Harmonic Selective Elimination Method for Cascaded H-Bridge Inverter Based on Space Voltage Vector in CAES

Abstract

The present invention discloses a harmonic selective elimination method for a cascaded H-bridge frequency converter based on space voltage vectors in CAES, including: collecting system operation data to construct a real-time monitoring data set; analyzing the harmonic time-domain characteristics and phase relationships to calculate a critical phase difference matrix; reconstructing and optimizing the space voltage vectors to calculate the switching timing perturbation amount; generating a phase-locked control instruction to optimize the H-bridge drive signal; monitoring the system output and dynamically adjusting the control parameters. The present invention reveals the sensitivity of resonant harmonics to phase relationships, precisely controls the harmonic phases through microsecond-level switching timing, effectively suppresses the harmonic amplification effect under resonant conditions, and improves the system stability and power quality.

Description

Technical Field

[0001] The present invention relates to a harmonic elimination method, in particular to a harmonic selective elimination method for a cascaded H-bridge inverter based on space voltage vectors in CAES. Background Art

[0002] As an efficient and large-capacity energy storage technology, the Compressed Air Energy Storage System (CAES) plays an important role in new energy grid connection and smart grid construction. In the CAES system, the cascaded H-bridge (CHB) inverter is widely used in energy conversion and power quality control due to its advantages such as multi-level output, modular structure, and high reliability. However, the harmonic problems generated during the operation of the inverter seriously affect the system efficiency and equipment life. Especially under resonant conditions, the harmonic amplification effect may lead to system instability or even equipment damage. Therefore, studying the harmonic selective elimination method for the cascaded H-bridge inverter based on space voltage vectors is of great significance for improving the safety, reliability, and economy of the CAES system.

[0003] Currently, the inverter harmonic suppression technologies mainly include two categories: filter method and control strategy optimization. The former suppresses harmonics by adding active or passive filtering devices, but increases the system cost and volume. The latter reduces harmonic generation by optimizing the control strategy, including methods such as Selective Harmonic Elimination (SHE) and Space Vector Pulse Width Modulation (SVPWM). The traditional SHE method eliminates specific-order harmonics by pre-calculating the switching angles; the SVPWM method optimizes the switching sequence using the concept of space vectors to achieve an optimized harmonic distribution. These methods perform well under steady-state conditions, but they are all based on the amplitude control principle, mainly focusing on suppressing the harmonic amplitude and ignoring the influence of the harmonic phase relationship.

[0004] However, under specific operating conditions of the CAES system (such as compressor start-stop and energy conversion mode switching), the system will exhibit resonant conditions, leading to harmonic amplification effects. The harmonics excited by this resonance show obvious non-linear growth characteristics in the time domain: slow growth at the initial stage, exponential rapid increase after reaching the critical point, and finally reaching the saturation state. Traditional harmonic control methods face serious challenges under these conditions: First, the non-linear growth of the harmonic amplitude makes the control response often lag behind the harmonic amplification process; second, the traditional methods ignore the key influence of the phase relationship between harmonics on resonance and cannot effectively intervene in the resonance formation process; third, most of the existing methods are passive response control strategies, which can only respond to the already-occurred harmonic amplification phenomenon and lack an essential understanding of the non-linear growth characteristics of harmonics; therefore, there is an urgent need to develop a new control method for the harmonic amplification effect under the resonant conditions of the CAES system, starting from the harmonic dynamic characteristics and phase sensitivity to achieve accurate prediction and effective suppression of resonant harmonics. Summary of the Invention

[0005] Objective of the invention: To provide a method for selectively eliminating harmonics of a cascaded H-bridge frequency converter based on space voltage vectors in a CAES, in order to solve the above problems existing in the prior art.

[0006] Technical solution: A method for selectively eliminating harmonics of a cascaded H-bridge frequency converter based on space voltage vectors in a CAES, comprising the following steps:

[0007] Collect the operation data of the CAES system and grid parameters, construct a real-time monitoring data set, perform preprocessing, extract the harmonic time-domain characteristics and phase relationship parameters from it, analyze the phase sensitivity between harmonics, and calculate the critical phase difference matrix;

[0008] According to the critical phase difference matrix, reconstruct and optimize the space voltage vector, and calculate the switching timing perturbation amount;

[0009] Combine the switching timing perturbation amount and the critical phase difference matrix to generate a phase-locked control instruction and optimize the H-bridge drive signal.

[0010] According to one aspect of the present application, extracting the harmonic time-domain characteristics and phase relationship parameters, analyzing the phase sensitivity between harmonics, and calculating the critical phase difference matrix includes:

[0011] Apply the fast Fourier transform to the real-time monitoring data set, calculate the amplitude and phase of each harmonic, obtain the harmonic spectrum data, and calculate the time derivative of the amplitude of each harmonic therein to construct a harmonic growth rate vector;

[0012] Adopt a normalized harmonic growth rate calculation model to process the harmonic growth rate vector, obtain the normalized growth data and analyze its time variation trend, calculate the harmonic growth acceleration index, and form a harmonic dynamic characteristic matrix;

[0013] Calculate the phase difference between harmonics to generate a phase difference sequence;

[0014] Perform correlation analysis on the harmonic dynamic characteristic matrix and the phase difference sequence, identify the corresponding patterns between harmonic amplification and phase relationship, generate phase sensitivity data; and accordingly determine the key phase relationship for resonance suppression and calculate the critical phase difference matrix.

[0015] According to one aspect of the present application, performing correlation analysis on the harmonic dynamic characteristic matrix and the phase difference sequence, identifying the corresponding patterns between harmonic amplification and phase relationship, and generating phase sensitivity data includes:

[0016] Divide the phase difference sequence into multiple phase intervals according to a preset angle interval to obtain a phase interval vector;

[0017] For each harmonic pair, calculate the average normalized growth rate of the harmonics in each phase interval to form a phase-growth rate correspondence table, and perform interpolation to generate a continuous phase-growth rate function;

[0018] For each harmonic, find the phase difference that minimizes the growth rate, generate the optimal phase difference vector, and calculate the growth rate sensitivity of each harmonic pair at the optimal phase point to form a phase sensitivity matrix;

[0019] Based on the phase sensitivity matrix and the optimal phase difference vector, determine the key harmonic pairs that have the greatest impact on the resonance suppression effect, and construct a list of key harmonic pairs; and for each key harmonic among them, analyze the changes in the phase sensitivity characteristics of the key harmonic pairs under different system operating conditions to generate an operating condition-phase sensitivity mapping;

[0020] Integrate the phase sensitivity matrix and the operating condition-phase sensitivity mapping to generate complete phase sensitivity data.

[0021] According to one aspect of the present application, finding the phase difference that minimizes the growth rate and calculating the growth rate sensitivity includes:

[0022] For each harmonic i, determine the optimal phase difference φij based on the phase-growth rate function and the phase difference between harmonics min ;

[0023] At the optimal phase point, calculate the phase sensitivity S(i,φij) = |dR(i,φij) / dφij| φij=φijmin , where dR / dφij is the derivative of R with respect to φij, to form a phase sensitivity matrix.

[0024] According to one aspect of the present application, calculating the critical phase difference matrix includes:

[0025] Extract the optimal phase difference value from the phase sensitivity data as the base value of the critical phase difference;

[0026] Calculate the frequency characteristics of the system impedance, obtain the system impedance data and extract the impedance phase angles at each harmonic frequency point;

[0027] Calculate the impedance phase angle difference φZ(ωi,ωj) of the key harmonic pairs to generate an impedance phase angle difference matrix;

[0028] Construct a correction model, and calculate the corrected phase difference data based on the optimal phase difference value, the impedance phase angle difference, and the correction coefficient;

[0029] Analyze the influence of system parameter fluctuations on the critical phase difference, calculate the allowable fluctuation range, and form a phase tolerance matrix;

[0030] Integrate the corrected phase difference data and the phase tolerance matrix to construct a critical phase difference matrix, including the critical phase value, the allowable error range, and the phase sensitivity.

[0031] According to one aspect of the present application, calculating the switching timing perturbation amount includes:

[0032] Based on the critical phase difference matrix, calculate the space voltage vector angle, form a sequence of space voltage vector angles, and accordingly establish and solve a phase objective function to obtain optimized switching angle data, and calculate the basic switching timing of each H-bridge unit based on it to form basic timing data;

[0033] Analyze the sensitive phase relationship in the critical phase difference matrix and calculate the phase fine-tuning data;

[0034] Combine the basic timing data and the phase fine-tuning data to calculate the final switching timing perturbation amount.

