Parallel time-domain simulation method for power system transient stability based on two-layer quantum solving

Abstract

The present application relates to the field of power system transient stability parallel time domain simulation and quantum computing technology, especially to a power system transient stability parallel time domain simulation method based on double-layer quantum solution.The present application divides the total simulation time interval into multiple sub-intervals to construct quantum rough operators;each sub-interval is divided into multiple small intervals, and the full time domain integrated correction equation set is constructed by using the block integrated parallel path, the quantum fine operator is constructed based on the small interval to solve the correction equation set, and the quantum fine calculation result of each sub-interval is obtained.The present application constructs a double-layer quantum solution system through quantum fine operators and quantum rough operators, divides the full time domain of transient stability time domain simulation into multiple sub-intervals for parallel solution, breaks the strict time sequence dependence under the traditional serial recursive framework, avoids the overall calculation process being completely constrained by the sequence of previous and subsequent time steps, and thus improves the overall calculation efficiency of transient stability time domain simulation.

Description

Technical Field

[0001] This invention relates to the field of parallel time-domain simulation and quantum computing technology for transient stability of power systems, and in particular to a parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution. Background Technology

[0002] In power system transient stability calculations, time-domain simulation holds a fundamental and dominant position. With the continuous integration of high proportions of renewable energy and power electronic equipment, new power systems exhibit "dual-high" characteristics, and their operating mode has shifted from source-following-load dynamics to multi-directional interaction between sources, grid, load, and storage, resulting in greater volatility and uncertainty in the power system and making stability problems more complex. Simultaneously, the expansion of power system scale has led to the curse of dimensionality in time-domain simulation, making it difficult for traditional classical computers to meet the efficiency requirements of real-time power grid simulation in the future.

[0003] With the development of quantum computing, theoretically, high-dimensional problems can be solved quickly by utilizing the superposition and entanglement properties of quantum states, based on the principles of quantum mechanics. This provides a new solution to the curse of dimensionality problem encountered in solving complex large-scale systems. Current research has used the HHL algorithm to construct a quantum Newton-Raphson method within a serial simulation framework to improve the efficiency of single-step simulations. While this method can effectively accelerate the solution efficiency of single-step simulations under ideal conditions, the entire simulation process is still limited by the time-series dependency of the recursion within the serial framework. For transient stability time-domain simulations, to ensure numerical stability, the simulation step size is generally set small. For medium- to long-term simulations, this means thousands or even tens of thousands of time-step recursions are required, and the serial framework still limits the overall efficiency of time-domain simulations. Classical simulations address the time-series dependency problem by introducing algorithms such as Parareal time-parallelism. However, this algorithm requires allocating each sub-interval to different classical processors for computation, and its effectiveness is highly dependent on the number of classical processors as parallelism increases, thus limiting the linear scaling of classical hardware.

[0004] It is evident that there is currently a lack of a quantum parallel computing method suitable for transient stability time-domain simulation of power systems that can alleviate timing dependence, reduce reliance on the parallel stacking of multiple classical processors, and improve the overall time-domain simulation efficiency. Summary of the Invention

[0005] To address the limitations of timing dependence in serial time-domain simulation and the reliance on multiple classical processors in parallel stacking for classical time-parallel methods, this invention proposes a parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution. This method can alleviate timing dependence while reducing reliance on multiple classical processors, thereby improving the efficiency of transient stability time-domain simulation.

[0006] The invention provides a parallel time-domain simulation method for power system transient stability based on two-layer quantum solution, which comprises the following steps: S1, establishing a time-domain simulation model for power system transient stability and obtaining initial system values through simulation ; S2, dividing the total simulation time interval into a plurality of sub-intervals by using the time division parallel idea; the sub-interval division points, the fault occurrence time and the fault clearing time are arranged in chronological order to form a sample point sequence; S3, constructing a quantum coarse operator by using a transient stability time-domain simulation method based on quantum Newton-Raphson method, performing quantum recursion on the sample point sequence in combination with system initial values, and extracting recursion results of each sub-interval division point, which are recorded as quantum coarse calculation results ; n is the index of a sub-interval division point, and N is the total number of sub-intervals; S4, dividing each sub-interval into a plurality of small intervals; S5, constructing a full-time-domain integrated correction equation by using blocked integrated parallel paths, constructing a quantum fine operator based on the small intervals to solve the correction equation, and obtaining quantum fine calculation results of each sub-interval; S6, performing serial correction on the quantum fine calculation results and quantum coarse calculation results of each sub-interval division point by using a differential-algebraic separation correction strategy, and obtaining serial correction results of each sub-interval division point; S7, determining whether all end points of sub-intervals satisfy the condition of convergence or locking; if the condition is not satisfied and k<N, locking the serial correction results of sub-intervals 1 to k, then updating k to k+1, and returning to step S5 to recalculate the quantum fine calculation results of sub-intervals k+1 to N; otherwise, outputting the simulation results and the number of serial correction iterations ; in the recursion process of quantum coarse calculation and quantum fine calculation, whenever encountering the fault occurrence time or the fault clearing time , updating algebraic variables through algebraic jump calculation by combining state differential variables to update the calculation result, and performing next-step recursion by using the updated calculation result.

