillation mode at the current time as the instantaneous frequency of that dominant oscillation mode, extract the instantaneous amplitude function of each dominant oscillation mode at the current time as the instantaneous amplitude of that dominant oscillation mode, and extract the phase angle of the analytic signal of each dominant oscillation mode after Hilbert transform at the current time as the instantaneous phase of that dominant oscillation mode.

[0020] Furthermore: The second step includes:

[0021] The oscillation energy of the dominant oscillation mode is calculated by integrating the instantaneous amplitude of each dominant oscillation mode over a preset time window.

[0022] The oscillation energy of each dominant oscillation mode is divided by the sum of the oscillation energies of all N dominant oscillation modes to calculate the proportion of oscillation energy of that dominant oscillation mode.

[0023] The first dominant oscillation mode to the Nth dominant oscillation mode are arranged in descending order of oscillation energy percentage, and the resulting sequence is used as the mode priority queue.

[0024] Furthermore: The third step includes:

[0025] The capacity allocation coefficient of an energy storage unit is calculated by dividing the real-time remaining capacity of each energy storage unit by the sum of the real-time remaining capacities of all energy storage units.

[0026] The damping current amplitude weighting coefficient of the energy storage unit for the i-th dominant oscillation mode is calculated by multiplying the oscillation energy ratio of the i-th dominant oscillation mode in the mode priority queue by the capacity allocation coefficient of the energy storage unit, and then multiplying by the preset upper limit of the total damping current amplitude.

[0027] Furthermore, the fourth step includes:

[0028] For the i-th dominant oscillation mode, a sine function is constructed. The angular frequency of the sine function is 2π times the instantaneous frequency of the dominant oscillation mode, and the initial phase of the sine function is the instantaneous phase of the dominant oscillation mode plus π radians. An anti-phase damping current reference waveform that is opposite to the dominant oscillation mode at the detection point is generated.

[0029] Measure the line impedance between each energy storage unit access point and the oscillation source, and extract the impedance angle of the line impedance as the electrical distance parameter;

[0030] The initial phase of the anti-phase damped current reference waveform is added to the impedance angle to calculate the initial phase after phase pre-compensation. The sine function is then reconstructed using the initial phase after phase pre-compensation. The pre-compensated damped current component value of the energy storage unit for the dominant oscillation mode is marked as an effective mapping mark to establish a cross-scale spatial correspondence between adjacent decomposition scales at the same geological boundary location.

[0031] Furthermore: Step 5 includes:

[0032] For each energy storage unit, the pre-compensated damping current component of the i-th dominant oscillation mode corresponding to the energy storage unit is multiplied by the damping current amplitude weighting coefficient of the energy storage unit for the i-th dominant oscillation mode to obtain the weighted damping current component.

[0033] The unique composite damping current command of the energy storage unit is calculated by algebraically summing all the weighted damping current components of i from 1 to N.

[0034] The unique composite damping current command and the pre-calculated overshoot compensation power command are encapsulated into the same control data frame and synchronously sent to the energy storage unit via industrial real-time Ethernet.

[0035] Furthermore, step six includes:

[0036] During the process of injecting a unique composite damping current command into each energy storage unit, the residual oscillation energy of each dominant oscillation mode is re-extracted at fixed time intervals, and the residual oscillation energy is used as the desired output value.

[0037] Using the damping current amplitude weighting coefficient and phase pre-compensation amount at the current moment as the parameters to be optimized, a cost function is constructed using the recursive least squares method with a forgetting factor. The minimization objective of the cost function is the weighted sum of the squared errors between the expected output value and the residual oscillation energy measured after actual injection.

[0038] Through recursive iterative calculation, the damping current amplitude weighting coefficient and phase pre-compensation amount corresponding to each energy storage unit are updated simultaneously, so that the output value of the cost function decreases after the updated parameters are substituted into the next iteration.

[0039] Furthermore, step seven includes:

[0040] At each time sampling point, the real-time value of the residual oscillation energy of all dominant oscillation modes is calculated. When the residual oscillation energy of each dominant oscillation mode is lower than the preset energy threshold in P consecutive time sampling points, it is determined that the preset time window meets the condition.

[0041] Using the amplitude of the unique composite damping current command at the current moment as the starting amplitude and zero as the target amplitude, an S-shaped curve is constructed as the amplitude decay trajectory. The slope of the midpoint of the S-shaped curve is greater than the slope of the starting point and the slope of the ending point, and the first derivative of the S-shaped curve is continuous.

[0042] The amplitude of each energy storage unit is multiplied by the unit waveform of the unique composite damping current command at each time point determined by the S-curve, and the actual injected current amplitude is gradually reduced until it is zero. Then the power connection between the energy storage unit and the traction network is disconnected, and the operation of exiting the active damping mode is completed.

[0043] The technological advancements achieved by this invention compared to existing technologies are as follows:

[0044] This invention achieves synchronous identification of multiple dominant oscillation modes by performing a Hilbert-Huang transform on the overhead contact line voltage signal. It then constructs a mode priority queue based on the oscillation energy ratio, generates anti-phase damping current components for different oscillation modes, and adaptively allocates and coordinates these components based on the remaining capacity of the energy storage unit. This allows the active damping process to simultaneously apply to multiple frequency oscillation modes. Compared to existing active damping strategies based on a single frequency assumption, this invention avoids energy injection problems caused by phase mismatch in non-target modes, achieves coordinated suppression of multi-mode oscillations, and improves the oscillation attenuation efficiency and system operational stability during traction network voltage recovery. Attached Figure Description

[0045] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0046] In the attached diagram:

[0047] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0048] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0049] like Figure 1 As shown, this invention discloses a method for traction network voltage recovery and oscillation suppression using overshoot compensation and active damping, comprising:

[0050] The first step is to perform Hilbert-Huang transform on the contact network voltage timing signal to extract the instantaneous frequency, instantaneous amplitude and instantaneous phase of each of the N dominant oscillation modes;

[0051] The second step is to calculate the oscillation energy ratio of each dominant oscillation mode based on its instantaneous amplitude, and then sort the N dominant oscillation modes from high to low according to their oscillation energy ratios to generate a mode priority queue.

[0052] The third step is to obtain the real-time remaining capacity of each energy storage unit along the line, and based on the real-time remaining capacity of each energy storage unit and the oscillation energy ratio of each dominant oscillation mode in the mode priority queue, calculate the damping current amplitude weighting coefficient corresponding to each energy storage unit for each dominant oscillation mode.

[0053] The fourth step is to generate an anti-phase damping current reference waveform at the detection point that is out of phase with the dominant oscillation mode based on the instantaneous frequency and instantaneous phase of the dominant oscillation mode. Then, based on the electrical distance between the access point of each energy storage unit and the oscillation source, perform independent phase pre-compensation on the anti-phase damping current reference waveform to obtain the pre-compensated damping current component of the energy storage unit for the dominant oscillation mode.

[0054] The fifth step is to linearly superimpose all the pre-compensated damping current components corresponding to each energy storage unit according to their respective damping current amplitude weighting coefficients to generate a unique composite damping current command for each energy storage unit, and then send the unique composite damping current command and overshoot compensation power to the corresponding energy storage unit simultaneously.

[0055] The sixth step involves real-time monitoring of the residual oscillation energy of each dominant oscillation mode during the injection of composite damping current into the energy storage unit. A recursive least squares method with a forgetting factor is used to simultaneously update the damping current amplitude weighting coefficient and phase pre-compensation amount corresponding to each energy storage unit online.

[0056] Step 7: When the residual oscillation energy of all dominant oscillation modes is lower than the preset energy threshold and continues for a preset time window, control each energy storage unit to gradually reduce the amplitude of its unique composite damping current according to the S-curve until it reaches zero, and exit the active damping mode.

