Novel power system condition number perception quantum electromagnetic transient simulation method and system

Abstract

The application discloses a novel power system condition number aware quantum electromagnetic transient simulation method and system, first, an electromagnetic transient node admittance equation is established and mapped into a quantum electromagnetic transient simulation equation; then, a condition number aware preconditioner is constructed to improve the equation ill-conditioning by combining the condition number characteristics of the node admittance matrix and the grounding topology structure of the power grid; further, a Krylov subspace low-dimensional equation is constructed based on the preconditioned equation, so as to reduce the quantum solving dimension and avoid the explicit current state preparation; finally, a quantum sequential optimizer is used to solve the low-dimensional subspace equation, and the electromagnetic transient results at each simulation time are obtained through iteration compensation. The method can improve the trainability of the variational quantum solving, reduce the number of quantum bits, the line depth and the sampling overhead, and improve the practicability and scalability of the quantum electromagnetic transient simulation under the current quantum hardware conditions.

Description

Technical Field

[0001] This invention belongs to the technical field of electromagnetic transient simulation of power systems, and mainly relates to a novel condition number-aware quantum electromagnetic transient simulation method and system for power systems. Background Technology

[0002] In recent years, with the continuous integration of high-proportion new energy sources and power electronic equipment into the power grid, new power systems are exhibiting characteristics such as high power electronics, strong nonlinearity, and rapid dynamic changes. This has led to increasingly higher demands on the computational accuracy and speed of electromagnetic transient simulation. Electromagnetic transient simulation typically requires repeatedly solving a system of linear equations formed by the nodal admittance matrices at each simulation moment. As the system scale expands and the number of converters, switching devices, and other equipment increases, the dimension of the nodal admittance equations continuously increases, resulting in time-consuming small-step electromagnetic transient simulations that cannot meet the requirements for real-time, high-fidelity simulation of large-scale new power systems.

[0003] With the development of quantum computing technology, solving electromagnetic transient problems using quantum computing has become a new technological approach. Quantum computing possesses properties such as quantum superposition and entanglement, enabling the representation and processing of linear equations in high-dimensional Hilbert spaces, thus potentially alleviating the large-scale computational burden in traditional electromagnetic transient simulations. Existing quantum electromagnetic transient simulation methods have attempted to map the EMTP nodal admittance equations to quantum linear equations and solve them using the HHL algorithm or variable quantum linear solvers. Among these, HHL-type methods theoretically have acceleration potential, but their quantum circuit depth increases with problem size, placing high demands on current noisy medium-sized quantum hardware; while variable quantum linear solvers are more suitable for current quantum hardware, they still suffer from problems such as training degradation and hardware resource constraints.

[0004] However, quantum electromagnetic transient simulation still faces several practical challenges for new power systems dominated by converters. On the one hand, the nodal admittance matrix of electromagnetic transients may be severely ill-conditioned; an excessively large matrix condition number can weaken the gradient of the loss function during the variational quantum solution process, leading to slow convergence, increased sampling overhead, and even degraded training. On the other hand, existing methods still consume significant resources in terms of right-hand side current quantum state preparation, local loss function sampling, quantum circuit execution counts, and qubit usage, making them difficult to adapt to the practical conditions of limited available qubits, restricted circuit depth, and limited batch sampling capabilities in current quantum hardware. Summary of the Invention

[0005] This invention addresses the problems of large computational scale, strong ill-conditioned nature of quantum electromagnetic transient equations, difficulty in training variable quantum solutions, and limited quantum hardware resources in existing technologies for electromagnetic transient simulation of novel power systems. It proposes a novel condition number-aware quantum electromagnetic transient simulation method and system for power systems. First, it establishes the nodal admittance equations for electromagnetic transients and maps them to quantum electromagnetic transient simulation equations. Then, combining the condition number characteristics of the nodal admittance matrix and the grid grounding topology, a condition number-aware preprocessor is constructed to improve the ill-conditioned nature of the equations. Further, based on the preprocessed equations, a low-dimensional Krylov subspace equation is constructed to reduce the quantum solution dimension and avoid explicit current state preparation. Finally, a quantum order optimizer is used to solve the low-dimensional subspace equations, and the electromagnetic transient results at each simulation time are obtained through iterative compensation. This invention improves the trainability of variable quantum solutions, reduces the number of qubits, line depth, and sampling overhead, and enhances the practicality and scalability of quantum electromagnetic transient simulation under current quantum hardware conditions.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a novel condition number-sensing quantum electromagnetic transient simulation method for power systems, comprising the following steps:

[0007] S1. Constructing the preprocessed quantum electromagnetic transient simulation equations: Based on the electromagnetic transient equivalent model of the novel power system, nodal admittance equations are established, and the nodal admittance matrix, nodal voltage vector, and nodal injected current vector in the nodal admittance equations are mapped to the Hilbert space corresponding to quantum computing to form the quantum electromagnetic transient simulation equations; based on the condition number characteristics of the nodal admittance matrix and the power grid grounding topology, a condition number-aware preprocessing matrix is ​​constructed, and the quantum electromagnetic transient simulation equations are preprocessed to obtain the preprocessed quantum electromagnetic transient simulation equations:

[0008]

[0009] Where G' represents the preprocessed quantized node admittance matrix. This represents the preprocessed node voltage quantum state. This represents the preprocessed node-injected current quantum state;

[0010] S2. Constructing the low-dimensional equations in the preprocessed Krylov subspace: Based on the preprocessed quantum electromagnetic transient simulation equations obtained in step S1, a Krylov subspace is constructed using the preprocessed node injection current quantum states as initial vectors. The preprocessed quantum electromagnetic transient simulation equations are then projected onto the Krylov subspace to obtain the low-dimensional subspace quantum linear equations:

[0011]

[0012] Among them, g mThis represents the low-dimensional subspace matrix obtained by projection. Represents the quantum state to be determined in a low-dimensional subspace. The default initial quantum state is used for quantum computers; the solution dimension of quantum linear equations is reduced through the Krylov subspace projection, and explicit quantum state preparation of the node injection current vector is avoided;

[0013] S3. Solve the low-dimensional subspace quantum linear equation using a quantum order optimizer: For the low-dimensional subspace quantum linear equation obtained in step S2, construct a variable quantum circuit and simplify the global loss function, and use a quantum order optimizer to perform parameter-by-parameter analytical updates on the variable quantum circuit parameters to obtain an approximate solution to the low-dimensional subspace quantum linear equation.

