Sensorless Flying Start Control Method for CAES High-Voltage Inverter

Abstract

The present invention discloses a sensorless coasting start control method for a CAES high-voltage frequency converter, including: collecting the output voltage and stator current data of the frequency converter; performing harmonic analysis on the normalized data, and identifying the position estimation dead zone through sensitivity evaluation; designing an orthogonal phase modulation sequence for the dead zone; applying the modulation sequence to generate a harmonic interference pattern; calculating the harmonic response differential fingerprint and extracting enhanced position features; simultaneously predicting and compensating the torque fluctuation during the modulation process to ensure system stability; achieving a smooth coasting start based on the accurate position. The position estimation dead zone problem is solved through the phase interference principle, and the position accuracy is improved to ±3.5°, significantly enhancing the start reliability.

Description

Technical Field

[0001] The present invention relates to power electronics technology, especially a sensorless coasting start control method for a CAES high-voltage frequency converter. Background Art

[0002] As an efficient large-scale energy storage solution, the compressed air energy storage (CAES) system plays an increasingly important role in renewable energy grid connection and power grid peak shaving. The control of the high-voltage frequency converter in the CAES system is the key to the operation efficiency and reliability of the whole system, and the coasting start process (referring to the control access when the motor is in a free rotation state) is particularly crucial. The sensorless control technology estimates the rotor position information, eliminates the expensive position sensor, reduces the system cost and complexity, and improves the system robustness. Therefore, it has a wide application prospect in the CAES high-voltage frequency converter system.

[0003] Currently, in the field of sensorless control, methods such as high-frequency signal injection method, model reference adaptive system (MRAS), and open-loop observer are mainly adopted. The high-frequency signal injection method injects high-frequency small signals on the stator side of the motor and uses the difference in motor impedance at different rotor positions to estimate the position information. The MRAS method performs parameter adaptation based on the error between the reference model and the adjustable model, and gradually approaches the actual rotor position. The open-loop observer uses the stator voltage and current information to deduce and calculate the rotor position through the motor mathematical model. In addition, there are also position estimation methods based on extended Kalman filter (EKF), sliding mode observer, and artificial intelligence. These methods have achieved certain application results under normal working conditions.

[0004] In summary, in the coasting start process of the CAES high-voltage frequency converter, the existing methods face severe challenges, such as the position estimation dead zone problem. In high-voltage and high-power scenarios, due to the magnetic field saturation effect and spatial harmonic distortion, the motor will show a state of fuzzy harmonic characteristics at some specific rotor positions (usually near the pole transition region), resulting in almost the same harmonic characteristics corresponding to different rotor positions, and the traditional methods cannot distinguish. In these dead zones, the position estimation error can reach ±25° electrical angle, seriously affecting the current control quality during the start process, causing overcurrent protection, torque shock, and even start failure. Summary of the Invention

[0005] The object of the invention is to provide a sensorless coasting start control method for a CAES high-voltage frequency converter, in order to solve at least one technical problem existing in the prior art.

[0006] Technical solution: A sensorless coasting start control method for a CAES high-voltage frequency converter includes:

[0007] Collect the output voltage data and stator current data of the frequency converter and filter them to obtain the filtered system data;

[0008] Perform harmonic analysis on the filtered system data, identify the position estimation dead zone interval and analyze its characteristics. Based on this, design a phase modulation sequence and apply it to generate a harmonic interference pattern. The system responds to the harmonic interference pattern to obtain a harmonic response data set;

[0009] Based on the harmonic response data set, construct a harmonic difference fingerprint, extract position features, and obtain the accurate rotor position;

[0010] Calculate the torque compensation amount according to the phase modulation sequence and the mechanical characteristics of the system, and generate an optimized control current;

[0011] Based on the accurate rotor position and the optimized control current, generate a control signal and send it down.

[0012] According to one aspect of the present application, the steps of obtaining the accurate rotor position include:

[0013] Perform harmonic analysis on the filtered system data, extract harmonic amplitude and phase information, and form a basic harmonic feature matrix;

[0014] Calculate the feature gradient data based on the basic harmonic feature matrix and compare it with a threshold value to identify the position estimation dead zone interval;

[0015] According to the characteristics of the position estimation dead zone interval, design multiple groups of orthogonal phase modulation sequences to form a phase modulation sequence matrix;

[0016] Apply the phase modulation sequence to the frequency converter control system in sequence, and collect multiple groups of harmonic response data sets;

[0017] Based on multiple groups of harmonic response data sets, calculate the difference between harmonic responses, and construct a harmonic difference fingerprint matrix;

[0018] Extract key features from the harmonic difference fingerprint matrix, and determine the accurate rotor position through feature matching.

[0019] According to one aspect of the present application, the steps of estimating the dead zone interval include:

[0020] Calculate the change rate of different harmonic components between adjacent rotor positions for the basic harmonic feature matrix, obtain a single-point harmonic sensitivity matrix and apply a sliding window average to it to eliminate the influence of local fluctuations, and obtain a smoothed harmonic sensitivity matrix;

[0021] Based on the importance weights of each harmonic component in the smoothed harmonic sensitivity matrix, calculate the weighted harmonic sensitivity and analyze its statistical distribution characteristics, and calculate an adaptive dead zone determination threshold according to the statistical distribution characteristics;

[0022] Compare the weighted harmonic sensitivity with the dead zone determination threshold, mark the position points below the threshold, and merge adjacent low-sensitivity points through connected component analysis to obtain the position estimation dead zone interval.

[0023] According to one aspect of the present application, the steps of forming the phase modulation sequence matrix include:

[0024] Analyze the position estimation dead zone interval, extract the interval width, center position, and harmonic feature difference degree of the adjacent region, form a set of dead zone characteristic parameters, and construct multiple sets of mutually orthogonal basic modulation vector sets based on this;

[0025] Calculate the optimal modulation depth coefficient according to the set of dead zone characteristic parameters and the current operating state of the system;

[0026] Combine the basic modulation vector set with the modulation depth coefficient, predict the gain characteristics of different modulation combinations in the current dead zone, and generate an expected gain matrix;

[0027] Based on the expected gain matrix and the pre-stored modulation timing parameter set, select the highest gain combination to generate a complete phase modulation sequence matrix.

[0028] According to one aspect of the present application, the steps of constructing the harmonic difference fingerprint matrix include:

[0029] Perform normalization processing on multiple sets of harmonic response data sets, obtain a normalized harmonic response set, and select a reference response from it to obtain a reference harmonic response;

[0030] Calculate the difference between each set of normalized harmonic responses and the reference harmonic response, and construct a first-order difference matrix;

[0031] Calculate the difference between the first-order differences generated by different modulation sequences, and construct a second-order difference matrix;

[0032] Non-linearly amplify the phase difference of the harmonics to obtain an enhanced phase difference;

[0033] Combine the first-order difference matrix, the second-order difference matrix, and the enhanced phase difference according to specific weights to construct a complete harmonic difference fingerprint matrix.

[0034] According to one aspect of the present application, the steps of determining the exact rotor position include:

[0035] Perform dimensionality reduction processing on the harmonic difference fingerprint matrix, obtain a dimensionality-reduced difference fingerprint, and perform feature importance evaluation, select the feature with the highest score, and form a key feature vector;

[0036] Calculate the matching degree between the key feature vector and the pre-established difference fingerprint reference library, obtain a position matching degree vector, analyze its peak distribution, and process the multi-peak fuzzy region to obtain a corrected matching degree vector;

[0037] Extract the highest matching region of the corrected matching degree vector and perform interpolation to obtain an interpolated matching curve and determine its peak position, which is used as the accurate rotor position.

[0038] According to one aspect of the present application, the steps of forming the phase modulation sequence matrix include:

[0039] Extract the parameters in the position estimation dead zone interval to form a dead zone characteristic parameter set, which at least includes the interval width;

[0040] Calculate the optimal modulation depth coefficient according to the interval width, the current amplitude, and the estimated rotational speed;

[0041] In the three-dimensional modulation space, construct at least three groups of basic vectors that satisfy the orthogonality condition to form a basic modulation vector set;

[0042] Combine the basic modulation vector set with the modulation depth coefficient to simulate and predict the gain characteristics of each modulation combination, and generate an expected gain matrix;

[0043] Based on the expected gain matrix and the pre-stored modulation timing parameter set, select the highest gain combination to generate the phase modulation sequence matrix.

[0044] According to one aspect of the present application, the steps of constructing the harmonic difference fingerprint matrix include:

[0045] Perform amplitude normalization on multiple groups of harmonic response data sets respectively to obtain a normalized harmonic response set;

[0046] From the normalized harmonic response set, select the response or average response in the standard modulation state and the non-modulation state as the reference harmonic response;

[0047] Calculate the point-by-point difference between each group of normalized harmonic responses and the reference harmonic response to form a first-order difference matrix;

[0048] Calculate the cross difference between the first-order difference matrices under different modulation sequences to form a second-order difference matrix;

[0049] Amplify the harmonic phase change in the dead zone through an exponential function to generate an enhanced phase difference;

[0050] Set a fusion weight according to the contribution degree of the harmonic components to the position identification, and synthesize the first-order difference matrix, the second-order difference matrix, and the enhanced phase difference to construct the harmonic difference fingerprint matrix.

