A method for solving the frequency stability domain of an electro-hydrogen coupling system

Abstract

This invention discloses a method for solving the frequency stability domain of an electric-hydrogen coupling system. First, the expression and boundary of the frequency stability domain of the electric-hydrogen coupling system are defined. Second, the operating parameter data of each heterogeneous frequency modulation unit are collected and preprocessed. Next, the critical power disturbance corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, time required to reach the maximum quasi-steady-state frequency deviation, maximum steady-state frequency deviation, and time required to reach the maximum steady-state frequency deviation are calculated and used as frequency stability constraints. Then, using the system's total inertia support capability, total primary frequency modulation capability, total secondary frequency modulation capability, and power disturbance as observed variables, the system's frequency modulation capability and frequency stability constraints are mapped to a three-dimensional feature space to form a closed frequency stability domain. Finally, the stability characteristics of the frequency stability domain are evaluated.

Description

Technical Field

[0001] This invention relates to the field of frequency stability in integrated electric-hydrogen energy systems, specifically a method for solving the frequency stability domain of an electric-hydrogen coupled system. Background Technology

[0002] The global energy transition is accelerating, with renewable energy sources such as wind and solar power continuously increasing their penetration rate in the power system. This has led to a significant decrease in the proportion of traditional synchronous generator units, resulting in a reduction in the system's equivalent inertia and weakened ability to withstand power disturbances, posing a severe challenge to the safe and stable operation of the frequency grid. Meanwhile, hydrogen energy technology, centered on proton exchange membrane electrolyzers and proton exchange membrane fuel cells, has become an important direction for solving the frequency problem of high-proportion renewable energy grid connection due to its bidirectional energy conversion characteristics and multi-timescale coordinated regulation capabilities. The electro-hydrogen coupling system, through a bidirectional mechanism of hydrogen storage in the electrolyzer and power generation in the fuel cell, can achieve both down-regulation and up-regulation, possessing full-timescale coordinated frequency regulation capabilities, providing a new path for frequency stability.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on power system frequency stability assessment. Existing methods mainly include analytical analysis, time-domain simulation numerical assessment, and machine learning data-driven methods. However, these methods are mostly geared towards pure power systems or single frequency regulation resources, making them difficult to adapt to electric-hydrogen coupled systems with heterogeneous frequency regulation resources. They suffer from three major shortcomings: first, they lack a unified theoretical framework for quantifying frequency security boundaries, making it impossible to integrate multiple types of constraints; second, for frequency indicators at multiple time scales, they lack boundary analysis methods that integrate the coordinated responses of heterogeneous resources; and third, they are mostly post-hoc analyses, lacking online engineering assessment processes and quantitative margin indicators, making it difficult to support real-time dispatch. Summary of the Invention

[0004] The purpose of this invention is to provide a method for solving the frequency stability domain of an electric-hydrogen coupled system, comprising the following steps:

[0005] Step 1) Based on the bidirectional conversion and multi-timescale cooperative characteristics of the electric-hydrogen coupling system, define the frequency stability domain expression of the electric-hydrogen coupling system;

[0006] Step 2) Define the frequency stability domain boundary of the electric-hydrogen coupling system based on the expression for the frequency stability domain of the electric-hydrogen coupling system;

[0007] Step 3) Collect the operating parameter data of each heterogeneous frequency modulation unit and preprocess the operating parameter data;

[0008] Step 4) Based on the preprocessed operating parameter data, calculate the critical power disturbance corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, time required to reach the maximum quasi-steady-state frequency deviation, maximum steady-state frequency deviation, and time required to reach the maximum steady-state frequency deviation, and use them as frequency stability constraints.

[0009] Step 5) Using the total inertia support capability, total primary frequency modulation capability, total secondary frequency modulation capability obtained from the electric-hydrogen coupling system and the power disturbance obtained in Step 4) as observation variables, the system frequency modulation capability and frequency stability constraint are mapped to the three-dimensional feature space to form a closed frequency stability domain.

[0010] Step 6) Evaluate the stability characteristics of the frequency stability domain.

[0011] Furthermore, in step 1), the frequency stability domain expression for the electric-hydrogen coupling system is as follows:

[0012] (1)

[0013] In the formula, This represents the system power disturbance. For the power flow balance equation and the constraints of the electric-hydrogen energy conversion, For the safety constraints of each piece of equipment, For frequency stability constraints, For frequency regulation reserve capacity constraints, x is the system state vector, t is the system operating time, and z is the frequency regulation unit type. , These are the maximum and minimum critical values ​​for frequency stability constraints, respectively. , These are the maximum and minimum frequency regulation reserve capacities, respectively.

[0014] Furthermore, in step 2), the frequency stability domain boundary of the electric-hydrogen coupling system is defined by the critical power disturbances corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, maximum quasi-steady-state frequency recovery time, maximum steady-state frequency deviation, and maximum steady-state frequency recovery time, respectively. , , , , and The hypersurface is composed of the system's total inertia support capability, total primary frequency modulation capability, and total secondary frequency modulation capability.

[0015] Furthermore, in step 3), the operating parameters of each heterogeneous frequency modulation unit include the rated capacity, inertia time constant, frequency modulation coefficient, frequency modulation reserve capacity, system damping coefficient, and frequency stability threshold of the synchronous generator, electrolyzer, and fuel cell.

[0016] Preprocessing refers to outlier removal and time synchronization.

[0017] Furthermore, in step 4), the analytical expression for the critical power disturbance is derived through the system frequency dynamic equation;

[0018] The system frequency dynamic equation is shown below:

[0019] (2)

[0020] (3)

[0021] In the formula, Let be the equivalent total inertia of the system at time t. Let be the system frequency deviation at time t. Let be the total primary frequency regulation power response of the system at time t. This represents the system power disturbance. The system damping coefficient is... , and These represent the rated capacities of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively. , and Let be the inertial constants of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively. , and These refer to the number of synchronous generators, fuel cells, and electrolyzers, respectively. , and These represent the primary frequency regulation output power of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

[0022] Furthermore, the derivation steps of the analytical expression for the power disturbance corresponding to the maximum rate of frequency change include:

[0023] Construct the system frequency change rate based on the system frequency dynamic equation. The expressions and constraints are as follows:

[0024] (4)

[0025] (5)

[0026] In the formula, RoCoF is the core indicator characterizing the system's inertia support capability;

[0027] At the maximum value, The system's primary frequency regulation response has not yet started. The analytical expression for the power disturbance corresponding to the maximum frequency deviation is obtained as follows:

[0028] (6)

[0029] In the formula, The total equivalent inertia of the system at the initial moment of the disturbance;

[0030] The derivation steps of the analytical expression for the power disturbance corresponding to the maximum frequency deviation include:

[0031] The system frequency dynamic equation is transformed into a non-homogeneous linear differential equation for solution, i.e.:

[0032] (7)

[0033] (8)

[0034] In the formula, The time it takes for the system frequency to reach the frequency dead zone threshold. For the overall frequency modulation coefficient, Let be the integration constant. The system frequency dead zone threshold, , and These are the frequency modulation response time constants of the synchronous generator, fuel cell, and electrolyzer, respectively. , and These are the primary frequency regulation power reserves for the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively.

