Power system post-disaster recovery parallel acceleration solving method based on quantum computing

By using the quantum agent Lagrangian relaxation algorithm in the post-disaster recovery optimization problem of power system, the problem is decomposed into multiple node sub-problems and quantized to solve it, the problems of non-convergence and slow convergence in the existing technology are solved, and efficient solution efficiency and superior convergence are achieved.

CN119558186AActive Publication Date: 2025-03-04XI AN JIAOTONG UNIV

Patent Information

Application Number
CN202411636465.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-15
Publication Date
2025-03-04
Estimated Expiration
2044-11-15

AI Technical Summary

Technical Problem

When solving the problem of post-disaster recovery optimization of power system, the existing technology has problems such as non-convergence and slow convergence speed, which affects the solution efficiency of post-disaster recovery optimization of power system.

Method used

The quantum agent Lagrangian relaxation algorithm based on quantum computing is used to decompose the original optimization problem into multiple node sub-problems, and the discrete optimization part is constructed into a quantum model for solving, and interactively solve it in combination with classical computing to realize parallel computing and quantum embedding accelerated computing.

Benefits of technology

It reduces the solution difficulty, realizes efficient parallel computing and quantum embedding accelerated computing, ensures better convergence, and improves the solution efficiency of power system post-disaster recovery optimization problems.

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Abstract

The invention belongs to the technical field of electric power system operation control, and relates to an electric power system post-disaster recovery parallel acceleration solving method based on quantum computing, which comprises the steps of 1, establishing a basic model of electric power system post-disaster recovery, 2, decomposing an original optimization problem into node sub-problems according to a quantum proxy Lagrange relaxation algorithm, 3, solving the post-disaster recovery model, continuously updating a Lagrange multiplier and a penalty factor in an iteration process, realizing optimal solution under interactive calculation of quantum calculation and classical calculation, and accelerating to obtain a post-disaster recovery scheme to guide actual safe operation of a power system; according to the method, the problem is decomposed into the multiple sub-problems with the node as the center, the sub-problems are divided into the discrete part and the continuous part to be solved, the solving difficulty is reduced, the effects of parallel computing and quantum embedding acceleration computing are achieved, complete optimization of the relaxation problem is not needed, and better convergence is guaranteed.
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Description

Technical Field

[0001] The present invention belongs to the technical field of power system operation control, and relates to a parallel accelerated solution method for post-disaster recovery of a power system based on quantum computing. Background Art

[0002] After an extreme disaster occurs, it is very important to quickly restore power supply to the power system after the disaster damage. Reasonable and efficient dispatch control and coordinated optimization are the basis for ensuring the safe and stable operation of the power grid. With the increasing scale of the power system, the complexity of the optimization problem and the computational burden have increased sharply, and faster and more efficient solution technologies are needed to meet these challenges.

[0003] Quantum computing uses "qubits" as the basic information unit and uses principles such as quantum superposition and entanglement for parallel computing. It can achieve exponential acceleration in certain specific optimization problems and is an important direction for the future development of computing. At present, quantum computing hardware includes quantum computers based on gate circuits, special-purpose quantum computers (such as coherent Bose quantum computers, coherent Ising machines, and quantum annealing computers), and quantum simulators based on classical computing. Although quantum hardware has entered the era of quantum intermediate noise scale (NISQ), the number of qubits of quantum processors is limited, but it still requires a lot of effort to achieve large-scale fault-tolerant general quantum computing.

[0004] The current exploration of quantum computing applications mainly includes four aspects: quantum combinatorial optimization, quantum parameter prediction, quantum artificial intelligence and quantum linear algebra operations. Quantum combinatorial optimization aims to find the optimal solution among many possible solutions with higher efficiency and accuracy. Currently available quantum optimization algorithms include quantum approximate optimization algorithm, variational quantum eigensolver, Grover search algorithm, etc. However, due to the limitations of NISQ hardware and software, these algorithms cannot directly solve large-scale optimization problems. A solution mode that adapts to the current development status is hybrid quantum classical computing, in which the global optimization problem can be decomposed into sub-problems that are solved interactively by classical computers and quantum computers.