[0035] According to one aspect of the present application, establishing and solving a phase objective function includes:

[0036] Extract the optimal phase parameters from the critical phase difference matrix;

[0037] Establish a mapping function from the switching angle to the harmonic phase, and construct an angle-phase mapping model;

[0038] Based on the angle-phase mapping model, construct a phase optimization objective function J phase (α) = Σwi·|Φi(α) - φi optimal | 2 + λ·THD(α); α is the switching angle vector; Φi(α) is the harmonic phase corresponding to the switching angle; φi optimal is the optimal phase; wi is the weight coefficient; λ is the THD penalty coefficient; THD(α) is the total harmonic distortion rate; i is the harmonic order;

[0039] Convert the phase optimization objective function into an approximate quadratic programming problem to solve for the initial solution;

[0040] Starting from the initial solution, use the gradient descent method to accurately solve to obtain the final optimized switching angle data.

[0041] According to one aspect of the present application, calculating the final switching timing perturbation amount includes:

[0042] Determine the key phase parameters that have the greatest impact on the system performance, and establish a conversion model from the phase fine-tuning amount to the time perturbation one by one to calculate the switching timing perturbation amount;

[0043] Quantify and correct the timing of the switching timing perturbation amount, and integrate the timing perturbation data of each harmonic pair to form the final switching timing perturbation amount.

[0044] According to one aspect of the present application, the steps of optimizing the H-bridge drive signal include:

[0045] Apply the switching timing perturbation amount to the basic switching timing to generate accurate switching timing data;

[0046] Taking the optimal phase relationship in the critical phase difference matrix as the target value, calculate the phase control deviation to form phase deviation data;

[0047] According to the phase deviation data, calculate the adjustment value of the perturbation amount, generate perturbation adjustment data and apply it to the precise switching timing data to form a closed-loop control timing;

[0048] Based on the closed-loop control timing, generate the drive signals of each H-bridge unit to achieve optimal control of the power unit.

[0049] According to one aspect of the present application, the steps of forming phase deviation data and generating perturbation adjustment data include:

[0050] Extract the target phase relationship from the critical phase difference matrix to construct control target data;

[0051] Calculate the actual harmonic phase of the voltage and current signals in real time to form measured phase data;

[0052] Calculate the actual phase difference to generate a measured phase difference vector;

[0053] Compare the control target data with the measured phase difference vector, and calculate the phase control deviation e phase = φ criticaltarget - φij measured , to form phase deviation data;

[0054] Through an adaptive controller, dynamically adjust the control parameters Kp(e) = Kp base ·(1 + αp·|e phase |) and Ki(e) = Ki base ·(1 + αi·|e phase | 2 ), to form control parameter adaptive data;

[0055] Implement the control algorithm, calculate the incremental adjustment value of the perturbation amount, and generate control increment data;

[0056] Combine feedback control and feedforward prediction, calculate the total control action, and update the perturbation adjustment data.

[0057] According to one aspect of the present application, the steps of monitoring the system output, calculating performance index data, and dynamically adjusting the phase-locking control parameters include:

[0058] Collect the voltage waveform data and current waveform data actually output by the system;

[0059] Calculate the real-time total harmonic distortion and each harmonic index to form harmonic performance indicators;

[0060] Calculate the deviation between the harmonic amplitude and phase and the target value, and generate harmonic control deviation data;

[0061] Establish a multi-objective evaluation system, comprehensively consider the harmonic suppression effect, phase control accuracy and system stability, and calculate the comprehensive performance index;

[0062] According to the harmonic control deviation data and the comprehensive performance index, dynamically adjust the control parameters and generate a parameter adjustment instruction;

[0063] Feed the parameter adjustment instruction back to the phase-locked controller to achieve closed-loop optimization.

[0064] According to one aspect of the present application, the step of dynamically adjusting the control parameters according to the harmonic control deviation data and the comprehensive performance index includes:

[0065] Evaluate the effectiveness of the current control strategy and construct control evaluation data;

[0066] Calculate the control parameter sensitivity S param = dCPI / dP, identify the key parameters, and form a parameter sensitivity matrix;

[0067] Construct a parameter optimization objective function with the comprehensive performance index as the optimization objective;

[0068] Use the gradient descent method with a decreasing step size to optimize the parameters and generate a parameter optimization sequence;

[0069] Constrain the parameter changes to ensure that the adjustment amplitude is within the safe range and form safe parameter adjustment data;

[0070] Based on the historical performance data, construct a parameter-performance mapping model to predict the performance of different parameter combinations;

[0071] Combine the gradient optimization and the model prediction results to determine the final parameter adjustment plan and form a parameter adjustment instruction.

[0072] Beneficial effects: The present invention reveals the sensitivity of the resonant harmonics to the phase relationship, precisely controls the harmonic phase through the microsecond-level switching timing, effectively suppresses the harmonic amplification effect under resonant conditions, and improves the system stability and power quality. Brief Description of the Drawings

[0073] Figure 1 is the flowchart of the present invention.

[0074] Figure 2 is the flowchart of the present invention for extracting the harmonic time-domain characteristics and phase relationship parameters, analyzing the phase sensitivity between harmonics, and calculating the critical phase difference matrix.

[0075] Figure 3It is a flowchart of the present invention for analyzing the harmonic dynamic characteristic matrix and phase difference sequence, identifying the corresponding mode of harmonic amplification and phase relationship, and generating phase sensitivity data.

[0076] Figure 4 It is a flowchart of the present invention for finding the phase difference value that minimizes the growth rate and calculating the growth rate sensitivity. Specific embodiments

[0077] As Figures 1 to 4 shown, a method for harmonic selective elimination of a cascaded H-bridge converter based on space voltage vector in CAES is provided, including:

[0078] S1. Collect the operation data of the CAES system and grid parameters, and construct a real-time monitoring data set, specifically:

[0079] Collect the output voltage and current signals of the cascaded H-bridge converter, and at the same time measure the key parameters of the CAES system working conditions (including compressor operation status, energy storage status and energy release status) and grid-side voltage, current and power factor, etc., construct a complete real-time monitoring data set containing timestamps, and perform high-speed sampling, preprocessing and data calibration to form a comprehensive digital representation of the system state.

[0080] S2. Process the real-time monitoring data set, extract the harmonic time-domain characteristics and phase relationship parameters, analyze the phase sensitivity between harmonics, calculate the critical phase difference matrix, and determine the key control parameters for resonance suppression. Specifically:

[0081] Perform a fast Fourier transform on the calibrated monitoring data, calculate the amplitudes and phases of each harmonic, analyze the normalized harmonic growth rate and its time variation trend, and determine the phase relationship between harmonics. By correlating and analyzing the harmonic dynamic characteristics and phase difference sequence, identify the corresponding mode of harmonic amplification and phase relationship, calculate the phase sensitivity, and combine the system impedance characteristics to determine the critical phase relationship that is most sensitive to resonance suppression, and construct a critical phase difference matrix containing the optimal phase difference value, allowable error range and phase sensitivity, providing a key parameter basis for subsequent control.

[0082] S3. According to the critical phase difference matrix, reconstruct and optimize the space voltage vector, calculate the switching timing perturbation amount, and achieve precise control of the harmonic phase. Specifically:

[0083] Based on the optimal phase relationship in the critical phase difference matrix, the traditional harmonic elimination problem is transformed into a phase optimization problem. An objective function that combines phase control and total harmonic distortion is constructed, and the optimal switching angle sequence is calculated by the gradient descent method. Based on the optimal switching angle, the basic switching timings of each H-bridge unit are calculated, and according to the sensitivity analysis of the key harmonic phases, a switching timing perturbation amount at the nanosecond level is generated to achieve precise control of the harmonic phases. At the same time, considering the hardware precision limitations and switching characteristics, quantization processing and error compensation are carried out.

[0084] S4. Combine the switching timing perturbation amount and the critical phase difference matrix to generate a phase-locked control instruction, optimize the H-bridge drive signal, and achieve precise control of each power unit. Specifically:

[0085] Integrate the basic switching timing and the perturbation amount to generate precise switching timing data. Design a phase-locked closed-loop controller, use the optimal phase relationship in the critical phase difference matrix as the target value, measure the actual phase difference in real time as the feedback quantity, calculate the control deviation, and adopt an adaptive PI control algorithm to dynamically adjust the perturbation amount. Apply a control strategy that combines feedforward and feedback to eliminate high-frequency oscillations, generate the final closed-loop control timing, and convert it into the precise drive signal of each H-bridge power unit to achieve real-time closed-loop control of the harmonic phases.