[0057] Specifically, the first step is to perform a Hilbert-Huang transform on the overhead contact line voltage time-series signal to extract the instantaneous frequency, instantaneous amplitude, and instantaneous phase of each of the N dominant oscillation modes. The purpose of this step is to separate multiple coexisting oscillation modes from the complex overhead contact line voltage time-series signal and obtain the frequency characteristics, energy intensity characteristics, and phase characteristics of each oscillation mode at the current moment, providing basic data support for subsequent oscillation energy assessment, damping current construction, and phase pre-compensation.

[0058] Because voltage fluctuations in traction power supply systems exhibit significant non-stationary and nonlinear characteristics, oscillation components from different oscillation sources often superimpose on the same voltage signal. For example, low-frequency power oscillations generated by the operation of the locomotive traction converter, dynamic oscillations generated by regenerative braking switching, and medium-frequency harmonic oscillations generated by the switching action of power electronic devices may all coexist. Traditional spectrum analysis methods typically only obtain average frequency information within a fixed time window, making it difficult to accurately reflect the dynamic process of oscillation frequency changes over time. Therefore, this embodiment employs the Hilbert-Huang transform to perform time-frequency analysis on the contact network voltage time-series signal to achieve adaptive separation of multimodal oscillations.

[0059] The overhead contact line voltage acquisition device continuously acquires the overhead contact line voltage timing signal and forms a continuous discrete sampling sequence. Let the acquired overhead contact line voltage timing signal be represented as... ,in, Indicates the sampling time. This indicates the contact network voltage value at the corresponding moment.

[0060] After obtaining the overhead contact line voltage time-series signal, empirical mode decomposition (EMD) is performed on it. EMD is a data-driven adaptive decomposition method. Its core idea is to decompose a complex signal layer by layer into multiple eigenmode function components with local single-component characteristics and a residual trend term. In specific processing, all local maxima in the overhead contact line voltage time-series signal are searched, and an upper envelope is constructed using spline interpolation; simultaneously, all local minima are searched, and a lower envelope is constructed using spline interpolation. Then, the average curves of the upper and lower envelopes are calculated, and candidate components are obtained by subtracting the average curves from the original signal.

[0061] For each candidate component obtained, it is determined whether it meets the intrinsic mode function (IMF) condition, which is that the number of extreme points and the number of zero-crossing points within the entire data interval do not differ by more than one, and the mean of the upper and lower envelopes is close to zero at any given time. If the condition is met, the component is identified as an IMF component; if the condition is not met, the screening process continues until the requirements are met.

[0062] After completing the first level of decomposition, the obtained intrinsic mode function components are subtracted from the original signal to obtain the remaining signal, and the above process is repeated. After multiple iterations, multiple intrinsic mode function components can be obtained:

[0063]

[0064] in, Indicates the first Each intrinsic mode function component This represents the total number of intrinsic mode functions obtained from the decomposition. This represents the residual trend term.

[0065] After empirical mode decomposition, different oscillation frequency components in the original overhead contact line voltage signal are mapped to different intrinsic mode function (IMF) components. Higher frequency oscillations are usually concentrated in the first few IMF components, while lower frequency oscillations are concentrated in the subsequent IMF components, thus achieving preliminary separation of multimodal oscillations.

[0066] Subsequently, Hilbert transform is performed on each intrinsic mode function component.

[0067] For the For each intrinsic mode function component, construct its corresponding analytic signal:

[0068]

[0069] in, Represents the Hilbert transform operator. It represents the imaginary unit.

[0070] After the analytical signal is established, the instantaneous amplitude function and instantaneous phase function of the intrinsic mode function component can be obtained simultaneously. The instantaneous amplitude function reflects the change in oscillation intensity of the corresponding oscillation mode at each moment. When the oscillation energy increases, the instantaneous amplitude increases synchronously; when the oscillation gradually decays, the instantaneous amplitude decreases synchronously.

[0071] The instantaneous phase function reflects the position of the corresponding oscillation mode in the current oscillation period and can be used to construct the reverse-phase damping current. After obtaining the instantaneous phase function, its time derivative yields the instantaneous frequency function. The instantaneous frequency function describes the dynamic process of the oscillation frequency changing with time and can accurately reflect the frequency drift phenomenon of the traction network oscillation and the frequency differences between different oscillation modes. Since the number of eigenmode function components obtained from empirical mode decomposition is usually large, and some of these components only correspond to weak disturbances, random noise, or measurement errors, it is necessary to further screen out the dominant oscillation modes that truly participate in the system oscillation process.

[0072] For each intrinsic mode function (IMF) component, its instantaneous amplitude function is statistically averaged over a preset analysis time window to obtain the corresponding time-averaged amplitude. When the time-averaged amplitude of an IMF component is greater than a preset amplitude threshold, it indicates that the component has consistently high oscillation energy within the analysis time window, and its corresponding oscillation mode has a real impact on the contact network voltage fluctuation; therefore, it is identified as the dominant oscillation mode. When the time-averaged amplitude is lower than the preset amplitude threshold, it is considered that the component mainly reflects background noise or local random disturbances and does not participate in the subsequent active damping control process.

[0073] After screening, assuming N dominant oscillation modes are retained, they are then sorted according to the magnitude of their corresponding time-averaged amplitudes. The dominant oscillation mode with the largest time-averaged amplitude indicates that it has the highest long-term oscillation energy and the most significant impact on the contact network voltage, and is therefore marked as the first dominant oscillation mode. The remaining dominant oscillation modes are marked as the second dominant oscillation mode, the third dominant oscillation mode, and so on up to the Nth dominant oscillation mode, in descending order of their time-averaged amplitudes.

[0074] After completing the identification of the dominant oscillation mode, the key state parameters of each dominant oscillation mode are extracted at the current control time. The function value at the current time is read from the corresponding instantaneous frequency function as the instantaneous frequency of the dominant oscillation mode. This parameter represents the real-time oscillation speed of the current oscillation mode. The function value at the current time is read from the corresponding instantaneous amplitude function as the instantaneous amplitude of the dominant oscillation mode. This parameter represents the real-time oscillation intensity of the current oscillation mode.

[0075] The phase angle at the current moment is read from the instantaneous phase function corresponding to the analytical signal, and used as the instantaneous phase of the dominant oscillation mode. This parameter characterizes the real-time phase position of the current oscillation mode in the current oscillation period. After the above processing, the original contact network voltage time sequence signal is decomposed into N independent dominant oscillation modes, and the instantaneous frequency, instantaneous amplitude, and instantaneous phase corresponding to each dominant oscillation mode are obtained. At this point, the system has completed the identification of the multi-mode oscillation structure of the traction network, establishing a unified data foundation for subsequent calculation of oscillation energy proportion, mode priority ranking, and generation of multi-mode composite damping current.

[0076] The second step involves calculating the oscillation energy percentage of each dominant oscillation mode based on its instantaneous amplitude. The N dominant oscillation modes are then sorted from highest to lowest oscillation energy percentage to generate a mode priority queue. After completing the first step, the system has identified N dominant oscillation modes from the overhead contact line voltage timing signal and obtained the instantaneous frequency, instantaneous amplitude, and instantaneous phase for each dominant oscillation mode. The instantaneous frequency reflects the oscillation velocity characteristics, the instantaneous phase reflects the oscillation state characteristics, and the instantaneous amplitude directly reflects the oscillation intensity carried by that oscillation mode in the current time period. Therefore, before entering active damping control, it is necessary to further assess the actual impact of each dominant oscillation mode on the current overhead contact line voltage fluctuations to determine which oscillation modes should be prioritized for use by limited energy storage resources.

[0077] Because different dominant oscillation modes differ in frequency range, duration, and amplitude variation patterns, judging their importance solely based on the instantaneous amplitude at a single moment is easily affected by short-term disturbances. For example, a high-frequency oscillation mode may have a large instantaneous amplitude at the current moment but a short duration; while a low-frequency oscillation mode, although having a slightly smaller instantaneous amplitude, persists and continuously injects oscillatory energy into the system. If ranking is based solely on the amplitude at a single point, it can easily lead to subsequent damping resource allocation deviating from the actual oscillation state. Therefore, this step uses oscillation energy as a unified evaluation index to quantitatively assess each dominant oscillation mode.