[0005] For the optimization problems of post-disaster recovery of power systems, most of them belong to mixed integer linear programming models. In order to cleverly utilize the advantages of quantum computing, two technical ideas are provided. The first is to expand the scale of quantum hardware. Achieving this goal requires major technical and engineering progress in quantum hardware. Although there have been direct applications of quantum annealing computers to solve commercial optimization problems, they still face scalability limitations. Another idea is to cleverly use decomposition and coordination algorithms. In recent years, domestic and foreign scholars have studied the application of decomposition algorithms in power systems, such as the alternating direction multiplier method, the proxy Lagrangian relaxation method, and the Benders decomposition algorithm. Existing scholars have made preliminary attempts to explore practical problems such as distributed unit combination of power systems, day-ahead dispatch optimization, grid reconstruction, and energy system energy management. It has been verified from theory and experiment that quantum computing has the potential advantage of accelerated computing, and the prospects are promising and still need further exploration.

[0006] However, in the above-mentioned existing studies, the use of the alternating direction multiplier method to solve the original optimization problem will not converge, and the Benders decomposition algorithm and the proxy Lagrangian relaxation method will have slow convergence speeds to varying degrees, which in turn affects the efficiency of solving the power system post-disaster recovery optimization problem. In addition, the existing research on quantum computing in the power field is not yet detailed in the consideration of unit modeling and power line transmission constraints, and the scalability and adaptability of the model need to be adjusted.

[0007] Therefore, a high-efficiency, low-difficulty, and good convergence solution method is needed to solve the above technical problems. Summary of the invention

[0008] The technical solution adopted by the present invention to solve the technical problem is: a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing, comprising the following steps:

[0009] Step 1: Establish a basic model for post-disaster recovery of the power system. The basic model includes: post-disaster recovery objective function, system balance and load constraint model, power transmission constraint model, and generator set operation constraint model;

[0010] Step 2: According to the quantum proxy Lagrangian relaxation algorithm, the original optimization problem is decomposed into various node sub-problems. In each node sub-problem, the discrete optimization part is first constructed into a quantized model for solution, and then the discrete variable solution value is passed to the continuous optimization part for solution;

[0011] Step 3: Use the quantum proxy Lagrangian relaxation algorithm to solve the post-disaster recovery model. During the iteration process, continuously update the Lagrangian multipliers, penalty factors, discrete optimization, and intermediate variable optimization results of continuous optimization sub-problems. Under the interactive calculation of quantum computing and classical computing, the optimal solution is achieved, and the post-disaster recovery plan is obtained faster to guide the actual safe operation of the power system.

[0012] Preferably, in step 1, the post-disaster recovery objective function is:

[0013]

[0014] In formula (1), represents a set of time periods, u g,t represents the start / stop 0 / 1 state variable of the g-th unit at time t, represents the active output power of the g-th unit at time t, represents the active load shedding of the i-th node at time t, represents the unit operating cost of unit g at time t, represents the unit start-up and shutdown cost of unit g at time t, represents the unit cost of load shedding of node i at time t, represents the set of power system nodes, Represents the set of generator sets under node i; the post-disaster recovery objective function specifically includes three parts: the first item is the load shedding cost, the second item is the generator set operation cost, and the third item is the generator set start-up and shutdown cost. The model aims to minimize the sum of these three costs.

[0015] Preferably, in step 1, the system balance and load constraint model is:

[0016]

[0017]

[0018] In formula (2) and formula (3), represents the active load of the ith node at time t; Formula (2) is the system power balance model, and Formula (3) is the node load shedding model.