[0086] S5. Monitor the system output, calculate the performance index data, dynamically adjust the phase-locked control parameters, and continuously optimize the harmonic control effect. Specifically:

[0087] Continuously collect the voltage and current waveforms of the actual system output, calculate the real-time total harmonic distortion and the amplitudes and phases of each harmonic, and monitor the deviation from the target value. Establish a multi-objective evaluation system that includes harmonic suppression effect, phase control accuracy, and system stability, and calculate the comprehensive performance index. Based on the performance evaluation results, analyze the sensitivity of the control parameters, construct a parameter-performance mapping model, and adopt a gradient optimization with a decreasing step size and a confidence weighting strategy to dynamically adjust the critical phase difference matrix and the controller parameters, forming a complete adaptive optimization loop to achieve continuous optimization of the harmonic control effect and improvement of the system adaptability.

[0088] According to one aspect of the present application, S1 is specifically:

[0089] S11. Collect the output voltage signal Uout(t) and the output current signal Iout(t) of the cascaded H-bridge inverter, and digitize them using a high-speed data acquisition system at a sampling frequency of 20 kHz to obtain the original voltage and current data.

[0090] S12. Measure the operating condition parameters of the CAES system, including the compressor operating state SP, the energy storage state SE, and the energy release state SR, and construct a system operating condition vector SW.

[0091] S13. Collect the grid-side voltage UN and grid-side current IN, calculate the grid-side power PN and grid-side power factor PFN, and form the grid state vector NS.

[0092] S14. Integrate the original voltage and current data, the system operating condition vector SW, and the grid state vector NS to construct a real-time monitoring data set RMD containing time stamps, and store it in segments with a time window of 100 ms.

[0093] S15. Preprocess the real-time monitoring data set RMD, including filtering high-frequency noise, compensating for sampling bias, and calibrating the amplitude, to obtain the calibrated monitoring data set CMD.

[0094] According to one aspect of the present application, S2 is specifically as follows:

[0095] S21. Apply the fast Fourier transform to the original voltage and current data in the calibrated monitoring data set CMD, calculate the amplitude Hi(t) and phase φi(t) of each harmonic, and obtain the harmonic spectrum data HSD.

[0096] S22. Calculate the time derivative dHi / dt of the amplitude of each harmonic in the harmonic spectrum data HSD, and construct a harmonic growth rate vector HGR to characterize the dynamic change characteristics of the harmonics. d is the partial derivative symbol.

[0097] S23. Establish a normalized harmonic growth rate Ri(t) calculation model, process the harmonic growth rate vector HGR, and obtain the normalized growth data NGD: Ri(t) = (dHi / dt) / Hi(t);

[0098] S24. Analyze the time variation trend of the normalized growth data NGD, and calculate the harmonic growth acceleration index Ai(t):

[0099] Ai(t) = dRi / dt, and form the harmonic dynamic characteristic matrix HDM.

[0100] S25. Analyze the phase relationship between adjacent harmonics, calculate the phase difference φij(t) = φi(t) - φj(t) between harmonics, and generate a phase difference sequence PDS.

[0101] S26. Conduct a correlation analysis on the harmonic dynamic characteristic matrix HDM and the phase difference sequence PDS, identify the corresponding patterns of harmonic amplification and phase relationship, and generate phase sensitivity data PSD.

[0102] S27. Based on the phase sensitivity data PSD, determine the phase relationship that is most sensitive to resonance suppression, and calculate the critical phase difference matrix CPM: CPM(i,j) = φ critical (i,j) = φi optimal - φjoptimal - φZ(ωi, ωj); where φZ(ωi, ωj) is the phase angle difference of the system impedance at the corresponding frequency.

[0103] According to one aspect of the present application, S3 is specifically:

[0104] S31. Based on the critical phase difference matrix CPM, calculate the space voltage vector angle θVS that can achieve the optimal phase relationship, and form a space vector angle sequence VAS.

[0105] S32. Convert the switching angle calculation of the traditional SHE method into a phase optimization problem, and establish an objective function:

[0106] J(α) = Σwi·|φi(α) - φi optimal | 2 + λ·THD(α);

[0107] where α is the switching angle vector, φi(α) is the harmonic phase corresponding to the switching angle, and φi optimal is the optimal phase from the critical phase difference matrix CPM, and obtain the objective function parameter set TFP.

[0108] S33. Use the gradient descent method to optimize the objective function in the objective function parameter set TFP, and calculate the optimal switching angle vector α optimal to obtain the optimized switching angle data OSD.

[0109] S34. Based on the optimized switching angle data OSD, calculate the basic switching timing t _switching_base of each H-bridge unit, and form the basic timing data BTD.

[0110] S35. Analyze the sensitive phase relationship in the critical phase difference matrix CPM, and calculate the phase fine-tuning amount Δφ fine that needs to be finely adjusted, and generate the phase fine-tuning data PFD.

[0111] S36. Convert the phase fine-tuning data PFD into a switching timing perturbation amount δt = Δφ fine / (2π·f);

[0112] where f is the fundamental frequency, and obtain the switching timing perturbation amount STD.

[0113] According to one aspect of the present application, S4 is specifically:

[0114] S41. Integrate the basic timing data BTD and the switching timing perturbation amount STD, and calculate the actual switching timing: t _switching_actual = t _switching_base ± δt, and generate the precise switching timing data PSD.

[0115] S42. Design a phase-locked closed-loop controller. Taking the optimal phase relationship in the critical phase difference matrix CPM as the target value and the actually measured phase difference as the feedback value, calculate the control deviation e phase = φ criticaltarget - φ criticalmeasured , and form phase deviation data PDD.

[0116] S43. According to the phase deviation data PDD, use the PI control algorithm to calculate the adjustment value of the perturbation amount: δt k+1 = δt k + Kp·e phase + Ki·∫e phase ·dt, and generate perturbation adjustment data DCD.

[0117] S44. Apply the perturbation adjustment data DCD to the precise switching timing data PSD to generate the updated closed-loop control timing CLT.

[0118] S45. Based on the closed-loop control timing CLT, generate the driving signal waveforms of each H-bridge unit, including the turn-on time, turn-off time, and modulation mode, to form the final H-bridge driving signal group HDS.

[0119] According to one aspect of the present application, S5 is specifically:

[0120] S51. Collect the voltage waveform data VWD and current waveform data CWD actually output by the system, and calculate the real-time total harmonic distortion THD measured , and form the harmonic performance index HPI.

[0121] S52. Monitor the amplitudes Hi measured and phases φi measured of each harmonic, and calculate the deviation from the target value:

[0122] e Hi = Hi target - Hi measured ; e φi = φi target - φi measured ; Generate harmonic control deviation data HCD.

[0123] S53. Establish a multi-objective evaluation index, comprehensively consider the THD suppression effect, harmonic phase control accuracy, and system stability, and calculate the comprehensive performance index CPI.

[0124] S54. According to the harmonic control deviation data HCD and the comprehensive performance index CPI, dynamically adjust the key parameters in the critical phase difference matrix CPM to generate a parameter adjustment instruction PAI.

[0125] Feedback the parameter adjustment instruction PAI to the phase-locked controller, update the control parameters of the perturbation adjustment data DCD, complete the closed-loop optimization, and continuously improve the harmonic control effect.

[0126] By precisely controlling the harmonic phase relationship, the problem of harmonic amplification effect under the resonance condition of the CAES system is solved. It is found and utilized that the harmonic amplification effect is highly sensitive to the phase relationship. Through precise regulation of the switching timing at the microsecond level, the effective suppression of the resonant harmonics is achieved, ensuring the accuracy and stability of harmonic control.

[0127] According to one aspect of the present application, S26 is specifically:

[0128] S261. Read the harmonic dynamic characteristic matrix HDM and the phase difference sequence PDS, and create a phase-growth rate mapping table PGRM to record the harmonic growth characteristics under different phase difference conditions.

[0129] S262. Divide the data in the phase difference sequence PDS into 72 phase intervals at 5° intervals to obtain a phase interval vector PIV.

[0130] S263. For each harmonic pair (i, j), traverse all intervals in the phase interval vector PIV, and statistically calculate the average normalized growth rate R avg (i, φij) of harmonic i in this phase interval to form a phase-growth rate correspondence table PGCT.

[0131] S264. Apply cubic spline interpolation to the data in the phase-growth rate correspondence table PGCT to generate a continuous phase-growth rate function R(i, φij) to form a continuous mapping function CMF.

[0132] S265. For each harmonic i in the continuous mapping function CMF, find the phase difference value φij that minimizes the growth rate min : φij min = argmin_φij R(i, φij) to generate an optimal phase difference vector OPDV.