[0078] The system first establishes a preset time window. This time window is synchronized with the analysis period for obtaining the parameters of the dominant oscillation mode in the first step, so that the calculation of oscillation energy can reflect the true energy contribution of each oscillation mode in the current time period.

[0079] For the The dominant oscillation mode, whose instantaneous amplitude function has been obtained in the first step, is denoted as . in, Indicates the first The dominant oscillation mode at time... The corresponding instantaneous amplitude.

[0080] Since the energy carried by the oscillation signal is proportional to the square of the oscillation amplitude, the system performs square integration on the instantaneous amplitude within a preset time window to calculate the oscillation energy of the corresponding dominant oscillation mode.

[0081]

[0082] in, Indicates the first The oscillation energy of the dominant oscillation mode This indicates the preset time window.

[0083] The essence of the above calculation process is to accumulate and statistically analyze the oscillation intensity released by the oscillation mode throughout the entire time window. If a dominant oscillation mode maintains a high amplitude for a long period within the time window, its oscillation energy will continue to accumulate and obtain a large value; if a dominant oscillation mode only experiences brief fluctuations at local moments, its accumulated oscillation energy will be relatively small. In this way, the influence of instantaneous abnormal fluctuations can be effectively eliminated, making the evaluation results more stable.

[0084] The system calculates the oscillation energy of all N dominant oscillation modes using the same method, thus obtaining the set of oscillation energies within the current time window. After obtaining the oscillation energy of each dominant oscillation mode, the system further calculates the total oscillation energy of all dominant oscillation modes:

[0085]

[0086] The total oscillation energy represents the total energy level carried by all dominant oscillation modes in the current overhead contact line voltage fluctuation.

[0087] Subsequently, to eliminate the influence of variations in absolute oscillation energy under different operating conditions on the subsequent control process, the system normalizes the oscillation energy of each dominant oscillation mode. The dominant oscillation mode, whose oscillation energy proportion is defined as ,in, Indicates the first The proportion of oscillation energy of each dominant oscillation mode.

[0088] The proportion of oscillation energy reflects the relative share of the dominant oscillation mode in the total oscillation energy. The larger the proportion, the greater the contribution of the oscillation mode to the current catenary voltage fluctuation; the smaller the proportion, the weaker the impact of the oscillation mode on the overall system oscillation. For example, if three dominant oscillation modes are detected at a certain moment, with their oscillation energies accounting for 50%, 30%, and 20% of the total oscillation energy respectively, it indicates that the first dominant oscillation mode accounts for more than half of the current system oscillation energy and is the most important target to suppress; the second dominant oscillation mode is next; and the third dominant oscillation mode has a relatively smaller impact.

[0089] After completing the calculation of all oscillation energy percentages, the system establishes an oscillation energy percentage list and sorts them in descending order from high to low according to the oscillation energy percentage. During the sorting process, the mode numbering order formed by the time average amplitude in the first step is no longer used. Instead, the oscillation energy percentages actually calculated within the current time window are dynamically sorted again. This ensures that the sorting results reflect the current oscillation state in real time.

[0090] When the oscillation energy percentage of a dominant oscillation mode is higher than that of other dominant oscillation modes, it is placed at the front of the queue; dominant oscillation modes with lower oscillation energy percentages are placed in subsequent positions.

[0091] After sorting, a mode priority queue is formed. The order in this queue represents the priority of resource allocation in subsequent active damping control. The dominant oscillation mode at the front of the queue indicates that it contributes the most to the current contact network voltage fluctuation, and therefore will receive a higher damping resource weight in the subsequent damping current allocation process; although the dominant oscillation mode at the back of the queue also participates in oscillation suppression, its allocation weight is relatively low.

[0092] Since the proportion of oscillation energy is dynamically calculated based on the real-time oscillation state, the mode priority queue is not fixed. After changes in traction load, switching of locomotive operating status, or intervention of energy storage unit control, the oscillation energy of each dominant oscillation mode may be redistributed. The system will continue to repeat this step in subsequent control cycles, recalculate the proportion of oscillation energy based on the latest obtained instantaneous amplitude, and dynamically update the mode priority queue, so that the entire active damping process always revolves around the most dominant oscillation mode.

[0093] After this step, the system not only obtains the oscillation energy percentage corresponding to each dominant oscillation mode, but also establishes a mode priority queue reflecting the influence of each dominant oscillation mode. This mode priority queue will serve as an important basis for calculating the damping current amplitude weighting coefficient in the next step, providing a quantitative foundation for the rational allocation of damping resources in the energy storage unit.

[0094] Step 3: Obtain the real-time remaining capacity of each energy storage unit along the line. Based on the real-time remaining capacity of each energy storage unit and the oscillation energy proportion of each dominant oscillation mode in the mode priority queue, calculate the damping current amplitude weighting coefficient corresponding to each energy storage unit for each dominant oscillation mode. After completing Step 1, the system has obtained dynamic characteristic parameters such as instantaneous frequency, instantaneous amplitude, and instantaneous phase corresponding to N dominant oscillation modes. After completing Step 2, the system further obtains the oscillation energy proportion of each dominant oscillation mode and establishes a mode priority queue. At this point, the system clearly knows which oscillation modes in the current traction network contribute the most oscillation energy and the relative importance among these oscillation modes.

[0095] However, simply identifying the oscillation modes that need to be prioritized for suppression is insufficient to directly implement active damping control. Since traction power supply systems typically have multiple distributed energy storage units along the line, the remaining energy storage levels of different units at any given time are not the same. If all energy storage units adopt the same damping output strategy, some units may over-discharge while others are underutilized, thus reducing overall damping efficiency. Therefore, before generating the damping current, the damping task needs to be rationally allocated based on the currently available remaining capacity of each energy storage unit and the importance of each dominant oscillation mode.

[0096] The core objective of this step is to establish a quantitative mapping relationship between energy storage resources and oscillation demand, so that the dominant oscillation mode with a higher proportion of oscillation energy can obtain more damping resources, while the energy storage units with larger remaining capacity can undertake more damping tasks, ultimately forming a damping current amplitude weighting coefficient for different dominant oscillation modes and different energy storage units.

[0097] The system first obtains real-time remaining capacity information of all energy storage units along the line through the energy storage management module.

[0098] Assuming deployment along the route The energy storage unit, the first The real-time remaining capacity of each energy storage unit at the current moment is expressed as follows: ,in, Indicates the first The remaining energy storage capacity of each energy storage unit is currently available for active damping control.

[0099] Real-time remaining capacity reflects the energy storage unit's ability to continuously output damping current. A higher remaining capacity indicates that the energy storage unit has a strong energy supply capacity; a lower remaining capacity indicates that its ability to participate in damping control is limited.

[0100] To enable the damping task to be adaptively allocated based on the energy storage resource level, the system normalizes the real-time remaining capacity of all energy storage units, first calculating the total remaining capacity of all energy storage units. This parameter represents the total energy storage resources available for active damping control across all energy storage units in the current system. The capacity allocation coefficient for each energy storage unit is then calculated. ,in, Indicates the first Capacity allocation coefficient for each energy storage unit.

[0101] The capacity allocation factor represents the proportion of the energy storage unit in all available energy storage resources. For example, if an energy storage unit accounts for 30% of the total remaining capacity, its capacity allocation factor is 0.3, which means that in the subsequent damping task allocation process, this energy storage unit will, in principle, undertake about 30% of the damping output task.

[0102] After calculating the capacity allocation coefficient, the system begins to allocate damping resources based on the mode priority queue generated in the second step. In the second step, the system has obtained the oscillation energy percentage corresponding to each dominant oscillation mode. The higher the oscillation energy percentage, the greater the contribution of the dominant oscillation mode to the current contact network voltage fluctuation, and more damping resources are needed to suppress it; dominant oscillation modes with lower oscillation energy percentages are allocated relatively fewer damping resources.

[0103] Let the modal priority queue contain the first... The oscillation energy percentage corresponding to each dominant oscillation mode is expressed as follows: ,in, Indicates the first The proportion of the dominant oscillation mode in the total oscillation energy.