[0019] Preferably, in step 1, the electric power transmission constraint model is:

[0020]

[0021]

[0022]

[0023]

[0024] In formulas (4)-(7), P ij,t and represents the active power and maximum transmission power passing through branch ij, M represents a sufficiently large constant, and X ij represents the reactance of branch ij, θi ,θ i,min ,θ i,max Respectively represent the phase angle amplitude, minimum phase angle value, maximum phase angle value, z of the i-th node ij,t represents the operating status of the transmission branch ij at time t, It indicates that node j is a node in the upstream node set with node i as its upstream node; Formula (4) is the upper and lower limit constraint model of power transmission of power line, Formula (5) is the power flow constraint model of line ij, Formula (6) is the upper and lower limit constraint of node phase angle, and Formula (7) is the node power balance constraint.

[0025] Preferably, the generator set operation constraint model is:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] In formula (8) to formula (16), and Respectively represent the maximum and minimum values ​​of the unit g output, RU g ,RD g They represent the ramp rate of power increase / decrease during normal operation of the generator set g, RSU g ,RSD g They represent the ramp rate and y of the unit when starting / stopping. g,t ,z g,t They represent the startup / shutdown action variables of the g-th unit at time t, y g,max ,z g,max Respectively represent the maximum start / stop times of the g-th unit, T g,on and T g,offThey represent the minimum duration of startup and shutdown respectively; Formula (8) is the upper and lower limit constraint model of the generator set output, Formula (9)-Formula (10) is the generator set climbing constraint model, and Formula (11)-Formula (16) is the generator set operating state constraint model.

[0036] Preferably, in step 2, the original optimization problem is decomposed into various node sub-problems as follows:

[0037] The original optimization problem will be decomposed into the following sub-problems represented by nodes:

[0038]

[0039]

[0040] In formula (17) and formula (18), represents the Lagrange multiplier corresponding to time t at the kth iteration, q t represents the continuous variable added by the relaxation term at time t, c k and c P They represent the penalty term coefficients respectively; Formula (18) relaxes the relaxation term

[0041] Preferably, in step 2, the discrete optimization part is constructed into a quantized model for solving the problem as follows:

[0042] The constrained optimization model is reconstructed into a binary unconstrained optimization model, and the constraints are converted into multiple penalty terms in the objective function; the details are as follows:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] In formula (19) to formula (31), H 2,i,t ,H 3,i,t ,H 4,i,t ,H 5,i,t The energy functions of the upper and lower limit constraint model of the generator output and the generator climbing constraint model, H 6,i,t ~H 9,i,t ,H 10,i ,H 11,i They represent the energy function of the generator set operation constraint model, P2~P 11 represents the corresponding penalty term coefficient, δ k,g , k=1,...,4 represents the relaxation term coefficient, Represents increasing state values ​​of a discrete variable.

[0057] Preferably, in step 2, the discrete variable solution value is passed to the continuous optimization part for solution as follows:

[0058] After the discrete problem is reconstructed, the number of qubits is calculated and mapped to the Q matrix, the Q matrix is ​​deployed in the quantum computer for solving, the evolution results are observed, the Hamiltonian results are analyzed and output;

[0059] The processing for continuous optimization problems includes: after obtaining the solution of the discrete optimization problem, passing it as known parameters to the continuous optimization problem, and solving the continuous optimization problem on a classical computer.

[0060] Preferably, the step 3 specifically includes:

[0061] After all subproblems have been solved in the kth iteration, determine whether the convergence condition is met. If the convergence condition is met, the iteration ends and the optimal result is output; if the convergence condition is not met, check whether the optimality condition is met and update the Lagrange multiplier according to formula (32); if at least one subproblem meets the optimality condition in one iteration, update the iteration step size and penalty term coefficient according to formula (33)-formula (35) based on the intermediate variable results of the two adjacent iterations of the kth iteration. If the penalty term coefficient is too large in the later stage, update it according to formula (36);

[0062]

[0063]

[0064]

[0065] ck+1 =c k β,β>1 (71)

[0066] c k+1 =c k β -1 ,β>1 (72)

[0067] In formula (33) to formula (36), α k represents the step size parameter, and β represents a preset constant parameter.