[0014] S4. Iterative compensation based on Krylov subspace solution to obtain electromagnetic transient simulation results: Based on the low-dimensional subspace approximation solution obtained in step S3, combined with the Krylov subspace basis vectors and preprocessing relations, the low-dimensional subspace approximation solution is reconstructed into node voltage correction quantities in the original electromagnetic transient simulation space; the node voltage is updated according to the node voltage correction quantities and the current residual is calculated. If the current residual meets the preset accuracy requirements, the current node voltage is output as the electromagnetic transient simulation result at the current simulation time; if the current residual does not meet the preset accuracy requirements, the current residual is used as the right-hand side term of the new correction equation, and the Krylov subspace projection, low-dimensional quantum solution and node voltage correction process are repeated until the preset accuracy requirements are met; the process is advanced sequentially according to the time step of the electromagnetic transient simulation to obtain the electromagnetic transient simulation results of the new power system within the preset simulation time range.

[0015] To achieve the above objectives, the present invention also adopts the following technical solution: a novel power system condition number sensing quantum electromagnetic transient simulation system, comprising a computer program, wherein the computer program, when executed by a processor, implements the steps of the novel power system condition number sensing quantum electromagnetic transient simulation method.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] (1) The method of the present invention starts from the ill-conditioned nature of the electromagnetic transient admittance matrix, which alleviates the problems of barren plateau, large sampling overhead of quantum circuit, complex preparation of right-hand term states and limited available qubits in the existing quantum electromagnetic transient simulation, and improves the practicality and scalability of quantum electromagnetic transient simulation on noisy medium-sized quantum hardware.

[0018] (2) In step S2 of the present invention, a topology-aware hybrid preprocessor is constructed based on the topology characteristics of the power grid grounding. The low grounding distance region and the high grounding distance region are distinguished by the topology grounding distance. Jacobi preprocessing and incomplete Cholesky preprocessing are used respectively to reduce the condition number of the admittance matrix and improve the trainability of the variable quantum linear solver. Subsequently, a simplified global loss function is constructed on the preprocessed quantum electromagnetic transient equation, and a quantum order optimizer is used to perform analytical sequential updates on the variable quantum line parameters, thereby reducing gradient calculation and sampling overhead.

[0019] (3) The method of the present invention projects the high-dimensional quantum electromagnetic transient equation into a low-dimensional subspace equation based on the preprocessing Krylov subspace, so that the right-hand side terms correspond to the default initial state of the quantum computer, avoiding explicit current state preparation, and obtains the node voltage and electromagnetic transient results at each simulation time by combining residual compensation iteration. Attached Figure Description

[0020] Figure 1 This is a flowchart of the steps of the novel power system condition number sensing quantum electromagnetic transient simulation method of the present invention;

[0021] Figure 2 This is a schematic diagram of the convergence results of the loss function before and after preprocessing in Embodiment 1 of the present invention;

[0022] Figure 3 This is a comparative schematic diagram of the quantum order optimizer optimization process in Embodiment 1 of the present invention;

[0023] Figure 4 This is a schematic diagram of the electromagnetic transient simulation results and errors of Embodiment 1 of the present invention;

[0024] Figure 4 (a) is a schematic diagram of the topology of a three-phase full-bridge converter;

[0025] Figure 4 (b) is a schematic diagram of the converter capacitor voltage and its corresponding error;

[0026] Figure 4 (c) is a schematic diagram of the inductor current and its corresponding error;

[0027] Figure 5 This is a schematic diagram of the electromagnetic transient simulation results and errors of Embodiment 2 of the present invention;

[0028] Figure 5 (a) is a schematic diagram of the improved IEEE 13-node system and photovoltaic power plant access topology;

[0029] Figure 5 (b) is a schematic diagram of the voltage waveform and its relative error at the A-phase connection point of node 7;

[0030] Figure 5 (c) is a schematic diagram of the current waveform and its relative error at the A-phase connection point of node 7;

[0031] Figure 6 This is a schematic diagram of the electromagnetic transient simulation results and errors of Embodiment 3 of the present invention;

[0032] Figure 6 (a) is a schematic diagram of the improved IEEE 69-node system and photovoltaic power plant access topology;

[0033] Figure 6 (b) shows the simulation results of the voltage at the connection point of node 67 under fault conditions and the corresponding error diagram;

[0034] Figure 6 (c) shows the simulation results of the current at the access point of node 67 under fault conditions and the corresponding error diagram. Detailed Implementation

[0035] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0036] Example 1

[0037] This embodiment is applied to the electromagnetic transient simulation of a three-phase full-bridge converter, such as... Figure 4 As shown in (a), the three-phase full-bridge converter is powered by an ideal three-phase AC power supply with an effective AC line voltage of 400V. A 4mF DC bus capacitor is installed on the DC side, and a 0.5mH filter inductor is used on the AC side. The initial load is 100Ω, which abruptly changes to 50Ω at 0.02s to simulate a load step disturbance. The converter uses SPWM modulation with a switching frequency of 2.5kHz, an electromagnetic transient simulation step size of 10μs, and a quantum electromagnetic transient simulation accuracy threshold of 10. -10 The depth of the variable quantum circuit is set to 3 layers. This example corresponds to an 8-node electromagnetic transient network, requiring 3 qubits for state encoding.

