System inertia boundary backstepping method based on frequency dynamic index and distributed node equivalent inertia analysis

Abstract

The invention relates to a system inertia boundary backstepping method based on frequency dynamic indexes and distributed node equivalent inertia analysis, and belongs to the field of power optimization. The method comprises the following steps: dividing a frequency response process into an inertia response stage, a primary frequency modulation stage and a secondary frequency modulation stage; constructing a multi-source frequency response unified equivalent model; an equivalent inertia boundary inversion method based on RoCoF and Nadr dual constraints is provided, a frequency safety boundary is converted into a constraint expression for the equivalent total inertia of a system, and an inertia boundary required under given power disturbance is reversely deduced; the method further comprises the steps of introducing static load voltage characteristic correction during inertia boundary inversion; the method further comprises the step of constructing a frequency support-oriented regionalization control strategy. According to the method, the safety support boundary of the low-inertia emergency power supply system is researched from the overall level and the regional level, and a theoretical basis is provided for refined frequency control and resource optimization layout.

Description

Technical Field

[0001] This invention belongs to the field of power optimization and relates to a method for back-calculating the system inertia boundary based on frequency dynamic indicators and the analysis of equivalent inertia of distributed nodes. Background Technology

[0002] In power systems, frequency is a core parameter reflecting the active power balance. When there is a power imbalance between total generation and total load, the system frequency will shift. In traditional power grids where synchronous generators are the primary power source, frequency changes are jointly regulated by rotor inertia and speed control systems. However, with the large-scale integration of new energy sources, the system inertia level has decreased significantly, and the frequency dynamic characteristics exhibit greater sensitivity and speed.

[0003] With the rapid development of renewable energy, new power sources such as wind power and photovoltaics are being connected to the grid on a large scale. These power sources mostly use power electronic interfaces, which, unlike traditional rotating mechanical synchronous generators, do not possess inherent mechanical inertia. This leads to a continuous decline in the overall inertia level of the power grid, resulting in faster frequency response and greater fluctuations, severely impacting the dynamic stability and operational safety of the system. Especially during disturbances such as large-scale generator tripping, line faults, or sudden load changes, the frequency sag rate (RoCoF) of low-inertia systems increases rapidly, and the frequency minimum point (Nadir) decreases significantly, potentially triggering protection maloperation, load shedding, or even system collapse.

[0004] In the process of building a new power system dominated by new energy sources, energy forms such as photovoltaics and hydropower are increasingly playing an important role. However, these energy sources themselves have a certain degree of uncertainty and volatility in output. For example, photovoltaic power generation is affected by external factors such as weather and changes in sunshine, and its output power has strong randomness; hydropower is affected by seasonal and human factors such as water level and flow scheduling. This uncertainty in output further exacerbates the uncertainty of system inertia changes and frequency fluctuations, increasing the complexity and urgency of frequency control.

[0005] For emergency power supply systems, the system structure is relatively independent, backup resources are insufficient, and frequency stability is more vulnerable. Quickly assessing the system's inertia support capability under expected frequency boundary conditions and deducing the required minimum and maximum equivalent inertia ranges are crucial for developing emergency control strategies and rationally deploying energy storage and virtual inertia resources. Summary of the Invention

[0006] The purpose of this invention is to provide a method for back-calculating the system inertia boundary based on frequency dynamic indicators and equivalent inertia analysis of distributed nodes. This method studies the safety support boundary of low-inertia emergency power supply systems from both overall and regional perspectives, providing a theoretical basis for refined frequency control and resource optimization layout.

[0007] To achieve the above objectives, the technical solution of this invention is: a method for back-calculating the system inertia boundary based on frequency dynamic indicators and equivalent inertia analysis of distributed nodes, comprising:

[0008] The frequency response process is divided into the inertial response stage, the primary frequency modulation stage, and the secondary frequency modulation stage.

[0009] Construct a unified equivalent model for multi-source frequency response;

[0010] A method for inverting the equivalent inertia boundary based on RoCoF and Nadir dual constraints is proposed. The frequency safety boundary is transformed into a constraint expression on the equivalent total inertia of the system, and the required inertia boundary under a given power disturbance is derived.

[0011] Furthermore, in the inertial response stage, the frequency dynamic process is described as follows:

[0012]

[0013] H represents the power imbalance caused by the disturbance, H is the system's equivalent inertia constant, and f0 is the system's rated frequency.

[0014] During the first frequency modulation phase, the frequency dynamic process is described as follows:

[0015]

[0016] T1 is the frequency modulation control time constant, K P For proportional control gain, This is a frequency reference value. It is a frequency function of time t;

[0017] During the secondary frequency modulation stage, the frequency dynamic process is described as follows:

[0018]

[0019] T2 is the response delay, K I For integral control gain, This represents the change in frequency.

[0020] Furthermore, the unified equivalent model of multi-source frequency response is constructed as follows:

[0021] ①The frequency response of the synchronous generator SG is described by the rotor motion equation:

[0022]

[0023] The equivalent inertia constant of the synchronous generator. Changes in synchronous generator power

[0024] ② The response form of the grid-connected inverter GFM is as follows:

[0025]

[0026] H gfm (t) can be dynamically adjusted, representing the inertia simulated by GFM-type devices. The power variation of a grid-connected inverter;

[0027] ③ In the unified modeling, the grid-connected inverter GFL is regarded as a "potential support source";

[0028] ④ The response model of a BESS (Body Safety System) energy storage system is often expressed as:

[0029]

[0030] K ω To simulate the inertia coefficient, K d The damping coefficient is... Indicates the change in frequency. This indicates the change in power of the energy storage system;

[0031] Taking all power supply types ①-④ into account, the total equivalent inertia of the system frequency response is expressed as:

[0032]

[0033] Denotes the equivalent inertia constant of the i-th grid-type inverter. This represents the simulated inertia coefficient of the j-th energy storage system.

[0034] Furthermore, the equivalent inertia boundary inversion method based on RoCoF and Nadir dual constraints is implemented as follows:

[0035] (1) Based on RoCoF, the minimum inertia assessment shows that the relationship between the rate of change of frequency (RoCoF) and the system inertia is simplified as follows:

[0036]

[0037] Therefore, the minimum inertia is:

[0038]

[0039] ΔP represents the power imbalance caused by the disturbance, f0 is the rated frequency, and RoCoF is the power imbalance caused by the disturbance. max The maximum allowable rate of frequency change; if the system inertia is lower than the minimum inertia, RoCoF will exceed the relay protection threshold and trigger a frequency safety event;

[0040] (2) Minimum inertia assessment based on Nadir:

[0041] ① Establish a comprehensive frequency response model:

[0042] Construct a frequency response model that can encompass various frequency regulation resources in the system. Its key features include: integrating multiple types of frequency regulation resources: the model not only includes traditional thermal power units and hydropower units, but also incorporates the frequency regulation function of power electronic power sources; considering the frequency regulation characteristics of new energy sources: the model includes the primary frequency regulation droop coefficient (R0) of power electronic power sources. w ) and virtual inertia coefficient (K VI ), to characterize its ability to support frequency;