[0007] preferably, the quantum fine calculation process of sub-interval n in step S5 comprises the following sub-steps: S51, dividing small intervals on the sub-interval n; initializing the simulation time step of each sub-interval as the starting end point of the sub-interval; S52. The implicit trapezoidal method is used to perform difference processing on the system's state differential equations. After elimination, the residual equations are formed together with the algebraic equations. The residual vector is solved based on the residual equations of each sub-interval. Then, the correction equations of each sub-interval are constructed. S53. Combine the correction equations of each sub-interval to reconstruct the correction equation set for the entire time domain; S54. Construct a quantum linear solver using the HHL algorithm to solve the corrected equation system and obtain the full-time domain corrected vector composed of the corrected vectors to be solved at each sub-interval division point n; use a classical computer to restore the full-time domain corrected vector to the independent corrected vectors of each sub-interval. S55. Determine whether all correction vectors have converged; If not, for the unconverged subinterval, update the system variables by combining the correction vector, then combine the correction equation and return to step S54; Yes, the simulation time step is obtained. Calculate the results of the sub-intervals on the above; then proceed to step S56; S56, Determine t n Is it the end time of subinterval n? No, then update t n Find the next subinterval division point adjacent to subinterval n; then return to step S52; Yes, then the simulation time step will be... The result of the sub-interval calculation is used as the quantum precision calculation result of the sub-interval division point n.

[0008] Preferably, the modified equation set constructed in step S53 is as follows: ; in, Represents the full-time residual vector. This represents the Jacobian matrix of the block-wise integration across the entire time domain. This represents the full-time correction vector to be solved; Given the residual vector of the known subinterval partition point n, it is obtained by solving the residual equation system of the subinterval; Let be the Jacobian matrix of the subinterval partition point n, which is obtained by differentiating the corresponding residual equation; Let n be the correction vector to be solved for the sub-interval division point n; The constraints of the corrected system of equations are: All are Hermitian matrices. Satisfying the power of 2 and It is a unit vector.

[0009] Preferably, let the state differential variables involved in the subsequent calculation of the corrected equations be denoted as... The algebraic variables involved in the subsequent calculation of the corrected system of equations are denoted as The state differential variable that is eliminated during dimensionality reduction is denoted as the intermediate differential variable. The algebraic variables that are eliminated during dimensionality reduction are denoted as intermediate algebraic variables. ; =( , ); The correction amount is the state differential variable for the subinterval division point n participating in the calculation of the subsequent corrected equation system. The algebraic variable correction amount for the subinterval division point n participating in the calculation of the subsequent corrected system of equations; In step S55, on each sub-interval, based on the correction vector... Calculate the next time step and Then use and Solving for the results and .

[0010] Preferably, in step S6, the state differential variables after correction for each sub-interval segmentation point are first obtained using the following formula. : ; ; in, and Let n represent the state differential variables in the coarse calculation results of the n-th quantum interval segmentation point in the k-th and (k-1)-th serial corrections, respectively. This represents the state differential variable correction amount of the sub-interval division point n in the k-th serial correction process; It is the state differential variable in the quantum precision calculation result of sub-interval partition point n in the k-th serial correction; k is the serial correction number, with an initial value of 0; when k>1, the serial correction result of sub-interval partition point n-1 after the (k-1)-th serial correction is used. Using this as the starting value, the quantum coarse calculation result of the subinterval partition point n is recursively derived using the quantum coarse operator on the corresponding subinterval. ; Then Substituting into the network algebraic equations and performing an algebraic jump calculation, we obtain the algebraic variables of the subinterval partition point n after the k-th serial correction. The serial correction result of the sub-interval segmentation point n after the k-th serial correction. =( , ).

[0011] Preferably, in step S7, the rotor angle is extracted from the serial correction results. As a criterion, if the absolute value of the difference between the rotor angle obtained in this serial correction and the rotor angle obtained in the previous serial correction converges, then the sub-interval division point n is deemed to satisfy the convergence condition.

[0012] Preferably, the simulation results output in step S7 include the serial correction results of all sub-interval division points and small-interval division points obtained from the last serial correction.

[0013] Preferably, in step S2, the total simulation time interval is first divided into multiple sub-intervals using a set large step size H, and then the endpoints of the sub-intervals and the time of fault occurrence are determined. and fault clearing time All of them were used as sample points.

[0014] The present invention proposes a parallel time-domain simulation system for transient stability of power systems based on two-layer quantum solution, characterized in that it includes a memory and a processor. The memory stores a computer program, and the processor is connected to the memory. The processor is used to execute the computer program to realize the parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution.

[0015] The present invention proposes a storage medium storing a computer program, which, when executed, is used to implement the aforementioned parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution.

[0016] The advantages of this invention are: (1) This invention constructs a two-layer quantum solution system by using quantum precise operator and quantum coarse operator, which divides the entire time domain of transient stable time domain simulation into multiple sub-intervals for parallel solution. This breaks the strict time sequence dependency under the traditional serial recursion framework, avoids the overall calculation process being completely constrained by the order of the preceding and following time steps, and thus improves the overall computational efficiency of transient stable time domain simulation.

[0017] (2) In view of the problem that classical time parallel methods rely on the parallel stacking of multiple classical processors under high parallelism, this invention proposes a block-integrated parallel quantum precision computing path, which reconstructs the transient correction equations corresponding to each sub-interval into a block-diagonal matrix linear equation system, and uses a single quantum processor to complete the integrated parallel solution, thereby reducing the dependence on the parallel stacking of multiple classical processors and providing a new implementation method for parallel time-domain simulation under the quantum framework.