[0038] A novel condition number-sensing quantum electromagnetic transient simulation method for power systems, such as Figure 1 As shown, it includes the following steps:

[0039] Step S1: Constructing the preprocessed quantum electromagnetic transient simulation equations: Based on the electromagnetic transient equivalent model of the new power system, establish the node admittance equations, and map the node admittance matrix, node voltage vector, and node injected current vector in the node admittance equations to the Hilbert space corresponding to quantum computing to form the quantum electromagnetic transient simulation equations; Based on the condition number characteristics of the node admittance matrix and the power grid grounding topology, construct the condition number-aware preprocessing matrix, and preprocess the quantum electromagnetic transient simulation equations to obtain the preprocessed quantum electromagnetic transient simulation equations.

[0040] S11. Based on the power electronic equipment, switching devices, passive branches, and network topology relationships in the new power system, establish the electromagnetic transient node admittance equation, which is as follows:

[0041]

[0042] Where G represents the nodal admittance matrix formed by the electromagnetic transient equivalent model, and v(t) represents the nodal voltage vector at the current simulation moment. This represents the externally injected current vector at the current simulation moment. The vector represents the historical current vector formed by the discretized model of inductors, capacitors, switching devices and power electronic equipment, and i(t) represents the node injection current vector.

[0043] In this embodiment, the original admittance model is an 8th-order model, and the corresponding EMTP equation is:

[0044]

[0045] S12. Extend the node admittance matrix to the Hilbert space dimension corresponding to the qubit, and normalize the node injection current vector to obtain the quantized node admittance matrix and the node injection current quantum state; when the dimension of the node admittance matrix G is N, select the one that satisfies Given the number of qubits n, construct the augmented quantized node admittance matrix:

[0046]

[0047] Where I represents the identity matrix used for dimension completion.

[0048] In this embodiment, because it itself satisfies Therefore, no augmentation is needed. The normalized nodal injection current vector is expressed as:

[0049]

[0050] This leads to the quantum electromagnetic transient simulation equation:

[0051]

[0052] in, This represents the voltage state of the node to be determined.

[0053] S13. Based on the condition number characteristics of the quantized node admittance matrix and the grounding topology of the novel power system, construct the condition number-aware preprocessing matrix M, specifically including the following steps:

[0054] S131: Determine the set of reference grounding nodes in the new power system The reference grounding node includes nodes connected to equivalent branches with strong grounding constraints, such as balancing nodes, high grounding susceptance branches, parallel compensation elements, grounding capacitors, and grounding power supplies; the network area to be processed is calculated based on the power grid topology. Compared to The topological grounding distance (TGD) is expressed as follows:

[0055]

[0056] in, This represents the shortest topology path length between node p and the reference ground node q;

[0057] The topological grounding distance is used to characterize the strength of the grounding reference constraint on the node voltage in the network region; the main source of the ill-conditioned admittance matrix is ​​determined based on the topological grounding distance; when the topological grounding distance of the network region to be processed is small, the node voltage is strongly constrained by the grounding reference, and the ill-conditioned admittance matrix mainly comes from the diagonal scale difference between the equivalent admittances of different nodes to ground; when the topological grounding distance of the network region to be processed is large, the node voltage is weakly constrained by the grounding reference, and the admittance matrix exhibits a weak grounding or approximately Laplace-type structure, and its ill-conditioned nature mainly comes from near-singular modes and weak voltage anchoring effects;

[0058] S132: Based on the preset topology grounding distance threshold The new power system is divided into low-topology grounding distance regions and high-topology grounding distance regions; when the network area satisfy When it is, it is determined to be a low topology grounding distance area; when the network area satisfy At that time, it was determined to be a high topology grounding distance region;

[0059] In this embodiment, due to the strong grounding coupling introduced by the load, parallel capacitor, and power supply connection, the system belongs to the low topology grounding distance region, and its topology grounding distance is 1.

[0060] S133: Construct a Jacobi preprocessing matrix for the low topological grounding distance region to normalize the diagonal scale differences of the admittance matrix in this region. Its expression is:

[0061]

[0062] Among them, G L M represents the admittance matrix sub-block corresponding to the low topology grounding distance region. J This represents the Jacobi preprocessing matrix corresponding to this region;

[0063] An incomplete Cholesky preprocessing matrix is ​​constructed for regions with high topological grounding distances to enhance the numerical anchoring capability of weak grounding regions and suppress near-singular modes. Its expression is as follows:

[0064]

[0065] Among them, L IC This represents the lower triangular factor obtained by performing an incomplete Cholesky decomposition on the admittance matrix sub-block corresponding to the high topological grounding distance region.

[0066] S134. Divide the quantized node admittance matrix into blocks according to the low-topology grounding distance region and the high-topology grounding distance region, and obtain:

[0067]

[0068] Among them, G H G represents the admittance matrix sub-block corresponding to the high topology grounding distance region. LH and G HL Representing coupling matrix sub-blocks between different regions; based on the Jacobi preprocessing matrix and the incomplete Cholesky preprocessing matrix, a condition number-aware hybrid preprocessing matrix is ​​constructed:

[0069]

[0070] Therefore, diagonal-scale ill-conditioning and weakly grounded structure ill-conditioning are suppressed for different grounding topology regions, thus obtaining the condition number-aware preprocessing matrix M for preprocessing quantum electromagnetic transient simulation equations.

[0071] In this embodiment, since the entire network belongs to the low TGD region, Jacobi preprocessing can effectively improve the condition number of the node admittance matrix.

[0072] S14. Decompose the condition number-aware preprocessing matrix obtained in step S13, let...

[0073]

[0074] Where L represents the decomposition factor of the preprocessed matrix, Represents the conjugate transpose of L;

[0075] Based on the aforementioned decomposition factor, the quantum electromagnetic transient simulation equations are preprocessed using a left-right symmetric approach, resulting in:

[0076]

[0077] remember , , Then, the preprocessed quantum electromagnetic transient simulation equations are obtained: .

[0078] Through the above steps, the original electromagnetic transient nodal admittance equation is transformed into a preprocessed quantum electromagnetic transient simulation equation, which reduces the matrix condition number while maintaining the physical structure of the nodal admittance matrix, and improves the numerical stability and trainability of the subsequent variable quantum solution process.

