Method and device for determining critical clearing time of power system, terminal equipment and storage medium

Abstract

The invention discloses a critical clearing time determination method and device of a power system, terminal equipment and a storage medium, which can track the operation parameter change of the system in real time, and combine the current operation parameter of a generator with a target transient domain for calculation every time a function value calculation operation is executed, so that the calculation efficiency is improved. According to the method, the function value reflecting the stability state of the system can be obtained, the target transient domain is a functional expression generated after the transient stability model of the power system is solved, and the stability characteristics of the system in different operation states are reflected, so that the current fault scene and the stability of the power system can be effectively combined. Furthermore, the function value corresponding to the current moment can be compared with a preset boundary threshold value, whether the system is about to lose stability or not can be judged, and finally the critical clearing time of the power system is obtained. According to the method, the stability characteristic of the system can be more comprehensively considered, so that the calculation accuracy of the critical clearing time is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of operation and control of power systems, and particularly to a method, device, terminal device, and storage medium for determining the critical clearing time of a power system. Background Art

[0002] The critical clearing time of a power system refers to the longest time required to remove the faulty part after a fault occurs in the system. By quickly and accurately calculating this time, it helps power system operators take timely measures, such as removing faulty lines or generators, to prevent system instability and reduce the likelihood and scope of faults.

[0003] However, in the existing process of determining the critical clearing time, the differential equations of the power system are often solved by numerical integration methods, that is, by simulating the dynamic response of the system after a fault occurs, and then determining the fault clearing time. This not only has a large amount of calculation and long time consumption, but also the time-domain simulation method usually can only obtain the results under specific fault scenarios, and cannot combine the fault scenarios of the power system with the stability of the power system for analysis to obtain the critical clearing time. That is, the influence of the stability of the power system is ignored when calculating the critical clearing time, resulting in a large deviation between the calculated result of the critical clearing time and the actual value, which may increase the risk of fault spread and system collapse. Summary of the Invention

[0004] Embodiments of the present invention provide a method, device, terminal device, and storage medium for determining the critical clearing time of a power system, which can combine the operating parameters of generators with the transient domain for calculation, so as to effectively combine the current fault scenario with the stability of the power system, and can effectively solve the problem in the prior art that the fault scenario of the power system cannot be combined with the stability of the power system for analysis to obtain the critical clearing time, resulting in a large deviation between the calculated result of the critical clearing time and the actual value.

[0005] An embodiment of the present invention provides a method for determining the critical clearing time of a power system, including:

[0006] When it is detected that a fault occurs in the power system, the moment when the fault occurs is used as the initial fault moment;

[0007] Repeat the following function value calculation operation until it is determined that there is a function value not less than a preset boundary threshold, and then generate the critical clearing time corresponding to the power system according to the initial fault moment and the current moment:

[0008] Obtain the current operating parameters corresponding to each generator of the power system at the current moment;

[0009] For each generator, a function value corresponding to the generator is calculated according to the current operating parameters of the generator and a target transient domain for measuring the stability of the system; wherein, the target transient domain is used to represent a functional expression generated after solving the transient stability model of the power system.

[0010] When it is determined that any function value is less than a preset boundary threshold, the next function value calculation operation is performed; wherein, the preset boundary threshold is used to represent the stability margin corresponding to the situation where the system cannot maintain stable operation.

[0011] Preferably, the generation of the target transient domain includes:

[0012] Obtain the operating parameters corresponding to each generator set in the power system;

[0013] Construct a transient stability model corresponding to the power system according to the operating parameters corresponding to each generator; wherein, the transient stability model is used to represent the response characteristics of the power system to restore the steady-state operating state after being disturbed.

[0014] Perform a polynomial transformation on the transient stability model to generate a polynomial model corresponding to the transient stability model in the polynomial space.

[0015] Based on a preset parameter set, a number of different preset positive definite polynomials, and a number of different preset positive numbers, perform iterative decomposition on the polynomial model. When it is determined that the polynomial model cannot be successfully decomposed, use the to-be-processed polynomial generated by the last decomposition as the target polynomial; wherein, the target polynomial includes: a number of state variables used to represent the operating parameters of the generator.

[0016] Perform a polynomial inverse transformation on the target polynomial to generate the target transient domain corresponding to the transient stability model.

[0017] Preferably, the operating parameters corresponding to the generator include: angular velocity, inertia constant, damping ratio, mechanical power, electromagnetic power, and rotor angle used to represent the angle between the generator and a preset reference generator; the transient stability model includes: a number of sub-transient stability models.

[0018] The construction of the transient stability model corresponding to the power system according to the operating parameters corresponding to each generator includes:

[0019] According to the rotor angles corresponding to each generator, divide each generator into a number of different generator sets; wherein, the rotor angle difference between any two generators in each generator set is not greater than a preset rotor angle threshold.

[0020] For each generator set, a sub-transient stability model corresponding to the generator set is constructed according to the angular velocity, inertia constant, damping ratio, mechanical power, and electromagnetic power corresponding to each generator in the generator set.

[0021] Preferably, the constructing a sub-transient stability model corresponding to the generator set according to the angular velocity, inertia constant, damping ratio, mechanical power, and electromagnetic power corresponding to each generator in the generator set includes:

[0022] Generating an average angular velocity corresponding to the generator set according to the angular velocity corresponding to each generator in the generator set and the number of generators;

[0023] Generating an average inertia constant corresponding to the generator set according to the inertia constant corresponding to each generator in the generator set and the number of generators;

[0024] Generating an average damping ratio corresponding to the generator set according to the damping ratio corresponding to each generator in the generator set and the number of generators;

[0025] Generating an average mechanical power corresponding to the generator set according to the mechanical power corresponding to each generator in the generator set and the number of generators;

[0026] Generating an average electromagnetic power corresponding to the generator set according to the electromagnetic power corresponding to each generator in the generator set and the number of generators;

[0027] Generating a sub-transient stability model corresponding to the generator set according to the average angular velocity, average inertia constant, average damping ratio, average mechanical power, and average electromagnetic power.