[0104] The system pre-sets an upper limit for the total damping current amplitude. This parameter represents the maximum damping current capability allowed for all energy storage units to output together within the current control cycle. Let the upper limit for the total damping current amplitude be... This parameter is used to limit the maximum current output level during active damping, ensuring that the damping control is always within the allowable operating range.

[0105] Subsequently, regarding the first The energy storage unit and the first For each dominant oscillation mode, the system considers both the importance of the dominant oscillation mode and the energy supply capacity of the energy storage unit, and calculates the corresponding damping current amplitude weighting coefficient:

[0106]

[0107] in, Indicates the first The energy storage unit is for the first The damping current amplitude weighting coefficients corresponding to each dominant oscillation mode.

[0108] This calculation process actually establishes a dual weighting mechanism. On the one hand, the proportion of oscillation energy determines the priority of oscillation demand. Dominant oscillation modes with a larger proportion of oscillation energy receive a larger weighting coefficient, thus gaining greater current injection capacity in the subsequent damping current construction process. On the other hand, the capacity allocation coefficient determines the capacity of the energy storage supply side. Energy storage units with larger remaining capacity receive a larger weighting coefficient, thus undertaking more damping tasks; energy storage units with smaller remaining capacity automatically reduce their output ratio. This forms a resource allocation mechanism driven by both the intensity of oscillation demand and the energy storage supply capacity.

[0109] For example, when a dominant oscillation mode accounts for 50% of the total oscillation energy and a certain energy storage unit accounts for 40% of the total remaining capacity, the energy storage unit will obtain a larger damping current amplitude weighting coefficient for the dominant oscillation mode; conversely, when the proportion of oscillation energy is low or the remaining capacity of the energy storage unit is small, the corresponding weighting coefficient will automatically decrease.

[0110] After the calculation is completed, the system will obtain a two-dimensional weight matrix. Each element in the matrix corresponds to the damping distribution relationship between an energy storage unit and a dominant oscillation mode. The rows of the matrix reflect the distribution of damping demand corresponding to different dominant oscillation modes, and the columns of the matrix reflect the distribution of damping capacity corresponding to different energy storage units. Through this matrix, the system can clearly know how much damping current amplitude each energy storage unit should contribute to each dominant oscillation mode.

[0111] The damping current amplitude weighting coefficient obtained at this point is not directly used as the final output current, but rather as an amplitude adjustment factor in the subsequent damping current generation process. Subsequent steps will construct an anti-phase damping current reference waveform based on the instantaneous frequency and phase corresponding to each dominant oscillation mode, and use the damping current amplitude weighting coefficient obtained in this step to configure the amplitude of the damping current components corresponding to each mode, thereby achieving coordinated suppression of multi-mode oscillations.

[0112] After this step, the system completes the mapping process from oscillation energy distribution to energy storage resource allocation, and establishes a set of damping current amplitude weighting coefficients for each dominant oscillation mode for each energy storage unit, so that subsequent active damping control can both prioritize the suppression of high-energy oscillation modes and make full use of the available energy storage resources of each energy storage unit along the line.

[0113] Step 4: For each dominant oscillation mode, an anti-phase damping current reference waveform, opposite in phase to the dominant oscillation mode at the detection point, is generated based on the instantaneous frequency and instantaneous phase of the dominant oscillation mode. Independent phase pre-compensation is then performed on this anti-phase damping current reference waveform according to the electrical distance between each energy storage unit's connection point and the oscillation source, yielding the pre-compensated damping current component for that energy storage unit in relation to the dominant oscillation mode. After completing Step 1, the system has obtained the instantaneous frequency, instantaneous amplitude, and instantaneous phase corresponding to each dominant oscillation mode; after completing Step 2, the system has determined the oscillation energy proportion and mode priority of each dominant oscillation mode in the current oscillation process; after completing Step 3, the system has calculated the corresponding damping current amplitude weighting coefficient for each energy storage unit for each dominant oscillation mode.

[0114] At this point, the system already knows which oscillation modes need to be suppressed, the importance of each oscillation mode, and the proportion of damping tasks that each energy storage unit should undertake. However, a key element is still missing: how to generate a damping current waveform that can directly act on the corresponding oscillation mode.

[0115] Active damping essentially involves injecting a current component into the system during the propagation of oscillating energy, with the direction opposite to that of the target oscillation mode. This current component continuously absorbs oscillating energy, thereby reducing the oscillation amplitude. To achieve this, the injected current must not only have the same frequency as the target oscillation mode but also maintain an opposite phase relationship. Only when the injected current and the target oscillation mode form a stable anti-phase interaction can the energy storage unit continuously absorb energy from the oscillating system, achieving oscillation attenuation.

[0116] Therefore, the task of this step is to construct a corresponding anti-phase damping current reference waveform for each dominant oscillation mode, and further consider the electrical propagation effect between the energy storage unit and the oscillation source, and perform phase pre-compensation processing on the waveform so that the damping current actually injected by the energy storage unit still maintains an accurate anti-phase state when it reaches the oscillation region.

[0117] For the first in the modal priority queue For each dominant oscillation mode, the system first reads the instantaneous frequency and instantaneous phase obtained in the first step.

[0118] Let the instantaneous frequency of the dominant oscillation mode at the current moment be... The corresponding instantaneous phase is ,in, Reflecting the current oscillation speed of the dominant oscillation mode, This reflects the current oscillation position of the dominant oscillation mode.

[0119] Since there is a fixed relationship between the angular frequency and the frequency of a sine wave, the system first calculates the angular frequency corresponding to the dominant oscillation mode:

[0120]

[0121] This angular frequency will be used as the frequency parameter for constructing the subsequent damped current waveform.

[0122] Subsequently, a reference waveform for the anti-phase damping current is constructed based on the current instantaneous phase of the dominant oscillation mode. "Anti-phase" means that the damping current maintains a 180-degree phase difference with the target oscillation mode. When the target oscillation is at its positive peak, the damping current is at its negative peak; when the target oscillation is at its negative peak, the damping current is at its positive peak, thus creating a continuous energy cancellation effect. Therefore, the system adds one phase to the current instantaneous phase of the dominant oscillation mode. Radius as the initial phase after inversion:

[0123]

[0124] in, This indicates the reference phase after inversion.

[0125] Using this angular frequency and the inverted reference phase, construct the inverted damped current reference waveform:

[0126]

[0127] in, Indicates the first The reference waveform of the reverse-phase damped current corresponding to each dominant oscillation mode.

[0128] The anti-phase damped current reference waveform generated at this time is a theoretical waveform established at the oscillation detection point, and its phase relationship is constructed based on the oscillation state measured at the detection point.

[0129] However, in actual traction power supply systems, energy storage units are typically distributed across different power supply sections, with varying transmission lines and electrical networks of different parameters existing between the connection points of each energy storage unit and the oscillation source. When the damping current is injected into the traction network from the energy storage unit, it needs to propagate through the lines to reach the oscillation zone.

[0130] During propagation, line inductance, capacitance, and line impedance all cause phase shifts. If these phase shifts are ignored, although the energy storage unit outputs a theoretically inverted waveform, it may actually be phase-lagging or phase-leading when it reaches the oscillation region, thus weakening the damping effect. In severe cases, it may even transform from absorbing oscillation energy to injecting energy into the oscillation system.

[0131] Therefore, phase pre-compensation processing needs to be performed for each energy storage unit. The system first determines the location of the oscillation source corresponding to the current dominant oscillation mode. The oscillation source can be determined by the preceding oscillation monitoring module, which corresponds to the region where the energy of the current dominant oscillation mode is most concentrated or the oscillation propagation initiation region. Subsequently, for the... Each energy storage unit measures the equivalent impedance of the line between its access point and the oscillation source.

[0132] Let the equivalent impedance of the line be expressed as The line impedance comprises resistive and reactive components, which together determine the phase change characteristics of the current during propagation. The system extracts the corresponding impedance angle from this line impedance. ,in, Indicates the first The energy storage unit is relative to the first Electrical distance parameters of the dominant oscillation mode oscillation source.

