A power system power flow calculation method based on quantum singular value transformation

Abstract

This invention relates to the fields of power system power flow calculation and quantum computing, and in particular to a power system power flow calculation method and system based on quantum singular value transformation (QSVT). The invention designs the objective function to be approximated by QSVT and the approximation polynomial satisfying parity and boundedness, converting the polynomial into a QSP phase sequence. Then, a QSVT circuit is constructed using the unitary operator U and the phase sequence to solve for the quantum state. Corrections for voltage and phase angle in the quantum state are extracted through quantum amplitude estimation and fed back to the classical controller for iteration to update the voltage and phase angle of the power system until the power flow calculation converges. This invention utilizes the QSVT framework to achieve polynomial approximation and phase sequence optimization, reducing computational complexity and avoiding convergence issues.

Description

Technical Field

[0001] This invention relates to the fields of power system power flow calculation and quantum computing technology, and in particular to a power system power flow calculation method based on quantum singular value transformation. Background Technology

[0002] As power grids expand in scale and complexity, traditional power flow calculations face bottlenecks in efficiency and accuracy, especially with the urgent need for real-time computing in the context of renewable energy integration and system dynamics. Existing quantum power flow methods have shown some feasibility in small-scale systems, but they generally suffer from high dependence on qubit resources, difficulty in precision control, and large quantum circuit depth, making them unsuitable for the computational needs of large-scale real-world power grids. Furthermore, they are limited to coarse simulations using linearized solvers and lack in-depth processing of the singular value structure of the power flow matrix.

[0003] Currently, the number of qubits available for power flow calculation is relatively limited. By utilizing the quantum singular value transform (QSVT) algorithm to eliminate the dependence on phase estimation, the required number of qubits can be reduced, and an efficient and scalable quantum power flow calculation model can be constructed, avoiding the non-convergence problem caused by over-reliance on quantum optimizers or multiple iterations. Summary of the Invention

[0004] To overcome the problems of high computational complexity and poor convergence of classical power flow algorithms in large-scale or ill power systems in the prior art, this invention proposes a power flow calculation method based on quantum singular value transformation.

[0005] This invention proposes a power flow calculation method for power systems based on quantum singular value transformation, comprising the following steps:

[0006] S1. Construct the power flow equation Ax=b based on the power grid topology and node parameters, where A is the Jacobian matrix, b is a constant vector, and x is the variable to be solved; normalize the Jacobian matrix A by block encoding to obtain the unitary operator U.

[0007] S2. The objective function that needs to be approximated in the design of QSVT And approximation polynomials that satisfy parity and boundedness , polynomial Convert to QSP phase sequence d is a polynomial The order of;

[0008] S3, Based on unitary operator U and phase sequence A QSVT circuit is constructed, the power deviation vector Δf calculated from the power flow is loaded into the quantum state, the QSVT circuit is run, and the QSVT output and quantum state are obtained after post-selection and amplitude amplification. ;

[0009] S4. Extracting quantum states through quantum amplitude estimation The correction values ​​for voltage and phase angle are fed back to the classical controller for iteration to update the voltage and phase angle of the power system until the power flow calculation converges.

[0010] Preferably, step S2 includes the following steps:

[0011] S21. Construct the objective function for Chebyshev polynomial approximation. y takes values ​​in the range [δ, 1], where δ is the set truncation error;

[0012] S22. Map the approximation interval [δ,1] onto [-1,1] to form a mapping function. Let t be a value in the interval [-1, 1], and y(t) represent the y-value corresponding to t; After parity processing, we get ;structure , It is a symbolic function;

[0013] ;

[0014] S23. Constructing a pairwise polynomial , ;exist middle z is the variable of the unit circle. i is an imaginary number. The phase angle corresponding to the singular value map;

[0015] S24. Constructing a pseudounitary matrix polynomial Then, by performing variable substitution, the Laurent polynomial is obtained. ;right Factorize to obtain the phase sequence d is a polynomial The order of;

