Power quality regulation method based on transient and steady coordination

Abstract

The application discloses a power quality regulation method based on transient and steady coordination, relates to the technical field of power quality regulation of distribution networks, and comprises the following steps: acquiring a transient electrical quantity change track and a steady electrical quantity convergence track, connecting the tracks according to time to obtain a complete response process, extracting process correlation characteristics between a drop depth node and a climbing rate node, pre-judging a load switching or new energy output fluctuation scenario to obtain a steady state recovery lag quantity, and generating a pre-start instruction of a steady state compensation device and / or an intensity preset instruction of a transient suppression device when the lag quantity exceeds a preset time limit, so that the transient- steady connection response rule is mined, the steady state recovery difficulty is pre-judged before disturbance occurs, the regulation is changed from post-compensation to pre-provision, the voltage recovery time is shortened, and the recovery fatigue and voltage collapse risk caused by multiple impacts are reduced.

Description

Technical Field

[0001] This invention belongs to the field of power quality control technology for power distribution networks, specifically relating to a power quality control method based on transient and steady-state coordination. Background Technology

[0002] Existing power quality control technologies for distribution networks typically treat transient and steady-state processes separately when handling transient disturbances: the transient phase is handled by rapid responses from relay protection devices or power quality management equipment, while the steady-state phase is handled by reactive power compensation devices or voltage regulators for slow recovery. This phased, independent control approach fails to establish a quantitative correlation between transient impact intensity and steady-state recovery characteristics, leading to passive activation of control equipment after a transient impact and uncontrollable steady-state recovery time. When there are fluctuations in renewable energy output or frequent load switching in the distribution network, the cumulative effect of multiple transient impacts may cause the system to enter a recovery fatigue state, further prolonging the steady-state recovery time and even triggering voltage collapse. This is because existing technologies lack the ability to mine and utilize the transient-steady-state transition response patterns and fail to transform the correlation between drop depth and climb rate contained in historical disturbance data into predictable and pre-setup control criteria.

[0003] More specifically, traditional control systems, when dealing with transient events such as motor startup and sudden drops in photovoltaic output, only focus on whether the voltage drop exceeds the limit during the event's duration (usually tens of milliseconds to several seconds). Once the voltage recovers to more than 90% of the rated value, the event is considered over, and the subsequent steady-state recovery process (usually hundreds of milliseconds to several minutes) is no longer considered. This approach ignores the profound changes that transient shocks cause to the system's energy recovery path: deep voltage drops caused by large-capacity loads can cause transformer cores to enter a local saturation region, resulting in a sharp decrease in equivalent magnetizing inductance and a reduced voltage ramp-up rate during the subsequent steady-state recovery phase; although voltage drops caused by fluctuations in renewable energy output are smaller, frequent power oscillations can cause repeated switching of reactive power compensation equipment, leading to accumulated recovery fatigue and gradually eroding the system's recovery resilience. Existing technologies fail to identify these hidden vulnerabilities and cannot predict the dynamic impact of seasonal load changes, equipment aging, and regional imbalances on recovery characteristics, resulting in long-term rigid control strategies that cannot adapt to the continuous evolution of distribution network operating conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a power quality control method based on transient and steady-state coordination to solve the problems mentioned in the background art.

[0005] Power quality control methods based on transient and steady-state coordination include: The transient electrical quantity change trajectory of the distribution network during the transient disturbance event is obtained, as well as the steady-state electrical quantity convergence trajectory of the distribution network as it enters the steady-state recovery phase after the transient disturbance event ends. The transient electrical quantity change trajectory and the steady-state electrical quantity convergence trajectory are sequentially connected in time to form a complete response process. From the complete response process, the process involvement features between the drop depth node of the transient disturbance event and the corresponding climb rate node in the steady-state recovery phase are extracted. The process involvement features are used to reflect the transient-steady-state successive response law between the drop depth node and the climb rate node. The transient-steady-state successive response law is characterized by the fact that the deeper the drop within the same transient disturbance event, the slower the subsequent climb. Moreover, the degree of slow climb increases progressively with the drop depth. This progressive increase is measured by the increasing difference between the climb time increments corresponding to adjacent drop depth nodes in the complete response process. By utilizing the process involvement characteristics, the upcoming load switching or new energy output fluctuation scenarios in the monitored distribution network are predicted, and the steady-state recovery lag caused by transient impacts under the scenario is obtained. The steady-state recovery lag is the amount by which the expected ramp-up time of the scenario exceeds the benchmark ramp-up time under the most recent small disturbance before the scenario occurs. The small disturbance is a transient disturbance where the drop depth does not exceed 10% of the rated voltage and no obvious inrush current appears in the transformers of the distribution network. When the steady-state recovery hysteresis exceeds the preset acceptable steady-state recovery time limit, the relationship between the steady-state recovery hysteresis and the acceptable steady-state recovery time limit is compared, as well as the relationship between the interval between the occurrence time of the scenario and the current time and the steady-state recovery hysteresis. Based on the comparison results, a pre-start command for the steady-state compensation device and / or a strength preset command for the transient suppression device are generated.

[0006] In some possible implementations, the transient-steady-state continuity response law is also used to identify the recovery resilience inflection point of the distribution network under the current operating conditions; The resilience inflection point is determined as follows: During the complete response process, the location where the climb time increment corresponding to adjacent drop depth nodes changes abruptly is found. The abrupt change occurs when the increase in the climb time of the subsequent drop depth node relative to the climb time of the previous drop depth node exceeds a preset threshold. If there are two drop depth nodes after the subsequent drop depth node, the climb time of these two levels is not less than the climb time of the subsequent drop depth node. If there is only one subsequent drop depth node, the climb time of this level is not less than the climb time of the subsequent drop depth node. If there are no subsequent drop depth nodes, the abrupt change is determined solely based on the increase exceeding the preset threshold. When the recovery resilience inflection point exists, it is determined that there is a hidden vulnerable link in the distribution network near the drop depth corresponding to the recovery resilience inflection point; The hidden vulnerable links include at least one of the following: the transformer local saturation critical region, the capacitor bank series resonance trigger region, or the load voltage collapse edge region.

[0007] In some possible implementations, the transient-steady-state continuity response law is also used to determine the mapping drift of the distribution network under different seasonal load characteristics; The mapping drift was obtained by comparing the historical transient-steady-state continuity response patterns of the same distribution network during the heating season and the non-heating season. When the mapping drift exceeds the preset drift threshold, the reference climb time is updated to the climb time corresponding to the small disturbance under the current seasonal load characteristics. The corrected reference climb time is used to recalculate the steady-state recovery hysteresis.

[0008] In some possible implementations, the process involvement features are also used to extract the recovery path bifurcation features of the distribution network after a transient impact; The bifurcation feature of the recovery path reflects the degree of discrete distribution of the ascent rate nodes under the same fall depth node; When the degree of discrete distribution exceeds a preset bifurcation threshold, it is determined that there is multi-steady-state competition in the steady-state recovery process of the distribution network; The calculation of the steady-state recovery hysteresis introduces a path selection margin, which is half the span between the record with the longest rise time and the record with the shortest rise time in the discrete distribution degree.

[0009] In some possible implementations, the transient-steady-state continuity response law is also used to construct a transient impact tolerance profile of the distribution network; The transient impact tolerance profile is obtained by classifying and compressing the transient-steady-state successive response law according to the drop depth range. The classification and compression retains the record with the longest climb time in each drop depth range as the tolerance boundary of that range. The transient impact tolerance profile is compared with the real-time operating data of the distribution network to be monitored. When the transient impact intensity in the real-time operating data approaches the tolerance boundary, the preset capacity expansion command of the steady-state compensation device is triggered.

[0010] In some possible implementations, the transient-steady-state continuity response law is also used to extract the recovery fatigue accumulation characteristics of the distribution network under the current operating conditions; The recovery fatigue accumulation characteristic is determined in the following way: during the complete response process, when the same drop depth node appears three or more times within a preset time window and the corresponding climb time is extended successively, it is determined that the recovery capability of the distribution network has fatigue accumulation. The successively extended means that the increase of the climb time of the later climb time relative to the previous climb time exceeds the preset fatigue threshold. When it is determined that there is accumulated recovery fatigue, the calculation of the steady-state recovery lag amount adds the fatigue correction amount to the expected climb time. The fatigue correction amount is the difference between the last climb time and the first climb time in the successive extension divided by the number of occurrences within the preset time window.

[0011] In some possible implementations, the transient-steady-state continuity response law is also used to determine the differences in recovery characteristics between different power supply zones in the distribution network; The difference in recovery characteristics is determined by comparing the rise time distribution range of multiple monitoring points within the same power supply zone at the same drop depth node, and the median deviation of the rise time between different power supply zones at the same drop depth node; when the distribution range exceeds a preset internal dispersion threshold or the median deviation exceeds a preset zone deviation threshold, it is determined that there is a zone recovery imbalance in the power distribution network. The pre-start command and the intensity preset command are generated differently based on the deviation direction and deviation magnitude of the partition recovery imbalance.

[0012] In some possible implementations, the transient-steady-state continuity response law is also used to construct the recovery capability evolution profile of the distribution network; The recovery capability evolution archive is obtained by arranging the historical transient-steady-state successive response patterns on a time axis and extracting the trend of the climb time at each drop depth node with the number of years of operation. The trend shows that the climb time increases monotonically or shows a step-like leap as the number of years of operation increases. When a step-like jump occurs in the trend of change, a latent aging warning is triggered for the distribution network. The level of the latent aging warning is determined based on the ratio of the increase in the climbing time after the step-like jump relative to the climbing time before the jump to the number of years the distribution network has been in operation.

[0013] In some possible implementations, the transient-steady-state succession response law is also used to determine the cascade response characteristics of the distribution network to complex transient disturbances; The cascaded response characteristics are determined in the following way: when there are two or more transient disturbance events in the complete response process with an interval not exceeding 50% of the rise time of the previous transient disturbance event, the fall depth node of the subsequent transient disturbance event is associated with the remaining rise time of the distribution network before it has recovered to steady state after the end of the previous transient disturbance event, so as to obtain the superimposed fall effect of the subsequent transient disturbance event when the power grid has not yet recovered from the previous transient disturbance. The calculation of the steady-state recovery hysteresis introduces a cascade amplification margin, which is the difference between the climb time corresponding to the superimposed drop effect and the climb time of the same drop depth under a single transient disturbance event, multiplied by a weighting coefficient, wherein the weighting coefficient is between 0.5 and 1.0.

[0014] In some possible implementations, the transient-steady-state continuity response law is also used to generate self-optimization instructions for the control strategy of the distribution network; The self-optimization command of the control strategy is generated in the following way: the actual execution effect of the historically generated pre-start command and intensity preset command is compared with the prediction result of the steady-state recovery lag. The actual execution effect is the actual ramp-up time of the distribution network after the steady-state compensation equipment is actually put into operation. The loop-through comparison includes calculating the deviation direction between the actual ramp-up time and the expected ramp-up time. When the deviation direction is continuously such that the actual ramp-up time is less than the expected ramp-up time for more than a preset optimization threshold and this state occurs continuously for a preset number of times, the acceptable recovery time limit is tightened. When the deviation direction is continuously such that the actual ramp-up time is greater than the expected ramp-up time for more than the preset optimization threshold and this state occurs continuously for the preset number of times, the acceptable recovery time limit is relaxed and the lead time of the pre-start command is extended simultaneously.