[0018] (3) After adopting the block-integrated parallel path, the present invention can effectively reduce the consumption of quantum resources while increasing the parallelism and shows high theoretical acceleration potential. It is beneficial to improve the overall performance of the parallel time-domain simulation of power system transient stability while taking into account both parallel efficiency and resource overhead.

[0019] (4) In summary, this invention divides the entire time domain into multiple sub-intervals, uses a quantum coarse operator to obtain the initial trajectory, and reconstructs the transient correction equations of each sub-interval into a block-diagonal matrix linear equation system. Then, it performs block-integrated parallel quantum fine computation, and combines differential algebraic separation correction to obtain the transient stability simulation results. In this invention, the quantum fine computation on each sub-interval can be performed by a single quantum processor, thereby alleviating the time-series dependence and the dependence on multiple classical processors, and improving the efficiency of transient stability time-domain simulation. Attached Figure Description

[0020] Figure 1 The flowchart is a method for parallel time-domain simulation of transient stability of power systems based on two-layer quantum solution proposed in this invention. Figure 2 A schematic diagram of time-parallel full-time domain sub-interval partitioning; Figure 3(a) shows the sub-interval division under the first fault timing; Figure 3(b) shows the sub-interval division under the second type of fault timing; Figure 3(c) shows the sub-interval division under the third type of fault timing; Figure 4 For block-integrated parallel quantum precision computing data interaction; Figure 5 This is a flowchart of quantum precision computing. Figure 6(a) shows the rotor angle difference between node 1 and node 2 under different parallelism (i.e., the number of subintervals N). Compare simulation results with serial benchmarks; Figure 6(b) shows the rotor angle difference between node 2 and node 3 under different parallelisms. Compare simulation results with serial benchmarks; Figure 6(c) shows the rotor angle difference between node 3 and node 1 under different parallelisms. Compare simulation results with serial benchmarks; Figure 7(a) Comparison of qubit consumption for different paths; Figure 7(b) Comparison of quantum gate consumption for different paths; Figure 8 Number of iterations, quantum circuit depth and theoretical speedup under different degrees of parallelism. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] Parameter definitions: The superscript "→" represents a system variable, the superscript "^" represents a coarse quantum calculation result, and the superscript "~" represents a fine quantum calculation result; the superscript "k" represents the number of serial corrections; the subscript "n0" represents the uncorrected calculation result of sub-interval division point n, and the subscript "cn" represents the corrected calculation result of sub-interval division point n.

[0023] like Figure 1 As shown in the figure, the proposed method for parallel time-domain simulation of transient stability of power systems based on two-layer quantum solution includes the following steps S1-S7.

[0024] S1. Establish a time-domain simulation model of the transient stability of the power system and complete the system simulation calculation to obtain the initial values ​​of the system. .

[0025] System variables include the state differential variables of the system of equations before dimensionality reduction. and algebraic variables ; and Only some parameters participate in the subsequent calculation of the modified equations. Let the state differential variables participating in the subsequent calculation of the modified equations be denoted as... The algebraic variables involved in the subsequent calculation of the corrected system of equations are denoted as The state differential variable that is eliminated during dimensionality reduction is denoted as the intermediate differential variable. The algebraic variables that are eliminated during dimensionality reduction are denoted as intermediate algebraic variables. ;but , .

[0026] make and The state differential variables at time t are respectively and algebraic variables , and These are the times at time t=0 (i.e., the initial moment of the simulation). and ; and These are the initial system values ​​for all differential and algebraic variables, respectively, i.e., the full simulation time. The initial value; ; This step establishes transient time-domain simulation models for each component of the system, including the synchronous generator model, load model, prime mover and its governor model, excitation system model, and network model. The system simulation values ​​are: .

[0027] Read the network topology parameters, line parameters, component parameters, fault occurrence time, fault clearing time, and total simulation duration of the power system to be simulated. Calculate the initial time of the full simulation based on the system's steady-state power flow results. The system's steady-state simulation values ​​are the initial values ​​of the system. Ultimately, the model of each component in the system comprises two parts: state differential equations and algebraic equations. The time-domain simulation of the transient stability of a power system can be described as a simulation value problem involving the following differential-algebraic equation system: ; In the formula, The system of differential equations for the system at time t. The system of algebraic equations for the system at time t; Calculate the time within the total simulation duration for the current time step. This represents the total simulation duration.

[0028] S2. The total simulation time is divided into multiple sub-intervals using the time-division parallel approach.

[0029] like Figure 2 As shown, the total simulation time interval The total simulation time interval is divided into N sub-intervals, and the sub-interval n is denoted as nn. , ,in , The length of each subinterval is H is the set large step size. The endpoints of the sub-intervals are T0, T1, T2, ..., T... n ... T N Let n be the subinterval split point, and let n be the subinterval split point T. n The total number of sub-interval division points is N+1. Specifically, the start and end times of each sub-interval are sequentially arranged and denoted as sub-interval division points 0~N. The simulation time corresponding to sub-interval n is (T... n-1 ,T n );T n-1 and T n These represent the times corresponding to the sub-interval division points n-1 and n, respectively.