[0051] According to one aspect of the present application, the steps of generating the optimized control current include:

[0052] Based on the phase modulation sequence and the accurate rotor position, predict the theoretical torque fluctuation amount during the modulation process;

[0053] Design a torque compensation sequence based on the theoretical torque ripple and system inertia characteristics;

[0054] Convert the torque compensation sequence into compensation current components and superimpose them on the original control current to form an optimized control current.

[0055] According to one aspect of the present application, the steps of designing the torque compensation sequence include:

[0056] Construct a parametric electromagnetic torque model based on the accurate rotor position and system operating state parameters, and output a set of torque model parameters;

[0057] Analyze the influence of the phase modulation sequence on the stator current, decompose the modulation effect into d-axis and q-axis components, and form a modulation current component matrix;

[0058] Calculate the static torque influence matrix based on the set of torque model parameters and the modulation current component matrix;

[0059] Apply the system dynamic response model to the static torque influence matrix to predict the time trajectory of torque changes and obtain the dynamic torque response curve;

[0060] Consider the superposition effect of consecutive applications of multiple modulation sequences, calculate the comprehensive torque ripple trajectory, extract the key characteristics of torque ripple, form the theoretical torque ripple, and accordingly design the basic compensation waveform with the opposite phase and optimize the timing to obtain the optimized compensation waveform;

[0061] Perform amplitude limiting and smoothing processing on the optimized compensation waveform to generate the final torque compensation sequence.

[0062] Beneficial effects: Achieve a smooth start of a flying car based on accurate position. Solve the position estimation dead zone problem through the phase interference principle, improve the position accuracy to ±3.5°, and significantly enhance the start reliability. Description of the Drawings

[0063] Figure 1 is the overall flowchart of the present invention.

[0064] Figure 2 is the flowchart of the present invention for obtaining the accurate rotor position.

[0065] Figure 3 is the flowchart of the present invention for estimating the dead zone interval.

[0066] Figure 4 is the flowchart of the present invention for forming the phase modulation sequence matrix.

[0067] Figure 5 is the flowchart of the present invention for constructing the harmonic difference fingerprint matrix.

[0068] Figure 6This is the flow chart of the present invention for determining the exact rotor position through feature matching. Detailed implementation manners

[0069] According to one aspect of the present application, a sensorless coasting start control method for a CAES high-voltage frequency converter is provided, including:

[0070] S1. Collect the three-phase output voltage data, stator current data and DC bus voltage of the frequency converter, perform high-precision band-pass filtering on the collected data to remove electromagnetic interference and high-frequency noise, convert the filtered three-phase data to the αβ coordinate system through Clarke transformation, and then perform normalization processing according to the DC bus voltage data to obtain a normalized αβ coordinate system data set suitable for harmonic analysis.

[0071] S2. Perform sliding window FFT harmonic analysis on the normalized αβ coordinate system data, extract the key harmonic amplitude and phase information, calculate the sensitivity of the harmonic characteristics to the rotor position, and identify the position estimation dead zone interval where the traditional method fails; design multiple groups of orthogonal phase modulation sequences according to the characteristics of the dead zone interval, and short-time apply these sequences through the frequency converter control interface to generate a controllable harmonic interference pattern; calculate the first-order difference and second-order difference based on the harmonic responses under different modulation conditions, and construct a high-dimensional harmonic difference fingerprint matrix in combination with a nonlinear enhancement function; finally, determine the high-precision rotor position through feature dimensionality reduction, importance evaluation and fingerprint matching.

[0072] S3. Based on the exact rotor position and phase modulation sequence, establish a parameterized electromagnetic torque model, analyze the influence of the modulation sequence on the stator current, and predict the static and dynamic torque fluctuations generated during the modulation process; design a torque compensation sequence with an anti-phase characteristic, perform timing optimization, amplitude correction and limiter smoothing processing; convert the optimized torque compensation sequence into a current compensation instruction, and superimpose it on the original control current to effectively eliminate the system disturbance caused by the modulation process, achieve stable control, and at the same time, monitor the system vibration and speed fluctuation in real time, and adaptively adjust the modulation depth and compensation intensity to ensure the stable operation of the system.

[0073] S4. According to the exact rotor position and estimated speed, divide the coasting start process into three stages: initial capture, acceleration transition and steady speed regulation, and select the corresponding control strategy parameters for each stage; establish a rotating coordinate system based on the exact rotor position to achieve precise control of the magnetic field direction; combine the current control strategy parameters, dq coordinate system current and optimized control current, and generate the optimal PWM control signal through the space vector pulse width modulation algorithm; continuously monitor the system performance indicators during the start process, and dynamically optimize the control strategy parameters through the difference analysis with the target performance indicators to achieve a reliable and stable coasting start of the CAES high-voltage frequency converter.

[0074] Such as Figures 1 to 6As shown, a sensorless coasting start control method for a CAES high-voltage frequency converter is provided, including:

[0075] S1. Collect the output voltage data and stator current data of the frequency converter, perform preliminary filtering processing, and obtain the filtered system data.

[0076] S11. Through a high-precision sampling circuit, collect three-phase voltage data U_abc, three-phase current data I_abc, and DC bus voltage data U_dc, and add unified timestamp data to form an original sampling data set.

[0077] S12. Apply an adaptive band-pass filtering algorithm to the original sampling data set to filter out electromagnetic interference and high-frequency noise, and obtain filtered voltage data U_abc_f and filtered current data I_abc_f.

[0078] S13. Convert the filtered voltage data U_abc_f and filtered current data I_abc_f to the αβ coordinate system through Clarke transformation, obtain αβ coordinate system voltage data U αβ and αβ coordinate system current data I αβ , and then perform normalization processing according to the DC bus voltage data U_dc to obtain a normalized αβ coordinate system data set D αβ _norm.

[0079] S2. Perform harmonic analysis on the filtered system data, identify the position estimation dead zone interval, generate a harmonic interference pattern by designing and applying a phase modulation sequence, reconstruct the harmonic difference fingerprint, and finally obtain the accurate rotor position.

[0080] S21. Apply a sliding window fast Fourier transform to the normalized αβ coordinate system data set D αβ _norm to extract the harmonic amplitude vector A_h and the harmonic phase vector Φ_h, and combine them to form a basic harmonic feature matrix H base .

[0081] S22. Calculate the sensitivity of the main harmonic components in the basic harmonic feature matrix H base to the rotor position, generate a feature gradient vector G_h, and identify and mark the position estimation dead zone interval D_zones by comparing with a set sensitivity threshold λ_threshold.

[0082] The position estimation dead zone automatic recognition technology based on harmonic sensitivity analysis accurately identifies and locates the areas where traditional methods fail by quantitatively analyzing the mapping sensitivity between harmonic characteristics and rotor position. It avoids the assumption of uniform distribution of position identifiability implicit in traditional sensorless control and is specifically optimized for the non-uniform position identification ability caused by magnetic field disturbances in the CAES system. It can automatically identify the position estimation dead zone, and the average positioning error is less than 2° electrical angle, greatly improving the pertinence and effectiveness of the subsequent phase interference sequence design, reducing unnecessary waste of computing resources, and making the entire control system operate more efficiently.

[0083] S23. According to the characteristics of the position estimation dead zone interval D_zones, design N groups (N = 3 - 5) of orthogonal phase modulation sequence matrices PMS. Each group of sequences contains different modulation depths and phase distributions, and is used to generate differentiated harmonic interference patterns.

[0084] The orthogonal phase interference sequence design method based on dead zone characteristics generates interference patterns that can maximize the enhancement of position characteristics by creating multiple groups of orthogonal modulation basis vectors and optimizing the modulation depth according to the system state. Introducing the orthogonal signal design concept into motor control realizes the selective enhancement of different position characteristics. In the CAES high-voltage inverter system, this method increases the feature distinguishability in the position estimation dead zone by 5 - 8 times. At the same time, due to its orthogonal design characteristics, the interference between modulation sequences is minimized, the information gain is maximized, and the modulation time required for position estimation is shortened from 50 - 80 ms of traditional methods to 15 - 25 ms, significantly improving the response speed and real-time performance of the control system.

[0085] S24. Apply each group of sequences in the phase modulation sequence matrix PMS to the system through the frequency converter control interface for a short time (<10 ms), and simultaneously collect the corresponding harmonic response data set R_h_set, which contains the complete harmonic information under N different modulation conditions.

[0086] S25. Based on the harmonic response data set R_h_set, calculate the difference in harmonic responses between different modulation sequences, and construct a harmonic difference fingerprint matrix DF_h, which contains the amplified position feature difference information.

[0087] The multi-level differential fingerprint construction technology calculates the first-order and second-order differences of the harmonic responses under different modulation conditions, and applies a non-linear enhancement function to construct a high-dimensional feature space, amplifying the weak position differences into significant feature differences. It solves the limitations of directly using amplitude and phase in traditional harmonic analysis, eliminates the common system noise through differential operations, and amplifies the key features through non-linear enhancement. It is especially suitable for the case of severe magnetic field disturbances in the CAES system. Among the dead zone position points with an original similarity of over 95%, it creates differential features with a similarity of less than 30%, making the position points that were almost indistinguishable originally highly distinguishable, and fundamentally solving the dead zone problem of position estimation.

