Quantum approximation optimization-based key transmission section search method and system, and readable medium

Abstract

A quantum approximation optimization-based key transmission section search method and system, and a readable medium. First, a topological structure of a power network model is established, then nodes are partitioned by means of quantum computing solution, and connecting lines between partitions of different solution modes are listed, so as to screen for the connecting lines between the partitions to form a transmission section. In the quantum approximation optimization-based key transmission section search method, a key transmission section in a complex power grid can be quickly and accurately searched out by using the super-strong parallel computing capability of quantum computing, overcoming the problems of slow computing speed, high computing difficulty, and the omission of sections of conventional traversal-type algorithms and power grid partition-type algorithms.

Description

A method, system, and readable medium for searching key power transmission sections based on quantum approximation optimization. Technical Field

[0001] This invention relates to the field of power grid safe and stable operation and power system optimized scheduling technology, and in particular to a key transmission section search method, system and readable medium based on quantum approximation optimization. Background Technology

[0002] With the development of new power systems, the large-scale integration of renewable energy sources with randomness, volatility, and intermittency into the grid has made the grid architecture increasingly complex and the power transmission capacity fluctuate more frequently. Simultaneously, the overlap of random grid faults and planned maintenance leads to continuous changes in the grid topology and complex and varied grid operation modes. Therefore, quickly and accurately locating and identifying critical transmission sections of the grid is of great significance for ensuring grid security.

[0003] Traditional traversal algorithms and power grid partitioning algorithms are increasingly unable to meet the needs of searching for key transmission sections in large power grids. These traditional algorithms all lead to problems such as slow calculation speed and missed selection of transmission sections.

[0004] With the rapid development of quantum computers, it has become possible to solve problems that are difficult to solve using classical computers. Quantum computing possesses unparalleled parallel computing capabilities compared to classical computing, thus exhibiting significant advantages in efficiency. Among these, quantum approximation optimization algorithms, as a cutting-edge quantum technology, demonstrate exponential speedup capabilities for solving combinatorial optimization problems and are one of the quantum algorithms for achieving quantum supremacy. Summary of the Invention

[0005] To overcome the shortcomings of existing transmission section search methods, such as slow calculation speed and missed selection of transmission sections, this invention proposes a key transmission section search method based on quantum approximation optimization, which can quickly and accurately search for and identify key transmission sections of the power grid.

[0006] This invention proposes a key transmission section search method based on quantum approximation optimization, comprising:

[0007] S1. Construct the power network model G=(V,E,w) rj ), where V is the set of nodes, E is the set of lines, and w rj To represent node v r and node v j The binary number representing the connection between them; w rj =1, indicating node v r and node v j There is a line connection between them: w rj =0, indicating node v r and node vj There is no wire connection between them:

[0008] S2. With minimizing the objective function C(x) as the optimization objective, construct topological cut sets to divide the nodes in the power network model into set A and set B;

[0009] The objective function is:

[0010] ;

[0011] Where n is the number of nodes, x r Assigning a value to node r, x j Assign a value to node j; the value of the node can be 0 or 1; e rj This represents the connection line between node r and node j; after the node assignment iteration is completed, nodes with a value of 0 are assigned to set A, and nodes with a value of 1 are assigned to set B.

[0012] S3. Establish the initial Hamiltonian H of the transmission section. B The objective Hamiltonian H of the transmission section is obtained by performing classical Ising model transformation and quantum transformation on the objective function C(x). C ;

[0013] S4. Calculate the initial Hamiltonian H. B unitary transformation U(H) B ,β a ) and the target Hamiltonian H C unitary transformation U(H) C ,γ a ); β a and γ a All of these are quantum variational parameters to be optimized;

[0014] S5. Calculate U(H) B ,β a ) and U(H C ,γ a The product of ) U(β) a ,γ a As a quantum parameter circuit model, let U(β) a ,γ a The quantized qubit string is denoted as |ψ P (β a ,γ a )>;

[0015] S6. Calculate the target Hamiltonian H C Expected value E(β) a ,γ a ), to minimize E(β) a ,γ a ) as the optimization objective iteration parameter βa and γ a And the iterated parameter β a and γ a Substitute the quantum bit string |ψ P (β a ,γ a According to |ψ>, P (β a ,γ a Different solutions partition the nodes;

[0016] S7. Filter the partitioning methods that satisfy the condition that the number of nodes in the two partitions is greater than or equal to the set first threshold and the connection line between the two partitions is less than or equal to the set second threshold, and count the set of connection lines between the two partitions in all the filtered partitioning methods as the transmission section.

