Method and device for evaluating fast frequency modulation requirement considering low penetration power recovery characteristic

Abstract

The application discloses a kind of fast frequency modulation demand evaluation method and device considering low penetration power recovery characteristics, method includes: constructing the system frequency response model of time-varying disturbance and fast frequency modulation response model considering in low penetration fault process;Frequency minimum point is obtained according to system frequency response model;With the inherent delay time of fast frequency modulation response model, ramp rate and action capacity upper limit construct optimization vector;According to optimization vector, initial optimization matrix is constructed;After abnormal vector elimination to initial optimization matrix according to frequency minimum point, the fitness of each vector is calculated according to preset target function, and the vector with highest fitness is selected as first vector;With first vector as update reference, first matrix is obtained by adaptive optimization through IAOA algorithm;Initial optimization matrix is updated to first matrix and iterative optimization is carried out;After iteration, the vector with highest fitness in last iteration is output.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control, and in particular to a method and apparatus for rapid frequency regulation demand assessment that takes into account low-power recovery characteristics. Background Technology

[0002] As new power systems with high proportions of renewable energy and power electronic equipment continue to evolve, the system's equivalent inertia is significantly weakened. When a grid short-circuit fault causes renewable energy units to enter LVRT (Low Voltage Ride-Through) mode, their active power drops sharply and instantaneously to prioritize reactive power support. Due to the lack of system inertia, this massive time-varying active power deficit will cause the system frequency to drop sharply at an extremely high rate of change, easily triggering low-frequency load shedding.

[0003] Existing methods for assessing the demand for fast frequency regulation (FM) have significant limitations. Firstly, traditional assessments often employ simplified step disturbance models, neglecting the dynamic "slope recovery" of active power from renewable energy sources after fault clearing. This fails to accurately reflect the cumulative impact of the power recovery hysteresis on the secondary frequency drop in the system. Secondly, existing methods often rely on time-consuming full electromagnetic transient simulations or analytical models that do not account for the triggering delay and active power limitations of the frequency regulation equipment. These methods cannot quantitatively characterize complex nonlinear coupling relationships, potentially leading to overly conservative assessment results or inaccurate predictions of actual operating conditions, posing significant safety risks. Furthermore, fine-grained optimization of FM capacity under multiple constraints faces two major challenges: the cascading of time-varying disturbances and nonlinear frequency regulation models significantly increases the order of the characteristic equations and the difficulty of global optimization; and numerical analytical calculations in low-inertia scenarios are highly susceptible to getting trapped in local outliers.

[0004] Therefore, a new technical solution is urgently needed to address the technical problem of how to accurately assess and configure the fast frequency regulation resource requirements of low-inertia power systems in low-voltage ride-through scenarios. Summary of the Invention

[0005] This invention provides a method and apparatus for assessing the fast frequency regulation demand considering low-voltage ride-through characteristics, in order to solve the technical problem of how to accurately assess and configure the fast frequency regulation resource demand of low-inertia power systems in low-voltage ride-through scenarios.

[0006] To achieve the above objectives, the present invention provides a fast frequency modulation requirement assessment method considering low-through-power recovery characteristics, comprising: Construct a system frequency response model that considers time-varying disturbances and fast frequency modulation response model during low-frequency failure; obtain the lowest frequency point based on the system frequency response model; construct an optimization vector based on the inherent delay time, ramp rate, and upper limit of action capacity of the fast frequency modulation response model; construct an initial optimization matrix based on the optimization vector. After removing outlier vectors from the initial optimization matrix based on the lowest frequency point, the fitness of each vector is calculated according to the preset objective function, and the vector with the highest fitness is selected as the first vector. Using the first vector as the update benchmark, the first matrix is ​​obtained through adaptive optimization using the IOA algorithm. The initial optimization matrix is ​​updated to the first matrix and iterative optimization is performed. After the iteration is completed, the vector with the highest fitness in the last iteration is output.

[0007] Preferably, the system frequency response model that considers time-varying disturbances and fast frequency modulation response during low-voltage fault construction includes: A piecewise function of active power deficit during the low voltage ride-through process is constructed with the fault occurrence time, fault clearing time, and active power recovery to steady state time as boundary points; a fast frequency regulation response model including inherent delay time, ramp rate, and upper limit of operating capacity is constructed. Construct a synchronous generator frequency response model in the form of a first-order equivalent transfer function; fit the system frequency response curve; and obtain the active power time-domain analytical expression of a single synchronous generator based on the synchronous generator frequency response model and the system frequency response curve. The system frequency response model is obtained based on the piecewise function of active power deficit, the fast frequency regulation response model, the active power time-domain analytical expression, and the system frequency response curve.

[0008] Preferably, the system frequency response curve is fitted; based on the synchronous generator frequency response model and the system frequency response curve, the active power time-domain analytical expression of a single synchronous generator unit is obtained, including: An exponential decay function with characteristic parameters is selected to fit the system frequency response curve; based on the synchronous generator frequency response model and the system frequency response curve, a preliminary active time-domain analytical expression for a single synchronous generator is obtained; the preliminary active time-domain analytical expression is corrected by nonlinear logic to obtain the active time-domain analytical expression.