[0016] ;

[0017] ;

[0018] ;

[0019] Among them, A(z) and B(z) are transition terms. A ( z )= P ( y ), ; , Represents phase sequence The 0th and kth phases in the matrix; uppercase Z represents the Pauli matrix; superscript... Indicates complex conjugate; i is an imaginary number;

[0020] S25, Order ,use and the principle of parity, for Recursively factorize the factorization expression to obtain the reduced-order expression. ;

[0021] ;

[0022] Iterate through d, d-1, ..., 1, and let Updated to Repeat this step; solve in sequence. until At that time, the output phase sequence .

[0023] Preferably, the objective function is:

[0024] ;

[0025] ;

[0026] in, Here, C is the regularization parameter; C is a constant. To improve convergence accuracy, .

[0027] Preferably, after step S25, the following steps are performed for phase verification:

[0028] S26. Using phase sequence pairs Backwards The result of the backward derivation is denoted as a polynomial. ,judge If the condition is met, proceed to step S3; otherwise, return to step S22 to reconstruct. ;

[0029] Inverse polynomial The method is as follows:

[0030] Rotate the signal operator according to the QSP rules. and phase rotation operator Alternating multiplication yields auxiliary operators ,Will Write it in matrix format and align its top-left element. Taking the real part yields the reconstructed polynomial ;

[0031] ;

[0032] in, and Representing phase respectively and The corresponding rotation angle, and From phase sequence , 1≤k≤d; This represents the rotation angle of signal y, where y takes values ​​in the interval [δ, 1]. Represents the calculated matrix elements. Represents paired polynomials, superscript Indicates complex conjugation.

[0033] Preferably, step S3 includes the following steps:

[0034] S31, let the unitary operator U and its reversible place. Alternating arrangement to construct QSVT quantum circuits ;

[0035] ;

[0036] in, , , and They represent , , and Phase rotation;

[0037] S32, Ax=b, after adjustment, we get , This is the adjusted result of the Jacobian matrix A. A Hermitian matrix whose order is an integer power of 2; The result of expanding b with zero-filled elements; Encoding to On the probability amplitude of each quantum, a quantum state is obtained. m is b ’ The order of;

[0038] ;

[0039] in, It calculates the ground state, which corresponds to the integer in binary representation. ; As the normalization factor, ; for The i-th element;

[0040] S33, will The quantum state is stored as input in the system register and initialized as follows: , Describe an auxiliary qubit and calculate the output state. Then, the final system state is obtained by measuring the auxiliary qubits and amplifying the amplitude. and the quantum state of the variable to be solved x ;

[0041] ;

[0042] ;

[0043] in, Representing quantum pair The approach, express The reverse; This indicates the probability of a successful measurement result of 0. This indicates a failed measurement result.

[0044] Preferred:

[0045] P(A ' )= ;

[0046] Where i is an imaginary number, , , and All are phases, and U is the unitary operator. Let U be the reversible set of U, and e be a natural number.

[0047] Preferably, in step S4, the quantum state is first... Performing a quantum Fourier transform yields the voltage amplitude correction values ​​at each node of the power system. and voltage phase angle correction Then amplify the target amplitude and determine the final system state. implement M Each measurement was performed, and the ground states were calculated statistically. Frequency of occurrence ,from Taking the square root of the real and imaginary parts respectively as classical estimates of the voltage correction. Classical estimates of phase angle correction The results of quantum measurement and Feedback is sent to the classic controller to update the node state; this process is repeated until convergence.

[0048] Preferably, in step S1, the power flow calculation equation Ax=b is first adjusted so that the adjusted Jacobian matrix... Elements are normalized to integer powers of 2 and satisfy the Hermitian matrix; the adjusted power flow calculation equation is: , It is obtained by expanding the order of b by filling it with zero elements; then... Write it as a linear combination of several unitary operators that can be implemented, and construct a block-coded unitary operator U as a unitary operator.