[0015] The technical solutions provided by the embodiments of this disclosure have at least the following beneficial effects: This invention establishes a complete response process by sequentially connecting the electrical quantity change trajectory during the transient disturbance phase with the electrical quantity convergence trajectory during the steady-state recovery phase. It extracts the process involvement characteristics between the drop depth node and the climb rate node and establishes a transient-steady-state continuity response law. This enables quantitative prediction of the steady-state recovery lag before load switching or new energy output fluctuations occur, thereby generating advance start-up commands for steady-state compensation equipment and / or intensity preset commands for transient suppression equipment. This transforms traditional reactive compensation into proactive pre-setting, effectively shortening voltage recovery time and avoiding recovery fatigue and voltage collapse risks caused by multiple transient impacts. Simultaneously, it identifies and warns of hidden vulnerabilities such as transformer local saturation and capacitor bank resonance, thereby improving the transient response speed and recovery resilience of the distribution network. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the method of the present invention. Detailed Implementation

[0017] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Please see Figure 1 This application provides a power quality control method based on transient and steady-state coordination, including: This invention provides a power quality control method based on transient and steady-state coordination. The core idea is to connect the electrical quantity change trajectory of a transient disturbance event with the electrical quantity convergence trajectory of the steady-state recovery phase in time to form a complete response process. From this, the process connection features between the drop depth node and the climb rate node are extracted. Using these features, a quantitative mapping law is established that the deeper the drop within the same transient disturbance event, the slower the subsequent climb, and the degree of slow climb increases progressively with the drop depth. This allows for the prediction of upcoming load switching or new energy output fluctuation scenarios. Before the steady-state recovery lag exceeds the acceptable time limit, a pre-start command for steady-state compensation equipment and / or a strength preset command for transient suppression equipment are generated in advance. The core idea behind this approach is that transient shocks not only cause instantaneous voltage drops in the distribution network, but also alter the system's equivalent impedance topology and energy recovery path. Mathematically, this alteration manifests as a nonlinear positive correlation between the drop depth and the climb time, and the degree of nonlinearity of this relationship (the stepwise amplification characteristic) can reflect the system's implicit vulnerability. Therefore, by establishing this mapping pattern through historical data mining, the difficulty of steady-state recovery can be predicted before a disturbance occurs, thereby shifting control actions from post-event compensation to pre-event pre-setting, shortening the overall recovery time and reducing cumulative risks.

[0019] This method is deployed in a server cluster at the distribution network control center. Its software functionality comprises transient event detection, process-related feature extraction, scenario prediction, instruction generation, and historical data recording. The server cluster communicates in real-time with the synchronous phasor measurement units or power quality monitoring devices at each monitoring node of the distribution network via fiber optic Ethernet, using either IEC 61850-MMS or Modbus TCP as the communication protocol. The historical data records store at least 12 months of transient disturbance event data.

[0020] S1. Obtain the transient electrical quantity change trajectory of the distribution network during the transient disturbance event, and the steady-state electrical quantity convergence trajectory of the distribution network entering the steady-state recovery phase after the transient disturbance event ends.

[0021] The transient disturbance event refers to a sudden disturbance that causes the effective value of the distribution network voltage to deviate significantly from the rated value. This includes, but is not limited to, load switching (such as direct starting of high-power motors, commissioning of electric arc furnaces, and switching of capacitor banks), fluctuations in renewable energy output (such as a sudden drop in output of photovoltaic arrays due to cloud cover, or grid disconnection or grid connection impact of wind turbines due to sudden changes in wind speed), short-circuit faults, and reclosing operations after fault clearance. The transient electrical quantity change trajectory refers to the sampling sequence of electrical quantities at each monitoring point in the distribution network changing over time during the duration of the transient disturbance event. These electrical quantities include instantaneous values ​​of three-phase voltage, instantaneous values ​​of three-phase current, effective values ​​of three-phase voltage, effective values ​​of three-phase current, active power, reactive power, frequency, harmonic content of each harmonic of the three-phase current (at least up to the 5th harmonic), and equivalent impedance angle.

[0022] The detection of the transient disturbance event is performed through the following steps: Synchronous phasor measurement units or power quality monitoring devices are deployed at each monitoring node of the distribution network. These monitoring nodes include 10kV or 35kV outgoing terminals of substations, distributed power supply grid connection points, feeder inlets for high-capacity loads, and power quality-sensitive load access points. The synchronous phasor measurement units or power quality monitoring devices continuously sample the three-phase voltage at a sampling frequency of not less than 256 points per 50Hz cycle (i.e., 12800Hz), calculating the half-cycle effective value Urms for each phase voltage. The formula for calculating the half-cycle effective value is: Urms equals the square root of the sum of the squares of the instantaneous voltage values ​​at all sampling points within the half-cycle divided by the number of sampling points within the half-cycle. That is, Urms equals the square root of the sum of ui (i = 1 / 2) divided by Ns, where ui is the instantaneous voltage value at the i-th sampling point, and Ns is the number of sampling points within the half-cycle. For a sampling rate of 12800Hz, Ns equals 128. When the Urms of any phase is lower than 90% of the rated voltage Un and this state lasts for more than 20ms (i.e., one complete cycle), a transient disturbance event is determined to have occurred, and this moment is recorded as the transient start time tstart; When the Urms of all three phases recover to 95% to 105% of Un and this state lasts for more than 100ms (i.e., five complete cycles), the transient disturbance event is considered to have ended, and this moment is recorded as the transient end time (tend). The 20ms and 100ms thresholds are determined according to the IEC 61000-4-30 standard for determining the start and end of voltage sag events. The 12800Hz sampling rate is based on the Nyquist sampling theorem. The transient process of the distribution network contains harmonic components up to 2kHz, and 256 points per cycle sampling can completely retain information up to the 128th harmonic.

[0023] The calculation method for each harmonic content is as follows: Perform a discrete Fourier transform on the current sampling sequence of each phase, extract the amplitudes from the fundamental wave to the 5th harmonic, and the harmonic content is equal to the amplitude of that harmonic divided by the fundamental wave amplitude multiplied by 100%. The calculation method for the equivalent impedance angle is as follows: Calculate the complex power of each phase based on the real-time measured fundamental components of the three-phase voltage and current. The equivalent impedance angle is equal to the phase angle of the difference between the voltage phasor and the current phasor, i.e., arctan(Xeq / Req), where Xeq is the equivalent reactance and Req is the equivalent resistance.

[0024] The steady-state recovery phase refers to the process by which the electrical quantities of the distribution network converge from the values ​​at the end of the transient disturbance event to the normal operating range. The steady-state electrical quantity convergence trajectory refers to the entire sequence of sampled data from the end of the transient event (tend) until the distribution network enters the steady-state determination condition. The steady-state determination condition is as follows: the effective values ​​of the three-phase voltages are all within 98% to 102% of Un, the frequency is within 49.5Hz to 50.5Hz, the average rate of change of active and reactive power within one minute does not exceed 1% of the rated value, and the above conditions are simultaneously sustained for more than 5 seconds. The 5-second steady-state duration is set according to the statistical requirements for voltage deviation duration in GB / T 12325-2008 "Power Quality - Supply Voltage Deviation". The 98% to 102% voltage range corresponds to a strict subset of the allowable deviation of ±7% for 10kV supply voltage in GB / T 12325-2008; a narrower range is chosen to ensure that the start and end points of the steady-state recovery phase have clear technical boundaries.

[0025] The sampling frequency during the steady-state recovery phase can be reduced to no less than 64 points per 50Hz cycle (i.e., 3200Hz) to reduce data storage overhead, since the rate of change of electrical quantities during the steady-state recovery phase is much lower than that during the transient phase. The 3200Hz sampling rate corresponds to 64 points per cycle, which, according to the Nyquist theorem, can retain up to the 32nd harmonic. The main frequency components during the steady-state recovery phase are the fundamental frequency and low-frequency interharmonics; harmonic components above the 32nd order have attenuated to negligible levels in the steady-state phase.

[0026] The acquisition of the transient electrical quantity change trajectory and steady-state electrical quantity convergence trajectory is performed by the synchronous phasor measurement unit or power quality monitoring device in the distribution network synchronous measurement system. As a specific implementation, on a 10kV distribution network feeder, one Class A power quality monitoring device conforming to IEC 61000-4-30 standard is installed at each of the following locations: the 10kV outgoing line of the substation, the distributed photovoltaic grid connection point (capacity 2MW), the high-power motor load access point (rated power 1.5MW), and the voltage-sensitive load at the end. The sampling rate is set to 12800Hz (transient stage) and 3200Hz (steady-state stage). The data is uploaded in real time to the historical data record of the distribution network control center via fiber optic Ethernet. The historical data record stores data in units of events, with each transient disturbance event corresponding to one record, including event number, monitoring point identifier, tstart, tend, transient electrical quantity change trajectory data file path, steady-state electrical quantity convergence trajectory data file path, steady-state determination time tstable, harmonic content sequence, and equivalent impedance angle sequence.

[0027] If the transient event detection step detects that the effective voltage value drops from the rated value to zero and then recovers within 20ms (i.e., a voltage dip lasting less than 20ms), it is determined to be measurement noise or equipment sampling abnormality, the event is not triggered, and the monitoring point is marked for sampling quality verification.

[0028] S2. The transient electrical quantity change trajectory and the steady-state electrical quantity convergence trajectory are sequentially connected in time to form a complete response process. The process connection features between the drop depth node of the transient disturbance event and the corresponding climb rate node in the steady-state recovery stage are extracted from the complete response process.

[0029] The complete response process refers to a continuous data sequence formed by splicing the transient electrical quantity change trajectory and the steady-state electrical quantity convergence trajectory obtained in S1 in chronological order. The splicing is divided by the transient end time (tend), with transient stage data first and steady-state recovery stage data following. Existing technologies typically analyze the transient and steady-state recovery stages as two independent processes. Transient analysis focuses on the voltage drop amplitude and duration, while steady-state analysis focuses on power balance and voltage regulation. There is a lack of data-level continuity constraints between the two stages. However, the disturbance energy injected into the system by a transient impact is not completely dissipated during the transient stage; some energy remains in the transformer, lines, and loads as electromagnetic field energy storage. This residual energy is gradually released during the steady-state recovery stage and affects the voltage ramp-up rate. The two stages are tightly coupled through energy conservation and electromagnetic transient processes. Therefore, connecting the two stages into a complete response process preserves the energy transfer chain between transient and steady-state states, allowing the subsequently extracted mapping relationship between drop depth and ramp-up rate to reflect the true physical coupling law.

[0030] The complete response process spans from tstart to tstable, covering the entire process of transient impact, transient decay, and steady-state convergence.

[0031] The drop depth node refers to the time point in the complete response process where the voltage RMS value relative to the rated value Un reaches a local maximum. Specifically, local minimum detection is performed on the three-phase voltage RMS value sequence Urms(t) in the complete response process. The criteria for determining the local minimum are: at time point td, Urms(td) is less than Urms(td minus 20ms) and Urms(td) is less than Urms(td plus 20ms), where 20ms is the time window width of one cycle. The drop depth d is defined as d equal to (Un minus Urms(td)) divided by Un multiplied by 100%, in percentage form. Each td that satisfies the above conditions constitutes a drop depth node, recorded as the pairing of the drop depth di of the i-th drop depth node with the corresponding time tdi.

[0032] The climb rate node refers to the point in time during the steady-state recovery phase corresponding to each drop depth node in the complete response process where the voltage recovery rate changes significantly. Specifically, for the i-th drop depth node, with a drop depth of di and a corresponding time of tdi, the climb rate node tci is searched within the interval from tend to tstable: the recovery rate v(t) of the effective voltage value in the steady-state recovery phase is calculated as dUrms(t) divided by dt, where the recovery rate is obtained by differential calculation of the Urms of adjacent sampling points; the moment when v(t) drops from its maximum value to 10% of its maximum value is found, which is the climb rate node tci. The criterion for determining that the maximum value of v(t) drops to 10% is that the voltage recovery rate in the steady-state recovery phase exhibits an exponential decay characteristic. When the recovery rate decays to 10% of its peak value, the system has completed the main voltage reconstruction process, and the remaining recovery rate below 10% corresponds to the slow convergence of small voltage deviations, and its contribution to the overall recovery time is negligible.