[0088] S26. Extract the main feature components from the harmonic differential fingerprint matrix DF_h, and match them with the pre-built differential fingerprint reference library DF ref for matching analysis, apply the weighted cosine similarity algorithm to calculate the matching degree, and determine the exact rotor position θ r .

[0089] Identify the position estimation dead zone through harmonic analysis, design and apply a phase modulation sequence, and generate a systematic method for differential fingerprints, enabling the system to accurately distinguish similar position points that cannot be distinguished by traditional methods. This method significantly changes the physical mechanism of position estimation, from "direct measurement" to the mode of "interference enhancement and then measurement". In the CAES high-voltage frequency converter with severe magnetic field disturbances, this method increases the position recognition rate of the dead zone area (about 15% of the entire electrical angular cycle) from 25% to over 95%, solving the blind area problem that has long troubled the sensorless control technology.

[0090] S3. Calculate and apply the torque compensation amount according to the phase modulation sequence and the mechanical characteristics of the system to eliminate the system fluctuations during the modulation process and ensure the system stability.

[0091] S31. Based on the phase modulation sequence matrix PMS and the current exact rotor position θ r , use the pre-calibrated torque influence model to calculate the theoretical torque fluctuation amount ΔT_theory during the modulation process.

[0092] S32. According to the theoretical torque fluctuation amount ΔT_theory and the system inertia characteristics, design the torque compensation sequence T_comp so that it forms an exact anti-phase cancellation effect with the torque fluctuation in terms of time and amplitude.

[0093] S33. Convert the torque compensation sequence T_comp into the corresponding compensation current component I_comp, and superimpose it on the original control current to form the optimized control current I_ctrl_opt, realizing the real-time compensation of torque fluctuations.

[0094] S34. The vibration data V_data and the rotational speed fluctuation data ω_var of the real-time monitoring system are monitored, the current system stability is evaluated, and the phase modulation depth parameter λ_mod and the compensation intensity coefficient K_comp are adaptively adjusted according to the stability index to ensure the stable operation of the system.

[0095] By accurately predicting the torque fluctuation during the phase modulation process and implementing active compensation, the problem of system perturbation that may be introduced by the phase interference enhancement method is effectively solved. The vibration and speed fluctuation that may occur during the modulation process are effectively prevented, enabling the CAES high-voltage frequency converter to operate smoothly during the overspeed start-up process, extending the service life of the equipment, and improving the system reliability.

[0096] S4. Based on the accurate rotor position and the system operating state, an optimal PWM control signal is generated to achieve a smooth overspeed start-up of the CAES high-voltage frequency converter.

[0097] S41. According to the accurate rotor position θ r and the estimated rotor speed ω r , the overspeed start-up process is divided into three stages: initial capture, acceleration transition, and constant speed regulation, and a corresponding control strategy parameter set P_ctrl is selected for each stage.

[0098] S42. Based on the accurate rotor position θ r , a rotating coordinate system (dq coordinate system) is established, and the current data I αβ in the αβ coordinate system is converted into the current I_dq in the dq coordinate system to achieve accurate control of the magnetic field direction.

[0099] S43. According to the current control strategy parameter set P_ctrl, the current I_dq in the dq coordinate system, and the optimized control current I_ctrl_opt, an optimal PWM control signal S pwm is generated through the space vector pulse width modulation (SVPWM) algorithm to control the power output of the frequency converter.

[0100] S44. Continuously monitor the system performance index set Perf (including start-up time, current impact, torque fluctuation, etc.) during the overspeed start-up process, and dynamically optimize the control strategy parameter set P_ctrl by comparing the difference with the target performance index Target perf to achieve adaptive optimization of the start-up process.

[0101] The sensorless overspeed start-up control method for the CAES high-voltage frequency converter based on the principle of phase interference enhancement generates a controllable harmonic interference pattern by actively modulating the motor control strategy, converts the position characteristics that cannot be distinguished by the traditional method into distinguishable differential fingerprints, and solves the position estimation dead zone problem in high-voltage and high-power scenarios.

[0102] According to one aspect of the present application, S22. Automatic identification of position estimation dead zone, specifically:

[0103] S221. Read the basic harmonic feature matrix H base , calculate the change rate of each harmonic component h (h = 1, 5, 7, 11, 13, etc.) at different rotor positions θ i and θ i +Δθ to obtain the single-point harmonic sensitivity matrix S_h point . The specific calculation formula is: S_h point (i, h) = |H base (i + 1, h) - H base (i, h)| / Δθ, where i represents the position index and h represents the harmonic component index. Δθ is the angular difference or angular increment between adjacent sampling points.

[0104] S222. Apply a moving window average with length L (L = 5 - 9) to each harmonic component of the single-point harmonic sensitivity matrix S_h point to eliminate the influence of local fluctuations and obtain the smoothed harmonic sensitivity matrix S_h_smooth. The calculation formula is: S_h_smooth(i, h) = (1 / L) * Σ(S_h point (i - j, h)), where j ranges from 0 to L - 1.

[0105] S223. Calculate the weighted harmonic sensitivity S_h weighted based on the importance weights W_h of each harmonic component in the smoothed harmonic sensitivity matrix S_h_smooth. The weight W_h is preset according to the average sensitivity of the harmonic in the normal region. The calculation formula is: S_h weighted (i) = Σ(W_h * S_h_smooth(i, h)), where W_h represents the importance weight of the h-th harmonic.

[0106] S224. Calculate its mean μ_S and standard deviation σ_S based on the statistical distribution characteristics of the weighted harmonic sensitivity S_h weighted , and set the adaptive threshold λ_threshold = μ_S - k*σ_S, where k is an adjustable parameter (usually taking 1.5 - 2.5). This threshold is dynamically adjusted according to the actual operating state of the system, and the dead zone determination threshold λ_threshold is output.

[0107] S225. Compare the weighted harmonic sensitivity S_h weighted with the dead zone determination threshold λ_threshold, and mark those that meet the condition S_h weighted(i) The position points where < λ_threshold are dead zone candidate points, and then perform connected component analysis to merge adjacent dead zone candidate points into continuous intervals, obtaining the position estimated dead zone intervals D_zones, which include the start angle θ_start, end angle θ_end, and center position θ_center of each dead zone.

[0108] By quantitatively analyzing the mapping sensitivity between harmonic characteristics and rotor position, this technique can automatically identify and accurately locate the regions where traditional sensorless control methods completely fail, with an average positioning error less than 2° electrical angle. It breaks through the "uniform distribution of position identifiability" assumption implicit in traditional sensorless control. Through the introduction of weighted harmonic sensitivity analysis and adaptive threshold determination, it is specifically optimized for the unique magnetic field disturbance problem in the CAES system. This technique not only significantly improves the pertinence and effectiveness of subsequent phase interference sequence design, reduces unnecessary waste of computing resources, but also provides key decision-making information for the system by identifying the accurate range and characteristics of the position estimated dead zone, enabling the entire control system to predict potential identification risk regions and take targeted measures in advance, thus achieving the efficient and stable operation of the control system in scenarios such as CAES high-voltage frequency converters with severe magnetic field disturbances and where traditional methods are prone to failure.

[0109] According to one aspect of the present application, S23. Phase interference sequence design, specifically:

[0110] S231. Read the position estimated dead zone intervals D_zones, extract key characteristic parameters for each dead zone interval, including the interval width W_zone, center position θ_center, and harmonic characteristic difference degree D_adjacent of adjacent regions, to form a dead zone characteristic parameter set Zone p arams.

[0111] S232. Based on the interval characteristics in the dead zone characteristic parameter set Zone p arams, design N groups (N = 3 - 5) of mutually orthogonal basic modulation forms to construct a basic modulation vector set B_mod. Orthogonality is ensured by verifying through the formula B_mod(i) • B_mod(j) = 0 (when i ≠ j), and each basis vector represents a unique phase modulation mode.

[0112] S233. According to the dead zone characteristic parameter set Zone pBased on the interval width W_zone in the arams and the current operating state of the system, the system state vector State_curr (including current magnitude, estimated speed, etc.), calculate the optimal modulation depth coefficient α_depth. This coefficient needs to balance the interference effect and system stability, and is calculated by the formula α_depth = f(W_zone, I_magnitude, ω_est), where f is a preset non-linear mapping function, and the output is the modulation depth coefficient α_depth.

[0113] S234. According to the mechanical and electrical time constants T_mech and T_elec of the system, design the optimal modulation timing, including the single modulation duration T_mod, sampling delay T_delay, and continuous modulation interval T i nterval, and output the modulation timing parameter set T p arams. These parameters satisfy the constraint conditions: T_mod << T_mech (ensuring that the mechanical system does not respond) and T_mod > 3*T_elec (ensuring that the electrical system fully responds).

[0114] S235. Combine the basic modulation vector set B_mod with the modulation depth coefficient α_depth, predict the gain characteristics of different modulation combinations in the current dead zone, and calculate the expected gain matrix G_exp through the simulation model. This matrix represents the improvement degree of each modulation method on the dead zone position identification ability.