[0009] Preferably, the system frequency response model obtained based on the active power deficit piecewise function, the fast frequency regulation response model, the active power time-domain analytical expression, and the system frequency response curve includes: The system frequency response curve is corrected based on the active time-domain analytical expression to obtain the corrected system frequency response curve; The dynamic response of the system to the low-voltage fault is deconstructed into the superposition of the zero-input response and the zero-state response. The zero-input response is constructed based on the active power time-domain analytical expression and the system frequency response correction curve. The zero-state response is constructed based on the active power deficit piecewise function, the fast frequency modulation response model and the active power time-domain analytical expression. Zero-input response includes the free response caused by the internal initial state, which corresponds to the response quantity accumulated by the system at the first moment after experiencing the initial step disturbance, including the state quantity of system frequency deviation and active power output of each unit; the first moment is the critical moment when the low-voltage crossing ends and active power begins to recover; zero-state response includes the response caused by external input, including the dynamic support increment of various resources in the system after the ramp disturbance. The system frequency response model for the low-voltage fault process is obtained based on the zero-input response and the zero-state response.

[0010] Preferably, outlier vector removal from the initial optimization matrix based on the lowest frequency point includes: For each vector, the criterion is calculated based on the point of lowest frequency: ; ; in, Indicates the point of lowest frequency; Tolerance coefficient; This refers to the steady-state frequency deviation of the system. If the system steady-state frequency deviation If the criterion is satisfied, then the fitness of the vector is set to positive infinity, and the vector is removed; the matrix after removal is denoted as the matrix to be optimized.

[0011] Preferably, the fitness of each vector is calculated according to a preset objective function, and the vector with the highest fitness is selected as the first vector, including: The preset objective functions include: ; ; in, For the first One vector; For the first The fitness of each vector; This is the capacity cost weighting coefficient. For the first The corresponding fast frequency modulation resource configuration capacity limit for each vector; This is a penalty item for exceeding system frequency security limits; For the first The lowest point of system frequency calculated under each vector; This refers to the system frequency safety limit. This is the penalty coefficient; The calculation must meet the following constraints: the absolute value of the maximum frequency change rate must be less than or equal to the preset maximum frequency change rate value, and the inherent delay time, ramp rate, and upper limit of motion capacity must be within the preset upper and lower limits. If the constraints are met, then the system frequency safety over-limit penalty term is applied. The value is 0; if the constraint conditions are not met, then the system frequency security over-limit penalty item is applied. The fitness is amplified exponentially and the corresponding vectors are eliminated. After calculation, select the vector with the highest fitness and denote it as the first vector. ,in, , and These represent the upper limit of action capacity, inherent delay time, and ramp rate in the first vector, respectively.

[0012] Preferably, the first matrix is ​​obtained by adaptive optimization using the IOA algorithm with the first vector as the update basis, including: In the In each iteration, the mathematical optimization speedup factor in the IOA algorithm is calculated. With mathematical optimization probability coefficient : ; ; in, For iteration rounds; T This represents the maximum number of iterations. and They are respectively The minimum and maximum value boundaries; Sensitivity coefficient; In each iteration, the IOA algorithm generates random numbers. , and Based on random numbers , and and and Choose the multiplication, division, addition, or subtraction update branch of the IOA algorithm, and update the vectors in the matrix to be optimized. The The parameters of each item are updated. After updating all the parameters of all vectors, the first matrix is ​​obtained.

[0013] Preferably, based on random numbers , and and and Choose the multiplication, division, addition, or subtraction update branch of the IOA algorithm, and update the vectors in the matrix to be optimized. The The parameters to be updated include: when If the system is in the early stages of evaluation or the safety boundary has not been locked, multiplication or division operators are activated to perform a large-scale parameter search, and vectors in the matrix to be optimized are... The The updates to the item parameters include: ; in, Indicates the first Vectors in the matrix to be optimized in the round of iteration The The update results of the item parameters; Represents the current first vector The first in Parameter values; and They represent the first The upper and lower limits of the search for the item parameter; Indicates control parameters; It is a minimal positive constant; when When, the vector in the matrix to be optimized The The updates to the item parameters include: ; The first matrix is ​​obtained after the update: ; in, , and They represent the first matrix, respectively. M The upper limit of the action capacity of each vector, the inherent delay time, and the ramp rate.

[0014] Preferably, iterative optimization includes an iteration termination condition: The iteration terminates when the maximum number of iterations or the highest value of fitness is reached and the number of consecutive preset rounds varies within a preset range.

[0015] The present invention also provides a fast frequency modulation demand assessment device that takes into account low-power recovery characteristics, for use with the method of the present invention, the device comprising a first module, a second module, a third module and a fourth module; The first module is used to construct a system frequency response model that considers time-varying disturbances and fast frequency modulation response during low-voltage faults; the lowest frequency point is obtained based on the system frequency response model. The second module is used to construct the optimization vector based on the inherent delay time, ramp rate, and upper limit of action capacity of the fast frequency modulation response model; and to construct the initial optimization matrix based on the optimization vector. The third module is used to remove outlier vectors from the initial optimization matrix based on the lowest frequency point, calculate the fitness of each vector according to the preset objective function, and select the vector with the highest fitness as the first vector. The fourth module is used to obtain the first matrix by adaptive optimization using the first vector as the update basis through the IOA algorithm; the initial optimization matrix is ​​updated to the first matrix and iterative optimization is performed; after the iteration is completed, the vector with the highest fitness in the last iteration is output.