[0133] Unlike traditional physical distance, electrical distance reflects the phase propagation characteristics of oscillating signals in the power grid. Even if two lines are of the same length, their electrical distances may differ due to differences in line parameters.

[0134] After obtaining the electrical distance parameters, the system superimposes these parameters onto the initial phase of the anti-phase damping current reference waveform to form a pre-compensated phase:

[0135]

[0136] in, Indicates the first The energy storage unit is for the first The pre-compensated initial phase corresponding to each dominant oscillation mode.

[0137] The significance of this treatment lies in compensating in advance for the expected phase change of the damping current during propagation, so that it can return to the ideal anti-phase position after propagating through the line.

[0138] Subsequently, the system reconstructs the damped current waveform using the pre-compensated initial phase:

[0139]

[0140] in, Indicates the first The energy storage unit is for the first The pre-compensated damped current component is formed by the dominant oscillation mode.

[0141] Thus, for any dominant oscillation mode, the system can generate multiple corresponding pre-compensated damped current components, and each energy storage unit has an independent pre-compensated phase. Therefore, even if multiple energy storage units participate in the suppression process of the same dominant oscillation mode at the same time, their output waveforms can automatically adapt to the electrical propagation characteristics of their respective locations.

[0142] Furthermore, by repeating the above process for all N dominant oscillation modes, the system will obtain multiple sets of pre-compensated damping current components corresponding to each energy storage unit. These pre-compensated damping current components correspond to different oscillation frequencies, different oscillation phases, and different electrical propagation paths, which essentially constitute a fractionalized damping current library for multimode oscillation.

[0143] The subsequent steps will call the damping current amplitude weighting coefficients calculated in the third step, perform amplitude weighting and linear superposition on these pre-compensated damping current components, thereby forming a unique composite damping current command for the final output of each energy storage unit, and realizing synchronous active damping control of multiple dominant oscillation modes.

[0144] Step 5: Linearly superimpose all pre-compensated damping current components corresponding to each energy storage unit according to their respective damping current amplitude weighting coefficients to generate a unique composite damping current command for each energy storage unit, and simultaneously send the unique composite damping current command and overshoot compensation power to the corresponding energy storage unit. After completing Step 1, the system has identified multiple dominant oscillation modes in the contact network voltage and obtained the instantaneous frequency, instantaneous amplitude, and instantaneous phase corresponding to each dominant oscillation mode; after completing Step 2, the system has calculated the oscillation energy proportion of each dominant oscillation mode and established a mode priority queue; after completing Step 3, the system has calculated the corresponding damping current amplitude weighting coefficient for each energy storage unit for each dominant oscillation mode based on the oscillation energy proportion and the real-time remaining capacity of the energy storage unit; after completing Step 4, the system has generated an anti-phase damping current reference waveform for each dominant oscillation mode and formed the corresponding pre-compensated damping current component by combining the electrical distance between each energy storage unit and the oscillation source.

[0145] At this point, each energy storage unit has acquired multiple sets of pre-compensated damped current components. These pre-compensated damped current components correspond to different dominant oscillation modes, and each component has an independent oscillation frequency, an independent phase compensation amount, and an independent damping target.

[0146] However, the energy storage converter can only receive one set of continuously output current control commands and cannot simultaneously and independently execute multiple sets of separate damped current waveforms. Therefore, it is necessary to integrate multiple pre-compensated damped current components constructed for different dominant oscillation modes into a unified control command, so that the energy storage unit can participate in the suppression process of multiple oscillation modes simultaneously through a single current injection.

[0147] The core task of this step is to maintain the independence of the damping effect of each dominant oscillation mode, and to weight and fuse multiple pre-compensated damping current components according to their importance to form a unique composite damping current command that can simultaneously cover all dominant oscillation modes.

[0148] For the For each energy storage unit, after the fourth step, the pre-compensated damping current components corresponding to all N dominant oscillation modes have been obtained.

[0149] Let the first The energy storage unit is for the first The pre-compensated damping current components formed by the dominant oscillation modes are expressed as follows: The pre-compensated damping current component already contains the instantaneous frequency information, phase reversal information, and electrical distance compensation information corresponding to the dominant oscillation mode, and therefore can accurately act on the corresponding oscillation mode.

[0150] Meanwhile, the third step has already obtained the first... The energy storage unit is for the first The damping current amplitude weighting coefficient corresponding to each dominant oscillation mode The damping current amplitude weighting coefficient reflects two aspects of information.

[0151] On the one hand, it reflects the first The contribution of the dominant oscillation mode to the total oscillation energy, on the other hand, reflects the degree of contribution of the first dominant oscillation mode to the total oscillation energy. The weighting coefficient represents the capacity of each energy storage unit within the total energy storage resources. Therefore, it essentially describes how much damping resources should be allocated to the corresponding dominant oscillation mode for each energy storage unit.

[0152] The system first performs weighted processing on the pre-compensated damping current component.

[0153] For the The pre-compensated damped current components corresponding to each dominant oscillation mode are adjusted in amplitude using the corresponding damped current amplitude weighting coefficients to obtain the weighted damped current components:

[0154]

[0155] in, Indicates the first The energy storage unit is for the first The weighted damped current components corresponding to each dominant oscillation mode.

[0156] After this processing, the damping current components corresponding to different dominant oscillation modes will automatically acquire different amplitude levels. For dominant oscillation modes with a higher proportion of oscillation energy, the corresponding weighting coefficient is larger, resulting in a larger amplitude of the weighted damping current component. For dominant oscillation modes with a lower proportion of oscillation energy, the corresponding weighting coefficient is smaller, resulting in a relatively smaller amplitude of the weighted damping current component.

[0157] At the same time, energy storage units with larger remaining capacity will have a higher capacity allocation coefficient, and their corresponding weighted damping current components will also have a greater output capacity, thus realizing the joint regulation of the oscillation demand side and the energy storage supply side.

[0158] After all weighting processes are completed, the system begins to perform damping current fusion.

[0159] For the Each energy storage unit algebraically adds the weighted damped current components corresponding to all dominant oscillation modes:

[0160]

[0161] in, Indicates the first The single composite damping current command ultimately generated by each energy storage unit.

[0162] This unique composite damping current command is essentially a linear superposition of multiple damping current components of different frequencies. These components include damping components for low-frequency power oscillations, mid-frequency harmonic oscillations, and other dominant oscillation modes. Since each damping current component has already undergone independent phase pre-compensation in the fourth step, it retains its ability to target its respective oscillation mode after superposition. In other words, although the energy storage unit ultimately outputs only a single composite current waveform, this waveform actually carries multiple frequency components, each corresponding to a different oscillation mode suppression task. This achieves the transformation from traditional single-frequency active damping to multi-mode collaborative active damping.

[0163] When the composite damping current is injected into the traction network, different frequency components will interact in opposite phase with the target oscillation mode within their respective frequency bands, thereby synchronously absorbing the oscillation energy of multiple oscillation modes. After generating the unique composite damping current command, the system further executes and synchronously encapsulates control commands. Since this invention not only employs an active damping strategy to suppress oscillations but also an overshoot compensation strategy to improve the contact network voltage recovery speed, the energy storage unit needs to receive two types of control information simultaneously. The unique composite damping current command is responsible for oscillation suppression, while the overshoot compensation power command is responsible for voltage recovery.

[0164] If the two types of control commands are transmitted independently, the communication delay difference may cause the two control actions to be out of sync, thus affecting the overall control effect. Therefore, the system encapsulates the unique composite damping current command and the pre-calculated overshoot compensation power command into the same control data frame. This control data frame contains at least the energy storage unit identification information, the unique composite damping current command, the overshoot compensation power command, and the time synchronization mark information. After encapsulation, the control center sends the command to the corresponding energy storage unit through the industrial real-time Ethernet. The industrial real-time Ethernet has deterministic latency characteristics and high-precision synchronization capabilities, which can ensure that multiple energy storage units receive control commands simultaneously under a unified time reference.