[0115] S236. Based on the expected gain matrix G_exp and the modulation timing parameter set T p arams, optimize and select the highest gain combination to generate the complete phase modulation sequence matrix PMS. This matrix contains N groups of modulation sequences, and each group of sequences contains complete information such as modulation type, depth, duration, and application time, expressed as PMS = {PMS1, PMS2,..., PMS_N}, where each PMS i is a complete modulation scheme.

[0116] By creating multiple sets of orthogonal modulation basis vectors and dynamically optimizing the modulation depth according to the current state of the system, a differential interference pattern that can maximize the enhancement of position features is generated. The orthogonal signal design technology introduces the concept of orthogonal basis in the field of signal processing into motor control, realizing the selective enhancement of different position features. In the CAES high-voltage frequency converter system, the feature recognition rate within the position estimation dead zone is increased by 5-8 times. At the same time, due to its orthogonal design characteristics, the interference between modulation sequences is minimized, the information gain is maximized, and the modulation time required for position estimation is shortened from 50-80 ms of the traditional method to 15-25 ms. The system response delay is significantly shortened, the control real-time performance is improved, enabling the frequency converter to capture the rotor position faster and establish effective control, thereby reducing the current peak and torque impact during the starting process, extending the equipment life, and improving the starting reliability and operation stability of the entire system. At the same time, the disturbance to the system is reduced, and the adaptability and robustness of the entire control system are improved.

[0117] According to one aspect of the present application, S25. Harmonic differential fingerprint construction, specifically:

[0118] S251. Read the harmonic response data set R_h_set, perform normalization processing on each set of data to eliminate the influence of the basic amplitude difference, and obtain the normalized harmonic response set R_h_norm. The normalization formula is: R_h_norm(i,j) = R_h_set(i,j) / max(|R_h_set(:,j)|), where i is the harmonic index and j is the modulation sequence index.

[0119] S252. From the normalized harmonic response set R_h_norm, select the harmonic response in the unmodulated state (or standard modulation state) as the reference, denoted as the reference harmonic response R_h base . If there is no clear reference state, calculate the average value of all responses as the reference: R_h base = (1 / N) * Σ(R_h_norm(:,j)), where j ranges from 1 to N.

[0120] S253. Calculate the difference between each set of normalized harmonic responses and the reference response, and construct the first-order difference matrix D1_h. The calculation formula is: D1_h(:,j) = R_h_norm(:,j) - R_h base , generating N sets of first-order difference features.

[0121] S254. Calculate the differences between the first-order differences generated by different modulation sequences, and construct the second-order difference matrix D2_h. The calculation formula is: D2_h(j,k) = D1_h(:,j) - D1_h(:,k), where j and k are the indices of different modulation sequences, satisfying j≠k, and generate N*(N - 1) / 2 second-order difference features.

[0122] S255. For the phase information of harmonics, especially the feature that the phase change is not obvious in the dead zone interval, apply the non-linear enhancement function F_enh to amplify the tiny phase differences and obtain the enhanced phase difference E p hase. The calculation formula is: E p hase = F_enh(phase(D2_h)), where F_enh is a user-defined non-linear enhancement function, for example, F_enh(x) = sign(x)*|x|^p, and p is the enhancement coefficient (usually taking values from 1.5 to 2.5).

[0123] S256. Combine the first-order difference matrix D1_h, the second-order difference matrix D2_h, and the enhanced phase difference E p hase according to specific weights W1, W2, and W p to construct the complete harmonic difference fingerprint matrix DF_h. The fusion formula is: DF_h = [W1D1_h, W2D2_h, W p *E p hase], forming a high-dimensional feature space, where different dimensions represent different types of response differences.

[0124] By calculating the first-order and second-order differences of harmonic responses under different modulation conditions and applying a non-linear enhancement function, a high-dimensional feature space is constructed, which amplifies the weak position differences into significant feature differences. It solves the limitations of directly using amplitude and phase in traditional harmonic analysis. The common system noise is eliminated through the difference operation, and the key features are amplified through non-linear enhancement, which is especially suitable for the working conditions with severe magnetic field disturbances in the CAES system. It changes the position recognition from "direct measurement" to the mode of "interference enhancement and re-measurement". Among the dead zone position points with a similarity of over 95% originally, differential features with a similarity of less than 30% are created. In practical applications, the position recognition rate in the dead zone area (accounting for about 15% of the entire electrical angle cycle) is increased from 25% to over 95%, completely solving the "blind zone problem" that has long troubled the sensorless control technology. The system can establish effective control at any rotor position, eliminating the "jamming" risk during the startup process and greatly improving the system reliability and startup success rate.

[0125] According to one aspect of the present application, S254 can also be:

[0126] Calculate the differences between the first-order differences generated by different modulation sequences, and construct the second-order difference matrix D2_h. For each pair of different modulation sequence indices i and j (where i ≠ j) and each harmonic component h, calculate D2_h(i,j,h) = D1_h(h,i) - D1_h(h,j) to form a three-dimensional second-order difference matrix. The first and second dimensions of this matrix represent the modulation sequence indices participating in the difference calculation, and the third dimension represents the harmonic component index, generating a total of N*(N - 1) / 2*H second-order difference features (where N is the number of modulation sequences and H is the number of harmonic components).

[0127] Through a systematic method of harmonic response normalization, phase-sensitive feature enhancement, and multi-dimensional fusion, the construction of highly distinguishable differential fingerprints is achieved. Not only the harmonic amplitude information is extracted, but also the processing of phase information is particularly strengthened. The small position feature differences caused by magnetic field disturbances in the CAES system are amplified through a non-linear enhancement function. At the position points where the traditional method completely fails (such as the pole transition region), the position estimation accuracy is improved from unestimable to within ±5°, solving the problem of reliable position identification during the coasting start process of the CAES high-voltage frequency converter.

[0128] According to one aspect of the present application, S26. Enhance position feature extraction and accurate estimation, specifically:

[0129] S261. Read the harmonic differential fingerprint matrix DF_h, apply principal component analysis (PCA) for dimensionality reduction, and retain the principal components with an explained variance ratio of up to 95% to obtain the dimensionality-reduced differential fingerprint DF reduced This step reduces the redundant dimensions of the feature space and improves the subsequent matching efficiency.

[0130] S262. Apply a feature importance evaluation algorithm to the dimensionality-reduced differential fingerprint DF reduced such as feature scoring based on the Fisher discriminant ratio, and select the top K features with the highest scores (K is usually taken as 10 - 20) to form the key feature vector KF vector These features are the most effective indicators for distinguishing different rotor positions.

[0131] S263. Calculate the matching degree between the key feature vector KF vector and each position sample in the pre-established differential fingerprint reference library DF ref to obtain the position matching degree vector M degree The matching degree calculation uses the weighted cosine similarity method: M degree (i) = Σ(W_k * KF vector (k) * DF ref (i,k)) / (||KF vector ||2 * ||DF ref(i,:)||2), where \(W_k\) is the weight of the \(k\)th feature, determined by its importance score.

[0132] S264. Analyze the peak distribution of the position matching degree vector \(M\) degree If there are multiple close peaks (with a difference < 5%), it is marked as the "fuzzy matching area". By calling an additional auxiliary feature set \(AF\_set\) (such as features based on other physical quantities) for auxiliary judgment, the matching ambiguity problem is solved, and the optimized corrected matching degree vector \(M\) is obtained. degreerefined .

[0133] S265. Perform high-precision interpolation on the highest matching degree area in the corrected matching degree vector \(M\) degreerefined to refine the positions between discrete sampling points, improve the angular resolution, and obtain the interpolated matching curve \(M\) i nterp. Cubic spline interpolation method is used for interpolation, and interpolation points with 10 times the density are inserted within the range of ±5 sampling points near the peak.

[0134] S266. Based on the peak characteristics (peak height, peak width, ratio of sub-peaks, etc.) of the interpolated matching curve \(M\) i nterp, calculate the confidence index \(Conf\) of the position estimation idx , and at the same time determine the angle corresponding to the peak as the accurate rotor position \(\theta\) r . If the confidence index \(Conf\) idx is lower than the threshold, an additional verification step is triggered or it is marked as a low-confidence estimate for reference in subsequent control strategies.

[0135] A method for accurate position estimation based on dimensionality reduction and feature importance evaluation selects the most discriminative features through PCA dimensionality reduction and Fisher discriminant ratio scoring, and then combines weighted cosine similarity matching and subsampling precision interpolation to achieve high-precision estimation of the rotor position. The information extraction efficiency of differential fingerprints is optimized. Through scientific dimensionality reduction and feature selection, key information is retained while the computational complexity is reduced. In the actual application of the CAES high-voltage frequency converter, the calculation time of position estimation is reduced from 180 μs of the traditional method to 65 μs, and at the same time the position resolution is increased from 5° to 0.5°, enabling high-precision position estimation to be completed within a strict real-time control period (usually < 100 μs), providing the possibility for high-performance control. The control system can make accurate decisions within strict time constraints, effectively preventing the triggering of system over-current protection and the occurrence of unstable states, providing the possibility for high-performance vector control, and finally achieving smooth torque output and efficient energy conversion during the startup process of the CAES system.

[0136] According to one aspect of the present application, S31. Phase modulation torque impact prediction, specifically:

[0137] S311. Based on the current exact rotor position θ r and the system operating state parameters State_sys (including current, flux linkage, etc.), construct a parameterized electromagnetic torque model M_em = f(θ, I, Ψ), where f represents the mapping relationship between the electromagnetic torque and each parameter, and output the torque model parameter set T_model p arams.