[0017] Preferably, step S7 is followed by step S8: selecting key transmission sections from the transmission sections, where the key transmission sections are the set of transmission sections corresponding to the key partitioning method; the key partitioning method satisfies the following conditions: deleting any connecting line between two partitions, and at least one of the remaining connecting lines between partitions has a corresponding power flow distribution factor greater than a set threshold.

[0018] When lines k and m belong to the same transmission section corresponding to the same zoning method, the formula for calculating the power flow distribution factor λ of line m after deleting line k is as follows:

[0019] ;

[0020] Where, q m (k) q represents the active power of line m after line k is removed. m (0) This represents the active power of line m when all lines in the power network model are intact.

[0021] Preferably, the initial Hamiltonian H B and the target Hamiltonian H C The calculation formula is as follows:

[0022] ;

[0023] ;

[0024] Where, σ b X Let n be the Pauli X matrix operator corresponding to node b, and n be the number of nodes; e rj Let w be the connection line between node r and node j, E be the set of lines, and w be the connection line between node r and node j. rj To represent node v r and node vj A binary number representing the connections between them;

[0025] σ r The value x represents the assignment of node r. r The classic Ising variable, σ j The value x represents the assignment of node j. j The classic Ising variable, σ r Z σ r The corresponding Pauli Z-matrix operator, σ j Z σ j The corresponding Pauli Z-matrix operator.

[0026] Preferably, the initial Hamiltonian H B unitary transformation U(H) B ,β a The calculation formula is as follows:

[0027] ;

[0028] Where RX is a quantum gate operation, β a Let r be the quantum variational parameter to be optimized in the RX gate, r be the node number, n be the number of nodes, and Π represent chain multiplication.

[0029] Preferably, the target Hamiltonian H C unitary transformation U(H) C ,γ a The calculation formula is as follows:

[0030] ;

[0031] Where CONT and RZ are both quantum gate operations; r and j are node indices, γ a These are the quantum variational parameters to be optimized in the RZ gate.

[0032] Preferred:

[0033] ;

[0034] Among them, U(β a ,γ a ) is U(H B ,β a ) and U(H C ,γ a The product of ) is |s>, where |s> is the quantum initial state and p is the set quantum depth.

[0035] Preferably, the first threshold is greater than or equal to 3; the second threshold is less than or equal to 10 and greater than or equal to 2.

[0036] Preferably, both the first threshold and the second threshold are taken from the set {3, 4, 5}.

[0037] The present invention proposes a key transmission section search system based on quantum approximation optimization, 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 implement the key transmission section search method based on quantum approximation optimization.

[0038] The present invention proposes a readable medium storing a computer program, which, when executed, is used to implement the aforementioned key transmission section search method based on quantum approximation optimization.

[0039] The advantages of this invention are:

[0040] (1) The key transmission section search method based on quantum approximation optimization proposed in this invention utilizes the super parallel computing capability of quantum computing to quickly and accurately search for key transmission sections in complex power grids, overcoming the problems of slow calculation speed, high computational difficulty, and missed selection of sections in traditional traversal algorithms and power grid partitioning algorithms.

[0041] (2) This invention first searches for transmission sections by solving the partitions using quantum computing, and then further searches for key transmission sections based on the transmission sections, thus realizing the search for transmission sections with two different widths, which can meet more needs for searching transmission sections.

[0042] (3) The present invention transforms the nodes and lines in the power grid topology into qubits and quantum gates based on the quantum approximation optimization algorithm, and uses the quantum circuit model to describe the power grid structure and physical characteristics more intuitively and effectively, thereby improving the accuracy of modeling.

[0043] (4) In view of the trend of increasing scale and complexity of future power grids, this invention proposes an efficient method to adapt to the development needs of new power systems and ensure the safe and stable operation and optimized scheduling of the power grid. Attached Figure Description

[0044] Figure 1 is a flowchart of the key power transmission section search method based on quantum approximation optimization of the present invention;

[0045] Figure 2 is a schematic diagram of the principle of the quantum approximation optimization algorithm of the present invention;

[0046] Figure 3 is a network topology diagram of the IEEE 14-node system of the present invention;

[0047] Figure 4 is a schematic diagram of the quantum circuit model of the IEEE 14-node system with a quantum depth of 1 according to the present invention. Detailed Implementation

[0048] 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 skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Referring to Figures 1 and 2, this embodiment presents a key transmission section search method based on quantum approximation optimization, which includes the following steps:

[0050] S1. Acquire power grid operation data online and model the power grid topology to obtain the power network model G=(V,E,w) rj ), where V is the set of nodes, E is the set of lines, and w rj To represent node v r and node v j The binary number representing the connection between them; w rj =1, indicating node v r and node v j There is a line connection between them: w rj =0, indicating node v r and node v j There is no wire connection between them.