[0043] ② Model simplification and equivalent analysis:

[0044] The model in ① can be simplified into an equivalent first-order inertial element model as shown in the following equation. This simplified model uses equivalent system parameters, including the equivalent inertia constant H. sys Equivalent adjustment coefficient R sys Equivalent response time constant T sys The coefficient K is used to describe the impact of replacing the synchronous machine with a power electronic power supply on the overall inertia and droop coefficient of the system:

[0045]

[0046] Where ΔP m and ΔP d These are the changes in reference power and the changes in output power, D sys It is the equivalent damping coefficient, and s is the complex frequency domain variable after Laplace transform;

[0047] ③ Solve for the minimum inertia:

[0048] First, input the maximum disturbance power ΔP. max and the constraint Δf at the lowest frequency min Next, the frequency response model is input, and by solving the time-domain response of the model, the dynamic change curve of the frequency after disturbance is analyzed under different system inertia levels. Finally, through iterative calculation or analytical methods, the minimum point Nadir of the frequency curve is found to be equal to the minimum frequency constraint Δf. min The system inertia Hsys is the minimum inertia requirement Hmin for satisfying the minimum frequency constraint. min,Nadi ;

[0049] (3) Inertia boundary interval

[0050] For a system simultaneously constrained by RoCoF and the minimum frequency point, the final minimum inertia is the larger value under both constraints, i.e.:

[0051]

[0052] Where: H min,Rocof H represents the minimum inertia of the system under RoCoF constraints. min,Nadir It represents the minimum inertia constrained by the lowest frequency point.

[0053] Furthermore, it also includes introducing static load voltage characteristic corrections when performing inertia boundary inversion.

[0054] Further, the static load voltage characteristics are corrected as follows:

[0055] When performing inertia boundary inversion, the voltage dependence of the static load should be taken into account in the expression for power imbalance caused by disturbance, and modified as follows:

[0056]

[0057] ΔP 负荷缓解 Derived from voltage changes and load types under disturbances, and approximated through static power flow simulation or empirical models. The power imbalance caused by the corrected disturbance. The power imbalance is caused by the initial disturbance.

[0058] Furthermore, this also includes developing regionalized control strategies oriented towards frequency support.

[0059] Furthermore, the frequency-supported regionalized control strategy is implemented as follows:

[0060] 1) Basis for regional division and zoning control logic

[0061] Based on the spatial heat map of node inertia index and cluster analysis results, the system is divided into multiple frequency support sub-regions. Each sub-region has relatively independent inertia characteristics and frequency response capabilities. Each sub-region is equipped with an independent local controller or frequency control coordinator (FCC) to achieve fast and localized disturbance suppression response.

[0062] The control objectives for each sub-region include: real-time monitoring of the frequency change rate RoCoF and the lowest frequency point Nadir index; determining whether the frequency boundary of the sub-region exceeds the limit; dynamically scheduling local energy storage and virtual inertia resources; and coordinating power support or frequency coordination based on the degree of frequency coupling with adjacent sub-regions.

[0063] 2) Virtual inertia / energy storage coordinated scheduling strategy

[0064] Within the framework of a regionalized control strategy, the following types of control response mechanisms should be established:

[0065] 1. Priority control mechanism: Nodes within the region are sorted in ascending order of node inertia index Hidx i, and energy storage or GFM power sources near nodes with weak inertia are prioritized.

[0066] 2. Disturbance sensing and scheduling mechanism: Based on the PMU or fast event identification system, determine the location of the disturbance source and prioritize the deployment of inertia regulation response within its influence area;

[0067] 3. RoCoF closed-loop feedback mechanism: Set the RoCoF threshold for each region. If the threshold is exceeded, the local energy storage will be dynamically injected with inertial power.

[0068] 4. Regional frequency dynamic prediction mechanism: Introduce a short-term frequency trend prediction model to schedule available inertia resources in advance and form feedforward suppression control logic;

[0069] 3) Regional coordination and border control

[0070] Since there are coupling boundaries in each region, a regional boundary frequency coordination mechanism needs to be designed: a frequency equalization controller (FEC) is set up to monitor the frequency difference between adjacent regional boundaries and implement coordinated adjustment; a bandwidth control method is used to filter the frequency of boundary nodes to alleviate frequency oscillation propagation; and a linkage activation mechanism is designed to guide the surrounding auxiliary regions to provide frequency support when the control response of the main region is insufficient.

[0071] 4) Regional coordination and border control

[0072] A regional frequency coordination center (R-FCC) is deployed at the dispatch master station to achieve multi-regional inertia monitoring and coordinated control; local frequency controllers are set up in key substations and microgrids, embedding RoCoF / Nadir detection modules and GFM controller interfaces; a regional frequency-power event library is built to support boundary policy self-learning and optimization; and regional frequency control is integrated into the distribution network active management system (ADMS) in conjunction with the source-grid-load-storage coordinated control framework.

[0073] Furthermore, the nodal inertia index is defined as follows:

[0074]

[0075] ΔPᵢ is the active disturbance allocated to the i-th node; f0 is the system rated frequency; dfᵢ / dt is the instantaneous frequency change rate of node i, obtained from the PMU or simulation results.

[0076] The present invention also provides a computer-readable storage medium having stored thereon computer program instructions executable by a processor, wherein when the processor executes the computer program instructions, it can implement the steps of any of the methods described above.

[0077] Compared with existing technologies, the present invention has the following advantages: The present invention proposes a system inertia boundary back-calculation method based on frequency dynamic indicators (RoCoF, Nadir) and equivalent inertia analysis of distributed nodes, which studies the safety support boundary of low inertia emergency power supply system from both overall and regional levels, providing a theoretical basis for refined frequency control and resource optimization layout. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0079] Figure 2 This is a typical low-voltage distribution network system.

[0080] Figure 3 This is the RoCoF-inertia curve.

[0081] Figure 4 The frequency curves are for three types of support schemes.

[0082] Figure 5 For Nadir-inertia and damping surfaces. Detailed Implementation

[0083] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0084] This invention provides a method for back-calculating the system inertia boundary based on frequency dynamic indicators and equivalent inertia analysis of distributed nodes, including:

[0085] The frequency response process is divided into the inertial response stage, the primary frequency modulation stage, and the secondary frequency modulation stage.

[0086] Construct a unified equivalent model for multi-source frequency response;

[0087] A method for inverting the equivalent inertia boundary based on RoCoF and Nadir dual constraints is proposed. The frequency safety boundary is transformed into a constraint expression on the equivalent total inertia of the system, and the required inertia boundary under a given power disturbance is derived.

[0088] When performing inertia boundary inversion, a correction based on static load voltage characteristics is introduced;

[0089] Construct a frequency-support-oriented regional control strategy.