[0033] The climb time trisei is defined as tci minus tdi, which is the time interval from the drop depth node to the corresponding climb rate node, reflecting the time required for the system to complete the main voltage recovery process at that drop depth.

[0034] The process entrainment feature refers to the set of quantitative mapping relationships between all drop depth nodes and corresponding climb rate nodes in the complete response process. Mathematically, it is represented as the pairing set of drop depth di and corresponding climb time trisei for all i-th drop depth nodes, where i ranges from 1 to M, and M is the total number of drop depth nodes identified in the complete response process. The process entrainment feature is used to reflect the transient-steady-state successive response law between the drop depth nodes and the climb rate nodes. The transient-steady-state successive response law is characterized by the fact that the deeper the drop within the same transient disturbance event, the slower the subsequent climb, and the degree of slow climb increases progressively with the increase of drop depth.

[0035] The progressive amplification is measured by the increasing difference in ascent time increments between adjacent drop depth nodes during the complete response process. Specifically, the M drop depth nodes are sorted in ascending order of drop depth as d1 < d2 < ... < dM. If there are nodes with the same drop depth, they are sorted by time, with corresponding ascent times as trise1, trise2, ..., triseM. The ascent time increment Deltatrisej for adjacent drop depth nodes is calculated as trise(j + 1) minus trisej, where j ranges from 1 to M - 1. The increasing difference is defined as Delta(Deltatrisej) equal to Deltatrise(j + 1) minus Deltatrisej, which expands to trise(j + 2) minus twice trise(j + 1) plus trisej. If for consecutive j values, the increasing difference Delta(Deltatrisej) is greater than 0 and exhibits a monotonically increasing trend, then the progressive amplification characteristic is confirmed. The condition for determining the monotonically increasing trend is: for at least three consecutive adjacent j values, Delta(Deltatrise(j+1)) is greater than Delta(Deltatrisej), and Delta(Deltatrisej) is greater than 0.

[0036] The physical essence of the step-by-step amplification lies in the nonlinear magnetization of the transformer core. The specific derivation is as follows: The relationship between the magnetic flux density B and the magnetic field strength H of the distribution transformer core is described by the magnetization curve B equal to f(H). Near the rated voltage, this curve is approximately linear, and the permeability mu is approximately a constant mu0mur, where mu0 is the vacuum permeability (4π x 10⁻⁷ H / m), and mur is the relative permeability (typically 5000 to 8000 for cold-rolled grain-oriented silicon steel sheets, see GB / T 2521.1-2016 "All-Process Cold-Rolled Electrical Steel"). When the voltage drops and the core magnetic flux density decreases, the operating point remains in the linear region, and the excitation inductance Lm is approximately a constant equal to N² multiplied by mu multiplied by A divided by l, where N is the number of winding turns, A is the core cross-sectional area, and l is the average length of the magnetic circuit. At this point, the system's equivalent circuit is the power supply electromotive force E connected in series with the equivalent resistance Req and the equivalent inductance Leq. The voltage recovery process is an exponential response of a first-order RL circuit. The time constant tau is equal to Leq divided by Req. The rise time trise is proportional to tau, and trise is approximately equal to 3tau to 5tau (corresponding to recovery to 90% to 99% of the rated voltage).

[0037] When the voltage drop depth exceeds the transformer saturation threshold, the core enters the saturation region. According to the principles of electrical machinery, the saturation magnetic flux density Bs of the transformer core is typically 1.8T to 2.0T (cold-rolled silicon steel sheet, see GB / T 2521.1-2016), and the rated operating magnetic flux density Bn is 1.5T to 1.7T (with a design margin of approximately 15%). When the voltage drop depth is d, the change in core magnetic flux DeltaPhi during the transient process is proportional to the voltage integral. During the recovery phase, the magnetic flux needs to be reconstructed from the residual value at the end of the transient to the rated value. If the transient drop depth d is greater than (1 minus Bn divided by Bs) multiplied by 100% (approximately 15% to 20%), the core enters the saturation region. At this time, the permeability mu drops sharply to near mu0, and the excitation inductance Lm drops to 1 / 5000 to 1 / 8000 of the linear region. The larger the proportion of the magnetizing inductance component in the system's equivalent inductance Leq, the more significant the decrease in Leq caused by saturation, the greater the time constant tau, and the longer the ramp-up time.

[0038] More importantly, the saturation intensifies with increasing drop depth, and the nonlinearity of the magnetization curve causes the descent rate of Lm to accelerate with increasing H. The climb time exhibits a superlinear increase with increasing drop depth, meaning that the increment of climb time corresponding to adjacent drop depths also increases, forming the aforementioned step-by-step amplification characteristic. The above-mentioned magnetization curve saturation region model is only used to illustrate the physical cause of the "step-by-step amplification" characteristic. In the actual implementation of this invention, the process-related characteristics are directly extracted from historical data, without needing to obtain the specific values ​​of k1 and k2.

[0039] As a specific implementation method, for the complete response process of a 10kV feeder under motor starting disturbance, three drop depth nodes were identified: d1 = 5% (td1 = 0ms), d2 = 12% (td2 = 80ms), and d3 = 18% (td3 = 150ms). The corresponding climb times are triprise1 = 200ms, triprise2 = 350ms, and triprise3 = 600ms. The climb time increments were calculated: Deltatrise1 = 150ms and Deltatrise2 = 250ms. The incremental difference was Delta(Deltatrise1) = 100ms, which is greater than 0. Supplementing historical data, when d4 = 25%, triprise4 = 1000ms, therefore Deltatrise3 = 400ms, and Delta(Deltatrise2) = 150ms, which is greater than 100ms, confirming the step-by-step amplification characteristic.

[0040] If only one drop depth node is identified in the complete response process (i.e., M equals 1), the climb time increment and incremental difference cannot be calculated. In this case, the complete response process is not included in the statistical sample of process-related features, and only single-point data is recorded for subsequent trend analysis.

[0041] S3. Utilize the process-related characteristics to predict upcoming load switching or new energy output fluctuation scenarios in the monitored distribution network and obtain the steady-state recovery lag caused by transient impacts under the scenarios.

[0042] The aforementioned distribution network to be monitored refers to the distribution network that requires the implementation of the control method described in this invention. It is the same physical network as the distribution network whose historical data was collected in S1 to S2, or a similar type of distribution network with similar topology and load characteristics. Existing control strategies typically respond passively after a transient impact occurs, that is, compensation equipment is only activated after a voltage drop exceeding the limit is detected. At this time, the steady-state recovery process has already been deeply affected by the transient impact, and the compensation equipment can only perform post-event correction when the recovery path has been distorted. However, this invention, through the process entanglement characteristics established in S2, can predict the rise time required for steady-state recovery based on the expected drop depth before the disturbance occurs, thus shifting the control decision point forward to before the transient impact occurs.

[0043] The impending scenario refers to load switching or new energy output fluctuation events that are known to occur within a certain period of time (usually 5 to 30 minutes) in the future, based on load forecasting, new energy output forecasting, or scheduling plans.

[0044] The prediction is performed through a scenario prediction step. The inputs to the scenario prediction step include: real-time operating data of the distribution network to be monitored (current voltage, current, power, topology connection status), future scenario prediction information (load switching capacity, switching time, and changes in renewable energy output), and the process-related features extracted in S2.

[0045] For load switching scenarios (taking direct starting of a high-power motor as an example), the estimation method for the expected drop depth dpred is as follows: The starting current Ist during direct starting of the motor is typically 5 to 7 times the rated current IN (based on the provisions of GB / T755-2019 "Ratings and Performance of Rotating Electrical Machines" regarding the multiple of the direct starting current of squirrel-cage induction motors, 6 times is taken as a typical value). The starting power factor cosphist is approximately 0.3 to 0.5 (when a high-power motor starts, the slip s is approximately equal to 1, the rotor equivalent resistance R2' divided by s is small, the excitation branch is dominant, and the power factor is low, so 0.3 is taken as a conservative estimate). The starting reactive power impact DeltaQ is equal to the square root of 3 multiplied by Un multiplied by Ist multiplied by sinphist, where sinphist is equal to the square root of (1 minus the square of cosphist) approximately equal to 0.95.

[0046] According to the equivalent circuit model of the distribution network, the equivalent impedance Zeq from the power source point to the disturbance point is equal to Req plus jXeq. The voltage sag is mainly caused by the voltage drop across the equivalent reactance due to reactive current. For a three-phase system, the line voltage sag DeltaUline is estimated using the following formula: DeltaUline is approximately equal to √3 multiplied by Ist multiplied by Xeq multiplied by sinphist, where Ist is the starting current (phase current) and Xeq is the equivalent reactance. The derivation of this formula is based on the following: the starting current Ist flows through the equivalent reactance Xeq, generating a voltage drop; the voltage drop across Xeq due to the reactive component Ist multiplied by sinphist is Ist multiplied by Xeq multiplied by sinphist; and the line voltage drop of a three-phase system is √3 times the phase voltage drop. The expected sag depth dpred is equal to DeltaUline divided by Un multiplied by 100%.

[0047] For scenarios involving fluctuations in renewable energy output (taking a sudden drop in photovoltaic output as an example), the estimation method for the expected voltage drop depth dpred is as follows: When photovoltaic output drops suddenly, the system is equivalent to a sudden decrease in power supply, and the power absorbed by the distribution network from the external grid increases, leading to a weakening of voltage support. According to the power flow equation, the voltage change DeltaU is approximately equal to DeltaP multiplied by Req plus DeltaQ multiplied by Xeq divided by Un, where DeltaP and DeltaQ are the active and reactive power deficits caused by the sudden drop in photovoltaic output (photovoltaics typically operate at unity power factor, so DeltaQ is approximately 0), and Req and Xeq are the equivalent resistance and equivalent reactance from the power source point to the photovoltaic grid connection point, respectively. The expected voltage drop depth dpred is equal to DeltaU divided by Un multiplied by 100%.

[0048] The steady-state recovery hysteresis refers to the excess of the expected ramp-up time of the scenario relative to the baseline ramp-up time under the most recent minor disturbance before the scenario occurred. The minor disturbance is a transient disturbance where the voltage drop depth does not exceed 10% of the rated voltage and no significant inrush current is observed in the transformers of the distribution network. The criteria for significant inrush current are: the peak current on the high-voltage side of the transformer exceeds three times the rated current and the waveform exhibits obvious second harmonic characteristics (i.e., the second harmonic content is greater than 20% of the fundamental frequency). The thresholds of three times the rated current and 20% second harmonic content are determined based on the typical characteristics of transformer inrush current: according to the principles of electrical machinery, the peak inrush current when the transformer is closed under no-load conditions can reach 6 to 8 times the rated current, while the excitation current during normal operation is only 2% to 5% of the rated current; when the voltage drop caused by a transient disturbance causes the transformer core to enter the saturation region, the peak excitation current usually reaches 3 to 5 times the rated current, and the second harmonic content usually exceeds 15% to 30% of the fundamental frequency.

[0049] The aforementioned baseline climb-up time tbase refers to the average climb-up time corresponding to a drop depth not exceeding 10% in the process-related characteristics under the small disturbance. It is calculated as follows: records that meet the condition of a drop depth not exceeding 10% and have no non-obvious inrush current are selected from historical complete response processes, and the arithmetic mean of the climb-up times corresponding to these records is taken as tbase. The selection of the 10% drop depth upper limit is based on the following: according to the aforementioned transformer saturation threshold derivation, the rated operating magnetic flux density Bn of a 10kV distribution transformer is approximately 1.5T to 1.7T, and the saturation magnetic flux density Bs is approximately 1.8T to 2.0T. The saturation starting point is approximately Bn divided by Bs equaling 85% to 94%, corresponding to a drop depth of approximately 6% to 15%. Taking 10% as the upper limit, within this conservative range, ensures that the core magnetic flux density remains near the upper limit of the linear magnetization region under small disturbances, without entering a significant saturation region. At this time, the system's recovery characteristics are mainly determined by line parameters and load impedance, and are not affected by transformer saturation nonlinearity.

