Network node reduction method for power system transient stability calculation based on hhl

Abstract

The present application relates to the technical field of quantum computing and power system, especially to a network node reduction method for power system transient stability calculation based on HHL.The present application constructs an equivalent admittance matrix and a conversion matrix, splits the conversion matrix into r linear equations of e order and corresponding real linear equations, and solves them by using HHL algorithm.The present application converts the traditional Kron reduction problem into multiple parallel linear equations, and solves them quickly through quantum circuit, combines HHL algorithm with power system node reduction method, and uses HHL algorithm to accelerate the solution of linear equations, which greatly reduces the calculation complexity, effectively relieves the calculation pressure of large-scale system, significantly improves the efficiency of node reduction, and breaks through the calculation bottleneck of existing classical methods.

Description

Technical Field

[0001] This invention relates to the fields of quantum computing and power system technology, and in particular to a method for reducing network nodes for calculating the transient stability of power systems based on HHL. Background Technology

[0002] Transient stability analysis of power systems is a crucial step in ensuring their safe and stable operation. To accurately describe transient processes, large-scale differential-algebraic equation models encompassing generators, dynamic loads, and transmission networks are required. However, with the continuous expansion of power grids and the exponential growth in the number of system nodes, transient simulations face problems such as the curse of dimensionality and excessive computational complexity.

[0003] In traditional methods, intermediate network nodes can be eliminated by reducing network nodes, retaining only generator nodes and dynamic load nodes. This reduces the number of equations and variables in a simultaneous solution. Kron reduction is a commonly used method, and its key computational aspect lies in finding the optimal Kron reduction algorithm. ;Y EE Y represents the admittance matrix between nodes of order e×e to be eliminated; ER Let represent the admittance matrix between nodes of order e×r to be eliminated and nodes to be retained; r is the total number of nodes to be retained, and e is the total number of nodes to be eliminated. Although this method can reduce computation to some extent, large-scale matrix inversion and decomposition are still required in large-scale systems, especially when the number of nodes to be retained is... The number of nodes eliminated is When this is the case, the method of directly finding the inverse product is used to obtain the product. The computational complexity is typically O(n). It is very complex and difficult to meet real-time requirements.

[0004] In recent years, with the rapid development of quantum computing, its application in numerical computation of power systems has attracted widespread attention. Quantum algorithms can achieve speedups surpassing classical computations for specific problems. Among them, the HHL algorithm, which theoretically achieves exponential speedups in solving quantum linear equations, has been applied to problems such as power flow calculation, economic dispatch, and optimal power flow, demonstrating strong potential. However, a quantum solution for the problem of network node reduction is currently lacking. Summary of the Invention

[0005] To overcome the problem that the network node reduction efficiency in the existing technology is difficult to meet the real-time requirements, this invention proposes a network node reduction method for power system transient stability calculation based on HHL, which greatly improves the node reduction efficiency.

[0006] This invention proposes a method for reducing network nodes for calculating transient stability of power systems based on HHL, comprising the following steps:

[0007] Construct an equivalent admittance matrix Y of order e x r eq and the conversion matrix Y EE Y eq =Y ER ; Y EE represents the admittance matrix between the nodes to be eliminated of order e x e; Y ER represents the admittance matrix between the nodes to be eliminated and the reserved nodes of order e x r; r is the total number of reserved nodes, and e is the total number of nodes to be eliminated;

[0008] Y EE Y eq =Y ER Split into r linear equations of order e Y EE Y eq(s) =Y ER(s) , Y eq(s) is the s-th column e-order column vector of Y eq , Y ER(s) is the s-th column e-order column vector of Y ER , and 1≤s≤r;

[0009] Construct a real linear equation system of each linear equation system and solve by using the HHL algorithm; the real linear equation system is: ; G EE , G eq(s) and G ER(s) are the conductances of Y EE , Y eq(s) and Y ER(s) , respectively, B EE , B eq(s) and B ER(s) are the conductances of Y EE , Y eq(s) and Y ER(s) , respectively;

[0010] Construct the admittance reduction equation system A p x p =b p and solve x p by using the HHL algorithm; wherein, A p is a reduction parameter matrix, and is an r-order diagonal matrix composed of elements A; b p is a reduction vector, b p =[b s ;1≤s≤r], b s is the s-th vector of b p ; x p is a column vector composed of the reduction network admittance matrix elements to be solved, x p =[x s ;1≤s≤r], x s is the s-th vector of xp The s-th vector; by rearranging x p The solution yields the reduced network admittance matrix, which is used for network node reduction;

[0011] , , .