[0049] Preferred:

[0050] ;

[0051] ;

[0052] in, Let A be the normalized matrix of the Jacobian matrix A. for Reversible; for The Hermitian processing results.

[0053] The present invention proposes a power flow calculation system based on quantum singular value transformation, comprising 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 power flow calculation method based on quantum singular value transformation.

[0054] The advantages of this invention are:

[0055] (1) The present invention proposes a power flow calculation method based on quantum singular value transformation. By transforming the high-dimensional matrix operations (such as Jacobian matrix inversion) in traditional power flow calculation into parallel processing of quantum circuits, the method utilizes the QSVT framework to achieve polynomial approximation and phase sequence optimization, thereby reducing computational complexity. Compared with classical algorithms, QSVT does not rely on classical optimizers for multiple rounds of parameter iteration updates. The present invention uses the polynomial approximation capability and regularization constraints of QSVT to ensure stable convergence of the calculation process and avoid convergence problems. This method can efficiently handle large-scale or ill-conditioned power systems, enabling power flow calculation to be completed quickly at a set accuracy, and is especially suitable for real-time power grid monitoring scenarios.

[0056] (2) This invention achieves an adaptive precision control mechanism through programmable phase parameters (i.e., phase sequence), and uses Chebyshev expansion to approximate the objective function with high precision, ensuring that the fitting error of the singular value spectrum of the matrix is ​​minimized. This invention introduces constraints... It overcomes the numerical divergence problem caused by ill-conditioned systems, improves the reliability and stability of power flow results, and provides accurate data support for power system planning and fault analysis.

[0057] (3) This invention adopts a quantum-classical hybrid architecture, extracts the correction amount through quantum amplitude estimation and feeds it back to the classical controller, which significantly reduces the dependence on classical computing resources. The iterative control mechanism ensures that the calculation process converges under limited resources, so that this method can not only reduce energy consumption, but also seamlessly integrate with existing power system platforms, and promote the development of power flow computing in an economical and energy-saving direction. Attached Figure Description

[0058] Figure 1 This is the main flowchart of a power system power flow calculation method based on quantum singular value transformation proposed in this invention;

[0059] Figure 2 This is a diagram of the IEEE 4-node network topology.

[0060] Figure 3 The results of solving the node voltage phase angle using the method of the present invention and the traditional Newton-Raphson method are shown in the embodiments.

[0061] Figure 4 The results of solving the node voltage amplitude using the method of the present invention and the traditional Newton-Raphson method are shown in the embodiments. Detailed Implementation

[0062] 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.

[0063] like Figure 1 , Figure 2 As shown in the figure, this embodiment proposes a power flow calculation method for power systems based on quantum singular value transformation. First, the Jacobian matrix of the power flow calculation equation formed by the traditional Newton-Raphson method is normalized and block-encoded, transforming it into a unitary operator (i.e., unitary operator U) that can be processed by quantum computing. Then, using the quantum singular value transformation framework, the objective function is approximated through Chebyshev polynomials, and an accurate quantum signal processing phase sequence is designed. Subsequently, a dedicated quantum circuit is built to load the power deviation vector into a quantum state and perform the transformation, thereby achieving quantum acceleration of core operations such as matrix inversion. Finally, voltage and phase angle corrections are extracted through quantum amplitude estimation and fed back to the classical controller for iterative updates until the convergence condition is met. This embodiment is specifically illustrated in steps S1-S4.

[0064] S1. Construct the Newton-Raphson power flow calculation equation Ax=b based on the power grid topology and node parameters, where A is the Jacobian matrix, b is a constant vector, and x is the variable to be solved, including the correction amount of voltage amplitude and phase angle. Normalize the Jacobian matrix A to make Ax=b satisfy the input of quantum singular value transformation.

[0065] This step S1 is specifically divided into the following steps S11-S13.

[0066] S11. Construct the target power flow calculation equations based on the Newton-Lambert method, forming the matrix equation Ax=b to be solved. Perform spectral normalization on the Jacobian matrix A to obtain the normalized matrix. .