[0133] Alternatively, for each harmonic i in the continuous mapping function CMF, determine the optimal phase difference value by minimizing the phase-growth rate function R(i, φij).

[0134] S(i, φij) represents the sensitivity of the i-th harmonic relative to the phase difference φij; i represents the harmonic order; φij represents the phase difference between the i-th harmonic and the j-th harmonic; R(i, φij) represents the normalized growth rate of the i-th harmonic under the phase difference φij; dR(i, φij) / dφij represents the partial derivative of the normalized growth rate R with respect to the phase difference φij.

[0135] S266. For each element of the optimal phase difference vector OPDV, calculate its corresponding growth rate sensitivity S(i, φij): S(i, φij) = |dR(i, φij) / dφij| φij=φijmin , to form the phase sensitivity matrix PSM. S(i, φij) = |dR(i, φij) / dφij| φij=φijmin ; indicating taking the absolute value of the derivative under the condition of φij = φij min .

[0136] S267. Based on the phase sensitivity matrix PSM and the optimal phase difference vector OPDV, determine the key harmonic pairs that have the greatest impact on the resonance suppression effect, construct the key harmonic pair list KHPL, and record the harmonic pairs whose phase sensitivity exceeds the threshold.

[0137] S268. For each pair of harmonics (i, j) in the key harmonic pair list KHPL, analyze the change in their phase-sensitive characteristics under different system operating conditions, and establish the operating condition-phase sensitivity mapping CPSM.

[0138] S269. According to the operating condition-phase sensitivity mapping CPSM and the phase sensitivity matrix PSM, extract and integrate the phase-sensitive characteristics of each harmonic pair to generate the complete phase sensitivity data PSD.

[0139] The phase sensitivity identification technology accurately quantifies the internal relationship between harmonic amplification and phase relationship by constructing a phase-growth rate mapping table and finding the optimal phase difference. It enables the system to directly associate the harmonic dynamic characteristics with the phase difference and find out the key phase relationships that have the greatest impact on resonance suppression. Under the resonance condition of the CAES system, this technology enables the control system to accurately identify the phase characteristics of key harmonic pairs with a phase sensitivity of up to 0.0112 (the traditional method is usually only about 0.001), and improves the harmonic suppression efficiency from 50% of the traditional method to 72.8%. It reveals that the phase relationship between high-order harmonics (such as between the 5th and 7th harmonics) has a greater impact on the system stability than the phase relationship with the fundamental wave.

[0140] According to one aspect of the present application, step S27 is specifically as follows:

[0141] S271. Read the phase sensitivity data PSD and the key harmonic pair list KHPL, and extract the optimal phase difference value φij optimal , as the base value of the initial critical phase difference.

[0142] S272. Collect the instantaneous voltage and current samples in the original voltage and current data, and calculate the system impedance frequency characteristic Z(ω): Z(ω) = FFT(Uout(t)) / FFT(Iout(t)), to obtain the system impedance data SID.

[0143] S273. Extract the impedance phase angle φZ(ωi) at each harmonic frequency point from the system impedance data SID to form the impedance phase angle vector IAV.

[0144] S274. For each pair of harmonics (i,j) in the key harmonic pair list KHPL, calculate its corresponding impedance phase angle difference φZ(ωi,ωj): φZ(ωi,ωj) = φZ(ωi) - φZ(ωj), to generate the impedance phase angle difference matrix IADM.

[0145] S275. Build a correction model, consider the influence of system impedance on the optimal phase difference, and calculate the corrected critical phase difference φ critical (i,j): φ critical (i,j) = φij optimal - φZ(ωi,ωj) + K_corr(i,j), where K_corr(i,j) is the correction coefficient obtained from the statistical analysis of historical data, to generate the corrected phase difference data CPDD.

[0146] S276. Conduct a robustness analysis on the corrected phase difference data CPDD, simulate the influence of system parameter fluctuations on the critical phase difference, and calculate the allowable fluctuation range Δφ allow (i,j), to form the phase tolerance matrix PTM.

[0147] S277. Integrate the corrected phase difference data CPDD and the phase tolerance matrix PTM to build a complete critical phase difference matrix CPM, which contains the following information: CPM(i,j) = {φ critical (i,j), Δφ allow (i,j), S(i,φij)}, where S(i,φij) is the phase sensitivity data obtained from the phase sensitivity matrix PSM.

[0148] S278. According to the phase sensitivity, assign a priority weight w(i,j) to each element in the critical phase difference matrix CPM to build a phase control priority vector PPV to guide the subsequent control strategy.

[0149] The critical phase difference matrix calculation method realizes the accurate determination of key parameters for harmonic control by comprehensively considering the system impedance characteristics and correction coefficients. Traditional methods ignore the influence of system impedance on the harmonic phase relationship, while the present invention extracts the system impedance frequency characteristic Z(ω) and calculates the impedance phase angle difference φZ(ωi, ωj) at each harmonic frequency point, establishing a complete correction model. This enables the control system to adapt to parameter fluctuations in the CAES system. Under the condition of a ±10% change in system impedance, the control effect fluctuation is only 8% (35% for traditional methods). By introducing the phase tolerance matrix PTM, the control system can adaptively determine the allowable fluctuation range of each harmonic phase, solving the problem of reduced control accuracy in traditional methods during dynamic changes in system parameters and ensuring continuous and efficient control during operating condition changes such as compressor startup and shutdown.

[0150] According to one aspect of the present application, step S32 is specifically as follows:

[0151] S321. Read the critical phase difference matrix CPM and the space vector angle sequence VAS, extract the optimal phase φi optimal and the corresponding weight w(i,j), and construct the phase target parameter set PTP.

[0152] S322. Construct the harmonic amplitude control objective function J of the traditional SHE method trad itional: J trad itional(α)= Σγi·(Hi(α) - Hi target ) 2 + γ0·(H1(α) - 1) 2 ; where α is the switching angle vector, Hi(α) is the corresponding harmonic amplitude, Hi target is the target harmonic amplitude (usually zero), and generate the traditional objective function parameter TFP trad .

[0153] S323. Establish the mapping function φi = Φi(α) from the switching angle to the harmonic phase. Through linearization analysis and numerical simulation, construct the angle-phase mapping model APM: Φi(α) = A i ·α + b i + ξi(α); where A i is the linear mapping matrix, b i is the bias vector, and ξi(α) is the non-linear correction term.

[0154] S324. Based on the angle-phase mapping model APM, convert the traditional SHE method into the phase optimization objective function J phase : J phase (α) = Σwi·|Φi(α) - φi optimal |2 + λ·THD(α) to generate the Phase Optimization Objective Function POF.

[0155] S325. Perform a second-order Taylor expansion on the non-linear correction term ξi(α) in the Phase Optimization Objective Function POF to obtain an approximate quadratic programming problem: J_approx(α) = (α - α0) T ·Q·(α - α0) + c T ·(α - α0) + d; where Q, c, and d are the quadratic term coefficient matrix, the linear term coefficient vector, and the constant term respectively, forming the Approximate Optimization Parameter Set AOP.

[0156] S326. Apply a quadratic programming solver to the quadratic programming problem represented by the Approximate Optimization Parameter Set AOP to calculate the initial optimal switching angle vector α init , forming the Initial Solution Vector ISV.

[0157] S327. Starting from the Initial Solution Vector ISV, accurately solve the original Phase Optimization Objective Function POF using the gradient descent method: α k+1 = α k - η·∇J phase (α k ); where η is the adaptive step size, determined by line search, generating the Optimization Iteration Sequence OIS.

[0158] S328. Set the convergence condition and stop the iteration when the change in the objective function is less than the threshold ε or the maximum number of iterations is reached: |J phase (α k+1 ) - J phase (α k )| < ε; obtaining the final Optimized Switching Angle Data OSD.

[0159] S329. Verify the harmonic control effect of the Optimized Switching Angle Data OSD, calculate the corresponding harmonic phase φi(α optimal ) and harmonic amplitude Hi(α optimal ), constructing the Harmonic Control Performance Data HCPD for evaluating the optimization effect.

[0160] The phase-based objective function optimization method transforms the harmonic amplitude control of the traditional SHE method into harmonic phase optimization and establishes a mapping function Φi(α) from the switching angle to the harmonic phase. This enables the control system to directly and precisely regulate the harmonic phase. Compared with the traditional method that only focuses on the harmonic amplitude, it realizes a deeper control of the essential characteristics of harmonics. By constructing the phase optimization objective function J_phase(α) = Σwi·|Φi(α) - φi_optimal|² + λ·THD(α) and combining quadratic programming and gradient descent solution techniques, the system can achieve more precise harmonic phase control in the CAES environment with complex voltage spectrum characteristics. Measured data shows that the calculation convergence speed of this method is increased by 65%, and the DSP processor load is reduced from 85% of the traditional method to 42%, significantly improving the real-time control ability.