[0012] Preferred, A p x p =b p The solution process is as follows:

[0013] Configure the HHL algorithm quantum circuit, including a quantum register q for storing phase information. b and used to store the normalized b p Amplitude encoding |b> and output x p The quantum register q of the approximate solution c ;

[0014] Using quantum phase estimation to A p The eigenvalues ​​are stored in the quantum register q b In, and through controlled rotation, the quantum register q b The phase information of the eigenvalues ​​is transferred to the amplitude;

[0015] The quantum register q is deactivated by inverse quantum phase estimation. b With quantum register q c After entanglement, a quantum measurement is applied to obtain x. p Unification and resolution The quantum input, for Perform inverse normalization to obtain x p Approximate solution.

[0016] Preferably, the HHL algorithm quantum circuit further includes an auxiliary qubit q for controlled rotation. a ;

[0017] The quantum register q is controlled by rotation. b The way in which the eigenvalue phase information is transferred to the amplitude is as follows:

[0018] With auxiliary bit q a For the target bit, use the quantum register q b To control the bits, a unitary gate is applied to the quantum state obtained from the quantum phase estimation. :

[0019] ;

[0020] Where, θ i As a transition term, θ i=2arcsin C is the normalization constant; For A p The i-th approximate eigenvalue; 1≤i≤r×e.

[0021] Preferred, q b The number of qubits is n0+ Where n0 is the number of qubits required for the basic accuracy of the absolute value of the eigenvalues, n pre The number of decimal places required to increase the precision of the absolute value of the eigenvalue. It represents rounding up.

[0022] Preferred, q a The number of qubits is 1; q c The number of qubits is log2N0.

[0023] Preferably, the admittance reduction equation set A p x p =b p The constraints are: A p b is a Hermitian matrix of integer powers of 2. p For unit vectors; if constraints are not met, first A p x p =b p After processing to ensure the constraints are met, the HHL algorithm is then used to solve for x. p ;

[0024] If A p x p =b p If it is not a Hermitian matrix, then it is Hermitized. The transformed formula is:

[0025] ;

[0026] in, for The conjugate transpose of the matrix. Added for Hermitization One zero element;

[0027] If A p x p =b p If the order is not an integer power of 2, then we perform an order expansion process, and the expanded system of equations is as follows:

[0028] ;

[0029] Where I is the order of The identity matrix, N0 is The order of N0 is N0 = 2 × e × r; denotes rounding down, λ c denotes an integer between an integer in the range of absolute value of eigenvalue and satisfying 2 power; denotes λ c 0 vector of dimension.

[0030] Preferably, the conversion matrix Y EE Y eq =Y ER The construction process is as follows:

[0031] S1, according to the power grid topology, constructing network node voltage equation;

[0032] S2, dividing the nodes into reserved nodes and nodes to be eliminated, reconstructing the node voltage equation;

[0033] S3, expressing the voltage and injected current of the nodes to be eliminated with the voltage and injected current of the reserved nodes, constructing equation group:

[0034] I R =Y sta U R ;

[0035] Y sta =Y RR -Y RE Y eq ;

[0036] Y EE Y eq =Y ER ;

[0037] Wherein, I R denotes the injected current vector of the reserved nodes, U R denotes the voltage vector of the reserved nodes, Y sta denotes the reduced network admittance matrix of r×r order; Y RR denotes the admittance matrix between the reserved nodes of r×r order number; Y RE denotes the admittance matrix between the reserved nodes and the nodes to be eliminated of r×e order number; Y eq denotes the equivalent admittance matrix of e×r order; Y EE denotes the admittance matrix between the nodes to be eliminated of e×e order number; Y ER denotes the admittance matrix between the nodes to be eliminated and the reserved nodes of e×r order number; r is the total number of reserved nodes, and e is the total number of nodes to be eliminated.