[0067] Elements in the Jacobian matrix A may exceed the input range [-1,1] of the quantum singular value transform. Spectral normalization of the Jacobian matrix can guarantee the normalization of the matrix. The elements fall into the input range [-1,1] of the quantum singular value transformation, laying the foundation for subsequent quantum singular value transformations.

[0068] Jacobian matrix normalized coefficients The calculation formula is as follows:

[0069] (1);

[0070] in, Aij is the element in the i-th row and j-th column of the Jacobian matrix A. Formula (1) means taking the element with the largest absolute value in the Jacobian matrix A as the coefficient. In this step, the spectral norm is estimated by summing the matrix elements using formula (1), which facilitates subsequent calculations.

[0071] The normalization formula is:

[0072] (2);

[0073] S12, For the normalized matrix Perform processing to make it satisfy the Hermitian matrix and extend its order to... The extended matrix is ​​denoted as , n is the matrix The minimum order required to fill with zeros during the order extension process.

[0074] Specifically, the first step in this process is to determine... If the matrix is ​​Hermitian, then perform the padding operation (zeroing to expand the matrix order, i.e., filling with zero elements to expand the matrix order) to make the matrix... Extended to the nearest The order is obtained If not, then Hermitization transformation needs to be performed according to formula (3), followed by padding, and then zero elements are filled and expanded to the nearest order. The order is obtained .

[0075] (3);

[0076] in, for Hermitian processing results; superscript This indicates that it can be reversed.

[0077] It can be seen that step S12 obtains the matrix. The process is expressed by the following formula:

[0078] ;

[0079] After expanding the Jacobian matrix, b also needs to be zeroed out and expanded according to formula (4) to make it so that... ; The result of the order extension of b is used for subsequent quantum encoding.

[0080] (4);

[0081] S13, will Write it as a linear combination of several unitary operators to construct a block-coded unitary operator U.

[0082] Specifically, in this step, firstly... Write the formula (5) as a linear combination of several unitary operators, then define the preparation operator P and the measurement operator Q in the auxiliary space, and combine them to form the unitary operator. I is the identity matrix; a quantum bit is introduced to project onto U so that it satisfies formula (6), and finally the block-coded unitary operator U is obtained as the unitary operator.

[0083] (5);

[0084] (6);

[0085] Where K represents the number of base operators used in the construction block encoding. It is a realizable unitary matrix. Let be the coefficient, satisfying .

[0086] S2. Design the objective function to be approximated in QSVT (Quantum Singular Value Transform). According to the objective function Design an approximation polynomial that satisfies both parity and boundedness. Then the polynomial Convert to QSP (Quantum Phase Processing) phase sequence For phase sequence Perform calculations and verification; , and These represent the 0th, d-1th, and dth phases in the phase sequence, respectively, where d is a polynomial. The order of.

[0087] S21. Since the singular values ​​of the unitary operator (i.e., the block-coded unitary operator U) are in the range [0,1], the objective function to be approximated is: , There is a small truncation error. To avoid the problem of singularities causing the computation to diverge when singular values ​​are present, the regularization parameter is obtained through Tikhonov regularization. At this point, the objective function is replaced with .

[0088] S22, Construction For the objective function in S21 To approach, , For symbolic functions, for The parity processing result is given by t, which is the value in the interval [-1,1], and y(t) represents the value in the interval [δ,1] corresponding to t.

[0089] In this step, the first step is to define the selected tolerance error. (If the internal tolerance of the Newton-Raphson method is...) ,but Then, through the linear transformation of formula (7), the approximation interval [δ,1] is mapped to [-1,1]; let the function t is the value in the interval [-1, 1], y(t) represents the value in the interval [δ, 1] corresponding to t, and y represents the value in the interval [δ, 1]. The Chebyshev polynomial expansion of the cutoff degree N is as follows Chebyshev polynomial Defined as For functions Chebyshev coefficient Calculate according to formula (8). Here Using Chebyshev polynomials of the first kind is more suitable for polynomial approximation calculations.