[0051] Let e rj If ∈E, then E={e rj |w rj =1, 1≤r≤n, 1≤j≤n};e rj Represents node v r and node v j The connection lines between them, where n is the number of nodes.

[0052] S2. Taking minimizing the objective function C(x) as the first optimization objective, construct topological cut sets to divide the nodes in the power network model into set A and set B;

[0053] The objective function is:

[0054] ;

[0055] Where n is the number of nodes, x r Assigning a value to node r, x j Assign a value to node j, where the value is either 0 or 1, and the nodes are divided into set A and set B based on the assigned value; e rj This represents the connection line between node r and node j;

[0056] In this step, with MinC(x) as the first optimization objective, we iterate through sets A and B until we fix the combination of A and B.

[0057] S3. Establish the initial Hamiltonian H of the transmission section. B The objective Hamiltonian H of the transmission section is obtained by performing classical Ising model transformation and quantum transformation on the objective function C(x). C ;

[0058] ;

[0059] Where, σ b X Let be the Pauli X matrix operator corresponding to node b;

[0060] Target Hamiltonian H of transmission section C The method to obtain x is as follows: First, set x r =(σ r +1) / 2、x j =(σ j Substituting +1) / 2 into the objective function and performing the classical Ising model transformation, we get:

[0061] ;

[0062] Where, σ r σ represents the classical Ising variable corresponding to node r. j σ represents the classical Ising variable corresponding to node j. r ∈{-1,1},σ j ∈{-1,1};

[0063] The objective function C(x) is quantized using quantum computing principles to obtain the target Hamiltonian H of the transmission section. C ;

[0064] ;

[0065] Where, σ r Z σ r The corresponding Pauli Z-matrix operator, σ j Z σ j The corresponding Pauli Z-matrix operator;

[0066] S4. Based on the quantum approximation optimization algorithm, transform the nodes in the power network model into qubits in quantum computing, and the lines in the power network model into quantum gates in quantum computing; calculate the initial Hamiltonian H. B unitary transformation U(H) B ,β a ) and the target Hamiltonian H C unitary transformation U(H) C ,γ a );

[0067] ;

[0068] Where, β a Let σ be the quantum variational parameter to be optimized in the RX gate, where i is an imaginary number; r X σ r The corresponding Pauli X matrix operator; Π represents chain multiplication;

[0069] ;

[0070] Where, γ a Let be the quantum variational parameter to be optimized in the RZ gate; i is an imaginary number.

[0071] CONT, RX, and RZ are all quantum gate operations.

[0072] S5. Calculate U(H) B ,β a ) and U(H C ,γ a The product of ) U(β) a ,γ a As a quantum parameter circuit model, let U(β) a ,γ a The quantized qubit string is denoted as |ψ P (β a ,γ a )>;

[0073] ;

[0074] Where p is the set quantum depth, i.e., the number of layers in the quantum parameter circuit; in the same layer of quantum parameter circuit, all RX gate parameter values ​​are the same, and all RZ gate parameter values ​​are the same; |s> is the quantum initial state;

[0075] ;

[0076] Where |+> represents a quantum bit, The symbol for tensor product is y, where n is the number of nodes; r > indicates that the r-th qubit is randomly generated, either |0> or |1>.

[0077] S6. Calculate the target Hamiltonian H C Expected value E(β) a ,γ a ), to minimize E(β) a ,γ a ) as the optimization objective iteration parameter β a and γ a And the iterated parameter βa and γ a Substitute the quantum bit string |ψ P (β a ,γ a )>, will |ψ P (β a ,γ a Partition the nodes corresponding to 0 and 1 in the array, and count |ψ P (β a ,γ a Different partitioning methods corresponding to different solutions;

[0078] It is worth noting that each layer of quantum parameter circuitry generates an array (β) a ,γ a The solution for each group (β) a ,γ a Generate one or more qubit strings |ψ P (β a ,γ a Therefore, S6 can obtain no fewer than p quantum depth partitioning methods.

[0079] S7. Filter out partitioning methods where the number of nodes in any partition is less than the set first threshold or the number of connecting lines between two partitions is greater than the set second threshold. For the remaining partitioning methods, count the set of connecting lines between two partitions as the transmission section.