[0028] Preferably, the sub-transient stability model corresponding to the generator set includes:

[0029]

[0030] Wherein, is the average inertia constant of the Kth generator set, ω AK is the average angular velocity of the Kth generator set, is the derivative corresponding to the average angular velocity ω n P mk is the average mechanical power of the Kth generator set, P ek is the average electromagnetic power of the Kth generator set, and λ is the damping ratio of the Kth generator set.

[0031] Preferably, when iteratively decomposing the polynomial model based on a preset parameter set, several different preset positive definite polynomials, and several different preset positive numbers, when it is determined that the polynomial model cannot be successfully decomposed, the polynomial to be processed generated by the last decomposition of the polynomial model is used as the target polynomial, including:

[0032] Repeatedly perform the following polynomial model decomposition operation until it is determined that the polynomial model cannot be successfully decomposed, and use the polynomial to be processed generated by the last decomposition of the polynomial model as the target polynomial:

[0033] Obtain a preset parameter set, several current preset positive definite polynomials corresponding to the current iteration number, and several current preset positive numbers corresponding to the current iteration number; where the preset positive definite polynomials and preset positive numbers corresponding to different iteration numbers are different;

[0034] According to the preset parameter set, each current preset positive definite polynomial, and each current preset positive number, convert each bilinear term in the polynomial model to generate several converted data terms;

[0035] According to the preset parameter set, each current preset positive definite polynomial, each current preset positive number, each converted data term, and the current polynomial, decompose the polynomial model; where when initially performing the polynomial model decomposition operation, decompose the polynomial model according to several randomly selected preset positive definite polynomials and several randomly selected current preset positive numbers to generate the current polynomial;

[0036] When it is determined that the polynomial model is successfully decomposed, use the polynomial to be processed generated by decomposing the polynomial model at the current iteration number as the current polynomial for the next execution of the polynomial model decomposition operation.

[0037] Preferably, when initially performing the polynomial model decomposition operation, decomposing the polynomial model according to several randomly selected preset positive definite polynomials and several randomly selected current preset positive numbers to generate the current polynomial includes:

[0038] When initially performing the polynomial model decomposition operation, under the preset positive definiteness constraint and the preset negative definiteness constraint, decompose the polynomial model according to several randomly selected preset positive definite polynomials and several randomly selected current preset positive numbers to generate the current polynomial;

[0039] Among them, the positive definiteness constraint is used to represent that each parameter in the polynomial generated by decomposing the polynomial model is a positive number;

[0040] The negative definiteness constraint is used to characterize that the derivative of the polynomial with respect to time generated when decomposing the polynomial model is negative.

[0041] Based on the above method embodiments, the present invention correspondingly provides apparatus embodiments.

[0042] An embodiment of the present invention provides a critical clearing time determination apparatus for a power system, including: a fault time determination module and a critical clearing time generation module;

[0043] The fault time determination module is configured to, when detecting that a fault occurs in the power system, use the time when the fault occurs as the initial fault time;

[0044] The critical clearing time generation module is configured to repeatedly perform the following function value calculation operation until it is determined that there is a function value not less than a preset boundary threshold, and then generate the critical clearing time corresponding to the power system according to the initial fault time and the current time:

[0045] Obtain the current operating parameters corresponding to each generator in the power system at the current time;

[0046] For each generator, calculate the function value corresponding to the generator according to the current operating parameters of the generator and the target transient domain for measuring system stability; wherein, the target transient domain is used to characterize the functional expression generated after solving the transient stability model of the power system;

[0047] When it is determined that any function value is less than the preset boundary threshold, perform the next function value calculation operation; wherein, the preset boundary threshold is used to characterize the stability margin when the system cannot maintain stable operation.

[0048] Based on the above method embodiments, the present invention correspondingly provides terminal device embodiments.

[0049] Another embodiment of the present invention provides a terminal device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the method for determining the critical clearing time of a power system described in the above embodiments of the present invention.

[0050] Based on the above method embodiments, the present invention correspondingly provides storage medium embodiments.

[0051] Another embodiment of the present invention provides a storage medium. The computer-readable storage medium includes a stored computer program. When the computer program runs, it controls the device where the computer-readable storage medium is located to execute the method for determining the critical clearing time of a power system described in the above embodiments of the present invention.

[0052] The implementation of the present invention has the following beneficial effects:

[0053] The embodiment of the present invention provides a method, device, terminal device and storage medium for determining the critical clearing time of a power system. When the present invention detects a fault in the power system, the moment of the fault occurrence is used as the initial fault moment, and the current operating parameters of each generator at the current moment are obtained in real time. As the fault develops, the operating parameters of the generator will change. By continuously repeating the function value calculation operation, the present invention can track the change of the system operating parameters in real time, and when performing the function value calculation operation each time, the current operating parameters of the generator are combined with the target transient domain for calculation, and a function value reflecting the system stability state can be obtained. Since the target transient domain is a functional formula generated after solving the transient stability model of the power system, it can reflect the stability characteristics of the system under different operating states, so that the current fault scenario can be effectively combined with the stability of the power system. Further, when calculating the function value corresponding to the generator, the function value corresponding to the current moment is compared with a preset boundary threshold to determine whether the system is about to lose stability, so as to obtain the critical clearing time of the power system. Compared with the prior art, the present invention avoids the limitation that the traditional time-domain simulation method can only obtain the results under specific fault scenarios, and can more comprehensively consider the stability characteristics of the system, thereby improving the accuracy of the critical clearing time calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a schematic flowchart of a method for determining the critical clearing time of a power system according to an embodiment of the present invention.

[0055] Figure 2 is a schematic flowchart of a method for determining the critical clearing time according to another embodiment of the present invention.

[0056] Figure 3 is a schematic diagram of the node system structure of a synchronous generator according to an embodiment of the present invention.

[0057] Figure 4 is a schematic diagram of the identification result of the generator coherency group according to an embodiment of the present invention.