[0016] The present invention has the following beneficial effects: The present invention provides a fast frequency modulation demand assessment method considering low-voltage ride-through power recovery characteristics. Firstly, it overcomes the limitation of traditional low-voltage ride-through assessments that only focus on instantaneous drop depth. It introduces the recovery slope of renewable energy power as a key control variable into the timing disturbance excitation function and uses it as an excitation input to a reduced-order system frequency response model that includes a fast frequency modulation response stage. This reveals the power overlap mechanism between the low-voltage ride-through recovery hysteresis period and the initial stage of fast frequency modulation, improving the safety redundancy of the demand assessment results under different operating conditions. Secondly, it utilizes improved arithmetic optimization of the nonlinear evolution characteristics of large-scale leaps in multiplication and division and micro-step approximations in addition and subtraction in existing algorithms. This transforms the original frequency modulation capacity weighting problem, which relied heavily on extensive offline simulations and consumed significant computational resources, into an analytical, directional, reduced-order optimization problem within a multidimensional mathematical constraint domain, greatly improving the convergence rate of the assessment calculation. Thirdly, addressing the computational divergence problem encountered in the frequency analysis model of new power systems, a consistency check based on physical boundaries is deeply embedded in the optimization algorithm. This avoids singular numerical jumps caused by improper optimization of the controller delay time constant, ensuring that the final evaluated fast frequency regulation demand satisfies both mathematical optimality and the robustness requirements of power system operation. The method of this invention accurately evaluates the fast frequency regulation demand in low-voltage scenarios with high renewable energy penetration, effectively improving the system's minimum frequency point and solving the frequency instability problem caused by the lack of frequency regulation resources in new power systems under low-voltage faults.

[0017] The fast frequency modulation demand assessment device of the present invention, which takes into account the low-penetration power recovery characteristics, is used in the method of the present invention and has the same beneficial effects as the method of the present invention.

[0018] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1This is a schematic diagram of the method flow of a preferred embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the power system topology according to a preferred embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram illustrating the changes in MOA and MOP with the number of iterations in a preferred embodiment of the present invention.

[0022] Figure 4 This is a schematic diagram of the optimal fitness convergence curve of the IOA algorithm in a preferred embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram showing the changes of MOA and MOP with the number of iterations in Scenario 2 of the preferred embodiment of the present invention.

[0024] Figure 6 This is a schematic diagram of the optimal fitness convergence curve of the IOA algorithm under scenario two of the preferred embodiments of the present invention. Detailed Implementation

[0025] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0026] See Figure 1 In a preferred embodiment of the present invention, a method for assessing fast frequency modulation requirements considering low-push-through power recovery characteristics is provided, comprising: S1. Construct a system frequency response model that considers time-varying disturbances and fast frequency modulation response during low-frequency failure; obtain the lowest frequency point based on the system frequency response model.

[0027] In a preferred embodiment of the present invention, the system frequency response model considering time-varying disturbances and fast frequency modulation response models during low-voltage fault construction includes: Construct a piecewise function for the active power deficit during the low-voltage ride-through process, using the fault occurrence time, fault clearing time, and active power recovery to steady state time as boundary points: Define the time when the low-voltage failure of the new energy source occurs as The fault duration is During the fault, the minimum voltage dropped to the per-unit value. After a disturbance occurs, to prioritize voltage support for the grid, the inverter needs to inject a large amount of reactive current into the grid. Limited by the converter capacity, its active power output will plummet to near zero. Once the fault is cleared, due to internal control delays and the dynamic limitations of the phase-locked loop, the unit's active power output cannot achieve a transient recovery. According to grid connection guidelines, for renewable energy units that did not disconnect from the grid during a fault, their active power recovery rate should be at least 20% of their rated active power per second to the state before the fault. Based on the above analysis, to quantify the impact of this process on system frequency, the active power deficit during the low-voltage ride-through process is modeled as a piecewise function as follows: ; in, This represents the active power of the unit before the failure. Voltage-power sag factor, This represents the maximum active power deficit during the fault period. The specified active power recovery rate, The time it takes for the active power to recover to a steady state.

[0028] Construct a fast frequency modulation response model that includes inherent latency, ramp rate, and upper limit of action capacity: Fast frequency regulation resources such as energy storage are abstracted into a general dynamic model with dead time, ramp-up limits, and capacity limits. In the time domain, the fast frequency regulation response model is: ; in, The inherent delay time includes both communication and action. The equivalent ramp rate for resources. The maximum capacity for FFR actions has been reached. After entering the capacity saturation period, a constant output is maintained. The mathematical relationship at this saturation point satisfies: ; Construct a synchronous unit frequency response model in the form of a first-order equivalent transfer function: Due to the heterogeneity and multi-resource coupling of new power systems, the models exhibit highly nonlinear characteristics, making simulation analysis complex and time-consuming. Therefore, to achieve rapid analysis of the frequency response of new power systems, a reduced-order equivalent processing is performed on the synchronous generator units. The corresponding equivalent parameters can be obtained through identification algorithms such as Thevenin equivalents or least squares methods. Considering the initial anti-regulation characteristics caused by the water hammer effect of the turbine and the reheat delay of the thermal power unit, a first-order equivalent transfer function with one zero and one pole is used to characterize the frequency response model of the synchronous generator units. ; in, , and These are the equivalent dynamic parameters corresponding to the low-order model; for hydroelectric generators, It is usually taken as a negative value to characterize its anti-modulation properties; For the Laplace operator; This represents the system frequency deviation.

[0029] Fit the system frequency response curve; based on the synchronous generator frequency response model and the system frequency response curve, obtain the active power time-domain analytical expression of a single synchronous generator; The system frequency response model is obtained based on the piecewise function of active power deficit, the fast frequency regulation response model, the active power time-domain analytical expression, and the system frequency response curve.