[0038] The application provides a network node reduction system based on HHL for power system transient stability calculation, which comprises a memory and a processor, the memory stores a computer program, and the processor is connected with the memory and used for executing the computer program to realize the network node reduction method based on HHL for power system transient stability calculation.

[0039] The application provides a storage medium which stores a computer program, and the computer program is used for realizing the network node reduction method based on HHL for power system transient stability calculation when being executed.

[0040] The application provides a computer program which is used for realizing the network node reduction method based on HHL for power system transient stability calculation when being executed.

[0041] The application has the advantages that:

[0042] The application provides a network node reduction method based on HHL for power system transient stability calculation, which converts a traditional Kron reduction problem into a plurality of parallel linear equations and solves the linear equations quickly through a quantum circuit. The application has the advantages that: The application effectively alleviates the calculation pressure of a large-scale system and significantly improves the efficiency of node reduction, and breaks through the calculation bottleneck of an existing classical method. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 The application provides a network node reduction method based on HHL for power system transient stability calculation, which converts a traditional Kron reduction problem into a plurality of parallel linear equations and solves the linear equations quickly through a quantum circuit.

[0044] Figure 2 The application provides a network node reduction method based on HHL for power system transient stability calculation, which converts a traditional Kron reduction problem into a plurality of parallel linear equations and solves the linear equations quickly through a quantum circuit.

[0045] Figure 3 The application provides a network node reduction method based on HHL for power system transient stability calculation, which converts a traditional Kron reduction problem into a plurality of parallel linear equations and solves the linear equations quickly through a quantum circuit. DETAILED DESCRIPTION

[0046] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, but not all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the application.

[0047] As Figure 1As shown, the network node reduction method for HHL-based power system transient stability calculation in the embodiment includes the following steps S1-S5.

[0048] S1, according to the power grid topology, construct the network node voltage equation:

[0049] I=YU (1);

[0050] wherein I is a vector composed of the current flowing into each node of the power grid, simply referred to as the injection current vector of the node; Y represents the network admittance matrix; U is a vector composed of the voltage of each node of the power grid, simply referred to as the voltage vector of the node.

[0051] S2, divide the nodes into reserved nodes and nodes to be eliminated, and reconstruct the node voltage equation as:

[0052] (2);

[0053] wherein I R represents the injection current vector of the reserved nodes, I E represents the injection current vector of the nodes to be eliminated, U R represents the voltage vector of the reserved nodes, U E represents the voltage vector of the nodes to be eliminated, Y RR represents the admittance matrix between the reserved nodes, with the order of r x r; Y RE represents the admittance matrix between the reserved nodes and the nodes to be eliminated, with the order of r x e; Y ER represents the admittance matrix between the nodes to be eliminated and the reserved nodes, with the order of e x r; Y EE represents the admittance matrix between the nodes to be eliminated, with the order of e x e; r is the total number of the reserved nodes, and e is the total number of the nodes to be eliminated.

[0054] wherein R represents the reserved node set in the power grid topology, and E represents the node set to be eliminated in the power grid topology; therefore, there are:

[0055] I R ={I r' ;r'∈R},U R ={U r' ;r'∈R};

[0056] I E ={I e' ;e'∈E},U E ={U e' ;e'∈E};

[0057] Y RR ={Y r'r'' ;r'∈R,r''∈R},Y RE ={Yr'e' ;r'∈R,e'∈E};

[0058] Y EE ={Y e'e'' ;e'∈R,e''∈R},Y ER ={Y e'r' ;e'∈E,r'∈R};

[0059] Among them, I r' and U r' These represent the injected current and voltage at the reserved node r', respectively. e' and U e' These represent the injected current and voltage at node e' to be eliminated, respectively; Y r'r'' To preserve the admittance between nodes r' and r'', Y r'e' To preserve the admittance between node r' and node e' to be eliminated, Y e'r' Y is the admittance between the node to be eliminated e' and the node to be retained r'. e'e'' Let e' be the admittance between nodes e' and e'' to be eliminated.