[0058] Figure 5 is a schematic diagram of the structure of a device for determining the critical clearing time of a power system according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0059] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0060] As Figure 1 shown, it is a schematic flowchart of a method for determining the critical clearing time of a power system provided by an embodiment of the present invention. The method for determining the critical clearing time of the power system includes:

[0061] Step S1: When a fault occurs in the power system is detected, the moment when the fault occurs is used as the initial fault moment.

[0062] Step S2: Repeat the following function value calculation operation until it is determined that there is a function value not less than the preset boundary threshold, then the critical clearing time corresponding to the power system is generated according to the initial fault moment and the current moment:

[0063] Obtain the current operating parameters corresponding to each generator in the power system at the current moment;

[0064] For each generator, calculate the function value corresponding to the generator according to the current operating parameters of the generator and the target transient domain for measuring system stability; wherein, the target transient domain is used to represent the functional formula generated after solving the transient stability model of the power system.

[0065] When it is determined that any function value is less than the preset boundary threshold, the next function value calculation operation is performed; wherein, the preset boundary threshold is used to represent the stability margin when the system cannot maintain stable operation.

[0066] For step S1, the power system fault is a dynamic process. From the occurrence of the fault to the removal of the fault, the operating parameters at each time point of the power system will change dynamically. Therefore, in order to monitor the operating parameters during the period from the occurrence of the fault to the removal of the fault and calculate the longest time required to remove the faulty part (i.e., the critical clearing time), the moment when the fault occurs is used as the initial fault moment, which can provide a clear time reference for subsequent fault analysis and determination of the clearing time.

[0067] For step S2, in a preferred embodiment, repeat the following function value calculation operation until it is determined that there is a function value not less than the preset boundary threshold, then the critical clearing time corresponding to the power system is generated according to the initial fault moment and the current moment:

[0068] Obtain the current operating parameters corresponding to each generator in the power system at the current moment;

[0069] For each generator, calculate the function value corresponding to the generator according to the current operating parameters of the generator and the target transient domain for measuring system stability; wherein, the target transient domain is used to represent the functional formula generated after solving the transient stability model of the power system;

[0070] When it is determined that any function value is less than the preset boundary threshold, perform the function value calculation operation for the next time; wherein, the preset boundary threshold is used to represent the stability margin corresponding to the situation where the system cannot maintain stable operation.

[0071] Illustratively, after a fault occurs in the power system, the stability state of the system changes continuously with time. When the function value at a certain moment reaches or exceeds the preset boundary threshold, this usually means that the system has approached or reached the limit of its stable operation. At this time, if no measures are taken immediately to cut off the fault, the system may lose stability, resulting in more serious consequences. Therefore, the embodiment of the present invention can determine the critical clearing time according to the time difference between this moment and the initial fault moment, ensure that measures are taken in time before the system is about to lose stability, and guarantee the safe operation of the power grid.

[0072] Then, by repeatedly performing the function value calculation operation, calculate the function value at each moment continuously, so as to reflect the operating state and stability state of the system in real time, and evaluate the current stability margin of the power system. It can be understood that the stability margin refers to the degree or range in which the power system can still maintain stable operation after being subjected to a certain disturbance. The preset boundary threshold is set to represent the stability margin corresponding to the situation where the system cannot maintain stable operation. When the function value of a certain state variable of the power system reaches or exceeds this threshold, it means that the stability margin of the system has been reduced to a certain extent, and the system may be about to lose stability.

[0073] Under the current fault scenario, based on the stability analysis of the power system, the present invention evaluates the stability of the system by calculating the function value of the current operating parameters of the generator, and the function value is closely related to the stability margin of the system. When the function value is small, it indicates that the stability margin of the system is large; when the function value increases, it indicates that the stability margin of the system is decreasing.

[0074] Specifically, when it is determined that there is a function value not less than the preset boundary threshold, it means that the state variable has approached or reached the critical value at which the system cannot maintain stable operation. At this time, the stability margin of the system is very small, and may even be zero or negative. Therefore, it can be considered that the system is not stable enough at this time, and the critical clearing time corresponding to the power system can be calculated according to the difference between the initial fault time and the current time (i.e., the time when a function value is not less than the preset boundary threshold).

[0075] Therefore, since the power system is a dynamic system and its state changes with factors such as time, load changes, and equipment failures, the present invention can make the critical clearing time evaluation have stronger dynamic response capabilities by calculating function values and stability margins, and can capture small changes in system stability, so as to obtain the critical clearing time that conforms to the actual operating state of the power system.

[0076] In a preferred embodiment, the generation of the target transient domain is obtained by transforming and solving the transient stability model, and there is:

[0077] Obtain the operating parameters corresponding to each generator set in the power system;

[0078] Construct a transient stability model corresponding to the power system according to the operating parameters corresponding to each generator; wherein, the transient stability model is used to characterize the response characteristics of the power system to restore the steady-state operating state after being disturbed;

[0079] Perform a polynomial transformation on the transient stability model to generate a polynomial model corresponding to the transient stability model in the polynomial space;

[0080] Based on a preset parameter set, several different preset positive definite polynomials, and several different preset positive numbers, perform iterative decomposition on the polynomial model. When it is determined that the polynomial model cannot be successfully decomposed, use the last decomposed polynomial to be processed as the target polynomial; wherein, the target polynomial includes: several state variables used to represent the operating parameters of the generator;

[0081] Perform a polynomial inverse transformation on the target polynomial to generate the target transient domain corresponding to the transient stability model.

[0082] Illustratively, the generator of the present invention is a synchronous generator, and the operating parameters corresponding to the synchronous generator include: angular velocity, inertia constant, damping ratio, mechanical power, electromagnetic power, and rotor angle used to characterize the angle between the generator and a preset reference generator; and the transient stability model is composed of several sub-transient stability models, and each sub-transient stability model corresponds to a synchronous generator set.