[0030] In a preferred embodiment of the present invention, the system frequency response curve is fitted; the active power time-domain analytical expression of a single synchronous generator unit is obtained based on the synchronous generator unit frequency response model and the system frequency response curve, including: To address the difficulty in accurately solving analytically due to the high coupling between system frequency and active power in frequency response models, a specific mathematical function can be constructed to approximate the transient frequency deviation trajectory of the system. This achieves effective decoupling of active power-frequency dynamic characteristics while ensuring computational accuracy. To accurately match the true frequency evolution trajectory of the system after disturbance, an exponential decay function with characteristic parameters is selected to fit the system frequency response curve. ; Under the influence of unbalanced active power disturbance Afterwards, the system frequency will drop to its lowest point, at which critical moment... The system frequency change rate is exactly zero. Combining the boundary conditions and extreme point characteristics at the transient initial moment, the characteristic parameters of the above fitting function can be rigorously derived as follows: , ,in This is the system's equivalent inertia.

[0031] Based on the synchronous generator frequency response model and the system frequency response curve, the preliminary active power time-domain analytical expression for a single synchronous generator is obtained: By performing a Laplace transform on the system frequency response curve, inputting it into the synchronous generator frequency response model, and then performing an inverse Laplace transform, the synchronous generator frequency response model can be derived. Preliminary active time-domain analytical expression: ; in, , and Synchronous generator units corresponding , and ; It is the natural base.

[0032] The initial active time-domain analytical expression is corrected using nonlinear logic to obtain the active time-domain analytical expression: Since different types of frequency modulation resources trigger the frequency modulation dead zone and reach the active power output limit at different times, it is necessary to perform nonlinear logic correction on the output power of various resources.

[0033] First, the energy required to overcome the frequency dead zone is characterized as the dead zone power loss that the frequency modulation resources need to compensate for before the output response: ; in, Synchronous generator unit The equivalent dead zone power; Synchronous generator unit The frequency response converted transfer function; Synchronous generator unit Frequency response dead zone threshold.

[0034] Secondly, when the unit reaches its maximum frequency regulation output, its active power output must be limited to the limit value.

[0035] The corrected active time-domain analytical expression is expressed as: ; in, Synchronous generator unit Maximum available active power capacity; Synchronous generator unit Dead zone power loss; It is a step function; The time to reach the limit value.

[0036] In a preferred embodiment of the present invention, the system frequency response model is obtained based on the active power deficit piecewise function, the fast frequency regulation response model, the active power time-domain analytical expression, and the system frequency response curve, including: First, the system frequency response curve is corrected based on the active power time-domain analytical expression, resulting in the corrected system frequency response curve: After correcting for dead zones and bandwidth limitations for various resources, the overall active power deficit of the system also changes. Based on the law of conservation of energy, the fitted system frequency must also be corrected accordingly. The corrected system frequency response curve is expressed as follows: ; in, The number of limiting units in the synchronous generator set; It is the integral variable.

[0037] Because the active power disturbance during the low-frequency ride-through (LTT) of renewable energy sources changes dynamically over time, the system frequency response no longer follows a single disturbance value. Therefore, it is necessary to determine the timing of the frequency minimum based on the matching relationship between the system inertia level, the magnitude of the active power deficit, the duration of the LLT, and the active power recovery rate after fault clearing. Specifically, the frequency minimum may occur either during the LLT fault duration or during the active power recovery phase. To accurately determine the system frequency minimum, an analytical strategy based on state discrimination is proposed: first, boundary discrimination is performed on the transient time period to which the frequency minimum belongs; then, the corresponding full-time domain system frequency analytical equation is established by combining the disturbance structure of the corresponding time period. This includes: The system frequency curve changes with the amount of unbalanced power. When the low-voltage-crossing renewable energy begins to recover active power, it is equivalent to superimposing a new time-variable disturbance on top of the initial step disturbance. Therefore, it is necessary to discuss the different disturbance forms in the two stages of the low-voltage-crossing fault: Phase 1: When the lowest point of the system frequency occurs during the sustained low-frequency breakdown of new energy sources, the system disturbance is only a step disturbance, and the system frequency will begin to rise before the active power of new energy sources recovers. Phase Two: When the lowest frequency point occurs during the active power recovery phase of new energy sources, the system disturbance is an initial step disturbance followed by a constant slope slope disturbance at a certain moment. At this time, the system frequency will continue to drop during the low-frequency recovery phase of new energy sources, and will only reach the lowest point during the active power recovery period or even after it ends.

[0038] The essential difference between the two transient frequency trajectories mentioned above is mainly reflected in the different positive and negative signs of the system frequency change rate at different stages. Based on this, the critical time node at which the low-voltage crossing ends and active power begins to recover is selected. Substituting this into the analytical expression for system frequency change, we can calculate the rate of change of system frequency at this point, and thus qualitatively determine the current power balance state of the system. (System frequency change rate) The solution is expressed as: ; in, This represents the total number of synchronous generator units; It represents the system's equivalent inertia.

[0039] If the calculated rate of change of the system frequency is greater than zero, it indicates that the system frequency is rising and the lowest point has occurred. Previously, during the sustained low-voltage phase of new energy sources; if the system frequency change rate is zero, it indicates that the power of various components in the system has reached equilibrium, and the lowest point occurs at this time. If the system frequency change rate is less than zero, it indicates that there is still an uncompensated active power deficit in the system, and the system frequency will continue to decline, with the lowest point appearing in [the following text is incomplete and likely refers to a different system frequency]. After that, the recovery phase begins.