[0138] S312. Read the phase modulation sequence matrix PMS, analyze the influence of each group of modulation sequences on the stator current, and decompose the modulation effect into the d-axis component ΔI_d and the q-axis component ΔI q , to form the modulation current component matrix ΔI_dq. The calculation formula is based on the voltage vector change before and after modulation and the system electrical equations.

[0139] S313. Based on the torque model parameter set T_model p arams and the modulation current component matrix ΔI_dq, calculate the torque change caused by the phase modulation in the static case, and obtain the static torque influence matrix ΔT_static. The calculation formula is: ΔT_static(j) = dT / dI_d * ΔI_dq(j,1) + dT / dI q * ΔI_dq(j,2), where j represents the index of different modulation sequences.

[0140] S314. Considering the system electrical and mechanical time constants, apply the system dynamic response model to the static torque influence matrix ΔT_static to predict the time trajectory of the torque change, and obtain the dynamic torque response curve ΔT_dyn(t). The calculation uses the second-order system response equation: ΔT_dyn(t) = ΔT_static * (1 - exp(-t / τ_e)) * exp(-t / τ_m), where τ_e and τ_m are the electrical and mechanical time constants respectively.

[0141] S315. Considering the superposition effect when multiple modulation sequences are applied continuously, calculate the comprehensive torque fluctuation trajectory ΔT_comp(t) of the complete modulation process through piecewise convolution. The calculation formula is: ΔT_comp(t) = Σ(ΔT_dyn(t-t_j) * u(t-t_j)), where t_j is the starting time of the jth modulation sequence, and u is the unit step function.

[0142] S316. Analyze the characteristics of the comprehensive torque fluctuation trajectory ΔT_comp(t), extract key features such as the maximum fluctuation amplitude ΔT_max, the average fluctuation amplitude ΔT_avg, and the fluctuation duration T_dur, and form the theoretical torque fluctuation amount ΔT_theory, providing an accurate prediction basis for subsequent torque compensation.

[0143] By analyzing the influence of phase modulation on current and torque, an accurate inverse-phase compensation signal is designed to eliminate the system fluctuations during the modulation process, innovatively solving the contradiction between enhancing the position estimation accuracy and maintaining the system stability. The core lies in predicting the torque fluctuations caused by the modulation sequence based on an accurate electromagnetic torque model, and designing a compensation sequence with inverse-phase characteristics to achieve fluctuation cancellation through precise control of time and amplitude. It is particularly suitable for the characteristics of high inertia and high power density of the CAES system. In practical applications, the speed fluctuations during the phase modulation process are reduced from 1.5% of the traditional method to below 0.3%, effectively preventing the unstable states that may occur during the flywheel start-up of high-voltage inverters. It not only significantly improves the system reliability and safety, reduces the mechanical stress of the equipment, and extends the service life of high-voltage motors and inverters, but also optimizes the energy conversion efficiency, reduces the system operation cost, provides key technical support for the large-scale application of compressed air energy storage systems, and has important value for promoting the integration of renewable energy into the grid and grid peak shaving.

[0144] According to one aspect of the present application, S32. Calculation of dynamic torque compensation amount, specifically:

[0145] S321. Read the theoretical torque fluctuation amount ΔT_theory, analyze its frequency characteristics and amplitude distribution, extract the main frequency components and their amplitudes and phases through fast Fourier transform, and construct the torque fluctuation characteristic vector T ripple _char.

[0146] S322. Based on the torque fluctuation characteristic vector T ripple _char, design a compensation signal with the opposite phase to generate the basic compensation waveform T_comp base (t). The calculation formula is: T_comp base (t) = -Σ(A i * sin(ω i *t + φ i ))), where A i , ω i and φ i are the amplitudes, angular frequencies and phases of each frequency component respectively.

[0147] S323. Considering the system transfer delay τ_delay, shift the basic compensation waveform T_comp base (t) forward along the time axis to generate the time-sequence optimized compensation waveform T_comp_adv(t) = T_comp base (t + τ_delay). The pre-stage compensation ensures that the compensation effect is precisely time-aligned with the torque fluctuation.

[0148] S324. Based on the feedback of historical compensation effects, calculate the amplitude correction coefficient K_amp and apply it to the time-sequence optimized compensation waveform T_comp_adv(t) to obtain the amplitude-corrected compensation waveform T_comp_adj(t) = K_amp * T_comp_adv(t). The correction coefficient is calculated through the iterative formula K_amp(n + 1) = K_amp(n) * (1 + α * E_n), where E_n is the residual error of the nth compensation and α is the learning rate.

[0149] S325. Based on the stability indicators (such as speed fluctuation, current margin, etc.) in the system state parameter State_sys, set safety constraint conditions, and perform amplitude limiting and smoothing processing on the amplitude-corrected compensation waveform T_comp_adj(t) to ensure that the compensation will not cause system instability, and obtain the safety-constrained compensation waveform T_comp_safe(t).

[0150] S326. Sample and discretize the safety-constrained compensation waveform T_comp_safe(t) within the time domain range of the modulation sequence to form the final torque compensation sequence T_comp, and convert it into a form that can be directly used by the control system to prepare for the compensation implementation in the next step.

[0151] Torque ripple prediction and compensation technology based on electromagnetic models and dynamic system responses, by analyzing the influence of phase modulation on current and torque, designs precise inverse compensation signals to eliminate system fluctuations during the modulation process. It solves the contradiction between enhancing position estimation accuracy and maintaining system stability, and is especially suitable for the characteristics of high inertia and high power density of CAES systems. Practical applications show that the speed fluctuation during the phase modulation process is reduced from 1.5% of the traditional method to below 0.3%, effectively preventing the unstable state that may occur during the flywheel start-up process of high-voltage inverters, significantly improving system reliability and safety, reducing equipment mechanical stress, and extending the service life of equipment.

[0152] Example 1, under a certain working condition, due to magnetic field disturbances in a high-voltage and high-power environment, the traditional sensorless method has an "estimation dead zone" at a specific rotor position, resulting in start-up failure. This method solves this problem through phase interference enhancement technology.

[0153] The system includes a CAES main system, a 10MW high-voltage synchronous motor, a high-voltage inverter control system, a voltage and current acquisition module, and a data processing unit. The motor parameters include a rated voltage of 10kV, a rated power of 10MW, a pole pair number p = 4, a rotor resistance Rr = 0.015Ω, a stator resistance Rs = 0.018Ω, a rotor inductance Lr = 0.12H, a stator inductance Ls = 0.15H, and a mutual inductance Lm = 4.6H.

[0154] The sampling frequency is set to 20 kHz, and the output voltage data U_abc and stator current data I_abc of the frequency converter are collected through three-phase voltage and current sensors. Apply a 5th-order Butterworth band-pass filter (cutoff frequency 50 Hz - 5 kHz) to the collected data to obtain the filtered voltage data U_abc_f and the filtered current data I_abc_f.

[0155] Convert the three-phase data to the αβ coordinate system through the Clarke transformation α Iα = (2 / 3)·Ia - (1 / 3)·Ib - (1 / 3)·Ic; Iβ = (1 / √3)·Ib - (1 / √3)·Ic; where: Iα is the α-axis current component; Iβ is the β-axis current component; Ia, Ib, Ic are the measured values of the three-phase currents; √ represents the square root. b -(1 / 3)·Ic; Iβ β =(1 / √3)·Ib b -(1 / √3)·Ic; where: Iβ α is the β-axis current component; Iα β is the α-axis current component; Ia, Ib b , Ic are the measured values of the three-phase currents; √ represents the square root.

[0156] When the three-phase currents Ia = 125 A, Ib = -60 A, Ic = -65 A are collected, it is calculated that Iα = (2 / 3)×125-(1 / 3)×(-60)-(1 / 3)×(-65)=125 A, Iβ = (1 / √3)×(-60)-(1 / √3)×(-65)=2.89 A. b =-60 A, Ic=-65 A, calculate to get Iα α =(2 / 3)×125-(1 / 3)×(-60)-(1 / 3)×(-65)=125 A, Iβ β =(1 / √3)×(-60)-(1 / √3)×(-65)=2.89 A.

[0157] Perform a similar transformation on the voltage data U_abc to obtain Uα and Uβ, and then normalize according to the DC bus voltage U_dc (for example, U_dc = 15 kV) to obtain the normalized αβ coordinate system data set Dα, Dβ. α and Uβ β , and then normalize according to the DC bus voltage U_dc (for example, U_dc = 15 kV) to obtain the normalized αβ coordinate system data set Dα α , β norm .

[0158] First, perform a sliding window FFT on the normalized αβ coordinate system data (window length is 512 points, overlap rate 50%), extract the amplitude and phase information of the 5th, 7th, 11th, and 13th harmonics to form the basic harmonic feature matrix H. base .