[0161] According to one aspect of the present application, calculating the switching timing perturbation in step S36 specifically includes:

[0162] S361. Read the phase fine-tuning data PFD and the optimized switching angle data OSD, extract the phase fine-tuning amount Δφ that needs to be finely adjusted, fine and construct a micro-radian phase adjustment vector MPAV in micro-radians.

[0163] S362. Analyze the phase sensitivity data S(i, φij) in the critical phase difference matrix CPM, determine the key phase adjustment parameters that have the greatest impact on the system performance, and generate a key phase parameter list KPPL.

[0164] S363. For each parameter in the key phase parameter list KPPL, establish an accurate time-phase conversion model: δt ij = Δφ fineij / (2π·f·n ij ); where f is the fundamental frequency, and n ij is the phase sensitivity adjustment coefficient, which is dynamically calculated according to the harmonic order to form time-phase transformation parameters TPTP.

[0165] S364. Considering the system hardware timing control accuracy τ min (usually at the nanosecond level), quantify the calculated time perturbation: δt quantized = round(δt / τ min )·τ min ; generate quantified timing adjustment data QTAD.

[0166] S365. Analyze the impact of the quantization error ε_quant = δt - δt quantized on the phase control accuracy, establish a compensation mechanism, and generate quantization error compensation data QECD.

[0167] S366. Consider the turn-on delay t on and turn-off delay t off of the H-bridge switching device, and establish a switching timing correction model: δt corrected = δt quantized + (t on - t off ) / 2; Form the corrected timing data CTD.

[0168] S367. According to the H-bridge topology and switching sequence, convert the corrected timing data CTD into the trigger timing adjustment amount δt gate of each power switching device, and generate the gate drive timing adjustment data GDTD.

[0169] S368. Integrate the timing perturbation data of each harmonic pair, consider the mutual influence when multiple harmonics are controlled simultaneously, and use the weighted average method to calculate the final perturbation amount: δt_final = Σwij·δt gatei j / Σw ij ; where w ij is the weight assigned based on the phase sensitivity, and form the final switching timing perturbation amount STD.

[0170] In one embodiment, S366 can also be: Consider the turn-on delay t_on and turn-off delay t_off of the H-bridge switching device and the quantization error compensation data QECD of the previous cycle, and establish a complete switching timing correction model: δt_corrected = δt_quantized + (t_on - t_off) / 2 + QECD[i-1]; where QECD[i-1] is the quantization error compensation value of the previous cycle, and through this mechanism, the average compensation of the quantization error is realized on multiple cycles to prevent the accumulation of the quantization error. After correction, the corrected timing data CTD is formed.

[0171] Considering the system hardware timing control accuracy and the turn-on and turn-off delay characteristics of the switching device, through quantization processing δt_quantized = round(δt / τ_min)·τ_min and switching timing correction δt_corrected = δt_quantized + (t_on - t_off) / 2, the gap between theoretical calculation and actual hardware implementation is solved. The harmonic phase control accuracy can be improved to ±1.5° (usually ±5° for traditional methods), and the response time is shortened from 25 ms of traditional methods to 3 ms, realizing the leading intervention of resonant harmonics, effectively preventing the exponential amplification of harmonics under resonant conditions, and ensuring the stable operation of the system under high power fluctuation conditions.

[0172] According to one aspect of the present application, step S42 is specifically as follows:

[0173] S421. Read the critical phase difference matrix CPM and the original voltage and current data, extract the target phase relationship φ criticaltarget , and construct the control target data CTD.

[0174] S422. Calculate the actual harmonic phase φi of the voltage and current signals in real time measured , using the sliding window fast Fourier transform: φi measured = angle(FFT_window(Uout(t), Iout(t))); form the measured phase data MPD.

[0175] S423. Based on the measured phase data MPD, calculate the actual phase difference φij measured = φi measured - φj measured , and generate the measured phase difference vector MPDV.

[0176] S424. Compare the target phase relationship in the control target data CTD with the measured phase difference vector MPDV, and calculate the phase control deviation e phase : e phase = φ criticaltarget - φij measured ; ensure that the deviation range is within [-π, π], and generate the phase deviation data PDD.

[0177] S425. Design an adaptive PI controller, and dynamically adjust the proportional coefficient Kp(e) and the integral coefficient Ki(e) according to the amplitude and change trend of the phase deviation: Kp(e) = Kp base ·(1 + αp·|e phase |); Ki(e) = Ki base ·(1 + αi·|e phase | 2 ); form the control parameter adaptive data CPAD.

[0178] S426. Implement the PI control algorithm with anti-integral saturation, and calculate the incremental adjustment value Δδt of the perturbation amount:

[0179] Δδt = Kp(e)·e phase + Ki(e)·∫e phase ·dt;

[0180] If |∫e phase ·dt| > I_max, then;

[0181] ∫e phase·dt = sign(∫e phase ·dt)·I_max;

[0182] End, generate control increment data CID.

[0183] Kp(e) represents the adaptive proportional coefficient, a proportional control parameter dynamically adjusted according to the phase deviation, used for the intensity of the controller response. Ki(e) represents the adaptive integral coefficient, an integral control parameter dynamically adjusted according to the phase deviation, used to eliminate the steady-state error. Kp_base represents the base proportional coefficient, which is the reference value of the proportional control and the default parameter value when the phase deviation is zero. Ki_base represents the base integral coefficient, which is the reference value of the integral control and the default parameter value when the phase deviation is zero. αp represents the proportional adaptive adjustment parameter, which determines the influence intensity of the phase deviation on the proportional coefficient. The larger the value, the more significant the adjustment effect of the deviation on the parameter. αi represents the integral adaptive adjustment parameter, which determines the influence intensity of the phase deviation on the integral coefficient. The larger the value, the more significant the adjustment effect of the deviation on the parameter. e_phase represents the phase control deviation, which represents the error between the actual phase difference and the target phase difference. The calculation formula is e_phase = φ_criticaltarget represents φij_measured, where φ_criticaltarget is the target critical phase difference and φij_measured is the measured phase difference.

[0184] S427. Apply the feedforward control enhancement mechanism, predict the phase change trend according to the system working conditions and historical response patterns, and calculate the feedforward compensation amount δt ff , and form the feedforward control data FFD.

[0185] S428. Integrate the feedback control and the feedforward control, and calculate the total control action: δt k+1 = δt k + Δδt + δt ff ; Generate the updated perturbation adjustment data DCD.

[0186] S429. Apply frequency domain filtering to the perturbation adjustment data DCD to eliminate the high-frequency oscillation components and ensure the smoothness of the control signal: δt_filtered = LPF(δt k+1 ); where LPF is a low-pass filter, and generate the filtered control data FCD.

[0187] S4210. Apply the filtered control data FCD to the precise switching timing data PSD to generate the final closed-loop control timing CLT and achieve phase-locked closed-loop control.

[0188] Enable the system to adaptively adjust the control intensity according to the characteristics of harmonic phase deviation under different working conditions, avoiding overshoot or underdamped response of traditional fixed-parameter controllers under large disturbance conditions. Combining the feedforward control enhancement mechanism and frequency-domain filtering technology, this method has achieved a significant improvement in THD from 10.3% to 2.8% during the start-stop process of the compressor in the CAES system, and the phase tracking accuracy has been improved to ±1.5°. In particular, this control mechanism can intervene in the control at the initial stage of small harmonic changes (when the amplitude change is not obvious but the growth rate begins to rise), effectively suppressing the nonlinear growth of harmonics.

[0189] According to one aspect of the present application, step S54 is specifically as follows:

[0190] S541. Read the harmonic control deviation data HCD and the comprehensive performance index CPI, evaluate the effectiveness of the current control strategy, and construct the control evaluation data CED.

[0191] S542. Based on the control evaluation data CED, calculate the control parameter sensitivity S param = dCPI / dP, identify the key parameters that have the greatest impact on the system performance, and form the parameter sensitivity matrix PSM_ctrl.

[0192] S543. Construct the parameter optimization objective function J param (P) = CPI(P), where P is the control parameter vector, including the phase-locked controller parameters and the critical phase difference, and generate the parameter optimization function POF param .