[0068] Preferably, the output optimal result includes: the operating status of the generator set during the post-disaster recovery process, the output dispatching result of the generator set, the load shedding result of each node, and the line flow result. The output optimal result will provide a reference for the grid dispatcher to make a post-disaster recovery plan in a short time, thus achieving the effect of quantum computing accelerating the post-disaster recovery process.

[0069] The beneficial effects of the present invention are:

[0070] The present invention proposes a quantum proxy Lagrangian relaxation algorithm to solve the model, decomposes the problem into multiple node-centered sub-problems, and divides the sub-problems into discrete parts and continuous parts for solution, thereby reducing the difficulty of solution. At the same time, the algorithm can achieve the effects of parallel computing and quantum embedded accelerated computing, without the need for complete optimization of the relaxation problem, and can ensure better convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a flow chart of a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing of the present invention;

[0072] Figure 2 It is a practical application and implementation schematic diagram of the present invention. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the relevant technologies in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] refer to Figures 1-2 The present invention provides a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing. The specific process includes steps 1 to 3. The flow chart is as follows: Figure 1 shown.

[0075] Step 1: Establish a basic model for post-disaster recovery of the power system. The basic model includes: post-disaster recovery objective function, system balance and load constraint model, power transmission constraint model, and generator operation constraint model. The details are as follows:

[0076] The post-disaster recovery objective function is shown in formula (1), which specifically includes three parts: the first item is the load shedding cost, the second item is the generator set operation cost, and the third item is the generator set start-up and shutdown cost. The model aims to minimize the sum of these three costs.

[0077]

[0078] In the formula, is a set of time periods, u g,t is the 0 / 1 state variable representing the start / stop of the g-th unit at time t, represents the active output power of the g-th unit at time t, is the active load shedding of the i-th node at time t; represents the unit operating cost of unit g at time t; represents the unit start-up and shutdown cost of unit g at time t; represents the unit cost of load shedding of node i at time t; is a collection of power system nodes; is the set of generator sets contained under node i.

[0079] The system balance and load constraint model is as follows: Formula (2) is the system power balance model, and Formula (3) is the node load shedding model.

[0080]

[0081]

[0082] In the formula, is the active load of the ith node at time t.

[0083] The power transmission constraint model is as follows: Formula (4) is the upper and lower limit constraint model of power line power transmission, Formula (5) is the line ij power flow constraint model, Formula (6) is the node phase angle upper and lower limit constraint, and Formula (7) is the node power balance constraint.

[0084]

[0085]

[0086]

[0087]

[0088] Where Pij,t and is the active power and maximum transmission power passing through branch ij; M is a sufficiently large constant; X ij is the reactance of branch ij; θ i ,θ i,min ,θ i,max are the phase angle amplitude, minimum phase angle value, and maximum phase angle value of the i-th node respectively. ij,t represents the operating status of the transmission branch ij at time t, Indicates that node j is a node in the set of nodes with node i as its upstream node.

[0089] The generator set operation constraint model is as follows: Formula (8) is the upper and lower limit constraint model of the generator set output, Formulas (9)-(10) are the generator set climbing constraint models, and Formulas (11)-(16) are the generator set operation state constraint models.

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] In the formula, and are the maximum and minimum values ​​of the unit g output, RU g ,RD g RSU is the ramp rate of power increase / decrease during normal operation of generator set g. g ,RSD g The ramp rate when the unit g starts / stops, y g,t ,z g,t is the variable representing the start / stop action of the g-th unit at time t, y g,max ,z g,max It indicates the maximum number of start / stop actions of the g-th unit, T g,on and T g,off Respectively represent the minimum duration of startup and shutdown.