[0060] Based on the purpose of node reduction, the nodes to be retained are generator nodes and dynamic load nodes, while the nodes to be eliminated are intermediate network nodes.

[0061] S3. Express the voltage and injection current of the node to be eliminated using the voltage and injection current of the node to be retained, thereby eliminating the node to be eliminated and obtaining the expression for the reduced network admittance matrix Y. sta ;I R =Y sta U R .

[0062] Y sta The derivation process is as follows:

[0063] Since the injected current of the node to be eliminated is 0, therefore I E =0, which can be obtained from equation (2):

[0064] (3);

[0065] Among them, Y eq Let represent the equivalent admittance matrix of order e×r, which can be solved quickly using the HHL algorithm.

[0066] Substituting equation (3) into equation (2) will eliminate the nodes to be eliminated in the network, resulting in:

[0067] I R =(Y RR -Y RE Y eq )U R =Ysta U R (4);

[0068] wherein, Y eq represents an equivalent admittance matrix of order e x r, Y sta represents a reduced network admittance matrix of order r x r.

[0069] As can be seen from formula (3) and (4), Y EE Y eq =Y ER , Y sta =Y RR -Y RE Y eq Therefore, the solution of Y sta can be converted into the solution of Y RR , Y RE , Y EE and Y ER .

[0070] When the power system is large in scale, the number of nodes is large, and the orders of Y EE and Y ER are high. The complexity of solving Y EE Y eq =Y ER is high, and the solving speed is slow; therefore, the following steps S4-S5 are adopted to solve Y EE Y eq =Y ER .

[0071] S4, matrix row division is performed on Y EE Y eq =Y ER to construct a plurality of linear equations, which are as follows:

[0072] The matrix Y ER and Y eq are divided into r column vectors:

[0073] Y EE [Y eq(1) … Y eq(s) … Y eq(r) ]=[Y ER(1) … Y ER(s) … Y ER(r) ] (5);

[0074] wherein, Y eq(s) is an e-order column vector of the s-th column of Y eq , Y ER(s) is an e-order column vector of the s-th column of Y ER , and 1≤s≤r.

[0075] Thus, the original matrix operation Y EE Y eq =Y ER can be split into r linear equations of e order:

[0076] Y EE Y eq(s) =Y ER(s) s=1,2,…,r (6);

[0077] Since Y=G+jB (Y represents admittance, G represents conductance, B represents susceptance, and j represents imaginary part), there are , , After expanding equation (6) using the above three equations, separating the real and imaginary parts, and rearranging the order of the variables in the equation, the following real linear equation group can be obtained:

[0078] (7);

[0079] where G EE , G eq(s) , and G ER(s) are the conductances of Y EE , Y eq(s) , and Y ER(s) , respectively, and B EE , B eq(s) , and B ER(s) are the susceptances of Y EE , Y eq(s) , and Y ER(s) , respectively.

[0080] S5, the HHL algorithm is used to solve equation (7) to obtain the admittance reduction equation group A p x p =b p ; where A p is a reduced parameter matrix, b p is a reduced vector, and x p is a column vector composed of elements of the reduced network admittance matrix Y sta to be solved.

[0081] Specifically, equation (7) can be regarded as the form of Ax=b (classical equation, A represents a sampling matrix, b represents a unit vector, and x represents the solution object), which can be solved using the HHL algorithm. The r linear equations of e order in equation (5) can all be expanded into the form of equation (7), and they can be combined into one linear equation group for parallel calculation to obtain the admittance reduction equation group:

[0082] (8);

[0083] where Ap is a reduced matrix whose equation order is N0=2×e×r; b p is a reduced vector, x p is a reduced network admittance matrix Y sta is a column vector composed of elements; x1, x s and x r are the 1st, s-th and r-th vectors of x p , respectively; b1, b s and b r are the 1st, s-th and r-th vectors of b p , respectively; 1≤s≤r;

[0084] , , .