[0083] When constructing the transient stability model, a transient stability model corresponding to the power system is constructed according to the operating parameters corresponding to each generator, including:

[0084] According to the rotor angles corresponding to each generator, each generator is divided into several different generator sets; wherein, the rotor angle difference between any two generators in each generator set is not greater than a preset rotor angle threshold;

[0085] For each generator set, a sub-transient stability model corresponding to the generator set is constructed according to the angular velocity, inertia constant, damping ratio, mechanical power, and electromagnetic power corresponding to each generator in the generator set.

[0086] Schematically, when constructing the sub-transient stability model corresponding to the generator set, the average angular velocity, average inertia constant, average damping ratio, average mechanical power, and average electromagnetic power of each generator set can be calculated, and then a functional formula of the sub-transient stability model is constructed according to each average value, so there is:

[0087] Generate the average angular velocity corresponding to the generator set according to the angular velocity corresponding to each generator in the generator set and the number of generators;

[0088] Generate the average inertia constant corresponding to the generator set according to the inertia constant corresponding to each generator in the generator set and the number of generators;

[0089] Generate the average damping ratio corresponding to the generator set according to the damping ratio corresponding to each generator in the generator set and the number of generators;

[0090] Generate the average mechanical power corresponding to the generator set according to the mechanical power corresponding to each generator in the generator set and the number of generators;

[0091] Generate the average electromagnetic power corresponding to the generator set according to the electromagnetic power corresponding to each generator in the generator set and the number of generators;

[0092] Generate a sub-transient stability model corresponding to the generator set according to the average angular velocity, average inertia constant, average damping ratio, average mechanical power, and average electromagnetic power. Among them, the sub-transient stability model corresponding to the generator set includes:

[0093]

[0094] Among them, M n is the average inertia constant of the nth generator set, ω n is the average angular velocity of the nth generator set, is the derivative corresponding to the average angular velocity ω n P mn is the average mechanical power of the nth generator set, Pen is the average electromagnetic power of the nth generator set, D n is the average damping ratio of the nth generator set.

[0095] Schematically, the present invention can group according to the rotor angle difference between generators, so as to ensure the similarity of the dynamic responses of the generators within each group, thereby improving the accuracy of the model. Moreover, parameter aggregation reduces the number of variables to be processed, reduces the computational complexity, and improves the computational efficiency. Therefore, the grouped processing enables the generators within each group to have similar dynamic characteristics, thereby improving the accuracy of the sub-transient stability model, and further improving the accuracy of the transient stability model.

[0096] By integrating the sub-transient stability models of each generator set, a transient stability model of the entire power system is constructed, realizing the modeling process from local to global, and enabling the transient stability model to accurately characterize the dynamic response characteristics of the power system after being disturbed, including the process of restoring to the steady state. Then, based on the combination of the transient stability model and the fault scenario, and calculating the critical clearing time, a comprehensive analysis of the stability of the entire power system can be carried out, avoiding the limitations of local analysis to obtain an accurate critical clearing time.

[0097] Furthermore, by performing polynomial transformation and iterative decomposition on the transient stability model, complex non-linear problems can be transformed into polynomial solving problems, reducing the solving difficulty. And during the iterative decomposition process, when the polynomial model cannot be successfully decomposed, the polynomial to be processed generated by the last decomposition is used as the target polynomial, ensuring the feasibility of the solution, so as to obtain a feasible target transient domain.

[0098] It can be understood that in the transient stability model, the dynamic response characteristics of the power system are described by a series of differential equations, and these differential equations reflect the variation laws of each state variable (such as the power angle, angular velocity, voltage of the generator, etc.) of the power system over time after being disturbed. By solving these differential equations, the dynamic response process of the power system after being disturbed can be obtained, so as to evaluate the transient stability of the system.

[0099] The transient domain, also known as the transient security domain, defines the state space range in which the power system can maintain transient stability after being disturbed. Specifically, the transient domain refers to a set in the power injection space before the fault of the system. When the operating point of the system is in this set, the power system can still maintain transient stability after a pre-conceived fault occurs.

[0100] By solving the transient domain, the transient stability of the power system under different disturbances can be evaluated, that is, transient stability analysis. The dynamic behavior of the power system after being subjected to large disturbances (such as short-circuit faults) can be obtained, especially whether the system can return to a stable operating state. As a key component of the power system, the operating parameters of the generator (such as power angle, angular velocity, voltage, etc.) will change significantly during the transient process. Therefore, based on the current operating parameters of the generator and the transient domain, and based on the functional formula corresponding to the transient domain, the stability state of the operating state of the generator at this time (i.e., the current operating parameters) during the transient process can be calculated. The change in its value can indicate whether the system is approaching a stable or unstable state. Then, by comparing the calculated function value with the boundary threshold, it can be judged whether the system is currently in a stable state or about to enter an unstable state.

[0101] When the function value approaches or exceeds the boundary threshold, it means that the system is about to enter an unstable state. Then, by analyzing the change trend of the function value over time, the time required for the system to transition from the current state to an unstable state, that is, the critical clearing time, can be evaluated.

[0102] In a preferred embodiment, as Figure 2 shown in the flowchart, the present invention can first construct a transient stability analysis model of a power system containing n synchronous generators, and then use the generator homology identification criterion to group the generators homologically; based on the homology grouping results, after transforming the transient stability analysis model of the power system containing n synchronous generators into a homological equivalent model (i.e., the transient stability model of the power system of the present invention), after performing polynomial transformation on the homological equivalent model, a polynomial model is obtained; the polynomial model is solved by the ring domain expansion method, so as to calculate the first optimal transient stability domain of the polynomial model in the polynomial space, and then the first optimal transient stability domain is processed by polynomial inverse transformation to obtain the second optimal transient stability corresponding to the original homological equivalent model. Finally, using the second optimal transient stability of the homological equivalent model, the critical clearing time of the system under different faults is calculated.