[0159] At the position i = 24 (corresponding to 120° electrical angle), the eigenvalue of the 7th harmonic H(24,7)=0.32, and the eigenvalue of the adjacent position i = 25 is H(25,7)=0.33. base (24,7)=0.32, the eigenvalue of the adjacent position i = 25 is H(25,7)=0.33, base (25,7)=0.33,

[0160] According to Sh(i,h) = |H(i,h)| point (i,h) = |H(i,h)| base(i + 1, h) - H base (i, h)| / Δθ; Calculate the sensitivity S_h of the 7th harmonic at this point point (24, 7) = |0.33 - 0.32| / 5° = 0.002 / degree.

[0161] For the calculated S_h point Apply a 7 - point moving average window to obtain the smoothed harmonic sensitivity matrix S_h_smooth.

[0162] Apply the preset weights W_5 = 0.2, W_7 = 0.3, W11 = 0.3, W13 = 0.2 to calculate the weighted harmonic sensitivity:

[0163] For the measured data, calculate S_h weighted The mean value μ_S = 0.0085 / degree and the standard deviation σ_S = 0.0032 / degree are obtained. Set k = 2. According to S_h weighted (i) = W_5·S_h_smooth(i, 5) + W_7·S_h_smooth(i, 7) + W11·S_h_smooth(i, 11) + W13·S_h_smooth(i, 13); Then the adaptive threshold λ_threshold = μ_S - k·σ_S = 0.0085 - 2×0.0032 = 0.0021 / degree.

[0164] By comparing S_h weighted and λ_threshold, two main dead zones are identified: D_zones = {{25° - 40°, 32.5°}, {205° - 220°, 212.5°}}, where each element contains {dead zone range, dead zone center position}.

[0165] For the identified dead zone intervals D_zones, design a phase interference sequence to enhance the position characteristics.

[0166] First, analyze the dead zone characteristics. For the dead zone {25° - 40°, 32.5°}, its width W_zone = 15°, and the difference degree of harmonic characteristics in the adjacent area D_adjacent = 0.22 (normalized value).

[0167] Design 3 groups of orthogonal basic modulation vectors: B_mod = {[1, 0, 0], [0, 1, 0], [0, 0, 1]}, corresponding to the modulation of the d - axis, q - axis, and zero - sequence components respectively.

[0168] Based on the current system state (current \(I_{magnitude} = 150A\), estimated speed \(\omega_{est}=0.2p.u.\)) and dead - zone width \(W_{zone}=15°\), calculate the optimal modulation depth coefficient:

[0169] According to \(\alpha_{depth}=0.1\cdot(W_{zone} / 10°)\cdot\sqrt{(I_{magnitude} / I}\) rated )\cdot(1 - \omega_{est} / \omega rated ); Calculate \(\alpha_{depth}=0.1\times(15° / 10°)\times\sqrt{150 / 200}\times(1 - 0.2 / 1.0)=0.1\times1.5\times0.866\times0.8 = 0.104\).

[0170] Design the modulation timing. Considering the system mechanical time constant \(T_{mech}=1.2s\), electrical time constant \(T_{elec}=25ms\), set: modulation duration \(T_{mod}=8ms\), sampling delay \(T_{delay}=2ms\), continuous modulation interval \(T\) i nterval = 5ms.

[0171] Combine the basic modulation vector \(B_{mod}\) and modulation depth coefficient \(\alpha_{depth}\) to generate the complete phase - modulation sequence matrix \(PMS\), which contains 3 groups of sequences:

[0172] PMS1: d - axis current modulation, depth \(0.104p.u.\), duration \(8ms\);

[0173] PMS2: q - axis current modulation, depth \(0.104p.u.\), duration \(8ms\);

[0174] PMS3: d - q combined modulation, d - axis depth \(0.074p.u.\), q - axis depth \(0.074p.u.\), duration \(8ms\).

[0175] Apply the designed phase - modulation sequence \(PMS\) to the system in sequence, and record the harmonic response under each sequence to obtain multiple groups of harmonic - response data sets \(R_{h - set}\).

[0176] Normalize the collected harmonic - response data. For example: for the 7th harmonic, the amplitudes under the three modulation sequences are \(R_{h - set}(7,1)=0.15\), \(R_{h - set}(7,2)=0.18\), \(R_{h - set}(7,3)=0.14\), and after normalization, they are \(R_{h - norm}(7,1)=0.83\), \(R_{h - norm}(7,2)=1.0\), \(R_{h - norm}(7,3)=0.78\).

[0177] Select the harmonic response \(R_{h}\) in the un - modulated state base as the reference (for example, the 7th - harmonic reference value \(R_{h}\)base (7)=0.16), calculate the first-order difference matrix:

[0178] According to the formula D1_h(h,j) = R_h_norm(h,j) - R_h base (h); Calculation results show that for the first-order differences of the 7th harmonic under three modulations: D1_h(7,1)=0.83-1.0=-0.17, D1_h(7,2)=1.0-1.0=0, D1_h(7,3)=0.78-1.0=-0.22.

[0179] Calculate the second-order difference matrix D2_h. For example, D2_h(1,2)=D1_h(:,1)-D1_h(:,2). For the 7th harmonic, D2_h(1,2,7)=-0.17-0=-0.17.

[0180] A nonlinear enhancement function is applied to the phase information: F_enh(x)=sign(x)·|x|^1.8. For example, for a phase difference of 0.05rad, the enhanced value is sign(0.05)·|0.05|^1.8=0.05^1.8=0.0068.

[0181] Finally, according to the weights W1=0.3, W2=0.5, W p =0.2 to fuse multi-dimensional differential features and construct a complete harmonic differential fingerprint matrix DF_h.

[0182] Apply PCA dimensionality reduction to the harmonic differential fingerprint matrix DF_h, retain the 12 principal components that explain 95% of the variance, and obtain the reduced dimensionality differential fingerprint DF reduced .

[0183] The importance of features is calculated based on the Fisher discriminant ratio, and the 15 features with the highest scores are selected to form the key feature vector KF vector For example, for the KF at position θ=32.5° vector , its first key eigenvalue is 0.135, which is consistent with the pre-built differential fingerprint reference library DF ref match.

[0184] According to formula M degree (i)=Σ(W_k·KF vector (k) DF ref (i,k)) /

[0185] (||KF vector ||2·||DF ref (i,:)||2);

[0186] For a specific KF vectorCalculation of the matching degree with the 35th record in the reference library (corresponding to the angle of 35°), assuming KF vector The L2 norm of is 0.5, DF ref (35,:) The L2 norm of is 0.6, W1 = 0.25, W2 = 0.2, W_3 = 0.15 (and so on), KF vector (1) = 0.135, KF vector (2) = 0.098, KF vector (3) = 0.112, DF ref (35,1) = 0.142, DF ref (35,2) = 0.101, DF ref (35,3) = 0.115,

[0187] Then the matching degree M degree (35)=(0.25×0.135×0.142 + 0.2×0.098×0.101 + 0.15×0.112×0.115 +...)

[0188] / (0.5×0.6)=0.0307 / 0.3 = 0.1023.

[0189] Perform cubic spline interpolation on the highest matching region (30° - 35°) in the matching degree vector M degreeref ined to obtain the interpolated matching curve M i nterp. Determine the peak position 32.8° as the exact rotor position θ r , and at the same time calculate the confidence index Conf idx =0.89 (value range 0 - 1).

[0190] Based on the current rotor position θ r =32.8° and the system operating state, construct a parametric electromagnetic torque model, and the electromagnetic torque expression M_em = (3 / 2)·p·[(L_d - L q )·I_d·I q + ψf·I q ; where: M_em is the electromagnetic torque; p is the number of pole pairs, with a value of 4; L_s is the stator inductance, with a value of 0.15H; L_σs is the stator leakage inductance, with a value of 0.03H; I_ds is the d-axis current component; I q s is the q-axis current component.

[0191] In one embodiment, M_em = (3 / 2)·p·[(L_d - L q )·I_d·I q + ψf·I q; M_em = (3 / 2)·p·[(L_s - L_md)·I q s·I_ds - (L_s - L_mq)·I_ds·I q s + ψf·I q s]. Ψf is the permanent magnet flux linkage; L_md is the d-axis mutual inductance; L_mq is the q-axis mutual inductance.

[0192] For the three modulation sequences in PMS, calculate their influence on the current. For example, the current change caused by sequence PMS1 (d-axis modulation 0.104 p.u.): ΔI_d = 15 A, ΔI q = -3 A.

[0193] Calculate the static torque influence ΔT_static(j) = (dM_em / dI_d)·ΔI_dq(j,1) + (dM_em / dI q )·ΔI_dq(j,2); where: ΔT_static(j) is the static torque change caused by modulation sequence j; dM_em / dI_d is the partial derivative of torque with respect to d-axis current; dM_em / dI q is the partial derivative of torque with respect to q-axis current; ΔI_dq(j,1) is the d-axis current change caused by modulation sequence j; ΔI_dq(j,2) is the q-axis current change caused by modulation sequence j.

[0194] For example, for sequence PMS1, at the current operating condition, dM_em / dI_d = -120 Nm / A, dM_em / dI q = 150 Nm / A,

[0195] then ΔT_static(1) = (-120 Nm / A)×15 A + (150 Nm / A)×(-3 A) = -1800 Nm - 450 Nm = -2250 Nm.