[0100] Step 2: According to the quantum agent Lagrangian relaxation algorithm, the original optimization problem is decomposed into various node sub-problems. In each node sub-problem, the discrete optimization part is first constructed into a quantized model for solution, and then the discrete variable solution value is passed to the continuous optimization part for solution.

[0101] The original problem will be decomposed into the following sub-problems represented by nodes:

[0102]

[0103] In the formula, is the Lagrange multiplier corresponding to time t in the kth iteration, q t is the continuous variable added as the relaxation term at time t. k and c P is the penalty coefficient.

[0104] Relaxation term It can be written as follows,

[0105]

[0106] The above node sub-problems are further divided into discrete optimization problems and continuous optimization problems. The processing for discrete problems is: reconstructing the constrained optimization model into a binary unconstrained optimization (QUBO) model, and converting the constraints into multiple penalty terms in the objective function. The details are as follows:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] In the formula, H 2,i,t ,H 3,i,t ,H 4,i,t ,H 5,i,t is the energy function of the generator set output upper and lower limit constraint model and the generator set ramp constraint model (8)-(10), H 6,i,t ~H 9,i,t ,H 10,i ,H 11,i is the energy function of the generator set operation constraint model, P2~P 11 is the corresponding penalty term coefficient, δ k,g ,k=1,...,4 is the relaxation term coefficient, is the increasing discrete variable state value.

[0121] After the discrete problem is reconstructed, the number of quantum bits is calculated and mapped to the Q matrix, the Q matrix is ​​deployed in a quantum computer for solution, the evolution results are observed, and the Hamiltonian results are analyzed and output.

[0122] The processing for continuous optimization problems is: after obtaining the solution to the discrete optimization problem, it is passed to the continuous optimization problem as a known parameter, and the continuous optimization problem is solved on a classical computer.

[0123] Step 3: Use the quantum proxy Lagrangian relaxation algorithm to solve the post-disaster recovery model, continuously update parameters such as Lagrangian multipliers and penalty factors during the iteration process, achieve the optimal solution under the interactive calculation of quantum computing and classical computing, and accelerate the post-disaster recovery plan to guide the actual safe operation of the power system.

[0124] Specifically, at the kth iteration, after all subproblems have been solved, it is determined whether the convergence condition is met. If the convergence condition is met, the iteration ends and the optimal result is output. If the convergence condition is not met, after checking whether the optimality condition is met, the Lagrange multiplier is updated according to formula (32). If at least one subproblem meets the optimality condition in one iteration, the iteration step size and penalty term coefficient are updated according to (33)-(35) based on the intermediate variable results of the two adjacent kth iterations. If the penalty term coefficient is too large in the later stage, it is updated according to formula (36).

[0125]

[0126]

[0127]

[0128] c k+1 =c kβ,β>1 (107)

[0129] c k+1 =c k β -1 ,β>1 (108)

[0130] In the formula, α k is the step size parameter, and β is a preset constant parameter.

[0131] The flow chart is as attached Figure 1 The output optimal results include: the operating status of the generator set during the post-disaster recovery process, the output dispatch results of the generator set, the load shedding results of each node, and the line flow results. The output optimal results will provide a reference for the grid dispatchers to make a post-disaster recovery plan in a short time, and achieve the effect of quantum computing to accelerate the post-disaster recovery process.

[0132] Example

[0133] This embodiment takes wind disaster as an example. Figure 2 As shown, after the model and algorithm are built, in order to realize the interaction between quantum computing and classical computing to accelerate the post-disaster recovery of the power system, the actual application process and schematic scheme are as follows:

[0134] Step 1: After the typhoon disaster occurs, the initial state parameters of the fault are confirmed as soon as possible as the input data of the above model. Each power node confirms the connection status between the classical computer and the quantum computer.

[0135] Step 2: Each power node interacts with the power dispatching and control center to grasp the fault repair process at each moment, and forms a sub-optimization problem based on the power node. After the discrete problem in the sub-optimization problem is converted by the quantum model, it is first transmitted from the personal PC to the quantum cloud platform and calls the actual quantum computer to return the calculation results, and then the intermediate results are passed to the continuous problem for further optimization and solution.