[0090] (7);

[0091] (8);

[0092] In formulas (7) and (8), t is a transition term and π is the value of pi.

[0093] Then to Perform parity processing and construct , For symbolic functions, for The result of parity processing.

[0094] (9);

[0095] Based on the objective function Since it is an odd function, it is necessary to ensure that... It is also an odd polynomial, so it is defined as follows: ,in For symbolic functions, satisfy , This represents the value of y taken on the interval [δ, 1]. The largest norm, express The maximum norm. The degree is estimated and calculated according to formula (10).

[0096] (10);

[0097] Where d is a polynomial The order of the polynomial is the highest degree of the polynomial. is the regularization parameter in S21; C is a constant, which can take the value 2.

[0098] S23, by Constructing a pairwise polynomial It satisfies the energy conservation equation (11):

[0099] (11);

[0100] Among them, in the paired polynomial There is And z is the variable of the unit circle. Where i is an imaginary number, The phase angle corresponding to the singular value mapping; Formula (11) represents the method for obtaining the target polynomial. and paired polynomials The total probability is 1.

[0101] S24. Next, construct a 2×2 paraunitary matrix polynomial. As shown in formula (12), the variable is then replaced with z, and formula (13) is written in Laurent polynomial form. Then factorize it into equation (14).

[0102] (12);

[0103] (13);

[0104] (14);

[0105] Among them, A(z) and B(z) are transition terms. A ( z )= P ( y ), ; , Represents phase sequence The 0th and kth phases in the equation, where d is the polynomial calculated by formula (10) above. The order; superscript Indicates complex conjugation.

[0106] S25. Then, recursively decompose formula (14), assuming... ,use And the principle of parity, exists Make right multiplication Then, multiply by the left. , eliminate highest ( The terms are reduced to form equation (15); diag represents a diagonal matrix;

[0107] (15);

[0108] Iterate through d, d-1, ..., 1, and let Updated to Repeat step S25; solve sequentially. until Z represents the Pauli matrix.

[0109] S26. Verify the obtained phase using the obtained phase sequence. Backwards The result of the backward derivation is denoted as a polynomial. Next, determine If the condition is met, proceed to step S3; otherwise, return to step S22 to reconstruct. Perform the calculation. Indicates the interval Calculated above The maximum norm.

[0110] Specifically, the reconstruction obtained in this step The method is as follows: rotate the signal operator according to the rules of quantum signal processing (QSP). and phase rotation operator Alternating multiplication yields auxiliary operators Write it in matrix format as formula (16), and adjust its top-left elements. Taking the real part yields the reconstructed polynomial .

[0111] (16);

[0112] (17);

[0113] in, and Representing phase respectively and The corresponding rotation angle, and From phase sequence , 1≤k≤d; This represents the rotation angle of signal y, where y takes values ​​in the interval [δ, 1]. Represents the calculated matrix elements. Represents paired polynomials, superscript Re denotes complex conjugation; Re denotes taking the real part.

[0114] (18);

[0115] (19);

[0116] Where i is an imaginary number.

[0117] S3, the unitary operator U based on S1, and the phase sequence of S2 A QSVT circuit is constructed to efficiently load the power deviation vector Δf calculated from the power flow calculation into the quantum state. The QSVT circuit is then run, and the output is obtained through post-selection and amplitude amplification. Post-selection refers to measuring the auxiliary qubits after the quantum circuit has finished running, retaining only the experimental data with a measurement result of 0, and discarding invalid data with a result of 1.

[0118] This step S3 specifically includes the following sub-steps S31-S33.

[0119] S31, Determine if included A system register containing 1 qubit, A block-encoding auxiliary register for 1 qubit and a quantum signal processing register containing 1 qubit. The value is determined by system input, usually Define phase rotation , It is a phase rotation gate, in which According to phase sequence Apply them one by one, and finally construct the QSVT quantum circuit alternately according to formula (20). .