[0080] Both the first and second thresholds can be set to 4, meaning the transmission section meets the following conditions: the number of nodes in both sections is greater than 4, and the number of connecting lines between the two sections is less than 4.

[0081] S8. Select key transmission sections from the transmission sections. The key section zoning method shall meet the following conditions:

[0082] Delete any connection between two partitions, and at least one of the remaining connection lines between the partitions will have a power flow distribution factor greater than a set threshold.

[0083] When lines k and m belong to the same transmission section corresponding to the same zoning method, the formula for calculating the power flow distribution factor λ of line m after deleting line k is as follows:

[0084] ;

[0085] Where, q m (k) q represents the active power of line m after line k is removed. m (0) This represents the active power of line m when all lines in the power network model are intact.

[0086] The following specific embodiments verify the above-mentioned key transmission section search method based on quantum approximation optimization.

[0087] This embodiment uses the IEEE 14-node system for verification. The network topology of the IEEE 14-node system is shown in Figure 2, which includes 14 nodes and 20 lines; the nodes include generator nodes and load nodes, and the lines include transmission lines and transformer branches.

[0088] In this embodiment, both the first threshold and the second threshold are set to 4. Higher quantum depth results in higher accuracy but slower computation speed; therefore, this embodiment sets p=4. As the quantum depth p increases, the quantum parameter circuits are repeatedly built in layers, and the corresponding parameter values ​​in each layer of the quantum parameter circuits will be different. In one layer of quantum parameter circuits, all RX gate parameter values ​​are the same, and all RZ gate parameter values ​​are the same.

[0089] In this embodiment, the quantum bit string |ψ P (β a ,γ a After solving and filtering, the partitioning methods that meet the condition "the number of nodes in each partition is not less than 4 and the number of connecting lines between two partitions is not greater than 4" are shown in Table 1.

[0090] Table 1. Search results for transmission sections and grid zoning information for the IEEE 14-bus system.

[0091] ;

[0092] In Table 1, l 4-7 This represents the line entity between node 4 and node 7, l 13-14 This represents the line entity between node 13 and node 14, and so on. r-j This represents the line entity between node r and node j. In this embodiment, all transmission sections are obtained as the line set {l}. 4-7 l 4-9 l 5-6 l 7-9 l 9-10 l 9-14 l 6-11 l 13-14 l 10-11}

[0093] After obtaining the six zoning methods shown in Table 1, the power flow distribution factor of other lines after the physical disconnection of each line in each transmission section is calculated, and the calculation results are shown in Table 2.

[0094] Table 2 Power flow distribution factors among zoned interconnects in the IEEE 14-node system

[0095] ;

[0096] As can be seen from Table 2 above, in partitioning method 14-1, we have:

[0097] When the line entity is disconnected 4-7 Line entity l 4-9 Flow distribution factor λ 4-9 =0.5299, Line entity l 5-6 Flow distribution factor λ 5-6 =0.4856;

[0098] When the line entity is disconnected 4-9 Line entity l 4-7 Flow distribution factor λ 4-7 =0.6567, Line entity l 5-6 Flow distribution factor λ 5-6 =0.3508;

[0099] When the line entity is disconnected 5-6 Line entity l 4-7 Flow distribution factor λ 4-7 =0.6650, line entity l 4-9 Flow distribution factor λ 4-9 =0.3821;

[0100] And so on.

[0101] As shown in Table 2, all six zoning methods in this implementation meet the screening criteria for key zoning methods. Therefore, the key transmission sections finally obtained in this embodiment are the line set {l}. 4-7 l 4-9 l 5-6 l 7-9 l 9-10 l 9-14 l 6-11 l 13-14 l 10-11}, which is the set of deduplicated connection lines for six partitioning methods.

[0102] To further verify the effectiveness of this method, this embodiment uses a traversal-based key transmission section search method for performance comparison. The experimental results are shown in Table 3.

[0103] Table 3 Comparison of Method Effects

[0104] ;

[0105] As can be seen, the key transmission section searched by this invention includes three additional line entities compared to the comparison method. 4-7 l 10-11l 13-14 Furthermore, this invention incorporates quantum algorithms for computation, resulting in higher efficiency and faster speed.

[0106] 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.

[0107] 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.