[0035] Based on the dynamic frequency change process, when the system frequency reaches its maximum frequency deviation... , The time corresponding to the system frequency reaching the maximum frequency deviation is shown below:

[0036] (9)

[0037] (10)

[0038] Substituting equation (9) into equation (7) yields the maximum frequency deviation of the system, i.e.:

[0039] (11)

[0040] The system frequency deviation is less than the maximum allowable frequency deviation of the system. To constrain the equation, we simplify equation (11) to obtain:

[0041] (12)

[0042] Expanding the logarithmic terms of equation (12) using Taylor series and retaining them down to the third order, we obtain the explicit analytical expression for the power disturbance corresponding to the maximum frequency deviation, as shown below:

[0043] (13)

[0044] Among them, the system equivalent primary frequency modulation response time constant As shown below:

[0045] (14)

[0046] In the formula, Let be the total primary frequency regulation power response of the system at time t.

[0047] Furthermore, the derivation steps of the analytical expression for the power disturbance corresponding to the quasi-steady-state frequency deviation include:

[0048] The quasi-steady-state frequency deviation and constraints are obtained from the system's frequency dynamic equation, as shown below:

[0049] (15)

[0050] In the formula, This represents the maximum permissible quasi-steady-state frequency deviation of the system.

[0051] Based on equation (15), the analytical expression for the power disturbance corresponding to the quasi-steady-state frequency deviation is further obtained, namely:

[0052] (16)

[0053] The derivation steps of the analytical expression for the power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation include:

[0054] The frequency recovery time is derived from the exponential function expression of the dynamic frequency response, i.e.:

[0055] (17)

[0056] The time required to reach the quasi-steady-state frequency deviation is obtained from equation (17) as follows:

[0057] (18)

[0058] The analytical expression for the power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation is further obtained as follows:

[0059] (19)

[0060] In the formula, The longest time required to reach the quasi-steady-state frequency deviation.

[0061] Furthermore, the derivation steps of the analytical expression for the power disturbance corresponding to the steady-state frequency deviation include:

[0062] The total secondary frequency modulation power response of the system after restoring the rated frequency through secondary frequency modulation is shown below:

[0063] (20)

[0064] In the formula, This is the second-order frequency modulation integral gain. This is the moment when the system reaches a quasi-steady state;

[0065] After one frequency modulation cycle to reach a quasi-steady state, the system frequency dynamic equation is as follows:

[0066] (twenty one)

[0067] When the system eventually reaches steady state Solving equation (21), we get:

[0068] (twenty two)

[0069] In the formula, This represents the maximum allowable steady-state frequency deviation of the system.

[0070] The analytical expression for the power disturbance corresponding to the steady-state frequency deviation is as follows:

[0071] (twenty three)

[0072] The derivation steps of the analytical expression for the power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation include:

[0073] The time required to reach the allowable steady-state frequency deviation is the time required for the system frequency to recover from the quasi-steady-state deviation to the allowable steady-state frequency deviation. The dynamic equation for the frequency recovery process is shown below:

[0074] (twenty four)

[0075] Differentiate both sides of equation (24) over time t, and then convert the quasi-steady-state frequency deviation. Substituting the values ​​yields the frequency recovery time. As shown below:

[0076] (25)

[0077] In the formula, The maximum time required to allow for secondary frequency modulation;

[0078] According to equation (25), the analytical expression for the power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation is obtained, namely:

[0079] (26)

[0080] Among them, the system equivalent second-order frequency modulation response time constant As shown below:

[0081] (27)

[0082] In the formula, , and These are the second-order frequency modulation integral gains of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

[0083] Furthermore, in step 6), the stability characteristics of the frequency stability domain are evaluated through the frequency stability margin index, the frequency stability domain volume index, and the boundary sensitivity index.

[0084] The frequency stability margin metric is used to quantify the safe distance of the current operating point relative to the boundary of the frequency stability domain.

[0085] The frequency stability domain volume index is used to quantify the volume of the frequency stability domain in three-dimensional feature space;

[0086] Boundary sensitivity index is used to quantify the degree of influence of changes in parameters of various dimensions on the boundary of the frequency stability domain.

[0087] Furthermore, the absolute frequency stability margin is the difference between the current power disturbance and the critical value at the boundary of the frequency stability domain. The normalized frequency stability margin is shown below:

[0088] (28)

[0089] In the formula, To support the current inertia support capability, For primary frequency modulation capability, This represents the current power disturbance. This represents the maximum tolerable disturbance under this frequency modulation configuration.

[0090] The volume of the frequency stability region is shown below:

[0091] (29)

[0092] In the formula, The geometric region of the three-dimensional frequency stability domain. , and These are the three-dimensional observation variables in the three-dimensional space where the geometric region is located;

[0093] The boundary sensitivity under the dominant constraint is shown below:

[0094] (30)

[0095] In the formula, This is the dominant constraint index under the current parameter configuration. These are the coordinate parameters in the three-dimensional feature space. The critical power perturbation corresponding to the dominant constraint;

[0096] The normalized boundary sensitivity is shown below:

[0097] (31)

[0098] In the formula, For parameters The current operating baseline value, This represents the critical boundary value under the baseline operating conditions.

[0099] The technical effects of this invention are undeniable. This invention effectively solves the technical problem of the difficulty in systematically quantifying the frequency security boundary of a power system with a high proportion of new energy grid connection.

[0100] First, by integrating multi-dimensional constraints such as power flow balance, electric-hydrogen energy conversion, equipment safety, and frequency stability in the high-dimensional power injection space, a unified theoretical framework for the frequency stability domain of the electric-hydrogen coupling system was constructed, enabling accurate characterization of the frequency safety boundary under disturbance scenarios.