[0120] (20);

[0121] In formula (20), U and Alternating arrangement, i.e. and The interval is U. and Between r is a positive integer; , , and They represent , , and Phase rotation;

[0122] S32, according to formula (21) Encoding to On the probability amplitude of each quantum, a quantum state is obtained. b ’ Let m be the extended order vector of the constant vector b, and m be the extension of b. ’ The order of.

[0123] (twenty one);

[0124] in, It calculates the ground state, which corresponds to the integer in binary representation. Normalization factor ; for The i-th element.

[0125] S33, will It is stored as input in the system register, and then the quantum state is initialized. , It is an auxiliary qubit used to control block encoding and subsequent selection. The mathematical operation corresponding to the QSVT circuit can be expressed by formula (22) to obtain the output state. Then, the final system state is obtained through post-selection (measuring auxiliary qubits) and amplitude amplification. and the quantum state of the variable to be solved x .

[0126] (twenty two);

[0127] (twenty three);

[0128] Where Z represents the Pauli matrix; Representing quantum pair The approach, express The reverse; This indicates that the measurement result is 0 (i.e. The probability of success, This indicates a failed measurement result; e is a natural number. Garbage and waste states represent redundant terms that might be measured in the measurement results, which can be understood as "unnecessary terms".

[0129] S4. Using quantum amplitude estimation to obtain quantum states from the pseudo-inverse operation of QSVT. The correction values ​​for voltage magnitude and phase angle (i.e., voltage correction ΔV and phase angle correction Δθ) are extracted and converted into usable classical numerical results through quantum measurement. These correction values ​​are then fed back to the classical controller to update the state variables (voltage and phase angle) of the power flow calculation. The process is iterated in the classical controller until the entire power flow calculation process converges.

[0130] Specifically, this step includes the following sub-steps.

[0131] S41, voltage correction ΔV, and phase angle correction Δθ correspond to quantum states respectively. The real and imaginary parts of the quantum register are used to divide the quantum register into an amplitude register and a phase register, and then the quantum Fourier transform (QFT) is used to... Mapping to the complex space, we get equation (24):

[0132] (twenty four);

[0133] N is the number of nodes in the power system. and The voltage magnitude correction and voltage phase angle correction for the i-th node are respectively; It calculates the ground state, which corresponds to the integer in binary representation. .

[0134] S42. Using the Grover operator Amplify the target amplitude according to equation (25), and for implement M Each measurement was performed, and the ground states were calculated statistically. Occurrence frequency , the classical estimate of the correction amount is obtained using formula (26) and .

[0135] (25);

[0136] (26);

[0137] where is the classical estimate of the voltage correction amount, is the classical estimate of the phase angle correction amount; Re represents taking the real part, Im represents taking the imaginary part; |x> is the right vector quantum state of the variable x to be solved, and <x| is the left vector quantum state of the variable x to be solved.

[0138] S43. Feed the quantum measurement results and back to the classical controller, update the node state, and judge whether the power flow calculation converges; the convergence condition can be set as: the two-norm of the power deviation vector is less than or equal to the set threshold ;

[0139] If not satisfied, return to step S42 and continue the iteration;

[0140] If so, output the power flow result V' = V + , θ' = θ + ; where, V' and θ' are the updated voltage amplitude and phase angle respectively, and V and θ are the current voltage amplitude and phase angle respectively.

[0141] The above method will be elaborated below in combination with specific embodiments.

[0142] In this embodiment, experiments are carried out on the IEEE four-node power system topology, where node 1 is a balanced node, nodes 2 and 3 are PQ nodes, and node 4 is a PV node. The system consists of 4 transmission lines, forming a loop network structure, and a generator is connected to each of node 1 and node 4.

[0143] In this embodiment, the power flow calculation is performed on the topology system shown Figure 2 respectively using the method of the present invention and the traditional Newton-Raphson method, and the results are statistically shown as Figure 3 , Figure 4 shown. In the figure, the solid line is the calculation result of the method of the present invention, and the dashed line is the calculation result of the traditional Newton-Raphson method.