[0090] The following is a detailed implementation process of the present invention.

[0091] 1. Frequency response mechanism of low inertia power systems

[0092] 1.1 Basic Principles and Specifications of Frequency Response

[0093] The frequency response process of a power system can generally be summarized as a dynamic adjustment process triggered by a disturbance, mainly including inertial response, primary frequency regulation, and secondary frequency regulation stages. Among them, the rate of change of frequency (RoCoF) and the lowest frequency point (Nadir) are two key indicators for measuring the frequency security of the system.

[0094] (1) Rate of change of frequency RoCoF

[0095] RoCoF (Rate of Change of Frequency) describes the rate of change of frequency, and its physical meaning is the amount of frequency change per unit time, usually expressed in Hz / s. Its expression is as follows:

[0096]

[0097] Where ΔP is the power imbalance caused by the disturbance (MW), H is the system's equivalent inertia constant (s), and f0 is the system's rated frequency (Hz). As can be seen from the above equation, the larger the system inertia, the smaller the RoCoF, the slower the frequency response, and the more stable the system.

[0098] High RoCoF values ​​may cause relay protection malfunctions and trigger equipment frequency tripping thresholds. Therefore, power grid companies in many countries and regions have clear restrictions on RoCoF. For example, ENTSO-E recommends limiting it to within 0.5 Hz / s, while China Southern Power Grid stipulates that it should not exceed 1 Hz / s.

[0099] (2) Lowest frequency point Nadir

[0100] After a disturbance occurs, the frequency will rapidly drop to a certain minimum point and then gradually recover. This minimum value is called the frequency trough (Nadir), and it is an important indicator for measuring the frequency stability margin of the system. If Nadir falls below a set value, the system may enter a low-frequency load shedding state, leading to a power outage.

[0101] Nadir and RoCoF together determine the overall strength of the system's response to disturbances. Unlike RoCoF, Nadir reflects the "result" of the frequency response, while RoCoF reflects the "speed" of the response process. Both need to be considered simultaneously in frequency security assessments.

[0102] (3) Relationship between frequency response and equivalent inertia

[0103] The system frequency response is directly coupled with the total inertia. After a power system is subjected to a disturbance, its frequency response is mainly affected by the following factors: the magnitude of the power imbalance (the size of the disturbance source), the level of the system's total inertia (including synchronous machines and virtual inertia), and the time delay and strategy of the controllers participating in the response (such as the primary frequency regulation time constant, energy storage controller delay, etc.). Therefore, the frequency dynamic equation can be expressed in a simplified form as:

[0104]

[0105] Frequency response is affected not only by the magnitude of the system's inertia but also by the system's topology and power flow. For example, in weakly connected regions or at end nodes, frequency fluctuations are larger and change faster when disturbances occur, and the RoCoF value is more likely to exceed the threshold, reflecting differences in local frequency support capabilities.

[0106] Furthermore, considering the diverse sources of inertia in systems containing new energy sources (synchronous machine inertia, virtual inertia, battery-supported inertia, etc.), the system's equivalent inertia exhibits dynamic variability. The time delay, startup threshold, and current limiting of different types of power supplies or control equipment involved in frequency regulation also affect frequency response characteristics.

[0107] 1.2 Segmented Frequency Dynamic Modeling

[0108] After a power system is subjected to a disturbance, its frequency response process can generally be divided into three typical stages: the inertia response stage, the primary frequency regulation stage, and the secondary frequency regulation stage. The frequency evolution characteristics and the dominant control mechanisms differ in each stage, therefore, a piecewise modeling approach should be used to describe them.

[0109] (1) Inertial response stage (0–1s)

[0110] The inertia response phase occurs within the first few hundred milliseconds to one second after a system disturbance. During this phase, rapid changes in system frequency are primarily suppressed by the rotating inertia of the synchronous generator or the virtual inertia simulated by the power electronic controller.

[0111] The frequency dynamics can be simplified by the classical rotor motion equations as follows:

[0112]

[0113] The rate of frequency drop during this phase is known as RoCoF, and its magnitude is inversely proportional to the system's equivalent inertia. Therefore, the speed at which the system frequency drops during this phase is determined by inertia, but there is no significant control intervention yet.

[0114] If the system contains grid-connected power sources such as virtual synchronous machines (VSGs) or drop-controlled energy storage, they can simulate the effect of rotating inertia through control strategies, providing support for this stage and effectively delaying the frequency drop.

[0115] (2) First frequency modulation stage (1–10s)

[0116] The primary frequency regulation stage occurs after the inertial response, when the frequency is in a deviated state. The active power output is adjusted by the main controller (such as the Pf control of the synchronous generator governor or inverter) to restore the frequency.

[0117] Its dynamic process can be approximated as a first-order time-lag control system, and the frequency change can be described as:

[0118]

[0119] Where T1 is the frequency modulation control time constant, K P This is a proportional control gain. During this stage, the system frequency drop is initially suppressed and tends to stabilize, but it may still be below the rated value.

[0120] (3) Secondary frequency regulation stage (>10s): When the system frequency has not fully recovered to the rated value due to the primary frequency regulation, the dispatching system will activate AGC (Automatic Generation Control) or the main control layer controller to fully restore the frequency. The response speed in this stage is relatively slow, and the objects of regulation include the main generators, pumped storage, load management system, etc.

[0121] The control strategy can be modeled as an integral control system:

[0122]

[0123] Where T2 is the response delay, K I This is for integral control gain.

[0124] (4) The significance of the application of the segmented model

[0125] The three-stage modeling approach can achieve the following functions:

[0126] 1) Clearly describe the dynamic evolution path of the frequency and analyze the dominant mechanisms at each stage;

[0127] 2) Provides a basis for deriving the inertia boundary and controller parameter settings;

[0128] 3) To guide the rational allocation and scheduling sequence of virtual inertia and primary frequency regulation energy storage resources;

[0129] 4) Supports optimized controller design for disturbance source response.

[0130] In low-inertia systems, frequency fluctuations respond more rapidly. Ignoring any stage may lead to model distortion or control failure. Therefore, systematic segmented modeling is a necessary prerequisite to ensure modeling accuracy and control effectiveness.

[0131] 1.3 Multi-source frequency response equivalent

[0132] In modern power systems, the diversity of power source types leads to differentiated dynamic behaviors in frequency response. Especially in low-inertia systems, in addition to synchronous generators, there are newer power sources such as grid-connected inverters (GFM), grid-linked inverters (GFL), and battery energy storage systems (BESS), each with its own unique frequency response characteristics. To assess the overall frequency support capability of the system, it is necessary to establish a unified equivalent model of multi-source frequency response.