[0165] Upon receiving the control data frame, each energy storage unit immediately parses the unique composite damping current command and overshoot compensation power command. The energy storage converter generates the corresponding current output according to the unique composite damping current command, and simultaneously performs power regulation according to the overshoot compensation power command. In this way, during the contact network voltage recovery process, the energy storage unit, on the one hand, quickly fills the energy deficit through overshoot compensation, driving the contact network voltage to recover rapidly; on the other hand, it continuously absorbs the oscillation energy of multiple dominant oscillation modes through the unique composite damping current, suppressing the oscillation phenomenon that may occur during the voltage recovery process.

[0166] After this step, the system completes the conversion from multimodal oscillation identification results to actual control commands. The pre-compensated damping current components corresponding to multiple dominant oscillation modes are unified and merged into a single composite damping current command, which is simultaneously issued to each energy storage unit along with the overshoot compensation power command. This enables the energy storage unit to simultaneously achieve voltage recovery and multimodal oscillation suppression within one control cycle, providing a direct control basis for subsequent online adaptive optimization.

[0167] Step 6: During the injection of composite damping current into the energy storage units, the residual oscillation energy of each dominant oscillation mode is monitored in real time. A recursive least squares method with a forgetting factor is used to simultaneously update the damping current amplitude weighting coefficient and phase pre-compensation amount for each energy storage unit online. After completing steps 1 to 5, the system has completed dominant oscillation mode identification, oscillation energy assessment, damping resource allocation, pre-compensation damping current construction, and unique composite damping current command generation. At this point, each energy storage unit is continuously injecting composite damping current into the traction network according to the corresponding control command and synchronously executing overshoot compensation power output.

[0168] However, the traction power supply system is essentially a continuously changing dynamic system. The locomotive's operating state is constantly changing, the regenerative braking power is constantly fluctuating, and the load distribution in different power supply sections is also constantly adjusting. Therefore, the dominant oscillation mode parameters obtained in the first step, the damping current amplitude weighting coefficient obtained in the third step, and the phase pre-compensation amount obtained in the fourth step all only reflect the optimal state at a certain moment.

[0169] As the system's operating status changes, the original parameter configuration may gradually deviate from the actual requirements.

[0170] For example, a dominant oscillation mode may occupy the main oscillation energy in the initial stage, but its energy decreases rapidly after damping control, while another oscillation mode gradually becomes the main source of oscillation; or, for example, due to the redistribution of traction load, the oscillation propagation path changes, and the original phase pre-compensation amount can no longer accurately offset the phase shift caused by line propagation.

[0171] If fixed parameter control is continued, the active damping effect will gradually decrease.

[0172] Therefore, this step introduces an online adaptive optimization mechanism during the active damping process. By continuously monitoring the oscillation suppression effect, the damping current amplitude weighting coefficient and phase pre-compensation amount are dynamically adjusted so that the control parameters always track the changes in the current system state.

[0173] At the start of this step, the system continues to output the unique composite damping current command generated in step five.

[0174] During the output process, a cyclic monitoring cycle is established at fixed time intervals. At each monitoring cycle, the system re-acquires the current contact network voltage timing signal and re-executes empirical mode decomposition and Hilbert analysis according to the Hilbert-Huang transform process in the first step. Through this process, the system can extract the instantaneous amplitude information of all dominant oscillation modes at the current moment.

[0175] Subsequently, the oscillation energy calculation method in the second step is used to recalculate the oscillation energy within the current time window for each dominant oscillation mode. Since active damping has already started to take effect at this time, the recalculated oscillation energy is no longer the original oscillation energy, but the remaining oscillation energy after damping control.

[0176] Let the first The residual oscillation energy corresponding to the current moment of each dominant oscillation mode is expressed as: ,in, Indicates the first The residual oscillation energy of each dominant oscillation mode still exists in the system after active damping.

[0177] The smaller the residual oscillation energy, the closer the current control parameter configuration is to the optimal state.

[0178] The greater the residual oscillation energy, the more room there is for optimization of the current control effect.

[0179] The system uses the residual oscillation energy corresponding to each dominant oscillation mode as the evaluation index of the current control cycle, and uses it as the target variable in the subsequent parameter optimization process.

[0180] For each energy storage unit, there are two types of important parameters that directly affect the damping effect in the current control process. The first type of parameter is the damping current amplitude weighting coefficient generated in the third step, which determines how much damping resources the energy storage unit allocates to each dominant oscillation mode. The second type of parameter is the phase pre-compensation amount generated in the fourth step, which determines whether the damping current can maintain the optimal anti-phase state after reaching the oscillation region.

[0181] Therefore, the system uses the current damping current amplitude weighting coefficient and the phase pre-compensation amount together to form the parameter vector to be optimized.

[0182] For the For an energy storage unit, the vector of parameters to be optimized can be represented as follows:

[0183]

[0184] The first half represents the set of damping current amplitude weighting coefficients, and the second half represents the set of phase pre-compensation quantities.

[0185] After establishing the parameter vector to be optimized, the system uses recursive least squares method with forgetting factor to construct an online optimization model.

[0186] The recursive least squares method with a forgetting factor is employed because this algorithm maintains strong tracking capabilities in environments with continuously changing parameters. Traditional least squares assigns equal weight to all historical data; as time progresses, older data has an increasing influence on the results, potentially leading to slow model response. In contrast, the recursive least squares method with a forgetting factor gradually reduces the importance of historical data, allowing the model to focus more on the latest operating state. Therefore, when traction load changes or oscillation modes shift, the system can adjust parameters more quickly.

[0187] The system constructs a cost function based on the currently measured residual oscillation energy. The cost function is used to measure the difference between the current control parameters and the ideal control state, and its optimization objective is to minimize the residual oscillation energy as much as possible.

[0188] The cost function can be expressed as:

[0189]

[0190] in, This represents the cost function value at the current moment. Indicates the forgetting factor, Indicates the first The oscillation energy error corresponding to each monitoring cycle.

[0191] Oscillation energy error reflects the deviation between the current control effect and the ideal control effect. When the residual oscillation energy is large, the error increases and the cost function value increases; when the residual oscillation energy gradually decreases, the error decreases and the cost function value decreases synchronously.

[0192] Due to the existence of the forgetting factor, data closer to the current moment has a higher weight, while the influence of earlier historical data gradually weakens. This ensures that parameter adjustments are always made around the current oscillation state.

[0193] The system then performs recursive iterative calculations. In each monitoring cycle, the system calculates the contribution of the current parameters to the oscillation suppression effect based on the latest obtained changes in residual oscillation energy.

[0194] If the residual oscillation energy corresponding to a dominant oscillation mode decreases slowly, it indicates that the current damping resource allocation is insufficient, and the system should appropriately increase the corresponding damping current amplitude weighting coefficient. If the residual oscillation energy corresponding to a dominant oscillation mode has been nearly eliminated, it indicates that the current damping resource investment is sufficient, and the system should appropriately reduce the corresponding damping current amplitude weighting coefficient to release more resources to other oscillation modes.

[0195] At the same time, the system analyzes the residual oscillation phase changes of each dominant oscillation mode. If a dominant oscillation mode still has significant residual energy, it indicates that there may be a phase deviation between the current damping current and the target oscillation. The system automatically corrects the corresponding phase pre-compensation amount according to the trend of residual oscillation energy changes, so that the damping current approaches the optimal anti-phase position again.

[0196] Through the above recursive optimization process, new damping current amplitude weighting coefficients and new phase pre-compensation quantities are continuously generated. The updated parameters immediately replace the original parameters in step five and re-participate in the construction process of the unique composite damping current command. Subsequently, the new unique composite damping current command is issued to the corresponding energy storage unit for continued execution. In the next monitoring cycle, the system measures the residual oscillation energy again and repeats the above optimization process.