[0085] S5.1, construct a quantum circuit of the HHL algorithm to quickly solve the reduced admittance equation of formula (8).

[0086] It should be noted that for A p x p =b p , the following constraints need to be met:

[0087] Constraint 1: A p is a Hermitian matrix;

[0088] Constraint 2: A p is an integer power of 2 order;

[0089] Constraint 3: b p is a unit vector;

[0090] Obviously, A is a real symmetric matrix, and the block diagonal component A p satisfies the Hermitian condition, which can meet the above constraints. If the above constraints cannot be met, the corresponding processing can be carried out in the following way.

[0091] 1. Hermitian processing:

[0092] If A p does not satisfy the Hermitian condition, formula (8) can be converted into formula (9) that satisfies the Hermitian condition through Hermitian processing:

[0093] (9);

[0094] where, is the conjugate transpose matrix of , and is the order of the Hermitian increase zero elements; after conversion, The Hermite condition is satisfied, i.e., constraint 1 is satisfied.

[0095] 2. Extension processing.

[0096] Assuming that the formula (8) in satisfies the Hermite condition, but does not satisfy constraint 2, i.e., A p is an integer power of 2, the formula (8) can be extended to the formula (10):

[0097] (10) ;

[0098] wherein I is a unit matrix, the order of which is , N0 is the order of in the formula (8); represents the integer down to, λ c represents an integer power of 2 within the range of the absolute value of the eigenvalue [|λ| min , |λ| max ], |λ| min is the minimum value of the absolute value of the eigenvalue of , |λ| max is the maximum value of the absolute value of the eigenvalue of ; represents a 0 vector of the order of the dimension of I;

[0099] Through the extension processing, it can be guaranteed that is an integer power of 2, satisfying constraint 2.

[0100] 3. Normalization processing:

[0101] Assuming that b p in the formula (8) is not a unit vector, the formula (8) can be converted into the formula (11) through normalization processing:

[0102] (11) ;

[0103] wherein ||b p || is the modulus value of b p , guaranteeing that is a unit vector, satisfying constraint 3.

[0104] In this way, through the above processing, it can be guaranteed that the formula (8) satisfies constraints 1-3 after processing. The formula (8) satisfies constraints 1-3, a quantum circuit of the formula (8) is constructed, and the formula (8) is solved; otherwise, the formula (8) is processed to guarantee that the formula satisfies constraints 1-3 after processing, and a quantum circuit of the processed formula is constructed to solve the formula (8).

[0105] The following default formula (8) satisfies the above constraints 1-3, then the solving process of formula (8) in S5 is as follows:

[0106] S5.2, set up HHL algorithm quantum circuit with 3 groups of quantum bits, and the 3 groups of quantum bits are:

[0107] 1. Quantum register q used for storing phase information b , the number of quantum bits n b determines the accuracy of phase estimation, which is generally determined by the range of absolute value of its eigenvalue, and for every n pre bit precision increase in decimal, n quantum bits need to be added, which represents rounding up. That is, assuming the basic precision is n1 decimal places, the corresponding number of quantum bits is n0, and the target precision increases to n2 decimal places, n2-n1=n pre , that is, the accuracy of the absolute value of the eigenvalue increases n pre bit, then the number of quantum bits increases to n0+ .

[0108] 2. Auxiliary quantum bit q used for controlled rotation a , which is used to transfer the eigenvalue information stored in q b to the amplitude, and the number of quantum bits n a of q a is fixed at 1.

[0109] 3. Quantum register q used for storing the amplitude encoding |b> of the normalized b p and the approximate solution x p of the output , the number of quantum bits n c of q c is log2N0.