[0030] At this point, the original simulation value problem is divided into the following: A series of interconnected sub-problems: ; In the formula, subscript Represents the sub-interval split point index. and Let n represent the state differential variable and algebraic variable at the subinterval division point n at time t, respectively; and They represent time respectively The state differential variables and algebraic variables on the interval n, that is, the state differential variables and algebraic variables on the starting time of the subinterval n; and Let n represent the initial values ​​of the state differential variable and the initial values ​​of the algebraic variable at the subinterval division point n, respectively.

[0031] Based on the above segmentation, the full-time transient stability simulation problem is transformed into: finding the state differential variables at the sub-interval segmentation points n=1, 2, ..., N. and algebraic variables Specifically, the calculation is performed step by step within each sub-interval, and the calculation between each sub-interval is parallel. Through continuous iterative correction, the calculation results of the sub-interval division points gradually approach the real full-time domain simulation trajectory.

[0032] Specifically, in step S2, a large step size H is used to set sub-interval division points on the total simulation time interval; and the sub-interval division points and the fault occurrence time are then set. and fault clearing time Arrange the sample points chronologically to form a sequence; if the fault occurs at the time... Or the time of fault clearance If a point overlaps with any sub-interval dividing point, it is merged; let the total number of sample points be M, where M≥N.

[0033] Specifically, in this embodiment, the total simulation time interval is first defined. Divide the interval into N sub-intervals with a large step size H; then, based on the time of fault occurrence... and fault clearing time By relating the data to the sub-intervals, we obtain the final sequence of sample points, which can be divided into the following three cases: S2A, as shown in Figure 3(a), the time of fault occurrence and fault clearing time Within the same subinterval m, the corresponding simulation time is This occurs within a short period; at this time, the number of sample points M = N + 2, and the time points corresponding to sample points 0 to M are: 0, T1, T2, ..., T m-1 , , T m T m+1 ... T N T1, T2, T m-1 T m T m+1 and TN These are the endpoint times for sub-intervals 1, 2, m-1, m, m+1, and N, respectively. S2B, as shown in Figure 3(b): Time of fault occurrence and fault clearing time Spanning different sub-intervals m and s, the corresponding simulation times are respectively and Among them, T m-1 and T m Let T represent the start and end times of subinterval m, respectively. s-1 and T s Let T and T' represent the start and end times of the sub-interval s, respectively. At this point, the number of sample points M = N + 2, and the time intervals corresponding to sample points 0 to M are: 0, T1, T2, ..., T... m-1 , T m T m+1 ... T s-1 , T s T s+1 ... T N T1, T2, T m-1 T m T m+1 T s-1 T s T s+1 、 and T N These are the endpoint times of sub-intervals 1, 2, m-1, m, m+1, s-1, s, s+1, and N, respectively. S2C, as shown in Figure 3(c): Fault occurrence time and fault clearing time It coincides exactly with the boundary of the sub-interval, at which point M=N, and the sample points correspond one-to-one with the sub-interval dividing points. This is the most ideal case for calculation.

[0034] S3. Construct a quantum coarse operator using a transient stability time-domain simulation method based on the quantum Newton-Raphson method, and recursively derive the quantum coarse calculation results for each sub-interval division point based on the initial system value. .

[0035] Specifically, in step S3, the initial value of the system is used as the initial value of the sub-interval division point 0. The initial values ​​for each sample point are recursively derived using the quantum Newton-Raphson method; the initial values ​​for the sub-interval division points are extracted from the sample points as the original quantum coarse calculation results. ; ; in, Represents the initial value of the system; This represents the original coarse quantum calculation result for sub-interval partition point 0 (which is also sample point 0); This represents the original coarse quantum calculation result for the subinterval partition point n; and Representing sample points respectively The original quantum coarse calculation result of sample point n, QG represents the quantum coarse operator based on the recursion of sub-intervals (more precisely, the step size between adjacent sample points).

[0036] It is worth noting that during the recursive process, when the sample point is the time when the fault occurs... Or the time of fault clearance If the quantum coarse calculation results are not updated, the specific method is as follows: update the quantum coarse calculation results from the sample points. Extracting state differential variables And perform algebraic jump calculations to obtain the algebraic variables after the jump; Replace the algebraic variables in the original text with the algebraic variables after the jump, and complete the process. renew.

[0037] Specifically, between two adjacent sample points, given the variables of the previous sample point n, a rough estimate of the next sample point n+1 can be obtained through iterative calculation using the quantum Newton-Raphson method; this is the quantum coarse calculation result. The specific method involves differentiating the state differential equations using the implicit trapezoidal rule to obtain a system of difference algebraic equations. After eliminating variables and reducing the dimensionality of this system, it is combined with the algebraic equations to form a residual equation system. The Newton-Raphson method is then used to obtain the transient stability correction equation system, and finally, the HHL algorithm is used to construct a quantum linear solver for efficient solution. Thus, given the initial values ​​of the system variables... and Under the premise that the quantum coarse calculation results of each sub-interval division point can be obtained by recursion on the sample point sequence, the result of each sub-interval division point can be obtained.

[0038] S4. In each subinterval, based on the small step size Set interval division points on the sub-interval, with each interval division point including both endpoints of the sub-interval; and record the time of fault occurrence. and fault clearing time Add it to the subinterval dividing point of the corresponding subinterval; two adjacent subinterval dividing points in the subinterval form a subinterval.

[0039] S5. Construct a full-time integrated modified equation system using a block-based integrated parallel path, and solve the modified equation system based on a quantum precise operator built on sub-intervals to obtain the quantum precise calculation results for each sub-interval; specifically as follows: Figure 4 As shown.