[0079] Step S2: Constructing the low-dimensional equations of the preprocessed Krylov subspace: Based on the preprocessed quantum electromagnetic transient simulation equations obtained in step S1, a Krylov subspace is constructed with the preprocessed node injection current quantum state as the initial vector, and the preprocessed quantum electromagnetic transient simulation equations are projected onto the Krylov subspace to obtain the low-dimensional subspace quantum linear equations.

[0080] S21: Based on the preprocessed quantum electromagnetic transient simulation equations obtained in step S1, determine the dimension of the Krylov subspace and construct the Krylov subspace in the preprocessed Hilbert space, specifically including the following steps:

[0081] S211: Based on the condition number of the preprocessed quantized node admittance matrix and the quantum linear solution error, estimate the minimum Krylov subspace dimension that satisfies the convergence requirement; let the condition number of the preprocessed quantized node admittance matrix G' be... The low-dimensional subspace solution error introduced by the quantum linear solver is Then the conservative estimate of the minimum Krylov subspace dimension that satisfies the convergence requirement is... and the corresponding minimum number of qubits for:

[0082]

[0083] In the actual solution process, it should be no less than The dimension is used as the candidate Krylov subspace dimension, and is gradually increased starting from the smallest candidate dimension, so as to reduce the number of qubits and the depth of quantum circuits while meeting the simulation accuracy requirements;

[0084] S212: Injecting current quantum states into pre-processed nodes As the initial vector for the Krylov subspace, construct a Krylov subspace of actual dimension m:

[0085]

[0086] in, m represents the actual Krylov subspace dimension used, which is used to transform the preprocessed high-dimensional quantum electromagnetic transient simulation equations into a low-dimensional subspace solution problem;

[0087] S22: The Krylov subspace is orthogonalized using the Lanczos process to generate an orthogonal basis for the Krylov subspace:

[0088]

[0089] in, The result is obtained by normalizing the quantum states of the pre-processed nodal injection current:

[0090]

[0091] The orthogonal basis X m Used to characterize the projection direction of the preprocessed quantum electromagnetic transient simulation equations in a low-dimensional subspace;

[0092] S23: Based on the Krylov subspace orthogonal basis, project the preprocessed quantized node admittance matrix onto the low-dimensional subspace to obtain the low-dimensional subspace matrix:

[0093]

[0094] Among them, g m The low-dimensional matrix g is obtained by projection onto the Krylov subspace; when an orthogonal basis is generated using the Lanczos process, the low-dimensional matrix g... m It has a real symmetric tridiagonal structure, which facilitates the solution of subsequent quantum linear equations;

[0095] S24: Constructing low-dimensional subspace quantum linear equations based on Galerkin orthogonality conditions; whereby, low-dimensional unsolved states are sought in the Krylov subspace. By making the residuals of the preprocessed quantum electromagnetic transient simulation equations orthogonal to the Krylov subspace, we obtain:

[0096]

[0097] Since the first basis vector of the Krylov subspace is... Normalization yields the following result: .in, , The default initial quantum state is used for quantum computers; after normalizing the right-hand side, a low-dimensional subspace quantum linear equation suitable for quantum solution is obtained:

[0098]

[0099] S25: Determine the reconstruction relationship between the low-dimensional subspace equations and the original quantum electromagnetic transient simulation equations; obtain the low-dimensional subspace solution. Then, a search direction basis is constructed based on the Krylov subspace orthogonal basis and the preprocessed matrix factorization factor:

[0100]

[0101] The low-dimensional subspace is demapped back to the original electromagnetic transient simulation space through the following relationship:

[0102]

[0103] Among them, Z m This represents the Krylov search direction basis after preprocessing relation transformation.

[0104] Through the above steps, the preprocessed quantum electromagnetic transient simulation equations are transformed into low-dimensional subspace equations with the default quantum initial state as the right-hand side, thereby avoiding the explicit quantum state preparation of the node injection current vector and reducing the number of qubits and the depth of quantum circuits.

[0105] Step S3: Solve the low-dimensional subspace quantum linear equation using a quantum order optimizer: For the low-dimensional subspace quantum linear equation obtained in step S2, construct a variable quantum circuit and simplify the global loss function, and use a quantum order optimizer to perform parameter-by-parameter analytical updates on the variable quantum circuit parameters to obtain an approximate solution to the low-dimensional subspace quantum linear equation.

[0106] S31: Construct a variable quantum circuit for the low-dimensional subspace quantum linear equation obtained in step S24; represent the quantum state to be solved using a parameterized variable quantum circuit:

[0107]

[0108] in, This represents a parameterized variable component quantum circuit. This represents the variational parameters to be optimized;

[0109] S32: Construct a simplified global loss function based on the low-dimensional subspace quantum linear equation; specifically, the low-dimensional subspace matrix g... mActing on variable quantum states and its right-hand side item The deviation between them is used as the optimization objective to construct the loss function:

[0110]

[0111] Where I represents the identity matrix; the simplified global loss function is used to characterize the solution residual of the quantum linear equation in the low-dimensional subspace, and avoids the additional measurement and sampling overhead caused by the normalized loss function on the preprocessed well-state system;

[0112] S33: The variable quantum circuit parameters are updated parameter by parameter using a quantum ordering optimizer, specifically including the following steps:

[0113] S331: In the current optimization round, select the j-th parameter to be updated in the variable component quantum circuit. And keeping the other variational parameters unchanged, the simplified global loss function is expressed in cosine form in the direction of this single parameter:

[0114]

[0115] in, , and These are the coefficients to be determined corresponding to the current parameter direction;

[0116] S332: Measure the simplified global loss function values ​​at the current parameter point and its positive and negative offset points respectively:

[0117]

[0118] And calculate based on the above measurement results:

[0119]

[0120] S333: Based on the complex quantity X j The phase determines the phase parameters of the cosine function:

[0121]

[0122] And obtain the analytical optimal update value of the j-th variational parameter.