[0103] Specifically, the dynamics of the synchronous generator can be described by the second-order swing equation. And randomly select a synchronous generator n as the reference machine. Then, the transient stability analysis model of the power system containing n synchronous generators can be expressed as:

[0104]

[0105] In the formula, is the derivative of the rotor angle of the i-th synchronous generator relative to the synchronous generator n, ω i is the angular velocity of the synchronous generator i; M i , D i are the inertia constant and damping ratio of the synchronous generator i respectively; Pmi is the mechanical power of synchronous generator i, which is a constant value; P ei is the electromagnetic power of synchronous generator i, E i is the internal electromotive force of synchronous generator i, E i is a constant value; G ij 、B ij are the conductance and susceptance between synchronous generator i and synchronous generator j respectively.

[0106] Furthermore, the generator homology identification criterion is:

[0107]

[0108] In the formula: δ in,t is the rotor angle of synchronous generator i relative to synchronous generator n at time t; δ jn,t is the rotor angle of synchronous generator j relative to synchronous generator n at time t, j = 1, 2,..., n - 1; τ is the time duration; δ∈ is the preset rotor angle threshold. Then, through the generator homology identification criterion, the rotor angle difference between two synchronous generators not greater than the preset rotor angle threshold can be divided into the same group, so that each group of generator sets has similar operating characteristics.

[0109] In a preferred embodiment, in addition to calculating the average angular velocity, average inertia constant, average damping ratio, average mechanical power, and average electromagnetic power of each group of generator sets, and then constructing the functional formula of the sub-transient stability model according to each average value, the present invention can also set the angular velocity, inertia constant, damping ratio, mechanical power, and electromagnetic power of each generator in each generator set to be the same. Then the process of constructing the homology equivalent model (i.e., the transient stability model of the power system of the present invention) is as follows:

[0110] After homology grouping, the angle center and angular velocity center of each machine group can be expressed as:

[0111]

[0112] In the formula:

[0113] Assume that each generator in the same homology machine group (i.e., the same group) has the same rotor angle, that is:

[0114]

[0115] Then the electromagnetic power of each generator in the same homology machine group can be expressed as:

[0116]

[0117] Assume that all synchronous generators have a consistent damping ratio, that is Then there is:

[0118]

[0119] Then the homology equivalent model can be:

[0120]

[0121] Schematically, is the inertia constant corresponding to the Kth generator set, is the angular velocity corresponding to the Kth generator set, is the derivative corresponding to the angular velocity ω n where P is the derivative corresponding to ω, mk is the mechanical power corresponding to the Kth generator set, and P ek is the electromagnetic power corresponding to the Kth generator set, and λ is the damping ratio corresponding to the Kth generator set.

[0122] Furthermore, when performing polynomial transformation, its expression is:

[0123]

[0124] Then the ordinary differential equation system of the transformed polynomial model can be:

[0125]

[0126] In the formula, are all polynomial functions, and the constraint G(z)=0 is used to constrain the trigonometric function terms in the electromagnetic power of the original system.

[0127] Furthermore, in a preferred embodiment, after generating the polynomial model of the transient stability model in the polynomial space, the process of iterative decomposition of the polynomial model is as follows:

[0128] Repeatedly execute the following polynomial model decomposition operation until it is determined that the polynomial model cannot be successfully decomposed, and use the polynomial to be processed generated by the last decomposition of the polynomial model as the target polynomial:

[0129] Obtain a preset parameter set, several current preset positive definite polynomials corresponding to the current iteration number, and several current preset positive numbers corresponding to the current iteration number; among them, the preset positive definite polynomials and preset positive numbers corresponding to different iteration numbers are all different;

[0130] According to the preset parameter set, each current preset positive definite polynomial, and each current preset positive number, convert each bilinear term in the polynomial model to generate several converted data items;

[0131] Decompose the polynomial model according to a set of preset parameters, each current preset positive definite polynomial, each current preset positive number, each transformed data item, and the current polynomial. When initially performing the polynomial model decomposition operation, decompose the polynomial model according to several randomly selected preset positive definite polynomials and several randomly selected current preset positive numbers to generate the current polynomial.

[0132] When it is determined that the polynomial model is successfully decomposed, use the polynomial to be processed generated by decomposing the polynomial model at the current iteration number as the current polynomial for the next execution of the polynomial model decomposition operation.

[0133] Among them, when initially performing the polynomial model decomposition operation, under the preset positive definiteness constraint and the preset negative definiteness constraint, decompose the polynomial model according to several randomly selected preset positive definite polynomials and several randomly selected current preset positive numbers to generate the current polynomial.

[0134] Among them, the positive definiteness constraint is used to represent that each parameter in the polynomial generated by decomposing the polynomial model is a positive number.

[0135] The negative definiteness constraint is used to represent that the derivative of the polynomial generated when decomposing the polynomial model with respect to time is negative.

[0136] It can be understood that when initially executed, a group is randomly selected from the preset positive definite polynomials and the set of positive numbers for decomposing the polynomial model, and the initial decomposition process is restricted by the positive definiteness constraint (ensuring that the parameters are positive numbers) and the negative definiteness constraint (ensuring that the derivative of the polynomial with respect to time is negative).

[0137] In each iteration, obtain the preset positive definite polynomial and positive number corresponding to the current iteration number, and then convert each bilinear term in the polynomial model to generate the transformed data item. Use the set of preset parameters, the current preset positive definite polynomial, the current preset positive number, and the transformed data item to decompose the polynomial model.

[0138] If the decomposition is successful, use the generated polynomial to be processed as the current polynomial for the next iteration. When it is determined that the polynomial model cannot be successfully decomposed, the iteration process terminates, and the polynomial to be processed generated in the last iteration is regarded as the target polynomial to obtain the finally solved transient domain. Then, through iterative decomposition and iterative bilinear term conversion, a simpler or more easily processed polynomial representation form can be found, thereby obtaining the optimal transient domain.