[0101] Secondly, based on the dynamic evolution law of system frequency, and taking into account the coordinated response characteristics of heterogeneous frequency modulation resources such as synchronous generators, electrolyzers and fuel cells, the boundary analytical expressions corresponding to the three stages of inertial response, primary frequency modulation and secondary frequency modulation were derived, and the frequency stability boundary characteristics under different frequency modulation resource configurations were clarified.

[0102] Next, a systematic online evaluation process was proposed, from data acquisition, parameter aggregation, boundary solution to the construction of a three-dimensional frequency stability domain. This process enables dimensionality reduction representation and intuitive visualization of high-dimensional frequency stability domains, effectively supporting online engineering applications.

[0103] Finally, based on the constructed three-dimensional frequency stability domain model, three types of quantitative indicators are proposed: frequency stability margin, domain volume, and boundary sensitivity. These indicators comprehensively characterize the frequency stability characteristics of the system from three dimensions: safety distance, operating space, and parameter influence. This provides a reliable theoretical basis and engineering method support for the optimal allocation and real-time scheduling decision of frequency regulation resources in the electric-hydrogen coupling system. Attached Figure Description

[0104] Figure 1 The evaluation process for the frequency stability domain of the electro-hydrogen coupling system of the present invention is as follows;

[0105] Figure 2 This invention uses the system power disturbance, total inertia support capability, and total primary frequency modulation capability as the three-dimensional FSR projection.

[0106] Figure 3 This invention uses the system power disturbance, total inertia support capability, and total secondary frequency modulation capability as the three-dimensional FSR projection.

[0107] Figure 4 The present invention is a three-dimensional FSR projection of the system power disturbance, total primary frequency modulation capability, and total secondary frequency modulation capability. Detailed Implementation

[0108] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0109] Example 1:

[0110] See Figures 1 to 4 A method for solving the frequency stability domain of an electric-hydrogen coupled system includes the following steps:

[0111] Step 1) Based on the bidirectional conversion and multi-timescale cooperative characteristics of the electric-hydrogen coupling system, define the frequency stability domain expression of the electric-hydrogen coupling system;

[0112] Step 2) Define the frequency stability domain boundary of the electric-hydrogen coupling system based on the expression for the frequency stability domain of the electric-hydrogen coupling system;

[0113] Step 3) Collect the operating parameter data of each heterogeneous frequency modulation unit and preprocess the operating parameter data;

[0114] Step 4) Based on the preprocessed operating parameter data, calculate the critical power disturbance corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, time required to reach the maximum quasi-steady-state frequency deviation, maximum steady-state frequency deviation, and time required to reach the maximum steady-state frequency deviation, and use them as frequency stability constraints.

[0115] Step 5) Using the total inertia support capability, total primary frequency modulation capability, total secondary frequency modulation capability obtained from the electric-hydrogen coupling system and the power disturbance obtained in Step 4) as observation variables, the system frequency modulation capability and frequency stability constraint are mapped to the three-dimensional feature space to form a closed frequency stability domain.

[0116] Step 6) Evaluate the stability characteristics of the frequency stability domain.

[0117] Example 2:

[0118] The main structure of this embodiment is the same as that of Embodiment 1. Further, in step 1), the frequency stability domain expression of the electric-hydrogen coupling system is as follows:

[0119] (1)

[0120] In the formula, This represents the system power disturbance. For the power flow balance equation and the constraints of the electric-hydrogen energy conversion, For the safety constraints of each piece of equipment, For frequency stability constraints, For frequency regulation reserve capacity constraints, x is the system state vector, t is the system operating time, and z is the frequency regulation unit type. , These are the maximum and minimum critical values ​​for frequency stability constraints, respectively. , These are the maximum and minimum frequency regulation reserve capacities, respectively.

[0121] Example 3:

[0122] The main structure of this embodiment is the same as any one of embodiments 1-2. Further, in step 2), the frequency stability domain boundary of the electric-hydrogen coupling system is defined by the critical power disturbances corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, maximum quasi-steady-state frequency recovery time, maximum steady-state frequency deviation, and maximum steady-state frequency recovery time, respectively. , , , , and The hypersurface is composed of the system's total inertia support capability, total primary frequency modulation capability, and total secondary frequency modulation capability.

[0123] Example 4:

[0124] The main structure of this embodiment is the same as any one of embodiments 1 to 3. Further, in step 3), the operating parameters of each heterogeneous frequency modulation unit include the rated capacity, inertia time constant, frequency modulation coefficient, frequency modulation reserve capacity, system damping coefficient and frequency stability threshold of the synchronous generator, electrolyzer and fuel cell.

[0125] Preprocessing refers to outlier removal and time synchronization.

[0126] Example 5:

[0127] The main structure of this embodiment is the same as any one of embodiments 1 to 4. Further, in step 4), the analytical expression of the critical power disturbance is derived by the system frequency dynamic equation.

[0128] The system frequency dynamic equation is shown below:

[0129] (2)

[0130] (3)

[0131] In the formula, Let be the equivalent total inertia of the system at time t. Let be the system frequency deviation at time t. Let be the total primary frequency regulation power response of the system at time t. This represents the system power disturbance. The system damping coefficient is... , and These represent the rated capacities of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively. , and Let be the inertial constants of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively. , and These refer to the number of synchronous generators, fuel cells, and electrolyzers, respectively. , and These represent the primary frequency regulation output power of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

[0132] Example 6:

[0133] The main structure of this embodiment is the same as any one of embodiments 1 to 5. Furthermore, the derivation steps of the analytical expression for the power disturbance corresponding to the maximum frequency change rate include:

[0134] Construct the system frequency change rate based on the system frequency dynamic equation. The expressions and constraints are as follows:

[0135] (4)

[0136] (5)

[0137] In the formula, RoCoF is the core indicator characterizing the system's inertia support capability;

[0138] At the maximum value, The system's primary frequency regulation response has not yet started. The analytical expression for the power disturbance corresponding to the maximum frequency deviation is obtained as follows:

[0139] (6)

[0140] In the formula, The total equivalent inertia of the system at the initial moment of the disturbance;

[0141] The derivation steps of the analytical expression for the power disturbance corresponding to the maximum frequency deviation include:

[0142] The system frequency dynamic equation is transformed into a non-homogeneous linear differential equation for solution, i.e.:

[0143] (7)

[0144] (8)

[0145] In the formula, The time it takes for the system frequency to reach the frequency dead zone threshold. For the overall frequency modulation coefficient, Let be the integration constant. The system frequency dead zone threshold, , and These are the frequency modulation response time constants of the synchronous generator, fuel cell, and electrolyzer, respectively. , and These are the primary frequency regulation power reserves for the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively.