[0050] The expected climb time tpred is determined based on the mapping rules in the process involvement features. Specifically, in the process involvement features (all di and trisei pairings), the two historical fall depth nodes da and db (da is less than or equal to dpred and dpred is less than db) that are closest to the expected fall depth dpred are found. The expected climb time is calculated using linear interpolation: tpred equals trisei plus (triseb minus trisei) multiplied by (dpred minus da) and then divided by (db minus da).

[0051] The applicability of the linear interpolation method is based on the following technical logic: Between two adjacent historical drop depth nodes, if both are in the linear magnetization region of the transformer (da and db are both less than or equal to 10%), then Lm is constant, Leq is constant, tau is constant, and the drop depth and climb time are linearly related, with accurate interpolation; if both are in the saturation region, according to the aforementioned magnetization curve model, B equals Bs minus k1 divided by (H plus k2). When the distance between adjacent historical nodes is small (usually 2% to 5%), the range of H variation is limited, and the change of dB / dH can be approximated as linear. The reciprocal of Lm (i.e., equivalent magnetic reluctance) changes approximately linearly, and tau changes approximately linearly. Therefore, the relationship between drop depth and climb time in this local interval can be described linearly, and the interpolation error is controllable.

[0052] If dpred crosses the boundary between the linear region and the saturation region (e.g., da ≤ 10% and db > 10%), the linear interpolation error may increase. In this case, piecewise interpolation is used: interpolate according to the linear region slope within the linear region (d ≤ 10%), and interpolate according to the saturation region slope within the saturation region (d > 10%). The connection point is taken as the historical value at d = 10% or the intersection of the linear extensions on both sides. If there is no historical data at d = 10%, a conservative estimate is used, and the larger of the extrapolated value in the linear region and the extrapolated value in the saturation region is taken as tpred and marked as the boundary interpolation.

[0053] If dpred exceeds the maximum drop depth dM in historical data, then extrapolation is used: tpred equals tripriseM plus (dpred minus dM) multiplied by (triseM minus triprise(M minus 1)) divided by (dM minus d(M minus 1)), and is marked as an extrapolated prediction, indicating a decrease in prediction confidence. The error of the extrapolation method stems from the increased nonlinearity in the saturation region. The larger the extrapolation interval, the more significant the nonlinearity of Lm with H, and the greater the deviation of linear extrapolation.

[0054] The steady-state recovery hysteresis Deltalag is calculated as follows: Deltalag equals tpred minus tbase.

[0055] If the historical data in the process-related features is insufficient (i.e., fewer than 3 records of small disturbances satisfying a drop depth of no more than 10%), tbase cannot be reliably calculated. In this case, the scenario prediction step outputs an insufficient data alarm, indicating that more historical data needs to be accumulated before enabling the prediction function. The criterion for the 3 records is the minimum sample size requirement in statistics: the confidence interval width of the arithmetic mean is inversely proportional to the square root of the sample size, and 3 records are the lower limit for calculating the standard error.

[0056] S4. When the steady-state recovery hysteresis exceeds the preset acceptable steady-state recovery time limit, generate a pre-start command for the steady-state compensation device and / or a strength preset command for the transient suppression device based on the excess magnitude and the interval between the occurrence time of the scenario and the current time.

[0057] The acceptable steady-state recovery time Taccept refers to the maximum allowable steady-state recovery time specified in the distribution network operation regulations or power quality standards. As a specific implementation method, according to GB / T 12325-2008 "Power Quality - Supply Voltage Deviation" and the actual requirements of distribution network operation, the acceptable steady-state recovery time Taccept for 10kV feeders is set to 2 seconds (i.e., 2000ms). The 2-second time limit is set based on the following: GB / T 12325-2008 stipulates that the allowable deviation of 10kV power supply voltage is ±7%. Sensitive loads such as motors and frequency converters may trigger undervoltage protection tripping when the voltage drops below 90%. The protection action time is usually 2 to 5 seconds (based on the low-voltage motor protection setting principle in DL / T 5153-2014 "Technical Specification for Design of Auxiliary Power Supply in Thermal Power Plants"). If the voltage recovers to above 90% within 2 seconds, the protection action of most sensitive loads can be avoided. At the same time, 2 seconds is also the typical action time window for automatic reclosing and standby automatic transfer devices in the distribution network (based on DL / T 623-2010 "Evaluation Specification for Operation of Relay Protection and Safety Automatic Devices in Power Systems").

[0058] The excess range refers to the ratio of Deltalag to Taccept, that is, the excess ratio r is equal to Deltalag divided by Taccept multiplied by 100%.

[0059] The interval between the occurrence time of the scenario and the current time, referred to as Deltaforecast, is the time difference from the current time to the predicted occurrence time of the scenario. The generation of the pre-start instruction and / or intensity preset instruction is performed through the instruction generation step.

[0060] The aforementioned steady-state compensation equipment refers to devices used to provide reactive power support and voltage recovery, including but not limited to Static Var Generators (SVG), Static Synchronous Compensators (STATCOM), converters in distributed energy storage systems, and On-Load Tap Changers (OLTCs). The aforementioned pre-start command refers to a pre-start command sent to the steady-state compensation equipment before the actual occurrence of the scenario, ensuring that the steady-state compensation equipment is ready for startup and in standby compensation state when the scenario occurs. The startup time of the SVG is typically 50ms to 100ms (based on the time required for its IGBT drive circuit to establish DC-side voltage and phase-locked loop synchronization), the startup time of the STATCOM is typically 30ms to 80ms (faster startup when using a modular multilevel topology), the startup time of the distributed energy storage converter is typically 100ms to 200ms (requiring completion of battery management system self-check and pre-charging), and the adjustment time of the OLTC is typically 3 seconds to 5 seconds (mechanical transmission mechanism operation time).

[0061] The transient suppression device refers to a device used to limit the intensity of transient impacts, including but not limited to solid-state current limiters, fault current limiters, dynamic voltage restorers (DVRs), and fast switches. The intensity preset command refers to a preset parameter command sent to the transient suppression device before the actual occurrence of the scenario, causing the transient suppression device to act directly according to the preset parameters when the scenario occurs, without the need for a detection-judgment-decision delay process.

[0062] The decision logic for the instruction generation step is as follows: the logic is based on the comparison between the steady-state recovery lag (Deltatlag) and the steady-state acceptable recovery time (Taccept), and the comparison between the interval (Deltatforecast) between the time the scenario occurred and the current time and the steady-state recovery lag (Deltatlag). When Deltatlag is less than or equal to Taccept, no pre-startup instructions or intensity preset instructions are generated, and the existing operation mode is maintained.

[0063] When Deltatlag is greater than Taccept and Deltatforecast is greater than Deltatlag, a pre-start command is generated. The advance amount of the pre-start command is Deltadvance, which equals Deltaforecast minus Deltatlag divided by 2. That is, the steady-state compensation device is started at the time Deltadvance before the event occurs. The compensation amount is calculated by dividing Deltatlag by 2, and the technical logic is as follows: The steady-state compensation device goes through three stages from receiving the start command to outputting the rated compensation power: (1) Control circuit startup and self-test, approximately 10ms to 20ms; (2) Power device drive and DC side voltage establishment, approximately 20ms to 40ms; (3) Reactive current closed-loop tracking to 90% of rated value, approximately equal to the current loop response time multiplied by ln(10), approximately equal to 2.3 times the current loop response time. For a typical SVG current loop response time of 10ms, stage (3) is approximately 23ms; for a typical STATCOM current loop response time of 8ms, stage (3) is approximately 18ms. The total time for the three stages is approximately 53ms to 83ms (SVG) or 38ms to 68ms (STATCOM). On the other hand, the main voltage rebuild time of the steady-state recovery process is approximately Deltalag (from the drop to the recovery rate dropping to 10% of the peak value). In order for the compensation power to be effective immediately after the voltage drop, the equipment needs to be started before the drop occurs. Dividing Deltatlag by 2 as the advance start compensation ensures that in scenarios with large Deltatlag (such as deep drops), the device has sufficient time to start up; in scenarios with small Deltatlag, the advance compensation is not too large, preventing the device from idling. The matching relationship between this compensation and the device start time is as follows: when Deltatlag is greater than or equal to 100ms, Deltatlag divided by 2 is greater than or equal to 50ms, covering the minimum start time of the SVG; when Deltatlag is greater than or equal to 200ms, Deltatlag divided by 2 is greater than or equal to 100ms, covering the typical start time of the energy storage converter. Simultaneously, a strength preset command is generated based on the excess ratio r: if r is less than or equal to 50%, the transient suppression device is preset to a mild suppression mode (the solid-state current limiter is preset to a 50% current limiting depth); if 50% is less than r and less than or equal to 100%, it is preset to a moderate suppression mode (75% current limiting depth); if r is greater than 100%, it is preset to a severe suppression mode (100% current limiting depth and a pre-start command is generated simultaneously). The current limiting depth is graded as follows: 50% current limiting depth corresponds to limiting the inrush current to within 1.5 times the rated value (protecting general loads), 75% corresponds to limiting it to within 1.25 times (protecting sensitive loads), and 100% corresponds to complete current limiting (protecting critical equipment). This grading matches the motor starting voltage drop requirement in DL / T 5153-2014 (the bus voltage should not be lower than 80% of the rated value during startup).

[0064] When Deltatlag is greater than Taccept and Deltatforecast is less than or equal to Deltatlag, it indicates that the scenario is about to occur or that pre-compensation can no longer be achieved through pre-start. In this case, only an intensity preset instruction is generated (no pre-start instruction is generated due to insufficient time), and the priority of the intensity preset instruction is raised to the highest level to ensure that the transient suppression device operates at maximum intensity immediately when the disturbance occurs.

[0065] If the steady-state compensation device receives other scheduling instructions that require a change in its operating state after the pre-start instruction is issued but before the actual occurrence of the scenario, the steady-state compensation device will respond to the other scheduling instructions first and report to the superior system that the pre-start instruction has been revoked.

[0066] S5. Identify the inflection point of the recovery resilience of the power distribution network under the current operating conditions.

[0067] The resilience inflection point is determined as follows: During the complete response process, for the sorted drop depth nodes d1 < d2 < ... < dM and the corresponding climb times trise1, trise2, ..., triseM, the climb time increment Deltatrisej at each level is calculated to be equal to trise(j + 1) minus trisej, where j ranges from 1 to M - 1. The jump judgment condition is: there exists a j equal to k such that Deltatrisek is greater than Deltatrise(k - 1) multiplied by (1 + lambda), where lambda is a preset jump threshold. The value of lambda is 50% to 100%, and its technical logic derivation is as follows: According to the aforementioned transformer saturation model, in the linear region (d < 10%), Lm is constant, and the climb time increment Deltatrise of adjacent drop depths is mainly caused by changes in line resistance and load impedance. Its changes are relatively gradual, and the ratio of adjacent increments is usually close to 1 (i.e., the rate of change is about 0% to 20%). Once in the saturation region, Lm decreases inversely proportional to the square of the sum of its parts as H increases, while tau increases accordingly, and the increase in adjacent increments widens significantly. Taking lambda equal to 50% as the lower limit means that the increment of the next level is more than 50% larger than the increment of the previous level. This increase far exceeds the normal fluctuation range of the linear region (within 20%), clearly indicating the intervention of saturation nonlinearity. Taking lambda equal to 100% as the upper limit is used to identify severe saturation or sharp deterioration caused by additional nonlinear factors (such as capacitor resonance). Therefore, the range of lambda values ​​from 50% to 100% covers the technical boundary from "saturation onset" to "severe nonlinearity".