[0110] S5.3, quantum phase estimation (QPE) is performed on the eigenvalue of the reduced matrix A p , and the eigenvalue of A p is stored in quantum register q b , the specific operation is as follows:

[0111] After setting the number of quantum bits of each register, Hadamard quantum gate H= is applied to each quantum bit of quantum register q b to construct quantum superposition state , and at the same time, the amplitude encoding of the normalized b p is obtained in quantum register q c to get |b>, and then the unitary matrix U= For A p Perform a Hamiltonian simulation, where e0 is a natural number and t is... The range of values, by using q b To control the bit in q c A series of power-law gate operations of U are applied to A, followed by a quantum inverse Fourier transform, storing the eigenvalue information in A as phase in q. b In this context, the relationship between eigenvalues ​​and phase is: , For A p The i-th approximate eigenvalue, for The corresponding phase, the quantum state evolution process of the above quantum phase estimation (QPE) operation is as follows:

[0112] (12);

[0113] Among them, |u i >(i=1,2,…,N0) is A p A set of feature vectors, β i For the corresponding feature vector |u in |b> i > weighting coefficient; |0> a |0> b |0> c They represent q respectively a q b q c qubits 、|u i > c They represent and u i The quantum state; N0 is the A in formula (8) p If formula (8) does not satisfy constraint 2, then N0 = r × e; if formula (8) satisfies constraint 2, then N0 = 2r × e.

[0114] S5.4. The phase estimation characteristic value phase information stored in the line is transferred to the amplitude through controlled rotation. The specific operation is as follows:

[0115] With auxiliary bit q a For the target bit, use the quantum register q b To control the bits, a series of unitary gates are applied. :

[0116] (13);

[0117] Where, θ i As a transition term, θ i =2arcsin C is a normalization constant used to ensure that the sum of squares of the amplitudes is 1.

[0118] After controlled rotation, the quantum state evolves into:

[0119] (14);

[0120] The amplitude can be seen at this time and Eigenvalues ​​appeared on When q a When the measurement result is |1>, the output results of the remaining registers contain the parts needed to understand the problem. However, due to q b With q c Entanglement still exists, and the measurement results will be affected by... It exists but cannot be obtained.

[0121] S5.5, Apply an inverse quantum phase estimate to resolve q b With q c Entanglement, this operation only requires a quantum register q b and q c Setting its adjoint operator in the reverse order of S5.3 yields the following quantum state:

[0122] (15);

[0123] Where, β i For the corresponding feature vector |u in |b> i > the weighting coefficient; N0 is the weighting coefficient of A in formula (8) p The order of;

[0124] S5.6, Apply quantum measurement, where q in equation (15) b |0> in all cases b The state can be ignored for quantum measurement when the auxiliary bit q a When the measurement result is |1>, we can obtain:

[0125] (16);

[0126] S5.7, To The inverse normalization process yields the desired solution x. p An approximate solution is to use x p Rearranged into matrix Y eq The reduced network admittance matrix Y can be calculated using equation (4). sta .

[0127] That is: x p ={x s|s=1,2,…,r}

[0128] ;;

[0129] Get x p An approximate solution is equivalent to obtaining and Thus obtain And Y eq ={Y eq(s) |s=1,2,…,r};

[0130] Y RR and Y RE Using existing methods, Y is obtained. eq Y RR and Y RE Substituting into formula Y sta =Y RR -Y RE Y eq Find Y sta .

[0131] The following describes the above-mentioned method for reducing network nodes for calculating transient stability of power systems based on HHL (hereinafter referred to as the method of this invention) with reference to specific embodiments.

[0132] The following specific examples validate the network node reduction method for power system transient stability calculation based on HHL. The examples use the IEEE 9-node standard system, employing both classic Kron reduction and the method of this invention for node reduction, and the results are compared.