[0193] S544. Use the gradient descent method with a decreasing step size to optimize the parameter optimization function POF param :

[0194] P k+1 = P k - η k ·∇J param (P k ); η k+1 = η k ·λ; where η k is the step size, and λ is the step size attenuation coefficient, and generate the parameter optimization sequence POS.

[0195] S545. Constrain the parameter changes in the parameter optimization sequence POS to ensure that the parameter adjustment amplitude is within the safe range: if |P k+1 - P k | > ΔP_max, then, P k+1 = P k + sign(P k+1 - P k)·ΔP_max; Form safety parameter adjustment data SPAD.

[0196] S546. Based on historical performance data, construct a parameter - performance mapping model CPI = M(P), and use the locally weighted regression analysis method to generate a parameter performance model PPM.

[0197] S547. Use the parameter performance model PPM to predict the performance indicators of different parameter combinations, and identify the optimal parameter combination P optimal , forming a predicted optimal parameter POP.

[0198] S548. Combine the gradient optimization result safety parameter adjustment data SPAD and the model prediction result predicted optimal parameter POP, and adopt a confidence - weighted strategy to determine the final parameter adjustment scheme: P_final = β·P_gradient + (1 - β)·P_model; where β is a weight coefficient dynamically adjusted based on data reliability, generating a final parameter scheme FPP.

[0199] S549. Convert the final parameter scheme FPP into specific control parameter adjustment instructions, including critical phase difference adjustment values, controller parameter adjustment values, etc., forming parameter adjustment instructions PAI.

[0200] S5410. Distribute the parameter adjustment instructions PAI to each control module of the system, including updating the key parameters of the critical phase difference matrix CPM and adjusting the control parameter adaptive data CPAD of the phase - locked controller, to complete the closed - loop optimization adjustment of the entire system.

[0201] Enable the system to continuously improve the control strategy according to the operation data, solve the problem of reduced control effect caused by parameter aging and system operating condition changes during the long - term operation of traditional methods. In the long - term operation test of the actual CAES system, enable the control parameters to adaptively track the changes in system characteristics and maintain the best control effect. By integrating the gradient optimization and model prediction results through the confidence - weighted strategy P_final, the system can quickly adapt when facing new operating conditions, the convergence time of the control parameters is shortened by 78%, avoiding the complex process of manual intervention and re - tuning parameters required by traditional methods, and improving the autonomy and reliability of the system.

[0202] This embodiment is for an actual CAES system, adopting a 7 - level cascaded H - bridge inverter topology, with a rated power of 2.5 MW, a DC bus voltage of 1500 V, and a switching frequency of 850 Hz. Severe harmonic amplification problems occur during the start - stop process of the compressor in this system. In particular, the 5th, 7th, and 11th harmonics will resonate under specific operating conditions, resulting in a THD exceeding 10%, affecting the system stability and equipment safety.

[0203] 1. Harmonic phase sensitivity identification process

[0204] In this embodiment, through long-term monitoring of the CAES system during the compressor start-stop phase, a large amount of voltage and current data was collected. After processing the collected data, the harmonic dynamic characteristic matrix HDM and the phase difference sequence PDS were obtained.

[0205] The following method is adopted: the average normalized growth rate R min (i, φij) in each phase interval [φ avg (i, φij) = (1 / N)·∑R k (i); where: R k (i) is the normalized growth rate of the k-th sample point in the interval; N is the number of sample points in the interval; φij is the phase difference between the i-th harmonic and the j-th harmonic; i is the harmonic order; j is the reference harmonic order.

[0206] Through calculation, the relationship data between the phase difference of the 5th harmonic relative to the fundamental wave and its growth rate was obtained. Some of the data is shown in the following table:

[0207] Phase range (°) <![CDATA[Average normalized growth rate R avg (5, φ51)]]> 0-5 0.035 5-10 0.032 ... ... 175-180 0.188 180-185 0.195 ... ... 265-270 -0.086 270-275 -0.092 ... ... 355-360 0.018

[0208] The optimal phase difference φij min = argmin_φij R(i, φij); where: R(i, φij) is the phase-growth rate function; φij is the phase difference between the i-th harmonic and the j-th harmonic; i is the harmonic order; j is the reference harmonic order.

[0209] Applying this calculation, the optimal phase difference of the 5th harmonic was identified as φ51 min = 273°, and at this time R(5, 273°) = -0.095, indicating that under this phase relationship, the 5th harmonic has the maximum suppression effect.

[0210] The phase sensitivity S(i, φij) = |dR(i, φij) / dφij|_φij=φij min ; where: R(i, φij) is the phase-growth rate function; φij is the phase difference; φij min is the optimal phase difference; dR / dφij is the derivative of R with respect to φij; i is the harmonic order; j is the reference harmonic order.

[0211] At the optimal phase point, it is calculated that S(5, 273°) = 0.0085, indicating that for every 1° change in phase, the normalized growth rate changes by approximately 0.0085. This value is much higher than the phase sensitivity in traditional harmonic control methods (usually about 0.001).

[0212] Through similar calculations, the phase sensitivity data of the following key harmonic pairs was identified:

[0213]

[0214] The last line of data is particularly noteworthy. It shows that the phase relationship between the 5th harmonic and the 7th harmonic (rather than the phase relationship with the fundamental wave) has a greater impact on the harmonic suppression effect, which is not considered in the traditional SHE method.

[0215] 2. Calculation process of the critical phase difference matrix

[0216] The phase angle differences are extracted from the system impedance measurement data: φZ(ω5,ω1) = 37°; φZ(ω7,ω1)= 52°; φZ(ω11,ω1) = 83°; φZ(ω5,ω7) = -15°;

[0217] The correction coefficients are obtained based on historical data analysis: K_corr(5,1) = 12°; K_corr(7,1) = 16°; K_corr(11,1) = 9°; K_corr(5,7) = 18°;

[0218] Read the calculation formula: the corrected critical phase difference φ critical (i,j) = φij optimal - φZ(ωi,ωj) + K_corr(i,j); where: φij optimal is the optimal phase difference; φZ(ωi,ωj) is the phase angle difference of the system impedance at the corresponding frequency; K_corr(i,j) is the correction coefficient; i is the harmonic order; j is the reference harmonic order; ωi is the angular frequency of the i-th harmonic; ωj is the angular frequency of the j-th harmonic.

[0219] Substitute the formula to calculate the corrected critical phase difference: φ critical (5,1) = 273° - 37° + 12° =248°; φ critical (7,1) = 304° - 52° + 16° = 268°; φ critical (11,1) = 92° - 83° + 9° =18°; φ critical (5,7) = 149° - (-15°) + 18° = 182°;

[0220] The method in step S276: the phase tolerance Δφ allow (i,j) = arctg(0.1 / S(i,φij)); where: S(i,φij) is the phase sensitivity; 0.1 is the allowable normalized growth rate increment threshold; i is the harmonic order; j is the reference harmonic order.

[0221] Calculate the phase tolerance for each harmonic pair: Δφ allow (5,1) = arctg(0.1 / 0.0085) = 85.1°; Δφ allow (7,1) = arctg(0.1 / 0.0073) = 85.8°; Δφ allow (11,1) = arctg(0.1 / 0.0064) =86.3°; Δφ allow (5,7) = arctg(0.1 / 0.0112) = 83.6°;

[0222] These data form the complete critical phase difference matrix CPM, guiding the subsequent control strategy design.

[0223] 3. Phase-based SHE method conversion

[0224] In this embodiment, the following weight settings are adopted: w5 = 0.4 (weight of the 5th harmonic); w7 = 0.3 (weight of the 7th harmonic); w11 = 0.2 (weight of the 11th harmonic); λ = 0.1 (THD penalty coefficient);

[0225] The optimal phase target value adopts the value in the critical phase difference matrix: φ5 optimal = 248° (relative to the fundamental wave); φ7 optimal = 268° (relative to the fundamental wave); φ11 optimal = 18° (relative to the fundamental wave);

[0226] Read the optimization model, and the phase optimization objective function J phase (α) = Σwi·|Φi(α) - φi optimal | 2 +λ·THD(α); where: α is the switching angle vector; Φi(α) is the harmonic phase corresponding to the switching angle; φi optimal is the optimal phase; wi is the weight coefficient; λ is the THD penalty coefficient; THD(α) is the total harmonic distortion rate; i is the harmonic order.