[0197] As the loop continues, the damping current amplitude weighting coefficient gradually converges to the optimal resource allocation state, and the phase pre-compensation amount gradually converges to the optimal phase matching state. Correspondingly, the residual oscillation energy of each dominant oscillation mode continues to decrease, and the output value of the cost function also shows a gradual decreasing trend. When the parameters are updated and entered into the next round of control calculation, the residual oscillation energy obtained by the system is further reduced compared to the previous cycle, thus forming a continuously optimized closed-loop control process.

[0198] From the perspective of the overall operation logic, the first step is responsible for identifying the oscillation structure, the second step is responsible for evaluating the oscillation intensity, the third step is responsible for allocating damping resources, the fourth step is responsible for constructing the pre-compensated damping current, the fifth step is responsible for generating a unique composite damping current command, and this step is responsible for continuously correcting the key control parameters generated by the first three steps and the fourth step.

[0199] Through this online adaptive optimization mechanism, the system can maintain the optimal damping configuration even when the traction network's operating state is constantly changing, ensuring that the multimodal oscillation suppression process is always in a dynamically optimal state, thus creating stable conditions for the safe exit of the subsequent active damping mode.

[0200] Step 7: When the residual oscillation energy of all dominant oscillation modes is lower than the preset energy threshold and remains below it for a preset time window, control each energy storage unit to gradually reduce the amplitude of its unique composite damping current according to an S-curve until it reaches zero, thus exiting the active damping mode. After completing steps 1 to 6, the system has established a complete multi-mode active damping closed-loop control system. Step 1 completes the identification of dominant oscillation modes; step 2 completes the oscillation energy assessment and mode priority ranking; step 3 completes the allocation of damping resources; step 4 completes the construction of pre-compensated damping current; step 5 completes the generation of the unique composite damping current command; and step 6 completes the online adaptive optimization of damping parameters.

[0201] After continuous damping control, the oscillation energy corresponding to each dominant oscillation mode gradually decreases, and the system gradually recovers from the oscillation state to a stable operating state. If active damping mode continues to operate at this point, the energy storage unit will continuously output damping current, which not only increases energy consumption but may also cause unnecessary disturbances to the already stabilized power grid. Therefore, once the oscillations have been effectively suppressed, the active damping mode needs to be exited promptly.

[0202] However, the exit from active damping mode cannot be achieved simply by instantaneous disconnection. This is because the unique composite damping current command generated in the fifth step is essentially still a dynamic current waveform formed by the superposition of multiple frequency components. If the damping current is suddenly reduced to zero at a certain moment, it will cause a sudden change in the power exchange relationship in the traction network.

[0203] Such abrupt change may cause new voltage disturbances or even re-excite the suppressed oscillation mode, thereby weakening the previous control effect. Therefore, this step adopts a gradual exit mechanism, which implements smooth decay control on the unique composite damping current to make the active damping process smoothly transition from the working state to the exit state, thereby avoiding the generation of secondary disturbances.

[0204] At the start of this step, the system continues the online monitoring process from step six. At each time sampling point, the system re-acquires the current contact network voltage timing signal and calculates the residual oscillation energy corresponding to all dominant oscillation modes according to the methods in steps one and two.

[0205] Let the first The residual oscillation energy of each dominant oscillation mode at the current sampling time is: ,in, This indicates the current time sampling point. The system pre-sets a unified oscillation elimination criterion, namely a preset energy threshold. This threshold is used to characterize the state boundary where oscillations have been effectively suppressed. When the residual oscillation energy of a dominant oscillation mode is higher than this threshold, it indicates that the oscillation mode still has significant energy accumulation, and active damping control needs to continue. When the residual oscillation energy of a dominant oscillation mode is lower than this threshold, it indicates that the oscillation mode has entered a weak oscillation state.

[0206] However, the detection results of a single sampling point alone cannot directly determine that the oscillation has been completely eliminated, because changes in traction load, locomotive operating status switching, and measurement noise may cause the residual oscillation energy to fluctuate in a short period of time. If the active damping mode is exited based solely on the instantaneous results, misjudgment may occur. Therefore, the system further introduces a duration criterion.

[0207] The system continuously analyzes the residual oscillation energy changes corresponding to each dominant oscillation mode over a continuous time range. When each dominant oscillation mode satisfies the following conditions across P consecutive time sampling points:

[0208]

[0209] in, This indicates the preset energy threshold.

[0210] This indicates that all dominant oscillation modes have maintained a low energy state throughout the entire monitoring period, with no obvious energy rebound. Based on this, the system determines that the active damping target has been achieved and assumes that the preset time window meets the exit conditions. After the exit conditions are determined, the system does not immediately stop the output of the unique composite damping current, but instead initiates the gradual exit process of the damping current.

[0211] The system reads the unique composite damping current command corresponding to the current moment, and assumes that the amplitude of the current unique composite damping current command is... This amplitude corresponds to the actual output level before the active damping is deactivated. The system uses this amplitude as the starting amplitude of the attenuation process and sets zero as the target amplitude. Then, a continuous and smooth S-shaped curve is constructed as the amplitude attenuation trajectory of the damping current. This S-shaped curve has the following characteristics: In the initial stage of attenuation, the slope of the curve is small, and the damping current decreases slowly to avoid sudden changes in the power balance of the grid due to a sudden decrease in the output current; as time progresses, the curve enters the middle region, and the slope of the curve gradually increases, and the rate of decrease of the damping current increases, so that the deactivation process can be completed within a reasonable time; when the attenuation process is nearing its end, the slope of the curve decreases again, and the damping current approaches zero in a more gradual manner to avoid new dynamic shocks before final disconnection.

[0212] The entire S-curve maintains a continuous first derivative, meaning that the rate of change of current at any given time is continuous and there are no abrupt changes. Therefore, the entire exit process will not generate additional high-frequency disturbances. After obtaining the S-curve, the system calculates the attenuation coefficient based on the position corresponding to the current exit time. Let the attenuation coefficient be... The attenuation coefficient ranges from 1 to 0.

[0213] The system then uses an attenuation coefficient to scale the amplitude of the unique composite damping current command generated in the fifth step. Let the unit waveform corresponding to the unique composite damping current command be... The actual output current during the exit process is expressed as:

[0214]

[0215] In this design, the unit waveform remains unchanged, while only the amplitude is continuously reduced.

[0216] This approach is significant because the unique composite damping current command contains frequency components corresponding to multiple dominant oscillation modes. Therefore, keeping the unit waveform structure unchanged means that the relative proportions between the damping components at each frequency remain constant.

[0217] During the exit process, the multimodal damping capability decays synchronously, without some frequency components disappearing prematurely while others persist. This avoids new modal energy imbalances during the exit phase. Subsequently, each energy storage unit continuously adjusts its output current based on the real-time amplitude determined by the S-curve. As time progresses, the amplitude of the unique composite damping current gradually decreases, and correspondingly, the damping energy injected by the energy storage unit into the traction network also decreases synchronously. When the S-curve reaches its end, the attenuation coefficient drops to zero, and the actual output current amplitude is completely zero. After the current is zeroed, the system continues to perform the final exit operation.

[0218] The controller sends a power connection disconnection command to the corresponding energy storage unit. The energy storage converter stops its active damping control function and disconnects the power exchange channel with the traction network. At this point, the active damping mode is completely exited. It should be noted that the online monitoring mechanism established in step six remains operational throughout the entire exit process, and the system continuously monitors the changes in residual oscillation energy corresponding to each dominant oscillation mode.

[0219] If, during the S-curve decay process, the residual oscillation energy of a dominant oscillation mode is detected to rise again and exceed the preset energy threshold, the exit process is immediately terminated, and the active damping optimization process corresponding to step six is ​​re-entered. This forms an exit confirmation and abnormal rollback mechanism. Only when all dominant oscillation modes remain in a low energy state until the current is completely zero will the system finally complete the active damping mode exit.

[0220] After this step, the system achieves a smooth transition from active damping operation to normal operation. The unique composite damping current output by the energy storage unit gradually decays along a continuous S-shaped trajectory, avoiding current surges and power spikes during control exit, while ensuring the stable maintenance of multi-mode oscillation suppression results, thus completing the closed-loop termination of the entire overshoot compensation and active damping coordinated control process.