[0123]

[0124] S334: Update the j-th variational parameter The process repeats steps S331 to S333 for the remaining variational parameters until a round of parameter order update is completed. If the simplified global loss function satisfies the preset convergence condition, the optimized variational parameters are output; otherwise, the next round of parameter order update continues. This avoids the explicit gradient estimation and line search process in traditional gradient descent.

[0125] S34: Obtain the optimized variational parameters through step S33. Substituting this into the parameterized variable quantum circuit, an approximate solution to the low-dimensional subspace equation is obtained:

[0126]

[0127] By utilizing the structural features of low-dimensional subspace equations and the cosine property of the loss function in the single-parameter direction through the above steps, we can achieve low-sampling and high-efficiency solutions to the Krylov subspace quantum linear equations.

[0128] Step S4: Iterative compensation based on Krylov subspace solution and obtaining electromagnetic transient simulation results: Based on the low-dimensional subspace approximation solution obtained in step S3, combined with the Krylov subspace basis vectors and preprocessing relations, the low-dimensional subspace approximation solution is reconstructed into node voltage correction quantities in the original electromagnetic transient simulation space; the node voltage is updated according to the node voltage correction quantities and the current residual is calculated. If the current residual meets the preset accuracy requirements, the current node voltage is output as the electromagnetic transient simulation result at the current simulation time; if the current residual does not meet the preset accuracy requirements, the current residual is used as the right-hand side term of the new correction equation, and the Krylov subspace projection, low-dimensional quantum solution and node voltage correction process are repeated until the preset accuracy requirements are met; the process is advanced sequentially according to the time step of the electromagnetic transient simulation to obtain the electromagnetic transient simulation results of the new power system within the preset simulation time range.

[0129] S41: Reconstruct the node voltage correction in the original electromagnetic transient simulation space based on the approximate solution of the low-dimensional subspace; wherein, if the low-dimensional subspace solution corresponding to the k-th residual correction equation is Then, based on the Krylov subspace basis vectors and preprocessing relations, we obtain:

[0130]

[0131] in, This represents the proportionality coefficient introduced by the normalization of the right-hand side during the k-th residual correction process. This represents the search direction basis obtained from the Krylov subspace basis vectors through preprocessing relation transformation during the k-th residual correction process;

[0132] S42: Based on the current residual, construct the residual correction equation, transforming the current error compensation problem into a problem of solving the node voltage correction amount. Its expression is:

[0133]

[0134] in, This represents the node voltage correction amount corresponding to the Kth iteration; for the residual correction equation, the Krylov subspace projection and quantum order optimization solution process described in claims 3 and 4 is repeated to obtain an approximate solution of the residual correction equation in the low-dimensional subspace;

[0135] S43: Update the node voltage quantum state using the aforementioned node voltage correction:

[0136]

[0137] Based on the node injection current quantum state and the current node voltage quantum state at the current simulation moment, calculate the current residual corresponding to the (k+1)th iteration. The current residual represents the deviation between the current node voltage after being substituted into the quantum electromagnetic transient simulation equation and the target node injection current, and its expression is:

[0138]

[0139] in, This represents the current residual in the (k+1)th iteration. Let represent the node voltage quantum state obtained in the (k+1)th iteration, represent the quantized node admittance matrix, and represent the node injected current quantum state;

[0140] Recalculate the current residual or relative residual error based on the updated node voltage quantum state; if the relative residual error meets the preset accuracy requirement:

[0141]

[0142] Then output As the node voltage result at the current simulation moment; if it does not meet the preset accuracy requirement, let k=k+1, and continue to execute S2 to S4 until the preset accuracy requirement is met or the preset maximum number of iterations is reached;

[0143] S44: After the node voltage results at the current simulation moment are determined, update the historical current term and externally injected current term in the electromagnetic transient simulation, and advance to the next simulation moment according to the preset simulation step size; repeat the preprocessing quantum electromagnetic transient equation construction, Krylov subspace low-dimensional projection, quantum order optimization solution and iterative compensation process at each simulation moment to obtain the electromagnetic transient simulation results of the new power system within the preset simulation time range.

[0144] The novel power system condition number-sensing quantum electromagnetic transient simulation method described in this invention can effectively complete the electromagnetic transient simulation calculation of a three-phase full-bridge converter, obtaining the corresponding simulated voltage and current results. Figure 2 This paper demonstrates the convergence of global and local loss functions before and after preprocessing in a three-phase full-bridge converter example. This comparison aims to compare the ability of different loss functions to represent the true residuals of quantum electromagnetic transient equations and illustrates the effect of condition number-aware preprocessing on the trainability of variational quantum solutions. Specifically, the global loss function directly represents the overall residuals of the quantum electromagnetic transient linear equations, while the local loss function, although improving trainability to some extent, has a weaker constraint on the true physical residuals. Figure 2 As can be seen, the untreated ill-conditioned system exhibits significant convergence stagnation under the global loss function. The area within the box in the figure shows that the optimization curve hardly decreases, indicating that the loss function's descent has stopped. This phenomenon suggests that severe matrix ill-conditioning can induce plateau-like training degradation. After the hybrid preprocessing of this invention, the global loss function under different optimizers recovers and effectively decreases, demonstrating that condition number-aware preprocessing can improve the trainability of the quantum solution process. Therefore, this invention, by improving the condition number of the quantized admittance matrix, can enhance the stability and reliability of global loss function optimization and avoid residual inconsistencies that may be caused by local loss functions.

[0145] Figure 3 This paper presents a comparison of the optimization trajectories of the quantum order optimizer with other optimizers. CG, L-BFGS-B, Powell, COBYLA, and Nelder-Mead represent the conjugate gradient method, the finite-memory BFGS method with boundary constraints, the Powell conjugate direction method, the linear approximation constraint optimization method, and the Nelder-Mead simplex method, respectively. These optimizers cover both gradient-based and gradient-free optimization strategies, used to compare the performance of different parameter training methods in the original ill-conditioned system and the preprocessed system. Figure 3 It can be seen that the quantum order optimizer exhibits the fastest objective function descent rate both before and after preprocessing, indicating that its single-parameter directional analytical update mechanism effectively reduces iteration overhead. In the original ill-conditioned system, although the quantum order optimizer can quickly reduce the global loss function to a small value, the actual physical residual remains at a relatively high level, indicating that spurious convergence, where the loss function and physical residual are inconsistent, may still occur under ill-conditioned matrix conditions. After condition number-aware preprocessing according to this invention, this inconsistency is significantly eliminated, and the descent of the objective function is consistent with the descent of the actual residual. Therefore, the quantum order optimizer has a higher convergence efficiency than conventional optimizers, and condition number-aware preprocessing further ensures the consistency between the optimization objective and the physical residual.