[0040] Based on the above judgment, the dynamic response of the system to the low-voltage fault is deconstructed into a superposition of the zero-input response and the zero-state response. The zero-input response includes the free response caused by the internal initial state, corresponding to the system's response at the first moment after experiencing the initial step disturbance. The accumulated response quantities include system frequency deviation and state quantities of active power output of each unit; first moment The critical moment when the low-voltage crossing ends and the active power begins to recover; the zero-state response includes the response caused by external inputs, including the dynamic support increment of various resources in the system after the slope disturbance.

[0041] Construct the zero-input response based on the active time-domain analytical expression and the system frequency response correction curve: ; The zero-state response is constructed based on the piecewise function of active power deficit, the fast frequency modulation response model, and the active power time-domain analytical expression: ; The system frequency response model for the low-voltage fault process is obtained based on the zero-input response and the zero-state response.

[0042] ; In a preferred embodiment of the present invention, obtaining the lowest frequency point based on the system frequency response model includes: By substituting the active power equations of each frequency regulation unit into the system frequency response model and using the finite difference Newton method for numerical iteration, the extreme time corresponding to the maximum system frequency deviation can be obtained. By substituting the obtained extreme time into the system frequency response correction curve, the minimum frequency point can be obtained. .

[0043] S2. Construct the optimization vector based on the inherent delay time, ramp rate, and upper limit of action capacity of the fast frequency modulation response model; construct the initial optimization matrix based on the optimization vector.

[0044] The first one is constructed based on inherent latency, ramp rate, and maximum action capacity. Optimization vector Represented as: ; in , and They represent the first The upper limit of the action capacity of each optimization vector, the inherent delay time, and the ramp rate.

[0045] Based on the optimization vector Perform initialization and construct the initial optimization matrix. X , is represented as: ; Where N represents the initial optimization matrix. X The total number of vectors.

[0046] S3. After removing outlier vectors from the initial optimization matrix based on the lowest frequency point, calculate the fitness of each vector according to the preset objective function, and select the vector with the highest fitness as the first vector.

[0047] In a preferred embodiment of the present invention, the outlier vector removal of the initial optimization matrix based on the lowest frequency point includes: For each vector, the criterion is calculated based on the point of lowest frequency: ; ; in, Indicates the point of lowest frequency; This is the tolerance factor, typically taken as 1.5 to 2.0; This refers to the steady-state frequency deviation of the system. If the system steady-state frequency deviation If the criteria are satisfied, the fitness of the vector is set to positive infinity, and the vector is discarded; the resulting matrix after discarding is denoted as the matrix to be optimized. The steady-state frequency deviation of the system is then determined. When the aforementioned judgment formula is satisfied, the system frequency security over-limit penalty term is applied. Since the fitness of the vector is positive infinity, we can further set the fitness of the vector to positive infinity.

[0048] The matrix to be optimized is represented as: ; in, M denoted as the total number of vectors in the matrix to be optimized.

[0049] In a preferred embodiment of the present invention, the fitness of each vector is calculated according to a preset objective function, and the vector with the highest fitness is selected as the first vector, including: The preset objective functions include: ; ; in, For the first One vector; For the first The fitness of each vector; This is the capacity cost weighting coefficient. For the first The corresponding fast frequency modulation resource configuration capacity limit for each vector; This is a penalty item for exceeding system frequency security limits; For the first The lowest point of system frequency calculated under each vector; This refers to the system frequency safety limit. This is the penalty coefficient; The following constraints must be met during the calculation: (1) The absolute value of the maximum frequency change rate must be less than or equal to the preset maximum frequency change rate value. : ; (2) The inherent delay time, ramp rate, and upper limit of motion capacity must be within the preset upper and lower limits: ; in, and These are the maximum action capacity. The lower and upper limits; and These are the inherent delay times. The lower and upper limits; and respectively the slope rate The lower and upper limits.

[0050] If the constraints are met, then the system frequency safety over-limit penalty term is applied. The value is 0; if the constraint conditions are not met, then the system frequency security over-limit penalty item is applied. The fitness is amplified exponentially and the corresponding vectors are eliminated. After calculation, select the vector with the highest fitness and denote it as the first vector. ,in, , and These represent the upper limit of action capacity, inherent delay time, and ramp rate in the first vector, respectively.

[0051] S4. Using the first vector as the update benchmark, the first matrix is ​​obtained through adaptive optimization using the IOA algorithm; the initial optimization matrix is ​​updated to the first matrix and iterative optimization is performed; after the iteration is completed, the vector with the highest fitness in the last iteration is output.

[0052] In a preferred embodiment of the present invention, the first matrix is ​​obtained by adaptive optimization using the IOA algorithm with the first vector as the update basis, including: Mathematical optimization speedup factor in IAOA algorithm With mathematical optimization probability coefficient The value of determines whether the algorithm performs a large-span interval search or a small-step precision search at the current stage.

[0053] In the In each iteration, the mathematical optimization speedup factor in the IOA algorithm is calculated. With mathematical optimization probability coefficient : ; ; in, For iteration rounds; T This represents the maximum number of iterations. and They are respectively The minimum and maximum bounds; as the iteration proceeds, It increases linearly from the minimum to the maximum; It is a dynamic coefficient that evolves nonlinearly with the number of iterations; This is the sensitivity coefficient, and its magnitude determines the rate of step size reduction.