[0133] (a) Synchronous Generator (SG)

[0134] Traditional synchronous generators possess inherent rotational inertia, and their frequency response is primarily described by the rotor motion equations:

[0135]

[0136] (ii) Grid-connected inverter (GFM)

[0137] GFM simulates the frequency response behavior of a synchronous generator by embedding algorithms such as a virtual synchronous machine (VSG), droop control, and virtual inertia control, and can inject "adjustable" virtual inertia into the system. Its response form is as follows:

[0138]

[0139] Where H gfm (t) can be dynamically adjusted and represents the inertia simulated by GFM-type devices.

[0140] (iii) Grid-connected inverter (GFL)

[0141] GFLs cannot set their own frequency and only operate with the system frequency, therefore they typically do not provide inertia support. However, in some cases, when used in conjunction with energy storage and controllers, they can participate in primary frequency regulation or virtual inertia adjustment. Therefore, in unified modeling, GFLs can be considered as "potential support sources".

[0142] (iv) Energy Storage System (BESS)

[0143] Energy storage devices, due to their rapid charging and discharging capabilities, are a key means of providing support for high frequencies. Their response model is often expressed as:

[0144]

[0145] Where K ω To simulate the inertia coefficient, K d This is the damping coefficient. The energy storage system can be configured as an inertial response device, a primary frequency regulation resource, or a RoCoF limit adjustment tool.

[0146] (v) Unified modeling method

[0147] Taking all the power supply types mentioned above into account, the total equivalent inertia of the system frequency response can be expressed as:

[0148]

[0149] The various parameters represent the effective inertia contributions from synchronous generators, grid-connected inverters, and energy storage. This modeling approach can be used to: simulate the frequency response process of low-inertia systems; estimate the trend of system inertia changes online; and design strategies and threshold settings for energy storage and controller participation in the frequency response. By constructing a unified frequency response model, not only can the synthesis mechanism of multi-source responses be revealed, but a modeling foundation is also laid for subsequent equivalent inertia inversion and nodal index calculation.

[0150] 2. System Frequency Boundary and Equivalent Frequency Inverse Deduction

[0151] 2.1 Principle of Inversion of Upper and Lower Limits of Equivalent Inertia

[0152] The safe operation of a power system relies on sufficient inertia support. Inertia not only determines the system's initial response speed to disturbances (RoCoF) but also affects the magnitude of frequency drop (Nadir). Under low inertia conditions, rapid frequency changes are more likely to trigger protection actions and load shedding. Therefore, a clear inertia boundary calculation method is needed to guide the system's operation within the frequency safety range. To this end, this invention proposes an equivalent inertia boundary inversion method based on dual constraints of RoCoF and Nadir. By transforming the frequency safety boundary into a constraint expression on the total system inertia, the required inertia boundary under a given power disturbance can be deduced.

[0153] (1) Minimum inertia assessment based on RoCoF. The rapid drop in system frequency at the initial stage of a disturbance is mainly dominated by equivalent inertia. The relationship between the rate of change of frequency (RoCoF) and system inertia can be simplified as follows:

[0154]

[0155] Therefore, the minimum inertia is:

[0156]

[0157] Where ΔP is the net power imbalance experienced by the system, f0 is the rated frequency, and RoCoF max This represents the maximum permissible rate of frequency change. If the system inertia falls below this value, RoCoF will exceed the relay protection threshold, triggering a frequency safety event.

[0158] (2) Minimum inertia assessment based on Nadir. The process mainly consists of the following three steps:

[0159] ① Establish a comprehensive frequency response model.

[0160] First, a frequency response model needs to be constructed that can cover various frequency regulation resources in the system. Its key features include: integration of multiple types of frequency regulation resources: the model not only includes traditional thermal power units and hydropower units, but also specifically incorporates the frequency regulation effect of power electronic power sources (such as wind power and photovoltaics); consideration of the frequency regulation characteristics of new energy sources: the model includes the primary frequency regulation droop coefficient (R0) of power electronic power sources. w ) and virtual inertia coefficient (K VI ), to characterize its ability to support frequency.

[0161] ② Model simplification and equivalence analysis.

[0162] The model in ① can be simplified into an equivalent first-order inertial element model as shown in the following equation. This simplified model uses equivalent system parameters, including the equivalent inertia constant H. sys Equivalent adjustment coefficient R sys Equivalent response time constant T sys The coefficient K is used to describe the impact of replacing the synchronous machine with a power electronic power supply on the overall inertia and droop coefficient of the system:

[0163]

[0164] Where ΔP m and ΔP d These are the changes in reference power and the changes in output power, D sys It is the equivalent damping coefficient, and s is the complex frequency domain variable after Laplace transform;

[0165] ③ Solve for the minimum inertia.

[0166] First, input the maximum disturbance power (ΔP). max ) and the minimum frequency constraint (Δf) min Next, the frequency response model is input. By solving the time-domain response of this model, the dynamic change curve of the frequency after disturbance can be analyzed under different system inertia levels. Finally, through iterative calculation or analytical methods, the minimum point (Nadir) of the frequency curve is found to be exactly equal to the minimum frequency constraint Δf. min The system inertia Hsys. This inertia value is the minimum inertia requirement (Hsys) for the system to satisfy the minimum frequency constraint. min,Nadi ).

[0167] (3) Inertia boundary interval

[0168] For a system simultaneously constrained by RoCoF and the minimum frequency point, the final minimum inertia is the larger value under both constraints, i.e.:

[0169]

[0170] Where: H min,Rocof H represents the minimum inertia of the system under RoCoF constraints. min,Nadir These are the minimum inertia (in the form of inertial constants) under the constraint of the lowest frequency point.

[0171] In summary, the method of inversely deriving the lower limit of equivalent inertia from the RoCoF-Nadir frequency boundary provides theoretical support and practical tools for frequency stability analysis of low-inertia emergency power supply systems.

[0172] 2.2 Correction of Static Load Voltage Characteristics

[0173] In the process of inertia boundary estimation, the power imbalance ΔP is usually regarded as the net power gap caused by the disturbance event. However, in actual system operation, there is a significant coupling relationship between load characteristics and voltage. Especially when the system frequency drops and voltage drops, some static loads will inevitably change, thereby indirectly affecting the system frequency response.

[0174] Static load models are typically classified into three types: constant impedance (Z), constant current (I), and constant power (P), collectively known as the ZIP model. The load power-voltage relationship can be expressed as:

[0175]

[0176] Where: P L0 V is the rated load power; a1, a2, and a3 are the proportion coefficients of constant impedance, constant current, and constant power loads, respectively, satisfying a1+a2+a3=1.

[0177] After a disturbance occurs, the voltage drop will lead to a reduction in the actual power absorbed by the load, a phenomenon known as the "load mitigation effect." This effect can mitigate the system power deficit and reduce the frequency descent rate to some extent. However, its impact is nonlinear and closely related to the load type.