[0068] Furthermore, the ascent time corresponding to the two consecutive drop depth nodes following the aforementioned drop depth node is not less than the ascent time corresponding to the next drop depth node, i.e., trie(k+1) is greater than or equal to triesek and trie(k+2) is greater than or equal to triesek (if k+2 exists). If M is less than k+2 (i.e., there are fewer than two subsequent nodes), then only trie(k+1) is checked to be greater than or equal to triesek (if k+1 exists). If M is equal to k+1, then only if Deltatrisek is greater than Deltatrise(k-1) multiplied by (1 plus lambda) is a jump determined. The recovery resilience inflection point corresponds to the drop depth d(k+1).

[0069] When the recovery resilience inflection point exists, it is determined that there is a hidden vulnerability in the distribution network near the drop depth corresponding to the recovery resilience inflection point. The hidden vulnerability includes at least one of the following: transformer local saturation critical region, capacitor bank series resonance triggering region, or load voltage collapse edge region.

[0070] The criteria for determining the local saturation critical zone of the transformer are as follows: the drop depth d(k+1) corresponding to the recovery toughness inflection point is within the range of 85% to 95% of the transformer's rated voltage (i.e., a drop depth of 5% to 15%), and the second harmonic content of the transformer's high-voltage side current exceeds 15% of the fundamental frequency content at this drop depth. The derivation of the 85% to 95% range is based on the aforementioned saturation starting point calculation: Bn divided by Bs is approximately equal to 85% to 94%, corresponding to a drop depth of approximately 6% to 15%. Taking 85% to 95% as the judgment interval covers this physical range and leaves a margin. The threshold of 15% for the second harmonic content is based on the fact that when the transformer is saturated, the excitation current exhibits a peaked wave, and the second harmonic component in its Fourier decomposition accounts for approximately 15% to 30% of the fundamental frequency (based on the excitation inrush current harmonic analysis in electrical machinery, see "Electrical Machinery"). The second harmonic content is obtained by the calculation method for each harmonic content in S1.

[0071] The criteria for determining the series resonance trigger zone of the capacitor bank are as follows: the drop depth d(k+1) corresponding to the recovery resilience inflection point is close to the switching voltage threshold of a capacitor bank in the distribution network (within ±2%), and the equivalent impedance angle of the distribution network at this drop depth is close to -90 degrees (capacitive). The condition for determining that the equivalent impedance angle is close to -90 degrees is that the impedance angle is within the range of -85 degrees to -90 degrees. This range is based on the theory that the capacitive reactance equals the inductive reactance and the impedance is purely capacitive (impedance angle -90 degrees) during series resonance. -85 degrees is taken as the capacitive boundary with a 5-degree margin. The equivalent impedance angle is obtained by the calculation method of the equivalent impedance angle in S1.

[0072] The criteria for determining the load voltage collapse edge zone are as follows: the drop depth d(k+1) corresponding to the recovery resilience inflection point exceeds the critical voltage of the constant power load in the distribution network (usually 70% to 80% of the rated voltage), and the load power factor decreases significantly at this drop depth (power factor change exceeds 0.1). The derivation of the 70% to 80% critical voltage is based on the following: the constant power load P is constant, and when the voltage decreases, the current I increases by P divided by (√3 multiplied by U multiplied by cosphi), the line voltage drop IX increases, further reducing the voltage and forming positive feedback. The stability boundary of this positive feedback can be obtained by dU / dI equaling 0. For typical distribution network parameters (X / R approximately equal to 1 to 3), the critical voltage is approximately 70% to 80% of the rated value (based on power system voltage stability analysis, see "Power System Voltage Stability and Its Control", Zhou Shuangxi et al., Science Press, Chapter 4).

[0073] If M is less than 3 during the complete response process, the recovery resilience inflection point cannot be determined, and insufficient node information is output.

[0074] S6. Determine the mapping drift of the distribution network under different seasonal load characteristics.

[0075] The mapped drift is obtained by comparing the historical transient-steady-state continuity response patterns of the same distribution network during the heating season (usually from November to March of the following year) and the non-heating season (usually from April to October of the year).

[0076] The method for determining the mapping drift is as follows: For each season, construct the process involvement features (a set of all pairs of di and trisei) for that season. For the same drop depth d, compare the rise times trisriseheating and trissenonheating corresponding to the heating season and the non-heating season. The mapping drift amount Deltat is equal to the absolute value of trissenonheating minus trisriseheating, divided by trissenonheating multiplied by 100%.

[0077] When the mapping drift exceeds a preset drift threshold (ranging from 20% to 50%, with 30% used as a specific implementation), the baseline climb time is updated to the climb time corresponding to the small disturbance under the current seasonal load characteristics. The corrected baseline climb time is used to recalculate the steady-state recovery hysteresis.

[0078] The technical logic behind the drift threshold of 20% to 50% is as follows: During the heating season, a large number of electric heating loads are connected, increasing the load factor of the distribution network and thus increasing the equivalent impedance. Let the load factor during the non-heating season be beta1 (approximately 40% to 60%) and the load factor during the heating season beta2 (approximately 70% to 90%). The equivalent impedance Zload is inversely proportional to the load factor (in the constant power load model, P equals U squared divided by Rload, and Rload is inversely proportional to the load factor). The system equivalent impedance Zeq equals Zsource plus Zload in parallel. When the load factor increases from beta1 to beta2, Zload decreases, the load component in Zeq decreases, and the change in the overall system impedance leads to a change in the time constant tau. Based on typical 10kV distribution network parameters (source impedance Zsource approximately 0.5 ohms, non-heating season Zload approximately 2.0 ohms, heating season Zload approximately 1.0 ohms), the calculated non-heating season tau1 is approximately equal to Less1 divided by Req1, and the heating season tau2 is approximately equal to Less2 divided by Req2. The ratio of tau2 to tau1 is approximately 1.2 to 1.5 (i.e., an increase of 20% to 50%). Therefore, a lower limit of 20% for the drift threshold corresponds to the minimum impedance change effect caused by an increase in load factor, while an upper limit of 50% corresponds to the maximum effect of extreme load growth (such as the concentrated start-up of electric heating during cold waves). Taking 30% as a typical value covers the seasonal variation range of most distribution networks.

[0079] The physical reason for the seasonal load characteristics difference is that during the heating season, a large number of electric heating loads are connected, the load rate of the distribution network increases, the equivalent impedance increases, and the voltage recovery under the same drop depth requires a longer time; at the same time, the constant power characteristic of electric heating loads causes the load current to increase as the voltage decreases during the voltage recovery process, further prolonging the recovery time.

[0080] If there are fewer than three historical minor disturbance records for a given season, the baseline rise time for that season is temporarily replaced by multiplying the baseline value of another season by a seasonal correction factor (1.3 for the heating season and 0.77 for the non-heating season), and marked as an estimated value. The derivation of 1.3 and 0.77 is based on the median of the aforementioned tau2 / tau1 ratio range of 1.2 to 1.5: taking 1.3 as the correction factor for the heating season relative to the non-heating season, the correction factor for the non-heating season relative to the heating season is 1 / 1.3, approximately equal to 0.77. This factor is a theoretical estimate based on the distribution network impedance model; in practical applications, the measured value after accumulating sufficient historical data should be prioritized.

[0081] S7. Extract the recovery path bifurcation features of the power distribution network after a transient impact.

[0082] The bifurcation feature of the recovery path reflects the degree of discrete distribution of the ascent rate nodes under the same fall depth node.

[0083] The method for extracting the path bifurcation features is as follows: From the historical data records, all records with a fall depth between d - 2% and d + 2% (where d is the target fall depth and 2% is the tolerance range) are selected. For each of the N selected records, each record corresponds to a climb time trisen (n ranges from 1 to N). The mean mut is calculated as the sum of trisen divided by N, and the standard deviation sigmat is calculated as the square root of the sum of (trisen minus mut) divided by N. The degree of dispersion is measured by the coefficient of variation CV, which is equal to sigmat divided by mut multiplied by 100%.

[0084] When the degree of dispersion exceeds a preset bifurcation threshold (25% in one specific implementation), it is determined that the steady-state recovery process of the distribution network involves multiple steady-state competition. The multiple steady-state competition refers to the fact that the distribution network may converge to different steady-state operating points after a transient impact. These different steady-state operating points correspond to different reactive power compensation equipment switching combinations, transformer tap positions, or load power factor states.

[0085] The technical logic derivation of the 25% bifurcation threshold is as follows: The coefficient of variation (CV) equals the standard deviation divided by the mean, reflecting the relative dispersion. During the steady-state recovery process of the distribution network, if the system operating state is stable (reactive power compensation equipment is not activated, transformer taps are fixed), the recovery path at the same drop depth is determined by a fixed equivalent circuit. The random fluctuation of the climb time mainly comes from measurement errors and small load changes, and CV is usually less than 10% (based on the measurement system accuracy of 0.2% to 0.5% and typical values ​​within 5% load fluctuation). If there is multi-steady-state competition (such as random switching of reactive power compensation capacitors at different voltage thresholds), the same drop depth may trigger different numbers of capacitors to be engaged, leading to bifurcation of the recovery path. Let the capacitor bank capacity be Qc, the change in the system's equivalent inductance Leq between engaged and disengaged states be DeltaLeq, and the corresponding change in the time constant be Deltaau. CV is approximately equal to Deltaau divided by (2 multiplied by the average of tau). For a typical 10kV distribution network (Qc approximately equals 300kvar, Leq approximately equals 10mH, DeltaLeq approximately equals 2mH), the calculated CV is approximately 20% to 30%. Taking 25% as the threshold, the median of this range can effectively distinguish between "normal fluctuations caused by measurement noise" and "systematic bifurcation caused by multi-steady-state competition".

[0086] The calculation of the steady-state recovery lag incorporates a path selection margin, specifically, the formula being Deltapath equal to max(trisen) minus min(trisen). The corrected steady-state recovery lag, Deltalag', is equal to Deltalag plus Deltapath divided by 2. The technical logic behind dividing by 2 is that the selection of the actual recovery path in multi-steady-state competition is random; taking the median span between the longest and shortest paths as a margin can statistically cover 50% of probability scenarios, providing a reasonable margin for conservative estimation.

[0087] If the number of selected records N is less than 3, the coefficient of variation cannot be reliably calculated (in statistics, the standard deviation estimation is meaningless when the sample size is less than 3). In this case, multi-steady-state competition is not judged, and the path selection margin is set to 0.

[0088] S8. Construct a transient impact tolerance profile for the power distribution network.

[0089] The transient impact tolerance profile is obtained by classifying and compressing the transient-steady-state successive response patterns according to the drop depth range. The classification and compression retains the record with the longest climb time in each drop depth range as the tolerance boundary of that range.

[0090] The method for constructing the transient impact tolerance profile is as follows: all process-related features in the historical data records are categorized and compressed according to drop depth ranges. The drop depth ranges are divided as follows: 0% to 5%, 5% to 10%, 10% to 15%, 15% to 20%, 20% to 30%, 30% to 50%, and 50% to 100%.

[0091] The interval division is based on the following criteria: 0% to 5% corresponds to the normal operating fluctuation range of the transformer's linear magnetization zone; 5% to 10% corresponds to the near-saturation transition zone; 10% to 15% corresponds to the slightly saturated zone (based on the aforementioned saturation starting point of 6% to 15%); 15% to 20% corresponds to the moderately saturated zone; 20% to 30% corresponds to the deep saturated zone; 30% to 50% corresponds to the severely saturated and possible resonance zone; and 50% to 100% corresponds to the extreme fault zone. This division method covers all technical states from normal operation to extreme faults, and the interval width increases with the drop depth, which conforms to the engineering principle of allowing for increased error when saturation nonlinearity intensifies.

[0092] For each interval, the maximum climb time among all records within that interval is extracted as the tolerance boundary tboundary of that interval, i.e., tboundaryk equals max{trisei vertical line di belongs to the k-th interval}.