[0040] Specifically, within each sub-interval, the quantum precise calculation results at each sub-interval division point are recursively derived using the quantum Newton-Raphson method. The quantum precise calculation result at the last sub-interval division point is then used as the quantum precise calculation result at the end point of the sub-interval (i.e., the final time). ; ; in, denoted as the quantum precise calculation result of the neutron interval division point n in the k-th serial correction, and QF represents the quantum precise operator based on the recursion of the small interval; and These are the state differential and algebraic variables of the sub-interval segmentation point n in the k-th serial correction. and These are the correction values ​​(i.e., the serial correction results) of the sub-interval segmentation point n-1 after the (k-1)th and kth serial corrections, respectively. and yes State differential variables and algebraic variables in the equation; .

[0041] It is worth noting that during quantum precision computing, when a fault occurs... Or the time of fault clearance It is necessary to combine the state differential variables. Updated via algebraic jump calculation Thus, the updated .

[0042] S6. Use a differential algebra separation correction strategy for serial correction.

[0043] This step S6 specifically includes the following sub-steps: S61. Correct the state differential variable.

[0044] Calculate the correction amount for the state differential variable: ; In the formula, This represents the state differential variable correction amount of the sub-interval division point n in the k-th serial correction process; This is the result of the quantum precision calculation of the neutron interval partition point n in the k-th serial correction. The state differential variable in; This is the result of the quantum coarse calculation of the neutron interval partition point n in the (k-1)th serial correction. The state differential variable in; ; QG represents the quantum coarse operator; Indicates the sample points in the k-th serial correction. The results of the quantum coarse calculation, Represents sample points The corrected variables; This indicates that in the k-th serial correction, based on sample points variables The quantum Newton-Raphson algorithm is used to recursively calculate the sample points. The quantum coarse calculation process; k represents the number of serial corrections; During the sample point recursion process, the variable for the next sample point is calculated using the quantum Newton-Raphson method based on the corrected variable of the previous sample point, serving as the quantum coarse calculation result; when the sample point is the time of fault occurrence... Or the time of fault clearance The result of the quantum coarse calculation An update is needed, specifically: based on the coarse quantum calculation results from the sample points. Extracting state differential variables And perform algebraic jump calculations to obtain the algebraic variables after the jump; then use the quantum coarse calculation results Replace the algebraic variables in the original text with the algebraic variables after the jump, and complete the coarse quantum calculation results. renew; This represents the coarse quantum calculation result of the neutron interval segmentation point n in the k-th serial correction. .

[0045] Thus, in both quantum fine computing and quantum coarse computing, whenever a fault occurs... Or the time of fault clearance Then, by combining the state differential variables and updating the algebraic variables through algebraic jump calculations, the updated calculation result X is obtained. In this way, it is equivalent to performing an initial value calculation of the system when the system state changes (fault occurs or fault is cleared), fully considering the impact of the system state change on the algebraic variables, so that the quantum recursion process closely follows the system state change and ensures the accuracy of the recursion.

[0046] Correcting the state differential variable using a correction factor: ; In the formula, Let n be the differential state variable of sub-interval partition point n after the kth serial correction. This represents the state differential variable in the coarse quantum calculation result of the n quantum interval division point in the k-th serial correction neutron.

[0047] S62, will Substituting the equations into the network algebraic equations and performing a first algebraic jump calculation, i.e., solving for the equations that satisfy... of which is an algebraic variable of the subinterval division point n after the k-th serial correction; obtaining serial correction results of end points of each subinterval of the system =( , ).

[0048] S7: extracting rotor angles from the serial correction results , and judging whether the following condition is satisfied: ; is the rotor angle of the subinterval division point n after the (k-1)-th serial correction; is a serial correction convergence tolerance; if the condition is not satisfied and k<N, locking the serial correction results of subintervals 1 to k, that is, locking the calculation results of all subinterval division points and small interval division points on subintervals 1 to k, then updating k to k+1, and returning to step S5 to recalculate subinterval division points k+1 to N; if the condition is satisfied, or the condition is not satisfied but k=N, outputting the simulation result and the number of serial correction iterations ; the simulation result is composed of the final serial correction results of each subinterval division point and small interval division point, and can be specifically expressed as a time curve δ(t) of the rotor angle.

[0049] It should be noted that, since subintervals 1 to k-1 have been locked, in step S7 it is only necessary to judge whether subintervals k to N satisfy . In the k-th serial correction, only subinterval division points k to N are updated.

[0050] In the above step S5, a full-time-domain integrated correction equation set is constructed by using block integrated parallel paths, a quantum refinement operator is constructed to solve the correction equation set, and quantum refinement calculation results of each subinterval are obtained.