[0227] Adopt the quadratic programming and gradient descent methods to solve this optimization problem, and finally obtain the optimized switching angle vector α optimal : α1 = 12.3°; α2 = 18.7°; α3 = 27.5°; α4 = 36.2°; α5 = 41.8°; α6 = 52.9°; α7 =61.4°;

[0228] 4. Calculation of switching timing perturbation

[0229] In this system, the fundamental frequency f = 50Hz, and the phase fine-tuning amount Δφ between harmonics 5 and 7 fine _57 = 2.5° (0.0436 radians). The phase sensitivity adjustment coefficient n_57 = 5,

[0230] Read the calculation formula: time-phase conversion δt i j = Δφ finei j / (2π·f·n i j); where: δt i j is the switching timing perturbation amount; Δφ finei j is the phase fine-tuning amount; f is the fundamental frequency; n i j is the phase sensitivity adjustment coefficient; i is the harmonic order; j is the reference harmonic order.

[0231] Substitute into the formula δt_57 = 0.0436 / (2π·50·5) = 2.77×10^-5 s = 27.7 μs;

[0232] Switching timing correction δt corrected = δt quantized + (t on - t off ) / 2; where: δt quantized is the quantized timing perturbation amount; t on is the turn-on delay; t off is the turn-off delay; δt corrected is the corrected timing perturbation amount.

[0233] The turn-on delay t of the IGBT module used in this system on = 1.2 μs, the turn-off delay t off = 0.8 μs, so (t on -t off ) / 2 = 0.2 μs. The system hardware timing control accuracy τ min = 0.5 μs, quantize 27.7 μs: δt quantized = round(27.7 / 0.5)·0.5 = 27.5 μs. The corrected timing perturbation amount: δt corrected = 27.5 + 0.2 = 27.7 μs.

[0234] By precisely controlling the switching timing, precise adjustment of the harmonic phase is achieved.

[0235] 5. Implementation of the phase-locked closed-loop controller

[0236] The parameters of the adaptive PI controller Kp(e) = Kp base·(1 + αp·|e phase |), Ki(e) = Ki base ·(1 + αi·|e phase | 2 ); where: Kp(e) is the adaptive proportional coefficient; Ki(e) is the adaptive integral coefficient; Kp base is the basic proportional coefficient; Ki base is the basic integral coefficient; αp, αi are the adaptive adjustment parameters; e phase is the phase deviation; e phase = φ criticaltarget - φij measured ; φ criticaltarget is the target critical phase difference; φij measured is the measured phase difference.

[0237] In this system, the control parameters are set as: Kp base = 0.8; Ki base = 0.3; αp = 2.5; αi = 5.0;

[0238] Suppose the phase difference φ57 measured between the 5th and 7th harmonics is measured at a certain moment to be φ57 = 176°, and the target value φ criticaltarget (5,7) = 182°, then the phase deviation: e phase = 182° - 176° = 6° (0.1047 radians)

[0239] Calculate the adaptive control parameters: Kp(e) = 0.8·(1 + 2.5·0.1047) = 1.01; Ki(e) = 0.3·(1 + 5.0·0.1047 2 ) = 0.305.

[0240] Read the calculation formula: The PI control increment Δδt = Kp(e)·e phase + Ki(e)·∫e phase ·dt; where: Δδt is the incremental adjustment value of the perturbation; Kp(e) is the adaptive proportional coefficient; Ki(e) is the adaptive integral coefficient; e phase is the phase deviation; ∫e phase ·dt is the integral value of the phase deviation.

[0241] Suppose the current integral value ∫e phase ·dt = 0.08 radians, then: Δδt = 1.01·0.1047 + 0.305·0.08 = 0.13 μs

[0242] The total control action δtk+1 = δt k + Δδt + δt ff ; where: δt k+1 is the updated perturbation; δt k is the current perturbation; Δδt is the perturbation increment; δt ff is the feedforward compensation amount.

[0243] Assume the current perturbation δt k = 27.7μs, and the feedforward compensation amount δt ff = 0.5μs, then: δt k+1 = 27.7 + 0.13 + 0.5 = 28.33μs. After this value is low-pass filtered, it is applied to the switching timing control to achieve phase-locked closed-loop control.

[0244] 6. Adaptive Parameter Optimization Process

[0245] Parameter Gradient Optimization P k+1 = P k - η k ·∇J param (P k ), η k+1 = η k ·λ; where: P k is the current parameter vector; P k+1 is the updated parameter vector; η k is the current step size; η k+1 is the updated step size; λ is the step size decay coefficient; ∇J param (P k ) is the gradient of the objective function with respect to the parameter; J param (P) is the parameter optimization objective function; J param (P) = CPI(P); CPI(P) is the comprehensive performance index.

[0246] In this embodiment, the critical phase difference φ critical (5, 7) is selected as the key optimization parameter, and the initial value is 182°. Set the initial step size η0 = 2.0, and the step size decay coefficient λ = 0.9.

[0247] Through experiments, it is measured that under a certain working condition, the comprehensive performance index CPI corresponding to different φ critical (5, 7) values is as follows:

[0248] <![CDATA[φ critical (5,7)(°)]]> CPI (the lower the performance, the better) 180 0.32 181 0.29 182 0.28 183 0.30 184 0.33

[0249] Calculate the gradient approximation: ∇J param(182°) ≈ [CPI(183°) - CPI(181°)] / 2 = (0.30 -0.29) / 2 = 0.005

[0250] First parameter update: P1 = 182° - 2.0·0.005 = 181.99°; step size update: η1 = 2.0·0.9 = 1.8.

[0251] Since the parameter change is very small, according to the safety constraint in step S545, the actual updated value adopted is 182°.

[0252] After multiple rounds of optimization, the system finally determines the optimal φ critical (5,7) = 182°, which is used to update the critical phase difference matrix CPM.

[0253] After applying this method, the harmonic control effect during the start-stop process of the CAES system compressor is significantly improved:

[0254] Harmonic suppression effect: The traditional SHE method has THD = 10.3% under resonant conditions; this method has THD = 2.8% under resonant conditions, and the suppression rate reaches 72.8%.

[0255] Response speed: The traditional method responds in about 25ms after resonance is detected; this method starts responding at the beginning of resonance, and the effective response time is about 3ms.

[0256] Control stability: With the traditional method, when the system parameters change by ±10%, the control effect fluctuates by 35%; with this method, under the same conditions, the control effect fluctuates by less than 8%.

[0257] System resource usage: The DSP processor load of the traditional method is about 85%; the DSP processor load of this method is about 42%.

[0258] This example verifies the significant advantages of the harmonic intervention technology based on phase reconstruction under the resonant conditions of the CAES system. It not only solves the harmonic amplification problem that is difficult to deal with by traditional methods, but also greatly reduces the computing resource usage and improves the real-time response capability of the system. This method breaks through the limitation of the traditional SHE method that only focuses on the harmonic amplitude and ignores the phase relationship, and creates a new idea for harmonic control.

[0259] In order to solve the problem of delayed control response caused by the nonlinear growth characteristics of harmonics, a harmonic growth trajectory prediction model was developed. By calculating the normalized growth rate and growth acceleration indicators, the critical point can be predicted 10-20ms in advance at the initial stage of harmonic amplification (when the amplitude does not change significantly but the growth rate begins to rise), thereby achieving early intervention in the resonance process.

[0260] In response to the problem that traditional methods ignore the harmonic phase relationship, the high sensitivity of the harmonic amplification effect to the phase relationship under resonant conditions is revealed. By constructing a phase-growth rate mapping and a critical phase difference matrix, the traditional harmonic amplitude control is transformed into precise harmonic phase control, creating a new dimension of harmonic control.

[0261] In response to the problem that existing methods are mainly passive response control strategies, a phase reconstruction harmonic intervention technology was developed. By accurately controlling the harmonic phase relationship through microsecond-level switching timing perturbations, the resonance formation process was actively intervened, and the control response time was shortened from 25ms in traditional methods to 3ms, thus achieving active suppression of resonant harmonics.

[0262] To address the problem of control failure caused by dynamic changes in system parameters, a phase-locked closed-loop control mechanism and parameter adaptive optimization process were designed. By real-time monitoring of the system output and dynamically adjusting the control parameters, the control effect fluctuation was reduced from 35% to below 8% when the system parameters changed by ±10%, ensuring the stability and reliability of harmonic control.

[0263] The preferred embodiments of the present invention are 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 belong to the protection scope of the present invention.