[0178] Therefore, when performing inertia boundary inversion, the voltage dependence of the static load should be taken into account in the ΔP expression, and it should be modified as follows:

[0179]

[0180] Where ΔP 负荷缓解 The inertia value is derived from voltage changes and load type under disturbances and can be approximated through static power flow simulation or empirical models. The introduction of this correction method will make the inertia calculation results closer to the actual system operating state, improving the reliability of frequency safety boundary analysis. In summary, the static load voltage characteristics have a significant impact on the system frequency evolution process, and the correction of ΔP is a crucial step in constructing an accurate inertia boundary analysis model.

[0181] 3. Node-level equivalent inertia and load support capacity

[0182] 3.1 Definition of Nodal Equivalent Inertia Index

[0183] In traditional power systems, system frequency response analysis is often based on the global average frequency, neglecting the dynamic inconsistencies in frequency between nodes caused by differences in electrical distance, power supply integration structure, and load characteristics. With a high proportion of renewable energy integration and a wide distribution of grid-connected power sources, system inertia exhibits significant spatial non-uniformity, resulting in substantial node-specific differences in frequency response. Therefore, introducing node-level inertia metrics to accurately characterize the local response capability of each node to disturbances is crucial for constructing a regionalized frequency support system.

[0184] Node-level equivalent inertia is a quantitative indicator that reflects the dynamic contribution of a node's local frequency, based on its disturbance response behavior. This indicator can be used to identify low-support regions, optimize virtual inertia configuration, and serve as input for area controller design.

[0185] (I) Definition of nodal inertia index

[0186] Considering the initial frequency change rate (RoCoF) dfᵢ / dt of the i-th node in a power system after being subjected to a disturbance ΔP, its node inertia index can be defined as:

[0187]

[0188] Where: ΔPᵢ is the active disturbance allocated to this node; f0 is the system's rated frequency; dfᵢ / dt is the instantaneous frequency change rate of node i, which can be obtained from the PMU or simulation results. The above indicators characterize the strength of each node's ability to "resist" frequency descent when facing system disturbances. The larger the value, the stronger the inertia support capability and the slower the frequency descent.

[0189] (II) Spatial Coupling and Distributed Modeling

[0190] The dynamic response of node frequencies is not only related to local power generation and load, but also affected by the system's electrical structure, mainly in the following two dimensions:

[0191] (1) Electrical distance between the node and the disturbance source: The greater the distance, the less the frequency change is affected by the disturbance;

[0192] (2) Inertia connection density of nodes: The more synchronous machines or grid-type power supplies connected, the greater the equivalent inertia.

[0193] A node response model is constructed by combining the disturbance transfer function and the generalized frequency response function (GFRF), thereby defining the dominant weights of frequency disturbances, which are then used for node inertia index inversion.

[0194]

[0195] Where wᵢ represents the node frequency response sensitivity weighting coefficient. This method can be constructed by combining the following two paths: (1) extracting the frequency dynamic propagation matrix based on the system linearization model; (2) training the response mapping relationship between node RoCoF and ΔP based on PMU observation data.

[0196] Furthermore, frequency propagation coupling is also manifested in the overlap of "inertia sensing regions," meaning that a disturbance simultaneously affects multiple nodes, but to varying degrees. Node inertia indices should reflect the "inertia exposure" under the influence of such local disturbances. In summary, the node equivalent inertia index provides an effective means of quantifying the spatial heterogeneity of frequency support, contributing to the construction of a flexible control strategy system guided by frequency dynamic capabilities, and is an indispensable supporting indicator in high-proportion renewable energy systems.

[0197] 3.2 Spatial Distribution Characteristics Analysis

[0198] The spatial distribution characteristics of nodal equivalent inertia refer to the regional differences and coupling patterns of inertia indices of each node under different power grid structures and operating conditions. These differences are jointly determined by various factors, including power grid topology, power source layout, load density, and the relative location of disturbance sources. In low-inertia systems, because the inertia sources are mainly grid-type power sources and are unevenly distributed, the response capabilities of each node to frequency disturbances exhibit significant spatial imbalances.

[0199] (I) Dominant Factors in Spatial Distribution of Inertia

[0200] (1) Power grid topology: The impedance and electrical distance between nodes determine the disturbance propagation path and rate, which in turn affect the timing and amplitude of the frequency dynamic response.

[0201] (2) Location of power supply and energy storage: Grid-type power supply or synchronous generator connected to dense areas have stronger local inertia support capabilities. Conversely, in the terminal areas with dense loads and lack of inertia, the frequency response capability is obviously insufficient.

[0202] (3) Location and type of disturbance source: Disturbances produce higher RoCoF at nearby nodes, increasing the sensitivity of inertia index; while distant nodes may respond with lag, reducing the accuracy of inertia identification.

[0203] (ii) Spatial heat map of nodal inertia

[0204] Based on the above characteristics, a spatial heatmap of the equivalent inertia index of nodes can be constructed, in the following form:

[0205] The vertical axis represents the system node number; the horizontal axis represents typical disturbance conditions (different locations and types of disturbance sources); the thermal color represents the Hidx i value, with darker colors indicating a stronger inertia contribution. This graph can clearly reveal vulnerable low-inertia regions (high RoCoF, low Hidx nodes), providing auxiliary basis for the optimized layout of virtual inertia or energy storage resources.

[0206] (III) Regional Trend Analysis and Cluster Identification

[0207] To further refine the spatial distribution characteristics, the nodal inertia index can be processed as follows:

[0208] Principal Component Analysis (PCA): Dimensionality reduction to extract the characteristic axes that mainly influence the inertia contribution of the region;

[0209] K-means clustering: partitions nodes according to their frequency response capabilities to identify regions with strong inertia, weak inertia, and coupling boundaries;

[0210] Construction of zoned disturbance response sensitivity matrix: quantifies the response intensity of each zone to external disturbances, and assists in formulating zoned control strategies.

[0211] (iv) Classification of Regional Support Capacity Levels

[0212] Based on the nodal inertia index and distribution pattern, the region can be divided into:

[0213] Class A nodes (inertia core area): possess high inertia source density and good support characteristics;

[0214] Type B nodes (transitional support zone): have some inertial support but are easily affected by external disturbances;

[0215] Class C nodes (weak frequency region): sparse inertia and slow response, requiring key control.

[0216] V) Analysis of Typical Power Grid Cases

[0217] Simulations were conducted on platforms such as the IEEE-39 node system and the actual distribution network model in southern China. The results show that the inertia is mainly concentrated in areas with dense synchronous machine access, such as main substations; some load end nodes experience frequency "fallback" time delay, with a larger RoCoF; deployment on Class C nodes can significantly reduce the maximum RoCoF and frequency Nadir.

[0218] In summary, the spatial distribution characteristics of nodal inertia directly determine the propagation patterns and control priorities of system frequency disturbances. By constructing spatial index heatmaps, performing cluster analysis, and classifying frequencies, important references can be provided for regional control strategy design and frequency security governance.