[0146] Based on the dynamic frequency change process, when the system frequency reaches its maximum frequency deviation... , The time corresponding to the system frequency reaching the maximum frequency deviation is shown below:

[0147] (9)

[0148] (10)

[0149] Substituting equation (9) into equation (7) yields the maximum frequency deviation of the system, i.e.:

[0150] (11)

[0151] The system frequency deviation is less than the maximum allowable frequency deviation of the system. To constrain the equation, we simplify equation (11) to obtain:

[0152] (12)

[0153] Expanding the logarithmic terms of equation (12) using Taylor series and retaining them down to the third order, we obtain the explicit analytical expression for the power disturbance corresponding to the maximum frequency deviation, as shown below:

[0154] (13)

[0155] Among them, the system equivalent primary frequency modulation response time constant As shown below:

[0156] (14)

[0157] In the formula, Let be the total primary frequency regulation power response of the system at time t.

[0158] Example 7:

[0159] The main structure of this embodiment is the same as any one of embodiments 1 to 6. Furthermore, the steps for deriving the analytical expression for the power disturbance corresponding to the quasi-steady-state frequency deviation include:

[0160] The quasi-steady-state frequency deviation and constraints are obtained from the system's frequency dynamic equation, as shown below:

[0161] (15)

[0162] In the formula, This represents the maximum permissible quasi-steady-state frequency deviation of the system.

[0163] Based on equation (15), the analytical expression for the power disturbance corresponding to the quasi-steady-state frequency deviation is further obtained, namely:

[0164] (16)

[0165] The derivation steps of the analytical expression for the power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation include:

[0166] The frequency recovery time is derived from the exponential function expression of the dynamic frequency response, i.e.:

[0167] (17)

[0168] The time required to reach the quasi-steady-state frequency deviation is obtained from equation (17) as follows:

[0169] (18)

[0170] The analytical expression for the power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation is further obtained as follows:

[0171] (19)

[0172] In the formula, The longest time required to reach the quasi-steady-state frequency deviation.

[0173] Example 8:

[0174] The main structure of this embodiment is the same as any one of embodiments 1 to 7. Furthermore, the derivation steps of the analytical expression for the power disturbance corresponding to the steady-state frequency deviation include:

[0175] The total secondary frequency modulation power response of the system after restoring the rated frequency through secondary frequency modulation is shown below:

[0176] (20)

[0177] In the formula, This is the second-order frequency modulation integral gain. This is the moment when the system reaches a quasi-steady state;

[0178] After one frequency modulation cycle to reach a quasi-steady state, the system frequency dynamic equation is as follows:

[0179] (twenty one)

[0180] When the system eventually reaches steady state Solving equation (21), we get:

[0181] (twenty two)

[0182] In the formula, This represents the maximum allowable steady-state frequency deviation of the system.

[0183] The analytical expression for the power disturbance corresponding to the steady-state frequency deviation is as follows:

[0184] (twenty three)

[0185] The derivation steps of the analytical expression for the power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation include:

[0186] The time required to reach the allowable steady-state frequency deviation is the time required for the system frequency to recover from the quasi-steady-state deviation to the allowable steady-state frequency deviation. The dynamic equation for the frequency recovery process is shown below:

[0187] (twenty four)

[0188] Differentiate both sides of equation (24) over time t, and then convert the quasi-steady-state frequency deviation. Substituting the values ​​yields the frequency recovery time. As shown below:

[0189] (25)

[0190] In the formula, The maximum time required to allow for secondary frequency modulation;

[0191] According to equation (25), the analytical expression for the power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation is obtained, namely:

[0192] (26)

[0193] Among them, the system equivalent second-order frequency modulation response time constant As shown below:

[0194] (27)

[0195] In the formula, , and These are the second-order frequency modulation integral gains of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

[0196] Example 9:

[0197] The main structure of this embodiment is the same as any one of embodiments 1 to 8. Further, in step 6), the stability characteristics of the frequency stability domain are evaluated by the frequency stability margin index, the frequency stability domain volume index, and the boundary sensitivity index.

[0198] The frequency stability margin metric is used to quantify the safe distance of the current operating point relative to the boundary of the frequency stability domain.

[0199] The frequency stability domain volume index is used to quantify the volume of the frequency stability domain in three-dimensional feature space;

[0200] Boundary sensitivity index is used to quantify the degree of influence of changes in parameters of various dimensions on the boundary of the frequency stability domain.

[0201] Example 10:

[0202] The main structure of this embodiment is the same as any one of embodiments 1 to 9. Furthermore, the absolute frequency stability margin is the difference between the current power disturbance and the critical value of the frequency stability domain boundary. The normalized frequency stability margin is as follows:

[0203] (28)

[0204] In the formula, To support the current inertia support capability, For primary frequency modulation capability, This represents the current power disturbance. This represents the maximum tolerable disturbance under this frequency modulation configuration.

[0205] The volume of the frequency stability region is shown below:

[0206] (29)

[0207] In the formula, The geometric region of the three-dimensional frequency stability domain. , and These are the three-dimensional observation variables in the three-dimensional space where the geometric region is located;

[0208] The boundary sensitivity under the dominant constraint is shown below:

[0209] (30)

[0210] In the formula, This is the dominant constraint index under the current parameter configuration. These are the coordinate parameters in the three-dimensional feature space. The critical power perturbation corresponding to the dominant constraint;

[0211] The normalized boundary sensitivity is shown below:

[0212] (31)

[0213] In the formula, For parameters The current operating baseline value, This represents the critical boundary value under the baseline operating conditions.

[0214] Example 11:

[0215] See Figures 1 to 3 The solution method for the frequency stability domain of an electric-hydrogen coupled system includes the following steps:

[0216] 1) Based on the bidirectional conversion and multi-timescale cooperative characteristics of the electric-hydrogen coupling system, the concept of the frequency stability domain of the electric-hydrogen coupling system is defined;

[0217] 2) Based on the concept of the frequency stability domain of an electric-hydrogen coupling system, define the boundary of the frequency stability domain of the electric-hydrogen coupling system;

[0218] 3) Based on the dynamic evolution law of system frequency, and taking into account the coordinated response characteristics of heterogeneous frequency modulation resources such as synchronous generators, electrolyzers and fuel cells, an evaluation method for the frequency stability domain is constructed.