[0139] And during the initial decomposition, by ensuring that the parameters in the polynomial are positive through positive definiteness constraints, the physical meaning and mathematical stability of the model can be maintained. By ensuring that the derivative of the polynomial with respect to time is negative through negative definiteness constraints, the convergence of the system over time can be ensured, thereby obtaining the polynomial for the initial decomposition. Subsequently, based on this polynomial for the initial decomposition, the polynomial can be expanded or iteratively adjusted, and thus the optimal transient domain can be gradually approximated. Moreover, during the iterative process of the present invention, each step is optimized based on the result of the previous step, thereby continuously improving the accuracy and efficiency of the solution, making the finally obtained target polynomial (i.e., the transient domain) more accurate to assist in the accurate calculation of the subsequent critical clearing time.

[0140] In a preferred embodiment, the present invention uses the annular domain expansion method to calculate the optimal transient stability domain, and there is:

[0141] Obtain the initial transient stability domain estimation result:

[0142] 1) Solve the initial Lyapunov function: Given the positive definite polynomials p0(z), l1(z), l2(z) and the positive number β0, let p = p0(z), β = β0, and solve the sum of squares programming problem (SOSP0), and the calculation formula is as follows:

[0143]

[0144] In the formula, the first line of constraints indicates that the initial Lyapunov function V0(z) needs to be positive definite on the set {z|G(z) = 0}\{0}; the second line of constraints indicates that the derivative of the initial Lyapunov function V0(z) with respect to time needs to be negative definite on the set {z|β - p(z) ≥ 0, G(z) = 0}\{0}.

[0145] 2) Calculate the maximum value of the initial critical value: Input V0(z) and the positive definite polynomial l2(z), and solve the sum of squares programming problem (SOSP0’):

[0146]

[0147] Save the maximum value of the initial critical value as c0, then the initial transient stability domain estimation D (1) (z) = {z|V0(z) ≤ c0, G(z) = 0}, after normalization D (1) (z) = {z|V (1) (z) ≤ 1, G(z) = 0}, where V (1) (z) = V0(z) / c0.

[0148] Furthermore, expand the initial transient stability domain estimation value:

[0149] 1) Eliminate the bilinear terms: Let \(k = 1\), input parameters \(\gamma\in(0,1]\), a sufficiently small positive number \(\mu_1\), and \(V (k) (z)\) and the positive definite polynomial \(l(z)\), and solve the sum of squares programming problem (SOSP1):

[0150]

[0151] Save the calculation result \(s_3\) as \(s 3r \), and retain \(V (k) (z)\), \(\mu_1\);

[0152] 2) Expansion of the initial transient stability region: Input \(\mu_1\), \(s 3r \), \(V (k) (z)\), the positive definite polynomial \(l(z)\), and a sufficiently small positive number \(\mu_2\), and solve the sum of squares programming problem (SOSP2):

[0153]

[0154] s.t.

[0155]

[0156] In the formula, D (k) (z)=\{z|V (k) (z)\leq1, G(z) = 0\} is the transient stability region obtained in the \(k\)-th iteration, \(D (k+1) (z)=\{z|V (k+1) (z)\leq1, G(z) = 0\} is the transient stability region obtained in the \((k + 1)\)-th iteration, and the set constraint is

[0157] Furthermore, if the sum of squares programming problem (SOSP2) is feasible, then continue to expand the transient stability region; otherwise, save \(V (k+1) (z)\) as \(V(z)\), output the finally obtained target transient region, that is, the functional expression generated after solving the transient stability model of the power system, and it corresponds to a critical value.

[0158] If continuing to expand the transient stability region, then save the calculation result \(V (k+1) (z)\), and the transient stability region can be denoted as \(D (k+1) (z)=\{z|V (k+1) (z)\leq1, G(z) = 0\}, and let \(k = k + 1\), and re-expand the estimated transient stability region;

[0159] Finally, output the optimal transient stability region in the polynomial space, which can be expressed as \(D p =\{z|V(z)\leq1, G(z) = 0\}; Calculate the optimal transient stability region of the initial power system through polynomial inverse transformation, which can be expressed as \(Db = {x | V(x) ≤ 1}。

[0160] It should be noted that represents a set of N - dimensional polynomial vectors composed of M state variables, represents a set of polynomials composed of M state variables, Σ M [z ] represents a set of sum - of - squares polynomials composed of M state variables.

[0161] Therefore, the target transient domain that can be finally obtained in the embodiment of the present invention can be: D b = {x | V(x) ≤ 1}, then each operating parameter x(t) collected during the fault can be substituted into D b = {x | V(x) ≤ 1} for calculating the corresponding function value, and when it is determined that V(x(t)) corresponding to any one operating parameter reaches c, that is, not less than c, and c is the critical value corresponding to the target transient domain, it can be used as the preset boundary threshold. Finally, the fault duration when V(x(t)) reaches c is calculated, and the corresponding fault duration is the critical clearing time of the system.

[0162] It can be understood that the present invention first obtains an initial Lyapunov function by solving the sum - of - squares programming problem (SOSP), and calculates the initial transient stability region estimation result accordingly. Then, through a series of iterative steps, including eliminating bilinear terms and expanding the initial transient stability region, the estimated transient stability region is gradually optimized and expanded. In each iteration, the corresponding sum - of - squares programming problem is solved to update the Lyapunov function and the transient stability region. When the iteration cannot further expand the transient stability region, the current Lyapunov function is regarded as the final result, and the corresponding target transient domain is output, and the optimal transient stability region under the initial power system is obtained through polynomial inverse transformation. Finally, the operating parameters collected during the fault are substituted into the target transient domain for calculation to determine the stability of the system and calculate the critical clearing time.

[0163] Therefore, through solving the sum - of - squares programming problem and iterative optimization steps in the embodiment of the present invention, a more accurate Lyapunov function and transient stability region estimation result can be obtained, so as to more accurately reflect the transient stability of the power system. Although it involves the solution of multiple sum - of - squares programming problems, the whole process is carried out in the polynomial space, which can improve the calculation efficiency while ensuring the accuracy.