[0136] Step 3: Perform iterative solution according to the quantum proxy Lagrangian relaxation algorithm. After meeting the convergence conditions, output the operating status results of the generator sets, the output dispatch results of the generator sets, the load shedding results of each node, and the line flow results during the post-disaster recovery process. After confirming that the optimization results are safe and reasonable, issue actual power dispatching commands to control the operation of the power system and support rapid post-disaster recovery.

[0137] Finally, after the post-disaster recovery of the power system is completed, the computational efficiency and performance of quantum computing are evaluated, and the post-disaster power dispatch experience and program evaluation work are summarized. For discrete problems, the present invention reconstructs the constrained optimization model into a binary unconstrained optimization (QUBO) model, providing a reference for converting the post-disaster recovery problem model into a quantum model. The quantum proxy Lagrangian relaxation algorithm process of the present invention can realize parallel computing sub-problems and quantum computing accelerated solution.

[0138] In summary, the present invention proposes a quantum proxy Lagrangian relaxation algorithm to solve the model, decomposes the problem into multiple node-centered sub-problems, and divides the sub-problems into discrete parts and continuous parts for solution, which reduces the difficulty of solution. At the same time, the algorithm can achieve the effects of parallel computing and quantum embedded accelerated computing, without the need for complete optimization of the relaxation problem, and can ensure better convergence. Therefore, the present invention has broad application prospects in the fields of rapid power restoration after disaster damage to the power system, reasonable and efficient dispatching control and coordinated optimization.

[0139] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing, characterized in that: The following steps are involved: Step 1: Establish a basic model for post-disaster recovery of the power system, the basic model including: post-disaster recovery objective function, system balance and load constraint model, power transmission constraint model, generator set operation constraint model; Step 2: According to the quantum proxy Lagrangian relaxation algorithm, the original optimization problem is decomposed into various node sub-problems. In each node sub-problem, the discrete optimization part is first constructed into a quantized model for solution, and then the discrete variable solution value is passed to the continuous optimization part for solution; Step 3: Use the quantum proxy Lagrangian relaxation algorithm to solve the post-disaster recovery model. During the iteration process, continuously update the Lagrangian multipliers, penalty factors, discrete optimization, and intermediate variable optimization results of continuous optimization sub-problems. Under the interactive calculation of quantum computing and classical computing, the optimal solution is achieved, and the post-disaster recovery plan is obtained faster to guide the actual safe operation of the power system.

2. According to claim 1, a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing is characterized in that: In step 1, the post-disaster recovery objective function is: In formula (1), represents a set of time periods, u g,t represents the start / stop 0 / 1 state variable of the g-th unit at time t, represents the active output power of the g-th unit at time t, represents the active load shedding of the i-th node at time t, represents the unit operating cost of unit g at time t, represents the unit start-up and shutdown cost of unit g at time t, represents the unit cost of load shedding of node i at time t, represents the set of power system nodes, Represents the set of generators contained under node i.

3. According to claim 1, a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing is characterized in that: In step 1, the system balance and load constraint model is: In formula (2) and formula (3), represents the active load of the ith node at time t; Formula (2) is the system power balance model, and Formula (3) is the node load shedding model.

4. According to claim 1, a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing is characterized in that: In step 1, the electric power transmission constraint model is: In formulas (4)-(7), P ij,t and represents the active power and maximum transmission power passing through branch ij, M represents a sufficiently large constant, and X ij represents the reactance of branch ij, θ i ,θ i,min ,θ i,max Respectively represent the phase angle amplitude, minimum phase angle value, maximum phase angle value, z of the i-th node ij,t represents the operating status of the transmission branch ij at time t, It indicates that node j is a node in the upstream node set with node i as its upstream node; Formula (4) is the upper and lower limit constraint model of power transmission of power line, Formula (5) is the power flow constraint model of line ij, Formula (6) is the upper and lower limit constraint of node phase angle, and Formula (7) is the node power balance constraint.