[0219] 4) To realize online evaluation and engineering application of frequency stability domain, a systematic evaluation process from data acquisition to stability domain construction is proposed;

[0220] 5) Based on the constructed three-dimensional frequency stability domain model, three types of quantitative indicators are proposed: frequency stability margin, domain volume, and boundary sensitivity.

[0221] Example 12:

[0222] Integrating multidimensional constraints within a high-dimensional power injection space, this system systematically characterizes the frequency stability margin and safety boundary under disturbance scenarios. The frequency stability domain of an electric-hydrogen coupled system is defined as the set of all power disturbances within the power injection space that simultaneously satisfy the power flow balance equations, electric-hydrogen energy conversion constraints, equipment operation safety constraints, frequency stability constraints, and frequency regulation reserve capacity constraints. Its mathematical expression is as follows:

[0223] (1)

[0224] The above formula For the set of frequency stable regions, This represents the system power disturbance. For the power flow balance equation and the constraints of the electric-hydrogen energy conversion, For the safety constraints of each piece of equipment, For frequency stability constraints, For frequency regulation reserve capacity constraints, x is the system state vector, t is the system operating time, and z is the frequency regulation unit type. and These are the maximum and minimum critical values ​​for frequency stability constraints, respectively. and These are the maximum and minimum frequency regulation reserve capacities, respectively.

[0225] Example 13:

[0226] The frequency stability domain boundary of an electro-hydrogen coupling system is the critical interface between frequency stability and instability in a high-dimensional power injection space. The frequency stability domain boundary is defined as follows:

[0227] Under specific operating conditions, in the high-dimensional power injection space of an electric-hydrogen coupled system, the high-dimensional nonlinear manifold consists of the power disturbances and system frequency regulation capabilities corresponding to all conditions that simultaneously satisfy the power flow balance equation, electric-hydrogen energy conversion constraints, and frequency regulation reserve capacity constraints, with at least one frequency stability index exactly reaching a safety threshold. Specifically, this boundary is defined by the critical power disturbances corresponding to the maximum rate of frequency change, maximum frequency deviation, maximum quasi-steady-state frequency deviation, maximum quasi-steady-state frequency recovery time, maximum steady-state frequency deviation, and maximum steady-state frequency recovery time, respectively. , , , , and The hypersurface is composed of the system's total inertia support capability, total primary frequency modulation capability, and total secondary frequency modulation capability.

[0228] Example 14:

[0229] Starting from the dynamic evolution law of system frequency, and taking into account the cooperative response characteristics of heterogeneous frequency modulation resources, the boundary analytical expressions corresponding to the three stages of inertial response, primary frequency modulation and secondary frequency modulation are derived respectively.

[0230] After the electric-hydrogen coupling system is subjected to power disturbance, considering the coordinated support of multiple types of frequency modulation resources, the system frequency dynamic equation can be expressed as:

[0231] (2)

[0232] (3)

[0233] The above formula Let be the equivalent total inertia of the system at time t. Let be the system frequency deviation at time t. Let be the total primary frequency regulation power response of the system at time t. This represents the system power disturbance. The system damping coefficient is... , and These represent the rated capacities of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively. , and Let be the inertial constants of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively. , and These refer to the number of synchronous generators, fuel cells, and electrolyzers, respectively. , and These represent the primary frequency regulation output power of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

[0234] 1) Power disturbance corresponding to the maximum rate of frequency change:

[0235] RoCoF is a core indicator characterizing the system's inertia support capability. From formula (2), the system frequency change rate can be obtained. The calculation method and constraints are as follows:

[0236] (4)

[0237] (5)

[0238] Considering The maximum value usually occurs at the initial moment of the power disturbance. If the system's primary frequency regulation response has not yet started, then formula (5) can be further simplified to:

[0239] (6)

[0240] The above formula Let be the total equivalent inertia of the system at the initial moment of the disturbance. From the above equation, it can be seen that the boundary of the frequency stability domain during the inertia response stage is uniquely determined by the total equivalent inertia of the system; the larger the inertia, the wider the boundary in this dimension.

[0241] 2) Power disturbance corresponding to the maximum frequency deviation:

[0242] When the system's maximum frequency deviation exceeds the set threshold, low-frequency load shedding and high-frequency tripping actions will be triggered. Therefore, the system frequency deviation must be less than the system's maximum allowable frequency deviation. By solving the frequency dynamic equation, we obtain... The parsing expression.

[0243] Solving equation (2) by converting it into a non-homogeneous linear differential equation yields the following result:

[0244] (7)

[0245] (8)

[0246] Based on the dynamic frequency change process, when the system frequency reaches its maximum frequency deviation, at this time... , The time corresponding to the system frequency reaching the maximum frequency deviation is:

[0247] (9)

[0248] (10)

[0249] Substituting formula (9) into formula (7), we can obtain the maximum frequency deviation of the system as:

[0250] (11)

[0251] The system frequency deviation must be less than the maximum allowable frequency deviation of the system. Formula (11) can be further simplified to:

[0252] (12)

[0253] Expanding the logarithmic terms of formula (12) using Taylor series and retaining only the third-order terms, we can obtain the explicit analytical expression for the power disturbance corresponding to the maximum frequency deviation:

[0254] (13)

[0255] Introducing the equivalent primary frequency modulation response time constant of the system Calculated by weighted average of the power reserves of each frequency modulation unit:

[0256] (14)

[0257] Formula (13) can then be further modified as follows:

[0258] (15)

[0259] 3) Power disturbance corresponding to quasi-steady-state frequency deviation:

[0260] After a frequency adjustment operation is completed, the system frequency tends to stabilize and enters the quasi-steady-state operation phase. At this time, the rate of frequency change approaches 0, and the frequency deviation is a constant. The quasi-steady-state frequency deviation must satisfy the following constraints:

[0261] (16)

[0262] The above formula The maximum permissible quasi-steady-state frequency deviation of the system; Equation (16) can be further simplified to:

[0263] (17)

[0264] 4) The power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation:

[0265] The frequency recovery time can be derived from the exponential function expression of the dynamic frequency response:

[0266] (18)

[0267] From the above formula, the time required to reach the quasi-steady-state frequency deviation can be obtained as:

[0268] (19)

[0269] The above formula can be further simplified to:

[0270] (20)

[0271] 5) Power disturbance corresponding to steady-state frequency deviation:

[0272] Primary frequency modulation can curb the increase of frequency deviation but cannot eliminate steady-state error; secondary frequency modulation (AGC) is required to restore the frequency to the rated value. The total AGC power regulation of the system can be expressed as:

[0273] (twenty one)

[0274] The above formula The integral gain of AGC characterizes the secondary frequency modulation capability. This is the moment when the system reaches a quasi-steady state.