[0219] 3.3 Regional Control Strategy

[0220] Based on the aforementioned analysis of nodal inertia indices and spatial distribution characteristics, a regionalized control strategy oriented towards frequency support can be further constructed to achieve rapid support and optimized resource allocation for high-risk areas. In multi-source low-inertia power systems, due to significant inertia heterogeneity and inconsistent response timing, a unified scheduling and control mechanism is insufficient to guarantee frequency security, necessitating the development of regional and hierarchical local control strategies.

[0221] (I) Basis for Regional Division and Zoning Control Logic

[0222] Based on the spatial heatmap of nodal inertia indices and the results of cluster analysis, the system can be divided into multiple frequency support sub-regions, each with relatively independent inertia characteristics and frequency response capabilities. Each region can be configured with an independent local controller or frequency control coordinator (FCC) to achieve fast, localized disturbance suppression response.

[0223] The control objectives for each sub-region include: real-time monitoring of the RoCoF and Nadir indices of the region; determining whether the frequency boundary of the region is exceeded; dynamically scheduling local energy storage and virtual inertia resources; and coordinating power support or frequency collaboration based on the degree of frequency coupling with adjacent regions.

[0224] (II) Virtual Inertia / Energy Storage Coordinated Scheduling Strategy

[0225] Under the framework of regionalized control strategies, the following types of control response mechanisms can be established:

[0226] 1. Priority control mechanism: Nodes within the region are sorted in ascending order of Hidx i, and energy storage or GFM power sources near nodes with weak inertia are prioritized.

[0227] 2. Disturbance sensing and scheduling mechanism: Based on the PMU or a fast event identification system, determine the location of the disturbance source and prioritize the deployment of inertia regulation response within its affected area;

[0228] 3. RoCoF closed-loop feedback mechanism: Set RoCoF threshold for each region. If the threshold is exceeded, the local energy storage will be dynamically injected with inertial power.

[0229] 4. Regional frequency dynamic prediction mechanism: Introduce a short-term frequency trend prediction model to schedule available inertia resources in advance and form feedforward suppression control logic.

[0230] (III) Regional Coordination and Boundary Control

[0231] Since there are coupling boundaries in each region, a regional boundary frequency coordination mechanism needs to be designed: a frequency equalization controller (FEC) is set up to monitor the frequency difference between adjacent regional boundaries and implement coordinated adjustment; a bandwidth control method is used to filter the frequency of boundary nodes to alleviate frequency oscillation propagation; and a linkage activation mechanism is designed to guide the surrounding auxiliary regions to provide frequency support when the control response of the main region is insufficient.

[0232] (iv) Regional coordination and border control

[0233] A regional frequency coordination center (R-FCC) is deployed at the dispatch master station to realize multi-regional inertia monitoring and coordinated control; local frequency controllers are set up in key substations and microgrids, embedding RoCoF / Nadir detection modules and GFM controller interfaces; a regional frequency-power event library is built to support boundary policy self-learning and optimization; and regional frequency control is integrated into the distribution network active management system (ADMS) in conjunction with the source-grid-load-storage coordinated control framework.

[0234] In summary, the regional control strategy is based on the analysis of the equivalent inertia index of nodes and spatial distribution characteristics. It constructs a multi-level control framework around the dynamic frequency behavior of the region, which includes local rapid response, boundary coordination, and priority scheduling of energy storage, to meet the core needs of frequency security governance for future high-proportion new energy systems.

[0235] 4. Simulation analysis and verification of safety support boundary

[0236] This invention uses a typical small power system example to systematically verify the proposed "RoCoF–Nadir dual-constraint inertia inversion algorithm," focusing on the following:

[0237] 1) Consistency between theoretical inertia boundary and time-domain simulation results;

[0238] 2) Sensitivity of inertia level, disturbance intensity, and damping parameters to frequency dynamics;

[0239] 3) Feasibility and effectiveness of different inertia compensation strategies in small systems.

[0240] 4.1 Experimental System and Model Parameters

[0241] This invention employs electrical and control parameters from a typical rural power distribution network system, and introduces a ZIP load model and a virtual inertia controllable source to investigate the load voltage dependence and the impact of energy storage / photovoltaic rapid support on the minimum inertia boundary. The system is simple but includes three types of dynamic elements: synchronous machine primary frequency regulation, damped load, cubic voltage load, and programmable virtual inertia, sufficient to capture the main physical mechanisms of RoCoF and Nadir. The proposed method is validated using a modified typical low-voltage power distribution network system, such as... Figure 2 As shown, all key values ​​are listed in Table 1.

[0242] Equivalent values ​​for distribution transformers and main power supply: A typical rural distribution transformer capacity of 400kVA is selected as the benchmark; the transformer short-circuit impedance is 4%, which conforms to the parameters of a typical distribution transformer; the transient impedance of the distribution network system is taken as 0.05pu, corresponding to the characteristics of a typical low-voltage distribution line; the energy storage and photovoltaic system adopts virtual synchronous machine (VSG) control, and its equivalent speed governor rate deviation is 2%, reflecting the typical control level of current distributed power generation fast primary frequency regulation.

[0243] Table 1 Key Set Values ​​for Electrical and Control Parameters of Rural Distribution Network Systems

[0244]

[0245] ZIP load model: coefficients (a1,a2,a3) = (0.4,0.2,0.4), taken from CIGRE Benchmark, suitable for distribution network environment, ensuring reasonable load power components and voltage fluctuation sensitivity under rated voltage; at the same time, when calculating distribution network inertia demand, the load voltage dependence effect automatically deducts the corresponding load power relief amount ΔPload, avoiding overestimation of inertia demand.

[0246] Virtual Inertia and Controllable Primary Support Sources: A 100kW / 200kWh energy storage (ES) system and a 300kW photovoltaic (PV) power generation unit are added to the system as virtual inertia and primary frequency support sources. These two systems are activated in stages under different control strategies. The energy storage system adopts a virtual synchronous machine (VSG) control mode, with an equivalent inertia set to 2s to provide rapid frequency support capability; the virtual inertia parameter of the PV power generation system is set to K. 𝜔 =0.5pu, without advance damping.

[0247] Disturbance settings: The simulation simulates a typical distribution network disturbance event where the load suddenly increases by 150kW (approximately 35% of the total system capacity) at 2 seconds to ensure that the system frequency (RoCoF and Nadir) and voltage are within the sensitive change range. The simulation also simulates the actual scenario where a high proportion of distributed renewable energy access leads to a gradual decrease in distribution network inertia by progressively reducing the system's equivalent inertia. The inertia range is set to 2.5–4 seconds, which fully covers the typical distribution network operating conditions where RoCoF and Nadir constraints alternately dominate.