[0146] Figure 4The electromagnetic transient simulation results of a three-phase full-bridge converter are presented, and the calculation results are compared with those of classical electromagnetic transient simulation, traditional quantum electromagnetic transient simulation based on a variational quantum linear solver, and the condition number-aware quantum electromagnetic transient simulation described in this invention. Figure 4 (a) The topology of the three-phase full-bridge converter is given. Figure 4 (b) shows the converter capacitor voltage and its corresponding error. Figure 4 (c) illustrates the inductor current and its corresponding error. This example involves a sudden load change at 0.02s, with the load varying from 100Ω to 50Ω, doubling the load power requirement. This is used to verify the tracking capability of the method of this invention for transient disturbances. Figure 4 It can be seen that the capacitor voltage and inductor current waveforms obtained by the method of this invention are basically consistent with the results of classical electromagnetic transient simulation, and can accurately reflect the electromagnetic transient response process of the three-phase full-bridge converter before and after load change; at the same time, the waveform error of the method of this invention remains within 10% throughout the entire simulation period. -10 The absence of significant error accumulation demonstrates the effectiveness of the method described in this invention in terms of simulation accuracy, convergence stability, and quantum resource utilization efficiency.

[0147] Example 2

[0148] This embodiment is applied to the electromagnetic transient simulation calculation of a converter-dominated power system with low topology grounding distance. The system is based on an improved IEEE 13-node system, with photovoltaic power plants connected at nodes 7 and 10. The photovoltaic power plants consist of 50 generating units, each using a three-phase full-bridge converter model. The corresponding electromagnetic transient network contains 839 nodes, with a DC-side voltage of 900V, a DC-side resistance of 0.5Ω, a DC-side capacitance of 8mF, an AC-side inductance of 1mH, and a switching frequency of 2500Hz. The IEEE 13-node subsystem in this system has multiple strongly grounded coupling nodes, and the DC-side reference node is retained in the converter series system. The overall topology grounding distance is 2, which falls within the low topology grounding distance region. Therefore, Jacobi preprocessing can effectively reduce the system matrix condition number.

[0149] According to the steps of the present invention, quantum electromagnetic transient simulation calculations are performed. In this embodiment, Jacobi preprocessing reduces the system matrix condition number from 15,338,375 to 2.289, which significantly improves the numerical stability and trainability of the quantum solution process. Figure 5 Simulation results of the improved IEEE 13-node system are presented. Among them, Figure 5 (a) To improve the IEEE 13-node system and photovoltaic power plant access topology, Figure 5 (b) shows the voltage waveform at the A-phase connection point of node 7 and its relative error. Figure 5(c) shows the current waveform at the A-phase connection point of node 7 and its relative error. In this example, the original electromagnetic transient linear equations have a dimension of 839. After preprocessing and Krylov subspace projection according to this invention, the dimension is reduced to 4. Only 2 qubits and 8 Pauli terms are needed to complete the low-dimensional subspace solution, thereby significantly reducing the number of quantum circuit executions. This transforms the originally difficult-to-execute 839-dimensional linear equation problem into an executable low-dimensional variational quantum linear solution problem.

[0150] Depend on Figure 5 (b) and Figure 5 (c) It can be seen that the VQLS solution based on the low-dimensional subspace equations is basically consistent with the classical electromagnetic transient simulation results, with both voltage and current errors remaining within 10. -8 Within the preset accuracy threshold of 10, and no significant error accumulation was observed. -10 In this invention, the method typically converges in only 2 to 3 iterations. Furthermore, on this executable low-dimensional equation, the quantum ordering optimizer exhibits higher sampling efficiency and optimization accuracy compared to the Adam optimizer, achieving a lower loss function value with fewer sampling iterations. Therefore, for complex converter-dominated systems including photovoltaic power plants and multiple converter units, this invention can effectively reduce quantum resource requirements while maintaining simulation accuracy, achieving accurate, stable, and resource-efficient electromagnetic transient simulation calculations.

[0151] Example 3

[0152] This embodiment is applied to the electromagnetic transient simulation calculation of a converter-dominated power system with high topology grounding distance. The system is based on an improved IEEE 69-bus system, with a photovoltaic power station containing 100 generating units connected at node 67, forming an electromagnetic transient network with over 1000 nodes. The converter parameters of the photovoltaic generating units are the same as in Embodiment 2, and an open-circuit fault is introduced between the photovoltaic power station and node 67 at t=0.027s to verify the applicability of the method in high topology grounding distance and fault disturbance scenarios. In this system, only node 1 serves as the reference grounding node, and the topology grounding distance of some radial network regions reaches 27, belonging to the high topology grounding distance region; while the topology grounding distance of the converter series system is 2, belonging to the low topology grounding distance region. Therefore, this embodiment uses a condition number-aware hybrid preprocessor to perform partitioned preprocessing for different regions.