[0275] After one frequency modulation cycle to reach a quasi-steady state, the system's frequency dynamic equation can be expressed as:

[0276] (twenty two)

[0277] When the system eventually reaches steady state Then the above formula can be further simplified to:

[0278] (twenty three)

[0279] but:

[0280] (twenty four)

[0281] 6) The power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation:

[0282] The time required to reach the allowable steady-state frequency deviation is the time required for the system frequency to recover from the quasi-steady-state deviation to the allowable steady-state frequency deviation. During the frequency recovery phase, the system inertial response phase is complete and can be considered zero. At this point, the system frequency dynamics are jointly determined by primary and secondary frequency modulation. The dynamic equation for the frequency recovery process can be characterized as:

[0283] (25)

[0284] Differentiate both sides of equation (25) with respect to time t, and then... Substituting this into the equation yields the frequency recovery time. for:

[0285] (26)

[0286] Formula (26) can be further simplified to obtain:

[0287] (27)

[0288] Introducing the system's equivalent second-order frequency modulation response time constant ,Establish and Relationship:

[0289] (28)

[0290] Formula (28) can be modified as follows:

[0291] (29)

[0292] Example 15:

[0293] A systematic evaluation process from data acquisition to stability domain construction is proposed.

[0294] To achieve online evaluation and engineering applications of frequency stability domains, a systematic evaluation process from data acquisition to stability domain construction is proposed. This process is as follows: Figure 1 As shown, the specific steps are as follows:

[0295] Step 1: Data Acquisition and Preprocessing. Collect parameters such as the rated capacity, inertia time constant, frequency regulation coefficient, and frequency regulation reserve capacity of the synchronous generator, electrolyzer, and fuel cell, as well as system damping coefficient and frequency stability threshold. Perform preprocessing operations such as outlier removal and time synchronization alignment.

[0296] Step 2: System Parameter Aggregation. Based on the operating parameters of each heterogeneous frequency modulation unit, calculate three types of aggregated characteristic parameters: the system's equivalent total inertia, total primary frequency modulation capability, and total secondary frequency modulation capability.

[0297] Step 3: Analytical solution of the boundary conditions at multiple time scales. Based on the analytical expressions for the power disturbances corresponding to the six types of frequency indices, calculate the critical power disturbances corresponding to the six types of indices: maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, time required to reach the maximum quasi-steady-state frequency deviation, maximum steady-state frequency deviation, and time required to reach the maximum steady-state frequency deviation.

[0298] Step 4: Dimensionality Reduction Mapping and Frequency Stability Domain Construction. Using the system's total inertia support capability, total primary frequency modulation capability, total secondary frequency modulation capability, and power disturbance as observed variables, the system's frequency modulation capability and six types of frequency stability constraints are mapped to a three-dimensional feature space. In this space, the frequency stability domain is represented as a closed geometry bounded by the aforementioned boundaries, and its boundary surface is the critical interface between frequency stability and instability. This method achieves dimensionality reduction representation and intuitive visualization of the high-dimensional frequency stability domain while preserving key physical information.

[0299] Step 5: Frequency stability domain visualization and quantitative analysis. The three-dimensional frequency stability domain and its boundary surface are graphically displayed to intuitively present the stability capability range and coupling relationship of the system in the three dimensions of inertia support, primary frequency modulation, and secondary frequency modulation. Based on the proposed quantitative indicators, frequency stability margin assessment and early warning analysis are carried out.

[0300] Example 16:

[0301] Based on the constructed three-dimensional frequency stability domain model, three types of quantitative indicators are proposed: frequency stability margin, domain volume, and boundary sensitivity, which characterize the frequency stability characteristics of the system from three dimensions: safety distance, operating space, and parameter influence.

[0302] (1) Frequency stability margin index

[0303] Frequency stability margin is used to quantify the safe distance of the current operating point relative to the boundary of the frequency stability domain, and is a core indicator for evaluating the system's ability to withstand power disturbances. In the three-dimensional feature space, let the current inertia support capability be... The primary frequency modulation capability is The current power disturbance is The maximum tolerable disturbance under this frequency modulation configuration can be obtained based on the analytical model of the frequency stability domain boundary. The absolute frequency stability margin is defined as the difference between the current power disturbance and the critical value at the boundary of the frequency stability domain. To facilitate tiered early warning and cross-sectional comparisons under different operating conditions, the normalized frequency stability margin is defined as follows:

[0304] (30)

[0305] The above formula This is the normalized frequency stability margin, representing the percentage of the safety margin between the current power disturbance and the system's maximum tolerable disturbance. When The system is in a frequency stable state, and its value represents the safety margin of the system from the frequency instability boundary under the current operating conditions. The larger the value, the more room the system can withstand additional power disturbances. The system is in a critically stable state. When This indicates that the current power disturbance has exceeded the system's frequency stability tolerance range, and its absolute value characterizes the degree to which the power disturbance exceeds the limit. By calculating the normalized frequency stability margin in real time, the system's frequency security status can be dynamically monitored, providing a quantitative basis for scheduling decisions and hierarchical early warning.

[0306] (2) Frequency stability domain volume index

[0307] The frequency stability domain volume index quantifies the volume of the frequency stability domain in a three-dimensional feature space, assesses the size of the frequency safety space that the system can accommodate, and reflects the overall frequency stability capability of the system.

[0308] (31)

[0309] In the formula: For the frequency stability domain volume, This represents the geometric region of the three-dimensional frequency stability domain. The larger the volume, the more diverse the power disturbance scenarios the system can safely handle, and the stronger its frequency stability robustness. A smaller volume indicates a narrower frequency safety margin, posing a potential stability risk. Monitoring... As the operating conditions change dynamically, a global assessment of the system's frequency stability capability can be achieved.