[0221] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for traction network voltage recovery and oscillation suppression using overshoot compensation and active damping, characterized in that, Includes the following steps: The first step is to perform Hilbert-Huang transform on the contact network voltage timing signal to extract the instantaneous frequency, instantaneous amplitude and instantaneous phase of each of the N dominant oscillation modes; The second step is to calculate the oscillation energy ratio of each dominant oscillation mode based on its instantaneous amplitude, and then sort the N dominant oscillation modes from high to low according to their oscillation energy ratios to generate a mode priority queue. The third step is to obtain the real-time remaining capacity of each energy storage unit along the line, and based on the real-time remaining capacity of each energy storage unit and the oscillation energy ratio of each dominant oscillation mode in the mode priority queue, calculate the damping current amplitude weighting coefficient corresponding to each energy storage unit for each dominant oscillation mode. The fourth step is to generate an anti-phase damping current reference waveform at the detection point that is out of phase with the dominant oscillation mode based on the instantaneous frequency and instantaneous phase of the dominant oscillation mode. Then, based on the electrical distance between the access point of each energy storage unit and the oscillation source, perform independent phase pre-compensation on the anti-phase damping current reference waveform to obtain the pre-compensated damping current component of the energy storage unit for the dominant oscillation mode. The fifth step is to linearly superimpose all the pre-compensated damping current components corresponding to each energy storage unit according to their respective damping current amplitude weighting coefficients to generate a unique composite damping current command for each energy storage unit, and then send the unique composite damping current command and overshoot compensation power to the corresponding energy storage unit simultaneously. The sixth step involves real-time monitoring of the residual oscillation energy of each dominant oscillation mode during the injection of composite damping current into the energy storage unit. A recursive least squares method with a forgetting factor is used to simultaneously update the damping current amplitude weighting coefficient and phase pre-compensation amount corresponding to each energy storage unit online. Step 7: When the residual oscillation energy of all dominant oscillation modes is lower than the preset energy threshold and continues for a preset time window, control each energy storage unit to gradually reduce the amplitude of its unique composite damping current according to the S-curve until it reaches zero, and exit the active damping mode.

2. The method for traction network voltage recovery and oscillation suppression with overshoot compensation and active damping according to claim 1, characterized in that, in the first step... include: Empirical mode decomposition is performed on the contact network voltage timing signal to obtain a set of intrinsic mode function components; Perform a Hilbert transform on each intrinsic mode function component and calculate the instantaneous amplitude function and instantaneous frequency function of that intrinsic mode function component; The intrinsic mode function components whose time average of instantaneous amplitude function is greater than a preset amplitude threshold are identified as dominant oscillation modes. The intrinsic mode function component with the largest time average of instantaneous amplitude function is marked as the first dominant oscillation mode, and the rest are marked as the second dominant oscillation mode to the Nth dominant oscillation mode in descending order of the time average of instantaneous amplitude function. Extract the instantaneous frequency function of each dominant oscillation mode at the current time as the instantaneous frequency of that dominant oscillation mode, extract the instantaneous amplitude function of each dominant oscillation mode at the current time as the instantaneous amplitude of that dominant oscillation mode, and extract the phase angle of the analytic signal of each dominant oscillation mode after Hilbert transform at the current time as the instantaneous phase of that dominant oscillation mode.

3. The method for traction network voltage recovery and oscillation suppression based on overshoot compensation and active damping according to claim 1, characterized in that, The second step includes: The oscillation energy of the dominant oscillation mode is calculated by integrating the instantaneous amplitude of each dominant oscillation mode over a preset time window. The oscillation energy of each dominant oscillation mode is divided by the sum of the oscillation energies of all N dominant oscillation modes to calculate the proportion of oscillation energy of that dominant oscillation mode. The first dominant oscillation mode to the Nth dominant oscillation mode are arranged in descending order of oscillation energy percentage, and the resulting sequence is used as the mode priority queue.

4. The method for traction network voltage recovery and oscillation suppression based on overshoot compensation and active damping according to claim 1, characterized in that, The third step includes: The capacity allocation coefficient of an energy storage unit is calculated by dividing the real-time remaining capacity of each energy storage unit by the sum of the real-time remaining capacities of all energy storage units. The damping current amplitude weighting coefficient of the energy storage unit for the i-th dominant oscillation mode is calculated by multiplying the oscillation energy ratio of the i-th dominant oscillation mode in the mode priority queue by the capacity allocation coefficient of the energy storage unit, and then multiplying by the preset upper limit of the total damping current amplitude.

5. The traction network voltage recovery and oscillation suppression method based on overshoot compensation and active damping according to claim 1, characterized in that, The fourth step includes: For the i-th dominant oscillation mode, a sine function is constructed. The angular frequency of the sine function is 2π times the instantaneous frequency of the dominant oscillation mode, and the initial phase of the sine function is the instantaneous phase of the dominant oscillation mode plus π radians. An anti-phase damping current reference waveform that is opposite to the dominant oscillation mode at the detection point is generated. Measure the line impedance between each energy storage unit access point and the oscillation source, and extract the impedance angle of the line impedance as the electrical distance parameter; The initial phase of the anti-phase damped current reference waveform is added to the impedance angle to calculate the initial phase after phase pre-compensation. The sine function is then reconstructed using the initial phase after phase pre-compensation. The pre-compensated damped current component value of the energy storage unit for the dominant oscillation mode is marked as an effective mapping mark to establish a cross-scale spatial correspondence between adjacent decomposition scales at the same geological boundary location.

6. The method for traction network voltage recovery and oscillation suppression based on overshoot compensation and active damping according to claim 1, characterized in that, The fifth step includes: For each energy storage unit, the pre-compensated damping current component of the i-th dominant oscillation mode corresponding to the energy storage unit is multiplied by the damping current amplitude weighting coefficient of the energy storage unit for the i-th dominant oscillation mode to obtain the weighted damping current component. The unique composite damping current command of the energy storage unit is calculated by algebraically summing all the weighted damping current components of i from 1 to N. The unique composite damping current command and the pre-calculated overshoot compensation power command are encapsulated into the same control data frame and synchronously sent to the energy storage unit via industrial real-time Ethernet.

7. The method for traction network voltage recovery and oscillation suppression based on overshoot compensation and active damping according to claim 1, characterized in that, Step six includes: During the process of injecting a unique composite damping current command into each energy storage unit, the residual oscillation energy of each dominant oscillation mode is re-extracted at fixed time intervals, and the residual oscillation energy is used as the desired output value. Using the damping current amplitude weighting coefficient and phase pre-compensation amount at the current moment as the parameters to be optimized, a cost function is constructed using the recursive least squares method with a forgetting factor. The minimization objective of the cost function is the weighted sum of the squared errors between the expected output value and the residual oscillation energy measured after actual injection. Through recursive iterative calculation, the damping current amplitude weighting coefficient and phase pre-compensation amount corresponding to each energy storage unit are updated simultaneously, so that the output value of the cost function decreases after the updated parameters are substituted into the next iteration.

8. The method for traction network voltage recovery and oscillation suppression based on overshoot compensation and active damping according to claim 1, characterized in that, Step seven includes: At each time sampling point, the real-time value of the residual oscillation energy of all dominant oscillation modes is calculated. When the residual oscillation energy of each dominant oscillation mode is lower than the preset energy threshold in P consecutive time sampling points, it is determined that the preset time window meets the condition. Using the amplitude of the unique composite damping current command at the current moment as the starting amplitude and zero as the target amplitude, an S-shaped curve is constructed as the amplitude decay trajectory. The slope of the midpoint of the S-shaped curve is greater than the slope of the starting point and the slope of the ending point, and the first derivative of the S-shaped curve is continuous. The amplitude of each energy storage unit is multiplied by the unit waveform of the unique composite damping current command at each time point determined by the S-curve, and the actual injected current amplitude is gradually reduced until it is zero. Then the power connection between the energy storage unit and the traction network is disconnected, and the operation of exiting the active damping mode is completed.

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