[0051] As shown in Figure 4 and Figure 5 , step S5 specifically comprises the following sub-steps: S51: setting a small step size h for quantum refinement calculation, wherein H can be divided exactly by h; setting small interval division points on subintervals based on the small step size h; adding both end points of the subinterval into the small interval division points, and adding a fault occurrence time and a fault clearing time into the small interval division points of the corresponding small intervals; initializing a simulation time step of each subinterval , is the moment corresponding to the simulation time step of the subinterval division point n on the full simulation time axis, T n-1 is the time of the subinterval division point n-1; n=0,1,2,……,N, and N is the total number of subintervals; S52. The implicit trapezoidal rule is used to perform difference analysis on the system's state differential equations. After elimination, the equations are combined with the algebraic equations to form the residual equations. The residual vectors are solved based on the residual equations for each sub-interval. Then, the corrected equations for each sub-interval are constructed. ; in, Given the residual vector of the known subinterval partition point n, it is obtained by solving the residual equation system of the subinterval; Let be the Jacobian matrix of the subinterval partition point n, which is obtained by differentiating the corresponding residual equation; Let n be the correction vector to be solved for the subinterval partition point n. =( , ); The correction amount is the state differential variable for the subinterval division point n participating in the calculation of the subsequent corrected equation system. The algebraic variable correction amount is used for the subinterval division point n in the subsequent calculation of the corrected system of equations.

[0052] S53. Combine the correction equations of each sub-interval to reconstruct the full-time domain correction equation set: ; In the formula, Represents the full-time residual vector. This represents the Jacobian matrix of the block-wise integration across the entire time domain. This represents the full-time correction vector to be solved, i.e. All are Hermitian matrices. Satisfying the power of 2 and It is a unit vector; if it does not meet the requirements, it needs to be Hermitized, expanded, and normalized before being combined.

[0053] S54. Construct a quantum linear solver using the HHL algorithm to solve the modified equation system and obtain... The solution is then processed by a classical computer. Restored to independent correction vectors for each subinterval =( , ); S55. Determine if the condition is met. , The set convergence tolerance for the quantum Newton-Raphson method; If the condition is not met, then for non-convergence ( The subintervals of ) are modified using the correction vector. renew and Then combine the modified equations into a new set of modified equations, and return to step S54; If satisfied, then utilize and The variable to be eliminated can be obtained by solving the problem. and Obtain the system's total variable vector Then proceed to step S56; S56, Determine t n Is it the end time of subinterval n? No, then update t n Find the next subinterval division point adjacent to subinterval n; then return to step S52; If yes, then the calculation result of the sub-interval division point n (i.e. the sub-interval division point corresponding to the end time of the sub-interval) will be used as the quantum precision calculation result.

[0054] The following specific embodiments verify the above-mentioned parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution.

[0055] This embodiment uses the IEEE-9-node standard test system. The generator adopts a fifth-order practical model, and the load adopts a comprehensive load model, divided into two parts: constant impedance load and dynamic load considering the electromechanical transient process of the induction motor. The excitation system adopts a classical third-order model, the prime mover and speed control system adopt a turbine speed control system, and the network adopts a quasi-steady-state model. The parameters of each component are shown in Tables 1, 2, 3, 4, and 5 below: Table 1. Circuit parameters of the IEEE-9 Node Standard Test System

[0056] Table 2 Parameters of the fifth-order practical model of the generator

[0057] In Table 2, S R T represents the generator capacity. J T' is the inertial time constant of the generator set. d0 Let T'' be the d-axis open-circuit transient time constant. d0 Let T'' be the open-circuit subtransient time constant of the generator's d-axis. q0 X is the open-circuit supertransient time constant of the generator's q-axis; d X' is the synchronous reactance of the generator's d-axis. d X is the transient reactance of the generator's d-axis; q X'' is the q-axis synchronous reactance of the generator. q For the generator's q-axis ultratransient reactance, Here, denoted as , is the stator winding resistance of the generator, and D is the steady damping coefficient.

[0058] Table 3 Exciter Parameters

[0059] In Table 3, T A and K A These represent the time constant and amplification factor of the inertial amplification element in the excitation system, T. F and K F These represent the time constant and amplification factor of the excitation negative feedback loop, respectively; T L and K L These are the exciter time constant and amplification factor, respectively; S E1 and S E2 These are the experimental constants related to the exciter saturation characteristics, satisfying S E E f =S E1 E f -S E2 E f S is the magnetomotive force of the generator stator. E This is the exciter saturation coefficient.

[0060] Table 4 Parameters of water turbine and governor

[0061] In Table 4, K δ T is the magnification factor of the centrifugal pendulum velocimeter. s Let δ be the time constant of the relay. i The static adjustment coefficient δ i =K i / K δ K i β is the hard feedback amplification factor; β is the soft feedback coefficient, β=K β / K δ T i and K β These are the soft feedback time constant and the amplification factor, respectively; T w is the water flow time constant.

[0062] Table 5 Dynamic Load Parameters

[0063] In Table 5, r s and X s These are the resistance and leakage reactance of the stator winding, respectively. m For the mutual inductance between the stator and rotor, r r and X r These are the equivalent resistance and leakage reactance of the rotor winding, respectively; T J The inertial time constant of the generator set, The initial slip rate of the dynamic load. For constant torque component weights, This is the load characteristic index.

[0064] For the high-order dynamic model parameters not provided in the original data of the IEEE-9 node standard test system, this embodiment has made reasonable additions based on typical empirical values.

[0065] Experimental setup: The total simulation time was reduced to 1.8s. The fault was set as a single-phase ground fault at node 7, with the fault occurrence time at 0.01s and the fault clearing time at 0.07s. After the fault was cleared, the system network topology and admittance matrix were restored to the pre-fault operating mode. The quantum precision calculation step size h was set to 0.01s, and the quantum Newton-Raphson convergence tolerance was used. Pick Serial correction convergence tolerance Pick The HHL algorithm's storage precision is set to retain one decimal place of the feature value. Accuracy. The simulation results of different parallelism degrees are analyzed, and the quantum resources of the block-integrated quantum parallel path and the distributed parallel path of the present invention are compared. Finally, the acceleration effect of the method of the present invention as the parallelism degree changes is analyzed through the quantum speedup ratio.