[0310] (3) Boundary sensitivity index

[0311] Boundary sensitivity is used to quantify the impact of parameter changes in various dimensions on the boundary of the frequency stability domain, revealing the differences in the marginal contribution of different frequency modulation resources to frequency stability. Considering that the dominant constraints may differ in different regions of three-dimensional space, the sensitivity of the frequency stability domain boundary to parameters under the dominant constraints is defined as follows:

[0312] (32)

[0313] In the formula: For boundary sensitivity, The dominant constraint index under the current parameter configuration, i.e. , The coordinate parameters in the three-dimensional feature space are taken as follows: , Let be the critical power perturbation corresponding to the dominant constraint. To eliminate dimensional differences, the normalized sensitivity is defined as:

[0314] (33)

[0315] In the formula: For parameters The current operating baseline value, This represents the critical boundary value under the baseline operating conditions. Characterization parameters The percentage change in the critical power disturbance at the frequency stability domain boundary when a 1% relative change occurs. A larger value indicates that the frequency modulation resources in this dimension have significant marginal benefits for expanding the frequency stability domain boundary. If the sensitivity is too low, increasing this type of resource will have limited effect. By comparing the normalized sensitivity of the three dimensions, the bottleneck dimensions that restrict the improvement of frequency stability can be quantitatively identified, providing a basis for decision-making on the optimal allocation of frequency modulation resources.

[0316] Example 17:

[0317] The application of the frequency stability domain in an electro-hydrogen coupling system is as follows:

[0318] To verify the effectiveness of the proposed frequency stability domain theoretical framework and method for the electric-hydrogen coupling system, this chapter constructs an improved IEEE 39-node test system containing a hydrogen energy subsystem. This system comprises three synchronous generators, two photovoltaic power plants, one wind farm, two fuel cell power plants, and two electrolyzers.

[0319] To verify the feasibility and effectiveness of the frequency stability domain evaluation method proposed in this patent, three simulation scenarios are designed as follows:

[0320] Scenario 1: Select the system power disturbance, total inertia support capacity and total primary frequency regulation capacity as three-dimensional observation variables, and fix the secondary frequency regulation capacity at 450MW;

[0321] Scenario 2: Select the system power disturbance, total inertia support capacity and total secondary frequency regulation capacity as three-dimensional observation variables, and fix the primary frequency regulation capacity at 550MW;

[0322] Scenario 3: Select the system power disturbance, total primary frequency regulation capability and total secondary frequency regulation capability as three-dimensional observation variables, and fix the inertia support capability at 275MW·s.

[0323] The results of the above three simulation scenarios are as follows: Figure 2 , Figure 3 and Figure 4 As shown. From Figure 2 , Figure 3 and Figure 4 Therefore, the frequency stability domain assessment method for the electric-hydrogen coupling system proposed in this patent can effectively characterize the frequency stability region of the system and be used to evaluate the system's frequency stability. Simulation results in three scenarios show that the system's total inertia support capability and total primary frequency modulation capability are the dominant factors determining the frequency stability domain boundary, while the influence of secondary frequency modulation capability is relatively limited. The physical reason for this is that the frequency stability domain boundary is mainly determined by the frequency change rate constraint and the maximum frequency deviation constraint, which correspond to the inertia response and the primary frequency modulation stage, respectively. Secondary frequency modulation mainly acts in the later stage of frequency recovery and has a smaller impact on the critical disturbance withstand capability.

[0324] Example 18:

[0325] The total inertia support capacity, total primary frequency modulation capacity, and total secondary frequency modulation capacity of the electric-hydrogen coupling system are known quantities. The equivalent total inertia, total primary frequency modulation capacity, and total secondary frequency modulation capacity of the system are obtained by summing the inertia, primary frequency modulation capacity, and secondary frequency modulation capacity of each frequency modulation unit.

[0326] The inertia of each frequency regulation unit is calculated using disturbance data, by substituting the rate of change of frequency and active power at the moment of disturbance (RoCoF) into the generator swing equation; or by identifying it through specialized tests such as load shedding tests and curve fitting.

[0327] The frequency regulation capability can be directly observed. Specifically, it involves analyzing the automatic response of the unit's active power after the grid frequency deviates from the dead zone using measured data, and evaluating indicators such as response speed (e.g., 30-second contribution rate), adjustment range, and stabilization time.

[0328] Secondary frequency regulation capability can be directly observed. Specifically, analyze the unit's ability to track AGC commands issued by the dispatcher, and observe its regulation rate (such as the percentage of load change per minute), regulation accuracy, and response time.

Claims

1. A method for solving the frequency stability domain of an electric-hydrogen coupled system, characterized in that, Includes the following steps: Step 1) Based on the bidirectional conversion and multi-timescale cooperative characteristics of the electric-hydrogen coupling system, define the frequency stability domain expression of the electric-hydrogen coupling system; Step 2) Define the frequency stability domain boundary of the electric-hydrogen coupling system based on the expression for the frequency stability domain of the electric-hydrogen coupling system; Step 3) Collect the operating parameter data of each heterogeneous frequency modulation unit and preprocess the operating parameter data; Step 4) Based on the preprocessed operating parameter data, calculate the critical power disturbance corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, time required to reach the maximum quasi-steady-state frequency deviation, maximum steady-state frequency deviation, and time required to reach the maximum steady-state frequency deviation, and use them as frequency stability constraints. Step 5) Using the total inertia support capability, total primary frequency modulation capability, total secondary frequency modulation capability obtained from the electric-hydrogen coupling system and the power disturbance obtained in Step 4) as observation variables, the system frequency modulation capability and frequency stability constraint are mapped to the three-dimensional feature space to form a closed frequency stability domain. Step 6) Evaluate the stability characteristics of the frequency stability domain.

2. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 1, characterized in that, In step 1), the frequency stability domain expression of the electric-hydrogen coupling system is as follows: (1) In the formula, This represents the system power disturbance. For the power flow balance equation and the constraints of the electric-hydrogen energy conversion, For the safety constraints of each piece of equipment, For frequency stability constraints, For frequency regulation reserve capacity constraints, x is the system state vector, t is the system operating time, and z is the frequency regulation unit type. , These are the maximum and minimum critical values ​​for frequency stability constraints, respectively. , These are the maximum and minimum frequency regulation reserve capacities, respectively.

3. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 1, characterized in that, In step 2), the frequency stability domain boundary of the electric-hydrogen coupling system is defined by the critical power disturbances corresponding to the maximum frequency change rate, maximum frequency deviation, maximum quasi-steady-state frequency deviation, maximum quasi-steady-state frequency recovery time, maximum steady-state frequency deviation, and maximum steady-state frequency recovery time, respectively. , , , , and The hypersurface is composed of the system's total inertia support capability, total primary frequency modulation capability, and total secondary frequency modulation capability.

4. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 1, characterized in that, In step 3), the operating parameters of each heterogeneous frequency modulation unit include the rated capacity, inertia time constant, frequency modulation coefficient, frequency modulation reserve capacity, system damping coefficient, and frequency stability threshold of the synchronous generator, electrolyzer, and fuel cell. Preprocessing refers to outlier removal and time synchronization.

5. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 1, characterized in that, In step 4), the analytical expression for the critical power disturbance is derived through the system frequency dynamic equation; The system frequency dynamic equation is shown below: (2) (3) In the formula, Let be the equivalent total inertia of the system at time t. Let be the system frequency deviation at time t. Let be the total primary frequency regulation power response of the system at time t. This represents the system power disturbance. The system damping coefficient is... , and These represent the rated capacities of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively. , and Let be the inertial constants of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively. , and These refer to the number of synchronous generators, fuel cells, and electrolyzers, respectively. , and These represent the primary frequency regulation output power of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

6. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 5, characterized in that, The derivation steps of the analytical expression for the power disturbance corresponding to the maximum rate of frequency change include: Construct the system frequency change rate based on the system frequency dynamic equation. The expressions and constraints are as follows: (4) (5) In the formula, RoCoF is the core indicator characterizing the system's inertia support capability; At the maximum value, The system's primary frequency regulation response has not yet started. The analytical expression for the power disturbance corresponding to the maximum frequency deviation is obtained as follows: (6) In the formula, The total equivalent inertia of the system at the initial moment of the disturbance; The derivation steps of the analytical expression for the power disturbance corresponding to the maximum frequency deviation include: The system frequency dynamic equation is transformed into a non-homogeneous linear differential equation for solution, i.e.: (7) (8) In the formula, The time it takes for the system frequency to reach the frequency dead zone threshold. For the overall frequency modulation coefficient, Let be the integration constant. The system frequency dead zone threshold, , and These are the frequency modulation response time constants of the synchronous generator, fuel cell, and electrolyzer, respectively. , and These are the primary frequency regulation power reserves for the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer, respectively. Based on the dynamic frequency change process, when the system frequency reaches its maximum frequency deviation... , The time corresponding to the system frequency reaching the maximum frequency deviation is shown below: (9) (10) Substituting equation (9) into equation (7) yields the maximum frequency deviation of the system, i.e.: (11) The system frequency deviation is less than the maximum allowable frequency deviation of the system. To constrain the equation, we simplify equation (11) to obtain: (12) Expanding the logarithmic terms of equation (12) using Taylor series and retaining them down to the third order, we obtain the explicit analytical expression for the power disturbance corresponding to the maximum frequency deviation, as shown below: (13) Among them, the system equivalent primary frequency modulation response time constant As shown below: (14) In the formula, Let be the total primary frequency regulation power response of the system at time t.

7. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 5, characterized in that, The steps to derive the analytical expression for the power disturbance corresponding to the quasi-steady-state frequency deviation include: The quasi-steady-state frequency deviation and constraints are obtained from the system's frequency dynamic equation, as shown below: (15) In the formula, This represents the maximum permissible quasi-steady-state frequency deviation of the system. Based on equation (15), the analytical expression for the power disturbance corresponding to the quasi-steady-state frequency deviation is further obtained, namely: (16) The derivation steps of the analytical expression for the power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation include: The frequency recovery time is derived from the exponential function expression of the dynamic frequency response, i.e.: (17) The time required to reach the quasi-steady-state frequency deviation is obtained from equation (17) as follows: (18) The analytical expression for the power disturbance corresponding to the time required to reach the allowable quasi-steady-state frequency deviation is further obtained as follows: (19) In the formula, The longest time required to reach the quasi-steady-state frequency deviation.

8. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 5, characterized in that, The derivation steps of the analytical expression for the power disturbance corresponding to the steady-state frequency deviation include: The total secondary frequency modulation power response of the system after restoring the rated frequency through secondary frequency modulation is shown below: (20) In the formula, This is the second-order frequency modulation integral gain. This is the moment when the system reaches a quasi-steady state; After one frequency modulation cycle to reach a quasi-steady state, the system frequency dynamic equation is as follows: (21) When the system eventually reaches steady state Solving equation (21), we get: (22) In the formula, This represents the maximum allowable steady-state frequency deviation of the system. The analytical expression for the power disturbance corresponding to the steady-state frequency deviation is as follows: (23) The derivation steps of the analytical expression for the power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation include: The time required to reach the allowable steady-state frequency deviation is the time required for the system frequency to recover from the quasi-steady-state deviation to the allowable steady-state frequency deviation. The dynamic equation for the frequency recovery process is shown below: (24) Differentiate both sides of equation (24) over time t, and then convert the quasi-steady-state frequency deviation. Substituting the values, we obtain the frequency recovery time. As shown below: (25) In the formula, The maximum time required to allow for secondary frequency modulation; According to equation (25), the analytical expression for the power disturbance corresponding to the time required to reach the allowable steady-state frequency deviation is obtained, namely: (26) Among them, the system equivalent second-order frequency modulation response time constant As shown below: (27) In the formula, , and These are the second-order frequency modulation integral gains of the i-th synchronous generator, the j-th fuel cell, and the k-th electrolyzer at time t, respectively.

9. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 1, characterized in that, In step 6), the stability characteristics of the frequency stability domain are evaluated using the frequency stability margin index, the frequency stability domain volume index, and the boundary sensitivity index. The frequency stability margin metric is used to quantify the safe distance of the current operating point relative to the boundary of the frequency stability domain. The frequency stability domain volume index is used to quantify the volume of the frequency stability domain in three-dimensional feature space; Boundary sensitivity index is used to quantify the degree of influence of changes in parameters of various dimensions on the boundary of the frequency stability domain.

10. The method for solving the frequency stability domain of an electro-hydrogen coupling system according to claim 9, characterized in that, The absolute frequency stability margin is the difference between the current power disturbance and the critical value at the boundary of the frequency stability domain. The normalized frequency stability margin is shown below: (28) In the formula, To support the current inertia support capability, For primary frequency modulation capability, This represents the current power disturbance. This represents the maximum tolerable disturbance under this frequency modulation configuration. The volume of the frequency stability region is shown below: (29) In the formula, The geometric region of the three-dimensional frequency stability domain. , and These are the three-dimensional observation variables in the three-dimensional space where the geometric region is located; The boundary sensitivity under the dominant constraint is shown below: (30) In the formula, This is the dominant constraint index under the current parameter configuration. These are the coordinate parameters in the three-dimensional feature space. The critical power perturbation corresponding to the dominant constraint; The normalized boundary sensitivity is shown below: (31) In the formula, For parameters The current operating baseline value, This represents the critical boundary value under the baseline operating conditions.

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