[0108] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

A key transmission section search method based on quantum approximation optimization, characterized in that, include: S1. Construct the power network model G=(V,E,w) rj ), where V is the set of nodes, E is the set of lines, and w rj To represent node v r and node v j A binary number representing the connections between them; S2. With minimizing the objective function as the optimization objective, construct topological cut sets to divide the nodes in the power network model into set A and set B; S3. Establish the initial Hamiltonian H of the transmission section. B The objective Hamiltonian H of the transmission section is obtained by performing classical Ising model transformation and quantum transformation on the objective function C(x). C ; S4. Calculate the initial Hamiltonian H. B unitary transformation U(H) B ,β a ) and the target Hamiltonian H C unitary transformation U(H) C ,γ a ); β a and γ a All of these are quantum variational parameters to be optimized; S5. Calculate U(H) B ,β a ) and U(H C ,γ a The product of ) U(β) a ,γ a As a quantum parameter circuit model, let U(β) a ,γ a The quantized qubit string is denoted as |ψ P (β a ,γ a )>; S6. Calculate the target Hamiltonian H C Expected value E(β) a ,γ a ), to minimize E(β) a ,γ a ) as the optimization objective iteration parameter β a and γ a And the iterated parameter β a and γ a Substitute the quantum bit string |ψ P (β a ,γ a According to |ψ>, P (β a ,γ a Different solutions partition the nodes; S7. Filter the partitioning methods that satisfy the condition that the number of nodes in the two partitions is greater than or equal to the set first threshold and the connection line between the two partitions is less than or equal to the set second threshold, and count the set of connection lines between the two partitions in all the filtered partitioning methods as the transmission section. The key transmission section search method based on quantum approximation optimization as described in claim 1 is characterized in that, The objective function is: ； Where n is the number of nodes, x r Assigning a value to node r, x j Assign a value to node j; the value of the node can be 0 or 1; e rj Let r be the connection line between node r and node j; after the node assignment iteration is completed, the nodes with a value of 0 are assigned to set A, and the nodes with a value of 1 are assigned to set B. The key transmission section search method based on quantum approximation optimization as described in claim 1 is characterized in that, Step S7 is followed by S8: Selecting key transmission sections from the transmission sections, where the key transmission sections are the set of transmission sections corresponding to the key partitioning method; The critical partitioning method meets the following conditions: if any connection line between two partitions is deleted, at least one of the remaining connection lines between the partitions has a power flow distribution factor greater than a set threshold. When lines k and m belong to the same transmission section corresponding to the same zoning method, the formula for calculating the power flow distribution factor λ of line m after deleting line k is as follows: ； Where, q m (k) q represents the active power of line m after line k is removed. m (0) This represents the active power of line m when all lines in the power network model are intact. The key transmission section search method based on quantum approximation optimization as described in claim 1 is characterized in that, Initial Hamiltonian H B and the target Hamiltonian H C The calculation formula is as follows: ； ； Where, σ b X Let n be the Pauli X matrix operator corresponding to node b, and n be the number of nodes; e rj Let w be the connection line between node r and node j, E be the set of lines, and w be the connection line between node r and node j. rj To represent node v r and node v j A binary number representing the connections between them; σ r The value x represents the assignment of node r. r The classic Ising variable, σ j The value x represents the assignment of node j. j The classic Ising variable, σ r Z σ r The corresponding Pauli Z-matrix operator, σ j Z σ j The corresponding Pauli Z-matrix operator. The key transmission section search method based on quantum approximation optimization as described in claim 4 is characterized in that, Initial Hamiltonian H B unitary transformation U(H) B ,β a The calculation formula is as follows: ； Where RX is a quantum gate operation, β a Let r be the quantum variational parameter to be optimized in the RX gate, r be the node number, n be the number of nodes, and Π represent chain multiplication. The key transmission section search method based on quantum approximation optimization as described in claim 4 is characterized in that, Target Hamiltonian H C unitary transformation U(H) C ,γ a The calculation formula is as follows: ； Where CONT and RZ are both quantum gate operations; r and j are node indices, γ a These are the quantum variational parameters to be optimized in the RZ gate. The key transmission section search method based on quantum approximation optimization as described in claim 1 is characterized in that: ； Among them, U(β a ,γ a ) is U(H B ,β a ) and U(H C ,γ a The product of ) is |s>, where |s> is the quantum initial state and p is the set quantum depth. The key transmission section search method based on quantum approximation optimization as described in claim 1 is characterized in that, The first threshold is greater than or equal to 3; the second threshold is less than or equal to 10 and greater than or equal to 2. A key transmission section search system based on quantum approximation optimization, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, the processor is connected to the memory, and the processor is used to execute the computer program to implement the key transmission section search method based on quantum approximation optimization as described in any one of claims 1-8. A readable medium, characterized in that, The system contains a computer program that, when executed, is used to implement the quantum approximation optimization-based key transmission section search method as described in any one of claims 1-8.

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