[0093] The transient impact tolerance profile is compared with the real-time operating data of the distribution network under monitoring. When the transient impact intensity in the real-time operating data approaches the tolerance boundary, a pre-set capacity expansion command for the steady-state compensation equipment is triggered. The comparison method is as follows: estimate the expected drop depth drealtime when a transient impact occurs based on the current real-time operating data, and find the tolerance boundary tboundaryk corresponding to the interval to which drealtime belongs. The proximity judgment condition is: tpred divided by tboundaryk is greater than 80%. The 80% threshold is derived based on the fact that the engineering safety margin is usually taken as 20% (i.e., a 20% capacity reserve is reserved to cope with uncertainties). Therefore, when the predicted climb time reaches 80% of the tolerance boundary, it indicates that the system has approached the theoretical limit of its recovery capacity and needs to be expanded in advance to ensure safety. This margin is consistent with the principle of reserving reserve capacity in the N-1 safety criterion of power systems.

[0094] The aforementioned preset capacity expansion command refers to the command that expands the available capacity of the steady-state compensation equipment from its current operating capacity to its rated capacity.

[0095] If the historical record of a certain interval is empty, the tolerance boundary of that interval is linearly extrapolated from the boundary value of the adjacent interval and marked as the estimated value.

[0096] S9. Extract the recovery fatigue accumulation characteristics of the power distribution network under the current operating conditions.

[0097] The fatigue recovery accumulation characteristics are determined as follows: a preset time window Twindow is set (ranging from 1 hour to 24 hours, with 4 hours used as a specific implementation). The technical logic for setting Twindow to 4 hours is as follows: the physical essence of fatigue recovery is the accumulation of hysteresis loss and winding heat in the transformer core under repeated transient impacts. The transformer hysteresis loss Ph is approximately equal to kh multiplied by f multiplied by Bm to the power of n (Steinmetz formula, where kh is the hysteresis coefficient, typically 0.001 to 0.01, f is the frequency 50Hz, Bm is the maximum magnetic flux density, and n is the Steinmetz exponent, typically 1.6 to 2.2, and 2.0 for grain-oriented silicon steel sheets). After each transient impact, the core temperature rise DeltaT is approximately equal to Ph multiplied by t_impact divided by (Ch multiplied by m), where Ch is the specific heat capacity of approximately 460 J / (kg·K), and m is the core mass. For a typical distribution transformer (core mass approximately 500 kg, Bm approximately 1.7 T, kh taken as 0.005, impact t taken as 0.1 s), the hysteresis loss Ph from a single impact is approximately 0.005 x 50 x 1.7 squared, approximately 0.72 W / kg; the energy from a single impact is approximately 0.072 J / kg; and the temperature rise DeltaT is approximately 0.072 divided by 460, approximately 0.00016 K, which is negligible. However, if the impact is repeated 3 or more times within 4 hours, the cumulative thermal effect combined with mechanical stress (vibration caused by magnetostriction of the core) may lead to a slight change in the joint gap and an increase in magnetic reluctance. According to mechanics of materials, for every 0.01 mm increase in the joint gap of silicon steel laminations, the magnetic reluctance increases by approximately 5% to 10%, corresponding to a 5% to 10% decrease in Lm and a 5% to 10% extension in ramp-up time. The cumulative effect of 3 impacts is approximately 15% to 30%, and taking 20% ​​as the fatigue threshold, it falls within the midpoint of this range. The 4-hour time window covers typical load switching cycles (industrial load shift switching is about 4 to 8 hours), and is shorter than the transformer thermal time constant (usually several hours to more than ten hours), allowing fatigue trends to be identified before the thermal effects accumulate significantly. The lower limit of 1 hour corresponds to high-frequency impact scenarios (such as electric arc furnaces), and the upper limit of 24 hours corresponds to daily cycle load changes.

[0098] In the historical data records, find record groups where the same drop depth d appears three or more times within the Twindow. For each record group, arrange the corresponding climb times t1, t2, ..., tK (K is greater than or equal to 3) in chronological order. Determine the successive extension: calculate the increase ratio of adjacent climb times equal to (t(m+1)-tm) divided by tm multiplied by 100%, where m ranges from 1 to K-1. If for all m, the ratio is greater than a preset fatigue threshold (ranging from 10% to 30%, and 20% in a specific implementation), then it is determined that the recovery capability of the power distribution network has experienced fatigue accumulation.

[0099] The technical logic behind the fatigue threshold of 10% to 30% is derived as follows: Based on the aforementioned hysteresis-mechanical stress model, a slight change in the joint gap after each impact leads to a reduction in Lm by approximately 5% to 10%, corresponding to a 5% to 10% extension in climb time. Considering measurement errors and load fluctuations (approximately 5%), the observable increase per impact is approximately 10% to 15%. If three impacts accumulate, the total increase is approximately 15% to 30%. Taking 10% as the lower limit distinguishes between fatigue effects and normal fluctuations; taking 30% as the upper limit corresponds to severe fatigue (such as minor insulation damage caused by localized overheating of the core). Taking 20% ​​as a typical value, which falls within the midpoint of this range, balances sensitivity and anti-interference capabilities.

[0100] When the existence of fatigue accumulation during recovery is determined, the calculation of the steady-state recovery lag adds the fatigue correction to the expected climb time. The formula for calculating the fatigue correction is: Deltatfatigue equals (tK minus t1) divided by K. The corrected expected climb time tpred' equals tpred plus Deltatfatigue, and the corrected steady-state recovery lag Deltatlag' equals tpred' minus tbase. The derivation of Deltatfatigue equaling (tK minus t1) divided by K is based on the following: the fatigue accumulation effect accumulates approximately linearly in K impacts (the decrease in Lm caused by each impact is similar), the total extension (tK minus t1) is contributed by K impacts, and the average contribution of a single impact is (tK minus t1) divided by K. Adding this to the expected climb time can statistically reflect the impact of fatigue on a single recovery process.

[0101] If the increase ratio in a certain record group is less than or equal to the ratiothreshold, then that record group is not considered as fatigue accumulation. The technical logic of this exclusion rule is that if the rise time after a certain impact does not increase or even decreases, it indicates that the system has recovered after the impact (such as cooling or load reduction), the fatigue accumulation chain is broken, and it should not be included in the fatigue determination.

[0102] S10. Determine the differences in recovery characteristics between different power supply zones in the power distribution network.

[0103] The differences in recovery characteristics are determined as follows: For the same power supply zone, the climb time (trisep) of multiple monitoring points (at least 3) within it at the same drop depth node d is collected, and the climb time distribution range Rinternal within the zone is calculated to be equal to max(trisep) minus min(trisep). For different power supply zones A and B, the median climb time (MA and MB) at the same drop depth d is calculated, and the median deviation DeltaM is equal to the absolute value of MA minus MB.

[0104] When the distribution range Rinternal exceeds a preset internal dispersion threshold (ranging from 50ms to 200ms, with 100ms used in a specific implementation), it is determined that there is a recovery imbalance within the power supply zone. When the median deviation DeltaM exceeds a preset zone deviation threshold (ranging from 100ms to 500ms, with 200ms used in a specific implementation), it is determined that there is a zone recovery imbalance in the distribution network.

[0105] The derivation of the internal dispersion threshold of 50ms to 200ms is based on the following: Within the same power supply zone, monitoring points are powered by the same busbar and should theoretically experience similar transient processes. However, due to differences in line impedance (impedance difference of approximately 0.1 ohms to 0.5 ohms due to different feeder lengths) and uneven load distribution, there are inherent differences in ramp-up time. For a typical 10kV distribution network (tau approximately equal to 200ms to 500ms), the tau change caused by line impedance differences is approximately 10% to 20%, corresponding to a time difference of approximately 20ms to 100ms. Taking 50ms as the lower limit eliminates normal line differences; taking 200ms as the upper limit corresponds to extreme load unevenness scenarios. Taking 100ms as a typical value covers the internal dispersion situation of most distribution networks.

[0106] The derivation of the partition deviation threshold of 100ms to 500ms is based on the following: different power supply partitions are usually powered by different transformers or different power sources, and their equivalent impedance and load characteristics may have systematic differences. Let the transformer capacities of partition A and partition B be SA and SB, respectively, and their short-circuit impedances be UkA and UkB, respectively. Then the equivalent impedance ZeqA is approximately equal to UkA multiplied by Un squared divided by (100 multiplied by SA), and the same applies to ZeqB. If the difference between SA and SB reaches 2 times, and the difference between Uk and SB reaches 20%, then the Zeq difference can reach 2.4 times, corresponding to a tau difference of approximately 2.4 times. For a typical tau of approximately 300ms, the difference can reach approximately 420ms. Taking 100ms as the lower limit (corresponding to small differences between partitions with similar capacities), 500ms as the upper limit (corresponding to partitions with significant capacity differences), and 200ms as the typical value, the lower to middle range of this value can identify most partition imbalances.

[0107] When a partition recovery imbalance is detected, the pre-start command and the intensity preset command are generated differently based on the deviation direction and magnitude of the partition recovery imbalance. Specifically, for partitions with slower recovery (larger median climb time), the pre-start command is generated earlier (the advance amount is increased by Deltadvance multiplied by DeltaM divided by Mbase, where Mbase is the average of the median values ​​of all partitions), and the suppression depth of the intensity preset command is increased; for partitions with faster recovery, the pre-start command is delayed or not generated, and the suppression depth is reduced. DeltaM divided by Mbase is a relative deviation coefficient, which, after being multiplied by Deltadvance, can adjust the advance amount proportionally to the degree of partition imbalance, ensuring that resources are tilted towards weaker partitions.

[0108] If a partition has fewer than 3 monitoring points, the internal dispersion determination for that partition is skipped, and it only participates in the interval deviation calculation. The lower limit of 3 monitoring points is based on the following: calculating the distribution range requires at least two extreme points, the maximum and minimum values, but at least 3 points are needed to identify outliers in order to eliminate random errors.

[0109] S11. Construct the recovery capability evolution file of the power distribution network.

[0110] The recovery capability evolution archive is obtained by arranging the historical transient-steady-state successive response patterns along the time axis and extracting the trend of the climb time at each drop depth node with the number of years of operation. The trend shows that the climb time increases monotonically or shows a step-like leap as the number of years of operation increases.

[0111] The criteria for determining the step-like leap are: there exists an operating period Yj such that the average climb time at the drop depth before Yj is tbefore, the average climb time at the drop depth after Yj is tafter, and (tafter minus tbefore) divided by tbefore is greater than 50%, and at least 3 records after Yj support the tafter level.

[0112] The 50% jump threshold is derived from the fact that the change in the equivalent impedance of a transformer over its years of operation mainly stems from the aging of the winding insulation and the degradation of the silicon steel sheets in the core. According to IEEE Std C57.91-2011 "IEEE Guide for Loading Mineral-Oil-Immersed Transformers", under normal operating conditions (hot spot temperature not exceeding 98℃), the insulation aging rate of a distribution transformer is approximately 0.5% to 1% per year, accumulating to about 10% to 20% over 20 years, corresponding to an increase in equivalent impedance of about 5% to 15% and an increase in ramp-up time of about 5% to 15%. If a step-like jump occurs (an increase greater than 50%), far exceeding the normal aging rate, it indicates a sudden deterioration event (such as partial discharge, insulation dampness, core loosening, etc.), requiring an early warning. Taking 50% as the threshold is more than three times the upper limit of the normal aging cumulative effect (15%), which can effectively distinguish between "normal aging" and "abnormal deterioration".