[0153] According to the steps of this invention, quantum electromagnetic transient simulation calculations are performed, and the simulation results are as follows: Figure 6 As shown. Figure 6 The paper presents the improved simulation topology of the IEEE 69-bus system, along with simulation results and corresponding errors for voltage and current under fault conditions. Figure 6 (a) Demonstrates the improved IEEE 69-node system and photovoltaic power plant access topology; Figure 6 (b) and Figure 6 (c) The simulation results and corresponding errors of the voltage and current at the node 67 connection point under fault conditions are shown respectively. In this example, a three-phase open-circuit fault is applied between the photovoltaic power station and node 67 at t=0.027s. In the EMT model, the branch admittance between node 67 and the photovoltaic power station is made approximately zero by updating the admittance matrix. Unlike the low topology grounding distance example, the improved IEEE 69-node system is a radial network, and only node 1 is used as the reference grounding node. The topology grounding distance of some feeder areas reaches 27, while the topology grounding distance of the converter subsystem is 2. Therefore, this invention uses a condition number-aware hybrid preprocessor to partition different regions, reducing the system matrix condition number from 1036988900 to 12.7307. After preprocessing the Krylov subspace projection, the original 1007-dimensional linear equation is reduced to a 4-dimensional quantum problem, which can be solved with only 2 qubits and 8 Pauli terms, significantly reducing the execution overhead of the quantum circuit.

[0154] Depend on Figure 6 (b) and Figure 6 (c) It can be seen that the voltage and current waveforms obtained by the method of the present invention are basically consistent with the results of classical electromagnetic transient simulation, and the errors are all kept within 10. −8 Within the preset accuracy range, and no significant error accumulation was observed. −10 The method of this invention typically converges within 3 to 5 iterations; simultaneously, the quantum ordering optimizer significantly reduces the number of samplings compared to the Adam optimizer. Therefore, this invention can also achieve accurate, stable, and resource-efficient electromagnetic transient simulation calculations for complex converter-dominated systems with high topological grounding distances, strong ill-conditioned behavior, and fault disturbances.

[0155] In summary, the method of this invention reduces the ill-conditioned nature of the nodal admittance matrix of electromagnetic transients in novel power systems through condition number-aware preprocessing, alleviating the training degradation problem caused by excessively large condition numbers during variational quantum solution. By using Krylov subspace projection, the high-dimensional quantum electromagnetic transient equations are transformed into low-dimensional subspace equations, reducing the number of qubits and the depth requirement of quantum circuits. Finally, the combination of a quantum order optimizer and an iterative compensation mechanism reduces sampling overhead. This method is beneficial for solving the curse of dimensionality and insufficient computational efficiency problems faced by classical computers in solving large-scale electromagnetic transient simulation problems, and promotes the practical application of quantum electromagnetic transient simulation methods under current noisy medium-sized quantum hardware conditions.

[0156] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A novel condition number-sensing quantum electromagnetic transient simulation method for power systems, characterized in that, Includes the following steps: S1. Constructing the preprocessed quantum electromagnetic transient simulation equations: Based on the electromagnetic transient equivalent model of the new power system, establish the node admittance equations, and map the node admittance matrix, node voltage vector, and node injection current vector in the node admittance equations to the Hilbert space corresponding to quantum computing to form the quantum electromagnetic transient simulation equations. Based on the condition number characteristics of the node admittance matrix and the power grid grounding topology, a condition number sensing preprocessing matrix is ​​constructed to preprocess the quantum electromagnetic transient simulation equations, resulting in preprocessed quantum electromagnetic transient simulation equations. S2. Constructing the low-dimensional equations of the preprocessed Krylov subspace: Based on the preprocessed quantum electromagnetic transient simulation equations obtained in step S1, construct the Krylov subspace with the preprocessed node injection current quantum state as the initial vector, and project the preprocessed quantum electromagnetic transient simulation equations onto the Krylov subspace to obtain the low-dimensional subspace quantum linear equations. S3. Solve the low-dimensional subspace quantum linear equation using a quantum order optimizer: For the low-dimensional subspace quantum linear equation obtained in step S2, construct a variable quantum circuit and simplify the global loss function. Use a quantum order optimizer to perform parameter-by-parameter analytical updates on the parameters of the variable quantum circuit to obtain an approximate solution to the low-dimensional subspace quantum linear equation. S4. Iterative compensation based on Krylov subspace solution and obtain electromagnetic transient simulation results: Reconstruct the low-dimensional subspace approximate solution obtained in step S3 into the node voltage correction amount in the original electromagnetic transient simulation space; Update the node voltage according to the node voltage correction amount and calculate the current residual. If the current residual meets the preset accuracy, output the current node voltage as the electromagnetic transient simulation result at the current simulation time; otherwise, use the current residual as the right-hand side term of the new correction equation and repeat steps S2-S4 until the preset accuracy is met, and output the electromagnetic transient simulation result.

2. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 1, characterized in that: The nodal admittance equation in step S1 is specifically as follows: ； Where G represents the nodal admittance matrix formed by the electromagnetic transient equivalent model, and v(t) represents the nodal voltage vector at the current simulation moment. This represents the externally injected current vector at the current simulation moment. Let i(t) represent the historical current vector, and i(t) represent the node injected current vector. The node admittance equation is extended to the Hilbert space dimension corresponding to the qubit, and the node injection current vector is normalized to obtain the quantized node admittance matrix and the node injection current quantum state; the extended quantized node admittance matrix is ​​as follows: ； Where I represents the identity matrix used for dimension completion; G is the node admittance matrix; The normalized vector of the injected current at the node is expressed as: ； in, Let i represent the quantized node current state, and i denote the augmented node injection current vector. To augment the 2-norm of the node current vector; The quantum electromagnetic transient simulation equations are as follows: ； in, Indicate the voltage state of the node to be determined; The quantum electromagnetic transient simulation equations are preprocessed using a left-right symmetric method to obtain the preprocessed quantum electromagnetic transient simulation equations: ； ， ， ； Where G' represents the preprocessed quantized node admittance matrix. This represents the preprocessed node voltage quantum state. This represents the preprocessed node-injected current quantum state, and L represents the factorization factor of the condition number-sensing preprocessing matrix. This represents the transpose of L. This represents the transpose of the inverse matrix L.

3. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 2, characterized in that: The specific method for constructing the condition number-aware preprocessing matrix M in step S1 is as follows: Determine the set of reference grounding nodes in the new power system Calculate the network region to be processed Compared to Topological grounding distance TGD: ； in, This represents the shortest topology path length between node p and the reference ground node q; Preset topology grounding distance threshold When network area satisfy When it is, it is determined to be a low topology grounding distance area; when the network area satisfy At that time, it was determined to be a high topology grounding distance region; For regions with low topological grounding distances, a Jacobi preprocessing matrix is ​​constructed, and its expression is as follows: ； Among them, G L M represents the admittance matrix sub-block corresponding to the low topology grounding distance region. J This represents the Jacobi preprocessing matrix corresponding to this region; An incomplete Cholesky preprocessing matrix is ​​constructed for regions with high topological grounding distances, and its expression is as follows: ； Among them, L IC This represents the lower triangular factor obtained by performing an incomplete Cholesky decomposition on the admittance matrix sub-block corresponding to the high topological grounding distance region. Dividing the quantized node admittance matrix into blocks according to the low-topology grounding distance region and the high-topology grounding distance region, we obtain: ； Among them, G H G represents the admittance matrix sub-block corresponding to the high topology grounding distance region. LH and G HL This represents a coupling matrix sub-block between different regions; Based on the Jacobi preprocessing matrix and the incomplete Cholesky preprocessing matrix, a condition number-aware hybrid preprocessing matrix M is constructed: 。 4. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 3, characterized in that: The main sources of ill-conditioned admittance matrix based on topological grounding distance (TGD) are as follows: When the topological grounding distance of the network region to be processed is small, the node voltage is strongly constrained by the grounding reference, and the ill-conditioned admittance matrix originates from the diagonal scale difference between the equivalent admittances of different nodes to ground; when the topological grounding distance of the network region to be processed is large, the node voltage is weakly constrained by the grounding reference, and the ill-conditioned admittance matrix originates from near-singular modes and weak voltage anchoring effects.

5. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 2, characterized in that: The method for constructing the Krylov subspace in step S2 is as follows: based on the condition number of the preprocessed quantized node admittance matrix and the quantum linear solution error, estimate the minimum Krylov subspace dimension that satisfies the convergence requirement. and the corresponding minimum number of qubits : ； in, Let G' be the condition number of the preprocessed quantized nodal admittance matrix. Low-dimensional subspace solution error introduced to quantum linear solvers; Injecting current quantum states into pre-processed nodes As the initial vector for the Krylov subspace, construct a Krylov subspace of actual dimension m: ； in, , where m represents the actual Krylov subspace dimension used.

6. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 5, characterized in that: In step S2, the Krylov subspace is orthogonalized using the Lanczos process to generate an orthogonal basis for the Krylov subspace. Based on this orthogonal basis, the preprocessed quantized node admittance matrix is ​​projected onto the low-dimensional subspace to obtain the low-dimensional subspace matrix. ； Among them, g m Let X be a low-dimensional matrix obtained by projection from the Krylov subspace. m It is an orthogonal basis of Krylov subspaces; A low-dimensional subspace quantum linear equation is constructed based on the Galerkin orthogonality condition; wherein, a low-dimensional unsolved state is sought in the Krylov subspace. By making the residuals of the preprocessed quantum electromagnetic transient simulation equations orthogonal to the Krylov subspace, we obtain the low-dimensional subspace quantum linear equations: ； Among them, g m This represents the low-dimensional subspace matrix obtained by projection. Represents the quantum state to be determined in a low-dimensional subspace. The default initial quantum state for a quantum computer.

7. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 6, characterized in that: The variable quantum circuit in step S3 is specifically as follows: ； in, This represents a parameterized variable component quantum circuit. This represents the variational parameters to be optimized; It is a variable quantum state; The simplified global loss function is to use the low-dimensional subspace matrix g m Acting on variable quantum states and its right-hand side item The deviation between them is used as the optimization objective, and the loss function is specifically as follows: ； in, The simplified global loss function, where I represents the identity matrix, g m This represents the low-dimensional subspace matrix obtained by projection. It is a variable quantum state.

8. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 7, characterized in that: The parameter-by-parameter parsing update in step S3 is as follows: Select the j-th parameter to be updated in the variable component quantum circuit. And keeping the other variational parameters unchanged, the simplified global loss function is expressed in cosine form in the direction of this single parameter: ； in, , and These are the coefficients to be determined corresponding to the current parameter direction; Measure the simplified global loss function values ​​at the current parameter point and its positive and negative offset points respectively: ； Based on the above measurement results, the solution is obtained by using trigonometric function transformations. , and The optimal update value for the j-th variational parameter is: ； Update the j-th variational parameter The above steps are then repeated for the remaining variational parameters until a round of parameter sequence updates is completed. The optimized variational parameters Substituting the parameterized variable quantum circuit, we obtain an approximate solution to the low-dimensional subspace equation: ； in, Represents the quantum state to be determined in a low-dimensional subspace. This represents a parameterized variable component quantum circuit. This represents the optimal parameters.

9. The novel power system condition number sensing quantum electromagnetic transient simulation method as described in claim 2, characterized in that: The low-dimensional subspace approximate deconstruction method in step S4 is as follows: based on the nodal voltage correction in the original electromagnetic transient simulation space, and using the Krylov subspace basis vectors and preprocessing relations, the following is obtained: ； in, This represents the proportionality coefficient introduced by the normalization of the right-hand side during the k-th residual correction process. This represents the search direction basis obtained from the Krylov subspace basis vectors through preprocessing relation transformation during the k-th residual correction process. The solution in the low-dimensional subspace corresponding to the k-th residual correction equation; Update the node voltage quantum state using node voltage correction. And recalculate the current residual based on the updated node voltage quantum state, specifically: ； in, This represents the current residual in the (k+1)th iteration. G represents the node voltage quantum state obtained in the (k+1)th iteration. q Represents the quantized nodal admittance matrix. Represents the quantum state of the injected current at the node; If the current residual error meets the preset accuracy requirement, then the output... Use the node voltage result at the current simulation moment; otherwise, let k=k+1, and repeat steps S2-S4 until the preset accuracy requirement is met or the preset maximum number of iterations is reached.

10. A novel power system condition number sensing quantum electromagnetic transient simulation system, comprising a computer program, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-9 above.

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