[0164] In a preferred embodiment, as Figure 3 shown, taking a large - scale power system with 73 nodes and 15 synchronous generators as the research object, let τ = 40s, δε = 10°, through the homology identification criterion, the identification result of the generator homology machine group is as Figure 4As shown, it can be concluded that synchronous generators G1 - G15 are respectively located at nodes 59 - 73, and the generators can be divided into four coherent generator groups, namely A1 = {G1, G8, G 10 , G 14 , G 15}, A2 = {G2, G4, G 11 , G 12 , G 13}, A3 = {G3, G5, G7, G9}, A4 = {G6}.

[0165] After constructing the sub - transient stability models corresponding to each coherent generator group, the corresponding transient stability model is obtained. By solving this transient stability model to obtain the transient domain, the fault operation conditions of the power system can be calculated based on the transient domain, and the stability margins corresponding to each operating parameter during the fault can be obtained to further evaluate the critical clearing time corresponding to the power system.

[0166] As Figure 5 shown, based on the above embodiments of the method for determining the critical clearing time of various power systems, the present invention correspondingly provides an apparatus - related embodiment;

[0167] An embodiment of the present invention provides a device for determining the critical clearing time of a power system, including: a fault time determination module and a critical clearing time generation module;

[0168] The fault time determination module is configured to use the time when a fault occurs in the power system as the initial fault time when detecting a fault in the power system;

[0169] The critical clearing time generation module is configured to repeatedly perform the following function value calculation operations until it is determined that there is a function value not less than a preset boundary threshold, and then generate the critical clearing time corresponding to the power system according to the initial fault time and the current time:

[0170] Obtain the current operating parameters corresponding to each generator in the power system at the current time;

[0171] For each generator, calculate the function value corresponding to the generator according to the current operating parameters of the generator and the target transient domain for measuring the system stability; wherein, the target transient domain is used to represent the functional formula generated after solving the transient stability model of the power system;

[0172] When it is determined that any function value is less than the preset boundary threshold, perform the next function value calculation operation; wherein, the preset boundary threshold is used to represent the stability margin corresponding to the situation where the system cannot maintain stable operation.

[0173] It should be noted that the device embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separated. The components shown as modules may or may not be physical modules. They may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. In addition, in the attached drawings of the device embodiments provided by the present invention, the connection relationships between the modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those of ordinary skill in the art can understand and implement this without creative efforts.

[0174] Those skilled in the art can clearly understand that for the convenience and brevity, the specific working process of the device described above can refer to the corresponding process in the foregoing method embodiments, and will not be elaborated here.

[0175] Based on the embodiments of the above various methods for determining the critical clearing time of a power system, the present invention correspondingly provides embodiments of a terminal device.

[0176] An embodiment of the present invention provides a terminal device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements a method for determining the critical clearing time of a power system according to any one of the method embodiments of the present invention.

[0177] The terminal device may be a computing terminal device such as a desktop computer, a notebook, a palm computer, and a cloud server. The terminal device may include, but is not limited to, a processor and a memory.

[0178] The so-called processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The processor is the control center of the terminal device, connecting various parts of the entire terminal device through various interfaces and lines.

[0179] The memory can be used to store the computer program. By running or executing the computer program stored in the memory and invoking the data stored in the memory, the processor realizes various functions of the terminal device. The memory mainly includes a program storage area and a data storage area. Among them, the program storage area can store the operating system, application programs required for at least one function, etc.; the data storage area can store data created according to the use of the mobile phone, etc. In addition, the memory can include high-speed random access memory, and can also include non-volatile memory, such as hard disks, memory, plug-in hard disks, smart media cards (SMCs), secure digital (SD) cards, flash cards, at least one magnetic disk storage device, flash memory device or other volatile solid-state storage devices.

[0180] Based on the embodiments of the above various methods for determining the critical clearing time of the power system, the present invention correspondingly provides an embodiment of the storage medium.

[0181] An embodiment of the present invention provides a storage medium, which includes a stored computer program. When the computer program runs, it controls the device where the computer-readable storage medium is located to execute a method for determining the critical clearing time of a power system according to any one of the method embodiments of the present invention.

[0182] The storage medium is a computer-readable storage medium, and the computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the above various method embodiments. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file or some intermediate form, etc. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0183] The above is the preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art of the present technology, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A method for determining the critical removal time of a power system, characterized in that: include: When a fault in the power system is detected, the time when the fault occurs is taken as the initial fault time; The following function value calculation operation is repeatedly performed until it is determined that there is a function value that is not less than the preset boundary threshold, then the critical removal time corresponding to the power system is generated according to the initial fault time and the current time: Obtain the current operating parameters corresponding to each generator in the power system at the current moment; For each generator, a function value corresponding to the generator is calculated based on the current operating parameters of the generator and a target transient domain used to measure system stability; wherein the target transient domain is used to represent a function generated after solving a transient stability model of the power system; When it is determined that any function value is less than a preset boundary threshold, the next function value calculation operation is performed; wherein the preset boundary threshold is used to characterize the stability margin corresponding to when the system cannot maintain stable operation.

2. A method for determining the critical removal time of a power system according to claim 1, characterized in that: The generation of the target transient domain includes: Obtain the operating parameters corresponding to each generator set in the power system; Constructing a transient stability model corresponding to the power system according to the operating parameters corresponding to each generator; wherein the transient stability model is used to characterize the response characteristics of the power system in restoring a steady-state operating state after being disturbed; Performing polynomial transformation on the transient stability model to generate a polynomial model corresponding to the transient stability model in a polynomial space; The polynomial model is iteratively decomposed based on a preset parameter set, a plurality of different preset positive definite polynomials and a plurality of different preset positive numbers. When it is determined that the polynomial model cannot be decomposed successfully, the polynomial to be processed generated by the last decomposition is used as a target polynomial; wherein the target polynomial includes: a plurality of state variables for representing the operating parameters of the generator; Performing an inverse polynomial transformation on the target polynomial to generate a target transient domain corresponding to the transient stability model.