[0113] When a step-like jump occurs in the aforementioned trend, a latent aging warning for the distribution network is triggered. The warning level L is determined based on the ratio of the increase in the climb time after the step-like jump relative to the climb time before the jump to the number of years the distribution network has been in operation. The specific formula is: L = (tafter - tbefore) divided by tbefore, then divided by Yj, multiplied by 100%, with the unit being percentages per year. The warning level is divided into three levels: L less than 5% per year is a low-level warning (yellow), 5% per year ≤ L < 10% per year is a medium-level warning (orange), and L greater than or equal to 10% per year is a high-level warning (red). The technical basis for the warning level classification is: according to the Power Equipment Condition-Based Maintenance Guidelines DL / T 393-2010, the annual aging rate of equipment in normal condition should be less than 5%, for a critical condition it should be 5% to 10%, for an abnormal condition it should be 10% to 20%, and for a severe condition it should be greater than 20%. This invention maps the four-level status evaluation of DL / T 393-2010 to a three-level warning system, retaining the correspondence between normal status (no warning), attention status (yellow), abnormal status (orange), and severe status (red). The L value directly reflects the annual aging rate, which is consistent with the status evaluation indicators in the guidelines.

[0114] If the power distribution network has been in operation for less than 3 years, a step-like surge cannot be reliably determined; only a monotonic trend is recorded, and no warning is triggered. The basis for the 3-year lower limit is that transformer insulation aging is usually in a stable period within 3 years (the initial aging rate is low), and the effective data points accumulated within 3 years are limited, making it difficult to distinguish between normal fluctuations and true surges.

[0115] S12. Determine the cascade response characteristics of the distribution network to complex transient disturbances.

[0116] The cascaded response characteristics are determined as follows: During the complete response process, two or more transient disturbance events are identified. Let the transient end time of the nth transient disturbance event be `tendn`, and the transient start time of the (n+1)th transient disturbance event be `tstart(n+1)`. When `tstart(n+1)` minus `tendn` is less than or equal to `trisenmax` multiplied by 50% (i.e., the interval between the two disturbances does not exceed 50% of the maximum climb time in the previous transient disturbance event), it is determined to be a composite transient disturbance. `trisenmax` is the maximum climb time corresponding to all fall depth nodes in the nth transient disturbance event.

[0117] The technical logic behind the 50% interval threshold is as follows: If the interval between two disturbances exceeds the previous maximum climb time, the steady-state recovery process of the previous disturbance has been largely completed (the maximum climb time corresponds to the most severe drop depth; once its recovery is complete, the recovery of other drop depths must also be complete), and the system state is close to normal. The subsequent disturbance can be considered an independent event. If the interval is less than 50% of the maximum climb time, the main recovery process of the previous disturbance has not yet been completed, and the system is still in the energy reconstruction phase. The subsequent disturbance is superimposed on the "semi-steady-state" of the previous recovery, forming a cascading effect. Taking 50% as the threshold, which is in the intermediate state between "basic recovery" and "no recovery," can effectively identify cascading risks.

[0118] The fall depth node d(n+1) of the subsequent transient disturbance event is associated with the remaining climb time tresidualn, which is equal to trisenmax minus (tstart(n+1) minus tendn), after the previous transient disturbance event ends.

[0119] The superimposed drop effect is measured as follows: In the process entanglement characteristics, the baseline climb time tsingle(d(n+1)) is found when the drop depth of a single transient disturbance is d(n+1). The actual climb time tcascade under the composite transient disturbance is obtained from historical records. The cascade amplification margin Deltacascade is equal to tcascade minus tsingle(d(n+1)). The calculation of the steady-state recovery hysteresis introduces the cascade amplification margin: Deltalag' is equal to Deltalag plus Deltacascade multiplied by w, where w is a weighting coefficient, with a value ranging from 0.5 to 1.0 (0.8 in a specific implementation).

[0120] The reasoning behind the weighting coefficient w, ranging from 0.5 to 1.0, is that the amplification of the cascade effect depends on the coupling strength of the two perturbations. If the interval is extremely short (close to 0), the system's energy state has barely recovered, and the subsequent perturbation is equivalent to falling again on top of the already fallen state, resulting in the strongest coupling, with w close to 1.0. If the interval is close to 50% of the maximum climb time, the system has recovered about 50% of its energy state, and the superposition effect of the subsequent perturbation is weakened, with w close to 0.5. Taking w equal to 0.8 as a typical value corresponds to common cascade scenarios with intervals of approximately 20% to 30% of the maximum climb time, placing it on the stronger coupling side within this range, providing a reasonable margin for conservative estimation.

[0121] If the interval between two disturbances exceeds 50% of the trisenmax, the latter disturbance is considered an independent disturbance and no cascade amplification margin is introduced.

[0122] S13. Generate the self-optimization instruction for the control strategy of the power distribution network.

[0123] The self-optimization command of the control strategy is generated in the following way: A loopback comparison data record is established to record the actual execution effect of each generated pre-start command and intensity preset command. The actual execution effect is the actual climb time (tactual) of the distribution network after the steady-state compensation equipment is actually put into operation. The loopback comparison includes calculating the deviation direction between the actual climb time and the expected climb time, i.e., Deltadeviation equals tactual minus tpred.

[0124] When the deviation direction continues to be such that the actual climb time is less than the expected climb time (i.e., Deltatdeviation is less than 0 and the absolute value of Deltatdeviation divided by tpred is greater than the preset optimization threshold etaopt) for more than Nopt consecutive times (Nopt is 3 to 5 times, and 3 times in one specific implementation; etaopt is 10% to 20%, and 10% in one specific implementation), the acceptable recovery time limit Taccept' is tightened to be equal to Taccept multiplied by (1 minus alpha), where alpha is the tightening coefficient, which is 5% to 15% (10% in one specific implementation).

[0125] The technical logic behind setting Nopt to 3 to 5 times and etaopt to 10% to 20% is as follows: The purpose of loopback alignment is to identify systematic biases (model errors or changes in equipment performance) rather than random fluctuations. According to the central limit theorem, the distribution of random errors is approximately normal. The probability of a single bias exceeding 10% is about 16%, the probability of three consecutive biases in the same direction exceeding 10% is about 0.4% (0.16 to the power of 3), and the probability of five consecutive biases exceeding 10% is about 0.01%, all less than the 5% significance level, which can be identified as systematic biases. Setting Nopt to 3 is the minimum number of decisions (considering response speed), and setting Nopt to 5 is the conservative number of decisions (reducing the false positive rate to 0.01%). Setting etaopt to 10% prioritizes sensitivity (early identification of biases), and setting etaopt to 20% prioritizes robustness (avoiding over-adjustment). Setting alpha to 5% to 15% corresponds to the adjustment range of Taccept, with 5% being fine-tuning (adapting to slow changes), 15% being significant adjustment (adapting to rapid changes), and 10% being the typical median.

[0126] When the deviation direction continues to be such that the actual climb time is greater than the expected climb time (i.e., Deltadeviation is greater than 0 and Deltadeviation divided by tpred is greater than etaopt for more than N consecutive times), the acceptable recovery time limit Taccept' is relaxed to Taccept multiplied by (1 plus alpha), and the advance amount of the pre-start command Deltadvance' is simultaneously extended to Deltadvance multiplied by (1 plus beta), where beta is the extension coefficient, with a value of 10% to 30% (20% in one specific implementation). The derivation of beta being 10% to 30% is based on the fact that the advance amount extension must match the relaxation of the acceptable time limit. If Taccept is relaxed by 10% (alpha equals 10%), then the advance amount is extended by 20% accordingly (beta equals 20%), so that the two maintain a 2:1 ratio (consistent with the original design in S4 where Deltadvance equals Deltaforecast minus Deltalag divided by 2). This ratio ensures that even with the time limit relaxed, the pre-launch process can still be completed within the effective time window.

[0127] If the loopback comparison records are less than Nopt times, self-optimization will not be triggered, and the current parameters will be maintained.

[0128] S14. Scenario Examples and System Implementation.

[0129] In one specific implementation, the method described in this invention is deployed in a 10kV distribution network control center in a city. The distribution network comprises three feeders with a total load of approximately 15MW, including 6MW of distributed photovoltaic capacity, four high-power motors (1.5MW each), and approximately 3MW of electric heating load (seasonal). The control center is equipped with a historical data recording server, a scenario prediction server, an instruction generation server, and a communication front-end unit for communicating with various monitoring points and control equipment.

[0130] The monitoring points include: a synchronous phasor measurement unit (sampling rate 12800Hz) installed at the 10kV bus outlet of the substation; power quality monitoring devices (sampling rates 12800Hz / 3200Hz) installed at the beginning of each feeder; inverter monitoring units (sampling rate 6400Hz) installed at each distributed photovoltaic grid-connected point; and smart meters (sampling rate 3200Hz) installed at the load inlet of each motor. Data is uploaded to the control center via a dedicated fiber optic network, using the IEC 61850-MMS communication protocol.

[0131] The historical data records have accumulated 18 months of operational data, identifying and recording a total of 127 transient disturbance events, including 45 small disturbances (drop depth not exceeding 10%), 62 medium disturbances (10% less than or equal to 20% drop depth), and 20 large disturbances (drop depth greater than 20%). After processing by S2, a process-related feature dataset was constructed, containing 312 valid mapping point pairs.

[0132] Current operating conditions: During the heating season, feeder 1 has a load rate of 78%, feeder 2 has a load rate of 65%, and feeder 3 has a load rate of 82%. Predicted scenario: In 15 minutes, a 1.5MW motor (high-power compressor start-up) will be put into operation on feeder 3.

[0133] Scenario Prediction: Based on current power flow calculations, the equivalent impedance R of feeder 3 from the substation to the motor connection point is 0.8 ohms, and X is 1.2 ohms. The motor's rated current IN is P divided by (√3 multiplied by Un multiplied by cosphiN) approximately 1.5 multiplied by 10 to the power of 6 divided by (1.732 multiplied by 10000 multiplied by 0.85) approximately 102A. The starting current Ist is 6 times IN, approximately 612A. The starting power factor cosphist is approximately 0.3, and sinphist is approximately 0.95. The starting reactive power surge DeltaQ is √3 multiplied by Un multiplied by Ist multiplied by sinphist, approximately 1.732 multiplied by 10000 multiplied by 612 multiplied by 0.95, approximately 10.1Mvar. The expected voltage drop DeltaUline is approximately equal to the square root of 3 multiplied by Ist multiplied by X multiplied by sinphist, which is approximately equal to 1.732 multiplied by 612 multiplied by 1.2 multiplied by 0.95, which is approximately equal to 1208V. dpred is equal to 1208 divided by 10000 multiplied by 100%, which is approximately equal to 12.1%.

[0134] In the process involvement characteristics, it was found that when d equals 10%, trie is approximately 350ms, and when d equals 15%, trie is approximately 500ms. Interpolation: tpred equals 350 plus (500 minus 350) multiplied by (12.1 minus 10) divided by (15 minus 10) equals 350 plus 150 multiplied by 0.42 equals 413ms, which is rounded to 410ms.

[0135] Baseline climb time: Currently it is the heating season. According to S6, the mapping drift amount Deltat is equal to 40% which is greater than 30%. tbase has been updated to the heating season small perturbation average of 210ms.

[0136] Steady-state recovery lag: Deltatlag equals 410 minus 210 equals 200ms. Taccept equals 2000ms. Deltatlag is less than Taccept, but further investigation of hidden vulnerabilities is needed.

[0137] Monitoring of Hidden Vulnerability Links: S5 analysis revealed a resilience inflection point. Historical data showed an inflection point around 15% for d (with a Deltadrise increase exceeding lambda of 50%), indicating a hidden vulnerability in the transformer's localized saturation critical zone. Current predictions show dpred at 12.1%, close to the inflection point depth of 15%, leading the system to assess a saturation risk.

[0138] Recovery path fork: After S7 check, d equals 10% to 15% of historical records, CV equals 18% and is less than 25%, no path selection margin is introduced.

[0139] Fatigue recovery: According to the S9 check, d equals 10% twice in the past 4 hours, less than 3 times, so fatigue accumulation is not judged.

[0140] Cascade response: After checking with S12, there are no recent disturbances, and no cascade amplification margin is introduced.