[0144] From Figure 3 , Figure 4It can be seen that the results of the present invention in calculating the node voltage phase angle and voltage magnitude are completely consistent with those of the traditional Newton-Layer method for power flow calculation, proving that the QSVT-based algorithm has the same numerical accuracy and correctness as the traditional method in this example.

[0145] Compared to classical algorithms, this invention replaces the most computationally intensive part of classical power flow (AC)—solving the large-scale sparse linear equations generated after repeated linearization (inversion / solution of linear systems (i.e., power flow calculation equations) on Jacobian matrices or augmented matrices)—with a "matrix function implementation" in quantum states. Under the premise of a large power grid scale (high number of buses / state dimension), sparse matrix (limited connectivity per bus), efficient block encoding, and controllable / preconditionable condition number, the QSVT-type quantum linear system (power flow calculation equations) solver can reduce the dependence on dimension from the classical polynomial level to an approximate logarithmic level. (Polynomial Logarithmic), where n0 is the order of the Jacobian matrix A.

[0146] Compared to the HHL algorithm, the advantage of the method in this invention is more directly reflected in the dependence of complexity on the condition number and accuracy. The classic formulation of HHL relies on phase estimation (QPE) to achieve eigenvalue decomposition and reciprocal mapping, often resulting in a large gate depth, stringent requirements on coherence time, and typically poor complexity due to its dependence on the condition number and accuracy. The order of magnitude, n1 is the condition number of the linear system Ax=b in HHL). The present invention theoretically achieves a linear dependency of "optimal order of magnitude" and better precision scaling (commonly expressed as...). This significantly reduces the risk of line depth and error accumulation while maintaining the same level of accuracy.

[0147] 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.

[0148] 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.

[0149] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A power flow calculation method for power systems based on quantum singular value transformation, characterized in that, Includes the following steps: S1. Construct the power flow equation Ax=b based on the power grid topology and node parameters, where A is the Jacobian matrix, b is a constant vector, and x is the variable to be solved; normalize the Jacobian matrix A by block encoding to obtain the unitary operator U. S2. The objective function that needs to be approximated in the design of QSVT And approximation polynomials that satisfy parity and boundedness , polynomial Convert to QSP phase sequence d is a polynomial The order of; S3, Based on unitary operator U and phase sequence A QSVT circuit is constructed, the power deviation vector Δf calculated from the power flow is loaded into the quantum state, the QSVT circuit is run, and the QSVT output and quantum state are obtained after post-selection and amplitude amplification. ; S4. Extracting quantum states through quantum amplitude estimation The correction values ​​for voltage and phase angle are fed back to the classical controller for iteration to update the voltage and phase angle of the power system until the power flow calculation converges. Step S3 includes the following steps: S31, let the unitary operator U and its reversible place. Alternating arrangement to construct QSVT quantum circuits ; in, , , and They represent , , and Phase rotation; S32, Ax=b, after adjustment, we get , This is the adjusted result of the Jacobian matrix A. A Hermitian matrix whose order is an integer power of 2; The result of expanding b with zero-filled elements; Encoding to On the probability amplitude of each quantum, a quantum state is obtained. m is b ’ The order of; in, It calculates the ground state, which corresponds to the integer in binary representation. ; As the normalization factor, ; for The i-th element; S33, will The quantum state is stored as input in the system register and initialized as follows: , Describe an auxiliary qubit and calculate the output state. Then, the final system state is obtained by measuring the auxiliary qubits and amplifying the amplitude. and the quantum state of the variable to be solved x ; in, Representing quantum pair The approach, express The reverse; This indicates the probability of a successful measurement result of 0. This indicates a failed measurement result.