[0248] 4.2 Overview of Theoretical Inertia Boundaries

[0249] 1) RoCoF constraint

[0250] The distribution network disturbance is set as a sudden load increase ΔP = 150kW, with a maximum permissible frequency change rate of RoCoF.max =0.75Hz / s, then the minimum inertia requirement of the distribution network can be expressed as:

[0251]

[0252] 2) Nadir constraint (taking |Δfmax|=0.8Hz)

[0253] Considering the inertia time of a single frequency modulation, φ = 8s, and the speed deviation of the speed controller, R = 0.02, the minimum inertia requirement is:

[0254]

[0255] 3) Comparison

[0256] Combining the two constraints mentioned above, the larger one is taken as the minimum inertia requirement of the system:

[0257]

[0258] 4.3 Minimum Inertia Example Based on RoCoF Constraints

[0259] To further verify the adaptability of the proposed method under distribution network conditions, a simulation analysis of minimum inertia under RoCoF constraints was conducted based on the aforementioned typical distribution network model.

[0260] The simulation settings are as follows: the disturbance is set to a sudden load increase ΔP = 150kW (accounting for approximately 35% of the distribution network capacity) at 2s; the initial frequency is 50Hz, the sampling period is 10ms, and the observation time window is 0–0.3s; the range of the equivalent inertia value is H = {2.5, 3.0, 3.5, 4.0} s; the maximum allowable RoCoF upper limit is set to 0.75Hz / s.

[0261] The simulation results are shown in Table 2:

[0262] Table 2 Initial Rocof and Decision under Different Equivalent Inertia

[0263]

[0264] Figure 3 The inverse relationship between RoCoF and inertia is visually demonstrated; when 𝐻<4, the initial slope completely crosses the 0.75Hz / s threshold.

[0265] Error analysis: The simulation-theoretical difference is <0.04Hz / s, which is due to the slight reduction of ΔP by the load relief PL(V);

[0266] Sensitivity: This indicates that increasing the inertia by 1 second in the 2–5s range can reduce the slope by 0.31 Hz / s;

[0267] Engineering significance: When the equivalent inertia of the distribution network is less than 3s, it is difficult to avoid exceeding the protection threshold by relying solely on the conventional P-f control response of distributed power sources (such as TGOV or Droop); it is necessary to actively inject virtual inertia and primary power support by linking GFM-type energy storage or PV grid-connected inverters to ensure the dynamic stability of system frequency; the method of this invention provides a practical means to reasonably infer the boundary of distribution network inertia and intervene in advance.

[0268] 4.4 Minimum Inertia Example Based on Minimum Frequency Constraint

[0269] Inertia scan: Two additional damping coefficients were added: R = 0.02 and 0.04; the simulation window was 0–15s, and the minimum frequency was recorded. The simulation results are shown in Table 3.

[0270] Table 3. Nadir and its determination under different equivalent inertia and damping coefficients.

[0271]

[0272] The data shows that increased damping can raise Nadir but has almost no effect on RoCoF, confirming the rule of thumb that "fast slopes rely on inertia and deep drops rely on damping".

[0273] Theoretical agreement: HNadir min≈3.75s, corresponding to a simulation of 3.5s which satisfies the 0.8Hz line.

[0274] Control implications: When the inertia margin is insufficient but RoCoF is acceptable, Nadir can be compensated by increasing the primary frequency regulation gain or enabling load frequency control; the results show that Nadir is more sensitive to damping parameters, but less dependent on the slope than RoCoF; R can be improved by the "fast-start photovoltaic + energy storage virtual inertia" technology, which can alleviate the risk of insufficient inertia while meeting the frequency drop constraint.

[0275] Compared with RoCoF constraints: if both constraints exist, the larger one (4.0s) shall prevail; in the scenario where ΔP < 180kW, the Nadir constraint may dominate.

[0276] 4.5 Comparison of Comprehensive Compensation Strategies

[0277] In the scenario with a reference inertia H=2.5s, to improve frequency dynamic stability, the following three types of available support resources are superimposed sequentially (see...). Figure 4 , Figure 5 ):

[0278] Option A: GFM energy storage for rapid support

[0279] Equipped with a 100kW / 200kWh energy storage device, it has a maximum output capacity of 300kW and operates in GFM mode. The virtual inertia constant is set to 2s, and the injection time lasts for 5s, realizing rapid inertia and primary power support functions.

[0280] Option B: Injection of Photovoltaic Virtual Inertia

[0281] Distributed photovoltaic devices enable virtual inertia control function through grid-connected inverters, and set virtual inertia gain K. ω =0.5pu, and the frequency detection bandwidth is set to 1.5Hz to reduce the system RoCoF peak.

[0282] Option C: Rapid load reduction on the load side

[0283] In the power distribution network, an interruptible industrial load (such as a small processing load) of 100kW can be quickly disconnected from the grid within 0.15s after the system frequency drops below a set threshold (such as 49.1Hz), thus achieving "power deficit reduction".

[0284] Comprehensive Strategy: The combined application of solutions A and C can effectively suppress frequency drops and initial slopes: the maximum RoCoF value is reduced from 0.86Hz / s to 0.68Hz / s; the lowest frequency point (Nadir) is increased from 49.05Hz to 49.28Hz; all loads operate in the safe zone to avoid frequency protection triggering.

[0285] The RoCoF constraint example shows that under the current disturbance intensity (load surge of 150kW), the theoretical critical value of system inertia demand is 4.0s. However, through the application of comprehensive strategies (especially GFM energy storage + rapid load reduction), the constraint target can be achieved while maintaining the existing physical inertia configuration, and the model-simulation error is controlled within 5%. The Nadir response further verifies the synergistic constraint characteristics between frequency drop and inertia-damping, indicating that multiple factors need to be coordinated and adjusted in the distribution network scenario.

[0286] The present invention also provides a computer-readable storage medium having stored thereon computer program instructions executable by a processor, wherein when the processor executes the computer program instructions, it can implement the steps of any of the methods described above.

[0287] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for back-calculating the system inertia boundary based on frequency dynamic indicators and equivalent inertia analysis of distributed nodes, characterized in that, include: The frequency response process is divided into the inertial response stage, the primary frequency modulation stage, and the secondary frequency modulation stage. Construct a unified equivalent model for multi-source frequency response; A method for inverting the equivalent inertia boundary based on RoCoF and Nadir dual constraints is proposed. The frequency safety boundary is transformed into a constraint expression on the equivalent total inertia of the system, and the required inertia boundary under a given power disturbance is derived.

2. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, During the inertial response phase, the frequency dynamic process is described as follows: H represents the power imbalance caused by the disturbance, H is the system's equivalent inertia constant, and f0 is the system's rated frequency. During the first frequency modulation phase, the frequency dynamic process is described as follows: T1 is the frequency modulation control time constant, K P For proportional control gain, This is a frequency reference value. It is a frequency function of time t; During the secondary frequency modulation stage, the frequency dynamic process is described as follows: T2 is the response delay, K I For integral control gain, This represents the change in frequency.

3. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, The unified equivalent model of multi-source frequency response is constructed as follows: ①The frequency response of the synchronous generator SG is described by the rotor motion equation: The equivalent inertia constant of the synchronous generator. Changes in synchronous generator power ② The response form of the grid-connected inverter GFM is as follows: H gfm (t) can be dynamically adjusted, representing the inertia simulated by GFM-type devices. The power variation of a grid-connected inverter; ③ In the unified modeling, the grid-connected inverter GFL is considered a "potential support source"; ④ The response model of a BESS (Body Safety System) energy storage system is often expressed as: K ω To simulate the inertia coefficient, K d The damping coefficient is... Indicates the change in frequency. This indicates the change in power of the energy storage system; Taking all power supply types ①-④ into account, the total equivalent inertia of the system frequency response is expressed as: Denotes the equivalent inertia constant of the i-th grid-type inverter. This represents the simulated inertia coefficient of the j-th energy storage system.

4. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, The equivalent inertia boundary inversion method based on RoCoF and Nadir dual constraints is implemented as follows: (1) Based on RoCoF, the minimum inertia assessment shows that the relationship between the rate of change of frequency (RoCoF) and the system inertia is simplified as follows: Therefore, the minimum inertia is: ΔP represents the power imbalance caused by the disturbance, f0 is the rated frequency, and RoCoF is the power imbalance caused by the disturbance. max The maximum allowable rate of frequency change; if the system inertia is lower than the minimum inertia, RoCoF will exceed the relay protection threshold and trigger a frequency safety event; (2) Minimum inertia assessment based on Nadir: ① Establish a comprehensive frequency response model: Construct a frequency response model that can encompass various frequency regulation resources in the system. Its key features include: integrating multiple types of frequency regulation resources: the model not only includes traditional thermal power units and hydropower units, but also incorporates the frequency regulation function of power electronic power sources; considering the frequency regulation characteristics of new energy sources: the model includes the primary frequency regulation droop coefficient (R0) of power electronic power sources. w ) and virtual inertia coefficient (K VI ), to characterize its ability to support frequency; ② Model simplification and equivalent analysis: The model in ① can be simplified into an equivalent first-order inertial element model as shown in the following equation. This simplified model uses equivalent system parameters, including the equivalent inertia constant H. sys Equivalent adjustment coefficient R sys Equivalent response time constant T sys The coefficient K is used to describe the impact of replacing the synchronous machine with a power electronic power supply on the overall inertia and droop coefficient of the system: Where ΔP m and ΔP d These are the changes in reference power and the changes in output power, D sys It is the equivalent damping coefficient, and s is the complex frequency domain variable after Laplace transform; ③ Solve for the minimum inertia: First, input the maximum disturbance power ΔP. max and the constraint Δf at the lowest frequency min Next, the frequency response model is input, and by solving the time-domain response of the model, the dynamic change curve of the frequency after disturbance is analyzed under different system inertia levels. Finally, through iterative calculation or analytical methods, the minimum point Nadir of the frequency curve is found to be equal to the minimum frequency constraint Δf. min The system inertia Hsys is the minimum inertia requirement Hmin for satisfying the minimum frequency constraint. min,Nadi ; (3) Inertia boundary interval For a system simultaneously constrained by RoCoF and the minimum frequency point, the final minimum inertia is the larger value under both constraints, i.e.: Where: H min,Rocof H represents the minimum inertia of the system under RoCoF constraints. min,Nadir It represents the minimum inertia constrained by the lowest frequency point.

5. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, It also includes introducing static load voltage characteristic correction when performing inertia boundary inversion.

6. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, The static load voltage characteristic correction is as follows: When performing inertia boundary inversion, the voltage dependence of the static load should be taken into account in the expression for power imbalance caused by disturbance, and modified as follows: ΔP 负荷缓解 Derived from voltage changes and load types under disturbances, and approximated through static power flow simulation or empirical models. The power imbalance caused by the corrected disturbance. The power imbalance is caused by the initial disturbance.

7. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, It also includes building a frequency-support-oriented regional control strategy.

8. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 1, characterized in that, The frequency-supported regionalized control strategy is implemented as follows: 1) Basis for regional division and zoning control logic Based on the spatial heat map of node inertia index and cluster analysis results, the system is divided into multiple frequency support sub-regions. Each sub-region has relatively independent inertia characteristics and frequency response capabilities. Each sub-region is equipped with an independent local controller or frequency control coordinator (FCC) to achieve fast and localized disturbance suppression response. The control objectives for each sub-region include: real-time monitoring of the frequency change rate RoCoF and the lowest frequency point Nadir index; determining whether the frequency boundary of the sub-region exceeds the limit; dynamically scheduling local energy storage and virtual inertia resources; and coordinating power support or frequency coordination based on the degree of frequency coupling with adjacent sub-regions. 2) Virtual inertia / energy storage coordinated scheduling strategy Within the framework of a regionalized control strategy, the following types of control response mechanisms should be established:

1. Priority control mechanism: Nodes within the region are sorted in ascending order of node inertia index Hidx i, and energy storage or GFM power sources near nodes with weak inertia are prioritized.

2. Disturbance sensing and scheduling mechanism: Based on the PMU or fast event identification system, determine the location of the disturbance source and prioritize the deployment of inertia regulation response within its influence area; 3. RoCoF closed-loop feedback mechanism: Set the RoCoF threshold for each region. If the threshold is exceeded, the local energy storage will be dynamically injected with inertial power.

4. Regional frequency dynamic prediction mechanism: Introduce a short-term frequency trend prediction model to schedule available inertia resources in advance and form feedforward suppression control logic; 3) Regional coordination and border control Since there are coupling boundaries in each region, a regional boundary frequency coordination mechanism needs to be designed: a frequency equalization controller (FEC) is set up to monitor the frequency difference between adjacent regional boundaries and implement coordinated adjustment; a bandwidth control method is used to filter the frequency of boundary nodes to alleviate frequency oscillation propagation; and a linkage activation mechanism is designed to guide the surrounding auxiliary regions to provide frequency support when the control response of the main region is insufficient. 4) Regional coordination and border control A regional frequency coordination center (R-FCC) is deployed at the dispatch master station to achieve multi-regional inertia monitoring and coordinated control; local frequency controllers are set up in key substations and microgrids, embedding RoCoF / Nadir detection modules and GFM controller interfaces; a regional frequency-power event library is built to support boundary policy self-learning and optimization; and regional frequency control is integrated into the distribution network active management system (ADMS) in conjunction with the source-grid-load-storage coordinated control framework.

9. The method for back-calculating the system inertia boundary based on frequency dynamic index and equivalent inertia analysis of distributed nodes according to claim 8, characterized in that, The nodal inertia index is defined as: ΔPᵢ is the active disturbance allocated to the i-th node; f0 is the system rated frequency; dfᵢ / dt is the instantaneous frequency change rate of node i, obtained from the PMU or simulation results.

10. A computer-readable storage medium having stored thereon computer program instructions executable by a processor, wherein when the processor executes the computer program instructions, it is able to implement the steps of the method as described in any one of claims 1-9.

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