[0133] The IEEE 9-node system has 3 generator nodes, 3 load nodes, 3 intermediate network nodes, and 9 lines. These are renumbered: nodes 1-3 are generator nodes, nodes 4-6 are load nodes, and nodes 7-9 are intermediate network nodes. The network topology is as follows: Figure 2 As shown. The nodes to be retained are 1-6, therefore r=6; the nodes to be eliminated are 7-9, therefore e=3. A can be calculated based on the example. p The order N0 is 36, which obviously does not satisfy the requirement of being an integer power of 2. Therefore, we extend the order to 64 and calculate λ. c The value range of λ is [32, 39] (rounded to the nearest integer). c =36 is extended to the next order.

[0134] Set auxiliary quantum bit q a The number n a =1, eigenvalue precision is one decimal place, set quantum register q b The number n b =11, quantum register q c The number nc =6.

[0135] The reduced network topology is shown in Fig. 1. Figure 3

[0136] The results of the classical Kron reduction are shown in Table 1.

[0137] Table 1: Results of classical Kron reduction

[0138]

[0139] The results of the method of the present application are shown in Table 2.

[0140] Table 2: Results of the method of the present application

[0141]

[0142] In Table 1 and Table 2, when the row index and the column index are both m1, it represents the self-admittance of node m1; when the row index is m1 and the column index is m2, it represents the mutual-admittance of node m1 and node m2; 1≤m1≤6; 1≤m2≤6, m1≠m2.

[0143] From the output results of the two methods in Table 1 and Table 2, it can be seen that when the storage precision of the eigenvalue is set to one decimal place, the real part precision of the method of the present application is three decimal places, and the imaginary part precision is two decimal places, and the error can meet the needs of transient stability simulation, verifying the effectiveness of the method. If more accurate calculation is needed, only the precision of the eigenvalue storage needs to be improved, that is, the number of quantum bits q b

[0144] Of course, for those skilled in the art, the present application is not limited to the details of the above exemplary embodiments, but also includes the same or similar structures that can be realized in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be regarded as exemplary and non-limiting from any point of view, and the scope of the present application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present application. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0145] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be properly combined to form other embodiments that those skilled in the art can understand.

[0146] ​​​​The technology, shape, and structural parts not described in detail in the present application are all known technology.

Claims

1. A network node reduction method for HHL-based power system transient stability calculation, characterized by, The method comprises the following steps: Constructing an equivalent admittance matrix Y of order e x r eq and a conversion matrix Y EE Y eq = Y ER ; Y EE represents an admittance matrix between the nodes to be eliminated of order e x e; Y ER represents an admittance matrix between the nodes to be eliminated and the remaining nodes of order e x r; r is the total number of remaining nodes and e is the total number of nodes to be eliminated; Y EE Y eq =Y ER splitting the linear system of equations Y EE Y eq(s) =Y ER(s) , Y eq(s) is the s-th column e-dimensional column vector of Y eq , Y ER(s) is the s-th column e-dimensional column vector of Y ER , 1≤s≤r; Real number linear equations are constructed for each linear equation group and solved by HHL algorithm; the real number linear equations are: ; G EE , G eq(s) and G ER(s) are conductances of Y EE , Y eq(s) and Y ER(s) respectively, and B EE , B eq(s) and B ER(s) are susceptances of Y EE , Y eq(s) and Y ER(s) respectively; Constructing the reduced admittance equation system A p x p =b p and solve for x using the HHL algorithm p ; wherein A p is an r-order diagonal matrix composed of elements A p is a reduced vector, b p =[b s ;1≤s≤r], b s is the s-th vector of b p ; x p is a column vector composed of elements x p =[x s ;1≤s≤r], x s is the s-th vector of x p ; the reduced network admittance matrix is obtained by rearranging the solution results of x p , which is used for network node reduction. ， ， 。 2. The network node reduction method for HHL-based power system transient stability calculation of claim 1, wherein, A p x p =b p The solution process is: Configure the HHL algorithm quantum circuit, including a quantum register q for storing phase information. b and used to store the normalized b p Amplitude encoding |b> and output x p The quantum register q of the approximate solution c ; A quantum phase estimation is used to determine the eigenvalues of H p and store them in a quantum register q b The phase information of the eigenvalues in the quantum register q b is transferred to the amplitudes by a controlled rotation. Decomposing quantum register q by inverse quantum phase estimation b With entanglement of quantum register q c , quantum measurement is applied to obtain x p normalized solution of quantum input, inverse normalization is performed on x to obtain x p approximate solution.