[0054] Due to the power index The existence of In the early to mid-stages of iteration, the algorithm can maintain relatively high values, ensuring a sufficiently large step size to overcome infeasible constraints; as the iteration progresses into the later stages... The algorithm exhibits non-linear accelerated convergence to 0, at which point the update step size is extremely small, ensuring that the algorithm ultimately converges very smoothly to the theoretically minimum capacity configuration solution. During the evaluation process, the mathematical optimization probability coefficients... Through nonlinear decay over the iterative process, in the early stages of evaluation, the lower... The high value endows the algorithm with strong global jump capability, enabling it to quickly cover the physically feasible region of the fast frequency modulation resource parameter space; in the later stages of evaluation, high values... The algorithm is guided to achieve high-precision convergence, thereby minimizing the precise allocation of fast frequency modulation resource requirements while satisfying the hard constraints of frequency security.

[0055] In each iteration, the IOA algorithm generates random numbers. , and Based on random numbers , and and and Choose the multiplication, division, addition, or subtraction update branch of the IOA algorithm, and update the vectors in the matrix to be optimized. The The parameters of each item are updated. After updating all the parameters of all vectors, the first matrix is ​​obtained.

[0056] In a preferred embodiment of the present invention, based on a random number , and and and Choose the multiplication, division, addition, or subtraction update branch of the IOA algorithm, and update the vectors in the matrix to be optimized. The The parameters to be updated include: when If the system is in the early stages of evaluation or the safety boundary has not been locked, multiplication or division operators are activated to perform a large-scale parameter search, and vectors in the matrix to be optimized are... The The updates to the item parameters include: ; in, Indicates the first Vectors in the matrix to be optimized in the round of iteration The The update results of the item parameters; Represents the current first vector The first in Parameter values; and They represent the first The upper and lower limits of the search for the item parameter; Indicates control parameters; It is a minimal positive constant; when When, the vector in the matrix to be optimized The The updates to the item parameters include: ; The first matrix is ​​obtained after the update: ; in, , and They represent the first matrix, respectively. M The upper limit of the action capacity of each vector, the inherent delay time, and the ramp rate.

[0057] In a preferred embodiment of the present invention, in each iteration, Generate random numbers Through its connection with The search direction for parameters is determined by comparing numerical values. When When the algorithm determines that the system frequency safety boundary cannot be determined at present, it activates the multiplication and division operators to perform a global search to roughly estimate the fast frequency modulation resource requirements, thereby quickly locating a rough range of fast frequency modulation resource capacity that can support frequency within the limit, avoiding the evaluation process from getting trapped in local optima. At this point, the algorithm determines that the corresponding fast frequency modulation (FM) configuration boundary has been locked, and switches the search mode to use addition and subtraction operators to perform a local search. Under the premise of satisfying system frequency security constraints, it attempts to reduce the FM capacity to ensure economic efficiency. In summary, in the initial stage of FM resource requirement assessment, When the capacity is smaller, the algorithm is more likely to perform multiplication and division operations, quickly escaping unreasonable capacity ranges; later... If the value is relatively large, the algorithm locks the frequency near the system's safe red line and performs addition and subtraction operations to reduce the capacity.

[0058] In a preferred embodiment of the present invention, the iterative optimization includes an iteration termination condition: The iteration terminates when the maximum number of iterations or the highest value of fitness is reached and the number of consecutive preset rounds varies within a preset range.

[0059] In a preferred embodiment of the present invention, the highest fitness value varying within a preset range for a consecutive preset number of rounds includes: The highest fitness value has a rate of change of less than 1% in consecutive iterations. .

[0060] The present invention provides a fast frequency modulation demand assessment method considering low-voltage ride-through power recovery characteristics. Firstly, it overcomes the limitation of traditional low-voltage ride-through assessments that only focus on instantaneous drop depth. It introduces the recovery slope of renewable energy power as a key control variable into the timing disturbance excitation function and uses it as an excitation input to a reduced-order system frequency response model that includes a fast frequency modulation response stage. This reveals the power overlap mechanism between the low-voltage ride-through recovery hysteresis period and the initial stage of fast frequency modulation, improving the safety redundancy of the demand assessment results under different operating conditions. Secondly, it utilizes improved arithmetic optimization of the nonlinear evolution characteristics of large-scale leaps in multiplication and division and micro-step approximations in addition and subtraction in existing algorithms. This transforms the original frequency modulation capacity weighting problem, which relied heavily on extensive offline simulations and consumed significant computational resources, into an analytical, directional, reduced-order optimization problem within a multidimensional mathematical constraint domain, greatly improving the convergence rate of the assessment calculation. Thirdly, addressing the computational divergence problem encountered in the frequency analysis model of new power systems, a consistency check based on physical boundaries is deeply embedded in the optimization algorithm. This avoids singular numerical jumps caused by improper optimization of the controller delay time constant, ensuring that the final evaluated fast frequency regulation demand satisfies both mathematical optimality and the robustness requirements of power system operation. The method of this invention accurately evaluates the fast frequency regulation demand in low-voltage scenarios with high renewable energy penetration, effectively improving the system's minimum frequency point and solving the frequency instability problem caused by the lack of frequency regulation resources in new power systems under low-voltage faults.