2. The power system power flow calculation method based on quantum singular value transformation as described in claim 1, characterized in that, Step S2 includes the following steps: S21. Construct the objective function for Chebyshev polynomial approximation. y takes values ​​in the range [δ, 1], where δ is the set truncation error; S22. Map the approximation interval [δ,1] onto [-1,1] to form a mapping function. Let t be a value on the interval [-1, 1], and y(t) represent the y-value corresponding to t; After parity processing, we get ;structure , It is a symbolic function; ； S23. Constructing a pairwise polynomial , ;exist middle z is the variable of the unit circle. i is an imaginary number. The phase angle corresponding to the singular value map; S24. Constructing a pseudounitary matrix polynomial Then, by performing variable substitution, the Laurent polynomial is obtained. ;right Factorize to obtain the phase sequence d is a polynomial The order of; Among them, A(z) and B(z) are transition terms. A ( z )= P ( y ), ; , Represents phase sequence The 0th and kth phases in the matrix; uppercase Z represents the Pauli matrix; superscript... Indicates complex conjugate; i is an imaginary number; S25, Order ,use and the principle of parity, for Recursively factorize the factorization expression to obtain the reduced-order expression. ; Iterate through d, d-1, ..., 1, and let Updated to Repeat this step; solve in sequence. until At that time, the output phase sequence .

3. The power flow calculation method for power systems based on quantum singular value transformation as described in claim 2, characterized in that, The objective function is: in, Here, C is the regularization parameter; C is a constant. To improve convergence accuracy, .

4. The power flow calculation method for power systems based on quantum singular value transformation as described in claim 2, characterized in that, Following step S25, the following steps are used for phase verification: S26. Using phase sequence pairs Backwards The result of the reverse reasoning is denoted as a polynomial. ,judge If the condition is met, proceed to step S3; otherwise, return to step S22 to reconstruct. ; Inverse polynomial The method is as follows: Rotate the signal operator according to the QSP rules. and phase rotation operator Alternating multiplication yields auxiliary operators ,Will Write it in matrix format and align its top-left element. Taking the real part yields the reconstructed polynomial ; in, and Representing phase respectively and The corresponding rotation angle, and From phase sequence , 1≤k≤d; This represents the rotation angle of signal y, where y takes values ​​in the interval [δ, 1]. Represents the calculated matrix elements. Represents paired polynomials, superscript Indicates complex conjugation.

5. The power flow calculation method for power systems based on quantum singular value transformation as described in claim 1, characterized in that: P(A ' )= Where i is an imaginary number, , , and All are phases, and U is the unitary operator. Let U be the reversible set of U, and e be a natural number.

6. The power flow calculation method for power systems based on quantum singular value transformation as described in claim 1, characterized in that, In step S4, the quantum state is first... Performing a quantum Fourier transform yields the voltage amplitude correction values ​​at each node of the power system. and voltage phase angle correction Then amplify the target amplitude and determine the final system state. implement M Each measurement was performed, and the ground states were calculated statistically. Frequency of occurrence ,from Taking the square root of the real and imaginary parts respectively as classical estimates of the voltage correction. Classical estimates of phase angle correction The results of quantum measurement and Feedback is sent to the classic controller to update the node state; this process is repeated until convergence.

7. The power flow calculation method for power systems based on quantum singular value transformation as described in claim 1, characterized in that, In step S1, the power flow calculation equation Ax=b is first adjusted to make the adjusted Jacobian matrix... Elements are normalized to integer powers of 2 and satisfy the Hermitian matrix; the adjusted power flow calculation equation is: , It is obtained by expanding the order of b by filling it with zero elements; then... Write it as a linear combination of several unitary operators that can be implemented, and construct a block-coded unitary operator U as a unitary operator.

8. The power flow calculation method for power systems based on quantum singular value transformation as described in claim 1, characterized in that: in, Let A be the normalized matrix of the Jacobian matrix A. for Reversible; for The Hermitian processing results.

9. A power flow calculation system for a power system based on quantum singular value transformation, 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 implement the power flow calculation method for a power system based on quantum singular value transformation as described in any one of claims 1-8.

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