Claims

1. A method for harmonic selective elimination of cascaded H-bridge inverters based on space voltage vectors in CAES, characterized in that, It includes the following steps: Collect the operation data of the CAES system and grid parameters, construct a real-time monitoring data set, preprocess it, extract the harmonic time-domain characteristics and phase relationship parameters from it, analyze the phase sensitivity between harmonics, and calculate the critical phase difference matrix; According to the critical phase difference matrix, reconstruct and optimize the space voltage vector, and calculate the switching timing perturbation; Combine the switching timing perturbation and the critical phase difference matrix to generate a phase-locked control instruction and optimize the H-bridge drive signal; Among them, extracting the harmonic time-domain characteristics and phase relationship parameters, analyzing the phase sensitivity between harmonics, and calculating the critical phase difference matrix includes: Apply the fast Fourier transform to the real-time monitoring data set, calculate the amplitude and phase of each harmonic, obtain the harmonic spectrum data, and calculate the time derivative of the amplitude of each harmonic among them to construct a harmonic growth rate vector; Adopt a normalized harmonic growth rate calculation model to process the harmonic growth rate vector, obtain the normalized growth data and analyze its time variation trend, calculate the harmonic growth acceleration index, and form a harmonic dynamic characteristic matrix; Calculate the phase difference between harmonics to generate a phase difference sequence; Perform correlation analysis on the harmonic dynamic characteristic matrix and the phase difference sequence, identify the corresponding patterns between harmonic amplification and phase relationship, generate phase sensitivity data; and determine the key phase relationship for resonance suppression based on this, and calculate the critical phase difference matrix; Calculating the switching timing perturbation includes: Based on the critical phase difference matrix, calculate the space voltage vector angle, form a space voltage vector angle sequence and establish and solve a phase target function based on it, obtain the optimized switching angle data and calculate the basic switching timing of each H-bridge unit based on it to form basic timing data; Analyze the sensitive phase relationship in the critical phase difference matrix and calculate the phase fine-tuning data; Combine the basic timing data and the phase fine-tuning data to calculate the final switching timing perturbation; Optimizing the H-bridge drive signal includes: Apply the switching timing perturbation to the basic switching timing to generate accurate switching timing data; Taking the optimal phase relationship in the critical phase difference matrix as the target value, calculate the phase control deviation to form phase deviation data; According to the phase deviation data, calculate the adjustment value of the perturbation, generate perturbation adjustment data and apply it to the accurate switching timing data to form a closed-loop control timing; Based on the closed-loop control timing, generate the drive signal of each H-bridge unit to achieve the optimal control of the power unit.

2. The method according to claim 1, characterized in that, Performing correlation analysis on the harmonic dynamic characteristic matrix and the phase difference sequence, identifying the corresponding patterns between harmonic amplification and phase relationship, and generating phase sensitivity data includes: Divide the phase difference sequence into multiple phase intervals according to a preset angle interval to obtain a phase interval vector; For each harmonic pair, calculate the average normalized growth rate of the harmonics in each phase interval to form a phase-growth rate correspondence table, and interpolate to generate a continuous phase-growth rate function; Find the phase difference value that minimizes the growth rate for each harmonic to generate an optimal phase difference vector, and calculate the growth rate sensitivity of each harmonic pair at the optimal phase point to form a phase sensitivity matrix; Based on the phase sensitivity matrix and the optimal phase difference vector, determine the key harmonic pairs that have the greatest impact on the resonance suppression effect, and construct a list of key harmonic pairs; for each key harmonic among them, analyze the changes in the phase sensitivity characteristics of the key harmonic pairs under different system operating conditions, and generate an operating condition-phase sensitivity mapping. Integrate the phase sensitivity matrix and the operating condition-phase sensitivity mapping to generate complete phase sensitivity data.

3. The method according to claim 2, wherein Find the phase difference that minimizes the growth rate and calculate the growth rate sensitivity, including: For each harmonic i, determine the optimal phase difference φij based on the phase-growth rate function and the phase difference between harmonics min ; At the optimal phase point, calculate the phase sensitivity S(i, φij) = |dR(i, φij) / dφij| φij=φijmin , where dR / dφij is the derivative of R with respect to φij, forming a phase sensitivity matrix.

4. The method according to claim 1, characterized in that Calculate the critical phase difference matrix, including: Extract the optimal phase difference from the phase sensitivity data as the base value of the critical phase difference. Calculate the system impedance frequency characteristics, obtain the system impedance data, and extract the impedance phase angles at each harmonic frequency point from it. Calculate the impedance phase angle difference φZ(ωi,ωj) of the key harmonic pairs to generate an impedance phase angle difference matrix. Construct a correction model, and calculate the corrected phase difference data based on the optimal phase difference, the impedance phase angle difference, and the correction coefficient. Analyze the impact of system parameter fluctuations on the critical phase difference, calculate the allowable fluctuation range, and form a phase tolerance matrix. Integrate the corrected phase difference data and the phase tolerance matrix to construct the critical phase difference matrix.

5. The method according to claim 1, characterized in that Establish and solve the phase objective function, including: Extract the optimal phase parameters from the critical phase difference matrix. Establish a mapping function from the switching angle to the harmonic phase, and construct an angle-phase mapping model. Based on the angle-phase mapping model, construct the phase optimization objective function J phase (α) = Σwi·|Φi(α) - φi optimal | 2 + λ·THD(α); α is the switching angle vector; Φi(α) is the harmonic phase corresponding to the switching angle; φi optimal is the optimal phase; wi is the weight coefficient; λ is the THD penalty coefficient; THD(α) is the total harmonic distortion rate; i is the harmonic order; Convert the phase optimization objective function into an approximate quadratic programming problem to solve for the initial solution. Starting from the initial solution, use the gradient descent method to accurately solve and obtain the final optimized switching angle data.

6. The method according to claim 1, characterized in that Calculate the final switching timing perturbation amount, including: Determine the key phase parameters that have the greatest impact on the system performance, and establish a conversion model from the phase fine-tuning amount to the time perturbation one by one to calculate the switching timing perturbation amount. Quantify and correct the switching timing perturbation amount, and integrate the timing perturbation data of each harmonic pair to form the final switching timing perturbation amount.

7. The method according to claim 1, wherein The steps to form the phase deviation data and generate the perturbation adjustment data include: Extract the target phase relationship from the critical phase difference matrix to construct the control target data. Real-time calculate the actual harmonic phases of the voltage and current signals to form the measured phase data. Calculate the actual phase difference to generate a measured phase difference vector. Compare the control target data with the measured phase difference vector, and calculate the phase control deviation e phase = φ criticaltarget - φij measured , and form phase deviation data; φ criticaltarget is the target phase relationship, φ ijmeasured is the actual phase difference; Through the adaptive controller, the control parameters Kp(e) = Kp base ·(1 + αp·|e phase |) and Ki(e) = Ki base ·(1 + αi·|e phase | 2 ) are dynamically adjusted to form the adaptive data of the control parameters; Among them, Kp(e) is the adaptive proportional coefficient; Ki(e) is the adaptive integral coefficient; Kp base is the basic proportional coefficient; Ki base is the basic integral coefficient; α p and α i are the adaptive adjustment parameters; e phase is the phase deviation; Implement the control algorithm, calculate the incremental adjustment value of the perturbation amount, and generate the control increment data. Combine feedback control and feedforward prediction to calculate the total control action and update the perturbation adjustment data.

8. The method according to claim 1, characterized in that The steps to monitor the system output, calculate the performance index data, and dynamically adjust the phase-locked control parameters include: Collect the voltage waveform data and current waveform data of the actual output of the system. Calculate the real-time total harmonic distortion and each harmonic index to form the harmonic performance index. Calculate the deviation between the harmonic amplitude and phase and the target values to generate the harmonic control deviation data. Establish a multi-objective evaluation system, comprehensively consider the harmonic suppression effect, phase control accuracy, and system stability, and calculate the comprehensive performance index. According to the harmonic control deviation data and the comprehensive performance index, dynamically adjust the control parameters to generate parameter adjustment instructions. Feed the parameter adjustment instructions back to the phase-locked controller to achieve closed-loop optimization.

9. The method according to claim 8, characterized in that, The steps to dynamically adjust the control parameters according to the harmonic control deviation data and the comprehensive performance index include: Evaluate the effectiveness of the current control strategy and construct control evaluation data; Calculate the sensitivity S of the control parameter param = dCPI / dP, identify the key parameters, and form a parameter sensitivity matrix; where CPI is the comprehensive performance index; P is the control parameter vector; Construct the parameter optimization objective function with the comprehensive performance index as the optimization objective; Use the gradient descent method with a decreasing step size to optimize the parameters and generate a parameter optimization sequence; Constrain the parameter changes to ensure that the adjustment range is within the safe range and form safe parameter adjustment data; Based on historical performance data, construct a parameter-performance mapping model to predict the performance of different parameter combinations; Combine the gradient optimization and the model prediction results to determine the final parameter adjustment plan and form a parameter adjustment instruction.

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