3. A method for determining the critical removal time of a power system according to claim 2, characterized in that: The operating parameters corresponding to the generator include: angular velocity, inertia constant, damping ratio, mechanical power, electromagnetic power, and a rotor angle used to characterize the angle between the generator and a preset reference generator; the transient stability model includes: a plurality of sub-transient stability models; The step of constructing a transient stability model corresponding to the power system according to the operating parameters corresponding to each generator includes: According to the rotor angles corresponding to the generators, the generators are divided into a number of different generator groups; wherein the rotor angle difference between any two generators in each generator group is not greater than a preset rotor angle threshold; For each generator set, a sub-transient stability model corresponding to the generator set is constructed according to the angular velocity, inertia constant, damping ratio, mechanical power and electromagnetic power corresponding to each generator in the generator set.

4. A method for determining the critical removal time of a power system according to claim 3, characterized in that: The sub-transient stability model corresponding to the generator set is constructed according to the angular velocity, inertia constant, damping ratio, mechanical power and electromagnetic power corresponding to each generator in the generator set, including: Generate an angular velocity mean value corresponding to the generator set according to the angular velocity corresponding to each generator in the generator set and the number of generators; According to the inertia constant corresponding to each generator in the generator set and the number of generators, a mean inertia constant corresponding to the generator set is generated; Generate a damping ratio mean value corresponding to the generator set according to the damping ratio corresponding to each generator in the generator set and the number of generators; Generate a mechanical power mean value corresponding to the generator set according to the mechanical power corresponding to each generator in the generator set and the number of generators; According to the electromagnetic power corresponding to each generator in the generator set and the number of generators, an average electromagnetic power corresponding to the generator set is generated; A sub-transient stability model corresponding to the generator set is generated according to the angular velocity mean value, the inertia constant mean value, the damping ratio mean value, the mechanical power mean value and the electromagnetic power mean value.

5. A method for determining the critical removal time of a power system according to claim 4, characterized in that: The sub transient stability model corresponding to the generator set includes: in, is the mean inertia constant of the Kth generator set, is the mean angular velocity of the Kth generator set, is the mean angular velocity ω n The corresponding derivative, P mk is the mean mechanical power of the Kth generator set, P ek is the mean electromagnetic power of the K-th generator set, and λ is the mean damping ratio of the K-th generator set.

6. A method for determining the critical removal time of a power system according to claim 5, characterized in that: The iterative decomposition of the polynomial model based on a preset parameter set, a plurality of different preset positive definite polynomials and a plurality of different preset positive numbers, and when it is determined that the polynomial model cannot be successfully decomposed, using the to-be-processed polynomial generated by the last decomposition of the polynomial model as the target polynomial, comprises: Repeat the following polynomial model decomposition operation until it is determined that the polynomial model cannot be decomposed successfully, and use the to-be-processed polynomial generated by the last decomposition of the polynomial model as the target polynomial: Obtaining a preset parameter set, a number of current preset positive definite polynomials corresponding to the current number of iterations, and a number of current preset positive numbers corresponding to the current number of iterations; wherein the preset positive definite polynomials and preset positive numbers corresponding to different numbers of iterations are different; According to the preset parameter set, each current preset positive definite polynomial and each current preset positive number, each bilinear term in the polynomial model is transformed to generate a plurality of transformed data terms; Decomposing the polynomial model according to a preset parameter set, each current preset positive definite polynomial, each current preset positive number, each converted data item and the current polynomial; wherein, when the polynomial model decomposition operation is performed for the first time, the polynomial model is decomposed according to a number of randomly selected preset positive definite polynomials and a number of randomly selected current preset positive numbers to generate the current polynomial; When it is determined that the polynomial model is successfully decomposed, the to-be-processed polynomial generated by decomposing the polynomial model at the current number of iterations is used as the current polynomial for the next execution of the polynomial model decomposition operation.

7. A method for determining the critical removal time of a power system according to claim 6, characterized in that: When the polynomial model decomposition operation is performed for the first time, the polynomial model is decomposed according to a number of randomly selected preset positive definite polynomials and a number of randomly selected current preset positive numbers to generate a current polynomial, including: When the polynomial model decomposition operation is performed for the first time, under a preset positive definiteness constraint and a preset negative definiteness constraint, the polynomial model is decomposed according to a number of randomly selected preset positive definite polynomials and a number of randomly selected current preset positive numbers to generate a current polynomial; The positive definiteness constraint is used to characterize that each parameter in the polynomial generated by decomposing the polynomial model is a positive number; The negative definiteness constraint is used to indicate that the derivative of the polynomial generated when the polynomial model is decomposed with respect to time is negative.

8. A device for determining critical removal time of an electric power system, characterized in that: include: Fault moment determination module and critical removal time generation module; The fault time determination module is used to, when a fault is detected in the power system, use the time when the fault occurs as the initial fault time; The critical removal time generation module is used to repeatedly perform the following function value calculation operation until it is determined that there is a function value that is not less than a preset boundary threshold, and then generate a critical removal time corresponding to the power system according to the initial fault time and the current time: Obtain the current operating parameters corresponding to each generator in the power system at the current moment; For each generator, a function value corresponding to the generator is calculated based on the current operating parameters of the generator and a target transient domain used to measure system stability; wherein the target transient domain is used to represent a function generated after solving a transient stability model of the power system; When it is determined that any function value is less than a preset boundary threshold, the next function value calculation operation is performed; wherein the preset boundary threshold is used to characterize the stability margin corresponding to when the system cannot maintain stable operation.

9. A terminal device, characterized in that: The method comprises a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, a method for determining a critical cut-off time of an electric power system as claimed in any one of claims 1 to 7 is implemented.

10. A storage medium, characterized in that: The storage medium includes a stored computer program, wherein when the computer program is executed, the device where the storage medium is located is controlled to execute a method for determining a critical cut-off time of a power system according to any one of claims 1 to 7.

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