[0061] In a preferred embodiment of the present invention, a fast frequency modulation requirement assessment device considering low-power recovery characteristics is also provided for use with the method of the present invention. The device includes a first module, a second module, a third module, and a fourth module. The first module is used to construct a system frequency response model that considers time-varying disturbances and fast frequency modulation response during low-voltage faults; the lowest frequency point is obtained based on the system frequency response model. The second module is used to construct the optimization vector based on the inherent delay time, ramp rate, and upper limit of action capacity of the fast frequency modulation response model; and to construct the initial optimization matrix based on the optimization vector. The third module is used to remove outlier vectors from the initial optimization matrix based on the lowest frequency point, calculate the fitness of each vector according to the preset objective function, and select the vector with the highest fitness as the first vector. The fourth module is used to obtain the first matrix by adaptive optimization using the first vector as the update basis through the IOA algorithm; the initial optimization matrix is ​​updated to the first matrix and iterative optimization is performed; after the iteration is completed, the vector with the highest fitness in the last iteration is output.

[0062] The fast frequency modulation demand assessment device of the present invention, which takes into account the low-penetration power recovery characteristics, is used in the method of the present invention and has the same beneficial effects as the method of the present invention.

[0063] Verification section: The method of this invention is verified using a real power system. The topology of the power system is as follows: Figure 2 As shown, G1 to G7 are 7 synchronous turbine units, W1 to W2 are 2 wind turbines, and 1 to 38 are nodes. Both test scenarios 1 and 2 consider short-circuit faults. The active power recovery time for scenario 1 is 2 seconds, and for scenario 2 it is 3 seconds. Frequency safety limits are set as follows: maximum frequency deviation 0.5 Hz, maximum frequency change rate 0.5 Hz / s. Evaluation results are shown in Tables 1 to 3. Table 1. Results of Fast Frequency Modulation Parameter Configuration ; Table 2 Comparison of Results for Different Evaluation Methods ; Table 3 Comparison of Frequency Indicators After Adding Fast Frequency Modulation Resources ; The results in Tables 1 to 3 show that the method of this invention can effectively raise the lowest point of the system frequency to 49.5Hz in low-frequency ride-through scenarios, and also significantly improves the system frequency change rate. For example, in scenario 1, after adding fast frequency regulation resources, the system frequency change rate increased from 0.71 to 0.41. As the active power recovery speed decreases, the active power capacity of fast frequency regulation increases from 320.97MW to 365.2MW, indicating that the method of this invention can effectively capture the low-frequency ride-through power recovery characteristics and provide corresponding improvements for different recovery speeds. Compared with the traditional single-dimensional configuration method of fast frequency regulation resource capacity, the single-dimensional configuration method requires a larger fast frequency regulation capacity (420.83MW) under the same fault scenario. This shows that the method of this invention combines safety with economy, maximizing the system's support capacity with minimal capacity. In summary, the method of this invention can accurately assess the fast frequency regulation resource requirements in different scenarios, configure capacity, response time, and ramp rate parameters that meet frequency safety requirements, and ensure optimal economy, providing effective guidance for actual power grids.

[0064] Figures 3 to 6 The graph shows the convergence of the metrics in scenario one and scenario two of the method of this invention. As can be seen from the graph, the method is robust and fast. In different scenarios, the algorithm reaches stability after about 25 iterations.

[0065] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for fast frequency modulation demand assessment considering low-suspension power recovery characteristics, characterized in that, include: Construct a system frequency response model that considers time-varying disturbances and a fast frequency modulation response model during low-frequency failure; obtain the lowest frequency point based on the system frequency response model; construct an optimization vector based on the inherent delay time, ramp rate, and upper limit of the action capacity of the fast frequency modulation response model; construct an initial optimization matrix based on the optimization vector. After removing outlier vectors from the initial optimization matrix based on the lowest frequency point, the fitness of each vector is calculated according to a preset objective function, and the vector with the highest fitness is selected as the first vector. Using the first vector as the update benchmark, the first matrix is ​​obtained through adaptive optimization using the IOA algorithm. The initial optimization matrix is ​​updated to the first matrix and iterative optimization is performed. After the iteration is completed, the vector with the highest fitness in the last iteration is output. The fitness of each vector is calculated based on the preset objective function, and the vector with the highest fitness is selected as the first vector, including: The preset objective function includes: ； ； in, For the first One vector; For the first The fitness of each vector; This is the capacity cost weighting coefficient. For the first The corresponding fast frequency modulation resource configuration capacity limit for each vector; This is a penalty item for exceeding system frequency security limits; For the first The lowest point of system frequency calculated under each vector; This refers to the system frequency safety limit. This is the penalty coefficient; The calculation must meet the following constraints: the absolute value of the maximum frequency change rate must be less than or equal to the preset maximum frequency change rate value, and the inherent delay time, ramp rate, and upper limit of motion capacity must be within the preset upper and lower limits. If the aforementioned constraints are met, the system frequency security violation penalty term will be set aside. The value is 0; if the constraint condition is not met, then the system frequency security violation penalty term applies. The fitness is amplified exponentially and the corresponding vectors are eliminated. After calculation, select the vector with the highest fitness and denote it as the first vector. ,in, , and These represent the upper limit of action capacity, inherent delay time, and ramp rate in the first vector, respectively.

2. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 1, characterized in that, The system frequency response model that considers time-varying disturbances and fast frequency modulation response during low-level fault construction includes: A piecewise function of active power deficit during the low voltage ride-through process is constructed with the fault occurrence time, fault clearing time, and active power recovery to steady state time as boundary points; a fast frequency regulation response model including inherent delay time, ramp rate, and upper limit of operating capacity is constructed. A first-order equivalent transfer function form of the synchronous generator frequency response model is constructed; the system frequency response curve is fitted; and the active power time-domain analytical expression of a single synchronous generator is obtained based on the synchronous generator frequency response model and the system frequency response curve. The system frequency response model is obtained based on the active power deficit piecewise function, the fast frequency regulation response model, the active power time-domain analytical expression, and the system frequency response curve.

3. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 2, characterized in that, Fit the system frequency response curve; based on the synchronous generator frequency response model and the system frequency response curve, obtain the active power time-domain analytical expression for a single synchronous generator, including: An exponential decay function with characteristic parameters is selected to fit the system frequency response curve; based on the synchronous generator frequency response model and the system frequency response curve, a preliminary active power time-domain analytical expression for a single synchronous generator is obtained; the preliminary active power time-domain analytical expression is corrected by nonlinear logic to obtain the active power time-domain analytical expression.

4. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 3, characterized in that, The system frequency response model, derived from the active power deficit piecewise function, the fast frequency modulation response model, the active power time-domain analytical expression, and the system frequency response curve, includes: The system frequency response curve is corrected according to the active time-domain analytical expression to obtain the corrected system frequency response curve. The dynamic response of the system to the low-voltage fault is deconstructed into the superposition of the zero-input response and the zero-state response. The zero-input response is constructed based on the active power time-domain analytical expression and the system frequency response correction curve. The zero-state response is constructed based on the active power deficit piecewise function, the fast frequency modulation response model and the active power time-domain analytical expression. The zero-input response includes the free response caused by the internal initial state, which corresponds to the response quantity accumulated by the system at the first moment after experiencing the initial step disturbance, including the system frequency deviation and the state quantity of the active power output of each unit; the first moment is the critical moment when the low-voltage crossing ends and the active power begins to recover; the zero-state response includes the response caused by the external input, including the dynamic support increment of various resources in the system after the ramp disturbance. The system frequency response model for the low-voltage fault process is obtained based on the zero-input response and the zero-state response.

5. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 4, characterized in that, The outlier vector removal process for the initial optimization matrix based on the lowest frequency point includes: For each vector, the determination formula is calculated based on the lowest frequency point: ； ； in, Indicates the point of lowest frequency; Tolerance coefficient; This refers to the steady-state frequency deviation of the system. This represents the maximum active power deficit during the fault period. D For system damping; If the system steady-state frequency deviation If the above criteria are satisfied, then the fitness of the vector is set to positive infinity, and the vector is removed; the matrix after removal is denoted as the matrix to be optimized.

6. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 5, characterized in that, Using the first vector as the update basis, the first matrix obtained by adaptive optimization through the IAOA algorithm includes: In the In each iteration, the mathematical optimization speedup factor in the IOA algorithm is calculated. With mathematical optimization probability coefficient : ； ； in, For iteration rounds; T This represents the maximum number of iterations. and They are respectively The minimum and maximum value boundaries; Sensitivity coefficient; In each iteration, the IOA algorithm generates random numbers. , and Based on random numbers , and and and Select the multiplication, division, addition, or subtraction update branch of the IOA algorithm, and update the vectors in the matrix to be optimized. The The parameters of each item are updated. After updating all the parameters of all vectors, the first matrix is ​​obtained.

7. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 6, characterized in that, Based on random numbers , and and and Select the multiplication, division, addition, or subtraction update branch of the IOA algorithm, and update the vectors in the matrix to be optimized. The The parameters to be updated include: when If the system is in the early stages of evaluation or the safety boundary has not been locked, multiplication or division operators are activated to perform a large-scale parameter search. The vectors in the matrix to be optimized... The The updates to the item parameters include: ； in, Indicates the first Vectors in the matrix to be optimized in the round of iteration The The update results of the item parameters; Indicates the current first vector The first in Parameter values; and They represent the first The upper and lower limits of the search for the item parameter; Indicates control parameters; It is a minimal positive constant; when When, the vectors in the matrix to be optimized The The updates to the item parameters include: ； The first matrix is ​​obtained after the update is complete: ； in, , and They respectively represent the first matrix. M The upper limit of the action capacity of each vector, the inherent delay time, and the ramp rate.

8. The fast frequency modulation demand assessment method considering low-through power recovery characteristics according to claim 7, characterized in that, The iterative optimization includes an iteration termination condition: The iteration terminates when the maximum number of iterations or the highest value of fitness is reached and the number of consecutive preset rounds varies within a preset range.

9. A fast frequency modulation demand assessment device considering low-through power recovery characteristics, used in the method according to any one of claims 1 to 8, characterized in that, The device includes a first module, a second module, a third module, and a fourth module; The first module is used to construct a system frequency response model that considers time-varying disturbances and a fast frequency modulation response model during low-voltage faults; and to obtain the lowest frequency point based on the system frequency response model. The second module is used to construct an optimization vector based on the inherent delay time, ramp rate, and upper limit of action capacity of the fast frequency modulation response model; and to construct an initial optimization matrix based on the optimization vector. The third module is used to remove outlier vectors from the initial optimization matrix based on the lowest frequency point, calculate the fitness of each vector according to a preset objective function, and select the vector with the highest fitness as the first vector. The fourth module is used to obtain the first matrix by adaptive optimization using the first vector as the update basis through the IOA algorithm; update the initial optimization matrix to the first matrix and perform iterative optimization; after the iteration is completed, output the vector with the highest fitness in the last iteration.

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