5. According to claim 1, a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing is characterized in that: The generator set operation constraint model is: In formula (8) to formula (16), and Respectively represent the maximum and minimum values ​​of the unit g output, RU g ,RD g They represent the ramp rate of power increase / decrease during normal operation of the generator set g, RSU g ,RSD g They represent the ramp rate and y of the unit when starting / stopping. g,t ,z g,t They represent the startup / shutdown action variables of the g-th unit at time t, y g,max ,z g,max Respectively represent the maximum start / stop times of the g-th unit, T g,on and T g,off They represent the minimum duration of startup and shutdown respectively; Formula (8) is the upper and lower limit constraint model of the generator set output, Formula (9)-Formula (10) is the generator set climbing constraint model, and Formula (11)-Formula (16) is the generator set operating state constraint model.

6. According to claim 1, a parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing is characterized in that: In step 2, the original optimization problem is decomposed into various node sub-problems: The original optimization problem will be decomposed into the following sub-problems represented by nodes: In formula (17) and formula (18), represents the Lagrange multiplier corresponding to time t at the kth iteration, q t represents the continuous variable added by the relaxation term at time t, c k and c P They represent the penalty term coefficients respectively; Formula (18) relaxes the relaxation term 7. A parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing according to claim 6, characterized in that: In step 2, the discrete optimization part is constructed into a quantized model for solving the problem as follows: The constrained optimization model is reconstructed into a binary unconstrained optimization model, and the constraints are converted into multiple penalty terms in the objective function; the details are as follows: In formula (19) to formula (31), H 2,i,t ,H 3,i,t ,H 4,i,t ,H 5,i,t The energy functions of the upper and lower limit constraint model of the generator output and the generator climbing constraint model, H 6,i,t ~H 9,i,t ,H 10,i ,H 11,i They represent the energy function of the generator set operation constraint model, P2~P 11 represents the corresponding penalty term coefficient, δ k,g , k=1,...,4 represents the relaxation term coefficient, Represents increasing state values ​​of a discrete variable.

8. The method for parallel acceleration of power system post-disaster recovery based on quantum computing according to claim 7 is characterized in that: In step 2, the discrete variable solution value is passed to the continuous optimization part for solution as follows: After the discrete problem is reconstructed, the number of qubits is calculated and mapped to the Q matrix, the Q matrix is ​​deployed in the quantum computer for solving, the evolution results are observed, the Hamiltonian results are analyzed and output; The processing for continuous optimization problems includes: after obtaining the solution of the discrete optimization problem, passing it as known parameters to the continuous optimization problem, and solving the continuous optimization problem on a classical computer.

9. The method for parallel acceleration of power system post-disaster recovery based on quantum computing according to claim 1 is characterized in that: The step 3 specifically includes: After all subproblems have been solved in the kth iteration, determine whether the convergence condition is met. If the convergence condition is met, the iteration ends and the optimal result is output; if the convergence condition is not met, check whether the optimality condition is met and update the Lagrange multiplier according to formula (32); if at least one subproblem meets the optimality condition in one iteration, update the iteration step size and penalty term coefficient according to formula (33)-formula (35) based on the intermediate variable results of the two adjacent iterations of the kth iteration. If the penalty term coefficient is too large in the later stage, update it according to formula (36); c k+1 =c k ·β,β>1 (35) c k+1 =c k ·b -1 ,β>1 (36) In formula (33)-(36), α k represents the step size parameter, and β represents a preset constant parameter.

10. A parallel accelerated solution method for post-disaster recovery of power systems based on quantum computing according to claim 9, characterized in that: The output optimal results include: the operating status results of the generator sets during the post-disaster recovery process, the output dispatch results of the generator sets, the load shedding results of each node, and the line flow results.

Citation Information

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