[0196] Considering the electrical time constant τ_e = 25 ms and the mechanical time constant τ_m = 1.2 s of the system, simulate the dynamic torque response: ΔT_dyn(t) = ΔT_static·(1 - e^(-t / τ_e))·e^(-t / τ_m); where: ΔT_dyn(t) is the dynamic torque response at time t; ΔT_static is the static torque influence; τ_e is the electrical time constant; τ_m is the mechanical time constant; t is the time variable.

[0197] For sequence PMS1, the dynamic torque response at t = 5 ms: ΔT_dyn(5 ms) = -2250 Nm×(1 - e^(-5 ms / 25 ms))×e^(-5 ms / 1.2 s) = -2250 Nm×0.181×0.996 = -406 Nm.

[0198] Analyze the torque ripple trajectory of the complete modulation process and extract the key features: the maximum ripple amplitude ΔT_max = -750 Nm, the average ripple amplitude ΔT_avg = -320 Nm, and the ripple duration T_dur = 45 ms.

[0199] Design an inverse compensation signal T_comp base (t) = -Σ(A i ·sin(ω i ·t + φ i )); where: T_comp base (t) is the basic compensation waveform; A i is the amplitude of the i-th frequency component; ω i is the angular frequency of the i-th frequency component; φ i is the phase of the i-th frequency component; t is the time variable.

[0200] For the main ripple frequency of 126.5 Hz, amplitude of 550 Nm, and phase of 0.8 rad, the compensation waveform is T_comp base (t) = -550 Nm·sin(126.5 Hz × 2π × t + 0.8 rad).

[0201] Considering the system transfer delay τ_delay = 3 ms, perform timing optimization T_comp_adv(t) = T_comp base (t + 3 ms).

[0202] Based on the historical compensation effect, calculate the amplitude correction factor K_amp = 1.15 and apply it to the compensation waveform T_comp_adj(t) = 1.15 × T_comp_adv(t).

[0203] According to the system stability constraint, limit the compensation waveform: |T_comp_safe(t)| ≤ 0.1 × T rated , where T rated is the rated torque of 95 kNm, so the limit value is 9.5 kNm.

[0204] The finally generated torque compensation sequence is discretized at a frequency of 10 kHz and converted into a q-axis current compensation command:

[0205] ΔI q _comp(t) = T_comp_safe(t) / (1.5·p·(L_s - L_σs)·I_ds); where: ΔI q_comp(t) is the q-axis current compensation; T_comp_safe(t) is the torque compensation after safety constraints; p is the number of pole pairs; L_s is the stator inductance; L_σs is the stator leakage inductance; I_ds is the current d-axis current.

[0206] For example, when T_comp_safe(t)=500Nm, I_ds=100A,

[0207] ΔI q _comp(t)=500Nm / (1.5×4×(0.15H-0.03H)×100A)=500Nm / 72Nm / A=6.94A.

[0208] After applying this method, during the sensorless flying start process of the 10MW high-voltage inverter of the CAES system:

[0209] Position estimation accuracy: In the "dead zone" of the traditional method, this method reduces the position estimation error from ±25° to ±3.5°.

[0210] The startup success rate increased from 72% with traditional methods to 98.5%. The peak current of the starting current surge was reduced from 2.8pu to 1.4pu. Torque ripple was reduced from 18% of the rated torque to 6%. The applicable speed range was expanded to the full range of 0-30% of the rated speed.

[0211] Practical tests show that this method successfully solves the "position estimation dead zone" problem in the sensorless flying start of CAES high-voltage inverters, significantly improving the starting reliability and smoothness.

[0212] Example 2: A precise rotor position estimation process based on phase interference enhancement is as follows:

[0213] The filtered αβ coordinate data D αβ _norm performs harmonic analysis. Taking the sampling frequency of 20kHz and the window length of 512 points as an example, FFT analysis is performed on the stator current data collected at a certain time to extract the amplitude and phase of the 5th, 7th, 11th and 13th harmonics to form the basic harmonic characteristic matrix H base For example, under a specific operating condition, the extracted harmonic features are: the 5th harmonic amplitude is 0.21 pu and the phase is 78°; the 7th harmonic amplitude is 0.32 pu and the phase is -112°; the 11th harmonic amplitude is 0.18 pu and the phase is 165°; and the 13th harmonic amplitude is 0.16 pu and the phase is -23°.

[0214] Calculate the feature gradient data according to the method of the above embodiment and identify the position estimation dead zone interval. For this case, the identified position estimation dead zone intervals are D_zones = {{25° - 40°, 32.5°}, {205° - 220°, 212.5°}}.

[0215] Based on the identified dead zone intervals, design the phase modulation sequences. According to the method of the above embodiment, after analyzing the dead zone characteristics, design three sets of orthogonal phase modulation sequences: PMS1 (d-axis modulation, depth 0.104 p.u., duration 8 ms), PMS2 (q-axis modulation, depth 0.104 p.u., duration 8 ms), PMS_3 (d-q combined modulation, d-axis depth 0.074 p.u., q-axis depth 0.074 p.u., duration 8 ms).

[0216] Apply these three sets of modulation sequences to the frequency converter control system in sequence. After each application, wait for a 2 ms stabilization time, then collect the current data and perform harmonic analysis to obtain multiple sets of harmonic response datasets R_h_set. For example, for the 7th harmonic, the amplitudes under the three sets of modulation sequences are R_h_set(7,1) = 0.15 p.u., R_h_set(7,2) = 0.18 p.u., R_h_set(7,3) = 0.14 p.u.

[0217] Construct the harmonic difference fingerprint matrix according to the method of the above embodiment, extract the position features, and finally obtain the accurate rotor position of 32.8°, which is close to the actual position of 32.5°, with an error of only 0.3° electrical angle.

[0218] Embodiment 3: In the process of constructing the harmonic difference fingerprint, the calculation of the second-order difference matrix is a key step. Taking the harmonic responses obtained from the above three sets of modulation sequences as an example, first calculate the normalized harmonic response set R_h_norm. The normalized values for the 7th harmonic are 0.83, 1.0, and 0.78 respectively.

[0219] Select the reference harmonic response (the response in the unmodulated state, for example, the reference value of the 7th harmonic is 0.16 p.u.), and then calculate the first-order difference: D1_h(7,1) = 0.83 - 1.0 = -0.17, D1_h(7,2) = 1.0 - 1.0 = 0, D1_h(7,3) = 0.78 - 1.0 = -0.22.

[0220] The second-order difference calculation process is as follows: First, calculate the differences between pairs of the three sets of modulation sequences. There are a total of C(3,2) = 3 sets of second-order differences:

[0221] D2_h(1,2,7) = D1_h(7,1) - D1_h(7,2) = -0.17 - 0 = -0.17.

[0222] D2_h(1, 3, 7) = D1_h(7, 1) - D1_h(7, 3) = -0.17 - (-0.22) = 0.05.

[0223] D2_h(2, 3, 7) = D1_h(7, 2) - D1_h(7, 3) = 0 - (-0.22) = 0.22.

[0224] The same second-order difference calculation is performed for each harmonic component to form the complete second-order difference matrix D2_h.

[0225] Example 4: Enhancement of position feature extraction and accurate estimation, the process is as follows:

[0226] For the harmonic difference fingerprint matrix DF _h (including first-order difference, second-order difference, and enhanced phase difference), principal component analysis (PCA) is first applied for dimensionality reduction. In this case, the original difference fingerprint dimension is 45 (5 main harmonics × 3 types of differences × 3 groups of modulation sequences). After dimensionality reduction by PCA, 12 principal components are retained, explaining 95.3% of the variance.

[0227] Next, the Fisher discriminant ratio is calculated to determine the feature importance. Let X i represent the values of the i-th feature at different rotor positions, and calculate the ratio of the between-group variance S b to the within-group variance S w : Fisher i = S b (X i ) / S w (X i ). For example, for a certain feature, the calculated Fisher value is 4.28, indicating that this feature has a high discrimination ability. Based on the Fisher values, the 15 features with the highest scores are selected to form the key feature vector KF vector .

[0228] Match and calculate KF vector with the pre-built difference fingerprint reference library DF ref . Taking the calculation of the matching degree between KF vector and the record at the 35° position in the reference library as an example: The L2 norm of KF vector is 0.5, and the L2 norm of DF ref (35, :) is 0.6. According to the formula in the example, the calculated M degree (35) = 0.1023. The same calculation is performed for all reference positions to obtain the complete position matching degree vector M degree .

[0229] Analyze M degreeThe peak distribution in it was found to have the highest matching degree in the 30° - 35° region. Cubic spline interpolation was applied to this region to increase the sampling point density by 10 times, and the interpolation matching curve M i nterp was obtained. The peak position 32.8° was determined from it as the precise rotor position, and at the same time, the confidence index Conf idx = 0.89 was calculated, indicating that the position estimation has a high credibility.

[0230] Example 5, The process of phase enhancement and feature fusion in differential fingerprint construction is as follows:

[0231] The specific form of the non - linear phase enhancement function is F _enh (x)=sign(x)×|x|^p, where p is the enhancement coefficient, which takes the value of 1.8 in this case. This function can effectively amplify small phase differences. For example, for a phase difference of 0.05 rad, after enhancement, it is sign(0.05)×|0.05|^1.8≈0.0068 rad. For a phase difference of 0.10 rad, after enhancement, it is sign(0.10)×|0.10|^1.8≈0.0158 rad, enhancing the distinguishability of small differences.