[0066] In this embodiment, simulations were performed for three parallelism degrees (i.e., the number of subintervals) N=6, 12, and 18, and the results were compared with classical quantum serial computing as a benchmark.

[0067] Referring to Figures 6(a), 6(b), and 6(c), δ 12 δ is the difference in rotor angle between the final nodes 1 and 2. 23 δ is the difference in rotor angle between the final nodes 2 and 3. 31 This represents the difference in rotor angle between node 3 and node 1. In the IEEE-9 node standard test system, nodes 1, 2, and 3 are all motors.

[0068] When N=6, the number of serial corrections reaches 6, and each time the convergence tolerance is not reached, meaning that all sub-intervals are locked; when N=12, the number of serial corrections reaches 12, and the first 11 times the convergence tolerance is not reached, meaning that the first 11 sub-intervals are locked; when N=18, the number of serial corrections reaches 3, and only the first 2 sub-intervals are locked.

[0069] The calculation results of the locked sub-interval are basically consistent with the serial calculation results; therefore, when N=6 and 12, the parallel calculation results are basically the same as the serial calculation results.

[0070] Observing Figures 6(a), 6(b), and 6(c), it can be seen that during the transient stable time-domain response process from 0 to 1.8 s, the final convergence results of the rotor angle differences under the three parallelisms (N=6, 12, and 18) are basically consistent with the quantum serial benchmark in terms of peak-valley timing and oscillation period. This indicates that the two-layer quantum architecture of "quantum coarse computation - quantum fine computation" can solve the strict timing dependence of transient simulation while making the time-parallel solution trajectory gradually approach the quantum serial benchmark solution.

[0071] In this embodiment, the resource consumption of the integrated computing of the present invention (i.e., constructing a modified set of equations and using a quantum processor for computation) is further compared with that of distributed computing (i.e., not constructing a modified set of equations and using N quantum processors to perform quantum computation on each sub-interval).

[0072] As can be seen from Figures 7(a) and 7(b), with the increase of parallelism, the proportion of qubits reduced by the integrated method compared with the distributed method increases from 47.3% for N=3 to 97.1% for N=45, and the growth law of the number of quantum gates is similar to that of the number of qubits.

[0073] In this embodiment, the performance of the method of the present invention under different parallelism N is further analyzed, and the theoretical speedup ratio is used as a benchmark. Quantitative quantum parallel simulation acceleration effect.

[0074] Theoretical speedup Based on the following simplifying assumptions: We assume that the time consumption of coarse-grained quantum computation is much less than that of fine-grained quantum computation; the main simulation time consumption of the parallel algorithm is in the equation solving stage of fine-grained quantum computation; and since the time complexity of the quantum algorithm is related to the depth of the quantum circuit, we further assume that the computation time required for each layer of the quantum circuit is the same. Therefore, the theoretical speedup can be approximated as: ; In the formula, This is an approximate theoretical speedup of quantum parallel algorithms compared to quantum serial algorithms. For the line depth of quantum serial computing For the line depth of quantum parallel computing. When When the quantum parallel algorithm is used, it has a speed-up effect; k is the number of serial corrections.

[0075] observe Figure 8 It is evident that when the parallelism is low, the theoretical speedup ratio is... At this point, the quantum parallel algorithm (i.e., the method of this invention) not only fails to accelerate the process but actually becomes slower than the normal serial architecture. When the parallelism increases beyond a certain threshold, Rapidly increasing, in At that point, the theoretical speedup ratio was 7.89. Further increasing the parallelism... It also shows a linear growth, in hour, The result reached 16.22. This demonstrates that the method of this invention exhibits excellent quantum parallel acceleration.

[0076] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0077] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0078] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution, characterized in that, comprising the following steps: S1. Establish a time-domain simulation model of the transient stability of the power system and obtain the initial values ​​of the system through simulation. ; S2. Utilize the time-division parallelism approach to divide the overall simulation time interval into multiple sub-intervals; the sub-interval division points and fault occurrence times... and fault clearing time Arrange the sample points in chronological order to form a sequence; S3. Construct a quantum coarse operator using a transient stability time-domain simulation method based on the quantum Newton-Raphson method. Combine this with the initial system value to perform quantum recursion on the sample point sequence. Extract the recursion results of each sub-interval segmentation point and record them as the quantum coarse calculation results. n is the index of the sub-interval dividing point, and N is the total number of sub-intervals; S4. dividing each subinterval into a plurality of small intervals; S5. constructing a full-time-domain integrated correction equation by using block-integrated parallel paths, constructing a quantum fine operator based on the small intervals to solve the correction equation, and obtaining quantum fine calculation results of each subinterval; S6. performing serial correction on the quantum fine calculation results and quantum coarse calculation results of each subinterval dividing point by using a differential algebraic separation correction strategy to obtain serial correction results of each subinterval dividing point; S7. determining whether all subinterval end points satisfy convergence or locking; if the condition is not satisfied and k < N, locking the serial correction results of subintervals 1 to k, then updating k to k+1, and returning to step S5 to recalculate the quantum fine calculation results of subintervals k+1 to N; Conversely, the simulation results and the number of serial correction iterations will be output. ; In the recursive process of quantum coarse computation and quantum fine computation, whenever a fault occurs... Or the time of fault clearance Then, by combining the state differential variables, the algebraic variables are updated through algebraic jump calculation to update the calculation results, and the updated calculation results are used for the next recursive step.

2. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 1, characterized in that, the quantum fine calculation process of the nth subinterval in step S5 comprises the following sub-steps: S51. Divide the subinterval n into smaller intervals; initialize the simulation time step for each subinterval. This is the starting endpoint of the sub-interval; S52. performing difference processing on the state differential equations of the system by an implicit trapezoidal method, forming a residual equation system together with algebraic equations after elimination, solving a residual vector based on the residual equation system of each subinterval; and then constructing a correction equation for each subinterval; S53. combining the correction equations of each subinterval to reconstruct a full-time-domain correction equation system; S54. constructing a quantum linear solver by using an HHL algorithm, solving the correction equation system to obtain a full-time-domain correction vector formed by correction vectors to be solved at subinterval dividing point n; restoring the full-time-domain correction vector into independent correction vectors of each subinterval by a classical computer; S55. determining whether all correction vectors converge; if not, updating system variables by combining the correction vectors for the unconverged subintervals, then combining the correction equations and returning to step S54; Yes, the simulation time step is obtained. Calculate the results of the sub-intervals on the above; then proceed to step S56; S56, Determine t n Is it the end time of subinterval n? No, then update t n Find the next subinterval division point adjacent to subinterval n; then return to step S52; Yes, then the simulation time step will be... The result of the sub-interval calculation is used as the quantum precision calculation result of the sub-interval division point n.

3. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 2, characterized in that, the correction equation system constructed in step S53 is: in, Represents the full-time residual vector. This represents the Jacobian matrix of the block-wise integration across the entire time domain. This represents the full-time correction vector to be solved; Given the residual vector of the known subinterval partition point n, it is obtained by solving the residual equation system of the subinterval; Let be the Jacobian matrix of the subinterval partition point n, which is obtained by differentiating the corresponding residual equation; Let n be the correction vector to be solved for the sub-interval division point n; The constraints of the corrected system of equations are: All are Hermitian matrices. Satisfying the power of 2 and It is a unit vector.

4. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 3, characterized in that, Let the state differential variables involved in the subsequent calculation of the modified equations be denoted as The algebraic variables involved in the subsequent calculation of the corrected system of equations are denoted as The state differential variable that is eliminated during dimensionality reduction is denoted as the intermediate differential variable. The algebraic variables that are eliminated during dimensionality reduction are denoted as intermediate algebraic variables. ; =( , ); The correction amount is the state differential variable for the subinterval division point n participating in the calculation of the subsequent corrected equation system. The algebraic variable correction amount for the subinterval division point n participating in the calculation of the subsequent corrected system of equations; In step S55, on each sub-interval, based on the correction vector... Calculate the next time step and Then use and Solving for the results and .

5. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 1, characterized in that, In step S6, the state differential variables after correction at each sub-interval division point are first obtained using the following formula. : in, and Let n represent the state differential variables in the coarse calculation results of the n-th quantum interval segmentation point in the k-th and (k-1)-th serial corrections, respectively. This represents the state differential variable correction amount of the sub-interval division point n in the k-th serial correction process; It is the state differential variable in the quantum precision calculation result of sub-interval partition point n in the k-th serial correction; k is the serial correction number, with an initial value of 0; when k>1, the serial correction result of sub-interval partition point n-1 after the (k-1)-th serial correction is used. Using this as the starting value, the quantum coarse calculation result of the subinterval partition point n is recursively derived using the quantum coarse operator on the corresponding subinterval. ; Then Substituting into the network algebraic equations and performing an algebraic jump calculation, we obtain the algebraic variables of the subinterval partition point n after the k-th serial correction. The serial correction result of the sub-interval segmentation point n after the k-th serial correction. =( , ).

6. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 1, characterized in that, In step S7, the rotor angle is extracted from the serial correction results. As a criterion, if the absolute value of the difference between the rotor angle obtained in this serial correction and the rotor angle obtained in the previous serial correction converges, then the sub-interval division point n is deemed to satisfy the convergence condition.

7. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 6, characterized in that, the simulation result output in step S7 comprises the serial correction results of all subinterval dividing points and small interval dividing points obtained by the last serial correction.

8. The parallel time-domain simulation method for transient stability of power systems based on two-layer quantum solution as described in claim 1, characterized in that, In step S2, the total simulation time interval is first divided into multiple sub-intervals using a set large step size H. Then, the endpoints of the sub-intervals and the time of fault occurrence are defined. and fault clearing time All of them were used as sample points.

9. A parallel time-domain simulation system for transient stability of a power system based on two-layer quantum solution, characterized in that, comprising a memory and a processor, wherein a computer program is stored in the memory, the processor is connected to the memory, and the processor is configured to execute the computer program to implement the power system transient stability parallel time-domain simulation method based on two-layer quantum solution according to any one of claims 1-8.

10. A storage medium, characterized in that, storing a computer program, wherein when executed, the computer program is used to implement the power system transient stability parallel time-domain simulation method based on two-layer quantum solution according to any one of claims 1-8.

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