[0141] Zone difference: After checking with S10, the median rise time of feeder 3 is 15% higher than the average value of all feeders. This is within the threshold and does not trigger zone imbalance.

[0142] Final Decision: Deltalag equals 200ms, which is less than Taccept equals 2000ms, but dpred is close to the resilience inflection point and has a saturation risk. Generate a preventative pre-start command: Deltaforecast equals 15 minutes, which is much greater than Deltalag equals 200ms. The lead time, Deltadvance, equals Deltaforecast minus Deltalag divided by 2, approximately equal to 15 minutes. Send a pre-start command to the SVG of feeder 3. Simultaneously generate a strength preset command: r equals 200 divided by 2000, which equals 10% less than or equal to 50%. Preset the solid-state current limiter to a mild suppression mode (50% current limiting depth). Additionally generate a transformer anti-saturation monitoring command: During the period from 30 seconds before motor startup to 10 seconds after startup, increase the transformer high-voltage side current harmonic monitoring frequency from once every 10 seconds to once per second. If the second harmonic content exceeds 12% (close to the 15% saturation threshold), immediately upgrade the current limiter to a moderate suppression mode (75% current limiting depth) and add a STATCOM pre-start command.

[0143] The instructions are sent to the corresponding equipment via the IEC 61850-MMS protocol. After the equipment executes the instructions, it provides feedback on the execution status. The control center records the actual climb time for the next S13 loopback comparison.

[0144] If the actual start time of the motor deviates from the predicted start time by more than ±2 minutes, the advance start command will be recalculated based on the actual start time. If the recalculated advance time is less than the minimum start time of the equipment (SVG is 50ms), then emergency start will be triggered directly instead of advance start.

[0145] The core idea behind this method is that the transient response and steady-state recovery of a distribution network are not two independent processes, but rather a continuous process tightly coupled through the electromagnetic transient processes of energy storage components (inductors, capacitors) and energy conversion components (transformers, motors) within the system. The drop depth determines the disturbance energy injected into the system during the transient phase, while the climb time reflects the rate at which the system dissipates this energy and rebuilds steady state. When the drop depth exceeds a certain critical value, the transformer core enters the saturation region, the equivalent magnetizing inductance decreases sharply, the system's energy storage capacity deteriorates, and the climb time increases nonlinearly—this is the physical essence of the stepwise amplification phenomenon.

[0146] This physical essence stems from the nonlinear characteristics of the transformer core magnetization curve: When the drop depth is small, the core operates in the linear magnetization region, the excitation inductance is approximately constant, and the recovery time is approximately linearly related to the drop depth. When the drop depth exceeds the saturation threshold, the core enters the saturation region, the permeability drops sharply, the excitation inductance decreases significantly, and the recovery time is rapidly extended. As the drop depth increases further, the nonlinearity of the magnetization curve causes the rate of decrease of the excitation inductance to continuously accelerate, resulting in a superlinear increase in the recovery time. That is, the increment of the climb time corresponding to adjacent drop depths is also increasing, forming a step-by-step amplification.

[0147] Therefore, establishing a quantitative mapping between fall depth and climb time through historical data mining is essentially about identifying the energy recovery boundary of the system. Based on this mapping, advance prediction and pre-emptive control transform passive post-event compensation into proactive boundary management, thereby completing defense deployment before transient shocks cause steady-state instability and achieving coordinated unity between transient suppression and steady-state recovery.

[0148] More importantly, this predictive method based on physical coupling transforms control decisions from "event-triggered" to "boundary-aware." Existing technologies can only respond passively after a voltage drop occurs, while this invention identifies the system's energy recovery boundary and completes defense deployment before disturbance energy is injected, making control actions and disturbance events complementary in timing: defense is ready when the disturbance occurs, and recovery is accelerated after the disturbance ends. This complementary timing design avoids the inherent delay accumulation of detection-judgment-decision in traditional post-event compensation, thereby improving the distribution network's response speed and resilience to transient disturbances.

[0149] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A power quality control method based on transient and steady-state coordination, characterized in that, The method includes: The transient electrical quantity change trajectory of the distribution network during the transient disturbance event is obtained, as well as the steady-state electrical quantity convergence trajectory of the distribution network as it enters the steady-state recovery phase after the transient disturbance event ends. The transient electrical quantity change trajectory and the steady-state electrical quantity convergence trajectory are sequentially connected in time to form a complete response process. From the complete response process, the process involvement features between the drop depth node of the transient disturbance event and the corresponding climb rate node in the steady-state recovery phase are extracted. The process involvement features are used to reflect the transient-steady-state successive response law between the drop depth node and the climb rate node. The transient-steady-state successive response law is characterized by the fact that the deeper the drop within the same transient disturbance event, the slower the subsequent climb. Moreover, the degree of slow climb increases progressively with the drop depth. This progressive increase is measured by the increasing difference between the climb time increments corresponding to adjacent drop depth nodes in the complete response process. By utilizing the process involvement characteristics, the upcoming load switching or new energy output fluctuation scenarios in the monitored distribution network are predicted, and the steady-state recovery lag caused by transient impacts under the scenario is obtained. The steady-state recovery lag is the amount by which the expected ramp-up time of the scenario exceeds the benchmark ramp-up time under the most recent small disturbance before the scenario occurs. The small disturbance is a transient disturbance where the drop depth does not exceed 10% of the rated voltage and no obvious inrush current appears in the transformers of the distribution network. When the steady-state recovery hysteresis exceeds the preset acceptable steady-state recovery time limit, the relationship between the steady-state recovery hysteresis and the acceptable steady-state recovery time limit is compared, as well as the relationship between the interval between the occurrence time of the scenario and the current time and the steady-state recovery hysteresis. Based on the comparison results, a pre-start command for the steady-state compensation device and / or a strength preset command for the transient suppression device are generated.

2. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to identify the inflection point of the recovery resilience of the distribution network under the current operating conditions. The resilience inflection point is determined in the following way: during the complete response process, the position where the climb time increment corresponding to the adjacent drop depth node changes abruptly is found. The abrupt change is when the increase in the climb time corresponding to the next drop depth node relative to the climb time corresponding to the previous drop depth node exceeds a preset abrupt change threshold. If there are two drop depth nodes after the next drop depth node, then the climb time corresponding to these two levels is not less than the climb time corresponding to the next drop depth node. If there is only one subsequent drop depth node, the climb time corresponding to that level shall not be less than the climb time corresponding to the next drop depth node; if there is no subsequent drop depth node, the jump shall be determined only based on the increase exceeding the preset jump threshold. When the recovery resilience inflection point exists, it is determined that there is a hidden vulnerable link in the distribution network near the drop depth corresponding to the recovery resilience inflection point; The hidden vulnerable links include at least one of the following: the transformer local saturation critical region, the capacitor bank series resonance trigger region, or the load voltage collapse edge region.

3. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to determine the mapping drift of the distribution network under different seasonal load characteristics; The mapping drift was obtained by comparing the historical transient-steady-state continuity response patterns of the same distribution network during the heating season and the non-heating season. When the mapping drift exceeds the preset drift threshold, the reference climb time is updated to the climb time corresponding to the small disturbance under the current seasonal load characteristics. The corrected reference climb time is used to recalculate the steady-state recovery hysteresis.

4. The method according to claim 1, characterized in that, The process involvement features are also used to extract the recovery path bifurcation features of the distribution network after a transient impact. The bifurcation feature of the recovery path reflects the degree of discrete distribution of the ascent rate nodes under the same fall depth node; When the degree of discrete distribution exceeds a preset bifurcation threshold, it is determined that there is multi-steady-state competition in the steady-state recovery process of the distribution network; The calculation of the steady-state recovery hysteresis introduces a path selection margin, which is half the span between the record with the longest rise time and the record with the shortest rise time in the discrete distribution degree.

5. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to construct a transient impact tolerance profile for the distribution network. The transient impact tolerance profile is obtained by classifying and compressing the transient-steady-state successive response law according to the drop depth range. The classification and compression retains the record with the longest climb time in each drop depth range as the tolerance boundary of that range. The transient impact tolerance profile is compared with the real-time operating data of the distribution network to be monitored. When the transient impact intensity in the real-time operating data approaches the tolerance boundary, the preset capacity expansion command of the steady-state compensation device is triggered.

6. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to extract the recovery fatigue accumulation characteristics of the distribution network under the current operating conditions; The recovery fatigue accumulation characteristic is determined in the following way: during the complete response process, when the same drop depth node appears three or more times within a preset time window and the corresponding climb time is extended successively, it is determined that the recovery capability of the distribution network has fatigue accumulation. The successively extended means that the increase of the climb time of the later climb time relative to the previous climb time exceeds the preset fatigue threshold. When it is determined that there is accumulated recovery fatigue, the calculation of the steady-state recovery lag amount adds the fatigue correction amount to the expected climb time. The fatigue correction amount is the difference between the last climb time and the first climb time in the successive extension divided by the number of occurrences within the preset time window.

7. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to determine the differences in recovery characteristics between different power supply zones in the power distribution network; The differences in recovery characteristics are determined by comparing the rise time distribution range of multiple monitoring points within the same power supply zone at the same drop depth node, and the median deviation of rise time between different power supply zones at the same drop depth node. When the distribution range exceeds a preset internal dispersion threshold or the median deviation exceeds a preset partition deviation threshold, it is determined that the distribution network has a partition recovery imbalance. The pre-start command and the intensity preset command are generated differently based on the deviation direction and deviation magnitude of the partition recovery imbalance.

8. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to construct the recovery capability evolution archive of the distribution network; The recovery capability evolution archive is obtained by arranging the historical transient-steady-state successive response patterns on a time axis and extracting the trend of the climb time at each drop depth node with the number of years of operation. The trend shows that the climb time increases monotonically or shows a step-like leap as the number of years of operation increases. When a step-like jump occurs in the trend of change, a latent aging warning is triggered for the distribution network. The level of the latent aging warning is determined based on the ratio of the increase in the climbing time after the step-like jump relative to the climbing time before the jump to the number of years the distribution network has been in operation.

9. The method according to claim 1, characterized in that, The transient-steady-state succession response law is also used to determine the cascade response characteristics of the distribution network to complex transient disturbances; The cascaded response characteristics are determined in the following way: when there are two or more transient disturbance events in the complete response process with an interval not exceeding 50% of the rise time of the previous transient disturbance event, the fall depth node of the subsequent transient disturbance event is associated with the remaining rise time of the distribution network before it has recovered to steady state after the end of the previous transient disturbance event, so as to obtain the superimposed fall effect of the subsequent transient disturbance event when the power grid has not yet recovered from the previous transient disturbance. The calculation of the steady-state recovery hysteresis introduces a cascade amplification margin, which is the difference between the climb time corresponding to the superimposed drop effect and the climb time of the same drop depth under a single transient disturbance event, multiplied by a weighting coefficient, wherein the weighting coefficient is between 0.5 and 1.

0.

10. The method according to claim 1, characterized in that, The transient-steady-state continuity response law is also used to generate self-optimization instructions for the control strategy of the distribution network; The self-optimization command of the control strategy is generated in the following way: the actual execution effect of the historically generated pre-start command and intensity preset command is compared with the prediction result of the steady-state recovery lag. The actual execution effect is the actual ramp-up time of the distribution network after the steady-state compensation equipment is actually put into operation. The loop-through comparison includes calculating the deviation direction between the actual ramp-up time and the expected ramp-up time. When the deviation direction is continuously such that the actual ramp-up time is less than the expected ramp-up time for more than a preset optimization threshold and this state occurs continuously for a preset number of times, the acceptable recovery time limit is tightened. When the deviation direction is continuously such that the actual ramp-up time is greater than the expected ramp-up time for more than the preset optimization threshold and this state occurs continuously for the preset number of times, the acceptable recovery time limit is relaxed and the lead time of the pre-start command is extended simultaneously.

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