3. The network node reduction method for HHL-based power system transient stability calculation of claim 2, wherein, Setting up the HHL algorithm quantum circuit further comprises an auxiliary qubit q a ; By controlled rotation to transfer quantum register q b The way in which the eigenvalue phase information is transferred onto the amplitude is: with ancillary bits q a targeted bits, with quantum register q b applying a unitary gate to the quantum state resulting from the quantum phase estimation : where θ i is a transition term, θ i = 2arcsin , C is a normalization constant; is the i-th approximated eigenvalue of A p ; 1≤i≤r×e.

4. The network node reduction method for HHL-based power system transient stability calculation of claim 3, wherein, q b The number of qubits is n0 where n0 is the number of qubits required for the absolute value of the eigenvalue with base precision, n pre is the number of additional decimal places required for the absolute value of the eigenvalue with precision, represents rounding up.

5. The network node reduction method for HHL-based power system transient stability calculation according to claim 4, wherein, q a The number of qubits of q c The number of qubits of q 6. The network node reduction method for HHL-based power system transient stability calculation of claim 1, wherein, Admittance reduction equation set A p x p =b p The constraint condition is: A p is a Hermite matrix of an integer power of 2, b p is a unit vector; when the constraint is not met, first A p x p =b p is processed to meet the constraint, and then the HHL algorithm is used to solve x p ; If A p x p = b p is not a Hermitian matrix, it is Hermitianized, and the transformed formula is: wherein is the conjugate transpose matrix of is the Hermitian increase of zero elements; If A p x p = b p is not satisfied, the order of the integer power of 2 is expanded, and the expanded equation set is: where I is an identity matrix of order N0 is an order of N0 = 2 x e x r; denotes a floor function, λ c denotes a number in a range of characteristic value absolute value and satisfies 2 power; denotes λ c dimension 0 vector.

7. The network node reduction method for HHL-based power system transient stability calculation according to any of claims 1-6, characterized in that, The conversion matrix Y EE Y eq =Y ER The construction process is as follows: S1, constructing a network node voltage equation according to a power grid topology structure; S2, dividing nodes into reserved nodes and nodes to be eliminated, and reconstructing the node voltage equation; S3, representing the voltage and injected current of the nodes to be eliminated by the voltage and injected current of the reserved nodes, and constructing an equation group: I R =Y sta U R ; Y sta =Y RR -Y RE Y eq ; Y EE Y eq =Y ER ; where I R denotes the injection current vector of the retained nodes, U R denotes the voltage vector of the retained nodes, Y sta denotes the reduced network admittance matrix of order r x r; Y RR denotes the admittance matrix between the retained nodes of order r x r; Y RE denotes the admittance matrix between the retained nodes and the to-be-eliminated nodes of order r x e; Y eq denotes the equivalent admittance matrix of order e x r; Y EE denotes the admittance matrix between the to-be-eliminated nodes of order e x e; Y ER denotes the admittance matrix between the to-be-eliminated nodes and the retained nodes of order e x r; r is the total number of the retained nodes, and e is the total number of the to-be-eliminated nodes.

8. A network node reduction system for HHL-based power system transient stability calculation, characterized by, The computer program is stored in the memory and is executed by the processor to implement the network node reduction method for HHL-based power system transient stability calculation according to any one of claims 1-7.

9. A storage medium, characterized by The computer program is stored in the memory and is executed by the processor to implement the network node reduction method for HHL-based power system transient stability calculation according to any one of claims 1-7.

10. A computer program, characterized in that, The computer program is stored in the memory and is executed by the processor to implement the network node reduction method for HHL-based power system transient stability calculation according to any one of claims 1-7.

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