[0232] In the process of multi - dimensional feature fusion, based on experimental verification, the fusion weights of the first - order difference, second - order difference, and phase difference are determined to be W1 = 0.3, W2 = 0.5, W p = 0.2 respectively. A higher weight is given to the second - order difference because it is the most sensitive to position changes. Taking the 7th harmonic as an example, the fused differential fingerprint value is 0.3×(-0.17)+0.5×0.22+0.2×0.0158≈0.0621. The same fusion is performed on all harmonic features to construct the complete harmonic differential fingerprint matrix DF_h.

[0233] Example 6, The execution process of overspeed start control is as follows:

[0234] After obtaining the precise rotor position, the system divides the overspeed start into three stages according to the rotor position and the estimated speed: initial capture (0 - 10% of the rated speed), acceleration transition (10% - 20% of the rated speed), and steady - speed regulation (20% - 30% of the rated speed).

[0235] For the initial capture stage, the control strategy parameters are set as: the d - axis current reference value I_ dref = 0.8 p.u., the q - axis current reference value I qref = 0.2 p.u., the current - loop proportional gain K pi = 8.5, the integral gain K ii = 120.

[0236] Based on the precise rotor position θ r= 32.8°, a rotating coordinate system is established, and the αβ coordinate system current (I α = 125 A, I β = 2.89 A) is converted to the dq coordinate system:

[0237] I_d = I α × cos(θ r ) + I β × sin(θ r ) = 125 × cos(32.8°) + 2.89 × sin(32.8°) = 106.8 A.

[0238] I q = -I α × sin(θ r ) + I β × cos(θ r ) = -125 × sin(32.8°) + 2.89 × cos(32.8°) = -65.8 A.

[0239] Combined with the torque compensation amount calculated above, the optimized control current I_ctrl_opt is generated. Finally, the PWM control signal is generated through the SVPWM algorithm to drive the frequency converter to output. During the startup process, the system performance indicators are continuously monitored, including the startup time (reaching 3.8 s), the current peak value (dropping to 1.4 p.u.), and the torque fluctuation (dropping to 6% of the rated torque). After comparing with the target performance indicators, the control parameters are dynamically optimized, realizing a smooth and reliable coasting startup process.

[0240] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A sensorless coasting start control method for a CAES high-voltage frequency converter, characterized in that Including: Collecting the output voltage data and stator current data of the frequency converter and filtering them to obtain the filtered system data; Performing harmonic analysis on the filtered system data, identifying the position estimation dead zone interval and analyzing its characteristics, designing a phase modulation sequence accordingly and applying it to generate a harmonic interference pattern, The system responds to the harmonic interference pattern to obtain a harmonic response data set, constructs a harmonic difference fingerprint based on this, extracts position features, and obtains the accurate rotor position; Calculating the torque compensation amount according to the phase modulation sequence and the mechanical characteristics of the system, and generating an optimized control current; Generating a control signal based on the accurate rotor position and the optimized control current and sending it down; The steps to obtain the accurate rotor position include: Performing harmonic analysis on the filtered system data, extracting harmonic amplitude and phase information, and forming a basic harmonic feature matrix; Calculating the feature gradient data based on the basic harmonic feature matrix and comparing it with a threshold value to identify the position estimation dead zone interval; Designing multiple groups of orthogonal phase modulation sequences according to the characteristics of the position estimation dead zone interval to form a phase modulation sequence matrix; Applying the phase modulation sequence to the frequency converter control system in sequence to collect multiple groups of harmonic response data sets; Calculating the difference between harmonic responses based on multiple groups of harmonic response data sets to construct a harmonic difference fingerprint matrix; Extracting key features from the harmonic difference fingerprint matrix and determining the accurate rotor position through feature matching; The steps to estimate the dead zone interval include: Calculating the change rate of different harmonic components between adjacent rotor positions for the basic harmonic feature matrix to obtain a single-point harmonic sensitivity matrix and applying a sliding window average to it to eliminate the influence of local fluctuations and obtain a smooth harmonic sensitivity matrix; Calculating the weighted harmonic sensitivity based on the importance weights of each harmonic component in the smooth harmonic sensitivity matrix and analyzing its statistical distribution characteristics, and calculating an adaptive dead zone determination threshold according to the statistical distribution characteristics; Comparing the weighted harmonic sensitivity with the dead zone determination threshold, marking the position points below the threshold, and merging adjacent low-sensitivity points through connected component analysis to obtain the position estimation dead zone interval; The steps to form the phase modulation sequence matrix include: Analyzing the position estimation dead zone interval, extracting the interval width, center position, and harmonic feature difference degree of the adjacent region to form a dead zone characteristic parameter set, and constructing multiple groups of mutually orthogonal basic modulation vector sets based on this; Calculating the optimal modulation depth coefficient according to the dead zone characteristic parameter set and the current operating state of the system; Combining the basic modulation vector set and the modulation depth coefficient to predict the gain characteristics of different modulation combinations in the current dead zone and generating an expected gain matrix; Based on the expected gain matrix and the pre-stored modulation timing parameter set, selecting the highest gain combination to generate a complete phase modulation sequence matrix; The steps to determine the accurate rotor position through feature matching include: Performing dimensionality reduction processing on the harmonic difference fingerprint matrix, obtaining the dimensionality-reduced difference fingerprint and evaluating the importance of features, selecting the features with the highest scores to form a key feature vector; Calculating the matching degree between the key feature vector and the pre-established difference fingerprint reference library to obtain a position matching degree vector and analyzing its peak distribution, and processing the multi-peak fuzzy region to obtain a corrected matching degree vector; Extract the highest matching region of the correction matching degree vector and perform interpolation to obtain an interpolated matching curve and determine its peak position, which is used as the accurate rotor position.

2. The method according to claim 1, characterized in that, The steps for constructing the harmonic difference fingerprint matrix include: Perform normalization processing on multiple groups of harmonic response data sets to obtain a normalized harmonic response set and select a reference response from it to obtain a reference harmonic response; Calculate the difference between each group of normalized harmonic responses and the reference harmonic response to construct a first-order difference matrix; Calculate the difference between the first-order differences generated by different modulation sequences to construct a second-order difference matrix; Nonlinearly amplify the phase difference of the harmonics to obtain an enhanced phase difference; Combine the first-order difference matrix, the second-order difference matrix, and the enhanced phase difference according to specific weights to construct a complete harmonic difference fingerprint matrix.

3. The method according to claim 1, characterized in that, The steps for forming a phase modulation sequence matrix include: Extract the parameters in the position estimation dead zone interval to form a dead zone characteristic parameter set, which at least includes the interval width; Calculate the optimal modulation depth coefficient according to the interval width, the current amplitude, and the estimated rotational speed; In a three-dimensional modulation space, construct at least three groups of basic vectors that satisfy the orthogonal condition to form a basic modulation vector set; Combine the basic modulation vector set with the modulation depth coefficient to simulate and predict the gain characteristics of each modulation combination to generate an expected gain matrix; Based on the expected gain matrix and the pre-stored modulation timing parameter set, select the highest gain combination to generate a phase modulation sequence matrix.

4. The method according to claim 2, wherein The steps for constructing the harmonic difference fingerprint matrix include: Perform amplitude normalization on multiple groups of harmonic response data sets respectively to obtain a normalized harmonic response set; Select the response in the standard modulation state, the non-modulation state, or the average response from the normalized harmonic response set as the reference harmonic response; Calculate the point-by-point difference between each group of normalized harmonic responses and the reference harmonic response to form a first-order difference matrix; Calculate the cross difference between the first-order difference matrices under different modulation sequences to form a second-order difference matrix; Amplify the harmonic phase change in the dead zone through an exponential function to generate an enhanced phase difference; Set a fusion weight according to the contribution degree of the harmonic components to position identification, and synthesize the first-order difference matrix, the second-order difference matrix, and the enhanced phase difference to construct a harmonic difference fingerprint matrix.

5. The method according to claim 1, wherein The steps for generating an optimized control current include: Based on the phase modulation sequence and the accurate rotor position, predict the theoretical torque fluctuation amount during the modulation process; Design a torque compensation sequence according to the theoretical torque fluctuation amount and the system inertia characteristics; Convert the torque compensation sequence into a compensation current component and superimpose it on the original control current to form an optimized control current.

6. The method according to claim 5, characterized in that, The steps for designing a torque compensation sequence include: Based on the accurate rotor position and the system operating state parameters, construct a parameterized electromagnetic torque model and output a torque model parameter set; Analyze the influence of the phase modulation sequence on the stator current, decompose the modulation effect into d-axis and q-axis components to form a modulation current component matrix; Based on the torque model parameter set and the modulation current component matrix, calculate a static torque influence matrix; Apply the system dynamic response model to the static torque influence matrix to predict the time trajectory of torque change to obtain a dynamic torque response curve; Considering the superposition effect of successive applications of multiple modulation sequences, calculate the comprehensive torque ripple trajectory, extract the key features of torque ripple, form the theoretical torque ripple quantity, and accordingly design the basic compensation waveform with opposite phases and optimize the timing sequence to obtain the optimized compensation waveform; Perform amplitude limiting and smoothing processing on the optimized compensation waveform to generate the final torque compensation sequence.

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